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iCogLabs-Dev
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Mathlib-Normalized-Sexpr

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cat-searcher/leandojo-benchmark-4-random
test
711
MeasureTheory.setLIntegral_tilted
Mathlib/MeasureTheory/Measure/Tilted.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>ENNReal.ofReal_lt_top</a>, <a>implies_true</a>]
case pos.h'f.h α : Type u_1 mα : MeasurableSpace α μ : Measure α f✝ : α → ℝ inst✝ : SFinite μ f : α → ℝ g : α → ℝ≥0∞ s : Set α hf : AEMeasurable f μ ⊢ ∀ (a : α), ENNReal.ofReal (rexp (f a) / ∫ (x : α), rexp (f x) ∂μ) < ⊤
(:forall a (:fv _uniq.40119) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.40119))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.40119) (:fv _uniq.40122))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.40119) (:c Real))"},{"name":"inst✝","sexp":"((:c MeasureTheory.SFinite) (:fv _uniq.40...
(:forall a :explicit (:fv FV0) (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c ENNReal.ofReal) (:arg :explicit 0 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:a...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"name":"mα","sexp":"(:app (:c MeasurableSpace) (:arg :explicit 0 ...
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[]
[{"source":"ENNReal.ofReal_lt_top","source_end":7654,"source_start":7633,"syntax_kind":"ident"},{"source":"implies_true","source_end":7668,"source_start":7656,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"user_name":"mα"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
24
29
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4e637f8810e3bbff6b551cf0b02abca7603b7783461d17c43c6eecfa360de603
8e2fd4636e4bb4bf41f279bf534d7e4ae8596da3e114ce474b102efc3f12aa3a
9bf9ffc9001b2c8dba6876e111edfb11451d885b7750fe77a97920577823216e
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
712
MeasureTheory.setLIntegral_tilted
Mathlib/MeasureTheory/Measure/Tilted.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have hf' : ¬ <a>MeasureTheory.Integrable</a> (fun x ↦ <a>Real.exp</a> (f x)) μ := by exact fun h ↦ hf (<a>Real.aemeasurable_of_aemeasurable_exp</a> h.1.<a>MeasureTheory.AEStronglyMeasurable.aemeasurable</a>)
case neg α : Type u_1 mα : MeasurableSpace α μ : Measure α f✝ : α → ℝ inst✝ : SFinite μ f : α → ℝ g : α → ℝ≥0∞ s : Set α hf : ¬AEMeasurable f μ ⊢ ∫⁻ (x : α) in s, g x ∂μ.tilted f = ∫⁻ (x : α) in s, ENNReal.ofReal (rexp (f x) / ∫ (x : α), rexp (f x) ∂μ) * g x ∂μ
case neg α : Type u_1 mα : MeasurableSpace α μ : Measure α f✝ : α → ℝ inst✝ : SFinite μ f : α → ℝ g : α → ℝ≥0∞ s : Set α hf : ¬AEMeasurable f μ hf' : ¬Integrable (fun x => rexp (f x)) μ ⊢ ∫⁻ (x : α) in s, g x ∂μ.tilted f = ∫⁻ (x : α) in s, ENNReal.ofReal (rexp (f x) / ∫ (x : α), rexp (f x) ∂μ) * g x ∂μ
((:c Eq) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.40119) (:fv _uniq.40122) ((:c MeasureTheory.Measure.restrict) (:fv _uniq.40119) (:fv _uniq.40122) ((:c MeasureTheory.Measure.tilted) (:fv _uniq.40119) (:fv _uniq.40122) (:fv _uniq.40131) (:fv _uniq.40494)) (:fv _uniq.40496)) (:lambda x (:fv _uniq.40119) ((:...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.40119))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.40119) (:fv _uniq.40122))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.40119) (:c Real))"},{"name":"inst✝","sexp":"((:c MeasureTheory.SFinite) (:fv _uniq.40...
(:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure.restrict) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure....
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{"children":[{"source":"have","sourceEnd":7679,"sourceStart":7675,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hf'","sourceEnd":7683,"sourceStart":7680,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hf'","sourceEnd":7683,"sourceStart":7680,"tag":"node"},...
[]
[{"source":"¬ Integrable (fun x ↦ exp (f x)) μ","source_end":7724,"source_start":7686,"syntax_kind":"«term¬_»"},{"source":"fun h ↦ hf (aemeasurable_of_aemeasurable_exp h.1.aemeasurable)","source_end":7807,"source_start":7743,"syntax_kind":"Lean.Parser.Term.fun"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"user_name":"mα"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
24
34
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c0c8adfc0b4f4ff4c976ac4e87cee3c1fa1f69889616d8944784ed772207bf6d
0e9665d5e398656f5224656f910384a1365645d1b7a8591f075e4f30acd76346
8ed464463c5c4e62be544311e2e214c8bfc39368d5a12e4e44191029892b5a07
c96d772964eedb9c820125dc22c9328030340b7d484f5852ca412f260deb4b49
cat-searcher/leandojo-benchmark-4-random
test
713
MeasureTheory.setLIntegral_tilted
Mathlib/MeasureTheory/Measure/Tilted.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [hf, <a>not_false_eq_true</a>, <a>MeasureTheory.tilted_of_not_aemeasurable</a>, <a>MeasureTheory.Measure.restrict_zero</a>, <a>MeasureTheory.lintegral_zero_measure</a>]
case neg α : Type u_1 mα : MeasurableSpace α μ : Measure α f✝ : α → ℝ inst✝ : SFinite μ f : α → ℝ g : α → ℝ≥0∞ s : Set α hf : ¬AEMeasurable f μ hf' : ¬Integrable (fun x => rexp (f x)) μ ⊢ ∫⁻ (x : α) in s, g x ∂μ.tilted f = ∫⁻ (x : α) in s, ENNReal.ofReal (rexp (f x) / ∫ (x : α), rexp (f x) ∂μ) * g x ∂μ
case neg α : Type u_1 mα : MeasurableSpace α μ : Measure α f✝ : α → ℝ inst✝ : SFinite μ f : α → ℝ g : α → ℝ≥0∞ s : Set α hf : ¬AEMeasurable f μ hf' : ¬Integrable (fun x => rexp (f x)) μ ⊢ 0 = ∫⁻ (x : α) in s, ENNReal.ofReal (rexp (f x) / ∫ (x : α), rexp (f x) ∂μ) * g x ∂μ
((:c Eq) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.40119) (:fv _uniq.40122) ((:c MeasureTheory.Measure.restrict) (:fv _uniq.40119) (:fv _uniq.40122) ((:c MeasureTheory.Measure.tilted) (:fv _uniq.40119) (:fv _uniq.40122) (:fv _uniq.40131) (:fv _uniq.40494)) (:fv _uniq.40496)) (:lambda x (:fv _uniq.40119) ((:...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.40119))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.40119) (:fv _uniq.40122))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.40119) (:c Real))"},{"name":"inst✝","sexp":"((:c MeasureTheory.SFinite) (:fv _uniq.40...
(:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure.restrict) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure....
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{"children":[{"source":"simp","sourceEnd":7816,"sourceStart":7812,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":7821,"sourceStart":7817,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":7821,"s...
[]
[{"source":"hf","source_end":7825,"source_start":7823,"syntax_kind":"ident"},{"source":"not_false_eq_true","source_end":7844,"source_start":7827,"syntax_kind":"ident"},{"source":"tilted_of_not_aemeasurable","source_end":7872,"source_start":7846,"syntax_kind":"ident"},{"source":"Measure.restrict_zero","source_end":7895,...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"user_name":"mα"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
24
37
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d68e30e55a8908b2717c9d78dece3087566c3b9b3956d428fb3fe91b7e717ada
c96d772964eedb9c820125dc22c9328030340b7d484f5852ca412f260deb4b49
a5b873d8b2f6bbb95b63591c762b4863dac1b8d39e4aaf1cd11cf26c854bcbb0
2f1e5e3f5d37e4818133b3885148a6a6853bb8a2747d085008fc9e526db5d517
cat-searcher/leandojo-benchmark-4-random
test
714
MeasureTheory.setLIntegral_tilted
Mathlib/MeasureTheory/Measure/Tilted.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>MeasureTheory.integral_undef</a> hf']
case neg α : Type u_1 mα : MeasurableSpace α μ : Measure α f✝ : α → ℝ inst✝ : SFinite μ f : α → ℝ g : α → ℝ≥0∞ s : Set α hf : ¬AEMeasurable f μ hf' : ¬Integrable (fun x => rexp (f x)) μ ⊢ 0 = ∫⁻ (x : α) in s, ENNReal.ofReal (rexp (f x) / ∫ (x : α), rexp (f x) ∂μ) * g x ∂μ
case neg α : Type u_1 mα : MeasurableSpace α μ : Measure α f✝ : α → ℝ inst✝ : SFinite μ f : α → ℝ g : α → ℝ≥0∞ s : Set α hf : ¬AEMeasurable f μ hf' : ¬Integrable (fun x => rexp (f x)) μ ⊢ 0 = ∫⁻ (x : α) in s, ENNReal.ofReal (rexp (f x) / 0) * g x ∂μ
((:c Eq) (:c ENNReal) ((:c OfNat.ofNat) (:c ENNReal) (:lit 0) ((:c Zero.toOfNat0) (:c ENNReal) (:c instENNRealZero))) ((:c MeasureTheory.lintegral) (:fv _uniq.40119) (:fv _uniq.40122) ((:c MeasureTheory.Measure.restrict) (:fv _uniq.40119) (:fv _uniq.40122) (:fv _uniq.40131) (:fv _uniq.40496)) (:lambda x (:fv _uniq.4011...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.40119))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.40119) (:fv _uniq.40122))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.40119) (:c Real))"},{"name":"inst✝","sexp":"((:c MeasureTheory.SFinite) (:fv _uniq.40...
(:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c ENNReal)) (:arg :explicit 1 (:lit 0))))))) (:arg :explicit 2 (:app (:c MeasureTheory.lintegr...
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{"children":[{"source":"rw","sourceEnd":7933,"sourceStart":7931,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7935,"sourceStart":7934,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Measure...
[]
[{"source":"integral_undef hf'","source_end":7953,"source_start":7935,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"user_name":"mα"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
24
38
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f063a72ae991bbb87dd7645a5972e8a0ef47375897b764bca0e370ce23369007
2f1e5e3f5d37e4818133b3885148a6a6853bb8a2747d085008fc9e526db5d517
1f388871a8fdfe465cd1ce70ee92b5df49ba138a6061871e39a2bca2967a24be
3faf0acd679a2096d8d616afd1a6d3b21f984c98b74fdde5c89f69a0e059c569
cat-searcher/leandojo-benchmark-4-random
test
715
MeasureTheory.setLIntegral_tilted
Mathlib/MeasureTheory/Measure/Tilted.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
case neg α : Type u_1 mα : MeasurableSpace α μ : Measure α f✝ : α → ℝ inst✝ : SFinite μ f : α → ℝ g : α → ℝ≥0∞ s : Set α hf : ¬AEMeasurable f μ hf' : ¬Integrable (fun x => rexp (f x)) μ ⊢ 0 = ∫⁻ (x : α) in s, ENNReal.ofReal (rexp (f x) / 0) * g x ∂μ
((:c Eq) (:c ENNReal) ((:c OfNat.ofNat) (:c ENNReal) (:lit 0) ((:c Zero.toOfNat0) (:c ENNReal) (:c instENNRealZero))) ((:c MeasureTheory.lintegral) (:fv _uniq.40119) (:fv _uniq.40122) ((:c MeasureTheory.Measure.restrict) (:fv _uniq.40119) (:fv _uniq.40122) (:fv _uniq.40131) (:fv _uniq.40496)) (:lambda x (:fv _uniq.4011...
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(:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c ENNReal)) (:arg :explicit 1 (:lit 0))))))) (:arg :explicit 2 (:app (:c MeasureTheory.lintegr...
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{"children":[{"source":"simp","sourceEnd":7963,"sourceStart":7959,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"user_name":"mα"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
24
41
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
587fdf97b5dae9cfdb160198b2e9891217f9e471519419b417b1655b97cce049
3faf0acd679a2096d8d616afd1a6d3b21f984c98b74fdde5c89f69a0e059c569
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
716
MeasureTheory.setLIntegral_tilted
Mathlib/MeasureTheory/Measure/Tilted.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact fun h ↦ hf (<a>Real.aemeasurable_of_aemeasurable_exp</a> h.1.<a>MeasureTheory.AEStronglyMeasurable.aemeasurable</a>)
α : Type u_1 mα : MeasurableSpace α μ : Measure α f✝ : α → ℝ inst✝ : SFinite μ f : α → ℝ g : α → ℝ≥0∞ s : Set α hf : ¬AEMeasurable f μ ⊢ ¬Integrable (fun x => rexp (f x)) μ
((:c Not) ((:c MeasureTheory.Integrable) (:c Real) (:c Real.normedAddCommGroup) (:fv _uniq.40119) (:fv _uniq.40122) (:lambda x (:fv _uniq.40119) ((:c Real.exp) ((:fv _uniq.40494) 0))) (:fv _uniq.40131)))
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.40119))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.40119) (:fv _uniq.40122))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.40119) (:c Real))"},{"name":"inst✝","sexp":"((:c MeasureTheory.SFinite) (:fv _uniq.40...
(:app (:c Not) (:arg :explicit 0 (:app (:c MeasureTheory.Integrable) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Real))))) (:arg :implicit-type 2 (:fv FV0)) (:arg :implicit 3) (:arg :explicit 4 (:lambda x :explicit (:fv FV0) (:app (:c Real.exp) (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"name":"mα","sexp":"(:app (:c MeasurableSpace) (:arg :explicit 0 ...
{"children":[{"source":"exact","sourceEnd":7742,"sourceStart":7737,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":7746,"sourceStart":7743,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":7748,"sourceStart":7747,"tag":"identifier"}],"kind":"null","source":"h","sourc...
[]
[{"source":"fun h ↦ hf (aemeasurable_of_aemeasurable_exp h.1.aemeasurable)","source_end":7807,"source_start":7743,"syntax_kind":"Lean.Parser.Term.fun"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"user_name":"mα"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
24
36
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5bdcd9f1791447d81a10ad56eaee7cfd5d197fac2c8d1714f504f5aad74e4c27
333c22930a7bf874aac78cb15453138151ca1c1bf44b655a1a9f6037a9486b51
ecbdb87b695a35e230bdd082597a4b3583800e72085e3a81f2d784e4a094d4b9
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
717
isPathConnected_iff_eq
Mathlib/Topology/Connected/PathConnected.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
constructor <;> rintro ⟨x, x_in, h⟩ <;> use x, x_in
X : Type u_1 Y : Type u_2 inst✝¹ : TopologicalSpace X inst✝ : TopologicalSpace Y x y z : X ι : Type u_3 F : Set X ⊢ IsPathConnected F ↔ ∃ x ∈ F, pathComponentIn x F = F
case right X : Type u_1 Y : Type u_2 inst✝¹ : TopologicalSpace X inst✝ : TopologicalSpace Y x✝ y z : X ι : Type u_3 F : Set X x : X x_in : x ∈ F h : ∀ {y : X}, y ∈ F → JoinedIn F x y ⊢ pathComponentIn x F = F case right X : Type u_1 Y : Type u_2 inst✝¹ : TopologicalSpace X inst✝ : TopologicalSpace Y x✝ y z : X ι : Type...
((:c Iff) ((:c IsPathConnected) (:fv _uniq.412420) (:fv _uniq.412426) (:fv _uniq.412441)) ((:c Exists) (:fv _uniq.412420) (:lambda x (:fv _uniq.412420) ((:c And) ((:c Membership.mem) (:fv _uniq.412420) ((:c Set) (:fv _uniq.412420)) ((:c Set.instMembership) (:fv _uniq.412420)) 0 (:fv _uniq.412441)) ((:c Eq) ((:c Set) (:...
[{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.412420))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.412423))"},{"name":"x","sexp":"(:fv _uniq.412420)"},{"name":"y","sexp":"(:fv _uniq.412420)"},{"name":"z","sexp"...
(:app (:c Iff) (:arg :explicit 0 (:app (:c IsPathConnected) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV8)))) (:arg :explicit 1 (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :exp...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.412420","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.412423","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"children":[{"children":[{"source":"constructor","sourceEnd":37005,"sourceStart":36994,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":37005,"sourceStart":36994,"tag":"node"},{"source":"<;>","sourceEnd":37009,"sourceStart":37006,"tag":"atom"},{"children":[{"source...
[]
[{"source":"⟨x, x_in, h⟩","source_end":37033,"source_start":37017,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"},{"source":"x","source_end":37043,"source_start":37042,"syntax_kind":"ident"},{"source":"x_in","source_end":37049,"source_start":37045,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.412420","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.412423","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal...
260
4
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5617fdcbfa9d78d7b45e218c6aa16533f9915f80aaefc7af1f65ae461a1b2444
654c6b627853127468bdfc21a0ea64b031e6f7b05bb60dd2aed0b00873098537
81c38b4562ddd112dc8c7a5d5eaaa29eabcb8c5a4f0ad1a1a781749f3b6fe103
3197032ae9cb8d657fdef01a5465becd514a57bbe12f5991311f779bd13ad6cb
cat-searcher/leandojo-benchmark-4-random
test
718
isPathConnected_iff_eq
Mathlib/Topology/Connected/PathConnected.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
ext y
case right X : Type u_1 Y : Type u_2 inst✝¹ : TopologicalSpace X inst✝ : TopologicalSpace Y x✝ y z : X ι : Type u_3 F : Set X x : X x_in : x ∈ F h : ∀ {y : X}, y ∈ F → JoinedIn F x y ⊢ pathComponentIn x F = F
case right.h X : Type u_1 Y : Type u_2 inst✝¹ : TopologicalSpace X inst✝ : TopologicalSpace Y x✝ y✝ z : X ι : Type u_3 F : Set X x : X x_in : x ∈ F h : ∀ {y : X}, y ∈ F → JoinedIn F x y y : X ⊢ y ∈ pathComponentIn x F ↔ y ∈ F
((:c Eq) ((:c Set) (:fv _uniq.412420)) ((:c pathComponentIn) (:fv _uniq.412420) (:fv _uniq.412426) (:fv _uniq.412521) (:fv _uniq.412441)) (:fv _uniq.412441))
[{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.412420))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.412423))"},{"name":"x✝","sexp":"(:fv _uniq.412420)"},{"name":"y","sexp":"(:fv _uniq.412420)"},{"name":"z","sexp...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c pathComponentIn) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV10)) (:arg :explicit 3 (:fv FV8)))) (:arg...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.412420","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.412423","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"ext","sourceEnd":37058,"sourceStart":37055,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":37060,"sourceStart":37059,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"y","sourceEnd":37060,"sourceStart":37059,"tag...
[{"role":"fresh_name","source":"y","source_end":37060,"source_start":37059,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.412420","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.412423","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal...
260
17
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
fa5452444aa57251b3a930a9b65bbd31d1d480a26e0b05978e7acb01314fe02b
abae582dd7469c63970a0d3cc68d849894cdc8624a91b719e45d6d3bddcc9377
37d49c45b1abbe86a4687a0eab685a29b148c16e65ed2a21b8d9a8fd1054d53a
ad67710d9da1f7568f8366b0b63eb11c4cfea20566b4c090a91f50207074a882
cat-searcher/leandojo-benchmark-4-random
test
719
isPathConnected_iff_eq
Mathlib/Topology/Connected/PathConnected.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact ⟨fun hy => hy.mem.2, h⟩
case right.h X : Type u_1 Y : Type u_2 inst✝¹ : TopologicalSpace X inst✝ : TopologicalSpace Y x✝ y✝ z : X ι : Type u_3 F : Set X x : X x_in : x ∈ F h : ∀ {y : X}, y ∈ F → JoinedIn F x y y : X ⊢ y ∈ pathComponentIn x F ↔ y ∈ F
((:c Iff) ((:c Membership.mem) (:fv _uniq.412420) ((:c Set) (:fv _uniq.412420)) ((:c Set.instMembership) (:fv _uniq.412420)) (:fv _uniq.413210) ((:c pathComponentIn) (:fv _uniq.412420) (:fv _uniq.412426) (:fv _uniq.412521) (:fv _uniq.412441))) ((:c Membership.mem) (:fv _uniq.412420) ((:c Set) (:fv _uniq.412420)) ((:c S...
[{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.412420))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.412423))"},{"name":"x✝","sexp":"(:fv _uniq.412420)"},{"name":"y✝","sexp":"(:fv _uniq.412420)"},{"name":"z","sex...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :e...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.412420","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.412423","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"exact","sourceEnd":37070,"sourceStart":37065,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":37074,"sourceStart":37071,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":37077,"sourceStart":37074,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source...
[]
[{"source":"⟨fun hy => hy.mem.2, h⟩","source_end":37098,"source_start":37071,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.412420","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.412423","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal...
260
18
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ac558afd370f2edd9e931cd10e7f601f5537c8db66a47ee17c7474d609842c6d
ad67710d9da1f7568f8366b0b63eb11c4cfea20566b4c090a91f50207074a882
93d9404717a49366bee3448f823173e1462ee708d4b57a44bf2fa35f5b88ff04
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
720
isPathConnected_iff_eq
Mathlib/Topology/Connected/PathConnected.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro y y_in
case right X : Type u_1 Y : Type u_2 inst✝¹ : TopologicalSpace X inst✝ : TopologicalSpace Y x✝ y z : X ι : Type u_3 F : Set X x : X x_in : x ∈ F h : pathComponentIn x F = F ⊢ ∀ {y : X}, y ∈ F → JoinedIn F x y
case right X : Type u_1 Y : Type u_2 inst✝¹ : TopologicalSpace X inst✝ : TopologicalSpace Y x✝ y✝ z : X ι : Type u_3 F : Set X x : X x_in : x ∈ F h : pathComponentIn x F = F y : X y_in : y ∈ F ⊢ JoinedIn F x y
(:forall y (:fv _uniq.412420) (:forall _ ((:c Membership.mem) (:fv _uniq.412420) ((:c Set) (:fv _uniq.412420)) ((:c Set.instMembership) (:fv _uniq.412420)) 0 (:fv _uniq.412441)) ((:c JoinedIn) (:fv _uniq.412420) (:fv _uniq.412426) (:fv _uniq.412441) (:fv _uniq.412566) 1)) :implicit)
[{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.412420))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.412423))"},{"name":"x✝","sexp":"(:fv _uniq.412420)"},{"name":"y","sexp":"(:fv _uniq.412420)"},{"name":"z","sexp...
(:forall y :implicit (:fv FV0) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.412420","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.412423","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"intro","sourceEnd":37109,"sourceStart":37104,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":37111,"sourceStart":37110,"tag":"identifier"},{"semanticRole":"scoped_local","source":"y_in","sourceEnd":37116,"sourceStart":37112,"tag":"identifier"}],"kind":"null","s...
[{"role":"fresh_name","source":"y","source_end":37111,"source_start":37110,"syntax_kind":"ident"},{"role":"fresh_name","source":"y_in","source_end":37116,"source_start":37112,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.412420","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.412423","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal...
260
23
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
6a011594359920b505676764db28f02641391c52ea1adfa0f65a08dc58194c0b
23f24608b1198bf44cf68b5a20aa40f6277fe418ac430c645b74db71bab1318b
ffb070730f2ef6dcd00e85834300ca05ec856f806dc3e8916d440048f7fbb751
8841a966df192866070cd354b20bb9747feff6c8757cb9e423cd7db2f1608415
cat-searcher/leandojo-benchmark-4-random
test
721
isPathConnected_iff_eq
Mathlib/Topology/Connected/PathConnected.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rwa [← h] at y_in
case right X : Type u_1 Y : Type u_2 inst✝¹ : TopologicalSpace X inst✝ : TopologicalSpace Y x✝ y✝ z : X ι : Type u_3 F : Set X x : X x_in : x ∈ F h : pathComponentIn x F = F y : X y_in : y ∈ F ⊢ JoinedIn F x y
((:c JoinedIn) (:fv _uniq.412420) (:fv _uniq.412426) (:fv _uniq.412441) (:fv _uniq.412566) (:fv _uniq.413247))
[{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.412420))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.412423))"},{"name":"x✝","sexp":"(:fv _uniq.412420)"},{"name":"y✝","sexp":"(:fv _uniq.412420)"},{"name":"z","sex...
(:app (:c JoinedIn) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV10)) (:arg :explicit 4 (:fv FV13)))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.412420","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.412423","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"rwa","sourceEnd":37124,"sourceStart":37121,"tag":"atom"},{"children":[{"source":"[","sourceEnd":37126,"sourceStart":37125,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":37129,"sourceStart":37126,"tag":"atom"}],"kind":"token.«← »","source"...
[]
[{"source":"h","source_end":37131,"source_start":37130,"syntax_kind":"ident"},{"source":"y_in","source_end":37140,"source_start":37136,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.412420","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.412423","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal...
260
24
exact
true
1
14
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e3f363817d5bae66cd8db90c41931bd3225069d53e014d6895c10d501769fd79
8841a966df192866070cd354b20bb9747feff6c8757cb9e423cd7db2f1608415
2252c64f161f72f29f763f74064d7e1fd8023ed0dde7fd9d1218e2d1059c5f17
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
722
Metric.Sigma.fst_eq_of_dist_lt_one
Mathlib/Topology/MetricSpace/Gluing.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
cases x
ι : Type u_1 E : ι → Type u_2 inst✝ : (i : ι) → MetricSpace (E i) x y : (i : ι) × E i h : dist x y < 1 ⊢ x.fst = y.fst
case mk ι : Type u_1 E : ι → Type u_2 inst✝ : (i : ι) → MetricSpace (E i) y : (i : ι) × E i fst✝ : ι snd✝ : E fst✝ h : dist ⟨fst✝, snd✝⟩ y < 1 ⊢ ⟨fst✝, snd✝⟩.fst = y.fst
((:c Eq) (:fv _uniq.36637) ((:c Sigma.fst) (:fv _uniq.36637) (:lambda i (:fv _uniq.36637) ((:fv _uniq.36642) 0)) (:fv _uniq.36765)) ((:c Sigma.fst) (:fv _uniq.36637) (:lambda i (:fv _uniq.36637) ((:fv _uniq.36642) 0)) (:fv _uniq.36766)))
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.36637) (:sort (+ u_2 1)))"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.36637) ((:c MetricSpace) ((:fv _uniq.36642) 0)))"},{"name":"x","sexp":"((:c Sigma) (:fv _uniq.36637) (:lambda i (:fv _uniq.36637) ((:fv _uniq.36642) 0)))"},{"name"...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Sigma.fst) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV4)))) (:arg :explicit 2 (:app (:c Sigma.fst) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV5)))))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36637","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36642","is_instance":false,"is_let":false,"name":"E","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"}...
{"children":[{"source":"cases","sourceEnd":16962,"sourceStart":16957,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":4,"semanticRole":"local","source":"x","sourceEnd":16964,"sourceStart":16963,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","so...
[]
[{"source":"x","source_end":16964,"source_start":16963,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36637","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36642","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
65
4
exact
true
1
6
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0d8e3366e83d5f36292b5fc0123d8b7b09161bb6e874a60250e5ca4e8c4fff8d
5727e862a39f634f3202ac48406ff7729ead5e92ab9b1ebdcdb03d64f721e7b5
16c799dbf0c27a1c7382aca1864f7ad0f033f71481b65b6752096693fd50667c
492eb69ae6f6879330b6a2ab2d1a389dd795f579af665b7cfc27bdfdd7da2507
cat-searcher/leandojo-benchmark-4-random
test
723
Metric.Sigma.fst_eq_of_dist_lt_one
Mathlib/Topology/MetricSpace/Gluing.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
cases y
case mk ι : Type u_1 E : ι → Type u_2 inst✝ : (i : ι) → MetricSpace (E i) y : (i : ι) × E i fst✝ : ι snd✝ : E fst✝ h : dist ⟨fst✝, snd✝⟩ y < 1 ⊢ ⟨fst✝, snd✝⟩.fst = y.fst
case mk.mk ι : Type u_1 E : ι → Type u_2 inst✝ : (i : ι) → MetricSpace (E i) fst✝¹ : ι snd✝¹ : E fst✝¹ fst✝ : ι snd✝ : E fst✝ h : dist ⟨fst✝¹, snd✝¹⟩ ⟨fst✝, snd✝⟩ < 1 ⊢ ⟨fst✝¹, snd✝¹⟩.fst = ⟨fst✝, snd✝⟩.fst
((:c Eq) (:fv _uniq.36637) ((:c Sigma.fst) (:fv _uniq.36637) (:lambda i (:fv _uniq.36637) ((:fv _uniq.36642) 0)) ((:c Sigma.mk) (:fv _uniq.36637) (:lambda i (:fv _uniq.36637) ((:fv _uniq.36642) 0)) (:fv _uniq.36800) (:fv _uniq.36801))) ((:c Sigma.fst) (:fv _uniq.36637) (:lambda i (:fv _uniq.36637) ((:fv _uniq.36642) 0)...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.36637) (:sort (+ u_2 1)))"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.36637) ((:c MetricSpace) ((:fv _uniq.36642) 0)))"},{"name":"y","sexp":"((:c Sigma) (:fv _uniq.36637) (:lambda i (:fv _uniq.36637) ((:fv _uniq.36642) 0)))"},{"name"...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Sigma.fst) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c Sigma.mk) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:fv FV6)))))) (:arg :explicit 2 (:app (:c...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36637","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36642","is_instance":false,"is_let":false,"name":"E","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"}...
{"children":[{"source":"cases","sourceEnd":16971,"sourceStart":16966,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":4,"semanticRole":"local","source":"y","sourceEnd":16973,"sourceStart":16972,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","so...
[]
[{"source":"y","source_end":16973,"source_start":16972,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36637","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36642","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
65
6
exact
true
1
7
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
cd85f0b95bbee99aea9b0c96b701cb59f6654b278d61265f840d924284e5a224
492eb69ae6f6879330b6a2ab2d1a389dd795f579af665b7cfc27bdfdd7da2507
03db406d69843143ee1f5bd7fd786b4c898ea24b8ddebbd7eb29755069c1f47b
4d2c2919bae77b07fb658432a5b5df79e1efedfbb1f6db53d9ee74d9f7ff3e81
cat-searcher/leandojo-benchmark-4-random
test
724
Metric.Sigma.fst_eq_of_dist_lt_one
Mathlib/Topology/MetricSpace/Gluing.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
contrapose! h
case mk.mk ι : Type u_1 E : ι → Type u_2 inst✝ : (i : ι) → MetricSpace (E i) fst✝¹ : ι snd✝¹ : E fst✝¹ fst✝ : ι snd✝ : E fst✝ h : dist ⟨fst✝¹, snd✝¹⟩ ⟨fst✝, snd✝⟩ < 1 ⊢ ⟨fst✝¹, snd✝¹⟩.fst = ⟨fst✝, snd✝⟩.fst
case mk.mk ι : Type u_1 E : ι → Type u_2 inst✝ : (i : ι) → MetricSpace (E i) fst✝¹ : ι snd✝¹ : E fst✝¹ fst✝ : ι snd✝ : E fst✝ h : ⟨fst✝¹, snd✝¹⟩.fst ≠ ⟨fst✝, snd✝⟩.fst ⊢ 1 ≤ dist ⟨fst✝¹, snd✝¹⟩ ⟨fst✝, snd✝⟩
((:c Eq) (:fv _uniq.36637) ((:c Sigma.fst) (:fv _uniq.36637) (:lambda i (:fv _uniq.36637) ((:fv _uniq.36642) 0)) ((:c Sigma.mk) (:fv _uniq.36637) (:lambda i (:fv _uniq.36637) ((:fv _uniq.36642) 0)) (:fv _uniq.36800) (:fv _uniq.36801))) ((:c Sigma.fst) (:fv _uniq.36637) (:lambda i (:fv _uniq.36637) ((:fv _uniq.36642) 0)...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.36637) (:sort (+ u_2 1)))"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.36637) ((:c MetricSpace) ((:fv _uniq.36642) 0)))"},{"name":"fst✝¹","sexp":"(:fv _uniq.36637)"},{"name":"snd✝¹","sexp":"((:fv _uniq.36642) (:fv _uniq.36800))"},{"na...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Sigma.fst) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c Sigma.mk) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV4)) (:arg :explicit 3 (:fv FV5)))))) (:arg :explicit 2 (:app (:c...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36637","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36642","is_instance":false,"is_let":false,"name":"E","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"}...
{"children":[{"source":"contrapose!","sourceEnd":16987,"sourceStart":16976,"tag":"atom"},{"children":[{"contextIndex":8,"semanticRole":"local","source":"h","sourceEnd":16989,"sourceStart":16988,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"null","source":"h","sourceEnd":16989,"sour...
[]
[{"source":"h","source_end":16989,"source_start":16988,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36637","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36642","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
65
7
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
982aa76fbffd7269c9eca0d8b23bae7aaae28a689250ce073bb770c033948235
4d2c2919bae77b07fb658432a5b5df79e1efedfbb1f6db53d9ee74d9f7ff3e81
f1c344e3174b14056331ea226f3666d6eca3c3126f1a2fbc18a81a0fe4db0cf9
63dfac4c8e19ad77835f8378500f1868a75c586cd3bc0651493a6ba0066b3ff9
cat-searcher/leandojo-benchmark-4-random
test
725
Metric.Sigma.fst_eq_of_dist_lt_one
Mathlib/Topology/MetricSpace/Gluing.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>Metric.Sigma.one_le_dist_of_ne</a> h
case mk.mk ι : Type u_1 E : ι → Type u_2 inst✝ : (i : ι) → MetricSpace (E i) fst✝¹ : ι snd✝¹ : E fst✝¹ fst✝ : ι snd✝ : E fst✝ h : ⟨fst✝¹, snd✝¹⟩.fst ≠ ⟨fst✝, snd✝⟩.fst ⊢ 1 ≤ dist ⟨fst✝¹, snd✝¹⟩ ⟨fst✝, snd✝⟩
((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c LinearOrder.toPartialOrder) (:c Real) (:c Real.linearOrder)))) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c Dist.dist) ((:c Sigma) (:fv _uniq.36637) (:lambda i (:fv _uniq.36637)...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.36637) (:sort (+ u_2 1)))"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.36637) ((:c MetricSpace) ((:fv _uniq.36642) 0)))"},{"name":"fst✝¹","sexp":"(:fv _uniq.36637)"},{"name":"snd✝¹","sexp":"((:fv _uniq.36642) (:fv _uniq.36800))"},{"na...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36637","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36642","is_instance":false,"is_let":false,"name":"E","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"}...
{"children":[{"source":"apply","sourceEnd":16997,"sourceStart":16992,"tag":"atom"},{"children":[{"name":"Metric.Sigma.one_le_dist_of_ne","semanticRole":"global","source":"one_le_dist_of_ne","sourceEnd":17015,"sourceStart":16998,"tag":"identifier"},{"children":[{"contextIndex":8,"semanticRole":"local","source":"h","sour...
[]
[{"source":"one_le_dist_of_ne h","source_end":17017,"source_start":16998,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36637","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36642","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
65
8
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
43d670462ae07441ff3aa43351dc849fb88831c28ddfba2cbc50852eb0b352b9
63dfac4c8e19ad77835f8378500f1868a75c586cd3bc0651493a6ba0066b3ff9
77438fb19f8be7cf0c92bab307c9109b222215ca542f0fc053a3d55d4b91e7b6
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
726
Polynomial.reverse_natDegree
Mathlib/Algebra/Polynomial/Reverse.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [f.natDegree_eq_reverse_natDegree_add_natTrailingDegree, <a>add_tsub_cancel_right</a>]
R : Type u_1 inst✝ : Semiring R f✝ f : R[X] ⊢ f.reverse.natDegree = f.natDegree - f.natTrailingDegree
((:c Eq) (:c Nat) ((:c Polynomial.natDegree) (:fv _uniq.49993) (:fv _uniq.49996) ((:c Polynomial.reverse) (:fv _uniq.49993) (:fv _uniq.49996) (:fv _uniq.50092))) ((:c HSub.hSub) (:c Nat) (:c Nat) (:c Nat) ((:c instHSub) (:c Nat) (:c instSubNat)) ((:c Polynomial.natDegree) (:fv _uniq.49993) (:fv _uniq.49996) (:fv _uniq....
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.49993))"},{"name":"f✝","sexp":"((:c Polynomial) (:fv _uniq.49993) (:fv _uniq.49996))"},{"name":"f","sexp":"((:c Polynomial) (:fv _uniq.49993) (:fv _uniq.49996))"}]
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Polynomial.natDegree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Polynomial.reverse) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:ins...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.49993","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.49996","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Semiring) (:arg :explici...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":12271,"sourceStart":12269,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12273,"sourceStart":12272,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",...
[]
[{"source":"f.natDegree_eq_reverse_natDegree_add_natTrailingDegree","source_end":12327,"source_start":12273,"syntax_kind":"ident"},{"source":"add_tsub_cancel_right","source_end":12350,"source_start":12329,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.49993","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.49996","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna...
72
2
exact
true
1
4
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d20314fac49f6c7f70edea6c452b579f19f710b78261b37dd92ed08903c6114d
1fe37fb01b78120fbf1fce09f5f6499ea799b459c38aa50646c52e86b4abbb2e
e9c8299cbcd415b4a4a9671f277c9bbe2c8bca2c8f14b4f3bd6ad5cd06a7fc6f
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
727
IsometryEquiv.image_closedBall
Mathlib/Topology/MetricSpace/Isometry.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← h.preimage_symm, h.symm.preimage_closedBall, <a>IsometryEquiv.symm_symm</a>]
ι : Type u_1 α : Type u β : Type v γ : Type w inst✝¹ : PseudoMetricSpace α inst✝ : PseudoMetricSpace β h✝ h : α ≃ᵢ β x : α r : ℝ ⊢ ⇑h '' Metric.closedBall x r = Metric.closedBall (h x) r
((:c Eq) ((:c Set) (:fv _uniq.48781)) ((:c Set.image) (:fv _uniq.48779) (:fv _uniq.48781) ((:c DFunLike.coe) ((:c IsometryEquiv) (:fv _uniq.48779) (:fv _uniq.48781) ((:c PseudoMetricSpace.toPseudoEMetricSpace) (:fv _uniq.48779) (:fv _uniq.48786)) ((:c PseudoMetricSpace.toPseudoEMetricSpace) (:fv _uniq.48781) (:fv _uniq...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"inst✝¹","sexp":"((:c PseudoMetricSpace) (:fv _uniq.48779))"},{"name":"inst✝","sexp":"((:c PseudoMetricSpace) (:fv _uniq.48781))"},{"name":"h✝","sexp":"((:c ...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:app (:c Set.image) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c IsometryEquiv) (:arg :explicit 0 (:fv FV1)) (:arg :expl...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48777","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48779","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":27160,"sourceStart":27158,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27162,"sourceStart":27161,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"...
[]
[{"source":"h.preimage_symm","source_end":27181,"source_start":27166,"syntax_kind":"ident"},{"source":"h.symm.preimage_closedBall","source_end":27209,"source_start":27183,"syntax_kind":"ident"},{"source":"symm_symm","source_end":27220,"source_start":27211,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48777","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48779","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
244
2
exact
true
1
10
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0b6af24c375e39b47503abbf2e22bc7128622150fcd8a024376c83535860cc08
bb815510c3ff4656dd23c68cf8fb60d3715a643ca925b42dc1ade66591becb3c
4685d6dabf9e35c1ec3292cd81cd9b3ae1c2696cd81724eef488fffda0ee0030
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
728
CategoryTheory.Limits.CoconeMorphism.ext
Mathlib/CategoryTheory/Limits/Cones.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
cases f
J : Type u₁ inst✝³ : Category.{v₁, u₁} J K : Type u₂ inst✝² : Category.{v₂, u₂} K C : Type u₃ inst✝¹ : Category.{v₃, u₃} C D : Type u₄ inst✝ : Category.{v₄, u₄} D F : J ⥤ C c c' : Cocone F f g : c ⟶ c' w : f.hom = g.hom ⊢ f = g
case mk J : Type u₁ inst✝³ : Category.{v₁, u₁} J K : Type u₂ inst✝² : Category.{v₂, u₂} K C : Type u₃ inst✝¹ : Category.{v₃, u₃} C D : Type u₄ inst✝ : Category.{v₄, u₄} D F : J ⥤ C c c' : Cocone F g : c ⟶ c' hom✝ : c.pt ⟶ c'.pt w✝ : ∀ (j : J), c.ι.app j ≫ hom✝ = c'.ι.app j w : { hom := hom✝, w := w✝ }.hom = g.hom ⊢ { h...
((:c Eq) ((:c Quiver.Hom) ((:c CategoryTheory.Limits.Cocone) (:fv _uniq.149741) (:fv _uniq.149744) (:fv _uniq.149751) (:fv _uniq.149754) (:fv _uniq.149779)) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c CategoryTheory.Limits.Cocone) (:fv _uniq.149741) (:fv _uniq.149744) (:fv _uniq.149751) (:fv _uniq.149754) (:fv _u...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.149741))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.149746))"},{"name":"C","sexp":"(:sort (+ u₃ 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Cat...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.Cocone) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV4)) (:arg :instance 3 (:instance-of...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.149741","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.149744","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Catego...
{"children":[{"source":"cases","sourceEnd":20150,"sourceStart":20145,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":12,"semanticRole":"local","source":"f","sourceEnd":20152,"sourceStart":20151,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","s...
[]
[{"source":"f","source_end":20152,"source_start":20151,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.149741","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.149744","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte...
126
4
exact
true
1
14
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5e13bd7e2b462f7095bccfb527663844c86e59b1da5bd35f4cc3bcf8559fb4d6
ffc3b104f1eda19ddec9bee5197d521c44d68d5b249aea85c54e068b208fb219
8933eda3eb04918aa220940c3af5081708ccaaf69fc8e82139d499b98a43bc01
1f24779872ab930779016ee8bf05ed646cb4e83de672e8365d11b7c3f5a7906e
cat-searcher/leandojo-benchmark-4-random
test
729
CategoryTheory.Limits.CoconeMorphism.ext
Mathlib/CategoryTheory/Limits/Cones.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
cases g
case mk J : Type u₁ inst✝³ : Category.{v₁, u₁} J K : Type u₂ inst✝² : Category.{v₂, u₂} K C : Type u₃ inst✝¹ : Category.{v₃, u₃} C D : Type u₄ inst✝ : Category.{v₄, u₄} D F : J ⥤ C c c' : Cocone F g : c ⟶ c' hom✝ : c.pt ⟶ c'.pt w✝ : ∀ (j : J), c.ι.app j ≫ hom✝ = c'.ι.app j w : { hom := hom✝, w := w✝ }.hom = g.hom ⊢ { h...
case mk.mk J : Type u₁ inst✝³ : Category.{v₁, u₁} J K : Type u₂ inst✝² : Category.{v₂, u₂} K C : Type u₃ inst✝¹ : Category.{v₃, u₃} C D : Type u₄ inst✝ : Category.{v₄, u₄} D F : J ⥤ C c c' : Cocone F hom✝¹ : c.pt ⟶ c'.pt w✝¹ : ∀ (j : J), c.ι.app j ≫ hom✝¹ = c'.ι.app j hom✝ : c.pt ⟶ c'.pt w✝ : ∀ (j : J), c.ι.app j ≫ hom...
((:c Eq) ((:c Quiver.Hom) ((:c CategoryTheory.Limits.Cocone) (:fv _uniq.149741) (:fv _uniq.149744) (:fv _uniq.149751) (:fv _uniq.149754) (:fv _uniq.149779)) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c CategoryTheory.Limits.Cocone) (:fv _uniq.149741) (:fv _uniq.149744) (:fv _uniq.149751) (:fv _uniq.149754) (:fv _u...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.149741))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.149746))"},{"name":"C","sexp":"(:sort (+ u₃ 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Cat...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.Cocone) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV4)) (:arg :instance 3 (:instance-of...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.149741","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.149744","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Catego...
{"children":[{"source":"cases","sourceEnd":20160,"sourceStart":20155,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":12,"semanticRole":"local","source":"g","sourceEnd":20162,"sourceStart":20161,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","s...
[]
[{"source":"g","source_end":20162,"source_start":20161,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.149741","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.149744","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte...
126
5
exact
true
1
15
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7d29f7e70ad7370202fdf3d88716a85eb4df26fe5b3a9f60c303c1e38b54f095
1f24779872ab930779016ee8bf05ed646cb4e83de672e8365d11b7c3f5a7906e
a3f2f74e996d2bff612576f3ab3419ce0806ba4e6a7852cdcbbf7ae6f094797f
0de87cbcd30ca6986bbdfec8526251736db6c020718c38306f2bafa0e1fd76b6
cat-searcher/leandojo-benchmark-4-random
test
730
CategoryTheory.Limits.CoconeMorphism.ext
Mathlib/CategoryTheory/Limits/Cones.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
congr
case mk.mk J : Type u₁ inst✝³ : Category.{v₁, u₁} J K : Type u₂ inst✝² : Category.{v₂, u₂} K C : Type u₃ inst✝¹ : Category.{v₃, u₃} C D : Type u₄ inst✝ : Category.{v₄, u₄} D F : J ⥤ C c c' : Cocone F hom✝¹ : c.pt ⟶ c'.pt w✝¹ : ∀ (j : J), c.ι.app j ≫ hom✝¹ = c'.ι.app j hom✝ : c.pt ⟶ c'.pt w✝ : ∀ (j : J), c.ι.app j ≫ hom...
((:c Eq) ((:c Quiver.Hom) ((:c CategoryTheory.Limits.Cocone) (:fv _uniq.149741) (:fv _uniq.149744) (:fv _uniq.149751) (:fv _uniq.149754) (:fv _uniq.149779)) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c CategoryTheory.Limits.Cocone) (:fv _uniq.149741) (:fv _uniq.149744) (:fv _uniq.149751) (:fv _uniq.149754) (:fv _u...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.149741))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.149746))"},{"name":"C","sexp":"(:sort (+ u₃ 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Cat...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.Cocone) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV4)) (:arg :instance 3 (:instance-of...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.149741","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.149744","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Catego...
{"children":[{"source":"congr","sourceEnd":20170,"sourceStart":20165,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.congr","source":"congr","sourceEnd":20170,"sourceStart":20165,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.149741","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.149744","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte...
126
6
exact
true
1
16
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
04f20c4f1566872c284f4468d44f7d20684e571ec4690740ffc4d8b11a2e3c29
0de87cbcd30ca6986bbdfec8526251736db6c020718c38306f2bafa0e1fd76b6
092b163cac48997cb6cc327c63cda260e694055f56ff3698a70cdfda80ffbb2b
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
731
Function.Periodic.const_sub
Mathlib/Algebra/Periodic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [← <a>sub_sub</a>, h.sub_eq]
α : Type u_1 β : Type u_2 γ : Type u_3 f g : α → β c c₁ c₂ x✝ : α inst✝ : AddCommGroup α h : Periodic f c a x : α ⊢ (fun x => f (a - x)) (x + c) = (fun x => f (a - x)) x
((:c Eq) (:fv _uniq.59030) ((:lambda x (:fv _uniq.59027) ((:fv _uniq.59037) ((:c HSub.hSub) (:fv _uniq.59027) (:fv _uniq.59027) (:fv _uniq.59027) ((:c instHSub) (:fv _uniq.59027) ((:c SubNegMonoid.toSub) (:fv _uniq.59027) ((:c AddGroup.toSubNegMonoid) (:fv _uniq.59027) ((:c AddCommGroup.toAddGroup) (:fv _uniq.59027) (:...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.59027) (:fv _uniq.59030))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.59027) (:fv _uniq.59030))"},{"name":"c","sexp":"(:fv _uniq.59027)"},{"name":"c₁","sexp"...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:lambda x :explicit (:fv FV0) (:app (:fv FV3) (:arg :explicit 0 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HSub) (:arg :expli...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.59027","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.59030","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":8328,"sourceStart":8324,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":8333,"sourceStart":8329,"tag":"atom"}],"kind":"nu...
[]
[{"source":"sub_sub","source_end":8346,"source_start":8339,"syntax_kind":"ident"},{"source":"h.sub_eq","source_end":8356,"source_start":8348,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.59027","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.59030","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
66
2
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ab91b42c7cc7022e921696bfd5f0f6bed0ecdf36696724518bf1f0fa491c478b
b7810b26c93c271efa8df2b38dc9d54eecec8c10fc863003fce754d70a2fba41
d130fc2ce3a65401032276a0c013e77af5a0638a9920374b040ca743d79c4735
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
732
ENNReal.toReal_eq_toReal_iff
Mathlib/Data/ENNReal/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>ENNReal.toReal</a>, <a>NNReal.coe_inj</a>, <a>ENNReal.toNNReal_eq_toNNReal_iff</a>]
α : Type u_1 a b c d : ℝ≥0∞ r p q : ℝ≥0 x y : ℝ≥0∞ ⊢ x.toReal = y.toReal ↔ x = y ∨ x = 0 ∧ y = ⊤ ∨ x = ⊤ ∧ y = 0
((:c Iff) ((:c Eq) (:c Real) ((:c ENNReal.toReal) (:fv _uniq.27448)) ((:c ENNReal.toReal) (:fv _uniq.27449))) ((:c Or) ((:c Eq) (:c ENNReal) (:fv _uniq.27448) (:fv _uniq.27449)) ((:c Or) ((:c And) ((:c Eq) (:c ENNReal) (:fv _uniq.27448) ((:c OfNat.ofNat) (:c ENNReal) (:lit 0) ((:c Zero.toOfNat0) (:c ENNReal) (:c instEN...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"a","sexp":"(:c ENNReal)"},{"name":"b","sexp":"(:c ENNReal)"},{"name":"c","sexp":"(:c ENNReal)"},{"name":"d","sexp":"(:c ENNReal)"},{"name":"r","sexp":"(:c NNReal)"},{"name":"p","sexp":"(:c NNReal)"},{"name":"q","sexp":"(:c NNReal)"},{"name":"x","sexp":"(:c ENNReal)"},{"...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c ENNReal.toReal) (:arg :explicit 0 (:fv FV9)))) (:arg :explicit 2 (:app (:c ENNReal.toReal) (:arg :explicit 0 (:fv FV10)))))) (:arg :explicit 1 (:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27232","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27234","is_instance":false,"is_let":false,"name":"a","sexp":"(:c ENNReal)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":18880,"sourceStart":18876,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":18885,"sourceStart":18881,"tag":"atom"}],"kind"...
[]
[{"source":"ENNReal.toReal","source_end":18901,"source_start":18887,"syntax_kind":"ident"},{"source":"NNReal.coe_inj","source_end":18917,"source_start":18903,"syntax_kind":"ident"},{"source":"toNNReal_eq_toNNReal_iff","source_end":18943,"source_start":18919,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27232","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27234","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
179
2
exact
true
1
10
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ce074d2e3b920fa0f1418b8fcdc9ffabca705d43ec121192ab9854f48ac13e66
25b9900930980b9991621f84c24b85db455cf26e6cbc5a9c30c9af560f484b3d
802680e1bfda24f029612a1a6fa3fb613c48318c9156d68b4b5071eb18de77a8
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
733
RCLike.smul_re
Mathlib/Analysis/RCLike/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>RCLike.real_smul_eq_coe_mul</a>, <a>RCLike.re_ofReal_mul</a>]
K : Type u_1 E : Type u_2 inst✝ : RCLike K r : ℝ z : K ⊢ re (r • z) = r * re z
((:c Eq) (:c Real) ((:c DFunLike.coe) ((:c AddMonoidHom) (:fv _uniq.48105) (:c Real) ((:c AddMonoid.toAddZeroClass) (:fv _uniq.48105) ((:c AddCommMonoid.toAddMonoid) (:fv _uniq.48105) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.48105) ((:c NonUnitalSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.48105) ...
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c RCLike) (:fv _uniq.48105))"},{"name":"r","sexp":"(:c Real)"},{"name":"z","sexp":"(:fv _uniq.48105)"}]
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AddMonoidHom) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c AddZeroClass) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48105","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48108","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":9983,"sourceStart":9981,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9985,"sourceStart":9984,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag...
[]
[{"source":"real_smul_eq_coe_mul","source_end":10005,"source_start":9985,"syntax_kind":"ident"},{"source":"re_ofReal_mul","source_end":10020,"source_start":10007,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48105","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48108","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
86
2
exact
true
1
5
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
dbf6d21b700d9fe4931b918f3455325f55ba2f4ae917d0839e0cc166f1e764b8
b12a5e2ba5e9f3b6d562d51581616e8602eeefe107711911c018297f2b0cf8d7
8c7dbc86bff9f7c91d7a21d094cbeb7fd8bc067a697cbf8c9f8596d50ae6b836
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
734
Set.encard_eq_two
Mathlib/Data/Set/Card.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨fun h ↦ ?_, fun ⟨x, y, hne, hs⟩ ↦ by rw [hs, <a>Set.encard_pair</a> hne]⟩
α : Type u_1 β : Type u_2 s t : Set α ⊢ s.encard = 2 ↔ ∃ x y, x ≠ y ∧ s = {x, y}
α : Type u_1 β : Type u_2 s t : Set α h : s.encard = 2 ⊢ ∃ x y, x ≠ y ∧ s = {x, y}
((:c Iff) ((:c Eq) (:c ENat) ((:c Set.encard) (:fv _uniq.61498) (:fv _uniq.61504)) ((:c OfNat.ofNat) (:c ENat) (:lit 2) ((:c instOfNatAtLeastTwo) (:c ENat) (:lit 2) ((:c CanonicallyOrderedCommSemiring.toNatCast) (:c ENat) (:c instENatCanonicallyOrderedCommSemiring)) ((:c instNatAtLeastTwo) ((:c OfNat.ofNat) (:c Nat) (:...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.61498))"}]
(:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c ENat)) (:arg :explicit 1 (:app (:c Set.encard) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c ENat)) (:arg :explicit 1 (:lit 2)) (:arg :instance 2 (:instance-of...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"refine","sourceEnd":15868,"sourceStart":15862,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":15872,"sourceStart":15869,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":15875,"sourceStart":15872,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","sourc...
[]
[{"source":"⟨fun h ↦ ?_, fun ⟨x, y, hne, hs⟩ ↦ by rw [hs, encard_pair hne]⟩","source_end":15944,"source_start":15869,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
70
4
exact
true
1
4
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e290570854654063d335a184861e658528269a130d2122fd8356437f805da3f2
c454d22655d95c275eb3017ae47beb917ea281533e6845b9f8287f18a023e7b1
5da2a65dc8fe83c1e4f3b1402fdbbc3ce2323a3b6ace7fc221d993dddbc10634
f7d334719e4f7225f553c206d0eed3e81a5e2d4de12a1f383b55c501d0f4667e
cat-searcher/leandojo-benchmark-4-random
test
735
Set.encard_eq_two
Mathlib/Data/Set/Card.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨x, hx⟩ := <a>Set.nonempty_of_encard_ne_zero</a> (s := s) (by rw [h]; simp)
α : Type u_1 β : Type u_2 s t : Set α h : s.encard = 2 ⊢ ∃ x y, x ≠ y ∧ s = {x, y}
case intro α : Type u_1 β : Type u_2 s t : Set α h : s.encard = 2 x : α hx : x ∈ s ⊢ ∃ x y, x ≠ y ∧ s = {x, y}
((:c Exists) (:fv _uniq.61498) (:lambda x (:fv _uniq.61498) ((:c Exists) (:fv _uniq.61498) (:lambda y (:fv _uniq.61498) ((:c And) ((:c Ne) (:fv _uniq.61498) 1 0) ((:c Eq) ((:c Set) (:fv _uniq.61498)) (:fv _uniq.61504) ((:c Insert.insert) (:fv _uniq.61498) ((:c Set) (:fv _uniq.61498)) ((:c Set.instInsert) (:fv _uniq.614...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"h","sexp":"((:c Eq) (:c ENat) ((:c Set.encard) (:fv _uniq.61498) (:fv _uniq.61504)) ((:c OfNat.ofNat) (:c ENat) (:lit 2) ((:c in...
(:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda y :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Ne) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 1) (:arg :explicit ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"obtain","sourceEnd":15953,"sourceStart":15947,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":15957,"sourceStart":15954,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEn...
[]
[{"source":"nonempty_of_encard_ne_zero (s := s) (by rw [h]; simp)","source_end":16022,"source_start":15969,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨x, hx⟩","source_end":15965,"source_start":15954,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
70
13
exact
true
1
5
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c44045710de3cd36e3e0fe25339ef7467bb77f22cf7cefbd96502afb2be159d5
f7d334719e4f7225f553c206d0eed3e81a5e2d4de12a1f383b55c501d0f4667e
1b9406b7d86eda3eadf97b76dde00fcce2cf3f2cba9edec2528fd07a0f92efcc
d59bdb0c89bfc59bd746cdcef91a1882a99ef8ad6801d15558ba39a877e69c66
cat-searcher/leandojo-benchmark-4-random
test
736
Set.encard_eq_two
Mathlib/Data/Set/Card.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>Set.insert_eq_of_mem</a> hx, ← <a>Set.insert_diff_singleton</a>, <a>Set.encard_insert_of_not_mem</a> (fun h ↦ h.2 <a>rfl</a>), ← <a>one_add_one_eq_two</a>, <a>WithTop.add_right_cancel_iff</a> (<a>WithTop.one_ne_top</a>), <a>Set.encard_eq_one</a>] at h
case intro α : Type u_1 β : Type u_2 s t : Set α h : s.encard = 2 x : α hx : x ∈ s ⊢ ∃ x y, x ≠ y ∧ s = {x, y}
case intro α : Type u_1 β : Type u_2 s t : Set α x : α h : ∃ x_1, s \ {x} = {x_1} hx : x ∈ s ⊢ ∃ x y, x ≠ y ∧ s = {x, y}
((:c Exists) (:fv _uniq.61498) (:lambda x (:fv _uniq.61498) ((:c Exists) (:fv _uniq.61498) (:lambda y (:fv _uniq.61498) ((:c And) ((:c Ne) (:fv _uniq.61498) 1 0) ((:c Eq) ((:c Set) (:fv _uniq.61498)) (:fv _uniq.61504) ((:c Insert.insert) (:fv _uniq.61498) ((:c Set) (:fv _uniq.61498)) ((:c Set.instInsert) (:fv _uniq.614...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"h","sexp":"((:c Eq) (:c ENat) ((:c Set.encard) (:fv _uniq.61498) (:fv _uniq.61504)) ((:c OfNat.ofNat) (:c ENat) (:lit 2) ((:c in...
(:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda y :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Ne) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 1) (:arg :explicit ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"rw","sourceEnd":16027,"sourceStart":16025,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16029,"sourceStart":16028,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":16032,"sourceSt...
[]
[{"source":"h","source_end":16225,"source_start":16224,"syntax_kind":"ident"},{"source":"insert_eq_of_mem hx","source_end":16052,"source_start":16033,"syntax_kind":"Lean.Parser.Term.app"},{"source":"insert_diff_singleton","source_end":16079,"source_start":16058,"syntax_kind":"ident"},{"source":"encard_insert_of_not_mem...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
70
23
exact
true
1
7
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b2c3b0c8bd95b15d6cfd02a2b1ee512a73f023a695398fcd779fedd8c2fa2c9e
d59bdb0c89bfc59bd746cdcef91a1882a99ef8ad6801d15558ba39a877e69c66
858a0262d9628219c56e89a33a16405932ebb83d4cd69136bf7e78534de62c60
e7b49ca290b2b0250a1db5d8e9ea7d173b53110f96a0dfac59b1a6d7d814b74c
cat-searcher/leandojo-benchmark-4-random
test
737
Set.encard_eq_two
Mathlib/Data/Set/Card.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨y, h⟩ := h
case intro α : Type u_1 β : Type u_2 s t : Set α x : α h : ∃ x_1, s \ {x} = {x_1} hx : x ∈ s ⊢ ∃ x y, x ≠ y ∧ s = {x, y}
case intro.intro α : Type u_1 β : Type u_2 s t : Set α x : α hx : x ∈ s y : α h : s \ {x} = {y} ⊢ ∃ x y, x ≠ y ∧ s = {x, y}
((:c Exists) (:fv _uniq.61498) (:lambda x (:fv _uniq.61498) ((:c Exists) (:fv _uniq.61498) (:lambda y (:fv _uniq.61498) ((:c And) ((:c Ne) (:fv _uniq.61498) 1 0) ((:c Eq) ((:c Set) (:fv _uniq.61498)) (:fv _uniq.61504) ((:c Insert.insert) (:fv _uniq.61498) ((:c Set) (:fv _uniq.61498)) ((:c Set.instInsert) (:fv _uniq.614...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"x","sexp":"(:fv _uniq.61498)"},{"name":"h","sexp":"((:c Exists) (:fv _uniq.61498) (:lambda x (:fv _uniq.61498) ((:c Eq) ((:c Set...
(:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda y :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Ne) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 1) (:arg :explicit ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"obtain","sourceEnd":16234,"sourceStart":16228,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":16238,"sourceStart":16235,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"y","sourceEn...
[]
[{"source":"h","source_end":16250,"source_start":16249,"syntax_kind":"ident"},{"source":"⟨y, h⟩","source_end":16245,"source_start":16235,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
70
31
exact
true
1
7
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
bfc9606ce93717cca1c155190702ebbcf463c69bfdba612863da72dd428015f3
e7b49ca290b2b0250a1db5d8e9ea7d173b53110f96a0dfac59b1a6d7d814b74c
a993fcfa458d398ddae3e83ab35b4c6a32bda948eeae5082473b353da7725b2a
2713be506dc6daa1ec87db58200013f46db2f57e0b0ea707294f0d0c299cab64
cat-searcher/leandojo-benchmark-4-random
test
738
Set.encard_eq_two
Mathlib/Data/Set/Card.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨x, y, by rintro rfl; exact (h.symm.subset <a>rfl</a>).2 <a>rfl</a>, ?_⟩
case intro.intro α : Type u_1 β : Type u_2 s t : Set α x : α hx : x ∈ s y : α h : s \ {x} = {y} ⊢ ∃ x y, x ≠ y ∧ s = {x, y}
case intro.intro α : Type u_1 β : Type u_2 s t : Set α x : α hx : x ∈ s y : α h : s \ {x} = {y} ⊢ s = {x, y}
((:c Exists) (:fv _uniq.61498) (:lambda x (:fv _uniq.61498) ((:c Exists) (:fv _uniq.61498) (:lambda y (:fv _uniq.61498) ((:c And) ((:c Ne) (:fv _uniq.61498) 1 0) ((:c Eq) ((:c Set) (:fv _uniq.61498)) (:fv _uniq.61504) ((:c Insert.insert) (:fv _uniq.61498) ((:c Set) (:fv _uniq.61498)) ((:c Set.instInsert) (:fv _uniq.614...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"x","sexp":"(:fv _uniq.61498)"},{"name":"hx","sexp":"((:c Membership.mem) (:fv _uniq.61498) ((:c Set) (:fv _uniq.61498)) ((:c Set...
(:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda y :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Ne) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 1) (:arg :explicit ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"refine","sourceEnd":16259,"sourceStart":16253,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":16263,"sourceStart":16260,"tag":"atom"},{"children":[{"contextIndex":5,"semanticRole":"local","source":"x","sourceEnd":16264,"sourceStart":16263,"tag":"identifier"},{"source":",","sourceEnd":16265,...
[]
[{"source":"⟨x, y, by rintro rfl; exact (h.symm.subset rfl).2 rfl, ?_⟩","source_end":16322,"source_start":16260,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
70
32
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
73529dfdef7173c5e15ae606d0aed03876ab9da69e490a32248be97f5a8e0ab4
2713be506dc6daa1ec87db58200013f46db2f57e0b0ea707294f0d0c299cab64
9c8b5863a2562084eda7aea2d02f3e197023096a33ad7136372bfb31b2e9701e
0396b4b84f333c11e2ca4f5460485f41c5ee7cd2309287e8ccf0b8db0a8f5fbc
cat-searcher/leandojo-benchmark-4-random
test
739
Set.encard_eq_two
Mathlib/Data/Set/Card.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← h, <a>Set.insert_diff_singleton</a>, <a>Set.insert_eq_of_mem</a> hx]
case intro.intro α : Type u_1 β : Type u_2 s t : Set α x : α hx : x ∈ s y : α h : s \ {x} = {y} ⊢ s = {x, y}
((:c Eq) ((:c Set) (:fv _uniq.61498)) (:fv _uniq.61504) ((:c Insert.insert) (:fv _uniq.61498) ((:c Set) (:fv _uniq.61498)) ((:c Set.instInsert) (:fv _uniq.61498)) (:fv _uniq.62314) ((:c Singleton.singleton) (:fv _uniq.61498) ((:c Set) (:fv _uniq.61498)) ((:c Set.instSingletonSet) (:fv _uniq.61498)) (:fv _uniq.63200))))
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"x","sexp":"(:fv _uniq.61498)"},{"name":"hx","sexp":"((:c Membership.mem) (:fv _uniq.61498) ((:c Set) (:fv _uniq.61498)) ((:c Set...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c Insert.insert) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Insert) (:arg :expli...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"rw","sourceEnd":16327,"sourceStart":16325,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16329,"sourceStart":16328,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":16332,"sourceSt...
[]
[{"source":"h","source_end":16334,"source_start":16333,"syntax_kind":"ident"},{"source":"insert_diff_singleton","source_end":16357,"source_start":16336,"syntax_kind":"ident"},{"source":"insert_eq_of_mem hx","source_end":16378,"source_start":16359,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
70
40
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
fcd0ab85dd696328b22f837881217945359bddb54dfb8b8a94e99c65b9051d09
0396b4b84f333c11e2ca4f5460485f41c5ee7cd2309287e8ccf0b8db0a8f5fbc
10e393312755fcb140784e01f99b18b1537f27993db8f10a022cb3eb11e93b2f
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
740
Set.encard_eq_two
Mathlib/Data/Set/Card.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [hs, <a>Set.encard_pair</a> hne]
α : Type u_1 β : Type u_2 s t : Set α x✝ : ∃ x y, x ≠ y ∧ s = {x, y} x y : α hne : x ≠ y hs : s = {x, y} ⊢ s.encard = 2
((:c Eq) (:c ENat) ((:c Set.encard) (:fv _uniq.61498) (:fv _uniq.61504)) ((:c OfNat.ofNat) (:c ENat) (:lit 2) ((:c instOfNatAtLeastTwo) (:c ENat) (:lit 2) ((:c CanonicallyOrderedCommSemiring.toNatCast) (:c ENat) (:c instENatCanonicallyOrderedCommSemiring)) ((:c instNatAtLeastTwo) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"x✝","sexp":"((:c Exists) (:fv _uniq.61498) (:lambda x (:fv _uniq.61498) ((:c Exists) (:fv _uniq.61498) (:lambda y (:fv _uniq.614...
(:app (:c Eq) (:arg :implicit-type 0 (:c ENat)) (:arg :explicit 1 (:app (:c Set.encard) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c ENat)) (:arg :explicit 1 (:lit 2)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":15919,"sourceStart":15917,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15921,"sourceStart":15920,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",...
[]
[{"source":"hs","source_end":15923,"source_start":15921,"syntax_kind":"ident"},{"source":"encard_pair hne","source_end":15940,"source_start":15925,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
70
7
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
cd9670b108f1de717d9f86ce57210cf2f09e7364f965a557ac2fa1820585b992
acbae951baba39861be6f59895792c5929b9122282bc7fce89ce780946fa0702
6fa6ce09084917b07fbeeb67c3d4de9707435503b17c34855c6c94c4ab49e576
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
741
Set.encard_eq_two
Mathlib/Data/Set/Card.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [h]
α : Type u_1 β : Type u_2 s t : Set α h : s.encard = 2 ⊢ s.encard ≠ 0
α : Type u_1 β : Type u_2 s t : Set α h : s.encard = 2 ⊢ 2 ≠ 0
((:c Ne) (:c ENat) ((:c Set.encard) (:fv _uniq.61498) (:fv _uniq.61504)) ((:c OfNat.ofNat) (:c ENat) (:lit 0) ((:c Zero.toOfNat0) (:c ENat) (:c instENatZero))))
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"h","sexp":"((:c Eq) (:c ENat) ((:c Set.encard) (:fv _uniq.61498) (:fv _uniq.61504)) ((:c OfNat.ofNat) (:c ENat) (:lit 2) ((:c in...
(:app (:c Ne) (:arg :implicit-type 0 (:c ENat)) (:arg :explicit 1 (:app (:c Set.encard) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c ENat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"rw","sourceEnd":16011,"sourceStart":16009,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16013,"sourceStart":16012,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":5,"semant...
[]
[{"source":"h","source_end":16014,"source_start":16013,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
70
18
exact
true
1
5
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
00ea9b6a552331d1cc56bcd07cf9088e89836fdf560b1c7abf018bdc2926ee54
c209610f19667b38a9ec8a57ad0c751902609285776dccac4d1cd42224f11d6d
8e1ff58c9c2ffe38f33c0acb9a280a2097eb986bf9afb4a3b7b955b60bd0b8f6
84f0d98cce3f1585d642ec7f5ee5d06d0e45b7162419714ef2a7b78f386d92b6
cat-searcher/leandojo-benchmark-4-random
test
742
Set.encard_eq_two
Mathlib/Data/Set/Card.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
α : Type u_1 β : Type u_2 s t : Set α h : s.encard = 2 ⊢ 2 ≠ 0
((:c Ne) (:c ENat) ((:c OfNat.ofNat) (:c ENat) (:lit 2) ((:c instOfNatAtLeastTwo) (:c ENat) (:lit 2) ((:c CanonicallyOrderedCommSemiring.toNatCast) (:c ENat) (:c instENatCanonicallyOrderedCommSemiring)) ((:c instNatAtLeastTwo) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))))) ((:c OfNat.ofNat) (:c EN...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"h","sexp":"((:c Eq) (:c ENat) ((:c Set.encard) (:fv _uniq.61498) (:fv _uniq.61504)) ((:c OfNat.ofNat) (:c ENat) (:lit 2) ((:c in...
(:app (:c Ne) (:arg :implicit-type 0 (:c ENat)) (:arg :explicit 1 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c ENat)) (:arg :explicit 1 (:lit 2)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c ENat)) (:arg :explicit 1 (:lit 2))))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-t...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"simp","sourceEnd":16021,"sourceStart":16017,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"ki...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
70
22
exact
true
1
5
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
46afc0a12be757fcf807dd3200e7053db5d2182986c063a1d31c34b805b2adf1
84f0d98cce3f1585d642ec7f5ee5d06d0e45b7162419714ef2a7b78f386d92b6
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
743
Set.encard_eq_two
Mathlib/Data/Set/Card.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro rfl
α : Type u_1 β : Type u_2 s t : Set α x : α hx : x ∈ s y : α h : s \ {x} = {y} ⊢ x ≠ y
α : Type u_1 β : Type u_2 s t : Set α x : α hx : x ∈ s h : s \ {x} = {x} ⊢ False
((:c Ne) (:fv _uniq.61498) (:fv _uniq.62314) (:fv _uniq.63200))
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"x","sexp":"(:fv _uniq.61498)"},{"name":"hx","sexp":"((:c Membership.mem) (:fv _uniq.61498) ((:c Set) (:fv _uniq.61498)) ((:c Set...
(:app (:c Ne) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)) (:arg :explicit 2 (:fv FV7)))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"rintro","sourceEnd":16278,"sourceStart":16272,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":16282,"sourceStart":16279,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl","sourceEnd":16282,"sourceStart":162...
[]
[{"source":"rfl","source_end":16282,"source_start":16279,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
70
37
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
939578085cbc57ae0a9d60d8521ebec12f80232fcd0446a6da5a3afaf8d7f22d
d936fcb602c6b37deb1483f2e3db4f24ec8f27bed9d1a018d8ccfb5c9481f043
09e128cd6787f35d3c063b643315aff1382388dafa4e55b6546fbf9dcecb02da
55b31c3ea65a68bd865a233377f40c460abd22088c567a86992e6d2c07b7117f
cat-searcher/leandojo-benchmark-4-random
test
744
Set.encard_eq_two
Mathlib/Data/Set/Card.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact (h.symm.subset <a>rfl</a>).2 <a>rfl</a>
α : Type u_1 β : Type u_2 s t : Set α x : α hx : x ∈ s h : s \ {x} = {x} ⊢ False
(:c False)
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.61498))"},{"name":"x","sexp":"(:fv _uniq.61498)"},{"name":"hx","sexp":"((:c Membership.mem) (:fv _uniq.61498) ((:c Set) (:fv _uniq.61498)) ((:c Set...
(:c False)
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"exact","sourceEnd":16289,"sourceStart":16284,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":16291,"sourceStart":16290,"tag":"atom"},{"children":[{"source":"h.symm.subset","sourceEnd":16304,"sourceStart":16291,"tag":"identifier"},{"children":[{"name":"rfl","semanti...
[]
[{"source":"(h.symm.subset rfl).2 rfl","source_end":16315,"source_start":16290,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61498","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61501","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
70
39
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0c1876d090eb79df6f75b4b0e4f3cc71415cd5afd9cfba8c1eb829f2ed3b109b
55b31c3ea65a68bd865a233377f40c460abd22088c567a86992e6d2c07b7117f
0221ba232a4d65aba0a967a1f729f193e7391c8b466ce3b14f1388ce9563c639
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
745
MeasureTheory.FiniteMeasure.injective_toWeakDualBCNN
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro μ ν hμν
Ω : Type u_1 inst✝⁷ : MeasurableSpace Ω R : Type u_2 inst✝⁶ : SMul R ℝ≥0 inst✝⁵ : SMul R ℝ≥0∞ inst✝⁴ : IsScalarTower R ℝ≥0 ℝ≥0∞ inst✝³ : IsScalarTower R ℝ≥0∞ ℝ≥0∞ inst✝² : TopologicalSpace Ω inst✝¹ : HasOuterApproxClosed Ω inst✝ : BorelSpace Ω ⊢ Injective toWeakDualBCNN
Ω : Type u_1 inst✝⁷ : MeasurableSpace Ω R : Type u_2 inst✝⁶ : SMul R ℝ≥0 inst✝⁵ : SMul R ℝ≥0∞ inst✝⁴ : IsScalarTower R ℝ≥0 ℝ≥0∞ inst✝³ : IsScalarTower R ℝ≥0∞ ℝ≥0∞ inst✝² : TopologicalSpace Ω inst✝¹ : HasOuterApproxClosed Ω inst✝ : BorelSpace Ω μ ν : FiniteMeasure Ω hμν : μ.toWeakDualBCNN = ν.toWeakDualBCNN ⊢ μ = ν
((:c Function.Injective) ((:c MeasureTheory.FiniteMeasure) (:fv _uniq.135621) (:fv _uniq.135624)) ((:c WeakDual) (:c NNReal) ((:c BoundedContinuousFunction) (:fv _uniq.135621) (:c NNReal) (:fv _uniq.135950) (:c instPseudoMetricSpaceNNReal)) (:c instNNRealCommSemiring) (:c NNReal.instTopologicalSpace) ((:c TopologicalSe...
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁷","sexp":"((:c MeasurableSpace) (:fv _uniq.135621))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c SMul) (:fv _uniq.135627) (:c NNReal))"},{"name":"inst✝⁵","sexp":"((:c SMul) (:fv _uniq.135627) (:c ENNReal))"},{"name":"inst✝⁴","sexp":"((:c...
(:app (:c Function.Injective) (:arg :implicit-type 0 (:app (:c MeasureTheory.FiniteMeasure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))))) (:arg :implicit-type 1 (:app (:c WeakDual) (:arg :explicit 0 (:c NNReal)) (:arg :explicit 1 (:app (:c Boun...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.135621","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.135624","is_instance":true,"is_let":false,"name":"inst✝⁷","sexp":"(:app (:c MeasurableSpace) (:ar...
{"children":[{"source":"intro","sourceEnd":30381,"sourceStart":30376,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"μ","sourceEnd":30384,"sourceStart":30382,"tag":"identifier"},{"semanticRole":"scoped_local","source":"ν","sourceEnd":30387,"sourceStart":30385,"tag":"identifier"},{"semanticRole":"sco...
[{"role":"fresh_name","source":"μ","source_end":30384,"source_start":30382,"syntax_kind":"ident"},{"role":"fresh_name","source":"ν","source_end":30387,"source_start":30385,"syntax_kind":"ident"},{"role":"fresh_name","source":"hμν","source_end":30393,"source_start":30388,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.135621","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.135624","is_instance":true,"is_let":false,"user_name":"inst✝⁷"},{"binder_role":":implicit","context_index":2,"inte...
146
4
exact
true
1
10
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
773fbaf4e9e100dcfcb559a95805c24d8a409e58e63014560512bebd3c827e2d
134344d39652fb947c235d72fd9c313c4b5f96899bf8fc7f8cb9fecc267e9c97
5359e627c3a4d5eaab2dc2ea026b9b0d7ed48918d771d4cb2e5aa9522c45c8b7
fabd389e9cb36482384559b847bd9713db81e19ddde87dcc53adc28564d13006
cat-searcher/leandojo-benchmark-4-random
test
746
MeasureTheory.FiniteMeasure.injective_toWeakDualBCNN
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>MeasureTheory.FiniteMeasure.ext_of_forall_lintegral_eq</a>
Ω : Type u_1 inst✝⁷ : MeasurableSpace Ω R : Type u_2 inst✝⁶ : SMul R ℝ≥0 inst✝⁵ : SMul R ℝ≥0∞ inst✝⁴ : IsScalarTower R ℝ≥0 ℝ≥0∞ inst✝³ : IsScalarTower R ℝ≥0∞ ℝ≥0∞ inst✝² : TopologicalSpace Ω inst✝¹ : HasOuterApproxClosed Ω inst✝ : BorelSpace Ω μ ν : FiniteMeasure Ω hμν : μ.toWeakDualBCNN = ν.toWeakDualBCNN ⊢ μ = ν
case h Ω : Type u_1 inst✝⁷ : MeasurableSpace Ω R : Type u_2 inst✝⁶ : SMul R ℝ≥0 inst✝⁵ : SMul R ℝ≥0∞ inst✝⁴ : IsScalarTower R ℝ≥0 ℝ≥0∞ inst✝³ : IsScalarTower R ℝ≥0∞ ℝ≥0∞ inst✝² : TopologicalSpace Ω inst✝¹ : HasOuterApproxClosed Ω inst✝ : BorelSpace Ω μ ν : FiniteMeasure Ω hμν : μ.toWeakDualBCNN = ν.toWeakDualBCNN ⊢ ∀ (...
((:c Eq) ((:c MeasureTheory.FiniteMeasure) (:fv _uniq.135621) (:fv _uniq.135624)) (:fv _uniq.142319) (:fv _uniq.142322))
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁷","sexp":"((:c MeasurableSpace) (:fv _uniq.135621))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c SMul) (:fv _uniq.135627) (:c NNReal))"},{"name":"inst✝⁵","sexp":"((:c SMul) (:fv _uniq.135627) (:c ENNReal))"},{"name":"inst✝⁴","sexp":"((:c...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c MeasureTheory.FiniteMeasure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:fv FV12)))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.135621","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.135624","is_instance":true,"is_let":false,"name":"inst✝⁷","sexp":"(:app (:c MeasurableSpace) (:ar...
{"children":[{"source":"apply","sourceEnd":30401,"sourceStart":30396,"tag":"atom"},{"name":"MeasureTheory.FiniteMeasure.ext_of_forall_lintegral_eq","semanticRole":"global","source":"ext_of_forall_lintegral_eq","sourceEnd":30428,"sourceStart":30402,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply e...
[]
[{"source":"ext_of_forall_lintegral_eq","source_end":30428,"source_start":30402,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.135621","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.135624","is_instance":true,"is_let":false,"user_name":"inst✝⁷"},{"binder_role":":implicit","context_index":2,"inte...
146
5
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ed3c55798316664dbebb4cddd2085e3cc1284465a52247d6078e38c84d1a6e3a
fabd389e9cb36482384559b847bd9713db81e19ddde87dcc53adc28564d13006
94e5402bcd57a7a5012cf24199441eda4ee6ae10c2e95f48c6b8783597b87e0f
1876bd410bfae4c120a2776632b70f04bdceaeac54683741a5dc54b9488f4f66
cat-searcher/leandojo-benchmark-4-random
test
747
MeasureTheory.FiniteMeasure.injective_toWeakDualBCNN
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro f
case h Ω : Type u_1 inst✝⁷ : MeasurableSpace Ω R : Type u_2 inst✝⁶ : SMul R ℝ≥0 inst✝⁵ : SMul R ℝ≥0∞ inst✝⁴ : IsScalarTower R ℝ≥0 ℝ≥0∞ inst✝³ : IsScalarTower R ℝ≥0∞ ℝ≥0∞ inst✝² : TopologicalSpace Ω inst✝¹ : HasOuterApproxClosed Ω inst✝ : BorelSpace Ω μ ν : FiniteMeasure Ω hμν : μ.toWeakDualBCNN = ν.toWeakDualBCNN ⊢ ∀ (...
case h Ω : Type u_1 inst✝⁷ : MeasurableSpace Ω R : Type u_2 inst✝⁶ : SMul R ℝ≥0 inst✝⁵ : SMul R ℝ≥0∞ inst✝⁴ : IsScalarTower R ℝ≥0 ℝ≥0∞ inst✝³ : IsScalarTower R ℝ≥0∞ ℝ≥0∞ inst✝² : TopologicalSpace Ω inst✝¹ : HasOuterApproxClosed Ω inst✝ : BorelSpace Ω μ ν : FiniteMeasure Ω hμν : μ.toWeakDualBCNN = ν.toWeakDualBCNN f : Ω...
(:forall f ((:c BoundedContinuousFunction) (:fv _uniq.135621) (:c NNReal) (:fv _uniq.135950) (:c instPseudoMetricSpaceNNReal)) ((:c Eq) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.135621) (:fv _uniq.135624) ((:c MeasureTheory.FiniteMeasure.toMeasure) (:fv _uniq.135621) (:fv _uniq.135624) (:fv _uniq.142319)) (...
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁷","sexp":"((:c MeasurableSpace) (:fv _uniq.135621))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c SMul) (:fv _uniq.135627) (:c NNReal))"},{"name":"inst✝⁵","sexp":"((:c SMul) (:fv _uniq.135627) (:c ENNReal))"},{"name":"inst✝⁴","sexp":"((:c...
(:forall f :explicit (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c NNReal)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c NNReal)))))) (:app (:c Eq) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.135621","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.135624","is_instance":true,"is_let":false,"name":"inst✝⁷","sexp":"(:app (:c MeasurableSpace) (:ar...
{"children":[{"source":"intro","sourceEnd":30436,"sourceStart":30431,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"f","sourceEnd":30438,"sourceStart":30437,"tag":"identifier"}],"kind":"null","source":"f","sourceEnd":30438,"sourceStart":30437,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source...
[{"role":"fresh_name","source":"f","source_end":30438,"source_start":30437,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.135621","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.135624","is_instance":true,"is_let":false,"user_name":"inst✝⁷"},{"binder_role":":implicit","context_index":2,"inte...
146
6
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ab5b3d5dbc3c475bc69e8cd4b5feb4d7f2d3f775f8da67dc078445948e734c39
1876bd410bfae4c120a2776632b70f04bdceaeac54683741a5dc54b9488f4f66
1b6adeb7609491c9394bb306e96476a63e76a33485b960b718905e46990895c7
bc9081c3d521f9d1ccdd3db38485493e1c4fcfe252c02caac8e05661341f5178
cat-searcher/leandojo-benchmark-4-random
test
748
MeasureTheory.FiniteMeasure.injective_toWeakDualBCNN
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have key := <a>congr_fun</a> (<a>congrArg</a> <a>DFunLike.coe</a> hμν) f
case h Ω : Type u_1 inst✝⁷ : MeasurableSpace Ω R : Type u_2 inst✝⁶ : SMul R ℝ≥0 inst✝⁵ : SMul R ℝ≥0∞ inst✝⁴ : IsScalarTower R ℝ≥0 ℝ≥0∞ inst✝³ : IsScalarTower R ℝ≥0∞ ℝ≥0∞ inst✝² : TopologicalSpace Ω inst✝¹ : HasOuterApproxClosed Ω inst✝ : BorelSpace Ω μ ν : FiniteMeasure Ω hμν : μ.toWeakDualBCNN = ν.toWeakDualBCNN f : Ω...
case h Ω : Type u_1 inst✝⁷ : MeasurableSpace Ω R : Type u_2 inst✝⁶ : SMul R ℝ≥0 inst✝⁵ : SMul R ℝ≥0∞ inst✝⁴ : IsScalarTower R ℝ≥0 ℝ≥0∞ inst✝³ : IsScalarTower R ℝ≥0∞ ℝ≥0∞ inst✝² : TopologicalSpace Ω inst✝¹ : HasOuterApproxClosed Ω inst✝ : BorelSpace Ω μ ν : FiniteMeasure Ω hμν : μ.toWeakDualBCNN = ν.toWeakDualBCNN f : Ω...
((:c Eq) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.135621) (:fv _uniq.135624) ((:c MeasureTheory.FiniteMeasure.toMeasure) (:fv _uniq.135621) (:fv _uniq.135624) (:fv _uniq.142319)) (:lambda x (:fv _uniq.135621) ((:c ENNReal.ofNNReal) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.135621) (:c N...
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁷","sexp":"((:c MeasurableSpace) (:fv _uniq.135621))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c SMul) (:fv _uniq.135627) (:c NNReal))"},{"name":"inst✝⁵","sexp":"((:c SMul) (:fv _uniq.135627) (:c ENNReal))"},{"name":"inst✝⁴","sexp":"((:c...
(:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.FiniteMeasure.toMeasure) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:a...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.135621","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.135624","is_instance":true,"is_let":false,"name":"inst✝⁷","sexp":"(:app (:c MeasurableSpace) (:ar...
{"children":[{"source":"have","sourceEnd":30445,"sourceStart":30441,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"key","sourceEnd":30449,"sourceStart":30446,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"key","sourceEnd":30449,"sourceStart":30446,"tag":"n...
[]
[{"source":"congr_fun (congrArg DFunLike.coe hμν) f","source_end":30494,"source_start":30453,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.135621","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.135624","is_instance":true,"is_let":false,"user_name":"inst✝⁷"},{"binder_role":":implicit","context_index":2,"inte...
146
7
exact
true
1
14
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f253309ad5eb17c26eda15de8a4157c0f06b8dbb74c80f4b80a1be8ec3571fa8
bc9081c3d521f9d1ccdd3db38485493e1c4fcfe252c02caac8e05661341f5178
57405a99c56d875d13db402bbe449286f8708590b2d652254647efb8289b28ec
4586195e256d18d6e02b44cbbbd2c43bc6c1872b60f2ac00232d4730eac94d66
cat-searcher/leandojo-benchmark-4-random
test
749
MeasureTheory.FiniteMeasure.injective_toWeakDualBCNN
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply (<a>ENNReal.toNNReal_eq_toNNReal_iff'</a> ?_ ?_).<a>Iff.mp</a> key
case h Ω : Type u_1 inst✝⁷ : MeasurableSpace Ω R : Type u_2 inst✝⁶ : SMul R ℝ≥0 inst✝⁵ : SMul R ℝ≥0∞ inst✝⁴ : IsScalarTower R ℝ≥0 ℝ≥0∞ inst✝³ : IsScalarTower R ℝ≥0∞ ℝ≥0∞ inst✝² : TopologicalSpace Ω inst✝¹ : HasOuterApproxClosed Ω inst✝ : BorelSpace Ω μ ν : FiniteMeasure Ω hμν : μ.toWeakDualBCNN = ν.toWeakDualBCNN f : Ω...
Ω : Type u_1 inst✝⁷ : MeasurableSpace Ω R : Type u_2 inst✝⁶ : SMul R ℝ≥0 inst✝⁵ : SMul R ℝ≥0∞ inst✝⁴ : IsScalarTower R ℝ≥0 ℝ≥0∞ inst✝³ : IsScalarTower R ℝ≥0∞ ℝ≥0∞ inst✝² : TopologicalSpace Ω inst✝¹ : HasOuterApproxClosed Ω inst✝ : BorelSpace Ω μ ν : FiniteMeasure Ω hμν : μ.toWeakDualBCNN = ν.toWeakDualBCNN f : Ω →ᵇ ℝ≥0...
((:c Eq) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.135621) (:fv _uniq.135624) ((:c MeasureTheory.FiniteMeasure.toMeasure) (:fv _uniq.135621) (:fv _uniq.135624) (:fv _uniq.142319)) (:lambda x (:fv _uniq.135621) ((:c ENNReal.ofNNReal) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.135621) (:c N...
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁷","sexp":"((:c MeasurableSpace) (:fv _uniq.135621))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c SMul) (:fv _uniq.135627) (:c NNReal))"},{"name":"inst✝⁵","sexp":"((:c SMul) (:fv _uniq.135627) (:c ENNReal))"},{"name":"inst✝⁴","sexp":"((:c...
(:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.FiniteMeasure.toMeasure) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:a...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.135621","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.135624","is_instance":true,"is_let":false,"name":"inst✝⁷","sexp":"(:app (:c MeasurableSpace) (:ar...
{"children":[{"source":"apply","sourceEnd":30502,"sourceStart":30497,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":30504,"sourceStart":30503,"tag":"atom"},{"children":[{"name":"ENNReal.toNNReal_eq_toNNReal_iff'","semanticRole":"global","source":"ENNReal.toNNReal_eq_toNNReal_iff'","sourc...
[]
[{"source":"(ENNReal.toNNReal_eq_toNNReal_iff' ?_ ?_).mp key","source_end":30551,"source_start":30503,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.135621","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.135624","is_instance":true,"is_let":false,"user_name":"inst✝⁷"},{"binder_role":":implicit","context_index":2,"inte...
146
8
exact
true
1
15
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
21173ada1be919d52c549fee6acaaf6413cd457de9066038abb6f56202a401e0
4586195e256d18d6e02b44cbbbd2c43bc6c1872b60f2ac00232d4730eac94d66
aea841c9af8b63eb4f71934f2230358a23cb58c03432104941b8fa03247d647f
b9fd09e5fc714d880c0e7322042c104dd6d5cb61dbc08e3fe7612f2d83ce1f99
cat-searcher/leandojo-benchmark-4-random
test
750
MeasureTheory.FiniteMeasure.injective_toWeakDualBCNN
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact (<a>BoundedContinuousFunction.lintegral_lt_top_of_nnreal</a> μ f).<a>LT.lt.ne</a>
Ω : Type u_1 inst✝⁷ : MeasurableSpace Ω R : Type u_2 inst✝⁶ : SMul R ℝ≥0 inst✝⁵ : SMul R ℝ≥0∞ inst✝⁴ : IsScalarTower R ℝ≥0 ℝ≥0∞ inst✝³ : IsScalarTower R ℝ≥0∞ ℝ≥0∞ inst✝² : TopologicalSpace Ω inst✝¹ : HasOuterApproxClosed Ω inst✝ : BorelSpace Ω μ ν : FiniteMeasure Ω hμν : μ.toWeakDualBCNN = ν.toWeakDualBCNN f : Ω →ᵇ ℝ≥0...
((:c Ne) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.135621) (:fv _uniq.135624) ((:c MeasureTheory.FiniteMeasure.toMeasure) (:fv _uniq.135621) (:fv _uniq.135624) (:fv _uniq.142319)) (:lambda ω (:fv _uniq.135621) ((:c ENNReal.ofNNReal) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.135621) (:c N...
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁷","sexp":"((:c MeasurableSpace) (:fv _uniq.135621))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c SMul) (:fv _uniq.135627) (:c NNReal))"},{"name":"inst✝⁵","sexp":"((:c SMul) (:fv _uniq.135627) (:c ENNReal))"},{"name":"inst✝⁴","sexp":"((:c...
(:app (:c Ne) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.FiniteMeasure.toMeasure) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:a...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.135621","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.135624","is_instance":true,"is_let":false,"name":"inst✝⁷","sexp":"(:app (:c MeasurableSpace) (:ar...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":30562,"sourceStart":30557,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":30564,"sourceStart":30563,"tag":"atom"},{"children":[{"name":"BoundedContinuousFunction.lintegral_lt_top_of_nnreal","semanticRole":"global","sourc...
[]
[{"source":"(lintegral_lt_top_of_nnreal μ f).ne","source_end":30599,"source_start":30563,"syntax_kind":"Lean.Parser.Term.proj"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.135621","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.135624","is_instance":true,"is_let":false,"user_name":"inst✝⁷"},{"binder_role":":implicit","context_index":2,"inte...
146
11
exact
true
1
15
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1f37340dbc29383c8032b30f59a36f7f971b64d6be6aed36b51af256f030babe
ed43b09b6ba5d8f54474e517b7da9278f7754bf3f69969ee1c3ff7f4389d2532
8d33660b48f894a63b85e3561b41d625cd15cf2f00cca3639b07e23c3eaa3aeb
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
751
MeasureTheory.FiniteMeasure.injective_toWeakDualBCNN
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact (<a>BoundedContinuousFunction.lintegral_lt_top_of_nnreal</a> ν f).<a>LT.lt.ne</a>
Ω : Type u_1 inst✝⁷ : MeasurableSpace Ω R : Type u_2 inst✝⁶ : SMul R ℝ≥0 inst✝⁵ : SMul R ℝ≥0∞ inst✝⁴ : IsScalarTower R ℝ≥0 ℝ≥0∞ inst✝³ : IsScalarTower R ℝ≥0∞ ℝ≥0∞ inst✝² : TopologicalSpace Ω inst✝¹ : HasOuterApproxClosed Ω inst✝ : BorelSpace Ω μ ν : FiniteMeasure Ω hμν : μ.toWeakDualBCNN = ν.toWeakDualBCNN f : Ω →ᵇ ℝ≥0...
((:c Ne) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.135621) (:fv _uniq.135624) ((:c MeasureTheory.FiniteMeasure.toMeasure) (:fv _uniq.135621) (:fv _uniq.135624) (:fv _uniq.142322)) (:lambda ω (:fv _uniq.135621) ((:c ENNReal.ofNNReal) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.135621) (:c N...
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁷","sexp":"((:c MeasurableSpace) (:fv _uniq.135621))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c SMul) (:fv _uniq.135627) (:c NNReal))"},{"name":"inst✝⁵","sexp":"((:c SMul) (:fv _uniq.135627) (:c ENNReal))"},{"name":"inst✝⁴","sexp":"((:c...
(:app (:c Ne) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.FiniteMeasure.toMeasure) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:a...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.135621","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.135624","is_instance":true,"is_let":false,"name":"inst✝⁷","sexp":"(:app (:c MeasurableSpace) (:ar...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":30610,"sourceStart":30605,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":30612,"sourceStart":30611,"tag":"atom"},{"children":[{"name":"BoundedContinuousFunction.lintegral_lt_top_of_nnreal","semanticRole":"global","sourc...
[]
[{"source":"(lintegral_lt_top_of_nnreal ν f).ne","source_end":30647,"source_start":30611,"syntax_kind":"Lean.Parser.Term.proj"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.135621","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.135624","is_instance":true,"is_let":false,"user_name":"inst✝⁷"},{"binder_role":":implicit","context_index":2,"inte...
146
16
exact
true
1
15
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
57705eff80629116cf3be2a57dade39ea7625d5cb27563ee904e62b77ed5e494
18a846d8f42b27dcdac176de7d53534e0dbcd134cb8fec6b755169b863286138
d6f956874164b00438087aa2834a851da828ded893eb63e32cc71efa0acffef9
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
752
Nat.digits_lt_base
Mathlib/Data/Nat/Digits.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rcases b with (_ | _ | b) <;> try simp_all
n b m d : ℕ hb : 1 < b hd : d ∈ b.digits m ⊢ d < b
case succ.succ n m d b : ℕ hd : d ∈ (b + 1 + 1).digits m ⊢ d < b + 1 + 1
((:c LT.lt) (:c Nat) (:c instLTNat) (:fv _uniq.45439) (:fv _uniq.45437))
[{"name":"n","sexp":"(:c Nat)"},{"name":"b","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"d","sexp":"(:c Nat)"},{"name":"hb","sexp":"((:c LT.lt) (:c Nat) (:c instLTNat) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))) (:fv _uniq.45437))"},{"name":"hd","sexp":"((:c Membership.mem) (:c Nat) ...
(:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:fv FV4)) (:arg :explicit 3 (:fv FV2)))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45347","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.45437","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Nat)"},{"binder_role":":implicit","context_ind...
{"children":[{"children":[{"source":"rcases","sourceEnd":15563,"sourceStart":15557,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":2,"semanticRole":"local","source":"b","sourceEnd":15565,"sourceStart":15564,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.ca...
[]
[{"source":"b","source_end":15565,"source_start":15564,"syntax_kind":"ident"},{"source":"(_ | _ | b)","source_end":15582,"source_start":15571,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45347","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.45437","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":implicit","context_index":3,"internal_name":"_un...
86
4
exact
true
1
6
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2e1e316e06c7a036c3d2549c339a3e61507656fdc7736cd0fbfd384ffef40c68
fb7fc1aa9f3fa0d808cccf5509c2d77ff1409f7f66ef6cb646ecc51a945cbe64
a85f9ed3d599cb97ad3ea11a899fbd6d608d9ec014af714525f87769df733824
8ddfbc86d462afff5ddcff3be5352eb56eb00ccec1711ae406b8287e3c6f9c16
cat-searcher/leandojo-benchmark-4-random
test
753
Nat.digits_lt_base
Mathlib/Data/Nat/Digits.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>Nat.digits_lt_base'</a> hd
case succ.succ n m d b : ℕ hd : d ∈ (b + 1 + 1).digits m ⊢ d < b + 1 + 1
((:c LT.lt) (:c Nat) (:c instLTNat) (:fv _uniq.45439) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.45492) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) ((:c OfNat.of...
[{"name":"n","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"d","sexp":"(:c Nat)"},{"name":"b","sexp":"(:c Nat)"},{"name":"hd","sexp":"((:c Membership.mem) (:c Nat) ((:c List) (:c Nat)) ((:c List.instMembership) (:c Nat)) (:fv _uniq.45439) ((:c Nat.digits) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c inst...
(:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instan...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45347","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.45438","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":implicit","context_ind...
{"children":[{"source":"exact","sourceEnd":15607,"sourceStart":15602,"tag":"atom"},{"children":[{"name":"Nat.digits_lt_base'","semanticRole":"global","source":"digits_lt_base'","sourceEnd":15623,"sourceStart":15608,"tag":"identifier"},{"children":[{"contextIndex":5,"semanticRole":"local","source":"hd","sourceEnd":15626...
[]
[{"source":"digits_lt_base' hd","source_end":15626,"source_start":15608,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45347","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.45438","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":3,"internal_name":"_un...
86
19
exact
true
1
5
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1130d4198c378c6f483c6fe7afcc0036f754ace4cf54fac31fdf2a4b1bfa3a93
8ddfbc86d462afff5ddcff3be5352eb56eb00ccec1711ae406b8287e3c6f9c16
1bcd07f29624c1c147be38a6b905562a1ef667f175e43efdf1bcb4774df39b9b
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
754
Nat.digits_lt_base
Mathlib/Data/Nat/Digits.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp_all
case succ.succ n m d b : ℕ hb : 1 < b + 1 + 1 hd : d ∈ (b + 1 + 1).digits m ⊢ d < b + 1 + 1
case succ.succ n m d b : ℕ hd : d ∈ (b + 1 + 1).digits m ⊢ d < b + 1 + 1
((:c LT.lt) (:c Nat) (:c instLTNat) (:fv _uniq.45439) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.45492) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) ((:c OfNat.of...
[{"name":"n","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"d","sexp":"(:c Nat)"},{"name":"b","sexp":"(:c Nat)"},{"name":"hb","sexp":"((:c LT.lt) (:c Nat) (:c instLTNat) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c i...
(:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instan...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45347","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.45438","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":implicit","context_ind...
{"children":[{"children":[{"children":[{"children":[{"source":"simp_all","sourceEnd":15599,"sourceStart":15591,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45347","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.45438","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":3,"internal_name":"_un...
86
16
exact
true
1
6
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b8af0c8e9340edfb746218e2420d5b7bf29ce905b6d15b75e62aab2aab3a940a
645944c68cb47c79dac2e028f4770d587f0414332d738e31336054080cea1d78
770a776fdf57bd2930634d5176197b90f459fb4a0a757471ffc33c700413d7a2
8ddfbc86d462afff5ddcff3be5352eb56eb00ccec1711ae406b8287e3c6f9c16
cat-searcher/leandojo-benchmark-4-random
test
755
Matrix.exp_neg
Mathlib/Analysis/NormedSpace/MatrixExponential.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Matrix.nonsing_inv_eq_ring_inverse</a>]
𝕂 : Type u_1 m : Type u_2 n : Type u_3 p : Type u_4 n' : m → Type u_5 𝔸 : Type u_6 inst✝⁹ : RCLike 𝕂 inst✝⁸ : Fintype m inst✝⁷ : DecidableEq m inst✝⁶ : Fintype n inst✝⁵ : DecidableEq n inst✝⁴ : (i : m) → Fintype (n' i) inst✝³ : (i : m) → DecidableEq (n' i) inst✝² : NormedCommRing 𝔸 inst✝¹ : NormedAlgebra 𝕂 𝔸 inst...
𝕂 : Type u_1 m : Type u_2 n : Type u_3 p : Type u_4 n' : m → Type u_5 𝔸 : Type u_6 inst✝⁹ : RCLike 𝕂 inst✝⁸ : Fintype m inst✝⁷ : DecidableEq m inst✝⁶ : Fintype n inst✝⁵ : DecidableEq n inst✝⁴ : (i : m) → Fintype (n' i) inst✝³ : (i : m) → DecidableEq (n' i) inst✝² : NormedCommRing 𝔸 inst✝¹ : NormedAlgebra 𝕂 𝔸 inst...
((:c Eq) ((:c Matrix) (:fv _uniq.53837) (:fv _uniq.53837) (:fv _uniq.53851)) ((:c NormedSpace.exp) (:fv _uniq.53834) ((:c Matrix) (:fv _uniq.53837) (:fv _uniq.53837) (:fv _uniq.53851)) ((:c NormedField.toField) (:fv _uniq.53834) ((:c DenselyNormedField.toNormedField) (:fv _uniq.53834) ((:c RCLike.toDenselyNormedField) ...
[{"name":"𝕂","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"p","sexp":"(:sort (+ u_4 1))"},{"name":"n'","sexp":"(:forall _ (:fv _uniq.53837) (:sort (+ u_5 1)))"},{"name":"𝔸","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁹","sexp":"((:c RCLike) (:fv _un...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:app (:c NormedSpace.exp) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Matrix) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:a...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.53834","is_instance":false,"is_let":false,"name":"𝕂","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.53837","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","co...
{"children":[{"source":"rw","sourceEnd":7575,"sourceStart":7573,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7577,"sourceStart":7576,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Matrix.nonsing_inv_e...
[]
[{"source":"nonsing_inv_eq_ring_inverse","source_end":7604,"source_start":7577,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.53834","is_instance":false,"is_let":false,"user_name":"𝕂"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.53837","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
45
4
exact
true
1
17
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f192f69b3b7c5ee5b9c26c8eccc6e4bcf8f05f289de410543d6821e71b10a8c2
167965ab015263c0f0ea20424d25678bfd6e17ce7d7f65ac4dd716befd09073e
40a6f9c02fa117d1cd94c17d090c1d81a3e8b94fd35850dba38470aa1970903b
d1f4f34bfd47d511f115271166e5ee4bc289b91403e850cb2db689c5f5e0b695
cat-searcher/leandojo-benchmark-4-random
test
756
Matrix.exp_neg
Mathlib/Analysis/NormedSpace/MatrixExponential.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
letI : <a>SeminormedRing</a> (<a>Matrix</a> m m 𝔸) := <a>Matrix.linftyOpSemiNormedRing</a>
𝕂 : Type u_1 m : Type u_2 n : Type u_3 p : Type u_4 n' : m → Type u_5 𝔸 : Type u_6 inst✝⁹ : RCLike 𝕂 inst✝⁸ : Fintype m inst✝⁷ : DecidableEq m inst✝⁶ : Fintype n inst✝⁵ : DecidableEq n inst✝⁴ : (i : m) → Fintype (n' i) inst✝³ : (i : m) → DecidableEq (n' i) inst✝² : NormedCommRing 𝔸 inst✝¹ : NormedAlgebra 𝕂 𝔸 inst...
𝕂 : Type u_1 m : Type u_2 n : Type u_3 p : Type u_4 n' : m → Type u_5 𝔸 : Type u_6 inst✝⁹ : RCLike 𝕂 inst✝⁸ : Fintype m inst✝⁷ : DecidableEq m inst✝⁶ : Fintype n inst✝⁵ : DecidableEq n inst✝⁴ : (i : m) → Fintype (n' i) inst✝³ : (i : m) → DecidableEq (n' i) inst✝² : NormedCommRing 𝔸 inst✝¹ : NormedAlgebra 𝕂 𝔸 inst...
((:c Eq) ((:c Matrix) (:fv _uniq.53837) (:fv _uniq.53837) (:fv _uniq.53851)) ((:c NormedSpace.exp) (:fv _uniq.53834) ((:c Matrix) (:fv _uniq.53837) (:fv _uniq.53837) (:fv _uniq.53851)) ((:c NormedField.toField) (:fv _uniq.53834) ((:c DenselyNormedField.toNormedField) (:fv _uniq.53834) ((:c RCLike.toDenselyNormedField) ...
[{"name":"𝕂","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"p","sexp":"(:sort (+ u_4 1))"},{"name":"n'","sexp":"(:forall _ (:fv _uniq.53837) (:sort (+ u_5 1)))"},{"name":"𝔸","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁹","sexp":"((:c RCLike) (:fv _un...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:app (:c NormedSpace.exp) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Matrix) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:a...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.53834","is_instance":false,"is_let":false,"name":"𝕂","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.53837","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","co...
{"children":[{"source":"letI","sourceEnd":7612,"sourceStart":7608,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":7613,"sourceStart":7613,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":7613,"sourceStart":7613,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","...
[]
[{"source":"SeminormedRing (Matrix m m 𝔸)","source_end":7647,"source_start":7615,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Matrix.linftyOpSemiNormedRing","source_end":7680,"source_start":7651,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.53834","is_instance":false,"is_let":false,"user_name":"𝕂"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.53837","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
45
7
exact
true
1
17
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
132c36017d77e1c1fffc845e74ba0eae1e9a77a33ed3c4fc1deb4183ff8b3dfb
d1f4f34bfd47d511f115271166e5ee4bc289b91403e850cb2db689c5f5e0b695
e7d16ea86f4f18bbd706c0c5d52adfee18e9ef00441e9256b3a88d21afa67734
129e68bf5d9c7d61aa192d6ea90ed360e1654caad6d4fe9009dd5e4535a30e94
cat-searcher/leandojo-benchmark-4-random
test
757
Matrix.exp_neg
Mathlib/Analysis/NormedSpace/MatrixExponential.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
letI : <a>NormedRing</a> (<a>Matrix</a> m m 𝔸) := <a>Matrix.linftyOpNormedRing</a>
𝕂 : Type u_1 m : Type u_2 n : Type u_3 p : Type u_4 n' : m → Type u_5 𝔸 : Type u_6 inst✝⁹ : RCLike 𝕂 inst✝⁸ : Fintype m inst✝⁷ : DecidableEq m inst✝⁶ : Fintype n inst✝⁵ : DecidableEq n inst✝⁴ : (i : m) → Fintype (n' i) inst✝³ : (i : m) → DecidableEq (n' i) inst✝² : NormedCommRing 𝔸 inst✝¹ : NormedAlgebra 𝕂 𝔸 inst...
𝕂 : Type u_1 m : Type u_2 n : Type u_3 p : Type u_4 n' : m → Type u_5 𝔸 : Type u_6 inst✝⁹ : RCLike 𝕂 inst✝⁸ : Fintype m inst✝⁷ : DecidableEq m inst✝⁶ : Fintype n inst✝⁵ : DecidableEq n inst✝⁴ : (i : m) → Fintype (n' i) inst✝³ : (i : m) → DecidableEq (n' i) inst✝² : NormedCommRing 𝔸 inst✝¹ : NormedAlgebra 𝕂 𝔸 inst...
((:c Eq) ((:c Matrix) (:fv _uniq.53837) (:fv _uniq.53837) (:fv _uniq.53851)) ((:c NormedSpace.exp) (:fv _uniq.53834) ((:c Matrix) (:fv _uniq.53837) (:fv _uniq.53837) (:fv _uniq.53851)) ((:c NormedField.toField) (:fv _uniq.53834) ((:c DenselyNormedField.toNormedField) (:fv _uniq.53834) ((:c RCLike.toDenselyNormedField) ...
[{"name":"𝕂","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"p","sexp":"(:sort (+ u_4 1))"},{"name":"n'","sexp":"(:forall _ (:fv _uniq.53837) (:sort (+ u_5 1)))"},{"name":"𝔸","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁹","sexp":"((:c RCLike) (:fv _un...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:app (:c NormedSpace.exp) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Matrix) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:a...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.53834","is_instance":false,"is_let":false,"name":"𝕂","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.53837","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","co...
{"children":[{"source":"letI","sourceEnd":7687,"sourceStart":7683,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":7688,"sourceStart":7688,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":7688,"sourceStart":7688,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","...
[]
[{"source":"NormedRing (Matrix m m 𝔸)","source_end":7718,"source_start":7690,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Matrix.linftyOpNormedRing","source_end":7747,"source_start":7722,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.53834","is_instance":false,"is_let":false,"user_name":"𝕂"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.53837","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
45
8
exact
true
1
18
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ae7d0bc37634be0870837bbb896d5aeff27a156456e8c6ce3e2022a51df9bf42
129e68bf5d9c7d61aa192d6ea90ed360e1654caad6d4fe9009dd5e4535a30e94
1db64fc2993310f2106237b8497af23edffc532659ea015223820407768d91ff
6127d37d138dc7f6e566ed404112f21688eb94bb71a10b741fb8f8c1be41a577
cat-searcher/leandojo-benchmark-4-random
test
758
Matrix.exp_neg
Mathlib/Analysis/NormedSpace/MatrixExponential.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
letI : <a>NormedAlgebra</a> 𝕂 (<a>Matrix</a> m m 𝔸) := <a>Matrix.linftyOpNormedAlgebra</a>
𝕂 : Type u_1 m : Type u_2 n : Type u_3 p : Type u_4 n' : m → Type u_5 𝔸 : Type u_6 inst✝⁹ : RCLike 𝕂 inst✝⁸ : Fintype m inst✝⁷ : DecidableEq m inst✝⁶ : Fintype n inst✝⁵ : DecidableEq n inst✝⁴ : (i : m) → Fintype (n' i) inst✝³ : (i : m) → DecidableEq (n' i) inst✝² : NormedCommRing 𝔸 inst✝¹ : NormedAlgebra 𝕂 𝔸 inst...
𝕂 : Type u_1 m : Type u_2 n : Type u_3 p : Type u_4 n' : m → Type u_5 𝔸 : Type u_6 inst✝⁹ : RCLike 𝕂 inst✝⁸ : Fintype m inst✝⁷ : DecidableEq m inst✝⁶ : Fintype n inst✝⁵ : DecidableEq n inst✝⁴ : (i : m) → Fintype (n' i) inst✝³ : (i : m) → DecidableEq (n' i) inst✝² : NormedCommRing 𝔸 inst✝¹ : NormedAlgebra 𝕂 𝔸 inst...
((:c Eq) ((:c Matrix) (:fv _uniq.53837) (:fv _uniq.53837) (:fv _uniq.53851)) ((:c NormedSpace.exp) (:fv _uniq.53834) ((:c Matrix) (:fv _uniq.53837) (:fv _uniq.53837) (:fv _uniq.53851)) ((:c NormedField.toField) (:fv _uniq.53834) ((:c DenselyNormedField.toNormedField) (:fv _uniq.53834) ((:c RCLike.toDenselyNormedField) ...
[{"name":"𝕂","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"p","sexp":"(:sort (+ u_4 1))"},{"name":"n'","sexp":"(:forall _ (:fv _uniq.53837) (:sort (+ u_5 1)))"},{"name":"𝔸","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁹","sexp":"((:c RCLike) (:fv _un...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:app (:c NormedSpace.exp) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Matrix) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:a...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.53834","is_instance":false,"is_let":false,"name":"𝕂","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.53837","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","co...
{"children":[{"source":"letI","sourceEnd":7754,"sourceStart":7750,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":7755,"sourceStart":7755,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":7755,"sourceStart":7755,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","...
[]
[{"source":"NormedAlgebra 𝕂 (Matrix m m 𝔸)","source_end":7793,"source_start":7757,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Matrix.linftyOpNormedAlgebra","source_end":7825,"source_start":7797,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.53834","is_instance":false,"is_let":false,"user_name":"𝕂"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.53837","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
45
9
exact
true
1
19
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
17801f1b470878dfe13e1544f8c4ba45e6cac1875ffeb7b53d309eceae9abe8d
6127d37d138dc7f6e566ed404112f21688eb94bb71a10b741fb8f8c1be41a577
2f816f069ecd3310e465dcc5b1f701f4d5001a2983b2bf1282e5bcfc16f2743e
4f83652c9f7ca5aad0a0ff1d09ddbaf5c47a732a6fc27f7c6aad65cca1f8e686
cat-searcher/leandojo-benchmark-4-random
test
759
Matrix.exp_neg
Mathlib/Analysis/NormedSpace/MatrixExponential.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact (<a>Ring.inverse_exp</a> _ A).<a>Eq.symm</a>
𝕂 : Type u_1 m : Type u_2 n : Type u_3 p : Type u_4 n' : m → Type u_5 𝔸 : Type u_6 inst✝⁹ : RCLike 𝕂 inst✝⁸ : Fintype m inst✝⁷ : DecidableEq m inst✝⁶ : Fintype n inst✝⁵ : DecidableEq n inst✝⁴ : (i : m) → Fintype (n' i) inst✝³ : (i : m) → DecidableEq (n' i) inst✝² : NormedCommRing 𝔸 inst✝¹ : NormedAlgebra 𝕂 𝔸 inst...
((:c Eq) ((:c Matrix) (:fv _uniq.53837) (:fv _uniq.53837) (:fv _uniq.53851)) ((:c NormedSpace.exp) (:fv _uniq.53834) ((:c Matrix) (:fv _uniq.53837) (:fv _uniq.53837) (:fv _uniq.53851)) ((:c NormedField.toField) (:fv _uniq.53834) ((:c DenselyNormedField.toNormedField) (:fv _uniq.53834) ((:c RCLike.toDenselyNormedField) ...
[{"name":"𝕂","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"p","sexp":"(:sort (+ u_4 1))"},{"name":"n'","sexp":"(:forall _ (:fv _uniq.53837) (:sort (+ u_5 1)))"},{"name":"𝔸","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁹","sexp":"((:c RCLike) (:fv _un...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:app (:c NormedSpace.exp) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Matrix) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:a...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.53834","is_instance":false,"is_let":false,"name":"𝕂","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.53837","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","co...
{"children":[{"source":"exact","sourceEnd":7833,"sourceStart":7828,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":7835,"sourceStart":7834,"tag":"atom"},{"children":[{"name":"Ring.inverse_exp","semanticRole":"global","source":"Ring.inverse_exp","sourceEnd":7851,"sourceStart":7835,"tag":"identifier"},{...
[]
[{"source":"(Ring.inverse_exp _ A).symm","source_end":7861,"source_start":7834,"syntax_kind":"Lean.Parser.Term.proj"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.53834","is_instance":false,"is_let":false,"user_name":"𝕂"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.53837","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
45
10
exact
true
1
20
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
55111b70a98c6ac16bbe23b96786111f6285084d74f40cff86f70a1b7b7de254
4f83652c9f7ca5aad0a0ff1d09ddbaf5c47a732a6fc27f7c6aad65cca1f8e686
bfaa4a0bc6a761849de9ed4e4754ae7b7d7288f6b43463482e9709208ae862cb
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
760
Nat.le_div_two_iff_mul_two_le
Mathlib/Data/ZMod/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Nat.le_div_iff_mul_le</a> <a>zero_lt_two</a>, ← <a>Int.ofNat_le</a>, <a>Int.ofNat_mul</a>, <a>Nat.cast_two</a>]
n m : ℕ ⊢ m ≤ n / 2 ↔ ↑m * 2 ≤ ↑n
((:c Iff) ((:c LE.le) (:c Nat) (:c instLENat) (:fv _uniq.134988) ((:c HDiv.hDiv) (:c Nat) (:c Nat) (:c Nat) ((:c instHDiv) (:c Nat) (:c Nat.instDiv)) (:fv _uniq.134987) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2))))) ((:c LE.le) (:c Int) (:c Int.instLEInt) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ...
[{"name":"n","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"}]
(:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.134987","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.134988","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"}]
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":42048,"sourceStart":42046,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":42050,"sourceStart":42049,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",...
[]
[{"source":"Nat.le_div_iff_mul_le zero_lt_two","source_end":42083,"source_start":42050,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Int.ofNat_le","source_end":42101,"source_start":42089,"syntax_kind":"ident"},{"source":"Int.ofNat_mul","source_end":42116,"source_start":42103,"syntax_kind":"ident"},{"source":"Nat.cas...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.134987","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.134988","is_instance":false,"is_let":false,"user_name":"m"}]
304
2
exact
true
1
2
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7eaa6ecd745060ea920318b1dd633d203f50a9b044e8f764fbda9961089f2d12
856adf8787e71020ec9a40b7c992f0b6efd87c81c324c352190ecdb58893a4d7
09b458c3bb5afb8d684261ac596a0a748afff82e003fa8b512373e8f2e5c2973
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
761
Int.floor_neg
Mathlib/Algebra/Order/Floor.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>le_neg</a>, <a>Int.ceil_le</a>, <a>Int.le_floor</a>, <a>Int.cast_neg</a>, <a>le_neg</a>]
F : Type u_1 α : Type u_2 β : Type u_3 inst✝¹ : LinearOrderedRing α inst✝ : FloorRing α z✝ : ℤ a : α z : ℤ ⊢ z ≤ ⌊-a⌋ ↔ z ≤ -⌈a⌉
((:c Iff) ((:c LE.le) (:c Int) ((:c Preorder.toLE) (:c Int) ((:c PartialOrder.toPreorder) (:c Int) ((:c StrictOrderedRing.toPartialOrder) (:c Int) ((:c LinearOrderedRing.toStrictOrderedRing) (:c Int) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:c Int) (:c Int.instLinearOrderedCommRing)))))) (:fv _uniq.221783) ((:c...
[{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedRing) (:fv _uniq.221654))"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.221654) (:fv _uniq.221660))"},{"name":"z✝","sexp":"(:c Int)"},{"name":"a","se...
(:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:app (:c Int.floor) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedRin...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.221651","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.221654","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":43984,"sourceStart":43982,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":43986,"sourceStart":43985,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",...
[]
[{"source":"le_neg","source_end":43992,"source_start":43986,"syntax_kind":"ident"},{"source":"ceil_le","source_end":44001,"source_start":43994,"syntax_kind":"ident"},{"source":"le_floor","source_end":44011,"source_start":44003,"syntax_kind":"ident"},{"source":"Int.cast_neg","source_end":44025,"source_start":44013,"synt...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.221651","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.221654","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
377
2
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ef440ae8316a9404e8d45a9c554834cbeb48809bad76fbb053939c62b554096c
55531c1b9c2ef3b712694e5eecebf692f5f5b4559e424427601592bcbaae784f
4abb2676bca38a5ee1935bd0684c923783d2bc5d0c199068f1e1905c8325643d
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
762
MeasureTheory.Measure.prod_sum
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp_rw [<a>MeasureTheory.Measure.prod_sum_left</a>, <a>MeasureTheory.Measure.prod_sum_right</a>, <a>MeasureTheory.Measure.sum_sum</a>]
α : Type u_1 α' : Type u_2 β : Type u_3 β' : Type u_4 γ : Type u_5 E : Type u_6 inst✝⁸ : MeasurableSpace α inst✝⁷ : MeasurableSpace α' inst✝⁶ : MeasurableSpace β inst✝⁵ : MeasurableSpace β' inst✝⁴ : MeasurableSpace γ μ μ' : Measure α ν ν' : Measure β τ : Measure γ inst✝³ : NormedAddCommGroup E inst✝² : SFinite ν ι : Ty...
((:c Eq) ((:c MeasureTheory.Measure) ((:c Prod) (:fv _uniq.125789) (:fv _uniq.125795)) ((:c Prod.instMeasurableSpace) (:fv _uniq.125789) (:fv _uniq.125795) (:fv _uniq.125807) (:fv _uniq.125813))) ((:c MeasureTheory.Measure.prod) (:fv _uniq.125789) (:fv _uniq.125795) (:fv _uniq.125807) (:fv _uniq.125813) ((:c MeasureThe...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"α'","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"β'","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"E","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁸","sexp":"((:c MeasurableSpace) (:fv _uniq.125789))"},{"name":...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2))))))))...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125789","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125792","is_instance":false,"is_let":false,"name":"α'","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":30961,"sourceStart":30954,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":30963,"sourceStart":30962,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source...
[]
[{"source":"prod_sum_left","source_end":30976,"source_start":30963,"syntax_kind":"ident"},{"source":"prod_sum_right","source_end":30992,"source_start":30978,"syntax_kind":"ident"},{"source":"sum_sum","source_end":31001,"source_start":30994,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125789","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125792","is_instance":false,"is_let":false,"user_name":"α'"},{"binder_role":":implicit","context_index":2,"internal_name":"...
111
2
exact
true
1
24
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b2eb0c54aee41bf7c3da4a5f2629c070c31a2fd13331fa91aff505ff548d7b77
50a2924dc9d05dd9fdeb7c62a4e434a0037ea30c63632f7b1550930ca684a410
04685428da244680511f7c8a14f9af64fd1507d71cb3edac3b2192b7715f729d
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
763
Nat.dist_cast_rat
Mathlib/Topology/Instances/Rat.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>Nat.dist_cast_real</a>, ← <a>Rat.dist_cast</a>]
x y : ℕ ⊢ dist ↑x ↑y = dist x y
x y : ℕ ⊢ dist ↑↑x ↑↑y = dist ↑x ↑y
((:c Eq) (:c Real) ((:c Dist.dist) (:c Rat) ((:c PseudoMetricSpace.toDist) (:c Rat) ((:c MetricSpace.toPseudoMetricSpace) (:c Rat) (:c Rat.instMetricSpace))) ((:c Nat.cast) (:c Rat) (:c Rat.instNatCast) (:fv _uniq.1805)) ((:c Nat.cast) (:c Rat) (:c Rat.instNatCast) (:fv _uniq.1806))) ((:c Dist.dist) (:c Nat) (:c Nat.in...
[{"name":"x","sexp":"(:c Nat)"},{"name":"y","sexp":"(:c Nat)"}]
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Dist.dist) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c Dist) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c NatCast)...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.1805","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.1806","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Nat)"}]
{"children":[{"source":"rw","sourceEnd":1900,"sourceStart":1898,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1902,"sourceStart":1901,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":1905,"sourceStart":...
[]
[{"source":"Nat.dist_cast_real","source_end":1924,"source_start":1906,"syntax_kind":"ident"},{"source":"Rat.dist_cast","source_end":1943,"source_start":1930,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.1805","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.1806","is_instance":false,"is_let":false,"user_name":"y"}]
20
4
exact
true
1
2
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
dc5168ff69b1621337e6852485100c4570b7c9ed08e2427cbfba4c84609d3886
8336e4777a707be9f2081e365ac79ce710efbc4d0379be36ba86c0f4dc0a90c7
44c156af31721f56bf9ab7c78f6f619e29c909e1570d3ed6fd4de17ac590f03e
f6254ad3ba92d955cc6b3435c38fb7cebc8e75fde0dd6f7505f083b224189a45
cat-searcher/leandojo-benchmark-4-random
test
764
Nat.dist_cast_rat
Mathlib/Topology/Instances/Rat.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
congr
x y : ℕ ⊢ dist ↑↑x ↑↑y = dist ↑x ↑y
((:c Eq) (:c Real) ((:c Dist.dist) (:c Real) ((:c PseudoMetricSpace.toDist) (:c Real) (:c Real.pseudoMetricSpace)) ((:c Rat.cast) (:c Real) (:c Real.instRatCast) ((:c Nat.cast) (:c Rat) (:c Rat.instNatCast) (:fv _uniq.1805))) ((:c Rat.cast) (:c Real) (:c Real.instRatCast) ((:c Nat.cast) (:c Rat) (:c Rat.instNatCast) (:...
[{"name":"x","sexp":"(:c Nat)"},{"name":"y","sexp":"(:c Nat)"}]
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Dist.dist) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Dist) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Rat.cast) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c RatCa...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.1805","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.1806","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Nat)"}]
{"children":[{"source":"congr","sourceEnd":1951,"sourceStart":1946,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.congr","source":"congr","sourceEnd":1951,"sourceStart":1946,"tag":"node"}
[]
[]
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.1805","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.1806","is_instance":false,"is_let":false,"user_name":"y"}]
20
9
exact
true
1
2
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a7656461bb1a7e93cc08e3993fccb43f7a456091148a3cb161230d2e05ce5746
f6254ad3ba92d955cc6b3435c38fb7cebc8e75fde0dd6f7505f083b224189a45
092b163cac48997cb6cc327c63cda260e694055f56ff3698a70cdfda80ffbb2b
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
765
Profinite.finiteCoproduct.ι_injective
Mathlib/Topology/Category/Profinite/Limits.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro x y hxy
α : Type w inst✝ : Finite α X : α → Profinite a : α ⊢ Function.Injective ⇑(ι X a)
α : Type w inst✝ : Finite α X : α → Profinite a : α x y : (forget Profinite).obj (X a) hxy : (ι X a) x = (ι X a) y ⊢ x = y
((:c Function.Injective) ((:c Prefunctor.obj) (:c Profinite) ((:c CategoryTheory.CategoryStruct.toQuiver) (:c Profinite) ((:c CategoryTheory.Category.toCategoryStruct) (:c Profinite) (:c Profinite.category))) (:sort (+ (:max w u) 1)) ((:c CategoryTheory.CategoryStruct.toQuiver) (:sort (+ (:max w u) 1)) ((:c CategoryThe...
[{"name":"α","sexp":"(:sort (+ w 1))"},{"name":"inst✝","sexp":"((:c Finite) (:fv _uniq.36138))"},{"name":"X","sexp":"(:forall _ (:fv _uniq.36138) (:c Profinite))"},{"name":"a","sexp":"(:fv _uniq.36138)"}]
(:app (:c Function.Injective) (:arg :implicit-type 0 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:c Profinite)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:c Profinite))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:sort Typ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36138","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.36141","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Finite) (:arg :explicit ...
{"children":[{"source":"intro","sourceEnd":7589,"sourceStart":7584,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":7591,"sourceStart":7590,"tag":"identifier"},{"semanticRole":"scoped_local","source":"y","sourceEnd":7593,"sourceStart":7592,"tag":"identifier"},{"semanticRole":"scoped_lo...
[{"role":"fresh_name","source":"x","source_end":7591,"source_start":7590,"syntax_kind":"ident"},{"role":"fresh_name","source":"y","source_end":7593,"source_start":7592,"syntax_kind":"ident"},{"role":"fresh_name","source":"hxy","source_end":7597,"source_start":7594,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36138","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.36141","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":2,"interna...
38
4
exact
true
1
4
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3865dc0060083a23744469dacbf121911444746b6c97eff5ecc2b8ac02eaec51
5b524ddd4180e55ddfbb81dfe5cdba1a6de6ac7c2ea85425729a6a57ada293ec
9d18871bcc40256d494e3c2910f4536b5629b313423890104c3b65cedfcfdac0
a857122da8a42353d9007a077e908b7d89efa624d78296eb964350db6f273d24
cat-searcher/leandojo-benchmark-4-random
test
766
Profinite.finiteCoproduct.ι_injective
Mathlib/Topology/Category/Profinite/Limits.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>eq_of_heq</a> (Sigma.ext_iff.mp hxy).2
α : Type w inst✝ : Finite α X : α → Profinite a : α x y : (forget Profinite).obj (X a) hxy : (ι X a) x = (ι X a) y ⊢ x = y
((:c Eq) ((:c Prefunctor.obj) (:c Profinite) ((:c CategoryTheory.CategoryStruct.toQuiver) (:c Profinite) ((:c CategoryTheory.Category.toCategoryStruct) (:c Profinite) (:c Profinite.category))) (:sort (+ (:max w u) 1)) ((:c CategoryTheory.CategoryStruct.toQuiver) (:sort (+ (:max w u) 1)) ((:c CategoryTheory.Category.toC...
[{"name":"α","sexp":"(:sort (+ w 1))"},{"name":"inst✝","sexp":"((:c Finite) (:fv _uniq.36138))"},{"name":"X","sexp":"(:forall _ (:fv _uniq.36138) (:c Profinite))"},{"name":"a","sexp":"(:fv _uniq.36138)"},{"name":"x","sexp":"((:c Prefunctor.obj) (:c Profinite) ((:c CategoryTheory.CategoryStruct.toQuiver) (:c Profinite) ...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:c Profinite)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:c Profinite))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:sort Type))))) (:arg :ex...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36138","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.36141","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Finite) (:arg :explicit ...
{"children":[{"source":"exact","sourceEnd":7605,"sourceStart":7600,"tag":"atom"},{"children":[{"name":"eq_of_heq","semanticRole":"global","source":"eq_of_heq","sourceEnd":7615,"sourceStart":7606,"tag":"identifier"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":7617,"sourceStart":7616,"tag":"atom"},{"...
[]
[{"source":"eq_of_heq (Sigma.ext_iff.mp hxy).2","source_end":7640,"source_start":7606,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36138","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.36141","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":2,"interna...
38
5
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b4d37a3accdaecfb325dd9cfdb99ee61421506dc7498942c7d3b4e047bfcb715
a857122da8a42353d9007a077e908b7d89efa624d78296eb964350db6f273d24
eddf4ae7b84358b96c74ceef6af7a0fe11cba230ff8fa613f421a94ede0850f1
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
767
Turing.ListBlank.ext
Mathlib/Computability/TuringMachine.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine <a>Turing.ListBlank.induction_on</a> L₁ fun l₁ ↦ <a>Turing.ListBlank.induction_on</a> L₂ fun l₂ H ↦ ?_
Γ : Type u_1 i : Inhabited Γ L₁ L₂ : ListBlank Γ ⊢ (∀ (i_1 : ℕ), L₁.nth i_1 = L₂.nth i_1) → L₁ = L₂
Γ : Type u_1 i : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1 ⊢ mk l₁ = mk l₂
(:forall _ (:forall i (:c Nat) ((:c Eq) (:fv _uniq.16476) ((:c Turing.ListBlank.nth) (:fv _uniq.16476) (:fv _uniq.16477) (:fv _uniq.16478) 0) ((:c Turing.ListBlank.nth) (:fv _uniq.16476) (:fv _uniq.16477) (:fv _uniq.16479) 0))) ((:c Eq) ((:c Turing.ListBlank) (:fv _uniq.16476) (:fv _uniq.16477)) (:fv _uniq.16478) (:fv ...
[{"name":"Γ","sexp":"(:sort (+ u_1 1))"},{"name":"i","sexp":"((:c Inhabited) (:fv _uniq.16476))"},{"name":"L₁","sexp":"((:c Turing.ListBlank) (:fv _uniq.16476) (:fv _uniq.16477))"},{"name":"L₂","sexp":"((:c Turing.ListBlank) (:fv _uniq.16476) (:fv _uniq.16477))"}]
(:forall _ :explicit (:forall i :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Turing.ListBlank.nth) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Inhabited) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 0))) ...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16476","is_instance":false,"is_let":false,"name":"Γ","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16477","is_instance":true,"is_let":false,"name":"i","sexp":"(:app (:c Inhabited) (:arg :explicit 0...
{"children":[{"source":"refine","sourceEnd":14992,"sourceStart":14986,"tag":"atom"},{"children":[{"name":"Turing.ListBlank.induction_on","semanticRole":"global","source":"ListBlank.induction_on","sourceEnd":15015,"sourceStart":14993,"tag":"identifier"},{"children":[{"contextIndex":3,"semanticRole":"local","source":"L₁"...
[]
[{"source":"ListBlank.induction_on L₁ fun l₁ ↦ ListBlank.induction_on L₂ fun l₂ H ↦ ?_","source_end":15079,"source_start":14993,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16476","is_instance":false,"is_let":false,"user_name":"Γ"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16477","is_instance":true,"is_let":false,"user_name":"i"},{"binder_role":":implicit","context_index":3,"internal_na...
76
4
exact
true
1
4
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0d43c982cfe3c83ae690a3d9e5124e85614717f6221e0da75f8312c735067871
ffc9ca0ac061e0d5868785f5ad51b11fe7a43cd48387d719896e45cd18bc446d
5c86bedceea66c7e2afe80c06a1791ef7b2ea74d15c44444fb17738d931fb034
53d32cfd571b5a0a8fbcaa44284955d294922ee1e4c28e7368f0ebbadd5ecf71
cat-searcher/leandojo-benchmark-4-random
test
768
Turing.ListBlank.ext
Mathlib/Computability/TuringMachine.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
wlog h : l₁.length ≤ l₂.length
Γ : Type u_1 i : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1 ⊢ mk l₁ = mk l₂
case inr Γ : Type u_1 i : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1 this : ∀ {Γ : Type u_1} [i : Inhabited Γ] {L₁ L₂ : ListBlank Γ} (l₁ l₂ : List Γ), (∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1) → l₁.length ≤ l₂.length → mk l₁ = mk l₂ h : ¬l₁.length ≤ l₂...
((:c Eq) ((:c Turing.ListBlank) (:fv _uniq.16476) (:fv _uniq.16477)) ((:c Turing.ListBlank.mk) (:fv _uniq.16476) (:fv _uniq.16477) (:fv _uniq.16518)) ((:c Turing.ListBlank.mk) (:fv _uniq.16476) (:fv _uniq.16477) (:fv _uniq.16551)))
[{"name":"Γ","sexp":"(:sort (+ u_1 1))"},{"name":"i","sexp":"((:c Inhabited) (:fv _uniq.16476))"},{"name":"L₁","sexp":"((:c Turing.ListBlank) (:fv _uniq.16476) (:fv _uniq.16477))"},{"name":"L₂","sexp":"((:c Turing.ListBlank) (:fv _uniq.16476) (:fv _uniq.16477))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.16476))"},{"n...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Turing.ListBlank) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Inhabited) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 1 (:app (:c Turing.ListBlank.mk) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Inhabited) (:a...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16476","is_instance":false,"is_let":false,"name":"Γ","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16477","is_instance":true,"is_let":false,"name":"i","sexp":"(:app (:c Inhabited) (:arg :explicit 0...
{"children":[{"source":"wlog","sourceEnd":15086,"sourceStart":15082,"tag":"atom"},{"children":[{"source":"h","sourceEnd":15088,"sourceStart":15087,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"h","sourceEnd":15088,"sourceStart":15087,"tag":"node"},{"source":":","sourceEnd":15090,"sourceStart":15089,"tag":"at...
[]
[{"source":"l₁.length ≤ l₂.length","source_end":15118,"source_start":15091,"syntax_kind":"«term_≤_»"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16476","is_instance":false,"is_let":false,"user_name":"Γ"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16477","is_instance":true,"is_let":false,"user_name":"i"},{"binder_role":":implicit","context_index":3,"internal_na...
76
5
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b33308f15b7673f44b48c50e4fdda1ed1ee777e026429210a4962612fa1470a0
53d32cfd571b5a0a8fbcaa44284955d294922ee1e4c28e7368f0ebbadd5ecf71
fcc0d103d09bea039c2a510b05d45464f950fd85bc186cca839487fc79e7e0a2
0cb90c2b80500dcd96cc4256cad78d4d1dd9280be7ea9b3c40d76cdd1c91de90
cat-searcher/leandojo-benchmark-4-random
test
769
Turing.ListBlank.ext
Mathlib/Computability/TuringMachine.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine <a>Quotient.sound'</a> (<a>Or.inl</a> ⟨l₂.length - l₁.length, ?_⟩)
Γ : Type u_1 i : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1 h : l₁.length ≤ l₂.length ⊢ mk l₁ = mk l₂
Γ : Type u_1 i : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1 h : l₁.length ≤ l₂.length ⊢ l₂ = l₁ ++ List.replicate (l₂.length - l₁.length) default
((:c Eq) ((:c Turing.ListBlank) (:fv _uniq.16588) (:fv _uniq.16589)) ((:c Turing.ListBlank.mk) (:fv _uniq.16588) (:fv _uniq.16589) (:fv _uniq.16592)) ((:c Turing.ListBlank.mk) (:fv _uniq.16588) (:fv _uniq.16589) (:fv _uniq.16593)))
[{"name":"Γ","sexp":"(:sort (+ u_1 1))"},{"name":"i","sexp":"((:c Inhabited) (:fv _uniq.16588))"},{"name":"L₁","sexp":"((:c Turing.ListBlank) (:fv _uniq.16588) (:fv _uniq.16589))"},{"name":"L₂","sexp":"((:c Turing.ListBlank) (:fv _uniq.16588) (:fv _uniq.16589))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.16588))"},{"n...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Turing.ListBlank) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Inhabited) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 1 (:app (:c Turing.ListBlank.mk) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Inhabited) (:a...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16588","is_instance":false,"is_let":false,"name":"Γ","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16589","is_instance":true,"is_let":false,"name":"i","sexp":"(:app (:c Inhabited) (:arg :explicit 0...
{"children":[{"source":"refine","sourceEnd":15243,"sourceStart":15237,"tag":"atom"},{"children":[{"name":"Quotient.sound'","semanticRole":"global","source":"Quotient.sound'","sourceEnd":15259,"sourceStart":15244,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":15261,"sourceStart":15260,"tag":"ato...
[]
[{"source":"Quotient.sound' (Or.inl ⟨l₂.length - l₁.length, ?_⟩)","source_end":15304,"source_start":15244,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16588","is_instance":false,"is_let":false,"user_name":"Γ"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16589","is_instance":true,"is_let":false,"user_name":"i"},{"binder_role":":implicit","context_index":3,"internal_na...
76
56
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9611cf38c8ad09094df53aff99330f46084ed8211699a83a8a9bf06df72906ac
d27733cc8d0d6dfcf78bd661a5d26964ddbe8da975d5b6a92e15216114437318
4ac5ad62235c85cab29bdff981aa77de2ab869777e9f8358265f66c389a2bfe2
9bdd474efcdc24053868cde91fcb578416db75a6fb111547456de65720527107
cat-searcher/leandojo-benchmark-4-random
test
770
Turing.ListBlank.ext
Mathlib/Computability/TuringMachine.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine <a>List.ext_get</a> ?_ fun i h h₂ ↦ <a>Eq.symm</a> ?_
Γ : Type u_1 i : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1 h : l₁.length ≤ l₂.length ⊢ l₂ = l₁ ++ List.replicate (l₂.length - l₁.length) default
case refine_1 Γ : Type u_1 i : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1 h : l₁.length ≤ l₂.length ⊢ l₂.length = (l₁ ++ List.replicate (l₂.length - l₁.length) default).length case refine_2 Γ : Type u_1 i✝ : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i :...
((:c Eq) ((:c List) (:fv _uniq.16588)) (:fv _uniq.16593) ((:c HAppend.hAppend) ((:c List) (:fv _uniq.16588)) ((:c List) (:fv _uniq.16588)) ((:c List) (:fv _uniq.16588)) ((:c instHAppendOfAppend) ((:c List) (:fv _uniq.16588)) ((:c List.instAppend) (:fv _uniq.16588))) (:fv _uniq.16592) ((:c List.replicate) (:fv _uniq.165...
[{"name":"Γ","sexp":"(:sort (+ u_1 1))"},{"name":"i","sexp":"((:c Inhabited) (:fv _uniq.16588))"},{"name":"L₁","sexp":"((:c Turing.ListBlank) (:fv _uniq.16588) (:fv _uniq.16589))"},{"name":"L₂","sexp":"((:c Turing.ListBlank) (:fv _uniq.16588) (:fv _uniq.16589))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.16588))"},{"n...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:fv FV6)) (:arg :explicit 2 (:app (:c HAppend.hAppend) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 2...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16588","is_instance":false,"is_let":false,"name":"Γ","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16589","is_instance":true,"is_let":false,"name":"i","sexp":"(:app (:c Inhabited) (:arg :explicit 0...
{"children":[{"source":"refine","sourceEnd":15313,"sourceStart":15307,"tag":"atom"},{"children":[{"name":"List.ext_get","semanticRole":"global","source":"List.ext_get","sourceEnd":15326,"sourceStart":15314,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":15328,"sourceStart":15327,"tag":"atom"},{"...
[]
[{"source":"List.ext_get ?_ fun i h h₂ ↦ Eq.symm ?_","source_end":15357,"source_start":15314,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16588","is_instance":false,"is_let":false,"user_name":"Γ"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16589","is_instance":true,"is_let":false,"user_name":"i"},{"binder_role":":implicit","context_index":3,"internal_na...
76
57
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
04b8de53d1ac18e9b5ee5465872f9ac78511d408db91a3ee9920cde24fd2e232
9bdd474efcdc24053868cde91fcb578416db75a6fb111547456de65720527107
685a18cfe6636326d274307d216c0641ac5564b276e90f13ed054b1d50bae1d9
88f079e911e27fe9c8c2967e4edf61572ec0a6af5be292e8c083fcfa62d93f9d
cat-searcher/leandojo-benchmark-4-random
test
771
Turing.ListBlank.ext
Mathlib/Computability/TuringMachine.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>Turing.ListBlank.nth_mk</a>] at H
case refine_2 Γ : Type u_1 i✝ : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i : ℕ), (mk l₁).nth i = (mk l₂).nth i h✝ : l₁.length ≤ l₂.length i : ℕ h : i < l₂.length h₂ : i < (l₁ ++ List.replicate (l₂.length - l₁.length) default).length ⊢ (l₁ ++ List.replicate (l₂.length - l₁.length) default).get ⟨i, h₂⟩ = l₂....
case refine_2 Γ : Type u_1 i✝ : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i : ℕ), l₁.getI i = l₂.getI i h✝ : l₁.length ≤ l₂.length i : ℕ h : i < l₂.length h₂ : i < (l₁ ++ List.replicate (l₂.length - l₁.length) default).length ⊢ (l₁ ++ List.replicate (l₂.length - l₁.length) default).get ⟨i, h₂⟩ = l₂.get ⟨i, ...
((:c Eq) (:fv _uniq.16588) ((:c List.get) (:fv _uniq.16588) ((:c HAppend.hAppend) ((:c List) (:fv _uniq.16588)) ((:c List) (:fv _uniq.16588)) ((:c List) (:fv _uniq.16588)) ((:c instHAppendOfAppend) ((:c List) (:fv _uniq.16588)) ((:c List.instAppend) (:fv _uniq.16588))) (:fv _uniq.16592) ((:c List.replicate) (:fv _uniq....
[{"name":"Γ","sexp":"(:sort (+ u_1 1))"},{"name":"i✝","sexp":"((:c Inhabited) (:fv _uniq.16588))"},{"name":"L₁","sexp":"((:c Turing.ListBlank) (:fv _uniq.16588) (:fv _uniq.16589))"},{"name":"L₂","sexp":"((:c Turing.ListBlank) (:fv _uniq.16588) (:fv _uniq.16589))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.16588))"},{"...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c List.get) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HAppend.hAppend) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16588","is_instance":false,"is_let":false,"name":"Γ","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16589","is_instance":true,"is_let":false,"name":"i✝","sexp":"(:app (:c Inhabited) (:arg :explicit ...
{"children":[{"source":"simp","sourceEnd":15446,"sourceStart":15442,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":15451,"sourceStart":15447,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":154...
[]
[{"source":"ListBlank.nth_mk","source_end":15469,"source_start":15453,"syntax_kind":"ident"},{"source":"H","source_end":15475,"source_start":15474,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16588","is_instance":false,"is_let":false,"user_name":"Γ"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16589","is_instance":true,"is_let":false,"user_name":"i✝"},{"binder_role":":implicit","context_index":3,"internal_n...
76
63
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
38b1ba38502fc73246fb281d2603b88687443b7e66bf97313a916bf3718c044d
78cdf35768fd8a956c4771231618244e78c2473cb1ad0adfa0c25926d1a8f911
0af0554bb921dfad2340272f1267cc544ad6441c95a5a056399bb852f2fa64ee
0f59a699a2d3f252a3d739dbed4ad14c1d6073dadea36194934b952bb823e337
cat-searcher/leandojo-benchmark-4-random
test
772
Turing.ListBlank.ext
Mathlib/Computability/TuringMachine.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
cases' <a>lt_or_le</a> i l₁.length with h' h'
case refine_2 Γ : Type u_1 i✝ : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i : ℕ), l₁.getI i = l₂.getI i h✝ : l₁.length ≤ l₂.length i : ℕ h : i < l₂.length h₂ : i < (l₁ ++ List.replicate (l₂.length - l₁.length) default).length ⊢ (l₁ ++ List.replicate (l₂.length - l₁.length) default).get ⟨i, h₂⟩ = l₂.get ⟨i, ...
case refine_2.inl Γ : Type u_1 i✝ : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i : ℕ), l₁.getI i = l₂.getI i h✝ : l₁.length ≤ l₂.length i : ℕ h : i < l₂.length h₂ : i < (l₁ ++ List.replicate (l₂.length - l₁.length) default).length h' : i < l₁.length ⊢ (l₁ ++ List.replicate (l₂.length - l₁.length) default).ge...
((:c Eq) (:fv _uniq.16588) ((:c List.get) (:fv _uniq.16588) ((:c HAppend.hAppend) ((:c List) (:fv _uniq.16588)) ((:c List) (:fv _uniq.16588)) ((:c List) (:fv _uniq.16588)) ((:c instHAppendOfAppend) ((:c List) (:fv _uniq.16588)) ((:c List.instAppend) (:fv _uniq.16588))) (:fv _uniq.16592) ((:c List.replicate) (:fv _uniq....
[{"name":"Γ","sexp":"(:sort (+ u_1 1))"},{"name":"i✝","sexp":"((:c Inhabited) (:fv _uniq.16588))"},{"name":"L₁","sexp":"((:c Turing.ListBlank) (:fv _uniq.16588) (:fv _uniq.16589))"},{"name":"L₂","sexp":"((:c Turing.ListBlank) (:fv _uniq.16588) (:fv _uniq.16589))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.16588))"},{"...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c List.get) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HAppend.hAppend) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16588","is_instance":false,"is_let":false,"name":"Γ","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16589","is_instance":true,"is_let":false,"name":"i✝","sexp":"(:app (:c Inhabited) (:arg :explicit ...
{"children":[{"source":"cases'","sourceEnd":15484,"sourceStart":15478,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"lt_or_le","semanticRole":"global","source":"lt_or_le","sourceEnd":15493,"sourceStart":15485,"tag":"identifier"},{"children":[{"contex...
[]
[{"source":"lt_or_le i l₁.length","source_end":15507,"source_start":15485,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16588","is_instance":false,"is_let":false,"user_name":"Γ"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16589","is_instance":true,"is_let":false,"user_name":"i✝"},{"binder_role":":implicit","context_index":3,"internal_n...
76
64
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8b4012ec9d77c3d10c8cbe525afe5677ed140d9703229316af5334daaab6cd8c
0f59a699a2d3f252a3d739dbed4ad14c1d6073dadea36194934b952bb823e337
db8b2e7dc68a6d5b0dc4928ac6e00a07854297eb7c5eb7fa4e6edc172a21844b
3ded1e3e5558cb1470112b566c4d6e4f0da069a156837e910b1be3738e95e0cd
cat-searcher/leandojo-benchmark-4-random
test
773
Turing.ListBlank.ext
Mathlib/Computability/TuringMachine.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
cases <a>le_total</a> l₁.length l₂.length <;> [skip; symm] <;> apply this <;> try assumption
case inr Γ : Type u_1 i : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1 this : ∀ {Γ : Type u_1} [i : Inhabited Γ] {L₁ L₂ : ListBlank Γ} (l₁ l₂ : List Γ), (∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1) → l₁.length ≤ l₂.length → mk l₁ = mk l₂ h : ¬l₁.length ≤ l₂...
case inr.inr.H Γ : Type u_1 i : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1 this : ∀ {Γ : Type u_1} [i : Inhabited Γ] {L₁ L₂ : ListBlank Γ} (l₁ l₂ : List Γ), (∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1) → l₁.length ≤ l₂.length → mk l₁ = mk l₂ h : ¬l₁.lengt...
((:c Eq) ((:c Turing.ListBlank) (:fv _uniq.16476) (:fv _uniq.16477)) ((:c Turing.ListBlank.mk) (:fv _uniq.16476) (:fv _uniq.16477) (:fv _uniq.16518)) ((:c Turing.ListBlank.mk) (:fv _uniq.16476) (:fv _uniq.16477) (:fv _uniq.16551)))
[{"name":"Γ","sexp":"(:sort (+ u_1 1))"},{"name":"i","sexp":"((:c Inhabited) (:fv _uniq.16476))"},{"name":"L₁","sexp":"((:c Turing.ListBlank) (:fv _uniq.16476) (:fv _uniq.16477))"},{"name":"L₂","sexp":"((:c Turing.ListBlank) (:fv _uniq.16476) (:fv _uniq.16477))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.16476))"},{"n...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Turing.ListBlank) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Inhabited) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 1 (:app (:c Turing.ListBlank.mk) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Inhabited) (:a...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16476","is_instance":false,"is_let":false,"name":"Γ","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16477","is_instance":true,"is_let":false,"name":"i","sexp":"(:app (:c Inhabited) (:arg :explicit 0...
{"children":[{"children":[{"children":[{"children":[{"source":"cases","sourceEnd":15129,"sourceStart":15124,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"le_total","semanticRole":"global","source":"le_total","sourceEnd":15138,"sourceStart":15130,"ta...
[]
[{"source":"le_total l₁.length l₂.length","source_end":15162,"source_start":15130,"syntax_kind":"Lean.Parser.Term.app"},{"source":"this","source_end":15194,"source_start":15190,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16476","is_instance":false,"is_let":false,"user_name":"Γ"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16477","is_instance":true,"is_let":false,"user_name":"i"},{"binder_role":":implicit","context_index":3,"internal_na...
76
10
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5216558cae3a3c3b3c477413b92fec38e1d559a3f82dc9068797f297000e1ed2
6d239217763e572400c631d83e4dc2651e156149cc833123ec91eeaf5b6d0bc6
9ed68f7dbf2d91c10b50ccfa6f3b747e8d5e3e863243a33c30f872a1a0acfab7
e9e240e34ba80dee56650d2c213af3572428f04e3527a328f5e5ec621770f601
cat-searcher/leandojo-benchmark-4-random
test
774
Turing.ListBlank.ext
Mathlib/Computability/TuringMachine.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro
case inr.inr.H Γ : Type u_1 i : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1 this : ∀ {Γ : Type u_1} [i : Inhabited Γ] {L₁ L₂ : ListBlank Γ} (l₁ l₂ : List Γ), (∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1) → l₁.length ≤ l₂.length → mk l₁ = mk l₂ h : ¬l₁.lengt...
case inr.inr.H Γ : Type u_1 i : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1 this : ∀ {Γ : Type u_1} [i : Inhabited Γ] {L₁ L₂ : ListBlank Γ} (l₁ l₂ : List Γ), (∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1) → l₁.length ≤ l₂.length → mk l₁ = mk l₂ h : ¬l₁.lengt...
(:forall i (:c Nat) ((:c Eq) (:fv _uniq.16476) ((:c Turing.ListBlank.nth) (:fv _uniq.16476) (:fv _uniq.16477) ((:c Turing.ListBlank.mk) (:fv _uniq.16476) (:fv _uniq.16477) (:fv _uniq.16551)) 0) ((:c Turing.ListBlank.nth) (:fv _uniq.16476) (:fv _uniq.16477) ((:c Turing.ListBlank.mk) (:fv _uniq.16476) (:fv _uniq.16477) (...
[{"name":"Γ","sexp":"(:sort (+ u_1 1))"},{"name":"i","sexp":"((:c Inhabited) (:fv _uniq.16476))"},{"name":"L₁","sexp":"((:c Turing.ListBlank) (:fv _uniq.16476) (:fv _uniq.16477))"},{"name":"L₂","sexp":"((:c Turing.ListBlank) (:fv _uniq.16476) (:fv _uniq.16477))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.16476))"},{"n...
(:forall i :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Turing.ListBlank.nth) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Inhabited) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Turing.ListBlank.mk) (:arg :implicit-type 0 (...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16476","is_instance":false,"is_let":false,"name":"Γ","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16477","is_instance":true,"is_let":false,"name":"i","sexp":"(:app (:c Inhabited) (:arg :explicit 0...
{"children":[{"source":"intro","sourceEnd":15223,"sourceStart":15218,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source":"intro","sourceEnd":15223,"sourceStart":15218,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16476","is_instance":false,"is_let":false,"user_name":"Γ"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16477","is_instance":true,"is_let":false,"user_name":"i"},{"binder_role":":implicit","context_index":3,"internal_na...
76
52
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3648c9588726ce2bf042af204d04a7bfb63e8619878d175574384e64accd20e7
e9e240e34ba80dee56650d2c213af3572428f04e3527a328f5e5ec621770f601
c432b372e0e30267e65e26a12a42c7957ab52e25dfe3c6d4b929213d88965e45
a4c4e4c25036d6ef5fc4961430409bc75255e774cfa076fa2dfd9993955e0816
cat-searcher/leandojo-benchmark-4-random
test
775
Turing.ListBlank.ext
Mathlib/Computability/TuringMachine.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [H]
case inr.inr.H Γ : Type u_1 i : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1 this : ∀ {Γ : Type u_1} [i : Inhabited Γ] {L₁ L₂ : ListBlank Γ} (l₁ l₂ : List Γ), (∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1) → l₁.length ≤ l₂.length → mk l₁ = mk l₂ h : ¬l₁.lengt...
((:c Eq) (:fv _uniq.16476) ((:c Turing.ListBlank.nth) (:fv _uniq.16476) (:fv _uniq.16477) ((:c Turing.ListBlank.mk) (:fv _uniq.16476) (:fv _uniq.16477) (:fv _uniq.16551)) (:fv _uniq.16834)) ((:c Turing.ListBlank.nth) (:fv _uniq.16476) (:fv _uniq.16477) ((:c Turing.ListBlank.mk) (:fv _uniq.16476) (:fv _uniq.16477) (:fv ...
[{"name":"Γ","sexp":"(:sort (+ u_1 1))"},{"name":"i","sexp":"((:c Inhabited) (:fv _uniq.16476))"},{"name":"L₁","sexp":"((:c Turing.ListBlank) (:fv _uniq.16476) (:fv _uniq.16477))"},{"name":"L₂","sexp":"((:c Turing.ListBlank) (:fv _uniq.16476) (:fv _uniq.16477))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.16476))"},{"n...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Turing.ListBlank.nth) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Inhabited) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Turing.ListBlank.mk) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16476","is_instance":false,"is_let":false,"name":"Γ","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16477","is_instance":true,"is_let":false,"name":"i","sexp":"(:app (:c Inhabited) (:arg :explicit 0...
{"children":[{"source":"rw","sourceEnd":15230,"sourceStart":15228,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15232,"sourceStart":15231,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":7,"semant...
[]
[{"source":"H","source_end":15233,"source_start":15232,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16476","is_instance":false,"is_let":false,"user_name":"Γ"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16477","is_instance":true,"is_let":false,"user_name":"i"},{"binder_role":":implicit","context_index":3,"internal_na...
76
53
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
85e6dee2ae7d29cb2686387b661b8a3f3f90cac758d269cdb213fc75dbf5e4aa
a4c4e4c25036d6ef5fc4961430409bc75255e774cfa076fa2dfd9993955e0816
353b5799251eb8d14b63e7b05bd9535bbe189f3fcde845e3e85a005f0a8e8107
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
776
Turing.ListBlank.ext
Mathlib/Computability/TuringMachine.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
assumption
case inr.inr.h Γ : Type u_1 i : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1 this : ∀ {Γ : Type u_1} [i : Inhabited Γ] {L₁ L₂ : ListBlank Γ} (l₁ l₂ : List Γ), (∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1) → l₁.length ≤ l₂.length → mk l₁ = mk l₂ h : ¬l₁.lengt...
((:c LE.le) (:c Nat) (:c instLENat) ((:c List.length) (:fv _uniq.16476) (:fv _uniq.16551)) ((:c List.length) (:fv _uniq.16476) (:fv _uniq.16518)))
[{"name":"Γ","sexp":"(:sort (+ u_1 1))"},{"name":"i","sexp":"((:c Inhabited) (:fv _uniq.16476))"},{"name":"L₁","sexp":"((:c Turing.ListBlank) (:fv _uniq.16476) (:fv _uniq.16477))"},{"name":"L₂","sexp":"((:c Turing.ListBlank) (:fv _uniq.16476) (:fv _uniq.16477))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.16476))"},{"n...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c List.length) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV6)))) (:arg :explicit 3 (:app (:c List.length) (:arg :implicit-type 0 (:fv FV1)) (:arg :expli...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16476","is_instance":false,"is_let":false,"name":"Γ","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16477","is_instance":true,"is_let":false,"name":"i","sexp":"(:app (:c Inhabited) (:arg :explicit 0...
{"children":[{"children":[{"children":[{"children":[{"source":"assumption","sourceEnd":15213,"sourceStart":15203,"tag":"atom"}],"kind":"Lean.Parser.Tactic.assumption","source":"assumption","sourceEnd":15213,"sourceStart":15203,"tag":"node"}],"kind":"null","source":"assumption","sourceEnd":15213,"sourceStart":15203,"tag...
[]
[]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16476","is_instance":false,"is_let":false,"user_name":"Γ"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16477","is_instance":true,"is_let":false,"user_name":"i"},{"binder_role":":implicit","context_index":3,"internal_na...
76
49
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
16abbd9b2a881cbe878f756610fd890019c34914991c976de84bf65fe4a510b7
c3ee3e04c18ea933a1ce378d0863cf81feec42f8b9eb82b2acba65727c4f4ad5
c081dd376ba93a530dd044cffc81e70953e86d86f7d0796dc26bc1597302573d
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
777
Turing.ListBlank.ext
Mathlib/Computability/TuringMachine.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>Nat.add_sub_cancel'</a> h, <a>List.length_append</a>, <a>List.length_replicate</a>]
case refine_1 Γ : Type u_1 i : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i_1 : ℕ), (mk l₁).nth i_1 = (mk l₂).nth i_1 h : l₁.length ≤ l₂.length ⊢ l₂.length = (l₁ ++ List.replicate (l₂.length - l₁.length) default).length
((:c Eq) (:c Nat) ((:c List.length) (:fv _uniq.16588) (:fv _uniq.16593)) ((:c List.length) (:fv _uniq.16588) ((:c HAppend.hAppend) ((:c List) (:fv _uniq.16588)) ((:c List) (:fv _uniq.16588)) ((:c List) (:fv _uniq.16588)) ((:c instHAppendOfAppend) ((:c List) (:fv _uniq.16588)) ((:c List.instAppend) (:fv _uniq.16588))) (...
[{"name":"Γ","sexp":"(:sort (+ u_1 1))"},{"name":"i","sexp":"((:c Inhabited) (:fv _uniq.16588))"},{"name":"L₁","sexp":"((:c Turing.ListBlank) (:fv _uniq.16588) (:fv _uniq.16589))"},{"name":"L₂","sexp":"((:c Turing.ListBlank) (:fv _uniq.16588) (:fv _uniq.16589))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.16588))"},{"n...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c List.length) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV6)))) (:arg :explicit 2 (:app (:c List.length) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HAppend.hAppend) (:arg :implicit-type 0 (:app (:c List) (:arg :e...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16588","is_instance":false,"is_let":false,"name":"Γ","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16589","is_instance":true,"is_let":false,"name":"i","sexp":"(:app (:c Inhabited) (:arg :explicit 0...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":15367,"sourceStart":15363,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":15372,"sourceStart":15368,"tag":"atom"}],"kind"...
[]
[{"source":"Nat.add_sub_cancel' h","source_end":15395,"source_start":15374,"syntax_kind":"Lean.Parser.Term.app"},{"source":"List.length_append","source_end":15415,"source_start":15397,"syntax_kind":"ident"},{"source":"List.length_replicate","source_end":15438,"source_start":15417,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16588","is_instance":false,"is_let":false,"user_name":"Γ"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16589","is_instance":true,"is_let":false,"user_name":"i"},{"binder_role":":implicit","context_index":3,"internal_na...
76
60
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
acae79a7df952cc57873261f55decf7bc7decc7ce08166889e28b5079bb1aa2e
7bafe575d9c27e83dfa39818b23be43a570a74fed1c362f39da68e945f8963b5
11083c693a4247981fa236ba9f6418933aedc0f6a390626a3f2c38448044056c
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
778
Turing.ListBlank.ext
Mathlib/Computability/TuringMachine.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>List.get_append</a> _ h', <a>List.get?_eq_get</a> h, <a>List.get?_eq_get</a> h', ← <a>List.getI_eq_get</a> _ h, ← <a>List.getI_eq_get</a> _ h', H]
case refine_2.inl Γ : Type u_1 i✝ : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i : ℕ), l₁.getI i = l₂.getI i h✝ : l₁.length ≤ l₂.length i : ℕ h : i < l₂.length h₂ : i < (l₁ ++ List.replicate (l₂.length - l₁.length) default).length h' : i < l₁.length ⊢ (l₁ ++ List.replicate (l₂.length - l₁.length) default).ge...
((:c Eq) (:fv _uniq.16588) ((:c List.get) (:fv _uniq.16588) ((:c HAppend.hAppend) ((:c List) (:fv _uniq.16588)) ((:c List) (:fv _uniq.16588)) ((:c List) (:fv _uniq.16588)) ((:c instHAppendOfAppend) ((:c List) (:fv _uniq.16588)) ((:c List.instAppend) (:fv _uniq.16588))) (:fv _uniq.16592) ((:c List.replicate) (:fv _uniq....
[{"name":"Γ","sexp":"(:sort (+ u_1 1))"},{"name":"i✝","sexp":"((:c Inhabited) (:fv _uniq.16588))"},{"name":"L₁","sexp":"((:c Turing.ListBlank) (:fv _uniq.16588) (:fv _uniq.16589))"},{"name":"L₂","sexp":"((:c Turing.ListBlank) (:fv _uniq.16588) (:fv _uniq.16589))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.16588))"},{"...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c List.get) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HAppend.hAppend) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16588","is_instance":false,"is_let":false,"name":"Γ","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16589","is_instance":true,"is_let":false,"name":"i✝","sexp":"(:app (:c Inhabited) (:arg :explicit ...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":15528,"sourceStart":15524,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":15533,"sourceStart":15529,"tag":"atom"}],"kind"...
[]
[{"source":"List.get_append _ h'","source_end":15555,"source_start":15535,"syntax_kind":"Lean.Parser.Term.app"},{"source":"List.get?_eq_get h","source_end":15575,"source_start":15557,"syntax_kind":"Lean.Parser.Term.app"},{"source":"List.get?_eq_get h'","source_end":15596,"source_start":15577,"syntax_kind":"Lean.Parser....
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16588","is_instance":false,"is_let":false,"user_name":"Γ"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16589","is_instance":true,"is_let":false,"user_name":"i✝"},{"binder_role":":implicit","context_index":3,"internal_n...
76
67
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f8891788e84f6472f509686efc775633369aa57ec56af7c1f4bbb1434ad10d44
a10829838520ed8b5ac10edf9189527a203c29d1bbab4c9566a5fd5e400e1b1b
d61e77249fba3931f78a5916650ace3b6ae49d03891de07a4f0838ecb2b663fb
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
779
Turing.ListBlank.ext
Mathlib/Computability/TuringMachine.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>List.get_append_right'</a> h', <a>List.get_replicate</a>, <a>List.get?_eq_get</a> h, <a>List.get?_len_le</a> h', ← <a>List.getI_eq_default</a> _ h', H, <a>List.getI_eq_get</a> _ h]
case refine_2.inr Γ : Type u_1 i✝ : Inhabited Γ L₁ L₂ : ListBlank Γ l₁ l₂ : List Γ H : ∀ (i : ℕ), l₁.getI i = l₂.getI i h✝ : l₁.length ≤ l₂.length i : ℕ h : i < l₂.length h₂ : i < (l₁ ++ List.replicate (l₂.length - l₁.length) default).length h' : l₁.length ≤ i ⊢ (l₁ ++ List.replicate (l₂.length - l₁.length) default).ge...
((:c Eq) (:fv _uniq.16588) ((:c List.get) (:fv _uniq.16588) ((:c HAppend.hAppend) ((:c List) (:fv _uniq.16588)) ((:c List) (:fv _uniq.16588)) ((:c List) (:fv _uniq.16588)) ((:c instHAppendOfAppend) ((:c List) (:fv _uniq.16588)) ((:c List.instAppend) (:fv _uniq.16588))) (:fv _uniq.16592) ((:c List.replicate) (:fv _uniq....
[{"name":"Γ","sexp":"(:sort (+ u_1 1))"},{"name":"i✝","sexp":"((:c Inhabited) (:fv _uniq.16588))"},{"name":"L₁","sexp":"((:c Turing.ListBlank) (:fv _uniq.16588) (:fv _uniq.16589))"},{"name":"L₂","sexp":"((:c Turing.ListBlank) (:fv _uniq.16588) (:fv _uniq.16589))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.16588))"},{"...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c List.get) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HAppend.hAppend) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16588","is_instance":false,"is_let":false,"name":"Γ","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16589","is_instance":true,"is_let":false,"name":"i✝","sexp":"(:app (:c Inhabited) (:arg :explicit ...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":15669,"sourceStart":15665,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":15674,"sourceStart":15670,"tag":"atom"}],"kind"...
[]
[{"source":"List.get_append_right' h'","source_end":15701,"source_start":15676,"syntax_kind":"Lean.Parser.Term.app"},{"source":"List.get_replicate","source_end":15721,"source_start":15703,"syntax_kind":"ident"},{"source":"List.get?_eq_get h","source_end":15741,"source_start":15723,"syntax_kind":"Lean.Parser.Term.app"},...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16588","is_instance":false,"is_let":false,"user_name":"Γ"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.16589","is_instance":true,"is_let":false,"user_name":"i✝"},{"binder_role":":implicit","context_index":3,"internal_n...
76
72
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ebed825f4e0bb6b96c6d613b95672f6e3eb1ebca0e1139b69e271248b3544a09
e4154aadc8ba0d660df24e1f8f0b535cb3e26bdbbda5985bdcc9cb43071b4ccc
4edca906612fd35184f1832389424aeaebd5366db020a1116fb935de23c80f02
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
802
IntermediateField.isSplittingField_iSup
Mathlib/FieldTheory/Adjoin.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
let F : <a>IntermediateField</a> K L := ⨆ i ∈ s, t i
F : Type u_1 inst✝⁵ : Field F E : Type u_2 inst✝⁴ : Field E inst✝³ : Algebra F E S : Set E α : E K : Type u_3 L : Type u_4 inst✝² : Field K inst✝¹ : Field L inst✝ : Algebra K L E1 E2 : IntermediateField K L ι : Type u_5 t : ι → IntermediateField K L p : ι → K[X] s : Finset ι h0 : ∏ i ∈ s, p i ≠ 0 h : ∀ i ∈ s, IsSplitti...
F✝ : Type u_1 inst✝⁵ : Field F✝ E : Type u_2 inst✝⁴ : Field E inst✝³ : Algebra F✝ E S : Set E α : E K : Type u_3 L : Type u_4 inst✝² : Field K inst✝¹ : Field L inst✝ : Algebra K L E1 E2 : IntermediateField K L ι : Type u_5 t : ι → IntermediateField K L p : ι → K[X] s : Finset ι h0 : ∏ i ∈ s, p i ≠ 0 h : ∀ i ∈ s, IsSpli...
((:c Polynomial.IsSplittingField) (:fv _uniq.270440) ((:c Subtype) (:fv _uniq.270443) (:lambda x (:fv _uniq.270443) ((:c Membership.mem) (:fv _uniq.270443) ((:c IntermediateField) (:fv _uniq.270440) (:fv _uniq.270443) (:fv _uniq.270446) (:fv _uniq.270449) (:fv _uniq.270691)) ((:c SetLike.instMembership) ((:c Intermedia...
[{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c Field) (:fv _uniq.270181))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.270187))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.270181) (:fv _uniq.270187) ((:c Semifield.toCommSemiring) (:fv _uniq.27...
(:app (:c Polynomial.IsSplittingField) (:arg :explicit 0 (:fv FV7)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV8)) (:arg :explicit 1 (:lambda x :explicit (:fv FV8) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV8)) (:arg :implicit-type 1 (:app (:c IntermediateField) (:arg :explicit 0 (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.270181","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.270184","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c Field) (:arg :explici...
{"children":[{"source":"let","sourceEnd":34622,"sourceStart":34619,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"F","sourceEnd":34624,"sourceStart":34623,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":3462...
[]
[{"source":"IntermediateField K L","source_end":34648,"source_start":34627,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⨆ i ∈ s, t i","source_end":34668,"source_start":34652,"syntax_kind":"«term⨆_,_»"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.270181","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.270184","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte...
211
4
exact
true
1
20
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
351ffdcf54aea6ff8408f9b53a6d3568cc8974211a5bdc236b45b67660da4b76
d25ffcb9dc77c59ceb80c0ebf8b1e965f13dd3283c4829dab4fc5481811d879d
1eab3364d5d7487c3636feb2912c26316ed2a37ab744fc88a8195bc507dc6a89
06e65d9619fe2ce5a3bb495f491097fd65c0ddd23a9432a0d05d23cbe3a5bd12
cat-searcher/leandojo-benchmark-4-random
test
803
IntermediateField.isSplittingField_iSup
Mathlib/FieldTheory/Adjoin.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have hF : ∀ i ∈ s, t i ≤ F := fun i hi ↦ <a>le_iSup_of_le</a> i (<a>le_iSup</a> (fun _ ↦ t i) hi)
F✝ : Type u_1 inst✝⁵ : Field F✝ E : Type u_2 inst✝⁴ : Field E inst✝³ : Algebra F✝ E S : Set E α : E K : Type u_3 L : Type u_4 inst✝² : Field K inst✝¹ : Field L inst✝ : Algebra K L E1 E2 : IntermediateField K L ι : Type u_5 t : ι → IntermediateField K L p : ι → K[X] s : Finset ι h0 : ∏ i ∈ s, p i ≠ 0 h : ∀ i ∈ s, IsSpli...
F✝ : Type u_1 inst✝⁵ : Field F✝ E : Type u_2 inst✝⁴ : Field E inst✝³ : Algebra F✝ E S : Set E α : E K : Type u_3 L : Type u_4 inst✝² : Field K inst✝¹ : Field L inst✝ : Algebra K L E1 E2 : IntermediateField K L ι : Type u_5 t : ι → IntermediateField K L p : ι → K[X] s : Finset ι h0 : ∏ i ∈ s, p i ≠ 0 h : ∀ i ∈ s, IsSpli...
((:c Polynomial.IsSplittingField) (:fv _uniq.270440) ((:c Subtype) (:fv _uniq.270443) (:lambda x (:fv _uniq.270443) ((:c Membership.mem) (:fv _uniq.270443) ((:c IntermediateField) (:fv _uniq.270440) (:fv _uniq.270443) (:fv _uniq.270446) (:fv _uniq.270449) (:fv _uniq.270691)) ((:c SetLike.instMembership) ((:c Intermedia...
[{"name":"F✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c Field) (:fv _uniq.270181))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.270187))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.270181) (:fv _uniq.270187) ((:c Semifield.toCommSemiring) (:fv _uniq.2...
(:app (:c Polynomial.IsSplittingField) (:arg :explicit 0 (:fv FV7)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV8)) (:arg :explicit 1 (:lambda x :explicit (:fv FV8) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV8)) (:arg :implicit-type 1 (:app (:c IntermediateField) (:arg :explicit 0 (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.270181","is_instance":false,"is_let":false,"name":"F✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.270184","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c Field) (:arg :explic...
{"children":[{"source":"have","sourceEnd":34675,"sourceStart":34671,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hF","sourceEnd":34678,"sourceStart":34676,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hF","sourceEnd":34678,"sourceStart":34676,"tag":"nod...
[]
[{"source":"∀ i ∈ s, t i ≤ F","source_end":34703,"source_start":34681,"syntax_kind":"Lean.«term∀__,_»"},{"source":"fun i hi ↦ le_iSup_of_le i (le_iSup (fun _ ↦ t i) hi)","source_end":34764,"source_start":34707,"syntax_kind":"Lean.Parser.Term.fun"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.270181","is_instance":false,"is_let":false,"user_name":"F✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.270184","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"int...
211
5
exact
true
1
21
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7a96a377ef1cfcb62c062f56db2cb0bf6efcc951463a738f056cb55a0b92161b
06e65d9619fe2ce5a3bb495f491097fd65c0ddd23a9432a0d05d23cbe3a5bd12
ef9392305732aaa7fd6dc2f9a6d38a8d68b3c7b96f82ae563615f2c3663d70d3
3d1e6c0b2dd6e5166ffea178186db9d49e67019b3637826ceaa55622b11494bb
cat-searcher/leandojo-benchmark-4-random
test
804
IntermediateField.isSplittingField_iSup
Mathlib/FieldTheory/Adjoin.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>IntermediateField.isSplittingField_iff</a>] at h ⊢
F✝ : Type u_1 inst✝⁵ : Field F✝ E : Type u_2 inst✝⁴ : Field E inst✝³ : Algebra F✝ E S : Set E α : E K : Type u_3 L : Type u_4 inst✝² : Field K inst✝¹ : Field L inst✝ : Algebra K L E1 E2 : IntermediateField K L ι : Type u_5 t : ι → IntermediateField K L p : ι → K[X] s : Finset ι h0 : ∏ i ∈ s, p i ≠ 0 h : ∀ i ∈ s, IsSpli...
F✝ : Type u_1 inst✝⁵ : Field F✝ E : Type u_2 inst✝⁴ : Field E inst✝³ : Algebra F✝ E S : Set E α : E K : Type u_3 L : Type u_4 inst✝² : Field K inst✝¹ : Field L inst✝ : Algebra K L E1 E2 : IntermediateField K L ι : Type u_5 t : ι → IntermediateField K L p : ι → K[X] s : Finset ι h0 : ∏ i ∈ s, p i ≠ 0 F : IntermediateFie...
((:c Polynomial.IsSplittingField) (:fv _uniq.270440) ((:c Subtype) (:fv _uniq.270443) (:lambda x (:fv _uniq.270443) ((:c Membership.mem) (:fv _uniq.270443) ((:c IntermediateField) (:fv _uniq.270440) (:fv _uniq.270443) (:fv _uniq.270446) (:fv _uniq.270449) (:fv _uniq.270691)) ((:c SetLike.instMembership) ((:c Intermedia...
[{"name":"F✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c Field) (:fv _uniq.270181))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.270187))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.270181) (:fv _uniq.270187) ((:c Semifield.toCommSemiring) (:fv _uniq.2...
(:app (:c Polynomial.IsSplittingField) (:arg :explicit 0 (:fv FV7)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV8)) (:arg :explicit 1 (:lambda x :explicit (:fv FV8) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV8)) (:arg :implicit-type 1 (:app (:c IntermediateField) (:arg :explicit 0 (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.270181","is_instance":false,"is_let":false,"name":"F✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.270184","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c Field) (:arg :explic...
{"children":[{"source":"simp","sourceEnd":34771,"sourceStart":34767,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":34776,"sourceStart":34772,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":347...
[]
[{"source":"isSplittingField_iff","source_end":34798,"source_start":34778,"syntax_kind":"ident"},{"source":"h","source_end":34804,"source_start":34803,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.270181","is_instance":false,"is_let":false,"user_name":"F✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.270184","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"int...
211
6
exact
true
1
22
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4259f57560f1925affb3455b19d874e1048e61cbcc9b1ea542e6ef0d9c30e26f
3d1e6c0b2dd6e5166ffea178186db9d49e67019b3637826ceaa55622b11494bb
ce52aa363c746d71947e4dbc5121a53dbe6535ccddb0465abe1c6f15f25831ef
1871b4a52099517f3258f880e2319dcf1b715971e320e1c88995d103bdf093ca
cat-searcher/leandojo-benchmark-4-random
test
805
IntermediateField.isSplittingField_iSup
Mathlib/FieldTheory/Adjoin.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨<a>Polynomial.splits_prod</a> (<a>algebraMap</a> K F) fun i hi ↦ <a>Polynomial.splits_comp_of_splits</a> (<a>algebraMap</a> K (t i)) (<a>IntermediateField.inclusion</a> (hF i hi)).<a>AlgHom.toRingHom</a> (h i hi).1, ?_⟩
F✝ : Type u_1 inst✝⁵ : Field F✝ E : Type u_2 inst✝⁴ : Field E inst✝³ : Algebra F✝ E S : Set E α : E K : Type u_3 L : Type u_4 inst✝² : Field K inst✝¹ : Field L inst✝ : Algebra K L E1 E2 : IntermediateField K L ι : Type u_5 t : ι → IntermediateField K L p : ι → K[X] s : Finset ι h0 : ∏ i ∈ s, p i ≠ 0 F : IntermediateFie...
F✝ : Type u_1 inst✝⁵ : Field F✝ E : Type u_2 inst✝⁴ : Field E inst✝³ : Algebra F✝ E S : Set E α : E K : Type u_3 L : Type u_4 inst✝² : Field K inst✝¹ : Field L inst✝ : Algebra K L E1 E2 : IntermediateField K L ι : Type u_5 t : ι → IntermediateField K L p : ι → K[X] s : Finset ι h0 : ∏ i ∈ s, p i ≠ 0 F : IntermediateFie...
((:c And) ((:c Polynomial.Splits) (:fv _uniq.270440) ((:c Subtype) (:fv _uniq.270443) (:lambda x (:fv _uniq.270443) ((:c Membership.mem) (:fv _uniq.270443) ((:c IntermediateField) (:fv _uniq.270440) (:fv _uniq.270443) (:fv _uniq.270446) (:fv _uniq.270449) (:fv _uniq.270691)) ((:c SetLike.instMembership) ((:c Intermedia...
[{"name":"F✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c Field) (:fv _uniq.270181))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.270187))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.270181) (:fv _uniq.270187) ((:c Semifield.toCommSemiring) (:fv _uniq.2...
(:app (:c And) (:arg :explicit 0 (:app (:c Polynomial.Splits) (:arg :implicit-type 0 (:fv FV7)) (:arg :implicit-type 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV8)) (:arg :explicit 1 (:lambda x :explicit (:fv FV8) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV8)) (:arg :implicit-type 1 (:app (:c Interm...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.270181","is_instance":false,"is_let":false,"name":"F✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.270184","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c Field) (:arg :explic...
{"children":[{"source":"refine","sourceEnd":34817,"sourceStart":34811,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":34825,"sourceStart":34822,"tag":"atom"},{"children":[{"children":[{"name":"Polynomial.splits_prod","semanticRole":"global","source":"splits_prod","sourceEnd":34836,"sourceStart":34825,"tag":"identi...
[]
[{"source":"⟨splits_prod (algebraMap K F) fun i hi ↦\n splits_comp_of_splits (algebraMap K (t i)) (inclusion (hF i hi)).toRingHom\n (h i hi).1,\n ?_⟩","source_end":34983,"source_start":34822,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.270181","is_instance":false,"is_let":false,"user_name":"F✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.270184","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"int...
211
7
exact
true
1
22
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3f131096f38d7bf1046c03c8da803394cf275a5a86eeb892c41f502107cb2bfa
1871b4a52099517f3258f880e2319dcf1b715971e320e1c88995d103bdf093ca
e9de898c4ab58ca18123984011566304c7f36d1488f980adb7d6ec4cbe909269
f1b478009fce3f15a370ed95630a40043a53a1a8eb868da68558ef92a53ed2d1
cat-searcher/leandojo-benchmark-4-random
test
806
IntermediateField.isSplittingField_iSup
Mathlib/FieldTheory/Adjoin.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>Polynomial.rootSet_prod</a> p s h0, ← <a>Set.iSup_eq_iUnion</a>, (@<a>IntermediateField.gc</a> K _ L _ _).<a>GaloisConnection.l_iSup₂</a>]
F✝ : Type u_1 inst✝⁵ : Field F✝ E : Type u_2 inst✝⁴ : Field E inst✝³ : Algebra F✝ E S : Set E α : E K : Type u_3 L : Type u_4 inst✝² : Field K inst✝¹ : Field L inst✝ : Algebra K L E1 E2 : IntermediateField K L ι : Type u_5 t : ι → IntermediateField K L p : ι → K[X] s : Finset ι h0 : ∏ i ∈ s, p i ≠ 0 F : IntermediateFie...
F✝ : Type u_1 inst✝⁵ : Field F✝ E : Type u_2 inst✝⁴ : Field E inst✝³ : Algebra F✝ E S : Set E α : E K : Type u_3 L : Type u_4 inst✝² : Field K inst✝¹ : Field L inst✝ : Algebra K L E1 E2 : IntermediateField K L ι : Type u_5 t : ι → IntermediateField K L p : ι → K[X] s : Finset ι h0 : ∏ i ∈ s, p i ≠ 0 F : IntermediateFie...
((:c Eq) ((:c IntermediateField) (:fv _uniq.270440) (:fv _uniq.270443) (:fv _uniq.270446) (:fv _uniq.270449) (:fv _uniq.270691)) ((:c iSup) ((:c IntermediateField) (:fv _uniq.270440) (:fv _uniq.270443) (:fv _uniq.270446) (:fv _uniq.270449) (:fv _uniq.270691)) (:fv _uniq.270722) ((:c ConditionallyCompleteLattice.toSupSe...
[{"name":"F✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c Field) (:fv _uniq.270181))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.270187))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.270181) (:fv _uniq.270187) ((:c Semifield.toCommSemiring) (:fv _uniq.2...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c IntermediateField) (:arg :explicit 0 (:fv FV7)) (:arg :explicit 1 (:fv FV8)) (:arg :instance 2 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV7))))) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV8))))) (:arg :instance 4 (:instance-of (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.270181","is_instance":false,"is_let":false,"name":"F✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.270184","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c Field) (:arg :explic...
{"children":[{"source":"simp","sourceEnd":34990,"sourceStart":34986,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":34995,"sourceStart":34991,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":349...
[]
[{"source":"rootSet_prod p s h0","source_end":35016,"source_start":34997,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Set.iSup_eq_iUnion","source_end":35040,"source_start":35022,"syntax_kind":"ident"},{"source":"(@gc K _ L _ _).l_iSup₂","source_end":35067,"source_start":35042,"syntax_kind":"Lean.Parser.Term.proj"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.270181","is_instance":false,"is_let":false,"user_name":"F✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.270184","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"int...
211
8
exact
true
1
22
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3cd7e143b072c53c89761f42f12063767b211357e3b8a774054ed80cd09c3c79
f1b478009fce3f15a370ed95630a40043a53a1a8eb868da68558ef92a53ed2d1
801931bebfb513d0544d4db9fc3894312115a6bb5588426e3e2f3f9dd4486b6f
aff29f61f6d214019184064865f4573326db7e2d96ab9fe45e6481e3fa984bbc
cat-searcher/leandojo-benchmark-4-random
test
807
IntermediateField.isSplittingField_iSup
Mathlib/FieldTheory/Adjoin.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>iSup_congr</a> fun i ↦ <a>iSup_congr</a> fun hi ↦ (h i hi).2
F✝ : Type u_1 inst✝⁵ : Field F✝ E : Type u_2 inst✝⁴ : Field E inst✝³ : Algebra F✝ E S : Set E α : E K : Type u_3 L : Type u_4 inst✝² : Field K inst✝¹ : Field L inst✝ : Algebra K L E1 E2 : IntermediateField K L ι : Type u_5 t : ι → IntermediateField K L p : ι → K[X] s : Finset ι h0 : ∏ i ∈ s, p i ≠ 0 F : IntermediateFie...
((:c Eq) ((:c IntermediateField) (:fv _uniq.270440) (:fv _uniq.270443) (:fv _uniq.270446) (:fv _uniq.270449) (:fv _uniq.270691)) ((:c iSup) ((:c IntermediateField) (:fv _uniq.270440) (:fv _uniq.270443) (:fv _uniq.270446) (:fv _uniq.270449) (:fv _uniq.270691)) (:fv _uniq.270722) ((:c ConditionallyCompleteLattice.toSupSe...
[{"name":"F✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c Field) (:fv _uniq.270181))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.270187))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.270181) (:fv _uniq.270187) ((:c Semifield.toCommSemiring) (:fv _uniq.2...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c IntermediateField) (:arg :explicit 0 (:fv FV7)) (:arg :explicit 1 (:fv FV8)) (:arg :instance 2 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV7))))) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV8))))) (:arg :instance 4 (:instance-of (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.270181","is_instance":false,"is_let":false,"name":"F✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.270184","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c Field) (:arg :explic...
{"children":[{"source":"exact","sourceEnd":35076,"sourceStart":35071,"tag":"atom"},{"children":[{"name":"iSup_congr","semanticRole":"global","source":"iSup_congr","sourceEnd":35087,"sourceStart":35077,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":35091,"sourceStart":35088,"tag":"atom"},{"chi...
[]
[{"source":"iSup_congr fun i ↦ iSup_congr fun hi ↦ (h i hi).2","source_end":35130,"source_start":35077,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.270181","is_instance":false,"is_let":false,"user_name":"F✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.270184","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"int...
211
9
exact
true
1
22
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
38de2ef34f2ec3fa3587bbc08a4616da7bd44de7d1b0cf4d4fe11bea8d3fbf07
aff29f61f6d214019184064865f4573326db7e2d96ab9fe45e6481e3fa984bbc
f94a76888c0b74e2f5635ebcc3d63e0f2148ea23ab4c3129fa2a120154919d74
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
808
Real.sInf_le_sSup
Mathlib/Data/Real/Archimedean.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rcases s.eq_empty_or_nonempty with (rfl | hne)
s : Set ℝ h₁ : BddBelow s h₂ : BddAbove s ⊢ sInf s ≤ sSup s
((:c LE.le) (:c Real) (:c Real.instLE) ((:c InfSet.sInf) (:c Real) (:c Real.instInfSet) (:fv _uniq.35618)) ((:c SupSet.sSup) (:c Real) (:c Real.instSupSet) (:fv _uniq.35618)))
[{"name":"s","sexp":"((:c Set) (:c Real))"},{"name":"h₁","sexp":"((:c BddBelow) (:c Real) (:c Real.instPreorder) (:fv _uniq.35618))"},{"name":"h₂","sexp":"((:c BddAbove) (:c Real) (:c Real.instPreorder) (:fv _uniq.35618))"}]
(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c InfSet.sInf) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c InfSet) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV1)))) (:a...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35618","is_instance":false,"is_let":false,"name":"s","sexp":"(:app (:c Set) (:arg :explicit 0 (:c Real)))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35619","is_instance":false,"is_let":false,"name":"h₁","sexp":"(:app (:c Bdd...
{"children":[{"children":[{"children":[{"children":[{"source":"rcases","sourceEnd":13384,"sourceStart":13378,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.eq_empty_or_nonempty","semanticRole":"global","source":"s.eq_empty_or_nonempty","sourceEnd":13407,"sour...
[]
[{"source":"s.eq_empty_or_nonempty","source_end":13407,"source_start":13385,"syntax_kind":"ident"},{"source":"(rfl | hne)","source_end":13424,"source_start":13413,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"},{"source":"sInf_empty","source_end":13444,"source_start":13434,"syntax_kind":"ident"},{"source":"sSup_emp...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35618","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35619","is_instance":false,"is_let":false,"user_name":"h₁"},{"binder_role":":explicit","context_index":3,"internal_name":"_u...
73
2
branch_opener
false
1
3
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0a7e6d40f34bfe106abc539691c172eb0839cfe85745ee5c4040c41221aa698c
dc7497af282ef4767690ccaf84833631efc92d744fa73f9b1d101ede570ac13e
ab08a3ea6a095e2a0f53ad54bdb61525ddf8999cc94777065f6f77cd02f457eb
49c8f1b1c4f7188b1e0755e8a03754589e36dfd56e3e44f89de8a3e3a68cbac8
cat-searcher/leandojo-benchmark-4-random
test
809
Real.sInf_le_sSup
Mathlib/Data/Real/Archimedean.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Real.sInf_empty</a>, <a>Real.sSup_empty</a>]
case inl h₁ : BddBelow ∅ h₂ : BddAbove ∅ ⊢ sInf ∅ ≤ sSup ∅
((:c LE.le) (:c Real) (:c Real.instLE) ((:c InfSet.sInf) (:c Real) (:c Real.instInfSet) ((:c EmptyCollection.emptyCollection) ((:c Set) (:c Real)) ((:c Set.instEmptyCollection) (:c Real)))) ((:c SupSet.sSup) (:c Real) (:c Real.instSupSet) ((:c EmptyCollection.emptyCollection) ((:c Set) (:c Real)) ((:c Set.instEmptyColl...
[{"name":"h₁","sexp":"((:c BddBelow) (:c Real) (:c Real.instPreorder) ((:c EmptyCollection.emptyCollection) ((:c Set) (:c Real)) ((:c Set.instEmptyCollection) (:c Real))))"},{"name":"h₂","sexp":"((:c BddAbove) (:c Real) (:c Real.instPreorder) ((:c EmptyCollection.emptyCollection) ((:c Set) (:c Real)) ((:c Set.instEmpty...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c InfSet.sInf) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c InfSet) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c EmptyC...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35671","is_instance":false,"is_let":false,"name":"h₁","sexp":"(:app (:c BddBelow) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c EmptyCollection.emptyCo...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":13432,"sourceStart":13430,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13434,"sourceStart":13433,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",...
[]
[{"source":"sInf_empty","source_end":13444,"source_start":13434,"syntax_kind":"ident"},{"source":"sSup_empty","source_end":13456,"source_start":13446,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35671","is_instance":false,"is_let":false,"user_name":"h₁"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35672","is_instance":false,"is_let":false,"user_name":"h₂"}]
73
7
exact
true
1
2
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d3a837c0e9ad2ddef83a08e66b2c03383cfef67365b1c2530646dcf670b46f7e
e7c2958422bac8ab58ed53d95b7c95064ac9d351ba0f7f7af98381e644da87da
4ab95a92d98f787de5f616758fbd124a65acba55f7eeff973b50f7fa315f18ab
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
810
Real.sInf_le_sSup
Mathlib/Data/Real/Archimedean.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>csInf_le_csSup</a> h₁ h₂ hne
case inr s : Set ℝ h₁ : BddBelow s h₂ : BddAbove s hne : s.Nonempty ⊢ sInf s ≤ sSup s
((:c LE.le) (:c Real) (:c Real.instLE) ((:c InfSet.sInf) (:c Real) (:c Real.instInfSet) (:fv _uniq.35618)) ((:c SupSet.sSup) (:c Real) (:c Real.instSupSet) (:fv _uniq.35618)))
[{"name":"s","sexp":"((:c Set) (:c Real))"},{"name":"h₁","sexp":"((:c BddBelow) (:c Real) (:c Real.instPreorder) (:fv _uniq.35618))"},{"name":"h₂","sexp":"((:c BddAbove) (:c Real) (:c Real.instPreorder) (:fv _uniq.35618))"},{"name":"hne","sexp":"((:c Set.Nonempty) (:c Real) (:fv _uniq.35618))"}]
(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c InfSet.sInf) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c InfSet) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV1)))) (:a...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35618","is_instance":false,"is_let":false,"name":"s","sexp":"(:app (:c Set) (:arg :explicit 0 (:c Real)))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35619","is_instance":false,"is_let":false,"name":"h₁","sexp":"(:app (:c Bdd...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":13468,"sourceStart":13463,"tag":"atom"},{"children":[{"name":"csInf_le_csSup","semanticRole":"global","source":"csInf_le_csSup","sourceEnd":13483,"sourceStart":13469,"tag":"identifier"},{"children":[{"contextIndex":2,"semanticRole":"local...
[]
[{"source":"csInf_le_csSup h₁ h₂ hne","source_end":13497,"source_start":13469,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35618","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35619","is_instance":false,"is_let":false,"user_name":"h₁"},{"binder_role":":explicit","context_index":3,"internal_name":"_u...
73
15
exact
true
1
4
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7322940dfed69251d629dee75ff78eade854b24cb1adafc2d5957b335e961837
9a564561a1b90fbeddbac39212fa2a621869caeb65ac414f7096c14149e016cd
29f2df818e8ed2794ee4850eaae1d530951fb198c8cb963c622ee95117cd924e
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
811
LieModule.isCompl_weightSpace_zero_posFittingComp
Mathlib/Algebra/Lie/Weights/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
let P : <a>LieSubmodule</a> R L M → Prop := fun N ↦ <a>IsCompl</a> (<a>LieModule.weightSpace</a> N 0) (<a>LieModule.posFittingComp</a> R L N)
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M ⊢ IsCompl (weightSpace M...
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
((:c IsCompl) ((:c LieSubmodule) (:fv _uniq.653128) (:fv _uniq.653131) (:fv _uniq.653134) (:fv _uniq.653137) (:fv _uniq.653140) (:fv _uniq.653185) (:fv _uniq.653797) (:fv _uniq.653811)) ((:c OmegaCompletePartialOrder.toPartialOrder) ((:c LieSubmodule) (:fv _uniq.653128) (:fv _uniq.653131) (:fv _uniq.653134) (:fv _uniq....
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.653128))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.653131))"},{"name":"inst✝⁷","sexp":"((:c LieAlg...
(:app (:c IsCompl) (:arg :implicit-type 0 (:app (:c LieSubmodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv FV2))))) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","c...
{"children":[{"source":"let","sourceEnd":28248,"sourceStart":28245,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"P","sourceEnd":28250,"sourceStart":28249,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":2825...
[]
[{"source":"LieSubmodule R L M → Prop","source_end":28280,"source_start":28253,"syntax_kind":"Lean.Parser.Term.arrow"},{"source":"fun N ↦ IsCompl (weightSpace N 0) (posFittingComp R L N)","source_end":28342,"source_start":28284,"syntax_kind":"Lean.Parser.Term.fun"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":2,"internal_name":"_...
89
4
exact
true
1
14
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8421b625e65cd37eb9145fcc4ad602ec9f2a0719f74c3df0ec1611648f2469c3
0304eb4696e1a8a77ec020d7a4bceadc37b55583d56395c42c12009ccc572079
1e13add97c3f8bd41714198b08bc5d19fea10321a78ba6f3a3c62e9a6fc9b3f0
45cf46804ff5b50fc780789fe1aaddb2b102013f86b56077030ca6ef560634ba
cat-searcher/leandojo-benchmark-4-random
test
812
LieModule.isCompl_weightSpace_zero_posFittingComp
Mathlib/Algebra/Lie/Weights/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
suffices P ⊤ by let e := <a>LieModuleEquiv.ofTop</a> R L M rw [← <a>LieModule.map_weightSpace_eq</a> e, ← <a>LieModule.map_posFittingComp_eq</a> e] exact (<a>LieSubmodule.orderIsoMapComap</a> e).isCompl_iff.mp this
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
((:c IsCompl) ((:c LieSubmodule) (:fv _uniq.653128) (:fv _uniq.653131) (:fv _uniq.653134) (:fv _uniq.653137) (:fv _uniq.653140) (:fv _uniq.653185) (:fv _uniq.653797) (:fv _uniq.653811)) ((:c OmegaCompletePartialOrder.toPartialOrder) ((:c LieSubmodule) (:fv _uniq.653128) (:fv _uniq.653131) (:fv _uniq.653134) (:fv _uniq....
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.653128))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.653131))"},{"name":"inst✝⁷","sexp":"((:c LieAlg...
(:app (:c IsCompl) (:arg :implicit-type 0 (:app (:c LieSubmodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv FV2))))) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","c...
{"children":[{"source":"suffices","sourceEnd":28353,"sourceStart":28345,"tag":"atom"},{"children":[{"children":[{"source":"","sourceEnd":28354,"sourceStart":28354,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":28354,"sourceStart":28354,"tag":"node"},{"children":[{"contextIndex":15,"semanticRole":"loc...
[]
[{"source":"P ⊤","source_end":28359,"source_start":28354,"syntax_kind":"Lean.Parser.Term.app"},{"source":"LieModuleEquiv.ofTop R L M","source_end":28402,"source_start":28376,"syntax_kind":"Lean.Parser.Term.app"},{"source":"map_weightSpace_eq e","source_end":28435,"source_start":28415,"syntax_kind":"Lean.Parser.Term.app...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":2,"internal_name":"_...
89
5
exact
true
1
15
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5812c11af1be2ab2be2a7a9997906fdc2588da10e21225436153f9931ecd6891
45cf46804ff5b50fc780789fe1aaddb2b102013f86b56077030ca6ef560634ba
5f1c48134544e59e26f255c4e44d958f6459db035e2efa74c359ce24ec8d19b1
c7fa20bcedca617164bb236ca3a33a774369bcee55651533cff51199f1de29a6
cat-searcher/leandojo-benchmark-4-random
test
813
LieModule.isCompl_weightSpace_zero_posFittingComp
Mathlib/Algebra/Lie/Weights/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine (<a>LieSubmodule.wellFounded_of_isArtinian</a> R L M).<a>WellFounded.induction</a> (C := P) _ fun N hN ↦ ?_
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
((:fv _uniq.657725) ((:c Top.top) ((:c LieSubmodule) (:fv _uniq.653128) (:fv _uniq.653131) (:fv _uniq.653134) (:fv _uniq.653137) (:fv _uniq.653140) (:fv _uniq.653185) (:fv _uniq.653797) (:fv _uniq.653811)) ((:c LieSubmodule.instTop) (:fv _uniq.653128) (:fv _uniq.653131) (:fv _uniq.653134) (:fv _uniq.653137) (:fv _uniq....
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.653128))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.653131))"},{"name":"inst✝⁷","sexp":"((:c LieAlg...
(:app (:fv FV15) (:arg :explicit 0 (:app (:c Top.top) (:arg :implicit-type 0 (:app (:c LieSubmodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:app (:c LieRin...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","c...
{"children":[{"source":"refine","sourceEnd":28538,"sourceStart":28532,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":28540,"sourceStart":28539,"tag":"atom"},{"children":[{"name":"LieSubmodule.wellFounded_of_isArtinian","semanticRole":"global","source":"LieSubmodule.wellFounded_of_isArtin...
[]
[{"source":"(LieSubmodule.wellFounded_of_isArtinian R L M).induction (C := P) _ fun N hN ↦ ?_","source_end":28622,"source_start":28539,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":2,"internal_name":"_...
89
14
exact
true
1
15
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
09ac7ebab7e20d0358a0e0302a1987abcf40bb96ca1067d12a5c816268c8d586
c7fa20bcedca617164bb236ca3a33a774369bcee55651533cff51199f1de29a6
777b15d8b9b44d48288df2c806afd1f1d64714e0e953fd1585ff82e1bcda5353
fdd43faeb387c71bf8714724d410d8cd25f85e9adad88ff782bfb3adda5b5503
cat-searcher/leandojo-benchmark-4-random
test
814
LieModule.isCompl_weightSpace_zero_posFittingComp
Mathlib/Algebra/Lie/Weights/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine <a>_private.Mathlib.Algebra.Lie.Weights.Basic.0.LieModule.isCompl_weightSpace_zero_posFittingComp_aux</a> R L N fun N' hN' ↦ ?_
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
((:fv _uniq.657725) (:fv _uniq.658627))
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.653128))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.653131))"},{"name":"inst✝⁷","sexp":"((:c LieAlg...
(:app (:fv FV15) (:arg :explicit 0 (:fv FV16)))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","c...
{"children":[{"source":"refine","sourceEnd":28631,"sourceStart":28625,"tag":"atom"},{"children":[{"name":"_private.Mathlib.Algebra.Lie.Weights.Basic.0.LieModule.isCompl_weightSpace_zero_posFittingComp_aux","semanticRole":"global","source":"isCompl_weightSpace_zero_posFittingComp_aux","sourceEnd":28675,"sourceStart":286...
[]
[{"source":"isCompl_weightSpace_zero_posFittingComp_aux R L N fun N' hN' ↦ ?_","source_end":28699,"source_start":28632,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":2,"internal_name":"_...
89
15
exact
true
1
17
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0093646d048d548fc0aa4abfc511e1e0fee20c9e976fb9596449c558839216f8
fdd43faeb387c71bf8714724d410d8cd25f85e9adad88ff782bfb3adda5b5503
3da29f780552ee4aaa880c476740b05599f90155b8d065e91126f1c739ddef3a
75e2acf31de0e1557574fba7f2c7ed9dcc227ce506125af930a0707ad5db86f1
cat-searcher/leandojo-benchmark-4-random
test
815
LieModule.isCompl_weightSpace_zero_posFittingComp
Mathlib/Algebra/Lie/Weights/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
suffices <a>IsCompl</a> (<a>LieModule.weightSpace</a> (N'.map N.incl) 0) (<a>LieModule.posFittingComp</a> R L (N'.map N.incl)) by let e := <a>LieSubmodule.equivMapOfInjective</a> N' N.injective_incl rw [← <a>LieModule.map_weightSpace_eq</a> e, ← <a>LieModule.map_posFittingComp_eq</a> e] at this exact (<a>LieSubmodule.o...
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
((:c IsCompl) ((:c LieSubmodule) (:fv _uniq.653128) (:fv _uniq.653131) ((:c Subtype) ((:c Subtype) (:fv _uniq.653134) (:lambda x (:fv _uniq.653134) ((:c Membership.mem) (:fv _uniq.653134) ((:c Submodule) (:fv _uniq.653128) (:fv _uniq.653134) ((:c CommSemiring.toSemiring) (:fv _uniq.653128) ((:c CommRing.toCommSemiring)...
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.653128))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.653131))"},{"name":"inst✝⁷","sexp":"((:c LieAlg...
(:app (:c IsCompl) (:arg :implicit-type 0 (:app (:c LieSubmodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explicit (:fv FV3) (:app (:c Membership.mem) (:arg :i...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","c...
{"children":[{"source":"suffices","sourceEnd":28710,"sourceStart":28702,"tag":"atom"},{"children":[{"children":[{"source":"","sourceEnd":28711,"sourceStart":28711,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":28711,"sourceStart":28711,"tag":"node"},{"children":[{"name":"IsCompl","semanticRole":"glob...
[]
[{"source":"IsCompl (weightSpace (N'.map N.incl) 0) (posFittingComp R L (N'.map N.incl))","source_end":28787,"source_start":28711,"syntax_kind":"Lean.Parser.Term.app"},{"source":"LieSubmodule.equivMapOfInjective N' N.injective_incl","source_end":28856,"source_start":28804,"syntax_kind":"Lean.Parser.Term.app"},{"source"...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":2,"internal_name":"_...
89
16
exact
true
1
19
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f5a5d1e9795f1cebc18c8a124e2b4b64dc07c6c6201b306be6d3c0c8eb7fb51e
75e2acf31de0e1557574fba7f2c7ed9dcc227ce506125af930a0707ad5db86f1
ddddbd7600781ad524890119f16eb2996f0247bf0049c3352ef7cf2542cf7b32
1e27f5dbc8bf8fc94485b3c58ba9398ab1de0d10ca304e6682ecca3f928cab05
cat-searcher/leandojo-benchmark-4-random
test
816
LieModule.isCompl_weightSpace_zero_posFittingComp
Mathlib/Algebra/Lie/Weights/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact hN _ (LieSubmodule.map_incl_lt_iff_lt_top.mpr hN')
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
((:c IsCompl) ((:c LieSubmodule) (:fv _uniq.653128) (:fv _uniq.653131) ((:c Subtype) (:fv _uniq.653134) (:lambda x (:fv _uniq.653134) ((:c Membership.mem) (:fv _uniq.653134) ((:c Submodule) (:fv _uniq.653128) (:fv _uniq.653134) ((:c CommSemiring.toSemiring) (:fv _uniq.653128) ((:c CommRing.toCommSemiring) (:fv _uniq.65...
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.653128))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.653131))"},{"name":"inst✝⁷","sexp":"((:c LieAlg...
(:app (:c IsCompl) (:arg :implicit-type 0 (:app (:c LieSubmodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explicit (:fv FV3) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","c...
{"children":[{"source":"exact","sourceEnd":29000,"sourceStart":28995,"tag":"atom"},{"children":[{"contextIndex":17,"semanticRole":"local","source":"hN","sourceEnd":29003,"sourceStart":29001,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":29005,"sourceStart":29004,"tag":"atom"}],"kind":"Lean.Pars...
[]
[{"source":"hN _ (LieSubmodule.map_incl_lt_iff_lt_top.mpr hN')","source_end":29051,"source_start":29001,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":2,"internal_name":"_...
89
25
exact
true
1
19
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
95c5754198927815d0a5cbb8b48b72820734cf39ef952ae06598413eef6e272d
1e27f5dbc8bf8fc94485b3c58ba9398ab1de0d10ca304e6682ecca3f928cab05
ea558053c1a69931b526c5b95055bb4d557ee7ad48000e7872d7ba26a67db41e
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
817
LieModule.isCompl_weightSpace_zero_posFittingComp
Mathlib/Algebra/Lie/Weights/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
let e := <a>LieModuleEquiv.ofTop</a> R L M
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
((:c IsCompl) ((:c LieSubmodule) (:fv _uniq.653128) (:fv _uniq.653131) (:fv _uniq.653134) (:fv _uniq.653137) (:fv _uniq.653140) (:fv _uniq.653185) (:fv _uniq.653797) (:fv _uniq.653811)) ((:c OmegaCompletePartialOrder.toPartialOrder) ((:c LieSubmodule) (:fv _uniq.653128) (:fv _uniq.653131) (:fv _uniq.653134) (:fv _uniq....
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.653128))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.653131))"},{"name":"inst✝⁷","sexp":"((:c LieAlg...
(:app (:c IsCompl) (:arg :implicit-type 0 (:app (:c LieSubmodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv FV2))))) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","c...
{"children":[{"source":"let","sourceEnd":28370,"sourceStart":28367,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"e","sourceEnd":28372,"sourceStart":28371,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{...
[]
[{"source":"LieModuleEquiv.ofTop R L M","source_end":28402,"source_start":28376,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":2,"internal_name":"_...
89
8
exact
true
1
16
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
71c6c09e6d624a2b7fede947ac9f116a7f2ff5045396cb2bdfde37aeb96e5bc1
56b614ec8ae6fb03d40fbb91e72f43f335062aa1b3c0e13d88837439311fbe53
15ea532c6d322995430d9d80058f86efc70a95e14cc5dc5f348ff72fdc9fdaa7
35f7ea17deaab338843e37cef95abf3ce018f75e454c34b7b450873f2fa11ade
cat-searcher/leandojo-benchmark-4-random
test
818
LieModule.isCompl_weightSpace_zero_posFittingComp
Mathlib/Algebra/Lie/Weights/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>LieModule.map_weightSpace_eq</a> e, ← <a>LieModule.map_posFittingComp_eq</a> e]
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
((:c IsCompl) ((:c LieSubmodule) (:fv _uniq.653128) (:fv _uniq.653131) (:fv _uniq.653134) (:fv _uniq.653137) (:fv _uniq.653140) (:fv _uniq.653185) (:fv _uniq.653797) (:fv _uniq.653811)) ((:c OmegaCompletePartialOrder.toPartialOrder) ((:c LieSubmodule) (:fv _uniq.653128) (:fv _uniq.653131) (:fv _uniq.653134) (:fv _uniq....
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.653128))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.653131))"},{"name":"inst✝⁷","sexp":"((:c LieAlg...
(:app (:c IsCompl) (:arg :implicit-type 0 (:app (:c LieSubmodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv FV2))))) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","c...
{"children":[{"source":"rw","sourceEnd":28409,"sourceStart":28407,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28411,"sourceStart":28410,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":28414,"sourceSt...
[]
[{"source":"map_weightSpace_eq e","source_end":28435,"source_start":28415,"syntax_kind":"Lean.Parser.Term.app"},{"source":"map_posFittingComp_eq e","source_end":28464,"source_start":28441,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":2,"internal_name":"_...
89
9
exact
true
1
17
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
bf456f6f9785073decd7ffc9ab62c3126ee738a5c3cab23c24f313b10163f48f
35f7ea17deaab338843e37cef95abf3ce018f75e454c34b7b450873f2fa11ade
0f659ef81d50d50cb6410e79e27bec921bfbbdab22f13bef84a5bce2b2c6eb9c
ab6baafe6a0fec263e666bd5fb907bdacbd92a82a3c4b6cee38f2c52eac50fca
cat-searcher/leandojo-benchmark-4-random
test
819
LieModule.isCompl_weightSpace_zero_posFittingComp
Mathlib/Algebra/Lie/Weights/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact (<a>LieSubmodule.orderIsoMapComap</a> e).isCompl_iff.mp this
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
((:c IsCompl) ((:c LieSubmodule) (:fv _uniq.653128) (:fv _uniq.653131) (:fv _uniq.653134) (:fv _uniq.653137) (:fv _uniq.653140) (:fv _uniq.653185) (:fv _uniq.653797) (:fv _uniq.653811)) ((:c OmegaCompletePartialOrder.toPartialOrder) ((:c LieSubmodule) (:fv _uniq.653128) (:fv _uniq.653131) (:fv _uniq.653134) (:fv _uniq....
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.653128))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.653131))"},{"name":"inst✝⁷","sexp":"((:c LieAlg...
(:app (:c IsCompl) (:arg :implicit-type 0 (:app (:c LieSubmodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv FV2))))) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","c...
{"children":[{"source":"exact","sourceEnd":28475,"sourceStart":28470,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":28477,"sourceStart":28476,"tag":"atom"},{"children":[{"name":"LieSubmodule.orderIsoMapComap","semanticRole":"global","source":"LieSubmodule.orderIsoMapComap","sourceEnd":28...
[]
[{"source":"(LieSubmodule.orderIsoMapComap e).isCompl_iff.mp this","source_end":28529,"source_start":28476,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":2,"internal_name":"_...
89
13
exact
true
1
17
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4657dcf27429c3d53509e1f882eb22bd8d54b3cea4c029f709c60ffe8d0909a7
ab6baafe6a0fec263e666bd5fb907bdacbd92a82a3c4b6cee38f2c52eac50fca
21ec02fefc6a9a35d52fc879582eb7dde82e1ff3bc0875d5fbfeaa81275a764b
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
820
LieModule.isCompl_weightSpace_zero_posFittingComp
Mathlib/Algebra/Lie/Weights/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
let e := <a>LieSubmodule.equivMapOfInjective</a> N' N.injective_incl
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
((:c IsCompl) ((:c LieSubmodule) (:fv _uniq.653128) (:fv _uniq.653131) ((:c Subtype) ((:c Subtype) (:fv _uniq.653134) (:lambda x (:fv _uniq.653134) ((:c Membership.mem) (:fv _uniq.653134) ((:c Submodule) (:fv _uniq.653128) (:fv _uniq.653134) ((:c CommSemiring.toSemiring) (:fv _uniq.653128) ((:c CommRing.toCommSemiring)...
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.653128))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.653131))"},{"name":"inst✝⁷","sexp":"((:c LieAlg...
(:app (:c IsCompl) (:arg :implicit-type 0 (:app (:c LieSubmodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explicit (:fv FV3) (:app (:c Membership.mem) (:arg :i...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","c...
{"children":[{"source":"let","sourceEnd":28798,"sourceStart":28795,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"e","sourceEnd":28800,"sourceStart":28799,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{...
[]
[{"source":"LieSubmodule.equivMapOfInjective N' N.injective_incl","source_end":28856,"source_start":28804,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":2,"internal_name":"_...
89
19
exact
true
1
20
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7ba46ab244e100cf431362fc029e8b8b0b68036f218970efc1e4caf31c6c4b57
60de5b0a29b5eceec70831738542917be8e2c3566e1e05cdab83f46d62131e0d
0ca3e259b289c30feef86c87ad97f69f5b6b4b47936e1546076d9fbb42405a02
2828c0188a06505e75d241fce081fd98ed34da4535a7cc0bea942c00ef357606
cat-searcher/leandojo-benchmark-4-random
test
821
LieModule.isCompl_weightSpace_zero_posFittingComp
Mathlib/Algebra/Lie/Weights/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>LieModule.map_weightSpace_eq</a> e, ← <a>LieModule.map_posFittingComp_eq</a> e] at this
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
((:c IsCompl) ((:c LieSubmodule) (:fv _uniq.653128) (:fv _uniq.653131) ((:c Subtype) ((:c Subtype) (:fv _uniq.653134) (:lambda x (:fv _uniq.653134) ((:c Membership.mem) (:fv _uniq.653134) ((:c Submodule) (:fv _uniq.653128) (:fv _uniq.653134) ((:c CommSemiring.toSemiring) (:fv _uniq.653128) ((:c CommRing.toCommSemiring)...
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.653128))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.653131))"},{"name":"inst✝⁷","sexp":"((:c LieAlg...
(:app (:c IsCompl) (:arg :implicit-type 0 (:app (:c LieSubmodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explicit (:fv FV3) (:app (:c Membership.mem) (:arg :i...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","c...
{"children":[{"source":"rw","sourceEnd":28863,"sourceStart":28861,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28865,"sourceStart":28864,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":28868,"sourceSt...
[]
[{"source":"this","source_end":28927,"source_start":28923,"syntax_kind":"ident"},{"source":"map_weightSpace_eq e","source_end":28889,"source_start":28869,"syntax_kind":"Lean.Parser.Term.app"},{"source":"map_posFittingComp_eq e","source_end":28918,"source_start":28895,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":2,"internal_name":"_...
89
20
exact
true
1
21
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e3cdf8a1cc072c317ddefef98a426773023e35594b1c129ccc08815d6845f18c
2828c0188a06505e75d241fce081fd98ed34da4535a7cc0bea942c00ef357606
6964fff87d43af6acaa7f37c94e2cdf3e9d78d604fea5f32583f3590a3cb02cf
685cb743090368546d7f912bab1c17c79e6823ffcb183b3551d057bc67fa136f
cat-searcher/leandojo-benchmark-4-random
test
822
LieModule.isCompl_weightSpace_zero_posFittingComp
Mathlib/Algebra/Lie/Weights/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact (<a>LieSubmodule.orderIsoMapComap</a> e).isCompl_iff.mpr this
K : Type u_1 R : Type u_2 L : Type u_3 M : Type u_4 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : LieAlgebra.IsNilpotent R L inst✝⁵ : AddCommGroup M inst✝⁴ : Module R M inst✝³ : LieRingModule L M inst✝² : LieModule R L M inst✝¹ : IsNoetherian R M inst✝ : IsArtinian R M P : LieSubmodule R L M →...
((:c IsCompl) ((:c LieSubmodule) (:fv _uniq.653128) (:fv _uniq.653131) ((:c Subtype) ((:c Subtype) (:fv _uniq.653134) (:lambda x (:fv _uniq.653134) ((:c Membership.mem) (:fv _uniq.653134) ((:c Submodule) (:fv _uniq.653128) (:fv _uniq.653134) ((:c CommSemiring.toSemiring) (:fv _uniq.653128) ((:c CommRing.toCommSemiring)...
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.653128))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.653131))"},{"name":"inst✝⁷","sexp":"((:c LieAlg...
(:app (:c IsCompl) (:arg :implicit-type 0 (:app (:c LieSubmodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explicit (:fv FV3) (:app (:c Membership.mem) (:arg :i...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","c...
{"children":[{"source":"exact","sourceEnd":28937,"sourceStart":28932,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":28939,"sourceStart":28938,"tag":"atom"},{"children":[{"name":"LieSubmodule.orderIsoMapComap","semanticRole":"global","source":"LieSubmodule.orderIsoMapComap","sourceEnd":28...
[]
[{"source":"(LieSubmodule.orderIsoMapComap e).isCompl_iff.mpr this","source_end":28992,"source_start":28938,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.653125","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.653128","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":2,"internal_name":"_...
89
24
exact
true
1
21
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
6a6f852096682fd05617f881688fc3f87ce0dfb07cb2c787384d1959ba31f9f8
685cb743090368546d7f912bab1c17c79e6823ffcb183b3551d057bc67fa136f
6b7f0c20f5dfdb697580aa8759034c102ec1b29f0a7d5c3ac51318091ee77a98
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
823
Fintype.mem_piFinset
Mathlib/Data/Fintype/Pi.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
constructor
α : Type u_1 inst✝¹ : DecidableEq α inst✝ : Fintype α γ : α → Type u_2 δ : α → Type u_3 s : (a : α) → Finset (γ a) t : (a : α) → Finset (δ a) f : (a : α) → δ a ⊢ f ∈ piFinset t ↔ ∀ (a : α), f a ∈ t a
case mp α : Type u_1 inst✝¹ : DecidableEq α inst✝ : Fintype α γ : α → Type u_2 δ : α → Type u_3 s : (a : α) → Finset (γ a) t : (a : α) → Finset (δ a) f : (a : α) → δ a ⊢ f ∈ piFinset t → ∀ (a : α), f a ∈ t a case mpr α : Type u_1 inst✝¹ : DecidableEq α inst✝ : Fintype α γ : α → Type u_2 δ : α → Type u_3 s : (a : α) → F...
((:c Iff) ((:c Membership.mem) (:forall a (:fv _uniq.1330) ((:fv _uniq.1352) 0)) ((:c Finset) (:forall a (:fv _uniq.1330) ((:fv _uniq.1352) 0))) ((:c Finset.instMembership) (:forall a (:fv _uniq.1330) ((:fv _uniq.1352) 0))) (:fv _uniq.1551) ((:c Fintype.piFinset) (:fv _uniq.1330) (:fv _uniq.1337) (:fv _uniq.1342) (:fv ...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.1330))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.1330))"},{"name":"γ","sexp":"(:forall _ (:fv _uniq.1330) (:sort (+ u_2 1)))"},{"name":"δ","sexp":"(:forall _ (:fv _uniq.1330) (:sort (+ u_3 1)))"},{"name":"s","sexp":"...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:forall a :explicit (:fv FV0) (:app (:fv FV4) (:arg :explicit 0 0)))) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:forall a :explicit (:fv FV0) (:app (:fv FV4) (:arg :explicit 0 0)))))) (:arg :instance 2 (:instance-of (:a...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1330","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1337","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c DecidableEq) (:arg :expli...
{"children":[{"source":"constructor","sourceEnd":1252,"sourceStart":1241,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":1252,"sourceStart":1241,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1330","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1337","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":2,...
8
4
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
6b9c1d5b604a921f5a0da1e776336f84d87224c227c184ab1d15fa60c3a85d9d
be104fb4fa129257d5f913a64a0e71e385dce586307e9539957d63582575489f
e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068
245a6014f8201c30f32aafd9919de0d84ac439e56ad5da661af11328915df1bb
cat-searcher/leandojo-benchmark-4-random
test
824
Fintype.mem_piFinset
Mathlib/Data/Fintype/Pi.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>Fintype.piFinset</a>, <a>Finset.mem_map</a>, <a>and_imp</a>, <a>forall_prop_of_true</a>, <a>exists_prop</a>, <a>Finset.mem_univ</a>, <a>exists_imp</a>, <a>Finset.mem_pi</a>]
case mp α : Type u_1 inst✝¹ : DecidableEq α inst✝ : Fintype α γ : α → Type u_2 δ : α → Type u_3 s : (a : α) → Finset (γ a) t : (a : α) → Finset (δ a) f : (a : α) → δ a ⊢ f ∈ piFinset t → ∀ (a : α), f a ∈ t a
case mp α : Type u_1 inst✝¹ : DecidableEq α inst✝ : Fintype α γ : α → Type u_2 δ : α → Type u_3 s : (a : α) → Finset (γ a) t : (a : α) → Finset (δ a) f : (a : α) → δ a ⊢ ∀ (x : (a : α) → a ∈ univ → δ a), (∀ (a : α), x a ⋯ ∈ t a) → { toFun := fun f a => f a ⋯, inj' := ⋯ } x = f → ∀ (a : α), f a ∈ t a
(:forall _ ((:c Membership.mem) (:forall a (:fv _uniq.1330) ((:fv _uniq.1352) 0)) ((:c Finset) (:forall a (:fv _uniq.1330) ((:fv _uniq.1352) 0))) ((:c Finset.instMembership) (:forall a (:fv _uniq.1330) ((:fv _uniq.1352) 0))) (:fv _uniq.1551) ((:c Fintype.piFinset) (:fv _uniq.1330) (:fv _uniq.1337) (:fv _uniq.1342) (:fv...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.1330))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.1330))"},{"name":"γ","sexp":"(:forall _ (:fv _uniq.1330) (:sort (+ u_2 1)))"},{"name":"δ","sexp":"(:forall _ (:fv _uniq.1330) (:sort (+ u_3 1)))"},{"name":"s","sexp":"...
(:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:forall a :explicit (:fv FV0) (:app (:fv FV4) (:arg :explicit 0 0)))) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:forall a :explicit (:fv FV0) (:app (:fv FV4) (:arg :explicit 0 0)))))) (:arg :instance 2 (:instance-of (:app (:c Membe...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1330","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1337","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c DecidableEq) (:arg :expli...
{"children":[{"source":"simp","sourceEnd":1262,"sourceStart":1258,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":1267,"sourceStart":1263,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":1267,"s...
[]
[{"source":"piFinset","source_end":1277,"source_start":1269,"syntax_kind":"ident"},{"source":"mem_map","source_end":1286,"source_start":1279,"syntax_kind":"ident"},{"source":"and_imp","source_end":1295,"source_start":1288,"syntax_kind":"ident"},{"source":"forall_prop_of_true","source_end":1316,"source_start":1297,"synt...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1330","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1337","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":2,...
8
9
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
39700ec5fa376be6fb5656b7934975b1e3db728a0a48215341e1d039c05d3701
63089bd1db188fbeae40d642aa72b8049e4b5901a217136954e0d286ecfbf74c
470e88f4a9fd400db8c578252897edcb0336c03568065c8340224247e4942e4a
b0ff6697633da9854c6f4f6bda80e2e9cd4e2366a5fda624ab218d5cc098a880
cat-searcher/leandojo-benchmark-4-random
test
825
Fintype.mem_piFinset
Mathlib/Data/Fintype/Pi.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro g hg hgf a
case mp α : Type u_1 inst✝¹ : DecidableEq α inst✝ : Fintype α γ : α → Type u_2 δ : α → Type u_3 s : (a : α) → Finset (γ a) t : (a : α) → Finset (δ a) f : (a : α) → δ a ⊢ ∀ (x : (a : α) → a ∈ univ → δ a), (∀ (a : α), x a ⋯ ∈ t a) → { toFun := fun f a => f a ⋯, inj' := ⋯ } x = f → ∀ (a : α), f a ∈ t a
case mp α : Type u_1 inst✝¹ : DecidableEq α inst✝ : Fintype α γ : α → Type u_2 δ : α → Type u_3 s : (a : α) → Finset (γ a) t : (a : α) → Finset (δ a) f : (a : α) → δ a g : (a : α) → a ∈ univ → δ a hg : ∀ (a : α), g a ⋯ ∈ t a hgf : { toFun := fun f a => f a ⋯, inj' := ⋯ } g = f a : α ⊢ f a ∈ t a
(:forall x (:forall a (:fv _uniq.1330) (:forall _ ((:c Membership.mem) (:fv _uniq.1330) ((:c Finset) (:fv _uniq.1330)) ((:c Finset.instMembership) (:fv _uniq.1330)) 0 ((:c Finset.univ) (:fv _uniq.1330) (:fv _uniq.1342))) ((:fv _uniq.1352) 1))) (:forall _ (:forall a (:fv _uniq.1330) ((:c Membership.mem) ((:fv _uniq.1352...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.1330))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.1330))"},{"name":"γ","sexp":"(:forall _ (:fv _uniq.1330) (:sort (+ u_2 1)))"},{"name":"δ","sexp":"(:forall _ (:fv _uniq.1330) (:sort (+ u_3 1)))"},{"name":"s","sexp":"...
(:forall x :explicit (:forall a :explicit (:fv FV0) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Fins...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1330","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1337","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c DecidableEq) (:arg :expli...
{"children":[{"source":"rintro","sourceEnd":1377,"sourceStart":1371,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"g","sourceEnd":1379,"sourceStart":1378,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"g","sourceEnd":1379,"sourceStart":1378,"tag":"...
[{"role":"fresh_name","source":"g","source_end":1379,"source_start":1378,"syntax_kind":"ident"},{"role":"fresh_name","source":"hg","source_end":1382,"source_start":1380,"syntax_kind":"ident"},{"role":"fresh_name","source":"hgf","source_end":1386,"source_start":1383,"syntax_kind":"ident"},{"role":"fresh_name","source":"...
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1330","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1337","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":2,...
8
10
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5e22ad0af7abbe236bfe615ed1683d449d10fad0458f4ff5663606ca78e0d435
b0ff6697633da9854c6f4f6bda80e2e9cd4e2366a5fda624ab218d5cc098a880
fb6e2412dbb1fbd5cd2e411cef3fc5f0140ba68e6629214ed098da440b63fdeb
e54aafcd06af3b56355caea270331ea6ff3ce4851c3eab59870a0dd0df68cec9
cat-searcher/leandojo-benchmark-4-random
test
826
Fintype.mem_piFinset
Mathlib/Data/Fintype/Pi.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← hgf]
case mp α : Type u_1 inst✝¹ : DecidableEq α inst✝ : Fintype α γ : α → Type u_2 δ : α → Type u_3 s : (a : α) → Finset (γ a) t : (a : α) → Finset (δ a) f : (a : α) → δ a g : (a : α) → a ∈ univ → δ a hg : ∀ (a : α), g a ⋯ ∈ t a hgf : { toFun := fun f a => f a ⋯, inj' := ⋯ } g = f a : α ⊢ f a ∈ t a
case mp α : Type u_1 inst✝¹ : DecidableEq α inst✝ : Fintype α γ : α → Type u_2 δ : α → Type u_3 s : (a : α) → Finset (γ a) t : (a : α) → Finset (δ a) f : (a : α) → δ a g : (a : α) → a ∈ univ → δ a hg : ∀ (a : α), g a ⋯ ∈ t a hgf : { toFun := fun f a => f a ⋯, inj' := ⋯ } g = f a : α ⊢ { toFun := fun f a => f a ⋯, inj' ...
((:c Membership.mem) ((:fv _uniq.1352) (:fv _uniq.2478)) ((:c Finset) ((:fv _uniq.1352) (:fv _uniq.2478))) ((:c Finset.instMembership) ((:fv _uniq.1352) (:fv _uniq.2478))) ((:fv _uniq.1551) (:fv _uniq.2478)) ((:fv _uniq.1550) (:fv _uniq.2478)))
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.1330))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.1330))"},{"name":"γ","sexp":"(:forall _ (:fv _uniq.1330) (:sort (+ u_2 1)))"},{"name":"δ","sexp":"(:forall _ (:fv _uniq.1330) (:sort (+ u_3 1)))"},{"name":"s","sexp":"...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:fv FV4) (:arg :explicit 0 (:fv FV12)))) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:app (:fv FV4) (:arg :explicit 0 (:fv FV12)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:fv FV4) (:arg :explicit 0 (:fv FV1...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1330","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1337","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c DecidableEq) (:arg :expli...
{"children":[{"source":"rw","sourceEnd":1395,"sourceStart":1393,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1397,"sourceStart":1396,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":1400,"sourceStart":...
[]
[{"source":"hgf","source_end":1404,"source_start":1401,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1330","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1337","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":2,...
8
11
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b84eb4abc05453d07160b84832243500b10152f81e0295022718aa2019fda10a
e54aafcd06af3b56355caea270331ea6ff3ce4851c3eab59870a0dd0df68cec9
1bb67ec9c419b884edff9a72b61943c6a3497bf8c4bb304b372cfc09887e2b43
028bfb4682742d01a739fd85d517c613465208bd6f1c7742b5a839537cee503d
cat-searcher/leandojo-benchmark-4-random
test
827
Fintype.mem_piFinset
Mathlib/Data/Fintype/Pi.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact hg a
case mp α : Type u_1 inst✝¹ : DecidableEq α inst✝ : Fintype α γ : α → Type u_2 δ : α → Type u_3 s : (a : α) → Finset (γ a) t : (a : α) → Finset (δ a) f : (a : α) → δ a g : (a : α) → a ∈ univ → δ a hg : ∀ (a : α), g a ⋯ ∈ t a hgf : { toFun := fun f a => f a ⋯, inj' := ⋯ } g = f a : α ⊢ { toFun := fun f a => f a ⋯, inj' ...
((:c Membership.mem) ((:fv _uniq.1352) (:fv _uniq.2478)) ((:c Finset) ((:fv _uniq.1352) (:fv _uniq.2478))) ((:c Finset.instMembership) ((:fv _uniq.1352) (:fv _uniq.2478))) ((:c DFunLike.coe) ((:c Function.Embedding) (:forall a (:fv _uniq.1330) (:forall _ ((:c Membership.mem) (:fv _uniq.1330) ((:c Finset) (:fv _uniq.133...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.1330))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.1330))"},{"name":"γ","sexp":"(:forall _ (:fv _uniq.1330) (:sort (+ u_2 1)))"},{"name":"δ","sexp":"(:forall _ (:fv _uniq.1330) (:sort (+ u_3 1)))"},{"name":"s","sexp":"...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:fv FV4) (:arg :explicit 0 (:fv FV12)))) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:app (:fv FV4) (:arg :explicit 0 (:fv FV12)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:fv FV4) (:arg :explicit 0 (:fv FV1...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1330","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1337","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c DecidableEq) (:arg :expli...
{"children":[{"source":"exact","sourceEnd":1415,"sourceStart":1410,"tag":"atom"},{"children":[{"contextIndex":10,"semanticRole":"local","source":"hg","sourceEnd":1418,"sourceStart":1416,"tag":"identifier"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"a","sourceEnd":1420,"sourceStart":1419,"tag":"ide...
[]
[{"source":"hg a","source_end":1420,"source_start":1416,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1330","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1337","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":2,...
8
14
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9254ebd05fff77fc7e798171e9ee8d549112c7f4cce3a198e003c539afb3c500
028bfb4682742d01a739fd85d517c613465208bd6f1c7742b5a839537cee503d
cbeaf57e0d97e0eedd97708e43fc51b15d4243d09eae0a00f6c948ab24358704
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
828
Fintype.mem_piFinset
Mathlib/Data/Fintype/Pi.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>Fintype.piFinset</a>, <a>Finset.mem_map</a>, <a>forall_prop_of_true</a>, <a>exists_prop</a>, <a>Finset.mem_univ</a>, <a>Finset.mem_pi</a>]
case mpr α : Type u_1 inst✝¹ : DecidableEq α inst✝ : Fintype α γ : α → Type u_2 δ : α → Type u_3 s : (a : α) → Finset (γ a) t : (a : α) → Finset (δ a) f : (a : α) → δ a ⊢ (∀ (a : α), f a ∈ t a) → f ∈ piFinset t
case mpr α : Type u_1 inst✝¹ : DecidableEq α inst✝ : Fintype α γ : α → Type u_2 δ : α → Type u_3 s : (a : α) → Finset (γ a) t : (a : α) → Finset (δ a) f : (a : α) → δ a ⊢ (∀ (a : α), f a ∈ t a) → ∃ a, (∀ (a_1 : α), a a_1 ⋯ ∈ t a_1) ∧ { toFun := fun f a => f a ⋯, inj' := ⋯ } a = f
(:forall _ (:forall a (:fv _uniq.1330) ((:c Membership.mem) ((:fv _uniq.1352) 0) ((:c Finset) ((:fv _uniq.1352) 0)) ((:c Finset.instMembership) ((:fv _uniq.1352) 0)) ((:fv _uniq.1551) 0) ((:fv _uniq.1550) 0))) ((:c Membership.mem) (:forall a (:fv _uniq.1330) ((:fv _uniq.1352) 0)) ((:c Finset) (:forall a (:fv _uniq.1330...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.1330))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.1330))"},{"name":"γ","sexp":"(:forall _ (:fv _uniq.1330) (:sort (+ u_2 1)))"},{"name":"δ","sexp":"(:forall _ (:fv _uniq.1330) (:sort (+ u_3 1)))"},{"name":"s","sexp":"...
(:forall _ :explicit (:forall a :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:fv FV4) (:arg :explicit 0 0))) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:app (:fv FV4) (:arg :explicit 0 0))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1330","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1337","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c DecidableEq) (:arg :expli...
{"children":[{"source":"simp","sourceEnd":1430,"sourceStart":1426,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":1435,"sourceStart":1431,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":1435,"s...
[]
[{"source":"piFinset","source_end":1445,"source_start":1437,"syntax_kind":"ident"},{"source":"mem_map","source_end":1454,"source_start":1447,"syntax_kind":"ident"},{"source":"forall_prop_of_true","source_end":1475,"source_start":1456,"syntax_kind":"ident"},{"source":"exists_prop","source_end":1488,"source_start":1477,"...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1330","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1337","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":2,...
8
19
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
723edbc81b9284682b460bb804d7f3ca29e2aaf233780e97630a132fb9cff54c
aa4da6b69aa1f5298090cd6510aff32996d3d4f48b572fa2e2996335ffab2332
60664ea80111194aba49dfb8bd9c4f3ac0721dd7de432ab7656e1f88bd4c6040
e579967680fbbf00bb8940b7abe78caebbb6bde77a53f1f628147890c6222eb7
cat-searcher/leandojo-benchmark-4-random
test
829
Fintype.mem_piFinset
Mathlib/Data/Fintype/Pi.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact fun hf => ⟨fun a _ => f a, hf, <a>rfl</a>⟩
case mpr α : Type u_1 inst✝¹ : DecidableEq α inst✝ : Fintype α γ : α → Type u_2 δ : α → Type u_3 s : (a : α) → Finset (γ a) t : (a : α) → Finset (δ a) f : (a : α) → δ a ⊢ (∀ (a : α), f a ∈ t a) → ∃ a, (∀ (a_1 : α), a a_1 ⋯ ∈ t a_1) ∧ { toFun := fun f a => f a ⋯, inj' := ⋯ } a = f
(:forall _ (:forall a (:fv _uniq.1330) ((:c Membership.mem) ((:fv _uniq.1352) 0) ((:c Finset) ((:fv _uniq.1352) 0)) ((:c Finset.instMembership) ((:fv _uniq.1352) 0)) ((:fv _uniq.1551) 0) ((:fv _uniq.1550) 0))) ((:c Exists) (:forall a (:fv _uniq.1330) (:forall _ ((:c Membership.mem) (:fv _uniq.1330) ((:c Finset) (:fv _u...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.1330))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.1330))"},{"name":"γ","sexp":"(:forall _ (:fv _uniq.1330) (:sort (+ u_2 1)))"},{"name":"δ","sexp":"(:forall _ (:fv _uniq.1330) (:sort (+ u_3 1)))"},{"name":"s","sexp":"...
(:forall _ :explicit (:forall a :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:fv FV4) (:arg :explicit 0 0))) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:app (:fv FV4) (:arg :explicit 0 0))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1330","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1337","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c DecidableEq) (:arg :expli...
{"children":[{"source":"exact","sourceEnd":1517,"sourceStart":1512,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":1521,"sourceStart":1518,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"hf","sourceEnd":1524,"sourceStart":1522,"tag":"identifier"}],"kind":"null","source":"hf","sou...
[]
[{"source":"fun hf => ⟨fun a _ => f a, hf, rfl⟩","source_end":1557,"source_start":1518,"syntax_kind":"Lean.Parser.Term.fun"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1330","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1337","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":2,...
8
20
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e789f85fcb0faf1ecca079e0312e48e424b642d818bae93fb78a4e040dddc054
e579967680fbbf00bb8940b7abe78caebbb6bde77a53f1f628147890c6222eb7
c896ac57a8fdab9d1c3fec880c94d8e7ccf91a0a8f6f3c0d5a5dff9b9411db5d
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
830
Set.image_id_eq
Mathlib/Data/Set/Image.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
ext
α : Type u_1 β : Type u_2 γ : Type u_3 ι : Sort u_4 ι' : Sort u_5 f : α → β s t : Set α ⊢ image id = id
case h.h α : Type u_1 β : Type u_2 γ : Type u_3 ι : Sort u_4 ι' : Sort u_5 f : α → β s t x✝¹ : Set α x✝ : α ⊢ x✝ ∈ id '' x✝¹ ↔ x✝ ∈ id x✝¹
((:c Eq) (:forall s ((:c Set) (:fv _uniq.25903)) ((:c Set) (:fv _uniq.25903))) ((:c Set.image) (:fv _uniq.25903) (:fv _uniq.25903) ((:c id) (:fv _uniq.25903))) ((:c id) ((:c Set) (:fv _uniq.25903))))
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort u_4)"},{"name":"ι'","sexp":"(:sort u_5)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.25903) (:fv _uniq.25906))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.25903))"},{"name":"...
(:app (:c Eq) (:arg :implicit-type 0 (:forall s :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c Set) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 1 (:app (:c Set.image) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:app (:c id) (:arg :implicit-type 0 (:fv FV0...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25903","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25906","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"ext","sourceEnd":14128,"sourceStart":14125,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":14128,"sourceStart":14125,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25903","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25906","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
129
4
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b1807b8d5e8f88d36a8b7aa7b6946d8cc1e2defd731b7bf12802feeaa01c101b
49b6b8989a340b563dfa4e61955c562377bf701b2cd7c5b0e29280651fbdecfc
a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de
e2aec0f377243d979387084ca9d7e85965509208b83e81bb19e4458f1df1670f
cat-searcher/leandojo-benchmark-4-random
test
831
Set.image_id_eq
Mathlib/Data/Set/Image.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
case h.h α : Type u_1 β : Type u_2 γ : Type u_3 ι : Sort u_4 ι' : Sort u_5 f : α → β s t x✝¹ : Set α x✝ : α ⊢ x✝ ∈ id '' x✝¹ ↔ x✝ ∈ id x✝¹
((:c Iff) ((:c Membership.mem) (:fv _uniq.25903) ((:c Set) (:fv _uniq.25903)) ((:c Set.instMembership) (:fv _uniq.25903)) (:fv _uniq.26040) ((:c Set.image) (:fv _uniq.25903) (:fv _uniq.25903) ((:c id) (:fv _uniq.25903)) (:fv _uniq.26018))) ((:c Membership.mem) (:fv _uniq.25903) ((:c Set) (:fv _uniq.25903)) ((:c Set.ins...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort u_4)"},{"name":"ι'","sexp":"(:sort u_5)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.25903) (:fv _uniq.25906))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.25903))"},{"name":"...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :e...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25903","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25906","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"simp","sourceEnd":14134,"sourceStart":14130,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"ki...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25903","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25906","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
129
6
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e9204786fed8654f60e5b604d3bab7a1d7b3862e1a714deba3b83fb95f0a53ee
e2aec0f377243d979387084ca9d7e85965509208b83e81bb19e4458f1df1670f
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
832
Complex.Gamma_integrand_deriv_integrable_A
Mathlib/Analysis/SpecialFunctions/Gamma/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
convert (<a>_private.Mathlib.Analysis.SpecialFunctions.Gamma.Basic.0.Complex.Gamma_integrand_interval_integrable</a> (s + 1) _ hX).<a>IntervalIntegrable.neg</a>
s : ℂ hs : 0 < s.re X : ℝ hX : 0 ≤ X ⊢ IntervalIntegrable (fun x => -(↑(rexp (-x)) * ↑x ^ s)) volume 0 X
((:c IntervalIntegrable) (:c Complex) (:c Complex.instNormedAddCommGroup) (:lambda x (:c Real) ((:c Neg.neg) (:c Complex) (:c Complex.instNeg) ((:c HMul.hMul) (:c Complex) (:c Complex) (:c Complex) ((:c instHMul) (:c Complex) (:c Complex.instMul)) ((:c Complex.ofReal') ((:c Real.exp) ((:c Neg.neg) (:c Real) (:c Real.in...
[{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Complex.re) (:fv _uniq.31102)))"},{"name":"X","sexp":"(:c Real)"},{"name":"hX","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c ...
(:app (:c IntervalIntegrable) (:arg :implicit-type 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Complex))))) (:arg :explicit 2 (:lambda x :explicit (:c Real) (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:ar...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31102","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.31103","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R...
{"children":[{"children":[{"children":[{"children":[{"source":"convert","sourceEnd":7817,"sourceStart":7810,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":"(","sourceEnd":7819,"sourceStart":7818,"tag":"atom"...
[]
[{"source":"(Gamma_integrand_interval_integrable (s + 1) _ hX).neg","source_end":7872,"source_start":7818,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"ofReal_exp","source_end":7899,"source_start":7889,"syntax_kind":"ident"},{"source":"ofReal_neg","source_end":7911,"source_start":7901,"syntax_kind":"ident"},{"sourc...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31102","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.31103","is_instance":false,"is_let":false,"user_name":"hs"},{"binder_role":":implicit","context_index":3,"internal_name":"_u...
32
2
branch_opener
false
1
4
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a533faf2f7d8419405618c80c4ecba2fc8c016f570402d17eea95d8ee4dc66f8
cf845dd779070d4870f74f29135c4ad67e7e0a271d9573aa3ef2353a0318bca1
3ac13613ae8ddbfc939c94f26ccd62d5f8a591c1bd9ae60b2eb31cc246e5058f
9e08aca4a911cd69020a40137f91d21e5fc2523f875bfb3db67a94237e6f8f17