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cat-searcher/leandojo-benchmark-4-random | test | 0 | CategoryTheory.Equivalence.invFunIdAssoc_hom_app | Mathlib/CategoryTheory/Equivalence.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp [<a>CategoryTheory.Equivalence.invFunIdAssoc</a>] | C : Type u₁
inst✝² : Category.{v₁, u₁} C
D : Type u₂
inst✝¹ : Category.{v₂, u₂} D
E : Type u₃
inst✝ : Category.{v₃, u₃} E
e : C ≌ D
F : D ⥤ E
X : D
⊢ (e.invFunIdAssoc F).hom.app X = F.map (e.counit.app X) | C : Type u₁
inst✝² : Category.{v₁, u₁} C
D : Type u₂
inst✝¹ : Category.{v₂, u₂} D
E : Type u₃
inst✝ : Category.{v₃, u₃} E
e : C ≌ D
F : D ⥤ E
X : D
⊢ 𝟙 (F.obj (e.functor.obj (e.inverse.obj X))) ≫ F.map (e.counitIso.hom.app X) ≫ 𝟙 (F.obj X) = F.map (e.counit.app X) | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.43465) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.43465) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.43465) (:fv _uniq.43468))) ((:c Prefunctor.obj) (:fv _uniq.43460) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.43460) ((:c CategoryTheory.Catego... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.43455))"},{"name":"D","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.43460))"},{"name":"E","sexp":"(:sort (+ u₃ 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Catego... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43455","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.43458","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"dsimp","sourceEnd":16885,"sourceStart":16880,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16887,"sourceStart":16886,"tag":"... | [] | [{"source":"invFunIdAssoc","source_end":16900,"source_start":16887,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43455","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.43458","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern... | 74 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9a86119d5b3d68553b0b51edbf0b89dea380546714a6ccdbed70228f33e95bd1 | dffd9e5f7277e3dd5f5c2b05fd9444fd40fb1096625378a428c0f4d27d25be5c | df424000f0610cd99fec8deefafb9c31a53914a9990d9d19565999e3581fc1de | 3f169408f4ae7788f16cd4417946ed197cdbd999c61cd92b3bbc4da17e7cff89 |
cat-searcher/leandojo-benchmark-4-random | test | 1 | CategoryTheory.Equivalence.invFunIdAssoc_hom_app | Mathlib/CategoryTheory/Equivalence.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | aesop_cat | C : Type u₁
inst✝² : Category.{v₁, u₁} C
D : Type u₂
inst✝¹ : Category.{v₂, u₂} D
E : Type u₃
inst✝ : Category.{v₃, u₃} E
e : C ≌ D
F : D ⥤ E
X : D
⊢ 𝟙 (F.obj (e.functor.obj (e.inverse.obj X))) ≫ F.map (e.counitIso.hom.app X) ≫ 𝟙 (F.obj X) = F.map (e.counit.app X) | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.43465) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.43465) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.43465) (:fv _uniq.43468))) ((:c Prefunctor.obj) (:fv _uniq.43460) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.43460) ((:c CategoryTheory.Catego... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.43455))"},{"name":"D","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.43460))"},{"name":"E","sexp":"(:sort (+ u₃ 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Catego... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43455","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.43458","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"aesop_cat","sourceEnd":16913,"sourceStart":16904,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"CategoryTheory.aesop_cat","source":"aesop_cat","sourceEnd":16913,"sourceStart":16904,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43455","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.43458","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern... | 74 | 5 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a1464b656f8b6903ba9259174c4aee8821e88dcec6cce325f6e4f1fabe716ea0 | 3f169408f4ae7788f16cd4417946ed197cdbd999c61cd92b3bbc4da17e7cff89 | 5121c016cd001463f39ee8c4444b84a277d6f4c7f9897d838d825f1c14f96636 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2 | ENNReal.le_rpow_one_div_iff | Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | nth_rw 1 [← <a>ENNReal.rpow_one</a> x] | x y : ℝ≥0∞
z : ℝ
hz : 0 < z
⊢ x ≤ y ^ (1 / z) ↔ x ^ z ≤ y | x y : ℝ≥0∞
z : ℝ
hz : 0 < z
⊢ x ^ 1 ≤ y ^ (1 / z) ↔ x ^ z ≤ y | ((:c Iff) ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrd... | [{"name":"x","sexp":"(:c ENNReal)"},{"name":"y","sexp":"(:c ENNReal)"},{"name":"z","sexp":"(:c Real)"},{"name":"hz","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.147588))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:fv FV1)) (:arg :explicit 3 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c Real)) (:arg :implic... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.147586","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.147587","is_instance":false,"is_let":false,"name":"y","sexp":"(:c ENNReal)"},{"binder_role":":implicit","c... | {"children":[{"source":"nth_rw","sourceEnd":31945,"sourceStart":31939,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"source":"1","sourceEnd":31947,"sourceStart":31946,"tag":"atom"}],"kind":"num","source":"1","sourceEnd":31947,"... | [] | [{"source":"rpow_one x","source_end":31963,"source_start":31953,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.147586","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.147587","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 234 | 4 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ef6fd48c85e99347641466cb8d615d9c7eaea980031e82a548a282d921a31f34 | 7259f8b186f55c724a2937abefb3b54b5c4888a7d9da11b2e88fa932b843a186 | 5e83fe96ed12ab903e4d32d0a33ea3dbc91fa9778c53c010dadc8e299424f126 | 5cf6b4b917cf658d7dbea03acbaf5bcb5e0e83d72e4e8e72ddc096da2a93f886 |
cat-searcher/leandojo-benchmark-4-random | test | 3 | ENNReal.le_rpow_one_div_iff | Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | nth_rw 1 [← @<a>mul_inv_cancel</a> _ _ z hz.ne'] | x y : ℝ≥0∞
z : ℝ
hz : 0 < z
⊢ x ^ 1 ≤ y ^ (1 / z) ↔ x ^ z ≤ y | x y : ℝ≥0∞
z : ℝ
hz : 0 < z
⊢ x ^ (z * z⁻¹) ≤ y ^ (1 / z) ↔ x ^ z ≤ y | ((:c Iff) ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrd... | [{"name":"x","sexp":"(:c ENNReal)"},{"name":"y","sexp":"(:c ENNReal)"},{"name":"z","sexp":"(:c Real)"},{"name":"hz","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.147588))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c ENNReal)) (:arg... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.147586","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.147587","is_instance":false,"is_let":false,"name":"y","sexp":"(:c ENNReal)"},{"binder_role":":implicit","c... | {"children":[{"source":"nth_rw","sourceEnd":31973,"sourceStart":31967,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"source":"1","sourceEnd":31975,"sourceStart":31974,"tag":"atom"}],"kind":"num","source":"1","sourceEnd":31975,"... | [] | [{"source":"@_root_.mul_inv_cancel _ _ z hz.ne'","source_end":32016,"source_start":31981,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.147586","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.147587","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 234 | 7 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f2aa74f55aab5ca970713f36e9b4b6354b93941a6362dfb796e4b9c2e9edfa9e | 5cf6b4b917cf658d7dbea03acbaf5bcb5e0e83d72e4e8e72ddc096da2a93f886 | f47e3dd1adf0c55ad4278f7450f5053d6467e3e4a88362b2206ae19e23a8b880 | a67623c6140f80c71152dd2161fb11d53293002679fbcafdeb4ec052353cc0b5 |
cat-searcher/leandojo-benchmark-4-random | test | 4 | ENNReal.le_rpow_one_div_iff | Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>ENNReal.rpow_mul</a>, ← <a>one_div</a>, @<a>ENNReal.rpow_le_rpow_iff</a> _ _ (1 / z) (by simp [hz])] | x y : ℝ≥0∞
z : ℝ
hz : 0 < z
⊢ x ^ (z * z⁻¹) ≤ y ^ (1 / z) ↔ x ^ z ≤ y | ((:c Iff) ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrd... | [{"name":"x","sexp":"(:c ENNReal)"},{"name":"y","sexp":"(:c ENNReal)"},{"name":"z","sexp":"(:c Real)"},{"name":"hz","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.147588))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c ENNReal)) (:arg... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.147586","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.147587","is_instance":false,"is_let":false,"name":"y","sexp":"(:c ENNReal)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":32022,"sourceStart":32020,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32024,"sourceStart":32023,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"ENNReal.rpow_mul... | [] | [{"source":"rpow_mul","source_end":32032,"source_start":32024,"syntax_kind":"ident"},{"source":"one_div","source_end":32045,"source_start":32038,"syntax_kind":"ident"},{"source":"@rpow_le_rpow_iff _ _ (1 / z) (by simp [hz])","source_end":32091,"source_start":32047,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.147586","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.147587","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 234 | 10 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b1ab5c90aa6a82f9602da8a8e3060fe97320376a4fd06dd8729a3e4db30958da | a67623c6140f80c71152dd2161fb11d53293002679fbcafdeb4ec052353cc0b5 | 7785f40295153fbee4fc131e674c273c0b8f183026ec0918f28e26d90df9ba9a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 5 | ENNReal.le_rpow_one_div_iff | Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [hz] | x y : ℝ≥0∞
z : ℝ
hz : 0 < z
⊢ 0 < 1 / z | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.... | [{"name":"x","sexp":"(:c ENNReal)"},{"name":"y","sexp":"(:c ENNReal)"},{"name":"z","sexp":"(:c Real)"},{"name":"hz","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.147588))"}] | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.147586","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.147587","is_instance":false,"is_let":false,"name":"y","sexp":"(:c ENNReal)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":32085,"sourceStart":32081,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"hz","source_end":32089,"source_start":32087,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.147586","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.147587","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 234 | 16 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 318332db8cc40212d3ff81569b471d07207b454ca7a47c91196cfd3a9384f2d5 | 40d7cdce76d6793c6f30c77d254346ba894274e7a82b56d575dc473ecadb7de5 | 199d5d52adca245380d9314e9608af40c4fb728e85bf299c4c3d783f9a3759fc | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 6 | Combinatorics.Line.apply_of_ne_none | Mathlib/Combinatorics/HalesJewett.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [l.apply, <a>Option.getD_of_ne_none</a> h] | α : Type u_1
ι : Type u_2
l : Line α ι
x : α
i : ι
h : l.idxFun i ≠ none
⊢ some ((fun x i => (l.idxFun i).getD x) x i) = l.idxFun i | ((:c Eq) ((:c Option) (:fv _uniq.4270)) ((:c Option.some) (:fv _uniq.4270) ((:lambda x (:fv _uniq.4270) (:lambda i (:fv _uniq.4271) ((:c Option.getD) (:fv _uniq.4270) ((:c Combinatorics.Line.idxFun) (:fv _uniq.4270) (:fv _uniq.4271) (:fv _uniq.4272) 0) 1))) (:fv _uniq.4273) (:fv _uniq.4274))) ((:c Combinatorics.Line.id... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c Combinatorics.Line) (:fv _uniq.4270) (:fv _uniq.4271))"},{"name":"x","sexp":"(:fv _uniq.4270)"},{"name":"i","sexp":"(:fv _uniq.4271)"},{"name":"h","sexp":"((:c Ne) ((:c Option) (:fv _uniq.4270)) ((:c Combinatorics.... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Option) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Option.some) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:lambda x :explicit (:fv FV1) (:lambda i :explicit (:fv FV2) (:app (:c Option.getD) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4270","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.4271","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":explicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":8656,"sourceStart":8654,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8658,"sourceStart":8657,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"l.apply","source_end":8665,"source_start":8658,"syntax_kind":"ident"},{"source":"Option.getD_of_ne_none h","source_end":8691,"source_start":8667,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4270","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.4271","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 32 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a002f917036656451958d52b461b3dfe1ceb53ac2a18288733b7e0c4d655400b | 12a9c80c6151abb9c89290622abad9c872d32cd53d1fab96abf5d208c6d3eea6 | 2490bddaa1a84e666fe917714eb5504d2ac934777568fd84bec76a1313c1d864 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 7 | CancelDenoms.cancel_factors_lt | Mathlib/Tactic/CancelDenoms/Core.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>mul_lt_mul_left</a>, ← ha, ← hb, ← <a>mul_assoc</a>, ← <a>mul_assoc</a>, <a>mul_comm</a> bd, <a>mul_lt_mul_left</a>] | α : Type u_1
inst✝ : LinearOrderedField α
a b ad bd a' b' gcd : α
ha : ad * a = a'
hb : bd * b = b'
had : 0 < ad
hbd : 0 < bd
hgcd : 0 < gcd
⊢ (a < b) = (1 / gcd * (bd * a') < 1 / gcd * (ad * b')) | α : Type u_1
inst✝ : LinearOrderedField α
a b ad bd a' b' gcd : α
ha : ad * a = a'
hb : bd * b = b'
had : 0 < ad
hbd : 0 < bd
hgcd : 0 < gcd
⊢ 0 < ad * bd
α : Type u_1
inst✝ : LinearOrderedField α
a b ad bd a' b' gcd : α
ha : ad * a = a'
hb : bd * b = b'
had : 0 < ad
hbd : 0 < bd
hgcd : 0 < gcd
⊢ 0 < 1 / gcd | ((:c Eq) (:sort 0) ((:c LT.lt) (:fv _uniq.7565) ((:c Preorder.toLT) (:fv _uniq.7565) ((:c PartialOrder.toPreorder) (:fv _uniq.7565) ((:c StrictOrderedRing.toPartialOrder) (:fv _uniq.7565) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.7565) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.7565) ((:c L... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedField) (:fv _uniq.7565))"},{"name":"a","sexp":"(:fv _uniq.7565)"},{"name":"b","sexp":"(:fv _uniq.7565)"},{"name":"ad","sexp":"(:fv _uniq.7565)"},{"name":"bd","sexp":"(:fv _uniq.7565)"},{"name":"a'","sexp":"(:fv _uniq.7565)"},{"name":"b'"... | (:app (:c Eq) (:arg :implicit-type 0 (:sort Prop)) (:arg :explicit 1 (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:fv FV4)))) (:arg :explicit 2 (:app (:c LT.lt) (:arg :implicit-type 0 (:fv... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7565","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.7566","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedField) (:arg ... | {"children":[{"source":"rw","sourceEnd":3198,"sourceStart":3196,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3200,"sourceStart":3199,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"mul_lt_mul_left","se... | [] | [{"source":"mul_lt_mul_left","source_end":3215,"source_start":3200,"syntax_kind":"ident"},{"source":"ha","source_end":3223,"source_start":3221,"syntax_kind":"ident"},{"source":"hb","source_end":3231,"source_start":3229,"syntax_kind":"ident"},{"source":"mul_assoc","source_end":3246,"source_start":3237,"syntax_kind":"ide... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7565","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.7566","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"internal_... | 19 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5dae85750679fad4d5b7fcbf7363aec54616c83482a6f7e4ed174f5b33aebb30 | dd901e805a6af48b79ef1187f060cb8d0e3622d4407db53f4aa953cd74cb3315 | 885ae8a5abeb74c2a76430a80a9c6564bcbcf926d9eafbb3e3d406a7472d3ff8 | 06e24609dca3c6571a94ce73574648a010e34f4ddc62c9506cd10e38b7f65b2f |
cat-searcher/leandojo-benchmark-4-random | test | 8 | CancelDenoms.cancel_factors_lt | Mathlib/Tactic/CancelDenoms/Core.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>mul_pos</a> had hbd | α : Type u_1
inst✝ : LinearOrderedField α
a b ad bd a' b' gcd : α
ha : ad * a = a'
hb : bd * b = b'
had : 0 < ad
hbd : 0 < bd
hgcd : 0 < gcd
⊢ 0 < ad * bd | ((:c LT.lt) (:fv _uniq.7565) ((:c Preorder.toLT) (:fv _uniq.7565) ((:c PartialOrder.toPreorder) (:fv _uniq.7565) ((:c StrictOrderedRing.toPartialOrder) (:fv _uniq.7565) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.7565) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.7565) ((:c LinearOrderedField.t... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedField) (:fv _uniq.7565))"},{"name":"a","sexp":"(:fv _uniq.7565)"},{"name":"b","sexp":"(:fv _uniq.7565)"},{"name":"ad","sexp":"(:fv _uniq.7565)"},{"name":"bd","sexp":"(:fv _uniq.7565)"},{"name":"a'","sexp":"(:fv _uniq.7565)"},{"name":"b'"... | (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV1)) (:arg :exp... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7565","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.7566","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedField) (:arg ... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":3303,"sourceStart":3298,"tag":"atom"},{"children":[{"name":"mul_pos","semanticRole":"global","source":"mul_pos","sourceEnd":3311,"sourceStart":3304,"tag":"identifier"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"had",... | [] | [{"source":"mul_pos had hbd","source_end":3319,"source_start":3304,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7565","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.7566","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"internal_... | 19 | 15 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7e3d99f2f2c3d19573cf8ca867e3fcf6aafe7627b8b1d2dbed31b766aa19ea7d | 3380636c3e642d0fe5bebfa1baae256c9cc972d10db439561eb9c84b3765fbe9 | 3aa627d27ef3b53e0c1b1a402cd3d9bc7f803bb554a29ac098eb43b8d5fc1698 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 9 | CancelDenoms.cancel_factors_lt | Mathlib/Tactic/CancelDenoms/Core.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>one_div_pos</a>.2 hgcd | α : Type u_1
inst✝ : LinearOrderedField α
a b ad bd a' b' gcd : α
ha : ad * a = a'
hb : bd * b = b'
had : 0 < ad
hbd : 0 < bd
hgcd : 0 < gcd
⊢ 0 < 1 / gcd | ((:c LT.lt) (:fv _uniq.7565) ((:c Preorder.toLT) (:fv _uniq.7565) ((:c PartialOrder.toPreorder) (:fv _uniq.7565) ((:c StrictOrderedRing.toPartialOrder) (:fv _uniq.7565) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.7565) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.7565) ((:c LinearOrderedField.t... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedField) (:fv _uniq.7565))"},{"name":"a","sexp":"(:fv _uniq.7565)"},{"name":"b","sexp":"(:fv _uniq.7565)"},{"name":"ad","sexp":"(:fv _uniq.7565)"},{"name":"bd","sexp":"(:fv _uniq.7565)"},{"name":"a'","sexp":"(:fv _uniq.7565)"},{"name":"b'"... | (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV1)) (:arg :exp... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7565","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.7566","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedField) (:arg ... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":3330,"sourceStart":3325,"tag":"atom"},{"children":[{"children":[{"name":"one_div_pos","semanticRole":"global","source":"one_div_pos","sourceEnd":3342,"sourceStart":3331,"tag":"identifier"},{"source":".","sourceEnd":3343,"sourceStart":3342... | [] | [{"source":"one_div_pos.2 hgcd","source_end":3349,"source_start":3331,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7565","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.7566","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"internal_... | 19 | 20 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 362a4d791f57bd638fd99572d205002beebd549ac145bef666dadca4936ce51c | 09963411d67a0f53f3027fb8bfb00f37fbf612c46d17423d4f1bfab7e12e369d | a7eec638dae8a1d3577cd0a4b5fdf4013f4573fa66da97598568edaf164d5703 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 10 | Batteries.BinomialHeap.Imp.Heap.WF.tail? | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Batteries.BinomialHeap.Imp.Heap.tail?</a>] | α : Type u_1
s : Heap α
le : α → α → Bool
n : Nat
tl : Heap α
hwf : WF le n s
⊢ Heap.tail? le s = some tl → WF le 0 tl | α : Type u_1
s : Heap α
le : α → α → Bool
n : Nat
tl : Heap α
hwf : WF le n s
⊢ Option.map (fun x => x.snd) (Heap.deleteMin le s) = some tl → WF le 0 tl | (:forall _ ((:c Eq) ((:c Option) ((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.163398))) ((:c Batteries.BinomialHeap.Imp.Heap.tail?) (:fv _uniq.163398) (:fv _uniq.163400) (:fv _uniq.163399)) ((:c Option.some) ((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.163398)) (:fv _uniq.163402))) ((:c Batteries.BinomialHeap.I... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"s","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.163398))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.163398) (:forall _ (:fv _uniq.163398) (:c Bool)))"},{"name":"n","sexp":"(:c Nat)"},{"name":"tl","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.163... | (:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Option) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap) (:arg :explicit 0 (:fv FV1)))))) (:arg :explicit 1 (:app (:c Batteries.BinomialHeap.Imp.Heap.tail?) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.163398","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.163399","is_instance":false,"is_let":false,"name":"s","sexp":"(:app (:c Batteries.BinomialHeap.Imp.Heap) (... | {"children":[{"source":"simp","sourceEnd":19669,"sourceStart":19665,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":19674,"sourceStart":19670,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":196... | [] | [{"source":"Heap.tail?","source_end":19686,"source_start":19676,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.163398","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.163399","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 61 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4f6ac670b68eecd8f3323ed78501f2c2f041bdea67448a3a0006aa197aa43d07 | 80a1848c1697a9998cef39dc0e85fabb01a2c48f5fd17d27e383e733b05bb526 | 995935239fec8ef60364f459de87d711c0ca2ab781571616fe99b415998a2017 | 8e365bf5d2527779ca0da8583cc83bd07cb6b8a55e1b2d8153177a80288dd8e0 |
cat-searcher/leandojo-benchmark-4-random | test | 11 | Batteries.BinomialHeap.Imp.Heap.WF.tail? | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro eq | α : Type u_1
s : Heap α
le : α → α → Bool
n : Nat
tl : Heap α
hwf : WF le n s
⊢ Option.map (fun x => x.snd) (Heap.deleteMin le s) = some tl → WF le 0 tl | α : Type u_1
s : Heap α
le : α → α → Bool
n : Nat
tl : Heap α
hwf : WF le n s
eq : Option.map (fun x => x.snd) (Heap.deleteMin le s) = some tl
⊢ WF le 0 tl | (:forall _ ((:c Eq) ((:c Option) ((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.163398))) ((:c Option.map) ((:c Prod) (:fv _uniq.163398) ((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.163398))) ((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.163398)) (:lambda _ ((:c Prod) (:fv _uniq.163398) ((:c Batteries.Binomial... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"s","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.163398))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.163398) (:forall _ (:fv _uniq.163398) (:c Bool)))"},{"name":"n","sexp":"(:c Nat)"},{"name":"tl","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.163... | (:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Option) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap) (:arg :explicit 0 (:fv FV1)))))) (:arg :explicit 1 (:app (:c Option.map) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.Bino... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.163398","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.163399","is_instance":false,"is_let":false,"name":"s","sexp":"(:app (:c Batteries.BinomialHeap.Imp.Heap) (... | {"children":[{"source":"intro","sourceEnd":19694,"sourceStart":19689,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"eq","sourceEnd":19697,"sourceStart":19695,"tag":"identifier"}],"kind":"null","source":"eq","sourceEnd":19697,"sourceStart":19695,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","sour... | [{"role":"fresh_name","source":"eq","source_end":19697,"source_start":19695,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.163398","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.163399","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 61 | 6 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1ebfdc2c2cfbd48fabccb6e653106e278d000966bf64c5a261f79fe7470fd61b | 8e365bf5d2527779ca0da8583cc83bd07cb6b8a55e1b2d8153177a80288dd8e0 | da30e2c904567f38c67db957e122f05e7f1935f4a389b4c677b35caa879cab97 | c8fae2d7ba2e32d150eb1c39e207ff5484f79971204489523f9aa71f215e6840 |
cat-searcher/leandojo-benchmark-4-random | test | 12 | Batteries.BinomialHeap.Imp.Heap.WF.tail? | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | match eq₂ : s.deleteMin le, eq with | <a>Option.some</a> (a, tl), <a>rfl</a> => exact hwf.deleteMin eq₂ | α : Type u_1
s : Heap α
le : α → α → Bool
n : Nat
tl : Heap α
hwf : WF le n s
eq : Option.map (fun x => x.snd) (Heap.deleteMin le s) = some tl
⊢ WF le 0 tl | ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.163398) (:fv _uniq.163400) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))) (:fv _uniq.163402)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"s","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.163398))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.163398) (:forall _ (:fv _uniq.163398) (:c Bool)))"},{"name":"n","sexp":"(:c Nat)"},{"name":"tl","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.163... | (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:lit 0)))))))... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.163398","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.163399","is_instance":false,"is_let":false,"name":"s","sexp":"(:app (:c Batteries.BinomialHeap.Imp.Heap) (... | {"children":[{"source":"match","sourceEnd":19705,"sourceStart":19700,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"eq₂","sourceEnd":19711,"sourceStart":19706,"tag... | [] | [{"source":"match eq₂ : s.deleteMin le, eq with\n | some (a, tl), rfl => ? rhs","source_end":19788,"source_start":19700,"syntax_kind":"Lean.Parser.Term.match"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.163398","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.163399","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 61 | 7 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9b8e1490a97cd2ccb2387740512f5d62d7b2e3abeb4fda4d3b58a8410b4e0a43 | c8fae2d7ba2e32d150eb1c39e207ff5484f79971204489523f9aa71f215e6840 | b35f73d05bbecd327ec25f679aab5d80e3201f5eeaae3810d5794d81d9d59497 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 13 | Batteries.BinomialHeap.Imp.Heap.WF.tail? | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hwf.deleteMin eq₂ | α : Type u_1
s : Heap α
le : α → α → Bool
n : Nat
tl✝ : Heap α
hwf : WF le n s
eq : Option.map (fun x => x.snd) (Heap.deleteMin le s) = some tl✝
a : α
tl : Heap α
eq₂ : Heap.deleteMin le s = some (a, tl)
⊢ WF le 0 ((fun x => x.snd) (a, tl)) | ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.163398) (:fv _uniq.163400) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))) ((:lambda _ ((:c Prod) (:fv _uniq.163398) ((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.163398))) ((:c Prod.snd) (:fv _uniq.163398) ((:c Batteries.BinomialHeap.Imp.Heap) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"s","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.163398))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.163398) (:forall _ (:fv _uniq.163398) (:c Bool)))"},{"name":"n","sexp":"(:c Nat)"},{"name":"tl✝","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.16... | (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:lit 0)))))))... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.163398","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.163399","is_instance":false,"is_let":false,"name":"s","sexp":"(:app (:c Batteries.BinomialHeap.Imp.Heap) (... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":19768,"sourceStart":19763,"tag":"atom"},{"children":[{"source":"hwf.deleteMin","sourceEnd":19782,"sourceStart":19769,"tag":"identifier"},{"children":[{"contextIndex":10,"semanticRole":"local","source":"eq₂","sourceEnd":19788,"sourceStart"... | [] | [{"source":"hwf.deleteMin eq₂","source_end":19788,"source_start":19769,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.163398","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.163399","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 61 | 9 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8f82f1b21b83c2eba3ad7265e7721f630382ba73884bf425bb469e805fb14157 | f3dcbe8b5588deb5fecffbb6dfc67c5ee3705136a287fecd7b5d067912aff465 | 9aa3d84923955b1c84c9a50ec52f574370f9ab6cd297450375ca394b022f9f90 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 14 | Ideal.span_singleton_eq_span_singleton | Mathlib/RingTheory/Ideal/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>dvd_dvd_iff_associated</a>, <a>le_antisymm_iff</a>, <a>and_comm</a>] | α✝ : Type u
β : Type v
a b : α✝
inst✝² : CommSemiring α✝
I : Ideal α✝
α : Type u
inst✝¹ : CommRing α
inst✝ : IsDomain α
x y : α
⊢ span {x} = span {y} ↔ Associated x y | α✝ : Type u
β : Type v
a b : α✝
inst✝² : CommSemiring α✝
I : Ideal α✝
α : Type u
inst✝¹ : CommRing α
inst✝ : IsDomain α
x y : α
⊢ span {y} ≤ span {x} ∧ span {x} ≤ span {y} ↔ x ∣ y ∧ y ∣ x | ((:c Iff) ((:c Eq) ((:c Ideal) (:fv _uniq.56439) ((:c CommSemiring.toSemiring) (:fv _uniq.56439) ((:c CommRing.toCommSemiring) (:fv _uniq.56439) (:fv _uniq.56440)))) ((:c Ideal.span) (:fv _uniq.56439) ((:c CommSemiring.toSemiring) (:fv _uniq.56439) ((:c CommRing.toCommSemiring) (:fv _uniq.56439) (:fv _uniq.56440))) ((:... | [{"name":"α✝","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.55747)"},{"name":"b","sexp":"(:fv _uniq.55747)"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.55747))"},{"name":"I","sexp":"((:c Ideal) (:fv _uniq.55747) ((:c CommSemiring.toSemiring) (:fv _uniq.55747)... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV7)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV7))))))) (:arg :explicit 1 (:app (:c Ideal.span) (:arg :implicit-type 0 (:fv FV7)) (:arg :instance 1 (:instance-of (:app (:c Se... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55747","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55749","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"rw","sourceEnd":19623,"sourceStart":19621,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":19625,"sourceStart":19624,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":19628,"sourceSt... | [] | [{"source":"dvd_dvd_iff_associated","source_end":19651,"source_start":19629,"syntax_kind":"ident"},{"source":"le_antisymm_iff","source_end":19668,"source_start":19653,"syntax_kind":"ident"},{"source":"and_comm","source_end":19678,"source_start":19670,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55747","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55749","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 179 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d38e4d4da0d1786296c55121c604606ec552ff0dfd09a5807ac4e71f422c5ddd | a867054574d8ae384de55288ece4264c3365adf18eb0a5d3691e67909c87a267 | 610ae4e61f032ddb0bf5d79c4c78408c0a3210409518c4665181fdfb50a89e99 | 064752df3b2893bb7efa0c1bb22edcb100ce08c6756bf41b32cbd45b444c2982 |
cat-searcher/leandojo-benchmark-4-random | test | 15 | Ideal.span_singleton_eq_span_singleton | Mathlib/RingTheory/Ideal/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>and_congr</a> <;> rw [<a>Ideal.span_singleton_le_span_singleton</a>] | α✝ : Type u
β : Type v
a b : α✝
inst✝² : CommSemiring α✝
I : Ideal α✝
α : Type u
inst✝¹ : CommRing α
inst✝ : IsDomain α
x y : α
⊢ span {y} ≤ span {x} ∧ span {x} ≤ span {y} ↔ x ∣ y ∧ y ∣ x | ((:c Iff) ((:c And) ((:c LE.le) ((:c Ideal) (:fv _uniq.56439) ((:c CommSemiring.toSemiring) (:fv _uniq.56439) ((:c CommRing.toCommSemiring) (:fv _uniq.56439) (:fv _uniq.56440)))) ((:c Preorder.toLE) ((:c Ideal) (:fv _uniq.56439) ((:c CommSemiring.toSemiring) (:fv _uniq.56439) ((:c CommRing.toCommSemiring) (:fv _uniq.56... | [{"name":"α✝","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.55747)"},{"name":"b","sexp":"(:fv _uniq.55747)"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.55747))"},{"name":"I","sexp":"((:c Ideal) (:fv _uniq.55747) ((:c CommSemiring.toSemiring) (:fv _uniq.55747)... | (:app (:c Iff) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV7)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV7))))))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Ideal) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55747","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55749","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"children":[{"source":"apply","sourceEnd":19687,"sourceStart":19682,"tag":"atom"},{"name":"and_congr","semanticRole":"global","source":"and_congr","sourceEnd":19697,"sourceStart":19688,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply and_congr","sourceEnd":19697,"sourceStart":19682,"... | [] | [{"source":"and_congr","source_end":19697,"source_start":19688,"syntax_kind":"ident"},{"source":"span_singleton_le_span_singleton","source_end":19738,"source_start":19706,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55747","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55749","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 179 | 9 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4c770ca8f110911adbfa8f92adc8d56227c9f781356ee1b14bef1d8ce7191b28 | 064752df3b2893bb7efa0c1bb22edcb100ce08c6756bf41b32cbd45b444c2982 | 8ded2f026ca73fd464e11f68ec4f7d97695a26691f4511a877fbaea5866762c6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 16 | MeasureTheory.OuterMeasure.comap_ofFunction | Mathlib/MeasureTheory/OuterMeasure/OfFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type ?u.25201
f : β → α
h : Monotone m ∨ Surjective f
⊢ (fun s => m (f '' s)) ∅ = 0 | α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type ?u.25201
f : β → α
h : Monotone m ∨ Surjective f
⊢ m ∅ = 0 | ((:c Eq) (:c ENNReal) ((:lambda s ((:c Set) (:fv _uniq.25075)) ((:fv _uniq.24976) ((:c Set.image) (:fv _uniq.25075) (:fv _uniq.24971) (:fv _uniq.25079) 0))) ((:c EmptyCollection.emptyCollection) ((:c Set) (:fv _uniq.25075)) ((:c Set.instEmptyCollection) (:fv _uniq.25075)))) ((:c OfNat.ofNat) (:c ENNReal) (:lit 0) ((:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:forall _ ((:c Set) (:fv _uniq.24971)) (:c ENNReal))"},{"name":"m_empty","sexp":"((:c Eq) (:c ENNReal) ((:fv _uniq.24976) ((:c EmptyCollection.emptyCollection) ((:c Set) (:fv _uniq.24971)) ((:c Set.instEmptyCollection) (:fv _uniq.24971)))) ((:c OfNat.ofNat) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:lambda s :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV3))) (:app (:fv FV1) (:arg :explicit 0 (:app (:c Set.image) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:fv FV4)) (:arg :explicit 3 0))))) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"name":"m","sexp":"(:forall _ :explicit (:app (:c Set) (:arg :exp... | {"children":[{"source":"simp","sourceEnd":8121,"sourceStart":8117,"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.24971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 26 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9eb58a6debd10dea1360f480d9f60eec0dbed4a70fead35bb08ecf663cf83dfe | 6fa764bb68a0001c0a57086c910c2b6b6ac94b5dbeffb69c7a5bfa1799156fba | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | dba43484cabe1f9e13ad39791f6575b13dda25d59451f5208aea173bdf2c9e26 |
cat-searcher/leandojo-benchmark-4-random | test | 17 | MeasureTheory.OuterMeasure.comap_ofFunction | Mathlib/MeasureTheory/OuterMeasure/OfFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [m_empty] | α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type ?u.25201
f : β → α
h : Monotone m ∨ Surjective f
⊢ m ∅ = 0 | ((:c Eq) (:c ENNReal) ((:fv _uniq.24976) ((:c EmptyCollection.emptyCollection) ((:c Set) (:fv _uniq.24971)) ((:c Set.instEmptyCollection) (:fv _uniq.24971)))) ((:c OfNat.ofNat) (:c ENNReal) (:lit 0) ((:c Zero.toOfNat0) (:c ENNReal) (:c instENNRealZero)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:forall _ ((:c Set) (:fv _uniq.24971)) (:c ENNReal))"},{"name":"m_empty","sexp":"((:c Eq) (:c ENNReal) ((:fv _uniq.24976) ((:c EmptyCollection.emptyCollection) ((:c Set) (:fv _uniq.24971)) ((:c Set.instEmptyCollection) (:fv _uniq.24971)))) ((:c OfNat.ofNat) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:fv FV1) (:arg :explicit 0 (:app (:c EmptyCollection.emptyCollection) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c EmptyCollection) (:arg :explicit 0 (:app (:c Set) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"name":"m","sexp":"(:forall _ :explicit (:app (:c Set) (:arg :exp... | {"children":[{"source":"simp","sourceEnd":8127,"sourceStart":8123,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8129,"sourceStart":8128,"tag":"atom"... | [] | [{"source":"m_empty","source_end":8136,"source_start":8129,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 26 | 6 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4f7c477c9c763d0e20e8a7c2f999d64c67997a33cf5ea662d3806323df288bb2 | dba43484cabe1f9e13ad39791f6575b13dda25d59451f5208aea173bdf2c9e26 | b5e651bfc1a187f89eed348c7fbf68d296a6339cfc47fecaca91bf0ad4522373 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 18 | MeasureTheory.OuterMeasure.comap_ofFunction | Mathlib/MeasureTheory/OuterMeasure/OfFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>le_antisymm</a> (<a>MeasureTheory.OuterMeasure.le_ofFunction</a>.2 fun s => ?_) fun s => ?_ | α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type u_2
f : β → α
h : Monotone m ∨ Surjective f
⊢ (comap f) (OuterMeasure.ofFunction m m_empty) = OuterMeasure.ofFunction (fun s => m (f '' s)) ⋯ | case refine_1
α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type u_2
f : β → α
h : Monotone m ∨ Surjective f
s : Set β
⊢ ((comap f) (OuterMeasure.ofFunction m m_empty)) s ≤ m (f '' s)
case refine_2
α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type u_2
f : β → α
h : Monotone m ∨ Surjective f
s : Set β
⊢ (Ou... | ((:c Eq) ((:c MeasureTheory.OuterMeasure) (:fv _uniq.25601)) ((:c DFunLike.coe) ((:c LinearMap) (:c ENNReal) (:c ENNReal) ((:c OrderedSemiring.toSemiring) (:c ENNReal) ((:c OrderedCommSemiring.toOrderedSemiring) (:c ENNReal) ((:c CanonicallyOrderedCommSemiring.toOrderedCommSemiring) (:c ENNReal) (:c ENNReal.instCanonic... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:forall _ ((:c Set) (:fv _uniq.24971)) (:c ENNReal))"},{"name":"m_empty","sexp":"((:c Eq) (:c ENNReal) ((:fv _uniq.24976) ((:c EmptyCollection.emptyCollection) ((:c Set) (:fv _uniq.24971)) ((:c Set.instEmptyCollection) (:fv _uniq.24971)))) ((:c OfNat.ofNat) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MeasureTheory.OuterMeasure) (:arg :explicit 0 (:fv FV4)))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"name":"m","sexp":"(:forall _ :explicit (:app (:c Set) (:arg :exp... | {"children":[{"source":"refine","sourceEnd":8153,"sourceStart":8147,"tag":"atom"},{"children":[{"name":"le_antisymm","semanticRole":"global","source":"le_antisymm","sourceEnd":8165,"sourceStart":8154,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":8167,"sourceStart":8166,"tag":"atom"},{"children... | [] | [{"source":"le_antisymm (le_ofFunction.2 fun s => ?_) fun s => ?_","source_end":8207,"source_start":8154,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 26 | 11 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 23d5debd34bd56481c85b1f22374367ebb1c611f8af8fc5dbccea9cdf6815f10 | 8c958c5f1318f5c9d09f9c3832c8bd4f9d09558a735ff5b49afe04cdf6847968 | 30d77a580821ea0c4f675dc42c9980ca4b8889d7fe53609f433e5d9b55fa95df | 121d0f4401424600d57dac09a5ce73dc65c01d6aa3e207b0db578864a09d335e |
cat-searcher/leandojo-benchmark-4-random | test | 19 | MeasureTheory.OuterMeasure.comap_ofFunction | Mathlib/MeasureTheory/OuterMeasure/OfFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.OuterMeasure.comap_apply</a>] | case refine_1
α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type u_2
f : β → α
h : Monotone m ∨ Surjective f
s : Set β
⊢ ((comap f) (OuterMeasure.ofFunction m m_empty)) s ≤ m (f '' s) | case refine_1
α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type u_2
f : β → α
h : Monotone m ∨ Surjective f
s : Set β
⊢ (OuterMeasure.ofFunction m m_empty) (f '' s) ≤ m (f '' s) | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:forall _ ((:c Set) (:fv _uniq.24971)) (:c ENNReal))"},{"name":"m_empty","sexp":"((:c Eq) (:c ENNReal) ((:fv _uniq.24976) ((:c EmptyCollection.emptyCollection) ((:c Set) (:fv _uniq.24971)) ((:c Set.instEmptyCollection) (:fv _uniq.24971)))) ((:c OfNat.ofNat) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.OuterMeasure) (:arg :explicit 0 (:fv FV4)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"name":"m","sexp":"(:forall _ :explicit (:app (:c Set) (:arg :exp... | {"children":[{"source":"rw","sourceEnd":8215,"sourceStart":8213,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8217,"sourceStart":8216,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MeasureTheory.OuterM... | [] | [{"source":"comap_apply","source_end":8228,"source_start":8217,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 26 | 16 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 463ee494d57ab1710dda81938d29d731eee96d40f81e67a8dc8a54fc516d2d46 | bc9a8c29c838f606ca5614738c1386cab6c2ae4cf9ae8efa9c083ab08da5bedc | 90926946b158f010c4dd4b11fe0adb6259babc5ab459c27d6e6f84b758f73d73 | 60837cf1685894178f0c24bd81c190b2bd906197bebc0341310eeb033f4ba906 |
cat-searcher/leandojo-benchmark-4-random | test | 20 | MeasureTheory.OuterMeasure.comap_ofFunction | Mathlib/MeasureTheory/OuterMeasure/OfFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>MeasureTheory.OuterMeasure.ofFunction_le</a> | case refine_1
α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type u_2
f : β → α
h : Monotone m ∨ Surjective f
s : Set β
⊢ (OuterMeasure.ofFunction m m_empty) (f '' s) ≤ m (f '' s) | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:forall _ ((:c Set) (:fv _uniq.24971)) (:c ENNReal))"},{"name":"m_empty","sexp":"((:c Eq) (:c ENNReal) ((:fv _uniq.24976) ((:c EmptyCollection.emptyCollection) ((:c Set) (:fv _uniq.24971)) ((:c Set.instEmptyCollection) (:fv _uniq.24971)))) ((:c OfNat.ofNat) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.OuterMeasure) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"name":"m","sexp":"(:forall _ :explicit (:app (:c Set) (:arg :exp... | {"children":[{"source":"apply","sourceEnd":8239,"sourceStart":8234,"tag":"atom"},{"name":"MeasureTheory.OuterMeasure.ofFunction_le","semanticRole":"global","source":"ofFunction_le","sourceEnd":8253,"sourceStart":8240,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply ofFunction_le","sourceEnd":8253,... | [] | [{"source":"ofFunction_le","source_end":8253,"source_start":8240,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 26 | 19 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 40f6cce5f427a1825cfccff091d63664f44fecf69516fcf223d057e066c94c29 | 60837cf1685894178f0c24bd81c190b2bd906197bebc0341310eeb033f4ba906 | 3a58322914149c8bc03423c77382da9fc8fe7051048b412831529ea524917998 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 21 | MeasureTheory.OuterMeasure.comap_ofFunction | Mathlib/MeasureTheory/OuterMeasure/OfFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.OuterMeasure.comap_apply</a>, <a>MeasureTheory.OuterMeasure.ofFunction_apply</a>, <a>MeasureTheory.OuterMeasure.ofFunction_apply</a>] | case refine_2
α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type u_2
f : β → α
h : Monotone m ∨ Surjective f
s : Set β
⊢ (OuterMeasure.ofFunction (fun s => m (f '' s)) ⋯) s ≤ ((comap f) (OuterMeasure.ofFunction m m_empty)) s | case refine_2
α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type u_2
f : β → α
h : Monotone m ∨ Surjective f
s : Set β
⊢ ⨅ t, ⨅ (_ : s ⊆ iUnion t), ∑' (n : ℕ), m (f '' t n) ≤ ⨅ t, ⨅ (_ : f '' s ⊆ iUnion t), ∑' (n : ℕ), m (t n) | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.toPartialOrder) (:c ENNReal) ((:c OrderedCommSemiring.toOrderedSemiring) (:c ENNReal) ((:c CanonicallyOrderedCommSemiring.toOrderedCommSemiring) (:c ENNReal) (:c ENNReal.instCanonicallyOrderedCommSe... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:forall _ ((:c Set) (:fv _uniq.24971)) (:c ENNReal))"},{"name":"m_empty","sexp":"((:c Eq) (:c ENNReal) ((:fv _uniq.24976) ((:c EmptyCollection.emptyCollection) ((:c Set) (:fv _uniq.24971)) ((:c Set.instEmptyCollection) (:fv _uniq.24971)))) ((:c OfNat.ofNat) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.OuterMeasure) (:arg :explicit 0 (:fv FV4)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"name":"m","sexp":"(:forall _ :explicit (:app (:c Set) (:arg :exp... | {"children":[{"source":"rw","sourceEnd":8261,"sourceStart":8259,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8263,"sourceStart":8262,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MeasureTheory.OuterM... | [] | [{"source":"comap_apply","source_end":8274,"source_start":8263,"syntax_kind":"ident"},{"source":"ofFunction_apply","source_end":8292,"source_start":8276,"syntax_kind":"ident"},{"source":"ofFunction_apply","source_end":8310,"source_start":8294,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 26 | 24 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1f75eb4bd95cd9be5160e179ee00f587322c3b8ee339b9993e2a7430db11db11 | d2ad96b5e21b37adf9d62fffd1a7aa6ea0a2c064a04d387dd3bc0e8601e8d0b4 | 21910d88e40e663663eab63d5aa6ab2e29ebe1678723d94a4c16b2d862997b38 | a679ad584b7e42fa088da50e1db8c913e74ee1bcaec12a01cf3dfa4ca5eada41 |
cat-searcher/leandojo-benchmark-4-random | test | 22 | MeasureTheory.OuterMeasure.comap_ofFunction | Mathlib/MeasureTheory/OuterMeasure/OfFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>iInf_mono'</a> fun t => ⟨fun k => f ⁻¹' t k, ?_⟩ | case refine_2
α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type u_2
f : β → α
h : Monotone m ∨ Surjective f
s : Set β
⊢ ⨅ t, ⨅ (_ : s ⊆ iUnion t), ∑' (n : ℕ), m (f '' t n) ≤ ⨅ t, ⨅ (_ : f '' s ⊆ iUnion t), ∑' (n : ℕ), m (t n) | case refine_2
α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type u_2
f : β → α
h : Monotone m ∨ Surjective f
s : Set β
t : ℕ → Set α
⊢ ⨅ (_ : s ⊆ ⋃ k, f ⁻¹' t k), ∑' (n : ℕ), m (f '' (fun k => f ⁻¹' t k) n) ≤
⨅ (_ : f '' s ⊆ iUnion t), ∑' (n : ℕ), m (t n) | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.toPartialOrder) (:c ENNReal) ((:c OrderedCommSemiring.toOrderedSemiring) (:c ENNReal) ((:c CanonicallyOrderedCommSemiring.toOrderedCommSemiring) (:c ENNReal) (:c ENNReal.instCanonicallyOrderedCommSe... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:forall _ ((:c Set) (:fv _uniq.24971)) (:c ENNReal))"},{"name":"m_empty","sexp":"((:c Eq) (:c ENNReal) ((:fv _uniq.24976) ((:c EmptyCollection.emptyCollection) ((:c Set) (:fv _uniq.24971)) ((:c Set.instEmptyCollection) (:fv _uniq.24971)))) ((:c OfNat.ofNat) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c iInf) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:forall _ :explicit (:c Nat) (:app (:c Set) (:arg :explicit 0 (:fv FV4))))) (:arg :instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"name":"m","sexp":"(:forall _ :explicit (:app (:c Set) (:arg :exp... | {"children":[{"source":"refine","sourceEnd":8322,"sourceStart":8316,"tag":"atom"},{"children":[{"name":"iInf_mono'","semanticRole":"global","source":"iInf_mono'","sourceEnd":8333,"sourceStart":8323,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":8337,"sourceStart":8334,"tag":"atom"},{"children... | [] | [{"source":"iInf_mono' fun t => ⟨fun k => f ⁻¹' t k, ?_⟩","source_end":8374,"source_start":8323,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 26 | 29 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c8022ad406fa9dbf1a039cece7136ea961fa3e2fb29cb9ac78f7374136375f59 | a679ad584b7e42fa088da50e1db8c913e74ee1bcaec12a01cf3dfa4ca5eada41 | 95aea4dab520b099d7f45fd7c3f5b9b1146ab53e15a541e90e44e9ec785bcced | 4bd8b84ce10b4ddfebe994cc47a7247ced12a6c3b36ba2ab8de459e9c348e44c |
cat-searcher/leandojo-benchmark-4-random | test | 23 | MeasureTheory.OuterMeasure.comap_ofFunction | Mathlib/MeasureTheory/OuterMeasure/OfFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>iInf_mono'</a> fun ht => ?_ | case refine_2
α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type u_2
f : β → α
h : Monotone m ∨ Surjective f
s : Set β
t : ℕ → Set α
⊢ ⨅ (_ : s ⊆ ⋃ k, f ⁻¹' t k), ∑' (n : ℕ), m (f '' (fun k => f ⁻¹' t k) n) ≤
⨅ (_ : f '' s ⊆ iUnion t), ∑' (n : ℕ), m (t n) | case refine_2
α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type u_2
f : β → α
h : Monotone m ∨ Surjective f
s : Set β
t : ℕ → Set α
ht : f '' s ⊆ iUnion t
⊢ ∃ (_ : s ⊆ ⋃ k, f ⁻¹' t k), ∑' (n : ℕ), m (f '' (fun k => f ⁻¹' t k) n) ≤ ∑' (n : ℕ), m (t n) | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c CompleteSemilatticeInf.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.toCompleteSemilatticeInf) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompletelyDis... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:forall _ ((:c Set) (:fv _uniq.24971)) (:c ENNReal))"},{"name":"m_empty","sexp":"((:c Eq) (:c ENNReal) ((:fv _uniq.24976) ((:c EmptyCollection.emptyCollection) ((:c Set) (:fv _uniq.24971)) ((:c Set.instEmptyCollection) (:fv _uniq.24971)))) ((:c OfNat.ofNat) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c iInf) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"name":"m","sexp":"(:forall _ :explicit (:app (:c Set) (:arg :exp... | {"children":[{"source":"refine","sourceEnd":8385,"sourceStart":8379,"tag":"atom"},{"children":[{"name":"iInf_mono'","semanticRole":"global","source":"iInf_mono'","sourceEnd":8396,"sourceStart":8386,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":8400,"sourceStart":8397,"tag":"atom"},{"children... | [] | [{"source":"iInf_mono' fun ht => ?_","source_end":8409,"source_start":8386,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 26 | 30 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cb839477805e2f2f9d61fce8e1e1b083d7d7b7a32d75460abcb8f199b01366cb | 4bd8b84ce10b4ddfebe994cc47a7247ced12a6c3b36ba2ab8de459e9c348e44c | 728744bd68e6750b38bb905d5173ca7eba413e548cbaa0c82197fbf508db9b7f | bba1c8b643a7539b9452ee3c69d3f1de34cf7eff228a2725a1738d9fd3b60890 |
cat-searcher/leandojo-benchmark-4-random | test | 24 | MeasureTheory.OuterMeasure.comap_ofFunction | Mathlib/MeasureTheory/OuterMeasure/OfFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.image_subset_iff</a>, <a>Set.preimage_iUnion</a>] at ht | case refine_2
α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type u_2
f : β → α
h : Monotone m ∨ Surjective f
s : Set β
t : ℕ → Set α
ht : f '' s ⊆ iUnion t
⊢ ∃ (_ : s ⊆ ⋃ k, f ⁻¹' t k), ∑' (n : ℕ), m (f '' (fun k => f ⁻¹' t k) n) ≤ ∑' (n : ℕ), m (t n) | case refine_2
α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type u_2
f : β → α
h : Monotone m ∨ Surjective f
s : Set β
t : ℕ → Set α
ht : s ⊆ ⋃ i, f ⁻¹' t i
⊢ ∃ (_ : s ⊆ ⋃ k, f ⁻¹' t k), ∑' (n : ℕ), m (f '' (fun k => f ⁻¹' t k) n) ≤ ∑' (n : ℕ), m (t n) | ((:c Exists) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.25601)) ((:c Set.instHasSubset) (:fv _uniq.25601)) (:fv _uniq.25757) ((:c Set.iUnion) (:fv _uniq.25601) (:c Nat) (:lambda k (:c Nat) ((:c Set.preimage) (:fv _uniq.25601) (:fv _uniq.24971) (:fv _uniq.25602) ((:fv _uniq.26308) 0))))) (:lambda i ((:c HasSubset.Subse... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:forall _ ((:c Set) (:fv _uniq.24971)) (:c ENNReal))"},{"name":"m_empty","sexp":"((:c Eq) (:c ENNReal) ((:fv _uniq.24976) ((:c EmptyCollection.emptyCollection) ((:c Set) (:fv _uniq.24971)) ((:c Set.instEmptyCollection) (:fv _uniq.24971)))) ((:c OfNat.ofNat) ... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV4)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV4))))))) (:arg :explicit 2 (:fv FV7)) (:arg :explicit 3 (:app (:c Set.i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"name":"m","sexp":"(:forall _ :explicit (:app (:c Set) (:arg :exp... | {"children":[{"source":"rw","sourceEnd":8416,"sourceStart":8414,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8418,"sourceStart":8417,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.image_subset_iff... | [] | [{"source":"Set.image_subset_iff","source_end":8438,"source_start":8418,"syntax_kind":"ident"},{"source":"ht","source_end":8462,"source_start":8460,"syntax_kind":"ident"},{"source":"preimage_iUnion","source_end":8455,"source_start":8440,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 26 | 31 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b160456bde87667ee956072709b98db8e6636f1ce66bfb4516cbbaccb7ab27c4 | bba1c8b643a7539b9452ee3c69d3f1de34cf7eff228a2725a1738d9fd3b60890 | a3132a74da0008baed7f088055688cddbbbd4ebc3eca9625e33a5d4512162ff7 | ef891223b7926d3aebe93605adde4ee98be81b92ee3cdaa76dcf70b3c7d1e4e3 |
cat-searcher/leandojo-benchmark-4-random | test | 25 | MeasureTheory.OuterMeasure.comap_ofFunction | Mathlib/MeasureTheory/OuterMeasure/OfFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨ht, <a>ENNReal.tsum_le_tsum</a> fun n => ?_⟩ | case refine_2
α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type u_2
f : β → α
h : Monotone m ∨ Surjective f
s : Set β
t : ℕ → Set α
ht : s ⊆ ⋃ i, f ⁻¹' t i
⊢ ∃ (_ : s ⊆ ⋃ k, f ⁻¹' t k), ∑' (n : ℕ), m (f '' (fun k => f ⁻¹' t k) n) ≤ ∑' (n : ℕ), m (t n) | case refine_2
α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type u_2
f : β → α
h : Monotone m ∨ Surjective f
s : Set β
t : ℕ → Set α
ht : s ⊆ ⋃ i, f ⁻¹' t i
n : ℕ
⊢ m (f '' (fun k => f ⁻¹' t k) n) ≤ m (t n) | ((:c Exists) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.25601)) ((:c Set.instHasSubset) (:fv _uniq.25601)) (:fv _uniq.25757) ((:c Set.iUnion) (:fv _uniq.25601) (:c Nat) (:lambda k (:c Nat) ((:c Set.preimage) (:fv _uniq.25601) (:fv _uniq.24971) (:fv _uniq.25602) ((:fv _uniq.26308) 0))))) (:lambda i ((:c HasSubset.Subse... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:forall _ ((:c Set) (:fv _uniq.24971)) (:c ENNReal))"},{"name":"m_empty","sexp":"((:c Eq) (:c ENNReal) ((:fv _uniq.24976) ((:c EmptyCollection.emptyCollection) ((:c Set) (:fv _uniq.24971)) ((:c Set.instEmptyCollection) (:fv _uniq.24971)))) ((:c OfNat.ofNat) ... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV4)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV4))))))) (:arg :explicit 2 (:fv FV7)) (:arg :explicit 3 (:app (:c Set.i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"name":"m","sexp":"(:forall _ :explicit (:app (:c Set) (:arg :exp... | {"children":[{"source":"refine","sourceEnd":8473,"sourceStart":8467,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":8477,"sourceStart":8474,"tag":"atom"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"ht","sourceEnd":8479,"sourceStart":8477,"tag":"identifier"},{"source":",","sourceEnd":8480,"sourc... | [] | [{"source":"⟨ht, ENNReal.tsum_le_tsum fun n => ?_⟩","source_end":8516,"source_start":8474,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 26 | 35 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4da809adf4ee47624088aba414033e17e66fcde2ff01a97aee1f2d15874ec5c1 | ef891223b7926d3aebe93605adde4ee98be81b92ee3cdaa76dcf70b3c7d1e4e3 | 7d946744a050c06e17ff20aacf68d1f02c6b6a3beb99731a1ca43667006ebafa | bbafd2e24b5cae2828fd679e1873f7d910ddc8cb229e0dfffaaec4fceed6de57 |
cat-searcher/leandojo-benchmark-4-random | test | 26 | MeasureTheory.OuterMeasure.comap_ofFunction | Mathlib/MeasureTheory/OuterMeasure/OfFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases' h with hl hr | case refine_2
α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type u_2
f : β → α
h : Monotone m ∨ Surjective f
s : Set β
t : ℕ → Set α
ht : s ⊆ ⋃ i, f ⁻¹' t i
n : ℕ
⊢ m (f '' (fun k => f ⁻¹' t k) n) ≤ m (t n) | case refine_2.inl
α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type u_2
f : β → α
s : Set β
t : ℕ → Set α
ht : s ⊆ ⋃ i, f ⁻¹' t i
n : ℕ
hl : Monotone m
⊢ m (f '' (fun k => f ⁻¹' t k) n) ≤ m (t n)
case refine_2.inr
α : Type u_1
m : Set α → ℝ≥0∞
m_empty : m ∅ = 0
β : Type u_2
f : β → α
s : Set β
t : ℕ → Set α
ht :... | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.toPartialOrder) (:c ENNReal) ((:c OrderedCommSemiring.toOrderedSemiring) (:c ENNReal) ((:c CanonicallyOrderedCommSemiring.toOrderedCommSemiring) (:c ENNReal) (:c ENNReal.instCanonicallyOrderedCommSe... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:forall _ ((:c Set) (:fv _uniq.24971)) (:c ENNReal))"},{"name":"m_empty","sexp":"((:c Eq) (:c ENNReal) ((:fv _uniq.24976) ((:c EmptyCollection.emptyCollection) ((:c Set) (:fv _uniq.24971)) ((:c Set.instEmptyCollection) (:fv _uniq.24971)))) ((:c OfNat.ofNat) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:fv FV1) (:arg :explicit 0 (:app (:c Set.image) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:fv FV5)) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"name":"m","sexp":"(:forall _ :explicit (:app (:c Set) (:arg :exp... | {"children":[{"source":"cases'","sourceEnd":8527,"sourceStart":8521,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":6,"semanticRole":"local","source":"h","sourceEnd":8529,"sourceStart":8528,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","sourc... | [] | [{"source":"h","source_end":8529,"source_start":8528,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24976","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 26 | 36 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ea65195ed95e3a65090b1898e12364f17e0020c60ab41d3c787b14e989620d7b | bbafd2e24b5cae2828fd679e1873f7d910ddc8cb229e0dfffaaec4fceed6de57 | 7146b7fd310ed574c3acb5ed84c6b3b87aad56dd53c44161c501aeb8183d1d34 | c46b8474dbc23f1fecdaa49ae581923a1c69a1188d41ee4620599bee5e232fa4 |
cat-searcher/leandojo-benchmark-4-random | test | 28 | IsGroupHom.inv_ker_one' | Mathlib/Deprecated/Subgroup.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : (f a)⁻¹ * f b = 1 := by rw [h, <a>mul_left_inv</a>] | G : Type u_1
H : Type u_2
A : Type u_3
a✝ a₁ a₂ b✝ c : G
inst✝¹ : Group G
inst✝ : Group H
f : G → H
hf : IsGroupHom f
a b : G
h : f a = f b
⊢ f (a⁻¹ * b) = 1 | G : Type u_1
H : Type u_2
A : Type u_3
a✝ a₁ a₂ b✝ c : G
inst✝¹ : Group G
inst✝ : Group H
f : G → H
hf : IsGroupHom f
a b : G
h : f a = f b
this : (f a)⁻¹ * f b = 1
⊢ f (a⁻¹ * b) = 1 | ((:c Eq) (:fv _uniq.41073) ((:fv _uniq.41805) ((:c HMul.hMul) (:fv _uniq.41070) (:fv _uniq.41070) (:fv _uniq.41070) ((:c instHMul) (:fv _uniq.41070) ((:c MulOneClass.toMul) (:fv _uniq.41070) ((:c Monoid.toMulOneClass) (:fv _uniq.41070) ((:c DivInvMonoid.toMonoid) (:fv _uniq.41070) ((:c Group.toDivInvMonoid) (:fv _uniq.... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"A","sexp":"(:sort (+ u_3 1))"},{"name":"a✝","sexp":"(:fv _uniq.41070)"},{"name":"a₁","sexp":"(:fv _uniq.41070)"},{"name":"a₂","sexp":"(:fv _uniq.41070)"},{"name":"b✝","sexp":"(:fv _uniq.41070)"},{"name":"c","sexp":"(:fv _uniq.4107... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:fv FV11) (:arg :explicit 0 (:app (:c HMul.hMul) (: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 HMul) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41070","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41073","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":16530,"sourceStart":16526,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":16531,"sourceStart":16531,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":16531,"sourceStart":16531,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"(f a)⁻¹ * f b = 1","source_end":16553,"source_start":16533,"syntax_kind":"«term_=_»"},{"source":"h","source_end":16565,"source_start":16564,"syntax_kind":"ident"},{"source":"mul_left_inv","source_end":16579,"source_start":16567,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41070","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41073","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 124 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 113d0a801894cb04aa3f186d354b437123fe7d5588f7a00836b6a4e2fe2fb494 | abb87e62cfa3121774e81cf79068caa1f72523921ff9d865908a5b1946010bb9 | da10bad03da9549401395b3779c76f03e5e360013e748e8d62a14af2426b6978 | 90ecafa850db74d74eaae5f4292e46425f74f4b133de1652017b1fc8572f9683 |
cat-searcher/leandojo-benchmark-4-random | test | 29 | IsGroupHom.inv_ker_one' | Mathlib/Deprecated/Subgroup.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [← hf.map_inv, ← hf.map_mul] at this | G : Type u_1
H : Type u_2
A : Type u_3
a✝ a₁ a₂ b✝ c : G
inst✝¹ : Group G
inst✝ : Group H
f : G → H
hf : IsGroupHom f
a b : G
h : f a = f b
this : (f a)⁻¹ * f b = 1
⊢ f (a⁻¹ * b) = 1 | ((:c Eq) (:fv _uniq.41073) ((:fv _uniq.41805) ((:c HMul.hMul) (:fv _uniq.41070) (:fv _uniq.41070) (:fv _uniq.41070) ((:c instHMul) (:fv _uniq.41070) ((:c MulOneClass.toMul) (:fv _uniq.41070) ((:c Monoid.toMulOneClass) (:fv _uniq.41070) ((:c DivInvMonoid.toMonoid) (:fv _uniq.41070) ((:c Group.toDivInvMonoid) (:fv _uniq.... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"A","sexp":"(:sort (+ u_3 1))"},{"name":"a✝","sexp":"(:fv _uniq.41070)"},{"name":"a₁","sexp":"(:fv _uniq.41070)"},{"name":"a₂","sexp":"(:fv _uniq.41070)"},{"name":"b✝","sexp":"(:fv _uniq.41070)"},{"name":"c","sexp":"(:fv _uniq.4107... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:fv FV11) (:arg :explicit 0 (:app (:c HMul.hMul) (: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 HMul) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41070","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41073","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rwa","sourceEnd":16586,"sourceStart":16583,"tag":"atom"},{"children":[{"source":"[","sourceEnd":16588,"sourceStart":16587,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":16591,"sourceStart":16588,"tag":"atom"}],"kind":"token.«← »","source"... | [] | [{"source":"hf.map_inv","source_end":16602,"source_start":16592,"syntax_kind":"ident"},{"source":"this","source_end":16627,"source_start":16623,"syntax_kind":"ident"},{"source":"hf.map_mul","source_end":16618,"source_start":16608,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41070","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41073","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 124 | 10 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 62d71749efae0337251929939c441b2db291f4ac1aa8f6fdaa819fd04bcc7390 | 90ecafa850db74d74eaae5f4292e46425f74f4b133de1652017b1fc8572f9683 | b8b1a7a17d20995734b69bc47e552d857f389943b363ef970822b8d66a3cdc2f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 30 | IsGroupHom.inv_ker_one' | Mathlib/Deprecated/Subgroup.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [h, <a>mul_left_inv</a>] | G : Type u_1
H : Type u_2
A : Type u_3
a✝ a₁ a₂ b✝ c : G
inst✝¹ : Group G
inst✝ : Group H
f : G → H
hf : IsGroupHom f
a b : G
h : f a = f b
⊢ (f a)⁻¹ * f b = 1 | ((:c Eq) (:fv _uniq.41073) ((:c HMul.hMul) (:fv _uniq.41073) (:fv _uniq.41073) (:fv _uniq.41073) ((:c instHMul) (:fv _uniq.41073) ((:c MulOneClass.toMul) (:fv _uniq.41073) ((:c Monoid.toMulOneClass) (:fv _uniq.41073) ((:c DivInvMonoid.toMonoid) (:fv _uniq.41073) ((:c Group.toDivInvMonoid) (:fv _uniq.41073) (:fv _uniq.4... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"A","sexp":"(:sort (+ u_3 1))"},{"name":"a✝","sexp":"(:fv _uniq.41070)"},{"name":"a₁","sexp":"(:fv _uniq.41070)"},{"name":"a₂","sexp":"(:fv _uniq.41070)"},{"name":"b✝","sexp":"(:fv _uniq.41070)"},{"name":"c","sexp":"(:fv _uniq.4107... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41070","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41073","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":16562,"sourceStart":16560,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16564,"sourceStart":16563,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":15,"seman... | [] | [{"source":"h","source_end":16565,"source_start":16564,"syntax_kind":"ident"},{"source":"mul_left_inv","source_end":16579,"source_start":16567,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41070","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41073","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 124 | 6 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 949d37e90733d526bbab59f45e65b5173a76e1b22c44b01d6887763cb07b62ac | 79c21ff3cdba0ec201d6dddfd02bc0470c810711dc9512b5fbf7a64221a90892 | d4b9eaad0af021d08ae4428ba5d231dc5abea6df810d693f2b5cf4dea25d6391 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 31 | Convex.thickening | Mathlib/Analysis/Convex/Normed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>add_ball_zero</a>] | ι : Type u_1
E : Type u_2
P : Type u_3
inst✝³ : SeminormedAddCommGroup E
inst✝² : NormedSpace ℝ E
inst✝¹ : PseudoMetricSpace P
inst✝ : NormedAddTorsor E P
s t : Set E
hs : Convex ℝ s
δ : ℝ
⊢ Convex ℝ (Metric.thickening δ s) | ι : Type u_1
E : Type u_2
P : Type u_3
inst✝³ : SeminormedAddCommGroup E
inst✝² : NormedSpace ℝ E
inst✝¹ : PseudoMetricSpace P
inst✝ : NormedAddTorsor E P
s t : Set E
hs : Convex ℝ s
δ : ℝ
⊢ Convex ℝ (s + ball 0 δ) | ((:c Convex) (:c Real) (:fv _uniq.25085) (:c Real.orderedSemiring) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.25085) ((:c SeminormedAddCommGroup.toAddCommGroup) (:fv _uniq.25085) (:fv _uniq.25091))) ((:c SMulZeroClass.toSMul) (:c Real) (:fv _uniq.25085) ((:c NegZeroClass.toZero) (:fv _uniq.25085) ((:c SubNegZeroMono... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.25085))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.25085) (:c Real.normedField) (:fv _uniq.25091))"},{"name":"i... | (:app (:c Convex) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c OrderedSemiring) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:app (:c SMul) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25082","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25085","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":2926,"sourceStart":2924,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2928,"sourceStart":2927,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":2931,"sourceStart":... | [] | [{"source":"add_ball_zero","source_end":2945,"source_start":2932,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25082","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25085","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 19 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0b08ea0b422b5f29c497a3c86ddd3a001b237b19e6f769bce43ce18767e347c1 | 8d3cc8ff7ecacf336a648c1a89378a9127166c37cb95894bef9f67ec1a2ad912 | 9691548f02b9e9b2a22f105070bb3b93a34d4dc426c06ed126d068f788589be3 | 6351cf48e2771b0af0f2f3f0ba1fd7ece0f74c48c8205059e2d7bb0bf2d20367 |
cat-searcher/leandojo-benchmark-4-random | test | 32 | Convex.thickening | Mathlib/Analysis/Convex/Normed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hs.add (<a>convex_ball</a> 0 _) | ι : Type u_1
E : Type u_2
P : Type u_3
inst✝³ : SeminormedAddCommGroup E
inst✝² : NormedSpace ℝ E
inst✝¹ : PseudoMetricSpace P
inst✝ : NormedAddTorsor E P
s t : Set E
hs : Convex ℝ s
δ : ℝ
⊢ Convex ℝ (s + ball 0 δ) | ((:c Convex) (:c Real) (:fv _uniq.25085) (:c Real.orderedSemiring) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.25085) ((:c SeminormedAddCommGroup.toAddCommGroup) (:fv _uniq.25085) (:fv _uniq.25091))) ((:c SMulZeroClass.toSMul) (:c Real) (:fv _uniq.25085) ((:c NegZeroClass.toZero) (:fv _uniq.25085) ((:c SubNegZeroMono... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.25085))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.25085) (:c Real.normedField) (:fv _uniq.25091))"},{"name":"i... | (:app (:c Convex) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c OrderedSemiring) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:app (:c SMul) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25082","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25085","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":2954,"sourceStart":2949,"tag":"atom"},{"children":[{"source":"hs.add","sourceEnd":2961,"sourceStart":2955,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":2963,"sourceStart":2962,"tag":"atom"},{"children":[{"name":"convex_ball","semanticRole":"global","s... | [] | [{"source":"hs.add (convex_ball 0 _)","source_end":2979,"source_start":2955,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25082","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25085","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 19 | 7 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 76b0c9c609fe324c0cccdc274606b45f043d3d7d82779642596aedb0c2029b34 | 6351cf48e2771b0af0f2f3f0ba1fd7ece0f74c48c8205059e2d7bb0bf2d20367 | a187193468f779e1c5f2f8482ea77670a48db6333f58f7ad60f3599e1f1e6c92 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 33 | SetTheory.PGame.zero_lf_inv' | Mathlib/SetTheory/Game/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert <a>SetTheory.PGame.lf_mk</a> _ _ <a>SetTheory.PGame.InvTy.zero</a> | xl xr : Type u_1
xL : xl → PGame
xR : xr → PGame
⊢ 0 ⧏ (mk xl xr xL xR).inv' | case h.e'_1
xl xr : Type u_1
xL : xl → PGame
xR : xr → PGame
⊢ 0 = invVal (fun i => xL ↑i) xR (fun i => (xL ↑i).inv') (fun i => (xR i).inv') InvTy.zero | ((:c SetTheory.PGame.LF) ((:c OfNat.ofNat) (:c SetTheory.PGame) (:lit 0) ((:c Zero.toOfNat0) (:c SetTheory.PGame) (:c SetTheory.PGame.instZero))) ((:c SetTheory.PGame.inv') ((:c SetTheory.PGame.mk) (:fv _uniq.508310) (:fv _uniq.508311) (:fv _uniq.508312) (:fv _uniq.508313)))) | [{"name":"xl","sexp":"(:sort (+ u_1 1))"},{"name":"xr","sexp":"(:sort (+ u_1 1))"},{"name":"xL","sexp":"(:forall _ (:fv _uniq.508310) (:c SetTheory.PGame))"},{"name":"xR","sexp":"(:forall _ (:fv _uniq.508311) (:c SetTheory.PGame))"}] | (:app (:c SetTheory.PGame.LF) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c SetTheory.PGame)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c SetTheory.PGame)) (:arg :explicit 1 (:lit 0))))))) (:arg :explicit 1 (:app (:c SetTheory.PGame.inv') (:ar... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.508310","is_instance":false,"is_let":false,"name":"xl","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.508311","is_instance":false,"is_let":false,"name":"xr","sexp":"(:sort Type)"},{"binder_role":":explicit",... | {"children":[{"source":"convert","sourceEnd":44505,"sourceStart":44498,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"SetTheory.PGame.lf_mk","semanticRole":"global","source":"lf_mk","sourceEnd":44511,"sourceStart":44506,"... | [] | [{"source":"lf_mk _ _ InvTy.zero","source_end":44526,"source_start":44506,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.508310","is_instance":false,"is_let":false,"user_name":"xl"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.508311","is_instance":false,"is_let":false,"user_name":"xr"},{"binder_role":":explicit","context_index":3,"internal_name":... | 186 | 4 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 438e5d60a1b9c60d078dbf3722ab9570f7f738b5841bfc78e9fd71b7fee3bcb2 | 06e1e06ee3709f8a36ff36d2a675650e86eb5bf702014788f6eeb71b303f374f | 14194efc0f7580841adefbd9725319fe5a16a9dc236cbf89aad71b94669bc642 | 06411f00d6c239625714a7c9362f5dc3eaa8ba5a5cb06219bcfafd9dba4d4497 |
cat-searcher/leandojo-benchmark-4-random | test | 34 | SetTheory.PGame.zero_lf_inv' | Mathlib/SetTheory/Game/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case h.e'_1
xl xr : Type u_1
xL : xl → PGame
xR : xr → PGame
⊢ 0 = invVal (fun i => xL ↑i) xR (fun i => (xL ↑i).inv') (fun i => (xR i).inv') InvTy.zero | ((:c Eq) (:c SetTheory.PGame) ((:c OfNat.ofNat) (:c SetTheory.PGame) (:lit 0) ((:c Zero.toOfNat0) (:c SetTheory.PGame) (:c SetTheory.PGame.instZero))) ((:c SetTheory.PGame.invVal) ((:c Subtype) (:fv _uniq.508310) (:lambda i (:fv _uniq.508310) ((:c LT.lt) (:c SetTheory.PGame) ((:c Preorder.toLT) (:c SetTheory.PGame) (:c... | [{"name":"xl","sexp":"(:sort (+ u_1 1))"},{"name":"xr","sexp":"(:sort (+ u_1 1))"},{"name":"xL","sexp":"(:forall _ (:fv _uniq.508310) (:c SetTheory.PGame))"},{"name":"xR","sexp":"(:forall _ (:fv _uniq.508311) (:c SetTheory.PGame))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c SetTheory.PGame)) (:arg :explicit 1 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c SetTheory.PGame)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c SetTheory.PGame)) (:arg :explicit 1 (:lit 0))))))) (:arg :explicit 2 (:app (... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.508310","is_instance":false,"is_let":false,"name":"xl","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.508311","is_instance":false,"is_let":false,"name":"xr","sexp":"(:sort Type)"},{"binder_role":":explicit",... | {"children":[{"source":"rfl","sourceEnd":44534,"sourceStart":44531,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":44534,"sourceStart":44531,"tag":"node"} | [] | [] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.508310","is_instance":false,"is_let":false,"user_name":"xl"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.508311","is_instance":false,"is_let":false,"user_name":"xr"},{"binder_role":":explicit","context_index":3,"internal_name":... | 186 | 5 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aa1871e148d5bc58ce8c0462f32b3bbf39b1cf6771c0a951af54470e613c4edf | 06411f00d6c239625714a7c9362f5dc3eaa8ba5a5cb06219bcfafd9dba4d4497 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 35 | NNReal.le_inv_iff_mul_le | Mathlib/Data/NNReal/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>mul_le_mul_left</a> (<a>pos_iff_ne_zero</a>.2 h), <a>mul_inv_cancel</a> h, <a>mul_comm</a>] | r p : ℝ≥0
h : p ≠ 0
⊢ r ≤ p⁻¹ ↔ r * p ≤ 1 | ((:c Iff) ((:c LE.le) (:c NNReal) ((:c Preorder.toLE) (:c NNReal) ((:c PartialOrder.toPreorder) (:c NNReal) ((:c StrictOrderedSemiring.toPartialOrder) (:c NNReal) (:c instNNRealStrictOrderedSemiring)))) (:fv _uniq.128970) ((:c Inv.inv) (:c NNReal) ((:c CanonicallyLinearOrderedSemifield.toInv) (:c NNReal) (:c NNReal.ins... | [{"name":"r","sexp":"(:c NNReal)"},{"name":"p","sexp":"(:c NNReal)"},{"name":"h","sexp":"((:c Ne) (:c NNReal) (:fv _uniq.128971) ((:c OfNat.ofNat) (:c NNReal) (:lit 0) ((:c Zero.toOfNat0) (:c NNReal) (:c instNNRealZero))))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c NNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c NNReal))))) (:arg :explicit 2 (:fv FV1)) (:arg :explicit 3 (:app (:c Inv.inv) (:arg :implicit-type 0 (:c NNReal)) (:arg :instance 1 (:instance-of (:app (:c Inv) (:arg... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.128970","is_instance":false,"is_let":false,"name":"r","sexp":"(:c NNReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.128971","is_instance":false,"is_let":false,"name":"p","sexp":"(:c NNReal)"},{"binder_role":":explicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":36674,"sourceStart":36672,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":36676,"sourceStart":36675,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"mul_le_mul_left (pos_iff_ne_zero.2 h)","source_end":36717,"source_start":36680,"syntax_kind":"Lean.Parser.Term.app"},{"source":"mul_inv_cancel h","source_end":36735,"source_start":36719,"syntax_kind":"Lean.Parser.Term.app"},{"source":"mul_comm","source_end":36745,"source_start":36737,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.128970","is_instance":false,"is_let":false,"user_name":"r"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.128971","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 346 | 2 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bd8072abea28f9588d80557660227e0252169d9553610a6f633c90ed25fbffc4 | 26c93cf1e52d9d0dc46731f6ba32e57060731bd1f7689de2b66fbac3500ed42f | 8d809046683ee6e62c83119019788068e16369a406f1ce18290479cd84e2cb36 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 36 | MeasureTheory.integrable_of_intervalIntegral_norm_bounded | Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hφ : <a>MeasureTheory.AECover</a> μ l _ := <a>MeasureTheory.aecover_Ioc</a> ha hb | ι : Type u_1
E : Type u_2
μ : Measure ℝ
l : Filter ι
inst✝² : l.NeBot
inst✝¹ : l.IsCountablyGenerated
inst✝ : NormedAddCommGroup E
a b : ι → ℝ
f : ℝ → E
I : ℝ
hfi : ∀ (i : ι), IntegrableOn f (Ioc (a i) (b i)) μ
ha : Tendsto a l atBot
hb : Tendsto b l atTop
h : ∀ᶠ (i : ι) in l, ∫ (x : ℝ) in a i..b i, ‖f x‖ ∂μ ≤ I
⊢ Inte... | ι : Type u_1
E : Type u_2
μ : Measure ℝ
l : Filter ι
inst✝² : l.NeBot
inst✝¹ : l.IsCountablyGenerated
inst✝ : NormedAddCommGroup E
a b : ι → ℝ
f : ℝ → E
I : ℝ
hfi : ∀ (i : ι), IntegrableOn f (Ioc (a i) (b i)) μ
ha : Tendsto a l atBot
hb : Tendsto b l atTop
h : ∀ᶠ (i : ι) in l, ∫ (x : ℝ) in a i..b i, ‖f x‖ ∂μ ≤ I
hφ : A... | ((:c MeasureTheory.Integrable) (:fv _uniq.129652) (:fv _uniq.129678) (:c Real) (:c Real.measurableSpace) (:fv _uniq.129690) (:fv _uniq.129661)) | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:c Real) (:c Real.measurableSpace))"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.129649))"},{"name":"inst✝²","sexp":"((:c Filter.NeBot) (:fv _uniq.129649) (:fv _uniq.129664))"},{"name":"ins... | (:app (:c MeasureTheory.Integrable) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:c Real)) (:arg :implicit 3) (:arg :explicit 4 (:fv FV9)) (:arg :explicit 5 (:fv FV2))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129649","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129652","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":31306,"sourceStart":31302,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hφ","sourceEnd":31310,"sourceStart":31307,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hφ","sourceEnd":31310,"sourceStart":31307,"tag":"nod... | [] | [{"source":"AECover μ l _","source_end":31327,"source_start":31313,"syntax_kind":"Lean.Parser.Term.app"},{"source":"aecover_Ioc ha hb","source_end":31348,"source_start":31331,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129649","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129652","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 150 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a979af8f09ef78ac6f1851a1e5b97f9e36fba22499cceeee478a9bac9d2d5711 | bb2b9f180b029d957de0fa71c7aac912af8a7282fc24d738e4c8fb48f3213f94 | 83f71f694672c2f764cb765be3a58ba7a6230b49eb84974c97458d00024708b1 | a7add540fdd5e6e4d22dd5bb7b072b97dfce2aca1951416ebb6b63007fb65611 |
cat-searcher/leandojo-benchmark-4-random | test | 37 | MeasureTheory.integrable_of_intervalIntegral_norm_bounded | Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine hφ.integrable_of_integral_norm_bounded I hfi (h.mp ?_) | ι : Type u_1
E : Type u_2
μ : Measure ℝ
l : Filter ι
inst✝² : l.NeBot
inst✝¹ : l.IsCountablyGenerated
inst✝ : NormedAddCommGroup E
a b : ι → ℝ
f : ℝ → E
I : ℝ
hfi : ∀ (i : ι), IntegrableOn f (Ioc (a i) (b i)) μ
ha : Tendsto a l atBot
hb : Tendsto b l atTop
h : ∀ᶠ (i : ι) in l, ∫ (x : ℝ) in a i..b i, ‖f x‖ ∂μ ≤ I
hφ : A... | ι : Type u_1
E : Type u_2
μ : Measure ℝ
l : Filter ι
inst✝² : l.NeBot
inst✝¹ : l.IsCountablyGenerated
inst✝ : NormedAddCommGroup E
a b : ι → ℝ
f : ℝ → E
I : ℝ
hfi : ∀ (i : ι), IntegrableOn f (Ioc (a i) (b i)) μ
ha : Tendsto a l atBot
hb : Tendsto b l atTop
h : ∀ᶠ (i : ι) in l, ∫ (x : ℝ) in a i..b i, ‖f x‖ ∂μ ≤ I
hφ : A... | ((:c MeasureTheory.Integrable) (:fv _uniq.129652) (:fv _uniq.129678) (:c Real) (:c Real.measurableSpace) (:fv _uniq.129690) (:fv _uniq.129661)) | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:c Real) (:c Real.measurableSpace))"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.129649))"},{"name":"inst✝²","sexp":"((:c Filter.NeBot) (:fv _uniq.129649) (:fv _uniq.129664))"},{"name":"ins... | (:app (:c MeasureTheory.Integrable) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:c Real)) (:arg :implicit 3) (:arg :explicit 4 (:fv FV9)) (:arg :explicit 5 (:fv FV2))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129649","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129652","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":31357,"sourceStart":31351,"tag":"atom"},{"children":[{"source":"hφ.integrable_of_integral_norm_bounded","sourceEnd":31397,"sourceStart":31358,"tag":"identifier"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"I","sourceEnd":31399,"sourceStart":31398,"tag":"i... | [] | [{"source":"hφ.integrable_of_integral_norm_bounded I hfi (h.mp ?_)","source_end":31413,"source_start":31358,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129649","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129652","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 150 | 5 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0e0a249c7059c76e2181f1c0c817fbc50bfd131c7dc57f91b012f44f6bfd0f0f | a7add540fdd5e6e4d22dd5bb7b072b97dfce2aca1951416ebb6b63007fb65611 | 04daddf3011434eb627f63a6e2d1aae39a694283613f91817ee95b49af210e85 | f663c95395b1884ed3c37caef1fdcf4fe586365b101beda13a921520c1098a37 |
cat-searcher/leandojo-benchmark-4-random | test | 38 | MeasureTheory.integrable_of_intervalIntegral_norm_bounded | Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards [ha.eventually (<a>Filter.eventually_le_atBot</a> 0), hb.eventually (<a>Filter.eventually_ge_atTop</a> 0)] with i hai hbi ht | ι : Type u_1
E : Type u_2
μ : Measure ℝ
l : Filter ι
inst✝² : l.NeBot
inst✝¹ : l.IsCountablyGenerated
inst✝ : NormedAddCommGroup E
a b : ι → ℝ
f : ℝ → E
I : ℝ
hfi : ∀ (i : ι), IntegrableOn f (Ioc (a i) (b i)) μ
ha : Tendsto a l atBot
hb : Tendsto b l atTop
h : ∀ᶠ (i : ι) in l, ∫ (x : ℝ) in a i..b i, ‖f x‖ ∂μ ≤ I
hφ : A... | case h
ι : Type u_1
E : Type u_2
μ : Measure ℝ
l : Filter ι
inst✝² : l.NeBot
inst✝¹ : l.IsCountablyGenerated
inst✝ : NormedAddCommGroup E
a b : ι → ℝ
f : ℝ → E
I : ℝ
hfi : ∀ (i : ι), IntegrableOn f (Ioc (a i) (b i)) μ
ha : Tendsto a l atBot
hb : Tendsto b l atTop
h : ∀ᶠ (i : ι) in l, ∫ (x : ℝ) in a i..b i, ‖f x‖ ∂μ ≤ I... | ((:c Filter.Eventually) (:fv _uniq.129649) (:lambda x (:fv _uniq.129649) (:forall _ ((:c LE.le) (:c Real) (:c Real.instLE) ((:c intervalIntegral) (:c Real) (:c Real.normedAddCommGroup) ((:c InnerProductSpace.toNormedSpace) (:c Real) (:c Real) (:c Real.RCLike) (:c Real.normedAddCommGroup) ((:c RCLike.innerProductSpace) ... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:c Real) (:c Real.measurableSpace))"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.129649))"},{"name":"inst✝²","sexp":"((:c Filter.NeBot) (:fv _uniq.129649) (:fv _uniq.129664))"},{"name":"ins... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:forall _ :explicit (: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 intervalIntegral) (:arg :impli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129649","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129652","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"filter_upwards","sourceEnd":31430,"sourceStart":31416,"tag":"atom"},{"children":[{"source":"[","sourceEnd":31432,"sourceStart":31431,"tag":"atom"},{"children":[{"children":[{"source":"ha.eventually","sourceEnd":31445,"sourceStart":31432,"tag":"identifier"},{"children":[{"children":[{"source":"("... | [] | [{"source":"hb.eventually (eventually_ge_atTop 0)","source_end":31512,"source_start":31475,"syntax_kind":"Lean.Parser.Term.app"},{"source":"ha.eventually (eventually_le_atBot 0)","source_end":31469,"source_start":31432,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129649","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129652","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 150 | 6 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e2d4b6030aa9798df06a2b5c583dd5bfaf2cf0b086242d7463ffec6a3a414a65 | f663c95395b1884ed3c37caef1fdcf4fe586365b101beda13a921520c1098a37 | 25af8db5994fb5236a714101198bd7ca0a576c26dc3669eeb50695cfa206b64c | 5e2157560008b055c8eef7ef07c7c6d16d8398cc0180782442a7862c190bda06 |
cat-searcher/leandojo-benchmark-4-random | test | 39 | MeasureTheory.integrable_of_intervalIntegral_norm_bounded | Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [← <a>intervalIntegral.integral_of_le</a> (hai.trans hbi)] | case h
ι : Type u_1
E : Type u_2
μ : Measure ℝ
l : Filter ι
inst✝² : l.NeBot
inst✝¹ : l.IsCountablyGenerated
inst✝ : NormedAddCommGroup E
a b : ι → ℝ
f : ℝ → E
I : ℝ
hfi : ∀ (i : ι), IntegrableOn f (Ioc (a i) (b i)) μ
ha : Tendsto a l atBot
hb : Tendsto b l atTop
h : ∀ᶠ (i : ι) in l, ∫ (x : ℝ) in a i..b i, ‖f x‖ ∂μ ≤ I... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c MeasureTheory.integral) (:c Real) (:c Real) (:c Real.normedAddCommGroup) ((:c InnerProductSpace.toNormedSpace) (:c Real) (:c Real) (:c Real.RCLike) (:c Real.normedAddCommGroup) ((:c RCLike.innerProductSpace) (:c Real) (:c Real.RCLike))) (:c Real.measurableSpace) ((:c MeasureT... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:c Real) (:c Real.measurableSpace))"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.129649))"},{"name":"inst✝²","sexp":"((:c Filter.NeBot) (:fv _uniq.129649) (:fv _uniq.129664))"},{"name":"ins... | (: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 MeasureTheory.integral) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129649","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129652","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rwa","sourceEnd":31537,"sourceStart":31534,"tag":"atom"},{"children":[{"source":"[","sourceEnd":31539,"sourceStart":31538,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":31542,"sourceStart":31539,"tag":"atom"}],"kind":"token.«← »","source"... | [] | [{"source":"intervalIntegral.integral_of_le (hai.trans hbi)","source_end":31590,"source_start":31543,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129649","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129652","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 150 | 7 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fd3fdb5ed018727f2d3e3b07481191dd669e0b9b964e9010bd7e7c6307d928fc | 5e2157560008b055c8eef7ef07c7c6d16d8398cc0180782442a7862c190bda06 | 0ea446eda2975ed98956801f2a7d7f5f2bbd5c96e1cc9fb56c7524d064c9bfee | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 40 | IntermediateField.separable_of_mem_isSeparable | Mathlib/FieldTheory/SeparableDegree.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>IntermediateField.minpoly_eq</a>] using <a>IsSeparable.separable</a> F (K := L) ⟨x, h⟩ | F : Type u
E : Type v
inst✝⁵ : Field F
inst✝⁴ : Field E
inst✝³ : Algebra F E
K : Type w
inst✝² : Field K
inst✝¹ : Algebra F K
L : IntermediateField F E
inst✝ : IsSeparable F ↥L
x : E
h : x ∈ L
⊢ (minpoly F x).Separable | ((:c Polynomial.Separable) (:fv _uniq.240365) ((:c Semifield.toCommSemiring) (:fv _uniq.240365) ((:c Field.toSemifield) (:fv _uniq.240365) (:fv _uniq.240370))) ((:c minpoly) (:fv _uniq.240365) (:fv _uniq.240367) ((:c EuclideanDomain.toCommRing) (:fv _uniq.240365) ((:c Field.toEuclideanDomain) (:fv _uniq.240365) (:fv _u... | [{"name":"F","sexp":"(:sort (+ u 1))"},{"name":"E","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁵","sexp":"((:c Field) (:fv _uniq.240365))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.240367))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.240365) (:fv _uniq.240367) ((:c Semifield.toCommSemiring) (:fv _uniq.240365... | (:app (:c Polynomial.Separable) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c minpoly) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explici... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.240365","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.240367","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":37888,"sourceStart":37883,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"minpoly_eq","source_end":37905,"source_start":37895,"syntax_kind":"ident"},{"source":"IsSeparable.separable F (K := L) ⟨x, h⟩","source_end":37956,"source_start":37913,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.240365","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.240367","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal... | 109 | 2 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b90f688a9807d9ba6256168c7f4d6d5e7109d04b574c59e2ff3d9d621924c556 | 3b7236c9145f5d36ceabe067f7619aebca1aa9c5fe469eae97f4435a18e302cf | 139493313ab6dec5992479601d6335300aa1e2104f6030ed9a8fad802402f4ce | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 41 | CochainComplex.mk'_d_1_0 | Mathlib/Algebra/Homology/HomologicalComplex.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | change <a>ite</a> (1 = 0 + 1) (d₀ ≫ 𝟙 X₁) 0 = d₀ | ι : Type u_1
V : Type u
inst✝¹ : Category.{v, u} V
inst✝ : HasZeroMorphisms V
X₀ X₁ X₂ : V
d₀ : X₀ ⟶ X₁
d₁ : X₁ ⟶ X₂
s : d₀ ≫ d₁ = 0
succ : (S : ShortComplex V) → (X₄ : V) ×' (d₂ : S.X₃ ⟶ X₄) ×' S.g ≫ d₂ = 0
succ' : {X₀ X₁ : V} → (f : X₀ ⟶ X₁) → (X₂ : V) ×' (d : X₁ ⟶ X₂) ×' f ≫ d = 0
⊢ (mk' X₀ X₁ d₀ fun {X₀ X₁} => succ... | ι : Type u_1
V : Type u
inst✝¹ : Category.{v, u} V
inst✝ : HasZeroMorphisms V
X₀ X₁ X₂ : V
d₀ : X₀ ⟶ X₁
d₁ : X₁ ⟶ X₂
s : d₀ ≫ d₁ = 0
succ : (S : ShortComplex V) → (X₄ : V) ×' (d₂ : S.X₃ ⟶ X₄) ×' S.g ≫ d₂ = 0
succ' : {X₀ X₁ : V} → (f : X₀ ⟶ X₁) → (X₂ : V) ×' (d : X₁ ⟶ X₂) ×' f ≫ d = 0
⊢ (if 1 = 0 + 1 then d₀ ≫ 𝟙 X₁ els... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.154455) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.154455) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.154455) (:fv _uniq.154458))) ((:c HomologicalComplex.X) (:c Nat) (:fv _uniq.154455) (:fv _uniq.154458) (:fv _uniq.154473) ((:c ComplexShape.up) (:c Nat) ... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.154455))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Limits.HasZeroMorphisms) (:fv _uniq.154455) (:fv _uniq.154458))"},{"name":"X₀","sexp":"(:fv _uniq.154455)"},{"name":"X₁"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c HomologicalComplex.X) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154453","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.154455","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"change","sourceEnd":39850,"sourceStart":39844,"tag":"atom"},{"children":[{"children":[{"name":"ite","semanticRole":"global","source":"ite","sourceEnd":39854,"sourceStart":39851,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":39856,"sourceStart":39855,"tag":"atom"},{"child... | [] | [{"source":"ite (1 = 0 + 1) (d₀ ≫ 𝟙 X₁) 0 = d₀","source_end":39896,"source_start":39851,"syntax_kind":"«term_=_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154453","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.154455","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":2,"internal... | 301 | 4 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d8d5ba2c7376461d4342cdc398295dc6eec2f0e18cfa8224697d6efb523a5635 | 4e1f6571a737bd726343ba925b478e45892a6cad4bab87f3f22fde792b98db6e | ebc61f65973ee531f0335ab1d450ba915e37df70d36a5e76a530cf665a1d6653 | 7f3bf0ac97d08f68189903624da614d9c1b78fdb3036f8a7130a221c586f517d |
cat-searcher/leandojo-benchmark-4-random | test | 42 | CochainComplex.mk'_d_1_0 | Mathlib/Algebra/Homology/HomologicalComplex.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>if_pos</a> <a>rfl</a>, <a>CategoryTheory.Category.comp_id</a>] | ι : Type u_1
V : Type u
inst✝¹ : Category.{v, u} V
inst✝ : HasZeroMorphisms V
X₀ X₁ X₂ : V
d₀ : X₀ ⟶ X₁
d₁ : X₁ ⟶ X₂
s : d₀ ≫ d₁ = 0
succ : (S : ShortComplex V) → (X₄ : V) ×' (d₂ : S.X₃ ⟶ X₄) ×' S.g ≫ d₂ = 0
succ' : {X₀ X₁ : V} → (f : X₀ ⟶ X₁) → (X₂ : V) ×' (d : X₁ ⟶ X₂) ×' f ≫ d = 0
⊢ (if 1 = 0 + 1 then d₀ ≫ 𝟙 X₁ els... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.154455) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.154455) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.154455) (:fv _uniq.154458))) (:fv _uniq.154475) (:fv _uniq.154477)) ((:c ite) ((:c Quiver.Hom) (:fv _uniq.154455) ((:c CategoryTheory.CategoryStruct.toQu... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.154455))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Limits.HasZeroMorphisms) (:fv _uniq.154455) (:fv _uniq.154458))"},{"name":"X₀","sexp":"(:fv _uniq.154455)"},{"name":"X₁"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV4)) (:arg :explicit 3 (:fv FV5)))) (:arg :explicit 1 (:app (:c ite) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154453","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.154455","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rw","sourceEnd":39901,"sourceStart":39899,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":39903,"sourceStart":39902,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"if_... | [] | [{"source":"if_pos rfl","source_end":39913,"source_start":39903,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Category.comp_id","source_end":39931,"source_start":39915,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154453","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.154455","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":2,"internal... | 301 | 5 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d5a9163644f06dc97792cf493572408a5832425b388821e031fd4c464398caa3 | 7f3bf0ac97d08f68189903624da614d9c1b78fdb3036f8a7130a221c586f517d | 3702c5a79863fea3093589088ec3e6215cd22b2a40442be2d50594b30a96ad1c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 43 | Equiv.Perm.prod_comp' | Mathlib/Algebra/BigOperators/Group/Finset.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert σ.prod_comp s (fun x => f x (σ.symm x)) hs | ι : Type u_1
κ : Type u_2
α : Type u_3
β : Type u_4
γ : Type u_5
s✝ s₁ s₂ : Finset α
a : α
f✝ g : α → β
inst✝ : CommMonoid β
σ : Equiv.Perm α
s : Finset α
f : α → α → β
hs : {a | σ a ≠ a} ⊆ ↑s
⊢ ∏ x ∈ s, f (σ x) x = ∏ x ∈ s, f x ((Equiv.symm σ) x) | case h.e'_2.a.h.e'_2
ι : Type u_1
κ : Type u_2
α : Type u_3
β : Type u_4
γ : Type u_5
s✝ s₁ s₂ : Finset α
a : α
f✝ g : α → β
inst✝ : CommMonoid β
σ : Equiv.Perm α
s : Finset α
f : α → α → β
hs : {a | σ a ≠ a} ⊆ ↑s
x✝ : α
a✝ : x✝ ∈ s
⊢ x✝ = (Equiv.symm σ) (σ x✝) | ((:c Eq) (:fv _uniq.43027) ((:c Finset.prod) (:fv _uniq.43024) (:fv _uniq.43027) (:fv _uniq.43052) (:fv _uniq.43403) (:lambda x (:fv _uniq.43024) ((:fv _uniq.43404) ((:c DFunLike.coe) ((:c Equiv.Perm) (:fv _uniq.43024)) (:fv _uniq.43024) (:lambda _ (:fv _uniq.43024) (:fv _uniq.43024)) ((:c Equiv.instFunLike) (:fv _uniq... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"κ","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"s✝","sexp":"((:c Finset) (:fv _uniq.43024))"},{"name":"s₁","sexp":"((:c Finset) (:fv _uniq.43024))"},{"name":"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c Finset.prod) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c CommMonoid) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 3 (:fv FV14)) (:arg :explicit 4 (:lambda x :explicit (:fv FV2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43018","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.43021","is_instance":false,"is_let":false,"name":"κ","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"convert","sourceEnd":20705,"sourceStart":20698,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"σ.prod_comp","sourceEnd":20718,"sourceStart":20706,"tag":"identifier"},{"children":[{"contextIndex":1... | [] | [{"source":"σ.prod_comp s (fun x => f x (σ.symm x)) hs","source_end":20750,"source_start":20706,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43018","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.43021","is_instance":false,"is_let":false,"user_name":"κ"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 137 | 4 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f47f014e9297abf09efd07e883e0faf71a8cdd9bba610973f3e06b9ab1f177ce | ef7dc74c69cdc0123b83e023efdf85fc0d2aa6f1e8b71dd2c980082da495bb57 | 8357362720578a51db6bedc4290b45865e69ab6b67d14d72149c693bd9365b29 | 3da535bedc53e304aed8d6c12d274d67ea20c6a0629b9c5c987d66ff234a4aa9 |
cat-searcher/leandojo-benchmark-4-random | test | 44 | Equiv.Perm.prod_comp' | Mathlib/Algebra/BigOperators/Group/Finset.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Equiv.symm_apply_apply</a>] | case h.e'_2.a.h.e'_2
ι : Type u_1
κ : Type u_2
α : Type u_3
β : Type u_4
γ : Type u_5
s✝ s₁ s₂ : Finset α
a : α
f✝ g : α → β
inst✝ : CommMonoid β
σ : Equiv.Perm α
s : Finset α
f : α → α → β
hs : {a | σ a ≠ a} ⊆ ↑s
x✝ : α
a✝ : x✝ ∈ s
⊢ x✝ = (Equiv.symm σ) (σ x✝) | ((:c Eq) (:fv _uniq.43024) (:fv _uniq.43859) ((:c DFunLike.coe) ((:c Equiv) (:fv _uniq.43024) (:fv _uniq.43024)) (:fv _uniq.43024) (:lambda _ (:fv _uniq.43024) (:fv _uniq.43024)) ((:c Equiv.instFunLike) (:fv _uniq.43024) (:fv _uniq.43024)) ((:c Equiv.symm) (:fv _uniq.43024) (:fv _uniq.43024) (:fv _uniq.43402)) ((:c DFu... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"κ","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"s✝","sexp":"((:c Finset) (:fv _uniq.43024))"},{"name":"s₁","sexp":"((:c Finset) (:fv _uniq.43024))"},{"name":"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:fv FV17)) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Equiv) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV2)))) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c FunLi... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43018","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.43021","is_instance":false,"is_let":false,"name":"κ","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":20755,"sourceStart":20753,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":20757,"sourceStart":20756,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Equiv.symm_apply... | [] | [{"source":"Equiv.symm_apply_apply","source_end":20779,"source_start":20757,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43018","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.43021","is_instance":false,"is_let":false,"user_name":"κ"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 137 | 5 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bcbe436fd6fb7ea2aa6f6992ccf740bcebd8728f9297070b1590e257d885787e | 3da535bedc53e304aed8d6c12d274d67ea20c6a0629b9c5c987d66ff234a4aa9 | 6f58f075be90bbf4874e56c4b39c10b359b7e5c2ce89bb0c25eb77946eda3c06 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 45 | Finmap.erase_toFinmap | Mathlib/Data/Finmap.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Finmap.erase</a>] | α : Type u
β : α → Type v
inst✝ : DecidableEq α
a : α
s : AList β
⊢ erase a ⟦s⟧ = ⟦AList.erase a s⟧ | ((:c Eq) ((:c Finmap) (:fv _uniq.35564) (:fv _uniq.35568)) ((:c Finmap.erase) (:fv _uniq.35564) (:fv _uniq.35568) (:fv _uniq.35575) (:fv _uniq.35931) ((:c AList.toFinmap) (:fv _uniq.35564) (:fv _uniq.35568) (:fv _uniq.35932))) ((:c AList.toFinmap) (:fv _uniq.35564) (:fv _uniq.35568) ((:c AList.erase) (:fv _uniq.35564) ... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:forall _ (:fv _uniq.35564) (:sort (+ v 1)))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.35564))"},{"name":"a","sexp":"(:fv _uniq.35564)"},{"name":"s","sexp":"((:c AList) (:fv _uniq.35564) (:fv _uniq.35568))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Finmap) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))) (:arg :explicit 1 (:app (:c Finmap.erase) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :instance 2 (:instance-of (:app (:c DecidableEq) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 3 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35564","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35568","is_instance":false,"is_let":false,"name":"β","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"}... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":15268,"sourceStart":15264,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"erase","source_end":15275,"source_start":15270,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35564","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35568","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 142 | 2 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a356ec16a94eb4f9ee3eb817faae8b6e29474d2224580884eda639c099b0db4d | 815b3da68cf881e40d2a118946ca747d06cc5199bfbde557487e53eba3bff177 | 758b81d79722503abba5f9a5152927bb58e41356502a7f43ce7c1fb04fcec548 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 46 | Filter.HasBasis.to_hasBasis' | Mathlib/Order/Filter/Bases.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨fun t => ⟨fun ht => ?_, fun ⟨i', hi', ht⟩ => <a>Filter.mem_of_superset</a> (h' i' hi') ht⟩⟩ | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
l l' : Filter α
p : ι → Prop
s : ι → Set α
t : Set α
i : ι
p' : ι' → Prop
s' : ι' → Set α
i' : ι'
hl : l.HasBasis p s
h : ∀ (i : ι), p i → ∃ i', p' i' ∧ s' i' ⊆ s i
h' : ∀ (i' : ι'), p' i' → s' i' ∈ l
⊢ l.HasBasis p' s' | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
l l' : Filter α
p : ι → Prop
s : ι → Set α
t✝ : Set α
i : ι
p' : ι' → Prop
s' : ι' → Set α
i' : ι'
hl : l.HasBasis p s
h : ∀ (i : ι), p i → ∃ i', p' i' ∧ s' i' ⊆ s i
h' : ∀ (i' : ι'), p' i' → s' i' ∈ l
t : Set α
ht : t ∈ l
⊢ ∃ i, p' i ∧ s' i ⊆ t | ((:c Filter.HasBasis) (:fv _uniq.14836) (:fv _uniq.14848) (:fv _uniq.14851) (:fv _uniq.14873) (:fv _uniq.14878)) | [{"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":"l","sexp":"((:c Filter) (:fv _uniq.14836))"},{"name":"l'","sexp":"((:c Filter) (:fv _uniq.14836))"},{"name":"p","sexp":"(... | (:app (:c Filter.HasBasis) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV4)) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:fv FV11)) (:arg :explicit 4 (:fv FV12))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14836","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14839","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":15477,"sourceStart":15471,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":15481,"sourceStart":15478,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":15484,"sourceStart":15481,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","sourc... | [] | [{"source":"⟨fun t => ⟨fun ht => ?_, fun ⟨i', hi', ht⟩ => mem_of_superset (h' i' hi') ht⟩⟩","source_end":15568,"source_start":15478,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14836","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14839","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 92 | 4 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2bf119b310a9ee07870adfe9fb51d755fe0acb09f4532b14e9876fabae225069 | 17ba5286e1b8c3b3e3c346b2d35d0d69da8dc8f52b39fee721794a8933d335f1 | f4d197f1d12dc37dfebfce7e49fe4c0b4ea18dbd69f4e21ed678a24470e97719 | 38730305f65c6c841e2c8b723a448f8a1ba22df758b0e02568cc06394f3cd7ad |
cat-searcher/leandojo-benchmark-4-random | test | 47 | Filter.HasBasis.to_hasBasis' | Mathlib/Order/Filter/Bases.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases hl.mem_iff.1 ht with ⟨i, hi, ht⟩ | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
l l' : Filter α
p : ι → Prop
s : ι → Set α
t✝ : Set α
i : ι
p' : ι' → Prop
s' : ι' → Set α
i' : ι'
hl : l.HasBasis p s
h : ∀ (i : ι), p i → ∃ i', p' i' ∧ s' i' ⊆ s i
h' : ∀ (i' : ι'), p' i' → s' i' ∈ l
t : Set α
ht : t ∈ l
⊢ ∃ i, p' i ∧ s' i ⊆ t | case intro.intro
α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
l l' : Filter α
p : ι → Prop
s : ι → Set α
t✝ : Set α
i✝ : ι
p' : ι' → Prop
s' : ι' → Set α
i' : ι'
hl : l.HasBasis p s
h : ∀ (i : ι), p i → ∃ i', p' i' ∧ s' i' ⊆ s i
h' : ∀ (i' : ι'), p' i' → s' i' ∈ l
t : Set α
ht✝ : t ∈ l
i : ι
hi : p... | ((:c Exists) (:fv _uniq.14848) (:lambda i (:fv _uniq.14848) ((:c And) ((:fv _uniq.14873) 0) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.14836)) ((:c Set.instHasSubset) (:fv _uniq.14836)) ((:fv _uniq.14878) 0) (:fv _uniq.15029))))) | [{"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":"l","sexp":"((:c Filter) (:fv _uniq.14836))"},{"name":"l'","sexp":"((:c Filter) (:fv _uniq.14836))"},{"name":"p","sexp":"(... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:lambda i :explicit (:fv FV4) (:app (:c And) (:arg :explicit 0 (:app (:fv FV11) (:arg :explicit 0 0))) (:arg :explicit 1 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14836","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14839","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rcases","sourceEnd":15577,"sourceStart":15571,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":"hl.mem_iff","sourceEnd":15588,"sourceStart":15578,"tag":"identifier"},{"source":".","sourceEnd":15589,"sourceStart":15... | [] | [{"source":"hl.mem_iff.1 ht","source_end":15593,"source_start":15578,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨i, hi, ht⟩","source_end":15614,"source_start":15599,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14836","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14839","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 92 | 5 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f13746b82608b0b8060b385ec7c750cefd272efc04ac2ece5f26dd02fe4905e7 | 38730305f65c6c841e2c8b723a448f8a1ba22df758b0e02568cc06394f3cd7ad | 3a70ea4596a08d87a813fa43efd691ffc8d4cae835866e603bf207cdaa8eb81b | 1744fd91eedc3523851b259088e9f46f5260e27b560f2b3a72eb469397ebd867 |
cat-searcher/leandojo-benchmark-4-random | test | 48 | Filter.HasBasis.to_hasBasis' | Mathlib/Order/Filter/Bases.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases h i hi with ⟨i', hi', hs's⟩ | case intro.intro
α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
l l' : Filter α
p : ι → Prop
s : ι → Set α
t✝ : Set α
i✝ : ι
p' : ι' → Prop
s' : ι' → Set α
i' : ι'
hl : l.HasBasis p s
h : ∀ (i : ι), p i → ∃ i', p' i' ∧ s' i' ⊆ s i
h' : ∀ (i' : ι'), p' i' → s' i' ∈ l
t : Set α
ht✝ : t ∈ l
i : ι
hi : p... | case intro.intro.intro.intro
α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
l l' : Filter α
p : ι → Prop
s : ι → Set α
t✝ : Set α
i✝ : ι
p' : ι' → Prop
s' : ι' → Set α
i'✝ : ι'
hl : l.HasBasis p s
h : ∀ (i : ι), p i → ∃ i', p' i' ∧ s' i' ⊆ s i
h' : ∀ (i' : ι'), p' i' → s' i' ∈ l
t : Set α
ht✝ : t ∈ l... | ((:c Exists) (:fv _uniq.14848) (:lambda i (:fv _uniq.14848) ((:c And) ((:fv _uniq.14873) 0) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.14836)) ((:c Set.instHasSubset) (:fv _uniq.14836)) ((:fv _uniq.14878) 0) (:fv _uniq.15029))))) | [{"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":"l","sexp":"((:c Filter) (:fv _uniq.14836))"},{"name":"l'","sexp":"((:c Filter) (:fv _uniq.14836))"},{"name":"p","sexp":"(... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:lambda i :explicit (:fv FV4) (:app (:c And) (:arg :explicit 0 (:app (:fv FV11) (:arg :explicit 0 0))) (:arg :explicit 1 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14836","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14839","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rcases","sourceEnd":15623,"sourceStart":15617,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"contextIndex":16,"semanticRole":"local","source":"h","sourceEnd":15625,"sourceStart":15624,"tag":"identifier"},{"children":[{"contextIndex":... | [] | [{"source":"h i hi","source_end":15630,"source_start":15624,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨i', hi', hs's⟩","source_end":15655,"source_start":15636,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14836","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14839","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 92 | 6 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 11c982e584de7fe7523e2644d001e0ce37485fe87b3941bfde9d5962266a008a | 1744fd91eedc3523851b259088e9f46f5260e27b560f2b3a72eb469397ebd867 | abd772b5ca55e4d63b9a091a6d9c5922f0c96fa7d4713f0b73e99260b3fa0e3e | e33d3a488043d3748038d253e38658ef89a79f2074473da8bb7fee720a505b57 |
cat-searcher/leandojo-benchmark-4-random | test | 49 | Filter.HasBasis.to_hasBasis' | Mathlib/Order/Filter/Bases.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨i', hi', hs's.trans ht⟩ | case intro.intro.intro.intro
α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
l l' : Filter α
p : ι → Prop
s : ι → Set α
t✝ : Set α
i✝ : ι
p' : ι' → Prop
s' : ι' → Set α
i'✝ : ι'
hl : l.HasBasis p s
h : ∀ (i : ι), p i → ∃ i', p' i' ∧ s' i' ⊆ s i
h' : ∀ (i' : ι'), p' i' → s' i' ∈ l
t : Set α
ht✝ : t ∈ l... | ((:c Exists) (:fv _uniq.14848) (:lambda i (:fv _uniq.14848) ((:c And) ((:fv _uniq.14873) 0) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.14836)) ((:c Set.instHasSubset) (:fv _uniq.14836)) ((:fv _uniq.14878) 0) (:fv _uniq.15029))))) | [{"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":"l","sexp":"((:c Filter) (:fv _uniq.14836))"},{"name":"l'","sexp":"((:c Filter) (:fv _uniq.14836))"},{"name":"p","sexp":"(... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:lambda i :explicit (:fv FV4) (:app (:c And) (:arg :explicit 0 (:app (:fv FV11) (:arg :explicit 0 0))) (:arg :explicit 1 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14836","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14839","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":15663,"sourceStart":15658,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":15667,"sourceStart":15664,"tag":"atom"},{"children":[{"contextIndex":23,"semanticRole":"local","source":"i'","sourceEnd":15669,"sourceStart":15667,"tag":"identifier"},{"source":",","sourceEnd":15670... | [] | [{"source":"⟨i', hi', hs's.trans ht⟩","source_end":15692,"source_start":15664,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14836","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14839","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 92 | 7 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 544895f9809721e37d947946ddba9c6f25b85b0ddf8aecf070dfdcfd312f3d25 | e33d3a488043d3748038d253e38658ef89a79f2074473da8bb7fee720a505b57 | 961359ccf92ee928d98b4097cb308dbd1db0a01f8e137fcb5a630c7378e1f3f0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 50 | FreeAlgebra.toTensor_ι | Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>FreeAlgebra.toTensor</a>] | R : Type u_1
inst✝² : CommSemiring R
M : Type u_2
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
m : M
⊢ toTensor (ι R m) = (TensorAlgebra.ι R) m | ((:c Eq) ((:c TensorAlgebra) (:fv _uniq.182529) (:fv _uniq.182532) (:fv _uniq.182535) (:fv _uniq.182538) (:fv _uniq.182722)) ((:c DFunLike.coe) ((:c AlgHom) (:fv _uniq.182529) ((:c FreeAlgebra) (:fv _uniq.182529) (:fv _uniq.182532) (:fv _uniq.182535)) ((:c TensorAlgebra) (:fv _uniq.182529) (:fv _uniq.182532) (:fv _uniq... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.182529))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c AddCommMonoid) (:fv _uniq.182535))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.182529) (:fv _uniq.182535) ((:c CommSemiring.toSemiring) (... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c TensorAlgebra) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:ins... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.182529","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.182532","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CommSemiring) (:arg :... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":14810,"sourceStart":14806,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"toTensor","source_end":14820,"source_start":14812,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.182529","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.182532","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inte... | 83 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f20d41e562db43902b1f023bb10d23186e40f0683ba33b53a403af47d7600aa0 | 874c2a5c037ff47dbef443b8029fd529d2c475c3730cf311ee33179a81702dd3 | 14f5733c46fdbb36a9357935b5149adb46cb617235d26815daa3842188ef90f0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 51 | Algebra.map_leftMulMatrix_localization | Mathlib/RingTheory/Localization/NormTrace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext i j | R : Type u_1
S : Type u_2
inst✝¹⁴ : CommRing R
inst✝¹³ : CommRing S
inst✝¹² : Algebra R S
Rₘ : Type u_3
Sₘ : Type u_4
inst✝¹¹ : CommRing Rₘ
inst✝¹⁰ : Algebra R Rₘ
inst✝⁹ : CommRing Sₘ
inst✝⁸ : Algebra S Sₘ
M : Submonoid R
inst✝⁷ : IsLocalization M Rₘ
inst✝⁶ : IsLocalization (algebraMapSubmonoid S M) Sₘ
inst✝⁵ : Algebra... | case a
R : Type u_1
S : Type u_2
inst✝¹⁴ : CommRing R
inst✝¹³ : CommRing S
inst✝¹² : Algebra R S
Rₘ : Type u_3
Sₘ : Type u_4
inst✝¹¹ : CommRing Rₘ
inst✝¹⁰ : Algebra R Rₘ
inst✝⁹ : CommRing Sₘ
inst✝⁸ : Algebra S Sₘ
M : Submonoid R
inst✝⁷ : IsLocalization M Rₘ
inst✝⁶ : IsLocalization (algebraMapSubmonoid S M) Sₘ
inst✝⁵ : ... | ((:c Eq) ((:c Matrix) (:fv _uniq.14499) (:fv _uniq.14499) (:fv _uniq.8327)) ((:c DFunLike.coe) ((:c RingHom) ((:c Matrix) (:fv _uniq.14499) (:fv _uniq.14499) (:fv _uniq.8026)) ((:c Matrix) (:fv _uniq.14499) (:fv _uniq.14499) (:fv _uniq.8327)) ((:c Matrix.nonAssocSemiring) (:fv _uniq.14499) (:fv _uniq.8026) ((:c Semirin... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁴","sexp":"((:c CommRing) (:fv _uniq.8026))"},{"name":"inst✝¹³","sexp":"((:c CommRing) (:fv _uniq.8029))"},{"name":"inst✝¹²","sexp":"((:c Algebra) (:fv _uniq.8026) (:fv _uniq.8029) ((:c CommRing.toCommSemiring) (:fv _uniq.80... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV19)) (:arg :explicit 1 (:fv FV19)) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c RingHom) (:arg :explicit 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV19)) (:arg :explicit 1 (:fv F... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.8026","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.8029","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"ext","sourceEnd":2068,"sourceStart":2065,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"i","sourceEnd":2070,"sourceStart":2069,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"i","sourceEnd":2070,"sourceStart":2069,"tag":"nod... | [{"role":"fresh_name","source":"i","source_end":2070,"source_start":2069,"syntax_kind":"ident"},{"role":"fresh_name","source":"j","source_end":2072,"source_start":2071,"syntax_kind":"ident"}] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.8026","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.8029","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 9 | 4 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4747b725fdbdb3f09f47647989e2aed05e3d8e0c480f22385b202e3370ec1be7 | 0d0a03d53ff0bf8cccdff04979b12d2d8e6e9dcab10d7f2cd31f67239c651da4 | a9a7858838d56587510e440c847bae11ef8d1a0c1ec173ba56623a40573a739a | 63317c806e77515fc1f78487b9e507197b1f4ee208a1675f1abaa379cfd106b7 |
cat-searcher/leandojo-benchmark-4-random | test | 52 | Algebra.map_leftMulMatrix_localization | Mathlib/RingTheory/Localization/NormTrace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Matrix.map_apply</a>, <a>RingHom.mapMatrix_apply</a>, <a>Algebra.leftMulMatrix_eq_repr_mul</a>, ← <a>map_mul</a>, <a>Basis.localizationLocalization_apply</a>, <a>Basis.localizationLocalization_repr_algebraMap</a>] | case a
R : Type u_1
S : Type u_2
inst✝¹⁴ : CommRing R
inst✝¹³ : CommRing S
inst✝¹² : Algebra R S
Rₘ : Type u_3
Sₘ : Type u_4
inst✝¹¹ : CommRing Rₘ
inst✝¹⁰ : Algebra R Rₘ
inst✝⁹ : CommRing Sₘ
inst✝⁸ : Algebra S Sₘ
M : Submonoid R
inst✝⁷ : IsLocalization M Rₘ
inst✝⁶ : IsLocalization (algebraMapSubmonoid S M) Sₘ
inst✝⁵ : ... | ((:c Eq) (:fv _uniq.8327) ((:c DFunLike.coe) ((:c RingHom) ((:c Matrix) (:fv _uniq.14499) (:fv _uniq.14499) (:fv _uniq.8026)) ((:c Matrix) (:fv _uniq.14499) (:fv _uniq.14499) (:fv _uniq.8327)) ((:c Matrix.nonAssocSemiring) (:fv _uniq.14499) (:fv _uniq.8026) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.8026) ((:c CommSe... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁴","sexp":"((:c CommRing) (:fv _uniq.8026))"},{"name":"inst✝¹³","sexp":"((:c CommRing) (:fv _uniq.8029))"},{"name":"inst✝¹²","sexp":"((:c Algebra) (:fv _uniq.8026) (:fv _uniq.8029) ((:c CommRing.toCommSemiring) (:fv _uniq.80... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c RingHom) (:arg :explicit 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV19)) (:arg :explicit 1 (:fv FV19)) (:arg :explicit 2 (:fv FV0)))) (:arg :explicit 1 (:app (:c Matrix) (:arg :explicit 0 (:fv FV... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.8026","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.8029","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"simp","sourceEnd":2079,"sourceStart":2075,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":2084,"sourceStart":2080,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":2084,"s... | [] | [{"source":"Matrix.map_apply","source_end":2102,"source_start":2086,"syntax_kind":"ident"},{"source":"RingHom.mapMatrix_apply","source_end":2127,"source_start":2104,"syntax_kind":"ident"},{"source":"leftMulMatrix_eq_repr_mul","source_end":2154,"source_start":2129,"syntax_kind":"ident"},{"source":"map_mul","source_end":... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.8026","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.8029","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 9 | 5 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 85cc646f1ac5a25cf4f9706317d2c4bd03b97c53aa45288da169c1858a64b46e | 63317c806e77515fc1f78487b9e507197b1f4ee208a1675f1abaa379cfd106b7 | 5f375291ee03087bcb251af548cd2e56641393de99d5e1a3faeebc2440f836ee | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 53 | Polynomial.Monic.degree_mul_comm | Mathlib/Algebra/Polynomial/Monic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases h : q = 0 | R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p q✝ r : R[X]
hp : p.Monic
q : R[X]
⊢ (p * q).degree = (q * p).degree | case pos
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p q✝ r : R[X]
hp : p.Monic
q : R[X]
h : q = 0
⊢ (p * q).degree = (q * p).degree
case neg
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p q✝ r : R[X]
hp : p.Monic
q : R[X]
h : ¬q = 0
⊢ (p * q).degree = (q * p).degree | ((:c Eq) ((:c WithBot) (:c Nat)) ((:c Polynomial.degree) (:fv _uniq.41781) (:fv _uniq.41796) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.41781) (:fv _uniq.41796)) ((:c Polynomial) (:fv _uniq.41781) (:fv _uniq.41796)) ((:c Polynomial) (:fv _uniq.41781) (:fv _uniq.41796)) ((:c instHMul) ((:c Polynomial) (:fv _uniq.41781)... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.41781)"},{"name":"b","sexp":"(:fv _uniq.41781)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.41781))"},{"n... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41781","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41783","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"by_cases","sourceEnd":7293,"sourceStart":7285,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":7295,"sourceStart":7294,"tag":"identifier"},{"source":":","sourceEnd":7297,"sourceStart":7296,"tag":"atom"}],"kind":"null","source":"h :","sourceEnd":7297,"sourceStart... | [] | [{"source":"q = 0","source_end":7303,"source_start":7298,"syntax_kind":"«term_=_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41781","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41783","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 52 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c1d2d73c3d20fa2326adb23114efbac261c0bc7c20c56b2531062e2b8197de33 | 11a14a1e346660e8ef9db5f0fa1dfa563cee04118ce1e7e8b1ff78bec255765a | a7f0aafc0c23f335ae3588ae25292fc573ed1b35dde0b52b648e36e9401a59ee | fe6bb892dc54dffc2f4639cb57ba30bf69c79ef8af06abdfc10539a77f512b56 |
cat-searcher/leandojo-benchmark-4-random | test | 54 | Polynomial.Monic.degree_mul_comm | Mathlib/Algebra/Polynomial/Monic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Polynomial.degree_mul'</a>, hp.degree_mul] | case neg
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p q✝ r : R[X]
hp : p.Monic
q : R[X]
h : ¬q = 0
⊢ (p * q).degree = (q * p).degree | case neg
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p q✝ r : R[X]
hp : p.Monic
q : R[X]
h : ¬q = 0
⊢ p.degree + q.degree = q.degree + p.degree
case neg
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p q✝ r : R[X]
hp : p.Monic
q : R[X]
h : ¬q = 0
⊢ p.leadingCoeff * q.leading... | ((:c Eq) ((:c WithBot) (:c Nat)) ((:c Polynomial.degree) (:fv _uniq.41781) (:fv _uniq.41796) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.41781) (:fv _uniq.41796)) ((:c Polynomial) (:fv _uniq.41781) (:fv _uniq.41796)) ((:c Polynomial) (:fv _uniq.41781) (:fv _uniq.41796)) ((:c instHMul) ((:c Polynomial) (:fv _uniq.41781)... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.41781)"},{"name":"b","sexp":"(:fv _uniq.41781)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.41781))"},{"n... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41781","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41783","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":7322,"sourceStart":7320,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7324,"sourceStart":7323,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Polynomial.degree_mu... | [] | [{"source":"degree_mul'","source_end":7335,"source_start":7324,"syntax_kind":"ident"},{"source":"hp.degree_mul","source_end":7350,"source_start":7337,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41781","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41783","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 52 | 10 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e2117d1a7324206b9efdd96b4dc5f7e647e6e166644eb4221b57ab93a553520d | 1e62df66855a127835447d97827b4798e92563f3b47959f4ba535b265d67f6a2 | acd9d9e75762edd684df8e3aad391b5e94f8723c63d09aa60ddd62c06d4493fa | 6f673da8ed1ab9a3664bbdfcbc435ca4c6087ff3d1b43f9b5a2b81d1e106cf6b |
cat-searcher/leandojo-benchmark-4-random | test | 55 | Polynomial.Monic.degree_mul_comm | Mathlib/Algebra/Polynomial/Monic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [h] | case pos
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p q✝ r : R[X]
hp : p.Monic
q : R[X]
h : q = 0
⊢ (p * q).degree = (q * p).degree | ((:c Eq) ((:c WithBot) (:c Nat)) ((:c Polynomial.degree) (:fv _uniq.41781) (:fv _uniq.41796) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.41781) (:fv _uniq.41796)) ((:c Polynomial) (:fv _uniq.41781) (:fv _uniq.41796)) ((:c Polynomial) (:fv _uniq.41781) (:fv _uniq.41796)) ((:c instHMul) ((:c Polynomial) (:fv _uniq.41781)... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.41781)"},{"name":"b","sexp":"(:fv _uniq.41781)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.41781))"},{"n... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41781","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41783","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":7313,"sourceStart":7309,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"h","source_end":7316,"source_start":7315,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41781","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41783","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 52 | 7 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bf8175d30938e2eeb94344d208e3764d8c055c3f639b20b893d76f5cea5cb07c | 3a2664adddc1d9bb71db32246bac1ba3b49c0e11cfddab21a497ffb5a9eb24c0 | 80b5426f4cd8afb2daab5c530b5abbdb5bd333c6b56653091017c22104b3e089 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 56 | Polynomial.Monic.degree_mul_comm | Mathlib/Algebra/Polynomial/Monic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>add_comm</a> _ _ | case neg
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p q✝ r : R[X]
hp : p.Monic
q : R[X]
h : ¬q = 0
⊢ p.degree + q.degree = q.degree + p.degree | ((:c Eq) ((:c WithBot) (:c Nat)) ((:c HAdd.hAdd) ((:c WithBot) (:c Nat)) ((:c WithBot) (:c Nat)) ((:c WithBot) (:c Nat)) ((:c instHAdd) ((:c WithBot) (:c Nat)) ((:c WithBot.add) (:c Nat) (:c instAddNat))) ((:c Polynomial.degree) (:fv _uniq.41781) (:fv _uniq.41796) (:fv _uniq.41809)) ((:c Polynomial.degree) (:fv _uniq.4... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.41781)"},{"name":"b","sexp":"(:fv _uniq.41781)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.41781))"},{"n... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :implicit-type 1 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :implicit-type 2 (:app (:c WithBot) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41781","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41783","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":7362,"sourceStart":7357,"tag":"atom"},{"children":[{"name":"add_comm","semanticRole":"global","source":"add_comm","sourceEnd":7371,"sourceStart":7363,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":7373,"sourceStar... | [] | [{"source":"add_comm _ _","source_end":7375,"source_start":7363,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41781","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41783","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 52 | 16 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 59db634a916c2840c436a837ca0b32f5ceb12dc1f19c880b2d0c828235abe0cc | 936919343a2aec6d04e6ad2fe2398c36db8e0c12bc0e5e3014b8f0efa7e5499c | 997838ad0346c8c17007d143290d2827fcd9a7db49373a123c0224aae96b4a4b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 57 | Polynomial.Monic.degree_mul_comm | Mathlib/Algebra/Polynomial/Monic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [hp.leadingCoeff, <a>one_mul</a>, <a>Polynomial.leadingCoeff_ne_zero</a>] | case neg
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p q✝ r : R[X]
hp : p.Monic
q : R[X]
h : ¬q = 0
⊢ p.leadingCoeff * q.leadingCoeff ≠ 0 | ((:c Ne) (:fv _uniq.41781) ((:c HMul.hMul) (:fv _uniq.41781) (:fv _uniq.41781) (:fv _uniq.41781) ((:c instHMul) (:fv _uniq.41781) ((:c NonUnitalNonAssocSemiring.toMul) (:fv _uniq.41781) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.41781) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.41781) (:fv _uniq.41... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.41781)"},{"name":"b","sexp":"(:fv _uniq.41781)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.41781))"},{"n... | (:app (:c Ne) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HMul.hMul) (: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 HMul) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41781","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41783","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":7384,"sourceStart":7381,"tag":"atom"},{"children":[{"source":"[","sourceEnd":7386,"sourceStart":7385,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Polynomial.Monic.leadingCoeff","sem... | [] | [{"source":"hp.leadingCoeff","source_end":7401,"source_start":7386,"syntax_kind":"ident"},{"source":"one_mul","source_end":7410,"source_start":7403,"syntax_kind":"ident"},{"source":"leadingCoeff_ne_zero","source_end":7432,"source_start":7412,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41781","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41783","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 52 | 21 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0fa2407d00a700a2ae94871e14180ca65a5e8f211901c45ad658ab57d8d6b322 | d8a0a0161b5c72da27fe69ce7e6ba1b8506feac0903218dfc057f8d5a24f7d76 | 30333ab8e1f01c9a3d3d2424f9dd9170fb035880d966e3ddc0bff459115ff4ce | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 58 | List.head_cyclicPermutations | Mathlib/Data/List/Rotate.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h : 0 < <a>List.length</a> (<a>List.cyclicPermutations</a> l) := <a>List.length_pos_of_ne_nil</a> (<a>List.cyclicPermutations_ne_nil</a> _) | α : Type u
l✝ l' l : List α
⊢ l.cyclicPermutations.head ⋯ = l | α : Type u
l✝ l' l : List α
h : 0 < l.cyclicPermutations.length
⊢ l.cyclicPermutations.head ⋯ = l | ((:c Eq) ((:c List) (:fv _uniq.34360)) ((:c List.head) ((:c List) (:fv _uniq.34360)) ((:c List.cyclicPermutations) (:fv _uniq.34360) (:fv _uniq.34390)) ((:c List.cyclicPermutations_ne_nil) (:fv _uniq.34360) (:fv _uniq.34390))) (:fv _uniq.34390)) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"l✝","sexp":"((:c List) (:fv _uniq.34360))"},{"name":"l'","sexp":"((:c List) (:fv _uniq.34360))"},{"name":"l","sexp":"((:c List) (:fv _uniq.34360))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c List.head) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c List.cyclicPermutations) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV4)))) (:arg :pr... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34360","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.34363","is_instance":false,"is_let":false,"name":"l✝","sexp":"(:app (:c List) (:arg :explicit 0 (:fv FV0)))... | {"children":[{"source":"have","sourceEnd":25495,"sourceStart":25491,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":25497,"sourceStart":25496,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":25497,"sourceStart":25496,"tag":"node"... | [] | [{"source":"0 < length (cyclicPermutations l)","source_end":25533,"source_start":25500,"syntax_kind":"«term_<_»"},{"source":"length_pos_of_ne_nil (cyclicPermutations_ne_nil _)","source_end":25587,"source_start":25537,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34360","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.34363","is_instance":false,"is_let":false,"user_name":"l✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 172 | 4 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 10e96f43e3e4f3f85682d8ee2ae99ee5008cc01b8d10546538d8fb1e3c9bcb6a | 1c2bf7ef96edb91cd43256e45ce05f0e43b6d96c87e8b7d93a8a510036105525 | 4add78709ddca503915449b894d2b2e632fe4b0ca16ff5fa9f71a5bddcbe66f0 | f4b81f548a19b735aad2f6472bf96d499d55812f5065ec9ce89896afda287c9e |
cat-searcher/leandojo-benchmark-4-random | test | 59 | List.head_cyclicPermutations | Mathlib/Data/List/Rotate.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>List.get_mk_zero</a> h, <a>List.get_cyclicPermutations</a>, <a>Fin.val_mk</a>, <a>List.rotate_zero</a>] | α : Type u
l✝ l' l : List α
h : 0 < l.cyclicPermutations.length
⊢ l.cyclicPermutations.head ⋯ = l | ((:c Eq) ((:c List) (:fv _uniq.34360)) ((:c List.head) ((:c List) (:fv _uniq.34360)) ((:c List.cyclicPermutations) (:fv _uniq.34360) (:fv _uniq.34390)) ((:c List.cyclicPermutations_ne_nil) (:fv _uniq.34360) (:fv _uniq.34390))) (:fv _uniq.34390)) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"l✝","sexp":"((:c List) (:fv _uniq.34360))"},{"name":"l'","sexp":"((:c List) (:fv _uniq.34360))"},{"name":"l","sexp":"((:c List) (:fv _uniq.34360))"},{"name":"h","sexp":"((:c LT.lt) (:c Nat) (:c instLTNat) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))) (... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c List.head) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c List.cyclicPermutations) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV4)))) (:arg :pr... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34360","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.34363","is_instance":false,"is_let":false,"name":"l✝","sexp":"(:app (:c List) (:arg :explicit 0 (:fv FV0)))... | {"children":[{"source":"rw","sourceEnd":25592,"sourceStart":25590,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":25594,"sourceStart":25593,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":25597,"sourceSt... | [] | [{"source":"get_mk_zero h","source_end":25611,"source_start":25598,"syntax_kind":"Lean.Parser.Term.app"},{"source":"get_cyclicPermutations","source_end":25635,"source_start":25613,"syntax_kind":"ident"},{"source":"Fin.val_mk","source_end":25647,"source_start":25637,"syntax_kind":"ident"},{"source":"rotate_zero","source... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34360","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.34363","is_instance":false,"is_let":false,"user_name":"l✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 172 | 5 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 875d31dcc8886ae3aa7ffaa72de43348e58626e522a01c100471df01ba19c152 | f4b81f548a19b735aad2f6472bf96d499d55812f5065ec9ce89896afda287c9e | bb8463510ccdb414529da6616332cbb8e92dfb48e7164d0a96f67ee0a5763618 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 60 | Cardinal.lift_natCast | Mathlib/SetTheory/Cardinal/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction n <;> simp [*] | α β : Type u
n : ℕ
⊢ lift.{u, v} ↑n = ↑n | ((:c Eq) (:c Cardinal) ((:c Cardinal.lift) ((:c Nat.cast) (:c Cardinal) (:c Cardinal.instNatCast) (:fv _uniq.94076))) ((:c Nat.cast) (:c Cardinal) (:c Cardinal.instNatCast) (:fv _uniq.94076))) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u 1))"},{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Cardinal)) (:arg :explicit 1 (:app (:c Cardinal.lift) (:arg :explicit 0 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Cardinal)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Cardinal))))) (:arg :explicit 2 (:fv FV3)))))) (:arg :explicit 2 (:app (:c N... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.93944","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93946","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":explicit","con... | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"induction","sourceEnd":53667,"sourceStart":53658,"tag":"atom"},{"children":[{"contextIndex":3,"semanticRole":"local","source":"n","sourceEnd":53669,"sourceStart":53668,"tag":"identifier"}],"kind":"null","source":"n","sourceEnd":53669,"sourceSta... | [] | [{"source":"n","source_end":53669,"source_start":53668,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.93944","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93946","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 392 | 2 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 685539b28559480fa1ccd4b62f11f5c6245ca17c314c92eee7c8287588189ea7 | 5914a6888a1676e975e42cf5783d3928d7db598e94f6e6d7bb4f37f860c1aa7b | 85ca99cb2d2c26ae913660c63ca0304200f841bdeade9fa1af82eafea84e2c0f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 61 | Algebra.trace_prod | Mathlib/RingTheory/Trace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>LinearMap.coprod_apply</a>, <a>Algebra.trace_prod_apply</a>] | R : Type u_1
S : Type u_2
T : Type u_3
inst✝¹² : CommRing R
inst✝¹¹ : CommRing S
inst✝¹⁰ : CommRing T
inst✝⁹ : Algebra R S
inst✝⁸ : Algebra R T
K : Type u_4
L : Type u_5
inst✝⁷ : Field K
inst✝⁶ : Field L
inst✝⁵ : Algebra K L
ι κ : Type w
inst✝⁴ : Fintype ι
b : Basis ι R S
inst✝³ : Module.Free R S
inst✝² : Module.Free R... | ((:c Eq) (:fv _uniq.86896) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.86896) (:fv _uniq.86896) ((:c CommSemiring.toSemiring) (:fv _uniq.86896) ((:c CommRing.toCommSemiring) (:fv _uniq.86896) (:fv _uniq.86905))) ((:c CommSemiring.toSemiring) (:fv _uniq.86896) ((:c CommRing.toCommSemiring) (:fv _uniq.86896) (:fv _uniq... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"T","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹²","sexp":"((:c CommRing) (:fv _uniq.86896))"},{"name":"inst✝¹¹","sexp":"((:c CommRing) (:fv _uniq.86899))"},{"name":"inst✝¹⁰","sexp":"((:c CommRing) (:fv _uniq.86902))"},{"name":"inst... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86896","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.86899","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":7862,"sourceStart":7860,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7864,"sourceStart":7863,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"coprod_apply","source_end":7876,"source_start":7864,"syntax_kind":"ident"},{"source":"trace_prod_apply","source_end":7894,"source_start":7878,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86896","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.86899","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 39 | 2 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 064cc2af28e80a2b711ec0f9b3fbfcce24ecaa181a79f388ae356c3a083559c7 | 7a0e21e36cae87022a0591348ee8f016cd5ee0e00b7a033a683b9e3ab43604f0 | d3dab32ba40e726595d266214023f0070a14340868acd4df277d28b7febac7b6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 62 | Order.pred_eq_iff_covBy | Mathlib/Order/SuccPred/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro rfl | α : Type u_1
β : Type u_2
inst✝² : PartialOrder α
inst✝¹ : PredOrder α
a b : α
inst✝ : NoMinOrder α
⊢ pred b = a → a ⋖ b | α : Type u_1
β : Type u_2
inst✝² : PartialOrder α
inst✝¹ : PredOrder α
b : α
inst✝ : NoMinOrder α
⊢ pred b ⋖ b | (:forall _ ((:c Eq) (:fv _uniq.40014) ((:c Order.pred) (:fv _uniq.40014) ((:c PartialOrder.toPreorder) (:fv _uniq.40014) (:fv _uniq.40020)) (:fv _uniq.40038) (:fv _uniq.40042)) (:fv _uniq.40040)) ((:c CovBy) (:fv _uniq.40014) ((:c Preorder.toLT) (:fv _uniq.40014) ((:c PartialOrder.toPreorder) (:fv _uniq.40014) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c PartialOrder) (:fv _uniq.40014))"},{"name":"inst✝¹","sexp":"((:c PredOrder) (:fv _uniq.40014) ((:c PartialOrder.toPreorder) (:fv _uniq.40014) (:fv _uniq.40020)))"},{"name":"a","sexp":"(:fv _uniq.40014)"},{"nam... | (:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Order.pred) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c PredOrder) (:arg :explicit 0 (:fv FV0)) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40014","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40017","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rintro","sourceEnd":34985,"sourceStart":34979,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":34989,"sourceStart":34986,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl","sourceEnd":34989,"sourceStart":349... | [] | [{"source":"rfl","source_end":34989,"source_start":34986,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40014","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40017","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 331 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | afa23cd06ba938f13c9a33432f17c9bce05423c6bf2dfaf34a00983189b8c6dc | 13664a87de5d06a422dd85cc3a597c172877d7a262058f5029913b3d96d21453 | 09e128cd6787f35d3c063b643315aff1382388dafa4e55b6546fbf9dcecb02da | e54648e74f948a80259ef6f8b8fa047d07d28f2d87350a48a76ad7635b76dad4 |
cat-searcher/leandojo-benchmark-4-random | test | 63 | Order.pred_eq_iff_covBy | Mathlib/Order/SuccPred/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Order.pred_covBy</a> _ | α : Type u_1
β : Type u_2
inst✝² : PartialOrder α
inst✝¹ : PredOrder α
b : α
inst✝ : NoMinOrder α
⊢ pred b ⋖ b | ((:c CovBy) (:fv _uniq.40014) ((:c Preorder.toLT) (:fv _uniq.40014) ((:c PartialOrder.toPreorder) (:fv _uniq.40014) (:fv _uniq.40020))) ((:c Order.pred) (:fv _uniq.40014) ((:c PartialOrder.toPreorder) (:fv _uniq.40014) (:fv _uniq.40020)) (:fv _uniq.40038) (:fv _uniq.40042)) (:fv _uniq.40042)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c PartialOrder) (:fv _uniq.40014))"},{"name":"inst✝¹","sexp":"((:c PredOrder) (:fv _uniq.40014) ((:c PartialOrder.toPreorder) (:fv _uniq.40014) (:fv _uniq.40020)))"},{"name":"b","sexp":"(:fv _uniq.40014)"},{"nam... | (:app (:c CovBy) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Order.pred) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40014","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40017","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":34999,"sourceStart":34994,"tag":"atom"},{"children":[{"name":"Order.pred_covBy","semanticRole":"global","source":"pred_covBy","sourceEnd":35010,"sourceStart":35000,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":35012,"sourceStart":35011,"tag":"atom"}],... | [] | [{"source":"pred_covBy _","source_end":35012,"source_start":35000,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40014","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40017","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 331 | 5 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d5fa40384f01f5bc0981425158b453c7d1f187b80817f161cc0da7bac16f5789 | e54648e74f948a80259ef6f8b8fa047d07d28f2d87350a48a76ad7635b76dad4 | a5d7d0f1a59db6f842f2c1905461fd37a05b769c1bbfe5b190bb9971aaf37699 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 64 | Set.wellFoundedOn_iff | Mathlib/Order/WellFoundedSet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have f : <a>RelEmbedding</a> (fun (a : s) (b : s) => r a b) fun a b : α => r a b ∧ a ∈ s ∧ b ∈ s := ⟨⟨(↑), <a>Subtype.coe_injective</a>⟩, by simp⟩ | ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
π : ι → Type u_5
r r' : α → α → Prop
f : β → α
s t : Set α
x y : α
⊢ s.WellFoundedOn r ↔ WellFounded fun a b => r a b ∧ a ∈ s ∧ b ∈ s | ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
π : ι → Type u_5
r r' : α → α → Prop
f✝ : β → α
s t : Set α
x y : α
f : (fun a b => r ↑a ↑b) ↪r fun a b => r a b ∧ a ∈ s ∧ b ∈ s
⊢ s.WellFoundedOn r ↔ WellFounded fun a b => r a b ∧ a ∈ s ∧ b ∈ s | ((:c Iff) ((:c Set.WellFoundedOn) (:fv _uniq.484) (:fv _uniq.514) (:fv _uniq.501)) ((:c WellFounded) (:fv _uniq.484) (:lambda a (:fv _uniq.484) (:lambda b (:fv _uniq.484) ((:c And) ((:fv _uniq.501) 1 0) ((:c And) ((:c Membership.mem) (:fv _uniq.484) ((:c Set) (:fv _uniq.484)) ((:c Set.instMembership) (:fv _uniq.484)) 1... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.481) (:sort (+ u_5 1)))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.484) (:forall _ (:fv _uniq.484) (:sort 0)))"},{"n... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Set.WellFoundedOn) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV8)) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:app (:c WellFounded) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda a :explicit (:fv FV1) (:lambda b :explicit (:fv FV1) (:app (:c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context... | {"children":[{"source":"have","sourceEnd":2979,"sourceStart":2975,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"f","sourceEnd":2981,"sourceStart":2980,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"f","sourceEnd":2981,"sourceStart":2980,"tag":"node"},{"ch... | [] | [{"source":"RelEmbedding (fun (a : s) (b : s) => r a b) fun a b : α => r a b ∧ a ∈ s ∧ b ∈ s","source_end":3073,"source_start":2984,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨⟨(↑), Subtype.coe_injective⟩, by simp⟩","source_end":3130,"source_start":3081,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.4... | 14 | 4 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | daa69d9178d0044060ac2bd78ddf2e2e0812e5d31516fc31042c5d605c1cd685 | 552b220efef7e853813549df72557926d1a8e9a2ba0ad90e0e2a269e14f399dd | e7dbc5b7d663441c7963f4f917723d77a86e72f38fc55a8d6eaeed97ea64f0e3 | 14c2810f847af25b854dfef741e6df32a63899e4084befad1bbc353c52f4916b |
cat-searcher/leandojo-benchmark-4-random | test | 65 | Set.wellFoundedOn_iff | Mathlib/Order/WellFoundedSet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨fun h => ?_, f.wellFounded⟩ | ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
π : ι → Type u_5
r r' : α → α → Prop
f✝ : β → α
s t : Set α
x y : α
f : (fun a b => r ↑a ↑b) ↪r fun a b => r a b ∧ a ∈ s ∧ b ∈ s
⊢ s.WellFoundedOn r ↔ WellFounded fun a b => r a b ∧ a ∈ s ∧ b ∈ s | ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
π : ι → Type u_5
r r' : α → α → Prop
f✝ : β → α
s t : Set α
x y : α
f : (fun a b => r ↑a ↑b) ↪r fun a b => r a b ∧ a ∈ s ∧ b ∈ s
h : s.WellFoundedOn r
⊢ WellFounded fun a b => r a b ∧ a ∈ s ∧ b ∈ s | ((:c Iff) ((:c Set.WellFoundedOn) (:fv _uniq.484) (:fv _uniq.514) (:fv _uniq.501)) ((:c WellFounded) (:fv _uniq.484) (:lambda a (:fv _uniq.484) (:lambda b (:fv _uniq.484) ((:c And) ((:fv _uniq.501) 1 0) ((:c And) ((:c Membership.mem) (:fv _uniq.484) ((:c Set) (:fv _uniq.484)) ((:c Set.instMembership) (:fv _uniq.484)) 1... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.481) (:sort (+ u_5 1)))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.484) (:forall _ (:fv _uniq.484) (:sort 0)))"},{"n... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Set.WellFoundedOn) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV8)) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:app (:c WellFounded) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda a :explicit (:fv FV1) (:lambda b :explicit (:fv FV1) (:app (:c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context... | {"children":[{"source":"refine","sourceEnd":3139,"sourceStart":3133,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":3143,"sourceStart":3140,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":3146,"sourceStart":3143,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"h"... | [] | [{"source":"⟨fun h => ?_, f.wellFounded⟩","source_end":3172,"source_start":3140,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.4... | 14 | 10 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3faf668ffd99fefe6050408aa3b11ffc2fb3b862902d83b73cff33af7d57faa5 | 14c2810f847af25b854dfef741e6df32a63899e4084befad1bbc353c52f4916b | 8bf972d142d5fb51de61f17467df7933e7577786734c25a9643068c038b01bcc | 795d26f8be0f549d55e2d2f7fbafbe729ca62800b4ab29f550cd2ae72fe6c302 |
cat-searcher/leandojo-benchmark-4-random | test | 66 | Set.wellFoundedOn_iff | Mathlib/Order/WellFoundedSet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>WellFounded.wellFounded_iff_has_min</a>] | ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
π : ι → Type u_5
r r' : α → α → Prop
f✝ : β → α
s t : Set α
x y : α
f : (fun a b => r ↑a ↑b) ↪r fun a b => r a b ∧ a ∈ s ∧ b ∈ s
h : s.WellFoundedOn r
⊢ WellFounded fun a b => r a b ∧ a ∈ s ∧ b ∈ s | ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
π : ι → Type u_5
r r' : α → α → Prop
f✝ : β → α
s t : Set α
x y : α
f : (fun a b => r ↑a ↑b) ↪r fun a b => r a b ∧ a ∈ s ∧ b ∈ s
h : s.WellFoundedOn r
⊢ ∀ (s_1 : Set α), s_1.Nonempty → ∃ m ∈ s_1, ∀ x ∈ s_1, ¬(r x m ∧ x ∈ s ∧ m ∈ s) | ((:c WellFounded) (:fv _uniq.484) (:lambda a (:fv _uniq.484) (:lambda b (:fv _uniq.484) ((:c And) ((:fv _uniq.501) 1 0) ((:c And) ((:c Membership.mem) (:fv _uniq.484) ((:c Set) (:fv _uniq.484)) ((:c Set.instMembership) (:fv _uniq.484)) 1 (:fv _uniq.514)) ((:c Membership.mem) (:fv _uniq.484) ((:c Set) (:fv _uniq.484)) (... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.481) (:sort (+ u_5 1)))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.484) (:forall _ (:fv _uniq.484) (:sort 0)))"},{"n... | (:app (:c WellFounded) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda a :explicit (:fv FV1) (:lambda b :explicit (:fv FV1) (:app (:c And) (:arg :explicit 0 (:app (:fv FV5) (:arg :explicit 0 1) (:arg :explicit 1 0))) (:arg :explicit 1 (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context... | {"children":[{"source":"rw","sourceEnd":3177,"sourceStart":3175,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3179,"sourceStart":3178,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"WellFounded.wellFoun... | [] | [{"source":"WellFounded.wellFounded_iff_has_min","source_end":3214,"source_start":3179,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.4... | 14 | 11 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e9788ca3dbf61f50d22637707a255bc4005deacd2335cc7053e366fa7d65bdf6 | 795d26f8be0f549d55e2d2f7fbafbe729ca62800b4ab29f550cd2ae72fe6c302 | 2c487d2f6cc81f31d0e1ec4a7330ba0b36d117b4a8df1338469e76593c2c8eb1 | 0417b5d20c779dd525c1bcd1c8085a838ac4f08ac2d385a2d7e6e2d31ea94b05 |
cat-searcher/leandojo-benchmark-4-random | test | 67 | Set.wellFoundedOn_iff | Mathlib/Order/WellFoundedSet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro t ht | ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
π : ι → Type u_5
r r' : α → α → Prop
f✝ : β → α
s t : Set α
x y : α
f : (fun a b => r ↑a ↑b) ↪r fun a b => r a b ∧ a ∈ s ∧ b ∈ s
h : s.WellFoundedOn r
⊢ ∀ (s_1 : Set α), s_1.Nonempty → ∃ m ∈ s_1, ∀ x ∈ s_1, ¬(r x m ∧ x ∈ s ∧ m ∈ s) | ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
π : ι → Type u_5
r r' : α → α → Prop
f✝ : β → α
s t✝ : Set α
x y : α
f : (fun a b => r ↑a ↑b) ↪r fun a b => r a b ∧ a ∈ s ∧ b ∈ s
h : s.WellFoundedOn r
t : Set α
ht : t.Nonempty
⊢ ∃ m ∈ t, ∀ x ∈ t, ¬(r x m ∧ x ∈ s ∧ m ∈ s) | (:forall s ((:c Set) (:fv _uniq.484)) (:forall _ ((:c Set.Nonempty) (:fv _uniq.484) 0) ((:c Exists) (:fv _uniq.484) (:lambda m (:fv _uniq.484) ((:c And) ((:c Membership.mem) (:fv _uniq.484) ((:c Set) (:fv _uniq.484)) ((:c Set.instMembership) (:fv _uniq.484)) 0 2) (:forall x (:fv _uniq.484) (:forall _ ((:c Membership.me... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.481) (:sort (+ u_5 1)))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.484) (:forall _ (:fv _uniq.484) (:sort 0)))"},{"n... | (:forall s :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV1))) (:forall _ :explicit (:app (:c Set.Nonempty) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 0)) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda m :explicit (:fv FV1) (:app (:c And) (:arg :explicit 0 (:app (:c Membershi... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context... | {"children":[{"source":"intro","sourceEnd":3223,"sourceStart":3218,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"t","sourceEnd":3225,"sourceStart":3224,"tag":"identifier"},{"semanticRole":"scoped_local","source":"ht","sourceEnd":3228,"sourceStart":3226,"tag":"identifier"}],"kind":"null","source":"... | [{"role":"fresh_name","source":"t","source_end":3225,"source_start":3224,"syntax_kind":"ident"},{"role":"fresh_name","source":"ht","source_end":3228,"source_start":3226,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.4... | 14 | 14 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bf602346673944303ca04e5c770b1f3dd52a2c51af46cfa4990e0161749235da | 0417b5d20c779dd525c1bcd1c8085a838ac4f08ac2d385a2d7e6e2d31ea94b05 | 0739bfdcdc031efb63257ff4b2cf0a312c689994658859969f8eae6b2c78c652 | 340a958a9282e24bdd4fdb061c71540ac9ba9b803b8403cde54ae240140fb55b |
cat-searcher/leandojo-benchmark-4-random | test | 68 | Set.wellFoundedOn_iff | Mathlib/Order/WellFoundedSet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases hst : (s ∩ t).<a>Set.Nonempty</a> | ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
π : ι → Type u_5
r r' : α → α → Prop
f✝ : β → α
s t✝ : Set α
x y : α
f : (fun a b => r ↑a ↑b) ↪r fun a b => r a b ∧ a ∈ s ∧ b ∈ s
h : s.WellFoundedOn r
t : Set α
ht : t.Nonempty
⊢ ∃ m ∈ t, ∀ x ∈ t, ¬(r x m ∧ x ∈ s ∧ m ∈ s) | case pos
ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
π : ι → Type u_5
r r' : α → α → Prop
f✝ : β → α
s t✝ : Set α
x y : α
f : (fun a b => r ↑a ↑b) ↪r fun a b => r a b ∧ a ∈ s ∧ b ∈ s
h : s.WellFoundedOn r
t : Set α
ht : t.Nonempty
hst : (s ∩ t).Nonempty
⊢ ∃ m ∈ t, ∀ x ∈ t, ¬(r x m ∧ x ∈ s ∧ m ∈ s)
case neg
ι : ... | ((:c Exists) (:fv _uniq.484) (:lambda m (:fv _uniq.484) ((:c And) ((:c Membership.mem) (:fv _uniq.484) ((:c Set) (:fv _uniq.484)) ((:c Set.instMembership) (:fv _uniq.484)) 0 (:fv _uniq.1850)) (:forall x (:fv _uniq.484) (:forall _ ((:c Membership.mem) (:fv _uniq.484) ((:c Set) (:fv _uniq.484)) ((:c Set.instMembership) (... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.481) (:sort (+ u_5 1)))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.484) (:forall _ (:fv _uniq.484) (:sort 0)))"},{"n... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda m :explicit (:fv FV1) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context... | {"children":[{"source":"by_cases","sourceEnd":3239,"sourceStart":3231,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hst","sourceEnd":3243,"sourceStart":3240,"tag":"identifier"},{"source":":","sourceEnd":3245,"sourceStart":3244,"tag":"atom"}],"kind":"null","source":"hst :","sourceEnd":3245,"sourceS... | [] | [{"source":"(s ∩ t).Nonempty","source_end":3264,"source_start":3246,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.4... | 14 | 15 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1048fa36222e17592c18c58ea3a9199fe326f638a07f1b15b16f7f7c86c86cfe | 340a958a9282e24bdd4fdb061c71540ac9ba9b803b8403cde54ae240140fb55b | 9347191d4ca2495f6e50e00cdd47ed64ef337ea43528b641171e9761573ac001 | ee3c64224469bea7c7668f9dd587c9295d2b827ed1f8dd64e1d1a40c69cc6d1a |
cat-searcher/leandojo-benchmark-4-random | test | 69 | Set.wellFoundedOn_iff | Mathlib/Order/WellFoundedSet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
π : ι → Type u_5
r r' : α → α → Prop
f : β → α
s t : Set α
x y : α
⊢ ∀ {a b : ↑s},
r ({ toFun := Subtype.val, inj' := ⋯ } a) ({ toFun := Subtype.val, inj' := ⋯ } b) ∧
{ toFun := Subtype.val, inj' := ⋯ } a ∈ s ∧ { toFun := Subtype.val, inj' := ⋯ } b ∈ s ↔
... | (:forall a ((:c Set.Elem) (:fv _uniq.484) (:fv _uniq.514)) (:forall b ((:c Set.Elem) (:fv _uniq.484) (:fv _uniq.514)) ((:c Iff) ((:c And) ((:fv _uniq.501) ((:c DFunLike.coe) ((:c Function.Embedding) ((:c Set.Elem) (:fv _uniq.484) (:fv _uniq.514)) (:fv _uniq.484)) ((:c Set.Elem) (:fv _uniq.484) (:fv _uniq.514)) (:lambda... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.481) (:sort (+ u_5 1)))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.484) (:forall _ (:fv _uniq.484) (:sort 0)))"},{"n... | (:forall a :implicit (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV8))) (:forall b :implicit (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV8))) (:app (:c Iff) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:fv FV5) (:arg :explicit 0 (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":3127,"sourceStart":3123,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.4... | 14 | 7 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 19e1189cfbb73d227ef0eab9233a9522315d024866ec9eda9168eec22c27b246 | 0428b2f7ac0a3e45a130233a48771cd90d240e65e4edd236ec10d1cf6373b0d3 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 70 | Set.wellFoundedOn_iff | Mathlib/Order/WellFoundedSet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Subtype.preimage_coe_nonempty</a>] at hst | case pos
ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
π : ι → Type u_5
r r' : α → α → Prop
f✝ : β → α
s t✝ : Set α
x y : α
f : (fun a b => r ↑a ↑b) ↪r fun a b => r a b ∧ a ∈ s ∧ b ∈ s
h : s.WellFoundedOn r
t : Set α
ht : t.Nonempty
hst : (s ∩ t).Nonempty
⊢ ∃ m ∈ t, ∀ x ∈ t, ¬(r x m ∧ x ∈ s ∧ m ∈ s) | case pos
ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
π : ι → Type u_5
r r' : α → α → Prop
f✝ : β → α
s t✝ : Set α
x y : α
f : (fun a b => r ↑a ↑b) ↪r fun a b => r a b ∧ a ∈ s ∧ b ∈ s
h : s.WellFoundedOn r
t : Set α
ht : t.Nonempty
hst : (Subtype.val ⁻¹' t).Nonempty
⊢ ∃ m ∈ t, ∀ x ∈ t, ¬(r x m ∧ x ∈ s ∧ m ∈ s) | ((:c Exists) (:fv _uniq.484) (:lambda m (:fv _uniq.484) ((:c And) ((:c Membership.mem) (:fv _uniq.484) ((:c Set) (:fv _uniq.484)) ((:c Set.instMembership) (:fv _uniq.484)) 0 (:fv _uniq.1850)) (:forall x (:fv _uniq.484) (:forall _ ((:c Membership.mem) (:fv _uniq.484) ((:c Set) (:fv _uniq.484)) ((:c Set.instMembership) (... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.481) (:sort (+ u_5 1)))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.484) (:forall _ (:fv _uniq.484) (:sort 0)))"},{"n... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda m :explicit (:fv FV1) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context... | {"children":[{"source":"rw","sourceEnd":3272,"sourceStart":3270,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3274,"sourceStart":3273,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":3277,"sourceStart":... | [] | [{"source":"Subtype.preimage_coe_nonempty","source_end":3307,"source_start":3278,"syntax_kind":"ident"},{"source":"hst","source_end":3315,"source_start":3312,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.4... | 14 | 20 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 53f54699c19d6d497e4a02a2c0edad38103cb95ba1c8d681b8657ad6a038becb | f8a0a73aa7a8735ecf1235151d04aee316b6ab2fa69d234df822b3c8b616e524 | f213e16cd48f05f3a585b1156dd8fd0a5eba8dfc4770e4a9b2a9c1341c653b54 | 4751e280dc8d2ad6d01c4f409e090075698a6c0f87a43cc887f9df6522aba32b |
cat-searcher/leandojo-benchmark-4-random | test | 71 | Set.wellFoundedOn_iff | Mathlib/Order/WellFoundedSet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases h.has_min (<a>Subtype.val</a> ⁻¹' t) hst with ⟨⟨m, ms⟩, mt, hm⟩ | case pos
ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
π : ι → Type u_5
r r' : α → α → Prop
f✝ : β → α
s t✝ : Set α
x y : α
f : (fun a b => r ↑a ↑b) ↪r fun a b => r a b ∧ a ∈ s ∧ b ∈ s
h : s.WellFoundedOn r
t : Set α
ht : t.Nonempty
hst : (Subtype.val ⁻¹' t).Nonempty
⊢ ∃ m ∈ t, ∀ x ∈ t, ¬(r x m ∧ x ∈ s ∧ m ∈ s) | case pos.intro.mk.intro
ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
π : ι → Type u_5
r r' : α → α → Prop
f✝ : β → α
s t✝ : Set α
x y : α
f : (fun a b => r ↑a ↑b) ↪r fun a b => r a b ∧ a ∈ s ∧ b ∈ s
h : s.WellFoundedOn r
t : Set α
ht : t.Nonempty
hst : (Subtype.val ⁻¹' t).Nonempty
m : α
ms : m ∈ s
mt : ⟨m, ms⟩ ∈... | ((:c Exists) (:fv _uniq.484) (:lambda m (:fv _uniq.484) ((:c And) ((:c Membership.mem) (:fv _uniq.484) ((:c Set) (:fv _uniq.484)) ((:c Set.instMembership) (:fv _uniq.484)) 0 (:fv _uniq.1850)) (:forall x (:fv _uniq.484) (:forall _ ((:c Membership.mem) (:fv _uniq.484) ((:c Set) (:fv _uniq.484)) ((:c Set.instMembership) (... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.481) (:sort (+ u_5 1)))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.484) (:forall _ (:fv _uniq.484) (:sort 0)))"},{"n... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda m :explicit (:fv FV1) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context... | {"children":[{"source":"rcases","sourceEnd":3326,"sourceStart":3320,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"h.has_min","sourceEnd":3336,"sourceStart":3327,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":3338,"sourceSt... | [] | [{"source":"h.has_min (Subtype.val ⁻¹' t) hst","source_end":3363,"source_start":3327,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨⟨m, ms⟩, mt, hm⟩","source_end":3394,"source_start":3369,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.4... | 14 | 23 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c3f7d995207fde19c568e11b6ea2133bf7ec220850147aa341ac3cdbb6b43bf1 | 4751e280dc8d2ad6d01c4f409e090075698a6c0f87a43cc887f9df6522aba32b | 7e4ad6ce12eb2b99ad19244fd1b82f9c7ab7b88ea6e41b6ad27b47909b5393ca | 5422e2c3ad36baf2ead65465ff74b8e70d1021d72f6d45c2beb5f55a6bfd18a2 |
cat-searcher/leandojo-benchmark-4-random | test | 72 | Set.wellFoundedOn_iff | Mathlib/Order/WellFoundedSet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨m, mt, fun x xt ⟨xm, xs, _⟩ => hm ⟨x, xs⟩ xt xm⟩ | case pos.intro.mk.intro
ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
π : ι → Type u_5
r r' : α → α → Prop
f✝ : β → α
s t✝ : Set α
x y : α
f : (fun a b => r ↑a ↑b) ↪r fun a b => r a b ∧ a ∈ s ∧ b ∈ s
h : s.WellFoundedOn r
t : Set α
ht : t.Nonempty
hst : (Subtype.val ⁻¹' t).Nonempty
m : α
ms : m ∈ s
mt : ⟨m, ms⟩ ∈... | ((:c Exists) (:fv _uniq.484) (:lambda m (:fv _uniq.484) ((:c And) ((:c Membership.mem) (:fv _uniq.484) ((:c Set) (:fv _uniq.484)) ((:c Set.instMembership) (:fv _uniq.484)) 0 (:fv _uniq.1850)) (:forall x (:fv _uniq.484) (:forall _ ((:c Membership.mem) (:fv _uniq.484) ((:c Set) (:fv _uniq.484)) ((:c Set.instMembership) (... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.481) (:sort (+ u_5 1)))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.484) (:forall _ (:fv _uniq.484) (:sort 0)))"},{"n... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda m :explicit (:fv FV1) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context... | {"children":[{"source":"exact","sourceEnd":3404,"sourceStart":3399,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":3408,"sourceStart":3405,"tag":"atom"},{"children":[{"contextIndex":18,"semanticRole":"local","source":"m","sourceEnd":3409,"sourceStart":3408,"tag":"identifier"},{"source":",","sourceEnd":3410,"source... | [] | [{"source":"⟨m, mt, fun x xt ⟨xm, xs, _⟩ => hm ⟨x, xs⟩ xt xm⟩","source_end":3466,"source_start":3405,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.4... | 14 | 24 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 667df010b57a5d350657e0d30cd495364d9ee5c217d30335ca2ab687412e4500 | 5422e2c3ad36baf2ead65465ff74b8e70d1021d72f6d45c2beb5f55a6bfd18a2 | 6cb8b5978471e6fd30f85c144884a4e6b25fdb60a0dded1d4f90190b456375f0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 73 | Set.wellFoundedOn_iff | Mathlib/Order/WellFoundedSet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases ht with ⟨m, mt⟩ | case neg
ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
π : ι → Type u_5
r r' : α → α → Prop
f✝ : β → α
s t✝ : Set α
x y : α
f : (fun a b => r ↑a ↑b) ↪r fun a b => r a b ∧ a ∈ s ∧ b ∈ s
h : s.WellFoundedOn r
t : Set α
ht : t.Nonempty
hst : ¬(s ∩ t).Nonempty
⊢ ∃ m ∈ t, ∀ x ∈ t, ¬(r x m ∧ x ∈ s ∧ m ∈ s) | case neg.intro
ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
π : ι → Type u_5
r r' : α → α → Prop
f✝ : β → α
s t✝ : Set α
x y : α
f : (fun a b => r ↑a ↑b) ↪r fun a b => r a b ∧ a ∈ s ∧ b ∈ s
h : s.WellFoundedOn r
t : Set α
hst : ¬(s ∩ t).Nonempty
m : α
mt : m ∈ t
⊢ ∃ m ∈ t, ∀ x ∈ t, ¬(r x m ∧ x ∈ s ∧ m ∈ s) | ((:c Exists) (:fv _uniq.484) (:lambda m (:fv _uniq.484) ((:c And) ((:c Membership.mem) (:fv _uniq.484) ((:c Set) (:fv _uniq.484)) ((:c Set.instMembership) (:fv _uniq.484)) 0 (:fv _uniq.1850)) (:forall x (:fv _uniq.484) (:forall _ ((:c Membership.mem) (:fv _uniq.484) ((:c Set) (:fv _uniq.484)) ((:c Set.instMembership) (... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.481) (:sort (+ u_5 1)))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.484) (:forall _ (:fv _uniq.484) (:sort 0)))"},{"n... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda m :explicit (:fv FV1) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context... | {"children":[{"source":"rcases","sourceEnd":3478,"sourceStart":3472,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":16,"semanticRole":"local","source":"ht","sourceEnd":3481,"sourceStart":3479,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","sou... | [] | [{"source":"ht","source_end":3481,"source_start":3479,"syntax_kind":"ident"},{"source":"⟨m, mt⟩","source_end":3498,"source_start":3487,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.4... | 14 | 29 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 25a8e92bcb89aa16d505aab47889d3dc350f54431b56cf00382a117d9ff60629 | 560005ccef9eae354220f63899d0ea9db7b230b702017e60411b9b3e86ad7158 | ced7bb8085626d607a3d36408a737337a83cad1e38f0e7b63ed7bdcf7c8ce93d | c0550761a9a2d246a8a87a87a3280fe77afa685745c39936206eb85590fa7332 |
cat-searcher/leandojo-benchmark-4-random | test | 74 | Set.wellFoundedOn_iff | Mathlib/Order/WellFoundedSet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨m, mt, fun x _ ⟨_, _, ms⟩ => hst ⟨m, ⟨ms, mt⟩⟩⟩ | case neg.intro
ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
π : ι → Type u_5
r r' : α → α → Prop
f✝ : β → α
s t✝ : Set α
x y : α
f : (fun a b => r ↑a ↑b) ↪r fun a b => r a b ∧ a ∈ s ∧ b ∈ s
h : s.WellFoundedOn r
t : Set α
hst : ¬(s ∩ t).Nonempty
m : α
mt : m ∈ t
⊢ ∃ m ∈ t, ∀ x ∈ t, ¬(r x m ∧ x ∈ s ∧ m ∈ s) | ((:c Exists) (:fv _uniq.484) (:lambda m (:fv _uniq.484) ((:c And) ((:c Membership.mem) (:fv _uniq.484) ((:c Set) (:fv _uniq.484)) ((:c Set.instMembership) (:fv _uniq.484)) 0 (:fv _uniq.1850)) (:forall x (:fv _uniq.484) (:forall _ ((:c Membership.mem) (:fv _uniq.484) ((:c Set) (:fv _uniq.484)) ((:c Set.instMembership) (... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.481) (:sort (+ u_5 1)))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.484) (:forall _ (:fv _uniq.484) (:sort 0)))"},{"n... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda m :explicit (:fv FV1) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context... | {"children":[{"source":"exact","sourceEnd":3508,"sourceStart":3503,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":3512,"sourceStart":3509,"tag":"atom"},{"children":[{"contextIndex":17,"semanticRole":"local","source":"m","sourceEnd":3513,"sourceStart":3512,"tag":"identifier"},{"source":",","sourceEnd":3514,"source... | [] | [{"source":"⟨m, mt, fun x _ ⟨_, _, ms⟩ => hst ⟨m, ⟨ms, mt⟩⟩⟩","source_end":3573,"source_start":3509,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.481","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.484","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.4... | 14 | 30 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d33ba3a5c80f129770ae13ef52849cb321a2a8e13082f7d4dcd053c3230c8955 | c0550761a9a2d246a8a87a87a3280fe77afa685745c39936206eb85590fa7332 | b3d209c1fb2c1be746ac8b498e4c828b9c548c312a5f5018e7a5e360a7ee9a8f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 75 | ExteriorAlgebra.ι_range_disjoint_one | Mathlib/LinearAlgebra/ExteriorAlgebra/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Submodule.disjoint_def</a>] | R : Type u1
inst✝⁴ : CommRing R
M : Type u2
inst✝³ : AddCommGroup M
inst✝² : Module R M
A : Type u_1
inst✝¹ : Semiring A
inst✝ : Algebra R A
⊢ Disjoint (LinearMap.range (ι R)) 1 | R : Type u1
inst✝⁴ : CommRing R
M : Type u2
inst✝³ : AddCommGroup M
inst✝² : Module R M
A : Type u_1
inst✝¹ : Semiring A
inst✝ : Algebra R A
⊢ ∀ x ∈ LinearMap.range (ι R), x ∈ 1 → x = 0 | ((:c Disjoint) ((:c Submodule) (:fv _uniq.177042) ((:c ExteriorAlgebra) (:fv _uniq.177042) (:fv _uniq.177045) (:fv _uniq.177047) (:fv _uniq.177050) (:fv _uniq.177663)) ((:c CommSemiring.toSemiring) (:fv _uniq.177042) ((:c CommRing.toCommSemiring) (:fv _uniq.177042) (:fv _uniq.177045))) ((:c NonUnitalNonAssocSemiring.to... | [{"name":"R","sexp":"(:sort (+ u1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.177042))"},{"name":"M","sexp":"(:sort (+ u2 1))"},{"name":"inst✝³","sexp":"((:c AddCommGroup) (:fv _uniq.177047))"},{"name":"inst✝²","sexp":"((:c Module) (:fv _uniq.177042) (:fv _uniq.177047) ((:c CommSemiring.toSemiring) (:fv _u... | (:app (:c Disjoint) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c ExteriorAlgebra) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.177042","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.177045","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :expl... | {"children":[{"source":"rw","sourceEnd":10830,"sourceStart":10828,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10832,"sourceStart":10831,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Submodule.disjoi... | [] | [{"source":"Submodule.disjoint_def","source_end":10854,"source_start":10832,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.177042","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.177045","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte... | 72 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ea9047126045b7f3d3acab448b0736b4756b3a545d13c08a145bccd00cee6002 | 3799d535a1eac331d24126f9fd94ecbe3e9da88da00365e6bad0ea796bc90fde | cc0f46836ba67570684ad55ab183b63ceea26ec18c7e646388e7e1e4dea22156 | 9f462d39e55d176db58cfc4fb7489ad9d02a1854eac2a25e23163d33e85a169d |
cat-searcher/leandojo-benchmark-4-random | test | 76 | ExteriorAlgebra.ι_range_disjoint_one | Mathlib/LinearAlgebra/ExteriorAlgebra/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro _ ⟨x, hx⟩ ⟨r, rfl : <a>algebraMap</a> R (<a>ExteriorAlgebra</a> R M) r = _⟩ | R : Type u1
inst✝⁴ : CommRing R
M : Type u2
inst✝³ : AddCommGroup M
inst✝² : Module R M
A : Type u_1
inst✝¹ : Semiring A
inst✝ : Algebra R A
⊢ ∀ x ∈ LinearMap.range (ι R), x ∈ 1 → x = 0 | case intro.intro
R : Type u1
inst✝⁴ : CommRing R
M : Type u2
inst✝³ : AddCommGroup M
inst✝² : Module R M
A : Type u_1
inst✝¹ : Semiring A
inst✝ : Algebra R A
x : M
r : R
hx : (ι R) x = (algebraMap R (ExteriorAlgebra R M)) r
⊢ (algebraMap R (ExteriorAlgebra R M)) r = 0 | (:forall x ((:c ExteriorAlgebra) (:fv _uniq.177042) (:fv _uniq.177045) (:fv _uniq.177047) (:fv _uniq.177050) (:fv _uniq.177663)) (:forall _ ((:c Membership.mem) ((:c ExteriorAlgebra) (:fv _uniq.177042) (:fv _uniq.177045) (:fv _uniq.177047) (:fv _uniq.177050) (:fv _uniq.177663)) ((:c Submodule) (:fv _uniq.177042) ((:c E... | [{"name":"R","sexp":"(:sort (+ u1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.177042))"},{"name":"M","sexp":"(:sort (+ u2 1))"},{"name":"inst✝³","sexp":"((:c AddCommGroup) (:fv _uniq.177047))"},{"name":"inst✝²","sexp":"((:c Module) (:fv _uniq.177042) (:fv _uniq.177047) ((:c CommSemiring.toSemiring) (:fv _u... | (:forall x :explicit (:app (:c ExteriorAlgebra) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.177042","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.177045","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :expl... | {"children":[{"source":"rintro","sourceEnd":10864,"sourceStart":10858,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"_","sourceEnd":10866,"sourceStart":10865,"tag":"atom"}],"kind":"Lean.Parser.Tactic.rcasesPat.ignore","source":"_","sourceEnd":10866,"sourceStart":10865,"tag":"node"}],"kind":"Lean.Parser... | [{"role":"fresh_name","source":"x","source_end":10871,"source_start":10870,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":10875,"source_start":10873,"syntax_kind":"ident"},{"role":"fresh_name","source":"r","source_end":10883,"source_start":10882,"syntax_kind":"ident"},{"role":"fresh_name","sourc... | [{"source":"⟨x, hx⟩","source_end":10878,"source_start":10867,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"},{"source":"⟨r, rfl : algebraMap R (ExteriorAlgebra R M) r = _⟩","source_end":10934,"source_start":10879,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.177042","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.177045","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte... | 72 | 7 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 683d2083e54a4bb42120ad7e37da39d3fab704458534cf26d921973e70d90329 | 9f462d39e55d176db58cfc4fb7489ad9d02a1854eac2a25e23163d33e85a169d | f19e2dda67abd5a4b8249a786ec145c7b569511f9d009d04173a3f29e61ba7e5 | 37039454d28c2bd5175518aff7ef580e4b5bbe1075dd03636654a408525a170d |
cat-searcher/leandojo-benchmark-4-random | test | 77 | ExteriorAlgebra.ι_range_disjoint_one | Mathlib/LinearAlgebra/ExteriorAlgebra/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>ExteriorAlgebra.ι_eq_algebraMap_iff</a> x] at hx | case intro.intro
R : Type u1
inst✝⁴ : CommRing R
M : Type u2
inst✝³ : AddCommGroup M
inst✝² : Module R M
A : Type u_1
inst✝¹ : Semiring A
inst✝ : Algebra R A
x : M
r : R
hx : (ι R) x = (algebraMap R (ExteriorAlgebra R M)) r
⊢ (algebraMap R (ExteriorAlgebra R M)) r = 0 | case intro.intro
R : Type u1
inst✝⁴ : CommRing R
M : Type u2
inst✝³ : AddCommGroup M
inst✝² : Module R M
A : Type u_1
inst✝¹ : Semiring A
inst✝ : Algebra R A
x : M
r : R
hx : x = 0 ∧ r = 0
⊢ (algebraMap R (ExteriorAlgebra R M)) r = 0 | ((:c Eq) ((:c ExteriorAlgebra) (:fv _uniq.177042) (:fv _uniq.177045) (:fv _uniq.177047) (:fv _uniq.177050) (:fv _uniq.177663)) ((:c DFunLike.coe) ((:c RingHom) (:fv _uniq.177042) ((:c ExteriorAlgebra) (:fv _uniq.177042) (:fv _uniq.177045) (:fv _uniq.177047) (:fv _uniq.177050) (:fv _uniq.177663)) ((:c Semiring.toNonAsso... | [{"name":"R","sexp":"(:sort (+ u1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.177042))"},{"name":"M","sexp":"(:sort (+ u2 1))"},{"name":"inst✝³","sexp":"((:c AddCommGroup) (:fv _uniq.177047))"},{"name":"inst✝²","sexp":"((:c Module) (:fv _uniq.177042) (:fv _uniq.177047) ((:c CommSemiring.toSemiring) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c ExteriorAlgebra) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instan... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.177042","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.177045","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :expl... | {"children":[{"source":"rw","sourceEnd":10939,"sourceStart":10937,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10941,"sourceStart":10940,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Ext... | [] | [{"source":"hx","source_end":10970,"source_start":10968,"syntax_kind":"ident"},{"source":"ι_eq_algebraMap_iff x","source_end":10963,"source_start":10941,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.177042","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.177045","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte... | 72 | 8 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1cabeccf17cab7bb26dce059208468e302d5aaba569cf99f1575c89be3bbcefd | 37039454d28c2bd5175518aff7ef580e4b5bbe1075dd03636654a408525a170d | 534d9968b6babe85be958cd633ead7b10e9bf4f3fcabb2786c8a6d9e130c8d4a | b8ac9b23d301eb66e0acc329eac357738243fd5e3b41e29f170d4587bffba080 |
cat-searcher/leandojo-benchmark-4-random | test | 78 | ExteriorAlgebra.ι_range_disjoint_one | Mathlib/LinearAlgebra/ExteriorAlgebra/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hx.2, <a>RingHom.map_zero</a>] | case intro.intro
R : Type u1
inst✝⁴ : CommRing R
M : Type u2
inst✝³ : AddCommGroup M
inst✝² : Module R M
A : Type u_1
inst✝¹ : Semiring A
inst✝ : Algebra R A
x : M
r : R
hx : x = 0 ∧ r = 0
⊢ (algebraMap R (ExteriorAlgebra R M)) r = 0 | ((:c Eq) ((:c ExteriorAlgebra) (:fv _uniq.177042) (:fv _uniq.177045) (:fv _uniq.177047) (:fv _uniq.177050) (:fv _uniq.177663)) ((:c DFunLike.coe) ((:c RingHom) (:fv _uniq.177042) ((:c ExteriorAlgebra) (:fv _uniq.177042) (:fv _uniq.177045) (:fv _uniq.177047) (:fv _uniq.177050) (:fv _uniq.177663)) ((:c Semiring.toNonAsso... | [{"name":"R","sexp":"(:sort (+ u1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.177042))"},{"name":"M","sexp":"(:sort (+ u2 1))"},{"name":"inst✝³","sexp":"((:c AddCommGroup) (:fv _uniq.177047))"},{"name":"inst✝²","sexp":"((:c Module) (:fv _uniq.177042) (:fv _uniq.177047) ((:c CommSemiring.toSemiring) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c ExteriorAlgebra) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instan... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.177042","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.177045","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :expl... | {"children":[{"source":"rw","sourceEnd":10975,"sourceStart":10973,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10977,"sourceStart":10976,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"contextInd... | [] | [{"source":"hx.2","source_end":10981,"source_start":10977,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"RingHom.map_zero","source_end":10999,"source_start":10983,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.177042","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.177045","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte... | 72 | 11 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 109811111a29e0698d7e10f405cefc56642de9cbd0c9a07b50da7174410cdb22 | b8ac9b23d301eb66e0acc329eac357738243fd5e3b41e29f170d4587bffba080 | 3a400ee67d0d131eb9a5ed0c46e0ef9b15b734afb15f63561faea041b59e2d2e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 79 | MulOpposite.unop_list_prod | Mathlib/Algebra/BigOperators/Group/List.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>MulOpposite.op_inj</a>, <a>MulOpposite.op_unop</a>, <a>MulOpposite.op_list_prod</a>, <a>List.map_reverse</a>, <a>List.map_map</a>, <a>List.reverse_reverse</a>, <a>MulOpposite.op_comp_unop</a>, <a>List.map_id</a>] | ι : Type u_1
α : Type u_2
β : Type u_3
M : Type u_4
N : Type u_5
P : Type u_6
G : Type u_7
inst✝ : Monoid M
l : List Mᵐᵒᵖ
⊢ unop l.prod = (map unop l).reverse.prod | ((:c Eq) (:fv _uniq.87303) ((:c MulOpposite.unop) (:fv _uniq.87303) ((:c List.prod) ((:c MulOpposite) (:fv _uniq.87303)) ((:c MulOpposite.instMul) (:fv _uniq.87303) ((:c MulOneClass.toMul) (:fv _uniq.87303) ((:c Monoid.toMulOneClass) (:fv _uniq.87303) (:fv _uniq.87315)))) ((:c MulOpposite.instOne) (:fv _uniq.87303) ((:... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"N","sexp":"(:sort (+ u_5 1))"},{"name":"P","sexp":"(:sort (+ u_6 1))"},{"name":"G","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝","sexp":"((:c Monoid) (:... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c MulOpposite.unop) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c List.prod) (:arg :implicit-type 0 (:app (:c MulOpposite) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 1 (:instance-of (:app (:c Mul) (:arg :explicit 0 (:app (:c M... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.87294","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.87297","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":35806,"sourceStart":35804,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":35808,"sourceStart":35807,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"op_inj","source_end":35818,"source_start":35812,"syntax_kind":"ident"},{"source":"op_unop","source_end":35827,"source_start":35820,"syntax_kind":"ident"},{"source":"MulOpposite.op_list_prod","source_end":35853,"source_start":35829,"syntax_kind":"ident"},{"source":"map_reverse","source_end":35866,"source_sta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.87294","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.87297","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 283 | 2 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | af7e1fcb4903c02210dc401ff7610d855e33a33fa1c1529f8a7cbbbbbaba7e98 | e3a9066e17d5c92cda2fdb0fc94bb2bd5f1f7e775b5ea8c9533425ec1307bc4f | 521047dea729829dca1eff7585ec7545d4d02ef01d7e564c914edf4bce536145 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 81 | PowerSeries.ker_coeff_eq_max_ideal | Mathlib/RingTheory/PowerSeries/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>RingHom.mem_ker</a>, <a>PowerSeries.maximalIdeal_eq_span_X</a>, <a>Ideal.mem_span_singleton</a>, <a>PowerSeries.X_dvd_iff</a>] | R : Type u_1
k : Type u_2
inst✝ : Field k
x✝ : k⟦X⟧
⊢ x✝ ∈ RingHom.ker (constantCoeff k) ↔ x✝ ∈ maximalIdeal k⟦X⟧ | ((:c Iff) ((:c Membership.mem) ((:c PowerSeries) (:fv _uniq.95736)) ((:c Ideal) ((:c PowerSeries) (:fv _uniq.95736)) ((:c PowerSeries.instSemiring) (:fv _uniq.95736) ((:c DivisionSemiring.toSemiring) (:fv _uniq.95736) ((:c Semifield.toDivisionSemiring) (:fv _uniq.95736) ((:c Field.toSemifield) (:fv _uniq.95736) (:fv _u... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"k","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c Field) (:fv _uniq.95736))"},{"name":"x✝","sexp":"((:c PowerSeries) (:fv _uniq.95736))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c PowerSeries) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:app (:c Ideal) (:arg :explicit 0 (:app (:c PowerSeries) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.95733","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.95736","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":14551,"sourceStart":14549,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":14553,"sourceStart":14552,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"RingHom.mem_ker","source_end":14568,"source_start":14553,"syntax_kind":"ident"},{"source":"maximalIdeal_eq_span_X","source_end":14592,"source_start":14570,"syntax_kind":"ident"},{"source":"Ideal.mem_span_singleton","source_end":14618,"source_start":14594,"syntax_kind":"ident"},{"source":"X_dvd_iff","source_... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.95733","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.95736","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 95 | 2 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9aba16f6e7a20bf10cdd57edcb9ad1707f536a9bf057acd670e6031ca7b63a52 | cab2d41644fee00678c599792661d312bc280cf2865582944871946c88f222b9 | 5a817cd56bab3eabab5d1040384bf02e4272f456c073141179f982e0e157b365 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 82 | Setoid.card_classes_ker_le | Mathlib/Data/Setoid/Partition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | classical exact <a>le_trans</a> (<a>Set.card_le_card</a> (<a>Setoid.classes_ker_subset_fiber_set</a> f)) (<a>Fintype.card_range_le</a> _) | α✝ : Type u_1
α : Type u_2
β : Type u_3
inst✝¹ : Fintype β
f : α → β
inst✝ : Fintype ↑(ker f).classes
⊢ Fintype.card ↑(ker f).classes ≤ Fintype.card β | ((:c LE.le) (:c Nat) (:c instLENat) ((:c Fintype.card) ((:c Set.Elem) ((:c Set) (:fv _uniq.1469)) ((:c Setoid.classes) (:fv _uniq.1469) ((:c Setoid.ker) (:fv _uniq.1469) (:fv _uniq.1470) (:fv _uniq.1472)))) (:fv _uniq.1473)) ((:c Fintype.card) (:fv _uniq.1470) (:fv _uniq.1471))) | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.1470))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.1469) (:fv _uniq.1470))"},{"name":"inst✝","sexp":"((:c Fintype) ((:c Set.Elem) ((:c Set) (:fv _un... | (: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 Fintype.card) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:app (:c Setoid.classes) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1112","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.1469","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"children":[{"children":[{"children":[{"source":"classical","sourceEnd":3333,"sourceStart":3324,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":3339,"sourceStart":3334,"tag":"atom"},{"children":[{"name":"le_trans","semanticRole":"global","source":"le_trans",... | [] | [{"source":"le_trans (Set.card_le_card (classes_ker_subset_fiber_set f)) (Fintype.card_range_le _)","source_end":3432,"source_start":3346,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1112","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.1469","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":3,"internal_name":"_uni... | 16 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8361dd9a04cea7862a7547e8a9014490ca8a58fdaf1170193de0361245203cfd | 312a03742e7b620356ca21d1ddb04386fa84cdf4ed49c60e57021bde28c472c5 | 6fedb88998fa18817fbc63d23a500fe6a6409f603a8224dfa8547da9db372746 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 83 | Setoid.card_classes_ker_le | Mathlib/Data/Setoid/Partition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>le_trans</a> (<a>Set.card_le_card</a> (<a>Setoid.classes_ker_subset_fiber_set</a> f)) (<a>Fintype.card_range_le</a> _) | α✝ : Type u_1
α : Type u_2
β : Type u_3
inst✝¹ : Fintype β
f : α → β
inst✝ : Fintype ↑(ker f).classes
⊢ Fintype.card ↑(ker f).classes ≤ Fintype.card β | ((:c LE.le) (:c Nat) (:c instLENat) ((:c Fintype.card) ((:c Set.Elem) ((:c Set) (:fv _uniq.1469)) ((:c Setoid.classes) (:fv _uniq.1469) ((:c Setoid.ker) (:fv _uniq.1469) (:fv _uniq.1470) (:fv _uniq.1472)))) (:fv _uniq.1473)) ((:c Fintype.card) (:fv _uniq.1470) (:fv _uniq.1471))) | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.1470))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.1469) (:fv _uniq.1470))"},{"name":"inst✝","sexp":"((:c Fintype) ((:c Set.Elem) ((:c Set) (:fv _un... | (: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 Fintype.card) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:app (:c Setoid.classes) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1112","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.1469","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":3339,"sourceStart":3334,"tag":"atom"},{"children":[{"name":"le_trans","semanticRole":"global","source":"le_trans","sourceEnd":3354,"sourceStart":3346,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":3356,"sourceStar... | [] | [{"source":"le_trans (Set.card_le_card (classes_ker_subset_fiber_set f)) (Fintype.card_range_le _)","source_end":3432,"source_start":3346,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1112","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.1469","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":3,"internal_name":"_uni... | 16 | 5 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d94bf2e6696941054a501adf84e61a0cbe57519bcdb684021e13853fbed4d31e | 312a03742e7b620356ca21d1ddb04386fa84cdf4ed49c60e57021bde28c472c5 | 7e239e0deebfbc108d8f08db031a513d02c84dfe16d8bc606e79fc74296fe577 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 84 | FiberPrebundle.mem_pretrivializationAt_source | Mathlib/Topology/FiberBundle/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [(a.pretrivializationAt b).<a>Pretrivialization.source_eq</a>, <a>Set.mem_preimage</a>, <a>Bundle.TotalSpace.proj</a>] | ι : Type u_1
B : Type u_2
F : Type u_3
X : Type u_4
inst✝³ : TopologicalSpace X
E : B → Type u_5
inst✝² : TopologicalSpace B
inst✝¹ : TopologicalSpace F
inst✝ : (x : B) → TopologicalSpace (E x)
a : FiberPrebundle F E
e : Pretrivialization F TotalSpace.proj
b : B
x : E b
⊢ { proj := b, snd := x } ∈ (a.pretrivializationA... | ι : Type u_1
B : Type u_2
F : Type u_3
X : Type u_4
inst✝³ : TopologicalSpace X
E : B → Type u_5
inst✝² : TopologicalSpace B
inst✝¹ : TopologicalSpace F
inst✝ : (x : B) → TopologicalSpace (E x)
a : FiberPrebundle F E
e : Pretrivialization F TotalSpace.proj
b : B
x : E b
⊢ b ∈ (a.pretrivializationAt b).baseSet | ((:c Membership.mem) ((:c Bundle.TotalSpace) (:fv _uniq.52052) (:fv _uniq.52055) (:fv _uniq.52066)) ((:c Set) ((:c Bundle.TotalSpace) (:fv _uniq.52052) (:fv _uniq.52055) (:fv _uniq.52066))) ((:c Set.instMembership) ((:c Bundle.TotalSpace) (:fv _uniq.52052) (:fv _uniq.52055) (:fv _uniq.52066))) ((:c Bundle.TotalSpace.mk... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"B","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"X","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.52058))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.52052) (:sort (+ u_5 1)))"},{"name":"inst✝²","se... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Bundle.TotalSpace) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV5)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Bundle.TotalSpace) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52049","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52052","is_instance":false,"is_let":false,"name":"B","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":43573,"sourceStart":43569,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":43578,"sourceStart":43574,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":435... | [] | [{"source":"(a.pretrivializationAt b).source_eq","source_end":43615,"source_start":43580,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"mem_preimage","source_end":43629,"source_start":43617,"syntax_kind":"ident"},{"source":"TotalSpace.proj","source_end":43646,"source_start":43631,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52049","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52052","is_instance":false,"is_let":false,"user_name":"B"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 158 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 11088cabf2412d5068e49623458dd59b778daff2aa775707adb6d8b081ac60f1 | f557137cd304438b49e12fce739b50566c6200e659be9d21b2fdb0d6c43786a5 | 992efffb6bf63fe26985c53b46c4783f7008ac36d1c5b6e46751516126fd0fc9 | 0f97983f120215d1d762d1d2d7d45b26af346abb30c39da5164d3a948f3f4287 |
cat-searcher/leandojo-benchmark-4-random | test | 85 | FiberPrebundle.mem_pretrivializationAt_source | Mathlib/Topology/FiberBundle/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact a.mem_base_pretrivializationAt b | ι : Type u_1
B : Type u_2
F : Type u_3
X : Type u_4
inst✝³ : TopologicalSpace X
E : B → Type u_5
inst✝² : TopologicalSpace B
inst✝¹ : TopologicalSpace F
inst✝ : (x : B) → TopologicalSpace (E x)
a : FiberPrebundle F E
e : Pretrivialization F TotalSpace.proj
b : B
x : E b
⊢ b ∈ (a.pretrivializationAt b).baseSet | ((:c Membership.mem) (:fv _uniq.52052) ((:c Set) (:fv _uniq.52052)) ((:c Set.instMembership) (:fv _uniq.52052)) (:fv _uniq.52275) ((:c Pretrivialization.baseSet) (:fv _uniq.52052) (:fv _uniq.52055) ((:c Bundle.TotalSpace) (:fv _uniq.52052) (:fv _uniq.52055) (:fv _uniq.52066)) (:fv _uniq.52069) (:fv _uniq.52072) ((:c Bu... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"B","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"X","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.52058))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.52052) (:sort (+ u_5 1)))"},{"name":"inst✝²","se... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:fv FV12)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52049","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52052","is_instance":false,"is_let":false,"name":"B","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":43655,"sourceStart":43650,"tag":"atom"},{"children":[{"source":"a.mem_base_pretrivializationAt","sourceEnd":43686,"sourceStart":43656,"tag":"identifier"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"b","sourceEnd":43688,"sourceStart":43687,"tag":"identifier... | [] | [{"source":"a.mem_base_pretrivializationAt b","source_end":43688,"source_start":43656,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52049","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52052","is_instance":false,"is_let":false,"user_name":"B"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 158 | 5 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b0e7405a0adc19086728af280539e000989407055793ae240da31e099a8fe5b8 | 0f97983f120215d1d762d1d2d7d45b26af346abb30c39da5164d3a948f3f4287 | bd90b4efc619b3b36660f4e2ac8f814071ce6933a08b1dc6fe80ba52e157de2a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 86 | Finset.noncommProd_singleton | Mathlib/Data/Finset/NoncommProd.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_cast | F : Type u_1
ι : Type u_2
α : Type u_3
β : Type u_4
γ : Type u_5
f✝ : α → β → β
op : α → α → α
inst✝¹ : Monoid β
inst✝ : Monoid γ
a : α
f : α → β
⊢ (↑{a}).Pairwise fun a b => Commute (f a) (f b) | F : Type u_1
ι : Type u_2
α : Type u_3
β : Type u_4
γ : Type u_5
f✝ : α → β → β
op : α → α → α
inst✝¹ : Monoid β
inst✝ : Monoid γ
a : α
f : α → β
⊢ {a}.Pairwise fun a b => Commute (f a) (f b) | ((:c Set.Pairwise) (:fv _uniq.31689) ((:c Finset.toSet) (:fv _uniq.31689) ((:c Singleton.singleton) (:fv _uniq.31689) ((:c Finset) (:fv _uniq.31689)) ((:c Finset.instSingleton) (:fv _uniq.31689)) (:fv _uniq.31715))) (:lambda a (:fv _uniq.31689) (:lambda b (:fv _uniq.31689) ((:c Commute) (:fv _uniq.31692) ((:c MulOneCla... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.31689) (:forall _ (:fv _uniq.31692) (:fv _uniq.31692)))"},{"name":"op","sexp... | (:app (:c Set.Pairwise) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Finset.toSet) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Singleton.singleton) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31683","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31686","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"norm_cast","sourceEnd":14929,"sourceStart":14920,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.tacticNorm_cast_","source":"norm_cast","sourceEnd":14929,"sourceStart":14920,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31683","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31686","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 90 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 79f22648ccbc3bd16f554e0244fa8237ad147992faee0bbce8bc3ea4479a3556 | f5dc824b6da809d20e57f8fdae721c2418b12f064f9be6546e4325c10e379a14 | 4526560ee387a60af0a3f42ddce7258b27dc8bd6782a63271dc2d5aa462e81b2 | 34747c61e1e8d843aefdc888a9254095b190ac25e63c8fed83af51701e81324d |
cat-searcher/leandojo-benchmark-4-random | test | 87 | Finset.noncommProd_singleton | Mathlib/Data/Finset/NoncommProd.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Set.pairwise_singleton</a> _ _ | F : Type u_1
ι : Type u_2
α : Type u_3
β : Type u_4
γ : Type u_5
f✝ : α → β → β
op : α → α → α
inst✝¹ : Monoid β
inst✝ : Monoid γ
a : α
f : α → β
⊢ {a}.Pairwise fun a b => Commute (f a) (f b) | ((:c Set.Pairwise) (:fv _uniq.31689) ((:c Singleton.singleton) (:fv _uniq.31689) ((:c Set) (:fv _uniq.31689)) ((:c Set.instSingletonSet) (:fv _uniq.31689)) (:fv _uniq.31715)) (:lambda a (:fv _uniq.31689) (:lambda b (:fv _uniq.31689) ((:c Commute) (:fv _uniq.31692) ((:c MulOneClass.toMul) (:fv _uniq.31692) ((:c Monoid.t... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.31689) (:forall _ (:fv _uniq.31692) (:fv _uniq.31692)))"},{"name":"op","sexp... | (:app (:c Set.Pairwise) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Singleton.singleton) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Singleton) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31683","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31686","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":14945,"sourceStart":14940,"tag":"atom"},{"children":[{"name":"Set.pairwise_singleton","semanticRole":"global","source":"Set.pairwise_singleton","sourceEnd":14968,"sourceStart":14946,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":14970,"sourceStart":149... | [] | [{"source":"Set.pairwise_singleton _ _","source_end":14972,"source_start":14946,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31683","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31686","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 90 | 5 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c5b777ed8f2a5688c08c15980931ab38ebb537774b5ae00e136f64dfd898e145 | 34747c61e1e8d843aefdc888a9254095b190ac25e63c8fed83af51701e81324d | 790078b4745dd20f1b52462a9ba441a9e1150a7ddec25c8acb0dafd8c82d749b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 88 | NFA.toDFA_correct | Mathlib/Computability/NFA.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext x | α : Type u
σ σ' : Type v
M : NFA α σ
⊢ M.toDFA.accepts = M.accepts | case h
α : Type u
σ σ' : Type v
M : NFA α σ
x : List α
⊢ x ∈ M.toDFA.accepts ↔ x ∈ M.accepts | ((:c Eq) ((:c Language) (:fv _uniq.6886)) ((:c DFA.accepts) (:fv _uniq.6886) ((:c Set) (:fv _uniq.6888)) ((:c NFA.toDFA) (:fv _uniq.6886) (:fv _uniq.6888) (:fv _uniq.6894))) ((:c NFA.accepts) (:fv _uniq.6886) (:fv _uniq.6888) (:fv _uniq.6894))) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"σ","sexp":"(:sort (+ v 1))"},{"name":"σ'","sexp":"(:sort (+ v 1))"},{"name":"M","sexp":"((:c NFA) (:fv _uniq.6886) (:fv _uniq.6888))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Language) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c DFA.accepts) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 2 (:app (:c NFA.toDFA) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6886","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6888","is_instance":false,"is_let":false,"name":"σ","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"ext","sourceEnd":4134,"sourceStart":4131,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":4136,"sourceStart":4135,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":4136,"sourceStart":4135,"tag":"nod... | [{"role":"fresh_name","source":"x","source_end":4136,"source_start":4135,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6886","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6888","is_instance":false,"is_let":false,"user_name":"σ"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 38 | 4 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c482937a0ebee55fc7a8e336e24a707357c8d2e908ce0cabe973d7697877c289 | ec57cb2c2f14f9a52d720c8a95ca3e1c80de37d3f2092a155886f50aeb04c37b | ee522618587c4a8062e9541e92fad69d5c6e7dbdf5366e9d82c63ebe3c1e08c5 | ebab50e26143735371f1a7d3eed362ec2d0c1f478b79fb0132f3f4bbaeedb1db |
cat-searcher/leandojo-benchmark-4-random | test | 89 | NFA.toDFA_correct | Mathlib/Computability/NFA.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>NFA.mem_accepts</a>, <a>DFA.mem_accepts</a>] | case h
α : Type u
σ σ' : Type v
M : NFA α σ
x : List α
⊢ x ∈ M.toDFA.accepts ↔ x ∈ M.accepts | case h
α : Type u
σ σ' : Type v
M : NFA α σ
x : List α
⊢ M.toDFA.evalFrom M.toDFA.start x ∈ M.toDFA.accept ↔ ∃ S ∈ M.accept, S ∈ M.evalFrom M.start x | ((:c Iff) ((:c Membership.mem) ((:c List) (:fv _uniq.6886)) ((:c Language) (:fv _uniq.6886)) ((:c instMembershipListLanguage) (:fv _uniq.6886)) (:fv _uniq.6949) ((:c DFA.accepts) (:fv _uniq.6886) ((:c Set) (:fv _uniq.6888)) ((:c NFA.toDFA) (:fv _uniq.6886) (:fv _uniq.6888) (:fv _uniq.6894)))) ((:c Membership.mem) ((:c ... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"σ","sexp":"(:sort (+ v 1))"},{"name":"σ'","sexp":"(:sort (+ v 1))"},{"name":"M","sexp":"((:c NFA) (:fv _uniq.6886) (:fv _uniq.6888))"},{"name":"x","sexp":"((:c List) (:fv _uniq.6886))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Language) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6886","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6888","is_instance":false,"is_let":false,"name":"σ","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"rw","sourceEnd":4141,"sourceStart":4139,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4143,"sourceStart":4142,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"NFA.mem_accepts","se... | [] | [{"source":"mem_accepts","source_end":4154,"source_start":4143,"syntax_kind":"ident"},{"source":"DFA.mem_accepts","source_end":4171,"source_start":4156,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6886","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6888","is_instance":false,"is_let":false,"user_name":"σ"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 38 | 5 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9b93bb34235f27b66d0214a0a48046b759c3e0636e110e30f5494cc13a5af0b3 | ebab50e26143735371f1a7d3eed362ec2d0c1f478b79fb0132f3f4bbaeedb1db | 9993012ca019a557925530f21eb069d2e4534a634202399c737a22c18eb67d9c | ad880839625a3e8b420a5880cbeab3e521b12cd43837f33b6dbf63f8b2459ce7 |
cat-searcher/leandojo-benchmark-4-random | test | 90 | NFA.toDFA_correct | Mathlib/Computability/NFA.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun ⟨w, h2, h3⟩ => ⟨w, h3, h2⟩ | case h.mpr
α : Type u
σ σ' : Type v
M : NFA α σ
x : List α
⊢ (∃ S ∈ M.accept, S ∈ M.evalFrom M.start x) → M.toDFA.evalFrom M.toDFA.start x ∈ M.toDFA.accept | (:forall _ ((:c Exists) (:fv _uniq.6888) (:lambda S (:fv _uniq.6888) ((:c And) ((:c Membership.mem) (:fv _uniq.6888) ((:c Set) (:fv _uniq.6888)) ((:c Set.instMembership) (:fv _uniq.6888)) 0 ((:c NFA.accept) (:fv _uniq.6886) (:fv _uniq.6888) (:fv _uniq.6894))) ((:c Membership.mem) (:fv _uniq.6888) ((:c Set) (:fv _uniq.6... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"σ","sexp":"(:sort (+ v 1))"},{"name":"σ'","sexp":"(:sort (+ v 1))"},{"name":"M","sexp":"((:c NFA) (:fv _uniq.6886) (:fv _uniq.6888))"},{"name":"x","sexp":"((:c List) (:fv _uniq.6886))"}] | (:forall _ :explicit (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda S :explicit (:fv FV1) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6886","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6888","is_instance":false,"is_let":false,"name":"σ","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":4199,"sourceStart":4194,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":4203,"sourceStart":4200,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":4207,"sourceStart":4204,"tag":"atom"},{"children":[{"sem... | [] | [{"source":"fun ⟨w, h2, h3⟩ => ⟨w, h3, h2⟩","source_end":4238,"source_start":4200,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6886","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6888","is_instance":false,"is_let":false,"user_name":"σ"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 38 | 19 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 517e167f9d26d8e1c0b25d907cdd03420c7229f828cee4532ce6be63dce96948 | 6d37503ed86f414f5af3fc717b73cb51ebf0fc7a25c11a22959923d9d2cd9169 | 59ea2745f7475cb5c3bbb20416df2f1e5322728b4809723ab6e0a956874dfd7a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 91 | FractionalIdeal.count_mul | Mathlib/RingTheory/DedekindDomain/Factorization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hv : <a>Irreducible</a> (<a>Associates.mk</a> v.asIdeal) := by apply v.associates_irreducible | R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
⊢ count K v (I * I') = count K v I + count K v I' | R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
⊢ count K v (I * I') = count K v I + count K v I' | ((:c Eq) (:c Int) ((:c FractionalIdeal.count) (:fv _uniq.73763) (:fv _uniq.73766) (:fv _uniq.73769) (:fv _uniq.73772) (:fv _uniq.74024) (:fv _uniq.74061) (:fv _uniq.74070) (:fv _uniq.74079) ((:c HMul.hMul) ((:c FractionalIdeal) (:fv _uniq.73763) (:fv _uniq.73766) ((:c nonZeroDivisors) (:fv _uniq.73763) ((:c Semiring.to... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.73763))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.73769))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.73763) (:fv _uniq.73769) ((:c CommRing.toCommSemiring) (:fv _uniq.7376... | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c FractionalIdeal.count) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"have","sourceEnd":17975,"sourceStart":17971,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hv","sourceEnd":17978,"sourceStart":17976,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hv","sourceEnd":17978,"sourceStart":17976,"tag":"nod... | [] | [{"source":"Irreducible (Associates.mk v.asIdeal)","source_end":18018,"source_start":17981,"syntax_kind":"Lean.Parser.Term.app"},{"source":"v.associates_irreducible","source_end":18055,"source_start":18031,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 46 | 4 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 95fe986fe0f6adf18787fd6030cd2084b6ffbe5a4eab7aa2e37d32db42647e3e | 2e5dd5c1c3764960073b14b4aeb091f7cf019748bb9a70d67d5d74fd2792f2d6 | fdde7d0b97d9487b38dac0dfdbc49190ae61f48274fd2e01d00d6659ae6f8111 | 8eed0fe074ee1189fea5863ca03013170e51a92c6199efa0d0a6080f07a9bf0c |
cat-searcher/leandojo-benchmark-4-random | test | 92 | FractionalIdeal.count_mul | Mathlib/RingTheory/DedekindDomain/Factorization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨a, J, ha, haJ⟩ := <a>FractionalIdeal.exists_eq_spanSingleton_mul</a> I | R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
⊢ count K v (I * I') = count K v I + count K v I' | case intro.intro.intro
R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha : a ≠ 0
haJ : I = ... | ((:c Eq) (:c Int) ((:c FractionalIdeal.count) (:fv _uniq.73763) (:fv _uniq.73766) (:fv _uniq.73769) (:fv _uniq.73772) (:fv _uniq.74024) (:fv _uniq.74061) (:fv _uniq.74070) (:fv _uniq.74079) ((:c HMul.hMul) ((:c FractionalIdeal) (:fv _uniq.73763) (:fv _uniq.73766) ((:c nonZeroDivisors) (:fv _uniq.73763) ((:c Semiring.to... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.73763))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.73769))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.73763) (:fv _uniq.73769) ((:c CommRing.toCommSemiring) (:fv _uniq.7376... | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c FractionalIdeal.count) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"obtain","sourceEnd":18064,"sourceStart":18058,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":18068,"sourceStart":18065,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEn... | [] | [{"source":"exists_eq_spanSingleton_mul I","source_end":18117,"source_start":18088,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨a, J, ha, haJ⟩","source_end":18084,"source_start":18065,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 46 | 7 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bcc8f53587156a66a854e69bd6f4d73c33d851aa045ca6b02ed17e4267e58231 | 8eed0fe074ee1189fea5863ca03013170e51a92c6199efa0d0a6080f07a9bf0c | 8504c3eed951dec6f5e3d858638875b8081ca8feb28116b88afaee04ec86b581 | 3c6e621aea18cd79b910cd7c39c00caba9081a7db7594b27c616c94f30e18d46 |
cat-searcher/leandojo-benchmark-4-random | test | 93 | FractionalIdeal.count_mul | Mathlib/RingTheory/DedekindDomain/Factorization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have ha_ne_zero : <a>Associates.mk</a> (<a>Ideal.span</a> {a} : <a>Ideal</a> R) ≠ 0 := by rw [<a>ne_eq</a>, <a>Associates.mk_eq_zero</a>, <a>Ideal.zero_eq_bot</a>, <a>Ideal.span_singleton_eq_bot</a>]; exact ha | case intro.intro.intro
R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha : a ≠ 0
haJ : I = ... | case intro.intro.intro
R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha : a ≠ 0
haJ : I = ... | ((:c Eq) (:c Int) ((:c FractionalIdeal.count) (:fv _uniq.73763) (:fv _uniq.73766) (:fv _uniq.73769) (:fv _uniq.73772) (:fv _uniq.74024) (:fv _uniq.74061) (:fv _uniq.74070) (:fv _uniq.74079) ((:c HMul.hMul) ((:c FractionalIdeal) (:fv _uniq.73763) (:fv _uniq.73766) ((:c nonZeroDivisors) (:fv _uniq.73763) ((:c Semiring.to... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.73763))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.73769))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.73763) (:fv _uniq.73769) ((:c CommRing.toCommSemiring) (:fv _uniq.7376... | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c FractionalIdeal.count) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"have","sourceEnd":18124,"sourceStart":18120,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"ha_ne_zero","sourceEnd":18135,"sourceStart":18125,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"ha_ne_zero","sourceEnd":18135,"sourceStart":... | [] | [{"source":"Associates.mk (Ideal.span {a} : Ideal R) ≠ 0","source_end":18184,"source_start":18138,"syntax_kind":"«term_≠_»"},{"source":"ne_eq","source_end":18204,"source_start":18199,"syntax_kind":"ident"},{"source":"Associates.mk_eq_zero","source_end":18227,"source_start":18206,"syntax_kind":"ident"},{"source":"Ideal.... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 46 | 8 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 711c7da4d6c63b154eea7fb8d35c2f1e2ca0726c6374d1225bb6d7552545a5be | 3c6e621aea18cd79b910cd7c39c00caba9081a7db7594b27c616c94f30e18d46 | 07b7de5155aaeb343b0a24184f96893280da3c03deaf7195d578c7b1bee1bc69 | 20779cb11f82e1b5c2bdb41236f78b21217d7f8073403cb86d393c255bf069dc |
cat-searcher/leandojo-benchmark-4-random | test | 94 | FractionalIdeal.count_mul | Mathlib/RingTheory/DedekindDomain/Factorization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hJ_ne_zero : <a>Associates.mk</a> J ≠ 0 := Associates.mk_ne_zero.mpr (<a>FractionalIdeal.ideal_factor_ne_zero</a> hI haJ) | case intro.intro.intro
R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha : a ≠ 0
haJ : I = ... | case intro.intro.intro
R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha : a ≠ 0
haJ : I = ... | ((:c Eq) (:c Int) ((:c FractionalIdeal.count) (:fv _uniq.73763) (:fv _uniq.73766) (:fv _uniq.73769) (:fv _uniq.73772) (:fv _uniq.74024) (:fv _uniq.74061) (:fv _uniq.74070) (:fv _uniq.74079) ((:c HMul.hMul) ((:c FractionalIdeal) (:fv _uniq.73763) (:fv _uniq.73766) ((:c nonZeroDivisors) (:fv _uniq.73763) ((:c Semiring.to... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.73763))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.73769))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.73763) (:fv _uniq.73769) ((:c CommRing.toCommSemiring) (:fv _uniq.7376... | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c FractionalIdeal.count) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"have","sourceEnd":18293,"sourceStart":18289,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hJ_ne_zero","sourceEnd":18304,"sourceStart":18294,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hJ_ne_zero","sourceEnd":18304,"sourceStart":... | [] | [{"source":"Associates.mk J ≠ 0","source_end":18328,"source_start":18307,"syntax_kind":"«term_≠_»"},{"source":"Associates.mk_ne_zero.mpr (ideal_factor_ne_zero hI haJ)","source_end":18387,"source_start":18332,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 46 | 18 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8f7eaf4cc424846634fc44db2c45acc76661de2c37c5a402d097baf68eb59ba8 | 20779cb11f82e1b5c2bdb41236f78b21217d7f8073403cb86d393c255bf069dc | bcbee11813d90c7b632b4227eccc4376c538a8b4979a700e668552a1f993fa53 | b709732b0573f78b742a440da29d12e1d1582c8e98f6744d2ee1bc07bd759def |
cat-searcher/leandojo-benchmark-4-random | test | 95 | FractionalIdeal.count_mul | Mathlib/RingTheory/DedekindDomain/Factorization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨a', J', ha', haJ'⟩ := <a>FractionalIdeal.exists_eq_spanSingleton_mul</a> I' | case intro.intro.intro
R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha : a ≠ 0
haJ : I = ... | case intro.intro.intro.intro.intro.intro
R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha ... | ((:c Eq) (:c Int) ((:c FractionalIdeal.count) (:fv _uniq.73763) (:fv _uniq.73766) (:fv _uniq.73769) (:fv _uniq.73772) (:fv _uniq.74024) (:fv _uniq.74061) (:fv _uniq.74070) (:fv _uniq.74079) ((:c HMul.hMul) ((:c FractionalIdeal) (:fv _uniq.73763) (:fv _uniq.73766) ((:c nonZeroDivisors) (:fv _uniq.73763) ((:c Semiring.to... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.73763))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.73769))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.73763) (:fv _uniq.73769) ((:c CommRing.toCommSemiring) (:fv _uniq.7376... | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c FractionalIdeal.count) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"obtain","sourceEnd":18396,"sourceStart":18390,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":18400,"sourceStart":18397,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a'","sourceE... | [] | [{"source":"exists_eq_spanSingleton_mul I'","source_end":18454,"source_start":18424,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨a', J', ha', haJ'⟩","source_end":18420,"source_start":18397,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 46 | 19 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a440d4b47ead7b8b6a7b6fe00b55e8f6ad075ac35c0941b4e160352d2a9cfd1c | b709732b0573f78b742a440da29d12e1d1582c8e98f6744d2ee1bc07bd759def | 181b0cd5e4e9ae180bd9f09ce5f2dcd808370d94b33d499c2cc2cf67c12cc96e | c53680dcf69ba24723a15817f91ad324fb6c7656aa3249c4e8d4f56e8894d7d9 |
cat-searcher/leandojo-benchmark-4-random | test | 96 | FractionalIdeal.count_mul | Mathlib/RingTheory/DedekindDomain/Factorization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have ha'_ne_zero : <a>Associates.mk</a> (<a>Ideal.span</a> {a'} : <a>Ideal</a> R) ≠ 0 := by rw [<a>ne_eq</a>, <a>Associates.mk_eq_zero</a>, <a>Ideal.zero_eq_bot</a>, <a>Ideal.span_singleton_eq_bot</a>]; exact ha' | case intro.intro.intro.intro.intro.intro
R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha ... | case intro.intro.intro.intro.intro.intro
R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha ... | ((:c Eq) (:c Int) ((:c FractionalIdeal.count) (:fv _uniq.73763) (:fv _uniq.73766) (:fv _uniq.73769) (:fv _uniq.73772) (:fv _uniq.74024) (:fv _uniq.74061) (:fv _uniq.74070) (:fv _uniq.74079) ((:c HMul.hMul) ((:c FractionalIdeal) (:fv _uniq.73763) (:fv _uniq.73766) ((:c nonZeroDivisors) (:fv _uniq.73763) ((:c Semiring.to... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.73763))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.73769))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.73763) (:fv _uniq.73769) ((:c CommRing.toCommSemiring) (:fv _uniq.7376... | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c FractionalIdeal.count) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"have","sourceEnd":18461,"sourceStart":18457,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"ha'_ne_zero","sourceEnd":18473,"sourceStart":18462,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"ha'_ne_zero","sourceEnd":18473,"sourceStart... | [] | [{"source":"Associates.mk (Ideal.span {a'} : Ideal R) ≠ 0","source_end":18523,"source_start":18476,"syntax_kind":"«term_≠_»"},{"source":"ne_eq","source_end":18543,"source_start":18538,"syntax_kind":"ident"},{"source":"Associates.mk_eq_zero","source_end":18566,"source_start":18545,"syntax_kind":"ident"},{"source":"Ideal... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 46 | 20 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e5d8e6d7b349912f49a9079387735e00f034e90bcc77c4aab944b5e6f80726f3 | c53680dcf69ba24723a15817f91ad324fb6c7656aa3249c4e8d4f56e8894d7d9 | 1b70950a168991ddaf60dbfb6d01f8106e6cdd9311eea1c392c1ccc413045df1 | b40264228c8a8f0d3c5f1294e5fa80574f7ba8cc312fac1739f7642108f8c67f |
cat-searcher/leandojo-benchmark-4-random | test | 97 | FractionalIdeal.count_mul | Mathlib/RingTheory/DedekindDomain/Factorization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hJ'_ne_zero : <a>Associates.mk</a> J' ≠ 0 := Associates.mk_ne_zero.mpr (<a>FractionalIdeal.ideal_factor_ne_zero</a> hI' haJ') | case intro.intro.intro.intro.intro.intro
R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha ... | case intro.intro.intro.intro.intro.intro
R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha ... | ((:c Eq) (:c Int) ((:c FractionalIdeal.count) (:fv _uniq.73763) (:fv _uniq.73766) (:fv _uniq.73769) (:fv _uniq.73772) (:fv _uniq.74024) (:fv _uniq.74061) (:fv _uniq.74070) (:fv _uniq.74079) ((:c HMul.hMul) ((:c FractionalIdeal) (:fv _uniq.73763) (:fv _uniq.73766) ((:c nonZeroDivisors) (:fv _uniq.73763) ((:c Semiring.to... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.73763))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.73769))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.73763) (:fv _uniq.73769) ((:c CommRing.toCommSemiring) (:fv _uniq.7376... | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c FractionalIdeal.count) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"have","sourceEnd":18633,"sourceStart":18629,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hJ'_ne_zero","sourceEnd":18645,"sourceStart":18634,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hJ'_ne_zero","sourceEnd":18645,"sourceStart... | [] | [{"source":"Associates.mk J' ≠ 0","source_end":18670,"source_start":18648,"syntax_kind":"«term_≠_»"},{"source":"Associates.mk_ne_zero.mpr (ideal_factor_ne_zero hI' haJ')","source_end":18735,"source_start":18678,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 46 | 30 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1efc8d64a5fa895c41996038771d7ebf39f2b94d09ba45efe907088486588aef | b40264228c8a8f0d3c5f1294e5fa80574f7ba8cc312fac1739f7642108f8c67f | b92542621201323080bb7a4e030aab3c54b233d3e2cb53254c766f6f011b9dc4 | 5a5d68666ccc85e21722cbcdcf4f0664f973e9d3fcaf80f13fa7c51762f13add |
cat-searcher/leandojo-benchmark-4-random | test | 98 | FractionalIdeal.count_mul | Mathlib/RingTheory/DedekindDomain/Factorization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h_prod : I * I' = <a>FractionalIdeal.spanSingleton</a> R⁰ ((<a>algebraMap</a> R K) (a * a'))⁻¹ * ↑(J * J') := by rw [haJ, haJ', <a>mul_assoc</a>, <a>mul_comm</a> (J : <a>FractionalIdeal</a> R⁰ K), <a>mul_assoc</a>, ← <a>mul_assoc</a>, <a>FractionalIdeal.spanSingleton_mul_spanSingleton</a>, <a>FractionalIdeal.coeId... | case intro.intro.intro.intro.intro.intro
R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha ... | case intro.intro.intro.intro.intro.intro
R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha ... | ((:c Eq) (:c Int) ((:c FractionalIdeal.count) (:fv _uniq.73763) (:fv _uniq.73766) (:fv _uniq.73769) (:fv _uniq.73772) (:fv _uniq.74024) (:fv _uniq.74061) (:fv _uniq.74070) (:fv _uniq.74079) ((:c HMul.hMul) ((:c FractionalIdeal) (:fv _uniq.73763) (:fv _uniq.73766) ((:c nonZeroDivisors) (:fv _uniq.73763) ((:c Semiring.to... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.73763))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.73769))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.73763) (:fv _uniq.73769) ((:c CommRing.toCommSemiring) (:fv _uniq.7376... | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c FractionalIdeal.count) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"have","sourceEnd":18742,"sourceStart":18738,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h_prod","sourceEnd":18749,"sourceStart":18743,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h_prod","sourceEnd":18749,"sourceStart":18743,"t... | [] | [{"source":"I * I' = spanSingleton R⁰ ((algebraMap R K) (a * a'))⁻¹ * ↑(J * J')","source_end":18826,"source_start":18752,"syntax_kind":"«term_=_»"},{"source":"haJ","source_end":18844,"source_start":18841,"syntax_kind":"ident"},{"source":"haJ'","source_end":18850,"source_start":18846,"syntax_kind":"ident"},{"source":"mu... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 46 | 31 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 79ce75bc64dc9126b61149e2fedbb92742e8dbfe623ad5e819993020caccd4c2 | 5a5d68666ccc85e21722cbcdcf4f0664f973e9d3fcaf80f13fa7c51762f13add | de320b45a3a0b9d4a4284e5ed9ea033358f9f2d4885bb5c1ec00874c7088670a | fe629343b461a29d589fa8a908b1baab4b15cbdc048443137bc21602400f3855 |
cat-searcher/leandojo-benchmark-4-random | test | 99 | FractionalIdeal.count_mul | Mathlib/RingTheory/DedekindDomain/Factorization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>FractionalIdeal.count_well_defined</a> K v hI haJ, <a>FractionalIdeal.count_well_defined</a> K v hI' haJ', <a>FractionalIdeal.count_well_defined</a> K v (<a>mul_ne_zero</a> hI hI') h_prod, ← <a>Associates.mk_mul_mk</a>, <a>Associates.count_mul</a> hJ_ne_zero hJ'_ne_zero hv, ← <a>Ideal.span_singleton_mul_span_sin... | case intro.intro.intro.intro.intro.intro
R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha ... | case intro.intro.intro.intro.intro.intro
R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha ... | ((:c Eq) (:c Int) ((:c FractionalIdeal.count) (:fv _uniq.73763) (:fv _uniq.73766) (:fv _uniq.73769) (:fv _uniq.73772) (:fv _uniq.74024) (:fv _uniq.74061) (:fv _uniq.74070) (:fv _uniq.74079) ((:c HMul.hMul) ((:c FractionalIdeal) (:fv _uniq.73763) (:fv _uniq.73766) ((:c nonZeroDivisors) (:fv _uniq.73763) ((:c Semiring.to... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.73763))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.73769))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.73763) (:fv _uniq.73769) ((:c CommRing.toCommSemiring) (:fv _uniq.7376... | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c FractionalIdeal.count) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"rw","sourceEnd":19056,"sourceStart":19054,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":19058,"sourceStart":19057,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Fra... | [] | [{"source":"count_well_defined K v hI haJ","source_end":19087,"source_start":19058,"syntax_kind":"Lean.Parser.Term.app"},{"source":"count_well_defined K v hI' haJ'","source_end":19120,"source_start":19089,"syntax_kind":"Lean.Parser.Term.app"},{"source":"count_well_defined K v (mul_ne_zero hI hI') h_prod","source_end":1... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 46 | 46 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a79155464e5565b827abd18613db27e1ca55d4cbba79b6d4ceb7dc82e2753645 | fe629343b461a29d589fa8a908b1baab4b15cbdc048443137bc21602400f3855 | 7c3d9f6b317460f2742a418454a371d55a229470d87b25bba1b1fc5b79b62177 | 79a7da5e3fc97b6c6c8c198c28fba01193b200fd9404609ffa1280d3d8648a68 |
cat-searcher/leandojo-benchmark-4-random | test | 100 | FractionalIdeal.count_mul | Mathlib/RingTheory/DedekindDomain/Factorization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | push_cast | case intro.intro.intro.intro.intro.intro
R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha ... | case intro.intro.intro.intro.intro.intro
R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha ... | ((:c Eq) (:c Int) ((:c HSub.hSub) (:c Int) (:c Int) (:c Int) ((:c instHSub) (:c Int) (:c Int.instSub)) ((:c Nat.cast) (:c Int) (:c instNatCastInt) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c Associates.count) ((:c Ideal) (:fv _uniq.73763) ((:c CommSemiring.toSemiring) (:fv _... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.73763))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.73769))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.73763) (:fv _uniq.73769) ((:c CommRing.toCommSemiring) (:fv _uniq.7376... | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:c Int)) (:arg :implicit-type 2 (:c Int)) (:arg :instance 3 (:instance-of (:app (:c HSub) (:arg :explicit 0 (:c Int)) (:arg :explicit 1 (:c Int)) (:arg :explicit 2 (:c Int))))) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"push_cast","sourceEnd":19390,"sourceStart":19381,"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":[... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 46 | 56 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ad72a7dbd6b3450dc562726c741360df1f9bcfa7a94d9b9e3ddb04437a09d555 | 79a7da5e3fc97b6c6c8c198c28fba01193b200fd9404609ffa1280d3d8648a68 | 5189104d9b5e7264ce49402b63410b1cd440d29f098c6f68c6d5dbb0f8982ff0 | 38287e267a55344cc3c2db92c3e5c11acb550be9c775ed55f0e3f038c082dd6d |
cat-searcher/leandojo-benchmark-4-random | test | 101 | FractionalIdeal.count_mul | Mathlib/RingTheory/DedekindDomain/Factorization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | case intro.intro.intro.intro.intro.intro
R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha ... | ((:c Eq) (:c Int) ((:c HSub.hSub) (:c Int) (:c Int) (:c Int) ((:c instHSub) (:c Int) (:c Int.instSub)) ((:c HAdd.hAdd) (:c Int) (:c Int) (:c Int) ((:c instHAdd) (:c Int) ((:c AddSemigroup.toAdd) (:c Int) ((:c AddMonoid.toAddSemigroup) (:c Int) ((:c AddMonoidWithOne.toAddMonoid) (:c Int) ((:c AddGroupWithOne.toAddMonoid... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.73763))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.73769))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.73763) (:fv _uniq.73769) ((:c CommRing.toCommSemiring) (:fv _uniq.7376... | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:c Int)) (:arg :implicit-type 2 (:c Int)) (:arg :instance 3 (:instance-of (:app (:c HSub) (:arg :explicit 0 (:c Int)) (:arg :explicit 1 (:c Int)) (:arg :explicit 2 (:c Int))))) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"ring","sourceEnd":19397,"sourceStart":19393,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":19397,"sourceStart":19393,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 46 | 57 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5161b5b5e55adc4a15a38f87e2384910e459791c5f51351fc733725bd3feb2b3 | 38287e267a55344cc3c2db92c3e5c11acb550be9c775ed55f0e3f038c082dd6d | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 |
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