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cat-searcher/leandojo-benchmark-4-random | test | 1,859 | CategoryTheory.EffectiveEpiFamily.transitive_of_finite | Mathlib/CategoryTheory/Sites/Coherent/CoherentTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>CategoryTheory.Coverage.saturate.transitive</a> X (<a>CategoryTheory.Sieve.generate</a> (<a>CategoryTheory.Presieve.ofArrows</a> Y π)) | C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y : α → C
π : (a : α) → Y a ⟶ X
h : EffectiveEpiFamily Y π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a
H : ∀ (a : α), EffectiveEpiFamily (Y_n a) (π_n a)
... | case a
C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y : α → C
π : (a : α) → Y a ⟶ X
h : EffectiveEpiFamily Y π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a
H : ∀ (a : α), EffectiveEpiFamily (Y_n a) (... | ((:c Membership.mem) ((:c CategoryTheory.Sieve) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1400)) ((:c Set) ((:c CategoryTheory.Sieve) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1400))) ((:c Set.instMembership) ((:c CategoryTheory.Sieve) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1400))) ((:c CategoryTheory.Sieve... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1379))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Precoherent) (:fv _uniq.1379) (:fv _uniq.1383))"},{"name":"X","sexp":"(:fv _uniq.1379)"},{"name":"α","sexp":"(:sort 1)"},{"name":"inst✝¹","sexp":"((:c Finite) ... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c CategoryTheory.Sieve) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV3)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c CategoryT... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Category) ... | {"children":[{"source":"apply","sourceEnd":2712,"sourceStart":2707,"tag":"atom"},{"children":[{"name":"CategoryTheory.Coverage.saturate.transitive","semanticRole":"constructor","source":"Coverage.saturate.transitive","sourceEnd":2741,"sourceStart":2713,"tag":"identifier"},{"children":[{"contextIndex":3,"semanticRole":"... | [] | [{"source":"Coverage.saturate.transitive X (Sieve.generate (Presieve.ofArrows Y π))","source_end":2785,"source_start":2713,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":2,... | 4 | 15 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 635f204d478a2e34691728a7a596469af7c662eefe7ab100fdde30b3ea5e7b3b | 5176c2d3399a9423d0de9d863e9a870fb70f06aed13efffb4aace9f15aa77800 | 058d37a8a6a0014b72e04e6b38e098b6741cc405056cbccbfe89810c6865f043 | 08921005d94834d05d89323060c2eccf0ad5a2f36d0c5fdfc4aa268b0d43e176 |
cat-searcher/leandojo-benchmark-4-random | test | 1,860 | CategoryTheory.EffectiveEpiFamily.transitive_of_finite | Mathlib/CategoryTheory/Sites/Coherent/CoherentTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | change <a>Nonempty</a> _ | C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y : α → C
π : (a : α) → Y a ⟶ X
h : EffectiveEpiFamily Y π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a
H : ∀ (a : α), EffectiveEpiFamily (Y_n a) (π_n a)
... | C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y : α → C
π : (a : α) → Y a ⟶ X
h : EffectiveEpiFamily Y π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a
H : ∀ (a : α), EffectiveEpiFamily (Y_n a) (π_n a)
... | ((:c CategoryTheory.Presieve.EffectiveEpimorphic) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1400) ((:c CategoryTheory.Presieve.ofArrows) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1400) ((:c Sigma) (:fv _uniq.2126) (:lambda a (:fv _uniq.2126) ((:fv _uniq.2131) 0))) (:lambda c ((:c Sigma) (:fv _uniq.2126) (:lambda ... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1379))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Precoherent) (:fv _uniq.1379) (:fv _uniq.1383))"},{"name":"X","sexp":"(:fv _uniq.1379)"},{"name":"α","sexp":"(:sort 1)"},{"name":"inst✝¹","sexp":"((:c Finite) ... | (:app (:c CategoryTheory.Presieve.EffectiveEpimorphic) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit 2) (:arg :explicit 3 (:app (:c CategoryTheory.Presieve.ofArrows) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Category) ... | {"children":[{"source":"change","sourceEnd":2416,"sourceStart":2410,"tag":"atom"},{"children":[{"name":"Nonempty","semanticRole":"global","source":"Nonempty","sourceEnd":2425,"sourceStart":2417,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":2427,"sourceStart":2426,"tag":"atom"}],"kind":"Lean.Pa... | [] | [{"source":"Nonempty _","source_end":2427,"source_start":2417,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":2,... | 4 | 10 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c181aaebaf1fe0ed0d74926b05249e4306e55980be8be46021d6183d84e05a93 | 9bc92f40e196c8218efeccd55a494e69de73397efa6a152a9c8f23b593ac8e29 | 64db6e3b701272c3e531262aa9c5dc690df65d6eb8fe96706dfd90776c7d167a | 780c2915b0dc3c83fee19d42aea6db237847d09c01114173393004d0bf28abb9 |
cat-searcher/leandojo-benchmark-4-random | test | 1,861 | CategoryTheory.EffectiveEpiFamily.transitive_of_finite | Mathlib/CategoryTheory/Sites/Coherent/CoherentTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>CategoryTheory.Sieve.forallYonedaIsSheaf_iff_colimit</a>] | C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y : α → C
π : (a : α) → Y a ⟶ X
h : EffectiveEpiFamily Y π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a
H : ∀ (a : α), EffectiveEpiFamily (Y_n a) (π_n a)
... | C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y : α → C
π : (a : α) → Y a ⟶ X
h : EffectiveEpiFamily Y π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a
H : ∀ (a : α), EffectiveEpiFamily (Y_n a) (π_n a)
... | ((:c Nonempty) ((:c CategoryTheory.Limits.IsColimit) ((:c CategoryTheory.Presieve.category) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1400) ((:c CategoryTheory.Sieve.arrows) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1400) ((:c CategoryTheory.Sieve.generate) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1400) ((:c ... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1379))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Precoherent) (:fv _uniq.1379) (:fv _uniq.1383))"},{"name":"X","sexp":"(:fv _uniq.1379)"},{"name":"α","sexp":"(:sort 1)"},{"name":"inst✝¹","sexp":"((:c Finite) ... | (:app (:c Nonempty) (:arg :explicit 0 (:app (:c CategoryTheory.Limits.IsColimit) (:arg :implicit-type 0 (:app (:c CategoryTheory.Presieve.category) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit 2) (:arg :explicit 3 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Category) ... | {"children":[{"source":"rw","sourceEnd":2434,"sourceStart":2432,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2436,"sourceStart":2435,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":2439,"sourceStart":... | [] | [{"source":"Sieve.forallYonedaIsSheaf_iff_colimit","source_end":2477,"source_start":2440,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":2,... | 4 | 11 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3c227471cb772ff0c78d7c8a83314fec97738ca1ab71e21cd9c345dfdedec2af | 780c2915b0dc3c83fee19d42aea6db237847d09c01114173393004d0bf28abb9 | 56d3ae096993dd1266cdd78dbfc2d21e23ed6481cd61d2cf23139be9b3bf71ce | eacc037cbfdcbeaf70405733557e14a1f8e33e3e5962a8c975ef89dd623978ce |
cat-searcher/leandojo-benchmark-4-random | test | 1,862 | CategoryTheory.EffectiveEpiFamily.transitive_of_finite | Mathlib/CategoryTheory/Sites/Coherent/CoherentTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun W => <a>CategoryTheory.coherentTopology.isSheaf_yoneda_obj</a> W _ h₂ | C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y : α → C
π : (a : α) → Y a ⟶ X
h : EffectiveEpiFamily Y π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a
H : ∀ (a : α), EffectiveEpiFamily (Y_n a) (π_n a)
... | (:forall W (:fv _uniq.1379) ((:c CategoryTheory.Presieve.IsSheafFor) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1400) ((:c Prefunctor.obj) (:fv _uniq.1379) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.1379) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.1379) (:fv _uniq.1383))) ((:c CategoryTheo... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1379))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Precoherent) (:fv _uniq.1379) (:fv _uniq.1383))"},{"name":"X","sexp":"(:fv _uniq.1379)"},{"name":"α","sexp":"(:sort 1)"},{"name":"inst✝¹","sexp":"((:c Finite) ... | (:forall W :explicit (:fv FV0) (:app (:c CategoryTheory.Presieve.IsSheafFor) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit 2) (:arg :explicit 3 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instan... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Category) ... | {"children":[{"source":"exact","sourceEnd":2488,"sourceStart":2483,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":2492,"sourceStart":2489,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"W","sourceEnd":2494,"sourceStart":2493,"tag":"identifier"}],"kind":"null","source":"W","sourc... | [] | [{"source":"fun W => coherentTopology.isSheaf_yoneda_obj W _ h₂\n -- Show that a covering sieve is a colimit, which implies the original set of arrows is regular\n -- epimorphic. We use the transitivity property of saturation","source_end":2542,"source_start":2489,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":2,... | 4 | 14 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5999b3235fc5f3db3744274aab7138c9e772cf2860ab3da463327b8c30a9223a | eacc037cbfdcbeaf70405733557e14a1f8e33e3e5962a8c975ef89dd623978ce | 5b6ec1fa766ae9dd7bf217be0ce9d15b0826a8bf41e4dbb0ff4df126761b5628 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,863 | CategoryTheory.EffectiveEpiFamily.transitive_of_finite | Mathlib/CategoryTheory/Sites/Coherent/CoherentTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>CategoryTheory.Coverage.saturate.of</a> | case a
C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y : α → C
π : (a : α) → Y a ⟶ X
h : EffectiveEpiFamily Y π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a
H : ∀ (a : α), EffectiveEpiFamily (Y_n a) (... | case a.hS
C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y : α → C
π : (a : α) → Y a ⟶ X
h : EffectiveEpiFamily Y π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a
H : ∀ (a : α), EffectiveEpiFamily (Y_n a... | ((:c CategoryTheory.Coverage.saturate) (:fv _uniq.1379) (:fv _uniq.1383) ((:c CategoryTheory.coherentCoverage) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1398)) (:fv _uniq.1400) ((:c CategoryTheory.Sieve.generate) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1400) ((:c CategoryTheory.Presieve.ofArrows) (:fv _uniq.137... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1379))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Precoherent) (:fv _uniq.1379) (:fv _uniq.1383))"},{"name":"X","sexp":"(:fv _uniq.1379)"},{"name":"α","sexp":"(:sort 1)"},{"name":"inst✝¹","sexp":"((:c Finite) ... | (:app (:c CategoryTheory.Coverage.saturate) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c CategoryTheory.coherentCoverage) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryThe... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Category) ... | {"children":[{"source":"apply","sourceEnd":2796,"sourceStart":2791,"tag":"atom"},{"name":"CategoryTheory.Coverage.saturate.of","semanticRole":"constructor","source":"Coverage.saturate.of","sourceEnd":2817,"sourceStart":2797,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Coverage.saturate.of","so... | [] | [{"source":"Coverage.saturate.of","source_end":2817,"source_start":2797,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":2,... | 4 | 20 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 103d5e9badeebd4a109555307208434e623922753dce7cd9e41746a6b17e088e | 6a3dd82b298932e7b61156bb1268b47d5fd058b09827fb1ef67a6fa1d43c4669 | dc0227b09b9657582d8261df9a3f3d1b013c33621661004e1c1a2a4b2c738964 | 48c42bdf1d06f6c742f29f4d1cf0c8f7b48968301310958a93ec3a40f87a2d8c |
cat-searcher/leandojo-benchmark-4-random | test | 1,864 | CategoryTheory.EffectiveEpiFamily.transitive_of_finite | Mathlib/CategoryTheory/Sites/Coherent/CoherentTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | use α, <a>inferInstance</a>, Y, π | case a.hS
C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y : α → C
π : (a : α) → Y a ⟶ X
h : EffectiveEpiFamily Y π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a
H : ∀ (a : α), EffectiveEpiFamily (Y_n a... | ((:c Membership.mem) ((:c CategoryTheory.Presieve) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1400)) ((:c Set) ((:c CategoryTheory.Presieve) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1400))) ((:c Set.instMembership) ((:c CategoryTheory.Presieve) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1400))) ((:c CategoryThe... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1379))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Precoherent) (:fv _uniq.1379) (:fv _uniq.1383))"},{"name":"X","sexp":"(:fv _uniq.1379)"},{"name":"α","sexp":"(:sort 1)"},{"name":"inst✝¹","sexp":"((:c Finite) ... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c CategoryTheory.Presieve) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV3)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Catego... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Category) ... | {"children":[{"source":"use","sourceEnd":2825,"sourceStart":2822,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"contextIndex":5,"semanticRole":"local","source":"α","sourceEnd":2828,"sourceStart":2826,"tag":"identifier"},{"sourc... | [] | [{"source":"α","source_end":2828,"source_start":2826,"syntax_kind":"ident"},{"source":"inferInstance","source_end":2843,"source_start":2830,"syntax_kind":"ident"},{"source":"Y","source_end":2846,"source_start":2845,"syntax_kind":"ident"},{"source":"π","source_end":2850,"source_start":2848,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":2,... | 4 | 21 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1c87f3201a46a752655344dd30669854966c0c73edf8ea01522a292561d3a950 | 48c42bdf1d06f6c742f29f4d1cf0c8f7b48968301310958a93ec3a40f87a2d8c | 3973e2542aeed287ac01778f458e02e554d99a16c2a3754886b04e42753d2b78 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,865 | CategoryTheory.EffectiveEpiFamily.transitive_of_finite | Mathlib/CategoryTheory/Sites/Coherent/CoherentTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro V f ⟨Y₁, h, g, ⟨hY, hf⟩⟩ | case a
C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y : α → C
π : (a : α) → Y a ⟶ X
h : EffectiveEpiFamily Y π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a
H : ∀ (a : α), EffectiveEpiFamily (Y_n a) (... | case a
C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y : α → C
π : (a : α) → Y a ⟶ X
h✝ : EffectiveEpiFamily Y π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a
H : ∀ (a : α), EffectiveEpiFamily (Y_n a) ... | (:forall Y (:fv _uniq.1379) (:forall f ((:c Quiver.Hom) (:fv _uniq.1379) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.1379) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.1379) (:fv _uniq.1383))) 0 (:fv _uniq.1400)) (:forall _ ((:c CategoryTheory.Sieve.arrows) (:fv _uniq.1379) (:fv _uniq.1383) (:f... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1379))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Precoherent) (:fv _uniq.1379) (:fv _uniq.1383))"},{"name":"X","sexp":"(:fv _uniq.1379)"},{"name":"α","sexp":"(:sort 1)"},{"name":"inst✝¹","sexp":"((:c Finite) ... | (:forall Y :strict-implicit (:fv FV0) (:forall f :strict-implicit (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 0) (:arg :explicit 3 (:fv FV3))) (:forall _ :explicit (:app (:c CategoryTheory.Sieve.arrows) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Category) ... | {"children":[{"source":"intro","sourceEnd":2861,"sourceStart":2856,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"V","sourceEnd":2863,"sourceStart":2862,"tag":"identifier"},{"semanticRole":"scoped_local","source":"f","sourceEnd":2865,"sourceStart":2864,"tag":"identifier"},{"children":[{"source":"⟨"... | [{"role":"fresh_name","source":"V","source_end":2863,"source_start":2862,"syntax_kind":"ident"},{"role":"fresh_name","source":"f","source_end":2865,"source_start":2864,"syntax_kind":"ident"},{"role":"fresh_name","source":"Y₁","source_end":2873,"source_start":2869,"syntax_kind":"ident"},{"role":"fresh_name","source":"h"... | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":2,... | 4 | 26 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cd799439773913269960f9213907314158aa57ffcbc9c63a490a4619fc6c70c1 | 561c26bbc9f3bd2acc396be8354090ec51dff5bfccce5807ae35105dfb5fc833 | f83aef0b13b07ba1dba811b21921c01ba72b236d67010d25c36d16a51d41fc1d | ad8b85c279f47b23eecec9734d1db46da14929a355c0c7cc445d5e2a29c80cec |
cat-searcher/leandojo-benchmark-4-random | test | 1,866 | CategoryTheory.EffectiveEpiFamily.transitive_of_finite | Mathlib/CategoryTheory/Sites/Coherent/CoherentTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hf, <a>CategoryTheory.Sieve.pullback_comp</a>] | case a
C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y : α → C
π : (a : α) → Y a ⟶ X
h✝ : EffectiveEpiFamily Y π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a
H : ∀ (a : α), EffectiveEpiFamily (Y_n a) ... | case a
C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y : α → C
π : (a : α) → Y a ⟶ X
h✝ : EffectiveEpiFamily Y π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a
H : ∀ (a : α), EffectiveEpiFamily (Y_n a) ... | ((:c CategoryTheory.Coverage.saturate) (:fv _uniq.1379) (:fv _uniq.1383) ((:c CategoryTheory.coherentCoverage) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1398)) (:fv _uniq.4406) ((:c CategoryTheory.Sieve.pullback) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1400) (:fv _uniq.4406) (:fv _uniq.4409) ((:c CategoryTheory... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1379))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Precoherent) (:fv _uniq.1379) (:fv _uniq.1383))"},{"name":"X","sexp":"(:fv _uniq.1379)"},{"name":"α","sexp":"(:sort 1)"},{"name":"inst✝¹","sexp":"((:c Finite) ... | (:app (:c CategoryTheory.Coverage.saturate) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c CategoryTheory.coherentCoverage) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryThe... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Category) ... | {"children":[{"source":"rw","sourceEnd":2903,"sourceStart":2901,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2905,"sourceStart":2904,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":2908,"sourceStart":... | [] | [{"source":"hf","source_end":2911,"source_start":2909,"syntax_kind":"ident"},{"source":"Sieve.pullback_comp","source_end":2932,"source_start":2913,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":2,... | 4 | 27 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 656ecd32e32ec66b7351e747f8dc832e920b12ce758e4c07d14ec2c5e74e9e36 | ad8b85c279f47b23eecec9734d1db46da14929a355c0c7cc445d5e2a29c80cec | af852f9136f0566a5dbc4bed7dc2261b5fd6978e0cb550039340b48972db244d | 54bd0a91b03f357334375bd6fe5bd86045f634d44045d5ee22a954e2b7b6fc09 |
cat-searcher/leandojo-benchmark-4-random | test | 1,867 | CategoryTheory.EffectiveEpiFamily.transitive_of_finite | Mathlib/CategoryTheory/Sites/Coherent/CoherentTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply (<a>CategoryTheory.coherentTopology</a> C).<a>CategoryTheory.GrothendieckTopology.pullback_stable'</a> | case a
C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y : α → C
π : (a : α) → Y a ⟶ X
h✝ : EffectiveEpiFamily Y π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a
H : ∀ (a : α), EffectiveEpiFamily (Y_n a) ... | case a.a
C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y : α → C
π : (a : α) → Y a ⟶ X
h✝ : EffectiveEpiFamily Y π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a
H : ∀ (a : α), EffectiveEpiFamily (Y_n a... | ((:c CategoryTheory.Coverage.saturate) (:fv _uniq.1379) (:fv _uniq.1383) ((:c CategoryTheory.coherentCoverage) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1398)) (:fv _uniq.4406) ((:c CategoryTheory.Sieve.pullback) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.4522) (:fv _uniq.4406) (:fv _uniq.4523) ((:c CategoryTheory... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1379))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Precoherent) (:fv _uniq.1379) (:fv _uniq.1383))"},{"name":"X","sexp":"(:fv _uniq.1379)"},{"name":"α","sexp":"(:sort 1)"},{"name":"inst✝¹","sexp":"((:c Finite) ... | (:app (:c CategoryTheory.Coverage.saturate) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c CategoryTheory.coherentCoverage) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryThe... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Category) ... | {"children":[{"source":"apply","sourceEnd":2943,"sourceStart":2938,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":2945,"sourceStart":2944,"tag":"atom"},{"children":[{"name":"CategoryTheory.coherentTopology","semanticRole":"global","source":"coherentTopology","sourceEnd":2961,"sourceStart":2945,"tag":... | [] | [{"source":"(coherentTopology C).pullback_stable'","source_end":2981,"source_start":2944,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":2,... | 4 | 31 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2bf527dcde32f90c3a62cb216c11a19e6cbf69f6a85a515d8d94feee7f5b2352 | 54bd0a91b03f357334375bd6fe5bd86045f634d44045d5ee22a954e2b7b6fc09 | dcc0b1bba7d6fb2b3465340d67766a16da584e7439a43ad1b61b5199b1243175 | b43544b4b00c175ac1a92cf6a6679121659da53ad74c652a7475ad2b98eaaba6 |
cat-searcher/leandojo-benchmark-4-random | test | 1,868 | CategoryTheory.EffectiveEpiFamily.transitive_of_finite | Mathlib/CategoryTheory/Sites/Coherent/CoherentTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>CategoryTheory.coherentTopology.mem_sieves_of_hasEffectiveEpiFamily</a> | case a.a
C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y : α → C
π : (a : α) → Y a ⟶ X
h✝ : EffectiveEpiFamily Y π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a
H : ∀ (a : α), EffectiveEpiFamily (Y_n a... | case a.a.a
C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y : α → C
π : (a : α) → Y a ⟶ X
h✝ : EffectiveEpiFamily Y π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a
H : ∀ (a : α), EffectiveEpiFamily (Y_n... | ((:c Membership.mem) ((:c CategoryTheory.Sieve) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.4522)) ((:c Set) ((:c CategoryTheory.Sieve) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.4522))) ((:c Set.instMembership) ((:c CategoryTheory.Sieve) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.4522))) ((:c CategoryTheory.Sieve... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1379))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Precoherent) (:fv _uniq.1379) (:fv _uniq.1383))"},{"name":"X","sexp":"(:fv _uniq.1379)"},{"name":"α","sexp":"(:sort 1)"},{"name":"inst✝¹","sexp":"((:c Finite) ... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c CategoryTheory.Sieve) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV17)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Category... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Category) ... | {"children":[{"source":"apply","sourceEnd":2991,"sourceStart":2986,"tag":"atom"},{"name":"CategoryTheory.coherentTopology.mem_sieves_of_hasEffectiveEpiFamily","semanticRole":"global","source":"coherentTopology.mem_sieves_of_hasEffectiveEpiFamily","sourceEnd":3044,"sourceStart":2992,"tag":"identifier"}],"kind":"Lean.Par... | [] | [{"source":"coherentTopology.mem_sieves_of_hasEffectiveEpiFamily\n -- Need to show that the pullback of the family `π_n` to a given `Y i` is effective epimorphic","source_end":3044,"source_start":2992,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":2,... | 4 | 32 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3169d1b9d1b4d938b8995b929b217f2960fd9fe2bf114efd55943aff9339fd5c | b43544b4b00c175ac1a92cf6a6679121659da53ad74c652a7475ad2b98eaaba6 | c0ce0d33b59fe732914b3fd87590804513aedef0e12272fda85b188e68580a16 | 877e38f3843de1828f3d897bd53b2b333c0648c7255c8dc4a0cb15733ac306e4 |
cat-searcher/leandojo-benchmark-4-random | test | 1,869 | CategoryTheory.EffectiveEpiFamily.transitive_of_finite | Mathlib/CategoryTheory/Sites/Coherent/CoherentTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨i⟩ := hY | case a.a.a
C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y : α → C
π : (a : α) → Y a ⟶ X
h✝ : EffectiveEpiFamily Y π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a
H : ∀ (a : α), EffectiveEpiFamily (Y_n... | case a.a.a.mk
C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y✝ : α → C
π : (a : α) → Y✝ a ⟶ X
h✝ : EffectiveEpiFamily Y✝ π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y✝ a
H : ∀ (a : α), EffectiveEpiFami... | ((:c Exists) (:sort 1) (:lambda α (:sort 1) ((:c Exists) ((:c Finite) 0) (:lambda _ ((:c Finite) 0) ((:c Exists) (:forall _ 1 (:fv _uniq.1379)) (:lambda Y (:forall _ 1 (:fv _uniq.1379)) ((:c Exists) (:forall a 2 ((:c Quiver.Hom) (:fv _uniq.1379) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.1379) ((:c Categor... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1379))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Precoherent) (:fv _uniq.1379) (:fv _uniq.1383))"},{"name":"X","sexp":"(:fv _uniq.1379)"},{"name":"α","sexp":"(:sort 1)"},{"name":"inst✝¹","sexp":"((:c Finite) ... | (:app (:c Exists) (:arg :implicit-type 0 (:sort Type)) (:arg :explicit 1 (:lambda α :explicit (:sort Type) (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Finite) (:arg :explicit 0 0))) (:arg :explicit 1 (:lambda _ :explicit (:app (:c Finite) (:arg :explicit 0 0)) (:app (:c Exists) (:arg :implicit-type 0 (:forall _ ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Category) ... | {"children":[{"source":"obtain","sourceEnd":3155,"sourceStart":3149,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":3159,"sourceStart":3156,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"i","sourceEnd":3... | [] | [{"source":"hY","source_end":3169,"source_start":3167,"syntax_kind":"ident"},{"source":"⟨i⟩","source_end":3163,"source_start":3156,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":2,... | 4 | 33 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e8db5504d9dad610f68a53edf3f23b288c27954ac8cf6c349966ec8bb1740b1e | 877e38f3843de1828f3d897bd53b2b333c0648c7255c8dc4a0cb15733ac306e4 | f7cfd042b6380a6bd8cbcf475e38293ef91db9e14bdbd9c30122a60097f061ca | 52f2a8288cbb80b32f203a717ef879a5398c095811cb7bab4254dfb9c0d7acd6 |
cat-searcher/leandojo-benchmark-4-random | test | 1,870 | CategoryTheory.EffectiveEpiFamily.transitive_of_finite | Mathlib/CategoryTheory/Sites/Coherent/CoherentTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨β i, <a>inferInstance</a>, Y_n i, π_n i, H i, fun b ↦ ⟨Y_n i b, (𝟙 _), π_n i b ≫ π i, ⟨(⟨i, b⟩ : Σ (i : α), β i)⟩, by simp⟩⟩ | case a.a.a.mk
C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y✝ : α → C
π : (a : α) → Y✝ a ⟶ X
h✝ : EffectiveEpiFamily Y✝ π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y✝ a
H : ∀ (a : α), EffectiveEpiFami... | ((:c Exists) (:sort 1) (:lambda α (:sort 1) ((:c Exists) ((:c Finite) 0) (:lambda _ ((:c Finite) 0) ((:c Exists) (:forall _ 1 (:fv _uniq.1379)) (:lambda Y (:forall _ 1 (:fv _uniq.1379)) ((:c Exists) (:forall a 2 ((:c Quiver.Hom) (:fv _uniq.1379) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.1379) ((:c Categor... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1379))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Precoherent) (:fv _uniq.1379) (:fv _uniq.1383))"},{"name":"X","sexp":"(:fv _uniq.1379)"},{"name":"α","sexp":"(:sort 1)"},{"name":"inst✝¹","sexp":"((:c Finite) ... | (:app (:c Exists) (:arg :implicit-type 0 (:sort Type)) (:arg :explicit 1 (:lambda α :explicit (:sort Type) (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Finite) (:arg :explicit 0 0))) (:arg :explicit 1 (:lambda _ :explicit (:app (:c Finite) (:arg :explicit 0 0)) (:app (:c Exists) (:arg :implicit-type 0 (:forall _ ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Category) ... | {"children":[{"source":"exact","sourceEnd":3179,"sourceStart":3174,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":3183,"sourceStart":3180,"tag":"atom"},{"children":[{"children":[{"contextIndex":10,"semanticRole":"local","source":"β","sourceEnd":3185,"sourceStart":3183,"tag":"identifier"},{"children":[{"contextInd... | [] | [{"source":"⟨β i, inferInstance, Y_n i, π_n i, H i, fun b ↦\n ⟨Y_n i b, (𝟙 _), π_n i b ≫ π i, ⟨(⟨i, b⟩ : Σ (i : α), β i)⟩, by simp⟩⟩","source_end":3334,"source_start":3180,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":2,... | 4 | 34 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fa785897994e33e4e361f6741d700b50876343e03dc078dd10ddd8e76a04ef03 | 52f2a8288cbb80b32f203a717ef879a5398c095811cb7bab4254dfb9c0d7acd6 | 4b54f7118a3b944feac6657ea74a34bf29d8d970c06ed31f419f18cfc33a492e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,871 | CategoryTheory.EffectiveEpiFamily.transitive_of_finite | Mathlib/CategoryTheory/Sites/Coherent/CoherentTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | C : Type u_1
inst✝³ : Category.{u_2, u_1} C
inst✝² : Precoherent C
X : C
α : Type
inst✝¹ : Finite α
Y✝ : α → C
π : (a : α) → Y✝ a ⟶ X
h✝ : EffectiveEpiFamily Y✝ π
β : α → Type
inst✝ : ∀ (a : α), Finite (β a)
Y_n : (a : α) → β a → C
π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y✝ a
H : ∀ (a : α), EffectiveEpiFamily (Y_n a) (π_... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.1379) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.1379) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.1379) (:fv _uniq.1383))) ((:fv _uniq.2133) (:fv _uniq.5219) (:fv _uniq.5361)) (:fv _uniq.1400)) ((:c CategoryTheory.CategoryStruct.comp) (:fv _uniq.1379) ((:... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1379))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Precoherent) (:fv _uniq.1379) (:fv _uniq.1383))"},{"name":"X","sexp":"(:fv _uniq.1379)"},{"name":"α","sexp":"(:sort 1)"},{"name":"inst✝¹","sexp":"((:c Finite) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:fv FV12) (:arg :explicit 0 (:fv FV18)) (:arg :explicit 1 (:fv FV21)))) (:arg :explicit 3 (:fv FV3)))) (:arg :explicit 1... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Category) ... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":3328,"sourceStart":3324,"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.1379","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":2,... | 4 | 37 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a9dfd726caa224263e8667372a504e38674b5443167bc2d5c846b764a4497cdb | 7f93b72618d902d2940fd6f4c562589ee11c829e3eb93dee895b31cd798a7385 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,872 | Matrix.zpow_bit1 | Mathlib/LinearAlgebra/Matrix/ZPow.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>bit1</a>, <a>Matrix.zpow_add_one_of_ne_neg_one</a>, <a>Matrix.zpow_bit0</a>] | n' : Type u_1
inst✝² : DecidableEq n'
inst✝¹ : Fintype n'
R : Type u_2
inst✝ : CommRing R
A : M
n : ℤ
⊢ A ^ bit1 n = A ^ n * A ^ n * A | case a
n' : Type u_1
inst✝² : DecidableEq n'
inst✝¹ : Fintype n'
R : Type u_2
inst✝ : CommRing R
A : M
n : ℤ
⊢ bit0 n ≠ -1 | ((:c Eq) ((:c Matrix) (:fv _uniq.108478) (:fv _uniq.108478) (:fv _uniq.108493)) ((:c HPow.hPow) ((:c Matrix) (:fv _uniq.108478) (:fv _uniq.108478) (:fv _uniq.108493)) (:c Int) ((:c Matrix) (:fv _uniq.108478) (:fv _uniq.108478) (:fv _uniq.108493)) ((:c instHPow) ((:c Matrix) (:fv _uniq.108478) (:fv _uniq.108478) (:fv _u... | [{"name":"n'","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.108478))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.108478))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.108493))"},{"name":"A","sexp":"((:c Matrix) (:fv _uniq.108478)... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV3)))) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV3)))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.108478","is_instance":false,"is_let":false,"name":"n'","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.108485","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c DecidableEq) (:arg :... | {"children":[{"source":"rw","sourceEnd":10448,"sourceStart":10446,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10450,"sourceStart":10449,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"bit1","semanticR... | [] | [{"source":"bit1","source_end":10454,"source_start":10450,"syntax_kind":"ident"},{"source":"zpow_add_one_of_ne_neg_one","source_end":10482,"source_start":10456,"syntax_kind":"ident"},{"source":"zpow_bit0","source_end":10493,"source_start":10484,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.108478","is_instance":false,"is_let":false,"user_name":"n'"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.108485","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_inde... | 69 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6b26908c58fa26393a0bb8607426d354978cc4bd9e2ed7b55ca38d55f7492ea2 | 0f46e8de76185316754bf578c939956a966fb8d62aa4a0565b26e8d451d9f843 | 38392352ed799c2c1c87fe8994b29dd01cfc912f1a501ca790514e301bdacbf3 | ec2ff2e3398ee6e2a767f1edfca938f1585ef315f31d9afb7117403af06055ba |
cat-searcher/leandojo-benchmark-4-random | test | 1,873 | Matrix.zpow_bit1 | Mathlib/LinearAlgebra/Matrix/ZPow.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro h | case a
n' : Type u_1
inst✝² : DecidableEq n'
inst✝¹ : Fintype n'
R : Type u_2
inst✝ : CommRing R
A : M
n : ℤ
⊢ bit0 n ≠ -1 | case a
n' : Type u_1
inst✝² : DecidableEq n'
inst✝¹ : Fintype n'
R : Type u_2
inst✝ : CommRing R
A : M
n : ℤ
h : bit0 n = -1
⊢ False | ((:c Ne) (:c Int) ((:c bit0) (:c Int) (:c Int.instAdd) (:fv _uniq.109473)) ((:c Neg.neg) (:c Int) (:c Int.instNegInt) ((:c OfNat.ofNat) (:c Int) (:lit 1) ((:c instOfNat) (:lit 1))))) | [{"name":"n'","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.108478))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.108478))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.108493))"},{"name":"A","sexp":"((:c Matrix) (:fv _uniq.108478)... | (:app (:c Ne) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c bit0) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c Add) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:fv FV7)))) (:arg :explicit 2 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.108478","is_instance":false,"is_let":false,"name":"n'","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.108485","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c DecidableEq) (:arg :... | {"children":[{"source":"intro","sourceEnd":10502,"sourceStart":10497,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":10504,"sourceStart":10503,"tag":"identifier"}],"kind":"null","source":"h","sourceEnd":10504,"sourceStart":10503,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"h","source_end":10504,"source_start":10503,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.108478","is_instance":false,"is_let":false,"user_name":"n'"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.108485","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_inde... | 69 | 9 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 94ca499d8de7cc5e351825c599f965c0395f288025131f7b49dcd2cb8a1d498f | ec2ff2e3398ee6e2a767f1edfca938f1585ef315f31d9afb7117403af06055ba | 5cf42e5c5e9faf9804f4b8005e32168f3a46b38347377087a457c72b727740cb | e84ec63a0b774f0a06405a8b2801ead0a259d60f84ca6a63392d15287d71aae1 |
cat-searcher/leandojo-benchmark-4-random | test | 1,874 | Matrix.zpow_bit1 | Mathlib/LinearAlgebra/Matrix/ZPow.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using <a>congr_arg</a> <a>Int.bodd</a> h | case a
n' : Type u_1
inst✝² : DecidableEq n'
inst✝¹ : Fintype n'
R : Type u_2
inst✝ : CommRing R
A : M
n : ℤ
h : bit0 n = -1
⊢ False | (:c False) | [{"name":"n'","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.108478))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.108478))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.108493))"},{"name":"A","sexp":"((:c Matrix) (:fv _uniq.108478)... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.108478","is_instance":false,"is_let":false,"name":"n'","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.108485","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c DecidableEq) (:arg :... | {"children":[{"source":"simpa","sourceEnd":10512,"sourceStart":10507,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"ch... | [] | [{"source":"congr_arg bodd h","source_end":10535,"source_start":10519,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.108478","is_instance":false,"is_let":false,"user_name":"n'"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.108485","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_inde... | 69 | 10 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d1b17d88a63749c8fc567bf1761b0a55c4c11a33b0890b40ca7a05232668e6b9 | e84ec63a0b774f0a06405a8b2801ead0a259d60f84ca6a63392d15287d71aae1 | 436c41ac6be71b0f89ea45a8e42126d470647c8710d0132863124a6ef620abc5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,875 | MeasureTheory.Measure.exists_measure_inter_spanningSets_pos | Mathlib/MeasureTheory/Measure/Typeclasses.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>not_iff_not</a>] | α : Type u_1
β : Type u_2
δ : Type u_3
ι : Type u_4
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
μ✝ ν ν₁ ν₂ : Measure α
s✝ t : Set α
inst✝¹ : MeasurableSpace α
μ : Measure α
inst✝ : SigmaFinite μ
s : Set α
⊢ (∃ n, 0 < μ (s ∩ spanningSets μ n)) ↔ 0 < μ s | α : Type u_1
β : Type u_2
δ : Type u_3
ι : Type u_4
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
μ✝ ν ν₁ ν₂ : Measure α
s✝ t : Set α
inst✝¹ : MeasurableSpace α
μ : Measure α
inst✝ : SigmaFinite μ
s : Set α
⊢ (¬∃ n, 0 < μ (s ∩ spanningSets μ n)) ↔ ¬0 < μ s | ((:c Iff) ((:c Exists) (:c Nat) (:lambda n (:c Nat) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLa... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.129697))"},{"name":"inst✝²","sexp":"((:c MeasurableSpace) (:fv _uniq.129700))"},{"name":"μ✝","sexp":"((:c... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :impli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129697","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129700","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":36698,"sourceStart":36696,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":36700,"sourceStart":36699,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":36703,"sourceSt... | [] | [{"source":"not_iff_not","source_end":36715,"source_start":36704,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129697","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129700","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 239 | 4 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e8734933f7c0efad7c10ef64a2e03ab311ccf36d27a66cb5803f46f6e1968b99 | c0a890faa7b33316b84c8be6c09a332e93064abff11d91c7bdf692d3003535a3 | d0b518e41547ec4015a90618c55f726be804004b17b9e910918dd6e965ce41f3 | f2f3fff6b47657b6279c5794aca5570748a535b7630ff35170d042454b62773e |
cat-searcher/leandojo-benchmark-4-random | test | 1,876 | MeasureTheory.Measure.exists_measure_inter_spanningSets_pos | Mathlib/MeasureTheory/Measure/Typeclasses.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>not_exists</a>, <a>not_lt</a>, <a>nonpos_iff_eq_zero</a>] | α : Type u_1
β : Type u_2
δ : Type u_3
ι : Type u_4
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
μ✝ ν ν₁ ν₂ : Measure α
s✝ t : Set α
inst✝¹ : MeasurableSpace α
μ : Measure α
inst✝ : SigmaFinite μ
s : Set α
⊢ (¬∃ n, 0 < μ (s ∩ spanningSets μ n)) ↔ ¬0 < μ s | α : Type u_1
β : Type u_2
δ : Type u_3
ι : Type u_4
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
μ✝ ν ν₁ ν₂ : Measure α
s✝ t : Set α
inst✝¹ : MeasurableSpace α
μ : Measure α
inst✝ : SigmaFinite μ
s : Set α
⊢ (∀ (x : ℕ), μ (s ∩ spanningSets μ x) = 0) ↔ μ s = 0 | ((:c Iff) ((:c Not) ((:c Exists) (:c Nat) (:lambda n (:c Nat) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.to... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.129697))"},{"name":"inst✝²","sexp":"((:c MeasurableSpace) (:fv _uniq.129700))"},{"name":"μ✝","sexp":"((:c... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Not) (:arg :explicit 0 (:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129697","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129700","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":36723,"sourceStart":36719,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":36728,"sourceStart":36724,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":367... | [] | [{"source":"not_exists","source_end":36740,"source_start":36730,"syntax_kind":"ident"},{"source":"not_lt","source_end":36748,"source_start":36742,"syntax_kind":"ident"},{"source":"nonpos_iff_eq_zero","source_end":36768,"source_start":36750,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129697","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129700","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 239 | 7 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 402d52a8d8bec9b36a5dcff8a306bb1abe6d28297ca564725b95403a79a433e7 | f2f3fff6b47657b6279c5794aca5570748a535b7630ff35170d042454b62773e | 6a1a12f4e29cee67f59e34104e7dbf69b640c7f5a242d83a72c5a879bea3ac10 | 6fa31acb1a2f76c0722c7fa124cd347d95a8eb691f2f2379c41d61d291a7a20a |
cat-searcher/leandojo-benchmark-4-random | test | 1,877 | MeasureTheory.Measure.exists_measure_inter_spanningSets_pos | Mathlib/MeasureTheory/Measure/Typeclasses.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>MeasureTheory.Measure.forall_measure_inter_spanningSets_eq_zero</a> s | α : Type u_1
β : Type u_2
δ : Type u_3
ι : Type u_4
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
μ✝ ν ν₁ ν₂ : Measure α
s✝ t : Set α
inst✝¹ : MeasurableSpace α
μ : Measure α
inst✝ : SigmaFinite μ
s : Set α
⊢ (∀ (x : ℕ), μ (s ∩ spanningSets μ x) = 0) ↔ μ s = 0 | ((:c Iff) (:forall x (:c Nat) ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.129697) (:fv _uniq.130049)) ((:c Set) (:fv _uniq.129697)) (:lambda _ ((:c Set) (:fv _uniq.129697)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.129697) (:fv _uniq.130049)) (:fv _uniq.130050)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.129697))"},{"name":"inst✝²","sexp":"((:c MeasurableSpace) (:fv _uniq.129700))"},{"name":"μ✝","sexp":"((:c... | (:app (:c Iff) (:arg :explicit 0 (:forall x :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129697","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129700","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":36777,"sourceStart":36772,"tag":"atom"},{"children":[{"name":"MeasureTheory.Measure.forall_measure_inter_spanningSets_eq_zero","semanticRole":"global","source":"forall_measure_inter_spanningSets_eq_zero","sourceEnd":36819,"sourceStart":36778,"tag":"identifier"},{"children":[{"... | [] | [{"source":"forall_measure_inter_spanningSets_eq_zero s","source_end":36821,"source_start":36778,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129697","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129700","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 239 | 8 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c3965c6d8f0217b631b3aa11104e2a575522f3a2538513843673fa54de1b0be2 | 6fa31acb1a2f76c0722c7fa124cd347d95a8eb691f2f2379c41d61d291a7a20a | e2a88f8b71ad84b71ec506cf45133a7dab6b6f4147d9a57fe3cebc687c8e035e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,878 | Set.image_sInter_subset | Mathlib/Data/Set/Lattice.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.sInter_eq_biInter</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
ι₂ : Sort u_6
κ : ι → Sort u_7
κ₁ : ι → Sort u_8
κ₂ : ι → Sort u_9
κ' : ι' → Sort u_10
S : Set (Set α)
f : α → β
⊢ f '' ⋂₀ S ⊆ ⋂ s ∈ S, f '' s | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
ι₂ : Sort u_6
κ : ι → Sort u_7
κ₁ : ι → Sort u_8
κ₂ : ι → Sort u_9
κ' : ι' → Sort u_10
S : Set (Set α)
f : α → β
⊢ f '' ⋂ i ∈ S, i ⊆ ⋂ s ∈ S, f '' s | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.137133)) ((:c Set.instHasSubset) (:fv _uniq.137133)) ((:c Set.image) (:fv _uniq.137130) (:fv _uniq.137133) (:fv _uniq.137267) ((:c Set.sInter) (:fv _uniq.137130) (:fv _uniq.137266))) ((:c Set.iInter) (:fv _uniq.137133) ((:c Set) (:fv _uniq.137130)) (:lambda s ((:c Set) (:fv _... | [{"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":"ι₂","sexp":"(:sort u_6)"},{"name":"κ","sexp":"(:forall _ (:fv _uniq.137139) (:sort u_7))"},{"name":"κ₁","sexp":"(:forall ... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 2 (:app (:c Set.image) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.137130","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.137133","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":64651,"sourceStart":64649,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":64653,"sourceStart":64652,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.sInter_eq_bi... | [] | [{"source":"sInter_eq_biInter","source_end":64670,"source_start":64653,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.137130","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.137133","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 543 | 4 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4917d31919a311cb010e49785c47dd03c35478a7cc7d3016947281776421b074 | c2751d71c31395b961a47d5a19082233dc263eb7f63810d52d55b7dcf63ae320 | ed32d361e3f0a6316d010a957f253e1efbcfd1f51b24b2c7cfa77573ab642c93 | b0e16e8586895d451440638dc7e5b88b147ffd34e0d3f3f419bf96a9667239c3 |
cat-searcher/leandojo-benchmark-4-random | test | 1,879 | Set.image_sInter_subset | Mathlib/Data/Set/Lattice.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Set.image_iInter₂_subset</a> | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
ι₂ : Sort u_6
κ : ι → Sort u_7
κ₁ : ι → Sort u_8
κ₂ : ι → Sort u_9
κ' : ι' → Sort u_10
S : Set (Set α)
f : α → β
⊢ f '' ⋂ i ∈ S, i ⊆ ⋂ s ∈ S, f '' s | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.137133)) ((:c Set.instHasSubset) (:fv _uniq.137133)) ((:c Set.image) (:fv _uniq.137130) (:fv _uniq.137133) (:fv _uniq.137267) ((:c Set.iInter) (:fv _uniq.137130) ((:c Set) (:fv _uniq.137130)) (:lambda i ((:c Set) (:fv _uniq.137130)) ((:c Set.iInter) (:fv _uniq.137130) ((:c Me... | [{"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":"ι₂","sexp":"(:sort u_6)"},{"name":"κ","sexp":"(:forall _ (:fv _uniq.137139) (:sort u_7))"},{"name":"κ₁","sexp":"(:forall ... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 2 (:app (:c Set.image) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.137130","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.137133","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"apply","sourceEnd":64679,"sourceStart":64674,"tag":"atom"},{"name":"Set.image_iInter₂_subset","semanticRole":"global","source":"image_iInter₂_subset","sourceEnd":64702,"sourceStart":64680,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply image_iInter₂_subset","sourceEnd":647... | [] | [{"source":"image_iInter₂_subset","source_end":64702,"source_start":64680,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.137130","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.137133","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 543 | 7 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0c6781b4fae1c551067cafa8b27bc8dc5554249fc09c31a1ad1940f3a52565a5 | b0e16e8586895d451440638dc7e5b88b147ffd34e0d3f3f419bf96a9667239c3 | 3868ba493354fc1ee683e0ff9ba309bd1782682da6108d39a82750de839aad06 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,880 | UniformOnFun.gen_eq_preimage_restrict | Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext uv | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
s s' : Set α
x : α
p : Filter ι
g : ι → α
𝔖 : Set (Set α)
S : Set α
V : Set (β × β)
⊢ UniformOnFun.gen 𝔖 S V =
Prod.map (S.restrict ∘ ⇑UniformFun.toFun) (S.restrict ∘ ⇑UniformFun.toFun) ⁻¹' UniformFun.gen (↑S) β V | case h
α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
s s' : Set α
x : α
p : Filter ι
g : ι → α
𝔖 : Set (Set α)
S : Set α
V : Set (β × β)
uv : (α →ᵤ[𝔖] β) × (α →ᵤ[𝔖] β)
⊢ uv ∈ UniformOnFun.gen 𝔖 S V ↔
uv ∈ Prod.map (S.restrict ∘ ⇑UniformFun.toFun) (S.restrict ∘ ⇑UniformFun.toFun) ⁻¹' UniformFun.gen (↑S) β ... | ((:c Eq) ((:c Set) ((:c Prod) ((:c UniformOnFun) (:fv _uniq.28516) (:fv _uniq.28519) (:fv _uniq.28979)) ((:c UniformOnFun) (:fv _uniq.28516) (:fv _uniq.28519) (:fv _uniq.28979)))) ((:c UniformOnFun.gen) (:fv _uniq.28516) (:fv _uniq.28519) (:fv _uniq.28979) (:fv _uniq.28980) (:fv _uniq.28981)) ((:c Set.preimage) ((:c Pr... | [{"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 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.28516))"},{"name":"s'","sexp":"((:c Set) (:fv _uniq.28516))"},{"name":"x","sexp":"(:fv _uniq.28516)"},{"name":"p","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c UniformOnFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV10)))) (:arg :explicit 1 (:app (:c UniformOnFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.28516","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28519","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"ext","sourceEnd":32399,"sourceStart":32396,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"uv","sourceEnd":32402,"sourceStart":32400,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"uv","sourceEnd":32402,"sourceStart":32400,"t... | [{"role":"fresh_name","source":"uv","source_end":32402,"source_start":32400,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.28516","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28519","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 106 | 4 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 115a2a2f8221af7d526eccec374fa09e4e8fefc02a51a8f55b9c66e786f1cccc | 3512bb117a602267abf827e495b63aa17981d647d116a6be72f17ecfd8e09aee | 8c961709e103ea09bbe800d120d2d01600252b73b92d030858c521d53c2d6de3 | 85503142f3585a804e2846102dac2a15e125ac32f1cce8a351776e7088ff948d |
cat-searcher/leandojo-benchmark-4-random | test | 1,881 | UniformOnFun.gen_eq_preimage_restrict | Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨fun h ⟨x, hx⟩ => h x hx, fun h x hx => h ⟨x, hx⟩⟩ | case h
α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
s s' : Set α
x : α
p : Filter ι
g : ι → α
𝔖 : Set (Set α)
S : Set α
V : Set (β × β)
uv : (α →ᵤ[𝔖] β) × (α →ᵤ[𝔖] β)
⊢ uv ∈ UniformOnFun.gen 𝔖 S V ↔
uv ∈ Prod.map (S.restrict ∘ ⇑UniformFun.toFun) (S.restrict ∘ ⇑UniformFun.toFun) ⁻¹' UniformFun.gen (↑S) β ... | ((:c Iff) ((:c Membership.mem) ((:c Prod) ((:c UniformOnFun) (:fv _uniq.28516) (:fv _uniq.28519) (:fv _uniq.28979)) ((:c UniformOnFun) (:fv _uniq.28516) (:fv _uniq.28519) (:fv _uniq.28979))) ((:c Set) ((:c Prod) ((:c UniformOnFun) (:fv _uniq.28516) (:fv _uniq.28519) (:fv _uniq.28979)) ((:c UniformOnFun) (:fv _uniq.2851... | [{"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 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.28516))"},{"name":"s'","sexp":"((:c Set) (:fv _uniq.28516))"},{"name":"x","sexp":"(:fv _uniq.28516)"},{"name":"p","sex... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c UniformOnFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV10)))) (:arg :explicit 1 (:app (:c UniformOnFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.28516","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28519","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":32410,"sourceStart":32405,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":32414,"sourceStart":32411,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":32417,"sourceStart":32414,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source... | [] | [{"source":"⟨fun h ⟨x, hx⟩ => h x hx, fun h x hx => h ⟨x, hx⟩⟩","source_end":32473,"source_start":32411,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.28516","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28519","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 106 | 5 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b5e044b0bea6922ce8bfd68c1301720e818e8da1687fe8380f5a32232ccadb58 | 85503142f3585a804e2846102dac2a15e125ac32f1cce8a351776e7088ff948d | 0cf3978c8e02b1d7d4b2cd7c0b3021633b9307d9ad94329d3f292d2a5119f4a9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,882 | MeasureTheory.locallyIntegrable_finset_sum | Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [← <a>Finset.sum_apply</a>] using <a>MeasureTheory.locallyIntegrable_finset_sum'</a> s hf | X : Type u_1
Y : Type u_2
E : Type u_3
F : Type u_4
R : Type u_5
inst✝⁵ : MeasurableSpace X
inst✝⁴ : TopologicalSpace X
inst✝³ : MeasurableSpace Y
inst✝² : TopologicalSpace Y
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedAddCommGroup F
f✝ g : X → E
μ : Measure X
s✝ : Set X
ι : Type u_6
s : Finset ι
f : ι → X → E
hf : ∀ i... | ((:c MeasureTheory.LocallyIntegrable) (:fv _uniq.39898) (:fv _uniq.39904) (:fv _uniq.39913) (:fv _uniq.39916) (:fv _uniq.39925) (:lambda a (:fv _uniq.39898) ((:c Finset.sum) (:fv _uniq.40997) (:fv _uniq.39904) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.39904) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.39904)... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"F","sexp":"(:sort (+ u_4 1))"},{"name":"R","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁵","sexp":"((:c MeasurableSpace) (:fv _uniq.39898))"},{"name":"inst✝⁴","sexp":"((:c TopologicalSpace) (:f... | (:app (:c MeasureTheory.LocallyIntegrable) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instan... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.39898","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.39901","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":18868,"sourceStart":18863,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"Finset.sum_apply","source_end":18895,"source_start":18879,"syntax_kind":"ident"},{"source":"locallyIntegrable_finset_sum' s hf","source_end":18937,"source_start":18903,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.39898","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.39901","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 71 | 2 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5f3654a18650efdc62c61c27996f60d582360468523708e98a34ec160d24f1db | 23beca373cabdefaf1fc26e0c6f3e58642ff0682f4bba8c492555a9d3f437994 | fb29883a7717969e3ffaca322d2d61f2666fa0d27c72e340abceb969d9c97a9c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,883 | Matrix.charpoly_map | Mathlib/LinearAlgebra/Matrix/Charpoly/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Matrix.charpoly</a>, <a>Matrix.charmatrix_map</a>, ← <a>Polynomial.coe_mapRingHom</a>, <a>Matrix.charpoly</a>, <a>RingHom.map_det</a>, <a>RingHom.mapMatrix_apply</a>] | R : Type u_1
S : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : CommRing S
m : Type u_3
n : Type u_4
inst✝³ : DecidableEq m
inst✝² : DecidableEq n
inst✝¹ : Fintype m
inst✝ : Fintype n
M₁₁ : Matrix m m R
M₁₂ : Matrix m n R
M₂₁ : Matrix n m R
M₂₂ M✝ : Matrix n n R
i j : n
M : Matrix n n R
f : R →+* S
⊢ (M.map ⇑f).charpoly = Polyn... | ((:c Eq) ((:c Polynomial) (:fv _uniq.78266) ((:c CommSemiring.toSemiring) (:fv _uniq.78266) ((:c CommRing.toCommSemiring) (:fv _uniq.78266) (:fv _uniq.78272)))) ((:c Matrix.charpoly) (:fv _uniq.78266) (:fv _uniq.78272) (:fv _uniq.78278) (:fv _uniq.78294) (:fv _uniq.78302) ((:c Matrix.map) (:fv _uniq.78278) (:fv _uniq.7... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.78263))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.78266))"},{"name":"m","sexp":"(:sort (+ u_3 1))"},{"name":"n","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝³","sexp":"((:c Decidab... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 1 (:app (:c Matrix.charpoly) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.78263","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.78266","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":3876,"sourceStart":3874,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3878,"sourceStart":3877,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"charpoly","source_end":3886,"source_start":3878,"syntax_kind":"ident"},{"source":"charmatrix_map","source_end":3902,"source_start":3888,"syntax_kind":"ident"},{"source":"Polynomial.coe_mapRingHom","source_end":3933,"source_start":3908,"syntax_kind":"ident"},{"source":"charpoly","source_end":3943,"source_sta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.78263","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.78266","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 2 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d9472fb38f41dffa0758c92785d0f80f1bb288d7d398b1f55cb61d22f2a3e8c7 | 76d39dd5fab61bfc227212249ee9c2b41b7cd19b3e45a541d842a026c5399f3e | 33cb447f0ce8ec1b7fe118ca73716d00cb0802b52d7a60130efbdd64ed0b0901 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,884 | Nat.digits_of_lt | Mathlib/Data/Nat/Digits.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>Nat.exists_eq_succ_of_ne_zero</a> hx with ⟨x, rfl⟩ | n b x : ℕ
hx : x ≠ 0
hxb : x < b
⊢ b.digits x = [x] | case intro
n b x : ℕ
hx : x.succ ≠ 0
hxb : x.succ < b
⊢ b.digits x.succ = [x.succ] | ((:c Eq) ((:c List) (:c Nat)) ((:c Nat.digits) (:fv _uniq.8819) (:fv _uniq.8820)) ((:c List.cons) (:c Nat) (:fv _uniq.8820) ((:c List.nil) (:c Nat)))) | [{"name":"n","sexp":"(:c Nat)"},{"name":"b","sexp":"(:c Nat)"},{"name":"x","sexp":"(:c Nat)"},{"name":"hx","sexp":"((:c Ne) (:c Nat) (:fv _uniq.8820) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"hxb","sexp":"((:c LT.lt) (:c Nat) (:c instLTNat) (:fv _uniq.8820) (:fv _uniq.8819))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c Nat.digits) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV3)))) (:arg :explicit 2 (:app (:c List.cons) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:app (:c List.nil... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8782","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.8819","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index... | {"children":[{"source":"rcases","sourceEnd":4848,"sourceStart":4842,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Nat.exists_eq_succ_of_ne_zero","semanticRole":"global","source":"exists_eq_succ_of_ne_zero","sourceEnd":4874,"sourceStart":4849,"tag":"... | [] | [{"source":"exists_eq_succ_of_ne_zero hx","source_end":4877,"source_start":4849,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨x, rfl⟩","source_end":4895,"source_start":4883,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8782","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.8819","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 33 | 4 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e9162e447bbf52b39e5fdc9ce3f8d8a02d43d738e9673af13a81f74eecb59818 | 0d007392e275dc6122ecfe33773d90a26d216addc4ff256bcb933da7c69bf6bd | 66c9c13995a43f93ee308dc90440dc3dc99b5437af5e5cb8b0c90e1bfc63cd14 | cec4e642bc293a014da19a20235f4fc0475e48545f6ae7619483d5973c1263bc |
cat-searcher/leandojo-benchmark-4-random | test | 1,885 | Nat.digits_of_lt | Mathlib/Data/Nat/Digits.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>Nat.exists_eq_add_of_le'</a> ((<a>Nat.le_add_left</a> 1 x).<a>LE.le.trans_lt</a> hxb) with ⟨b, rfl⟩ | case intro
n b x : ℕ
hx : x.succ ≠ 0
hxb : x.succ < b
⊢ b.digits x.succ = [x.succ] | case intro.intro
n x : ℕ
hx : x.succ ≠ 0
b : ℕ
hxb : x.succ < b + succ 1
⊢ (b + succ 1).digits x.succ = [x.succ] | ((:c Eq) ((:c List) (:c Nat)) ((:c Nat.digits) (:fv _uniq.8819) ((:c Nat.succ) (:fv _uniq.8855))) ((:c List.cons) (:c Nat) ((:c Nat.succ) (:fv _uniq.8855)) ((:c List.nil) (:c Nat)))) | [{"name":"n","sexp":"(:c Nat)"},{"name":"b","sexp":"(:c Nat)"},{"name":"x","sexp":"(:c Nat)"},{"name":"hx","sexp":"((:c Ne) (:c Nat) ((:c Nat.succ) (:fv _uniq.8855)) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"hxb","sexp":"((:c LT.lt) (:c Nat) (:c instLTNat) ((:c Nat.succ) (:fv _uniq.8... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c Nat.digits) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Nat.succ) (:arg :explicit 0 (:fv FV3)))))) (:arg :explicit 2 (:app (:c List.cons) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8782","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.8819","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index... | {"children":[{"source":"rcases","sourceEnd":4904,"sourceStart":4898,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Nat.exists_eq_add_of_le'","semanticRole":"global","source":"Nat.exists_eq_add_of_le'","sourceEnd":4929,"sourceStart":4905,"tag":"identi... | [] | [{"source":"Nat.exists_eq_add_of_le' ((Nat.le_add_left 1 x).trans_lt hxb)","source_end":4966,"source_start":4905,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨b, rfl⟩","source_end":4984,"source_start":4972,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8782","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.8819","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 33 | 5 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4040b477d87e975e93297bd61d6b49b257ae1e1d10858c9512b10ed06d6957ee | cec4e642bc293a014da19a20235f4fc0475e48545f6ae7619483d5973c1263bc | c13d8a479ea386b1000fd530b396e461099d69d9ec9457898d373f6afdc948f9 | f278bb35c519eacc83345a7d0dcff5e38ecd4dfda408ad850b34f40229049510 |
cat-searcher/leandojo-benchmark-4-random | test | 1,886 | Nat.digits_of_lt | Mathlib/Data/Nat/Digits.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Nat.digits_add_two_add_one</a>, <a>Nat.div_eq_of_lt</a> hxb, <a>Nat.digits_zero</a>, <a>Nat.mod_eq_of_lt</a> hxb] | case intro.intro
n x : ℕ
hx : x.succ ≠ 0
b : ℕ
hxb : x.succ < b + succ 1
⊢ (b + succ 1).digits x.succ = [x.succ] | ((:c Eq) ((:c List) (:c Nat)) ((:c Nat.digits) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.9024) ((:c Nat.succ) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) ((:c Nat.succ) (:fv _uniq.8855))) ((:c List.cons) (:c Nat) ((:c Nat.succ) (:fv _uniq.8855... | [{"name":"n","sexp":"(:c Nat)"},{"name":"x","sexp":"(:c Nat)"},{"name":"hx","sexp":"((:c Ne) (:c Nat) ((:c Nat.succ) (:fv _uniq.8855)) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"b","sexp":"(:c Nat)"},{"name":"hxb","sexp":"((:c LT.lt) (:c Nat) (:c instLTNat) ((:c Nat.succ) (:fv _uniq.8... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c Nat.digits) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8782","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.8855","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index... | {"children":[{"source":"rw","sourceEnd":4989,"sourceStart":4987,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4991,"sourceStart":4990,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Nat.digits_add_two_a... | [] | [{"source":"digits_add_two_add_one","source_end":5013,"source_start":4991,"syntax_kind":"ident"},{"source":"div_eq_of_lt hxb","source_end":5031,"source_start":5015,"syntax_kind":"Lean.Parser.Term.app"},{"source":"digits_zero","source_end":5044,"source_start":5033,"syntax_kind":"ident"},{"source":"mod_eq_of_lt hxb","sou... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8782","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.8855","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 33 | 6 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 18225fd9dd3088326ad69f32e62ea12c688a226e4c7de7054a71d788fdecbf50 | f278bb35c519eacc83345a7d0dcff5e38ecd4dfda408ad850b34f40229049510 | 84c7f5e04ed8160240bdd73fb8f724fcfd37a43dd6379d429fceb5de03b79a2a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,887 | Hyperreal.infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg | Mathlib/Data/Real/Hyperreal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Hyperreal.infinitePos_neg</a>, ← <a>neg_pos</a>, ← <a>neg_mul_neg</a>, ← <a>Hyperreal.infinitesimal_neg</a>] | x y : ℝ*
⊢ x.InfiniteNeg → ¬y.Infinitesimal → y < 0 → (x * y).InfinitePos | x y : ℝ*
⊢ (-x).InfinitePos → ¬(-y).Infinitesimal → 0 < -y → (-x * -y).InfinitePos | (:forall _ ((:c Hyperreal.InfiniteNeg) (:fv _uniq.85290)) (:forall _ ((:c Not) ((:c Hyperreal.Infinitesimal) (:fv _uniq.85291))) (:forall _ ((:c LT.lt) (:c Hyperreal) ((:c Preorder.toLT) (:c Hyperreal) ((:c PartialOrder.toPreorder) (:c Hyperreal) ((:c StrictOrderedRing.toPartialOrder) (:c Hyperreal) ((:c LinearOrderedR... | [{"name":"x","sexp":"(:c Hyperreal)"},{"name":"y","sexp":"(:c Hyperreal)"}] | (:forall _ :explicit (:app (:c Hyperreal.InfiniteNeg) (:arg :explicit 0 (:fv FV1))) (:forall _ :explicit (:app (:c Not) (:arg :explicit 0 (:app (:c Hyperreal.Infinitesimal) (:arg :explicit 0 (:fv FV2))))) (:forall _ :explicit (:app (:c LT.lt) (:arg :implicit-type 0 (:c Hyperreal)) (:arg :instance 1 (:instance-of (:app ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.85290","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Hyperreal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.85291","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Hyperreal)"}] | {"children":[{"source":"rw","sourceEnd":37919,"sourceStart":37917,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":37921,"sourceStart":37920,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":37924,"sourceSt... | [] | [{"source":"infinitePos_neg","source_end":37940,"source_start":37925,"syntax_kind":"ident"},{"source":"neg_pos","source_end":37953,"source_start":37946,"syntax_kind":"ident"},{"source":"neg_mul_neg","source_end":37970,"source_start":37959,"syntax_kind":"ident"},{"source":"infinitesimal_neg","source_end":37993,"source_s... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.85290","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.85291","is_instance":false,"is_let":false,"user_name":"y"}] | 323 | 4 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2ff2f7cd0fdc666bad3a232abf196a0b9fecce2a36896aee8140a3c17c17cc3f | 599dfd935c995e059d04a0912e1577399eaa3b69d94bc8b7e709fa0b7704a6e8 | 2d8d7687c3b483293f627b1c628242c0c3ab5655b225627cec44f6955403c329 | 22f656fd2bc14b5348923cea984f3b43d15acedafe37a51418a1e851c1c9f551 |
cat-searcher/leandojo-benchmark-4-random | test | 1,888 | Hyperreal.infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg | Mathlib/Data/Real/Hyperreal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_pos</a> | x y : ℝ*
⊢ (-x).InfinitePos → ¬(-y).Infinitesimal → 0 < -y → (-x * -y).InfinitePos | (:forall _ ((:c Hyperreal.InfinitePos) ((:c Neg.neg) (:c Hyperreal) ((:c Ring.toNeg) (:c Hyperreal) ((:c StrictOrderedRing.toRing) (:c Hyperreal) ((:c LinearOrderedRing.toStrictOrderedRing) (:c Hyperreal) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:c Hyperreal) ((:c LinearOrderedField.toLinearOrderedCommRing) (:c... | [{"name":"x","sexp":"(:c Hyperreal)"},{"name":"y","sexp":"(:c Hyperreal)"}] | (:forall _ :explicit (:app (:c Hyperreal.InfinitePos) (:arg :explicit 0 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Hyperreal)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Hyperreal))))) (:arg :explicit 2 (:fv FV1))))) (:forall _ :explicit (:app (:c Not) (:arg :explicit 0 (:app (:c Hyperreal.... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.85290","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Hyperreal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.85291","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Hyperreal)"}] | {"children":[{"source":"exact","sourceEnd":38002,"sourceStart":37997,"tag":"atom"},{"name":"Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_pos","semanticRole":"global","source":"infinitePos_mul_of_infinitePos_not_infinitesimal_pos","sourceEnd":38055,"sourceStart":38003,"tag":"identifier"}],"kind":"Lean.Pars... | [] | [{"source":"infinitePos_mul_of_infinitePos_not_infinitesimal_pos","source_end":38055,"source_start":38003,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.85290","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.85291","is_instance":false,"is_let":false,"user_name":"y"}] | 323 | 10 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c6b75324394dd09297e21696ea8f445389230ff9549b56f4996fdd45f75c55d9 | 22f656fd2bc14b5348923cea984f3b43d15acedafe37a51418a1e851c1c9f551 | ec7cdd45dc69bd73a2e5c78a82cdb1ec737e3c332dadfc1b372035599c783b27 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,889 | OpenEmbedding.tendsto_nhds_iff' | Mathlib/Topology/Maps.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Filter.Tendsto</a>, ← <a>Filter.map_map</a>, hf.map_nhds_eq] | X : Type u_1
Y : Type u_2
Z : Type u_3
ι : Type u_4
f : X → Y
g : Y → Z
inst✝² : TopologicalSpace X
inst✝¹ : TopologicalSpace Y
inst✝ : TopologicalSpace Z
hf : OpenEmbedding f
l : Filter Z
x : X
⊢ Tendsto (g ∘ f) (𝓝 x) l ↔ Tendsto g (𝓝 (f x)) l | X : Type u_1
Y : Type u_2
Z : Type u_3
ι : Type u_4
f : X → Y
g : Y → Z
inst✝² : TopologicalSpace X
inst✝¹ : TopologicalSpace Y
inst✝ : TopologicalSpace Z
hf : OpenEmbedding f
l : Filter Z
x : X
⊢ map g (𝓝 (f x)) ≤ l ↔ Tendsto g (𝓝 (f x)) l | ((:c Iff) ((:c Filter.Tendsto) (:fv _uniq.43828) (:fv _uniq.43834) ((:c Function.comp) (:fv _uniq.43828) (:fv _uniq.43831) (:fv _uniq.43834) (:fv _uniq.43845) (:fv _uniq.43841)) ((:c nhds) (:fv _uniq.43828) (:fv _uniq.43848) (:fv _uniq.43940)) (:fv _uniq.43939)) ((:c Filter.Tendsto) (:fv _uniq.43831) (:fv _uniq.43834) ... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"Z","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.43828) (:fv _uniq.43831))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.43831) (:fv _uniq.43834))"},{"name":"inst✝²","s... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :explicit 2 (:app (:c Function.comp) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV2)) (:arg :explicit 3 (:fv FV5)) (:arg :explicit 4 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43828","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.43831","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":25348,"sourceStart":25346,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":25350,"sourceStart":25349,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Filter.Tendsto",... | [] | [{"source":"Tendsto","source_end":25357,"source_start":25350,"syntax_kind":"ident"},{"source":"map_map","source_end":25370,"source_start":25363,"syntax_kind":"ident"},{"source":"hf.map_nhds_eq","source_end":25386,"source_start":25372,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43828","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.43831","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 202 | 4 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 202584e18e811464a128065e501cf9d024f7ad935377185f2a5d78c72621119f | cb79752e2cc2f3c29ee9cdc0eaf94ea83014045d5a815aaa9cfe5b64af4ffe4b | 8c6ebc9d11fa1b1f3929359aebfa6fc5577e4a10af94c9f24757d8610f4f9d3f | 2bffdbf1fabf78091ffa2736f82b5cd1e426bdcf1311993e70a244008f99b668 |
cat-searcher/leandojo-benchmark-4-random | test | 1,890 | OpenEmbedding.tendsto_nhds_iff' | Mathlib/Topology/Maps.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | X : Type u_1
Y : Type u_2
Z : Type u_3
ι : Type u_4
f : X → Y
g : Y → Z
inst✝² : TopologicalSpace X
inst✝¹ : TopologicalSpace Y
inst✝ : TopologicalSpace Z
hf : OpenEmbedding f
l : Filter Z
x : X
⊢ map g (𝓝 (f x)) ≤ l ↔ Tendsto g (𝓝 (f x)) l | ((:c Iff) ((:c LE.le) ((:c Filter) (:fv _uniq.43834)) ((:c Preorder.toLE) ((:c Filter) (:fv _uniq.43834)) ((:c PartialOrder.toPreorder) ((:c Filter) (:fv _uniq.43834)) ((:c Filter.instPartialOrder) (:fv _uniq.43834)))) ((:c Filter.map) (:fv _uniq.43831) (:fv _uniq.43834) (:fv _uniq.43845) ((:c nhds) (:fv _uniq.43831) (... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"Z","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.43828) (:fv _uniq.43831))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.43831) (:fv _uniq.43834))"},{"name":"inst✝²","s... | (:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 2 (:app (:c Filter.map) (:arg :implicit-type 0 (:fv FV1)) (:arg :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43828","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.43831","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rfl","sourceEnd":25392,"sourceStart":25389,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":25392,"sourceStart":25389,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43828","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.43831","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 202 | 10 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 079ba76190647753baec5083a1727a4254ab58180e41835f8e438fad367d24d7 | 2bffdbf1fabf78091ffa2736f82b5cd1e426bdcf1311993e70a244008f99b668 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,891 | Polynomial.pow_mul_divByMonic_rootMultiplicity_eq | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>Polynomial.Monic</a> ((<a>Polynomial.X</a> - <a>Polynomial.C</a> a) ^ <a>Polynomial.rootMultiplicity</a> a p) := (<a>Polynomial.monic_X_sub_C</a> _).<a>Polynomial.Monic.pow</a> _ | R : Type u
S : Type v
T : Type w
A : Type z
a✝ b : R
n : ℕ
inst✝ : Ring R
p✝ q p : R[X]
a : R
⊢ (X - C a) ^ rootMultiplicity a p * (p /ₘ (X - C a) ^ rootMultiplicity a p) = p | R : Type u
S : Type v
T : Type w
A : Type z
a✝ b : R
n : ℕ
inst✝ : Ring R
p✝ q p : R[X]
a : R
this : ((X - C a) ^ rootMultiplicity a p).Monic
⊢ (X - C a) ^ rootMultiplicity a p * (p /ₘ (X - C a) ^ rootMultiplicity a p) = p | ((:c Eq) ((:c Polynomial) (:fv _uniq.236816) ((:c Ring.toSemiring) (:fv _uniq.236816) (:fv _uniq.236831))) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.236816) ((:c Ring.toSemiring) (:fv _uniq.236816) (:fv _uniq.236831))) ((:c Polynomial) (:fv _uniq.236816) ((:c Ring.toSemiring) (:fv _uniq.236816) (:fv _uniq.236831))) (... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a✝","sexp":"(:fv _uniq.236816)"},{"name":"b","sexp":"(:fv _uniq.236816)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c Ring) (:fv _uniq.236816)... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.236816","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.236818","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":25357,"sourceStart":25353,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":25358,"sourceStart":25358,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":25358,"sourceStart":25358,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"Monic ((X - C a) ^ rootMultiplicity a p)","source_end":25400,"source_start":25360,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(monic_X_sub_C _).pow _","source_end":25427,"source_start":25404,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.236816","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.236818","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 108 | 4 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6b6fca3109c45bfe43fc66061ce20586eb08c609ad0130c51a6cad48d4828ffd | c7740f8c7235c9dd0427c6243bb1a789adb5452d70a86081f6899e0dbb111743 | 5225836b8cbbb0aa2240b396ff74fb5880461733fefb18e25e4e02368510d3de | 0eecaab68aecdb8f5d3d498e24596beff8df4e38149965aa2d30ea7848e6126d |
cat-searcher/leandojo-benchmark-4-random | test | 1,892 | Polynomial.pow_mul_divByMonic_rootMultiplicity_eq | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | conv_rhs => rw [← <a>Polynomial.modByMonic_add_div</a> p this, (<a>Polynomial.modByMonic_eq_zero_iff_dvd</a> this).2 (<a>Polynomial.pow_rootMultiplicity_dvd</a> _ _)] | R : Type u
S : Type v
T : Type w
A : Type z
a✝ b : R
n : ℕ
inst✝ : Ring R
p✝ q p : R[X]
a : R
this : ((X - C a) ^ rootMultiplicity a p).Monic
⊢ (X - C a) ^ rootMultiplicity a p * (p /ₘ (X - C a) ^ rootMultiplicity a p) = p | R : Type u
S : Type v
T : Type w
A : Type z
a✝ b : R
n : ℕ
inst✝ : Ring R
p✝ q p : R[X]
a : R
this : ((X - C a) ^ rootMultiplicity a p).Monic
⊢ (X - C a) ^ rootMultiplicity a p * (p /ₘ (X - C a) ^ rootMultiplicity a p) =
0 + (X - C a) ^ rootMultiplicity a p * (p /ₘ (X - C a) ^ rootMultiplicity a p) | ((:c Eq) ((:c Polynomial) (:fv _uniq.236816) ((:c Ring.toSemiring) (:fv _uniq.236816) (:fv _uniq.236831))) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.236816) ((:c Ring.toSemiring) (:fv _uniq.236816) (:fv _uniq.236831))) ((:c Polynomial) (:fv _uniq.236816) ((:c Ring.toSemiring) (:fv _uniq.236816) (:fv _uniq.236831))) (... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a✝","sexp":"(:fv _uniq.236816)"},{"name":"b","sexp":"(:fv _uniq.236816)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c Ring) (:fv _uniq.236816)... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.236816","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.236818","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"conv_rhs","sourceEnd":25438,"sourceStart":25430,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":"=>","sourceEnd":25441,"sourceStart":25439,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"sou... | [] | [{"source":"modByMonic_add_div p this","source_end":25481,"source_start":25456,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(modByMonic_eq_zero_iff_dvd this).2 (pow_rootMultiplicity_dvd _ _)","source_end":25557,"source_start":25491,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.236816","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.236818","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 108 | 5 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 74f82e6a09276d705961ab0d696609ce136ad3d63486e298877cbed31edcdafc | 0eecaab68aecdb8f5d3d498e24596beff8df4e38149965aa2d30ea7848e6126d | 8ef53fe8d8fa0ef393905e9326527e0c856f759e124aa319db62e0a23d268a0a | 1e7bde2290ab87857ee9456d73c34af454b6f56d5f2b3a499d61699817428250 |
cat-searcher/leandojo-benchmark-4-random | test | 1,893 | Polynomial.pow_mul_divByMonic_rootMultiplicity_eq | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | R : Type u
S : Type v
T : Type w
A : Type z
a✝ b : R
n : ℕ
inst✝ : Ring R
p✝ q p : R[X]
a : R
this : ((X - C a) ^ rootMultiplicity a p).Monic
⊢ (X - C a) ^ rootMultiplicity a p * (p /ₘ (X - C a) ^ rootMultiplicity a p) =
0 + (X - C a) ^ rootMultiplicity a p * (p /ₘ (X - C a) ^ rootMultiplicity a p) | ((:c Eq) ((:c Polynomial) (:fv _uniq.236816) ((:c Ring.toSemiring) (:fv _uniq.236816) (:fv _uniq.236831))) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.236816) ((:c Ring.toSemiring) (:fv _uniq.236816) (:fv _uniq.236831))) ((:c Polynomial) (:fv _uniq.236816) ((:c Ring.toSemiring) (:fv _uniq.236816) (:fv _uniq.236831))) (... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a✝","sexp":"(:fv _uniq.236816)"},{"name":"b","sexp":"(:fv _uniq.236816)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c Ring) (:fv _uniq.236816)... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.236816","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.236818","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":25565,"sourceStart":25561,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"ki... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.236816","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.236818","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 108 | 11 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 97c140beb3c27c9409da2017f5bf3ec9611e27a6b1b05ad1b2500c4c6d2efe9e | 1e7bde2290ab87857ee9456d73c34af454b6f56d5f2b3a499d61699817428250 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,894 | WeierstrassCurve.Affine.evalEval_polynomial_zero | Mathlib/AlgebraicGeometry/EllipticCurve/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>WeierstrassCurve.Affine.evalEval_polynomial</a>, <a>zero_add</a>, <a>zero_sub</a>, <a>MulZeroClass.mul_zero</a>, <a>zero_pow</a> <| <a>Nat.succ_ne_zero</a> _] | R : Type u
inst✝ : CommRing R
W : Affine R
⊢ evalEval 0 0 W.polynomial = -W.a₆ | ((:c Eq) (:fv _uniq.48850) ((:c Polynomial.evalEval) (:fv _uniq.48850) ((:c CommSemiring.toSemiring) (:fv _uniq.48850) ((:c CommRing.toCommSemiring) (:fv _uniq.48850) (:fv _uniq.48853))) ((:c OfNat.ofNat) (:fv _uniq.48850) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.48850) ((:c CommMonoidWithZero.toZero) (:fv _uniq.48850) ... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.48850))"},{"name":"W","sexp":"((:c WeierstrassCurve.Affine) (:fv _uniq.48850))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Polynomial.evalEval) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lit 0)) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48850","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48853","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommRing) (:arg :explici... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":9290,"sourceStart":9286,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":9295,"sourceStart":9291,"tag":"atom"}],"kind":"nu... | [] | [{"source":"evalEval_polynomial","source_end":9316,"source_start":9297,"syntax_kind":"ident"},{"source":"zero_add","source_end":9326,"source_start":9318,"syntax_kind":"ident"},{"source":"zero_sub","source_end":9336,"source_start":9328,"syntax_kind":"ident"},{"source":"mul_zero","source_end":9346,"source_start":9338,"sy... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48850","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48853","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":2,"interna... | 31 | 2 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0f823a189b64c3076d5596ff14290efe8ff493748820c631b57dc2340949e84e | 822261dfd90d08bc2c4f2b8275cca359d0a2a8385b975ab940b1bd7cfad3961e | e1b71ad2c9061ae06a5533ee7a55514f3d9822e628e209a411384f5b0c1b28e0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,895 | Fin.min_val | Mathlib/Data/Fin/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | n m : ℕ
a : Fin n
⊢ min (↑a) n = ↑a | ((:c Eq) (:c Nat) ((:c Min.min) (:c Nat) (:c instMinNat) ((:c Fin.val) (:fv _uniq.7528) (:fv _uniq.7731)) (:fv _uniq.7528)) ((:c Fin.val) (:fv _uniq.7528) (:fv _uniq.7731))) | [{"name":"n","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"a","sexp":"((:c Fin) (:fv _uniq.7528))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Min.min) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c Min) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Fin.val) (:arg :implicit 0) (:arg :explicit 1 (:fv FV3)))) (:arg :explicit 3 (:fv FV0)))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7528","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7530","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":9632,"sourceStart":9628,"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.7528","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7530","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":3,"internal_name":"_uniq... | 87 | 2 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e3288b7997a5504ebc80b05d96019d6e06dfa836568fd15f96f0d4bf5806db6d | 47f2f17a5785ee37e25e0153d0170a45afebc18d88c07c918ce0ef88f2b5ca39 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,896 | not_summable_indicator_mod_of_antitone_of_neg | Mathlib/Analysis/SumOverResidueClass.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>ZMod.natCast_zmod_val</a> k, <a>summable_indicator_mod_iff_summable</a>] | m : ℕ
hm : NeZero m
f : ℕ → ℝ
hf : Antitone f
n : ℕ
hn : f n < 0
k : ZMod m
⊢ ¬Summable ({n | ↑n = k}.indicator f) | m : ℕ
hm : NeZero m
f : ℕ → ℝ
hf : Antitone f
n : ℕ
hn : f n < 0
k : ZMod m
⊢ ¬Summable fun n => f (m * n + k.val) | ((:c Not) ((:c Summable) (:c Real) (:c Nat) (:c Real.instAddCommMonoid) ((:c UniformSpace.toTopologicalSpace) (:c Real) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.pseudoMetricSpace))) ((:c Set.indicator) (:c Nat) (:c Real) (:c Real.instZero) ((:c setOf) (:c Nat) (:lambda n (:c Nat) ((:c Eq) ((:c ZMod) (:... | [{"name":"m","sexp":"(:c Nat)"},{"name":"hm","sexp":"((:c NeZero) (:c Nat) ((:c LinearOrderedCommMonoidWithZero.toZero) (:c Nat) (:c Nat.instLinearOrderedCommMonoidWithZero)) (:fv _uniq.17393))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"hf","sexp":"((:c Antitone) (:c Nat) (:c Real) ((:c PartialOrde... | (:app (:c Not) (:arg :explicit 0 (:app (:c Summable) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Real))))) (:arg :explicit 4 (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17393","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.17394","is_instance":true,"is_let":false,"name":"hm","sexp":"(:app (:c NeZero) (:arg :implicit-type 0 ... | {"children":[{"source":"rw","sourceEnd":3214,"sourceStart":3212,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3216,"sourceStart":3215,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":3219,"sourceStart":... | [] | [{"source":"ZMod.natCast_zmod_val k","source_end":3243,"source_start":3220,"syntax_kind":"Lean.Parser.Term.app"},{"source":"summable_indicator_mod_iff_summable","source_end":3280,"source_start":3245,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17393","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.17394","is_instance":true,"is_let":false,"user_name":"hm"},{"binder_role":":implicit","context_index":3,"internal_n... | 4 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 56cb2da9fc38044ddd30176d36a933f91bb6aeee3f50fc8674d4ceb22c67ade6 | 9ad0dabdbe600abbb589ac339b55b83911045156df3c9d3a97c297edd3be751f | f983feb611d58cd7c1bf4bb0a215d50fc749dfb4707b7eeb860426b0750f57b8 | cf6626401b20ea5a0320471218a05b327e0598cfcd23b746d694de525b8c791a |
cat-searcher/leandojo-benchmark-4-random | test | 1,897 | not_summable_indicator_mod_of_antitone_of_neg | Mathlib/Analysis/SumOverResidueClass.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>not_summable_of_antitone_of_neg</a> (hf.comp_monotone <| (<a>Covariant.monotone_of_const</a> m).<a>Monotone.add_const</a> k.val) <| (hf <| (<a>Nat.le_mul_of_pos_left</a> n <a>Fin.size_pos'</a>).<a>LE.le.trans</a> <| <a>Nat.le_add_right</a> ..).<a>LE.le.trans_lt</a> hn | m : ℕ
hm : NeZero m
f : ℕ → ℝ
hf : Antitone f
n : ℕ
hn : f n < 0
k : ZMod m
⊢ ¬Summable fun n => f (m * n + k.val) | ((:c Not) ((:c Summable) (:c Real) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:c Real) (:c Real.instAddCommGroup)) ((:c UniformSpace.toTopologicalSpace) (:c Real) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.pseudoMetricSpace))) (:lambda n (:c Nat) ((:fv _uniq.17395) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c... | [{"name":"m","sexp":"(:c Nat)"},{"name":"hm","sexp":"((:c NeZero) (:c Nat) ((:c LinearOrderedCommMonoidWithZero.toZero) (:c Nat) (:c Nat.instLinearOrderedCommMonoidWithZero)) (:fv _uniq.17393))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"hf","sexp":"((:c Antitone) (:c Nat) (:c Real) ((:c PartialOrde... | (:app (:c Not) (:arg :explicit 0 (:app (:c Summable) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Real))))) (:arg :explicit 4 (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17393","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.17394","is_instance":true,"is_let":false,"name":"hm","sexp":"(:app (:c NeZero) (:arg :implicit-type 0 ... | {"children":[{"source":"exact","sourceEnd":3289,"sourceStart":3284,"tag":"atom"},{"children":[{"children":[{"name":"not_summable_of_antitone_of_neg","semanticRole":"global","source":"not_summable_of_antitone_of_neg","sourceEnd":3321,"sourceStart":3290,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceE... | [] | [{"source":"not_summable_of_antitone_of_neg\n (hf.comp_monotone <| (Covariant.monotone_of_const m).add_const k.val) <|\n (hf <| (Nat.le_mul_of_pos_left n Fin.size_pos').trans <| Nat.le_add_right ..).trans_lt hn","source_end":3492,"source_start":3290,"syntax_kind":"«term_<|_»"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17393","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.17394","is_instance":true,"is_let":false,"user_name":"hm"},{"binder_role":":implicit","context_index":3,"internal_n... | 4 | 8 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fb5708c7c187cb2bb7eaea7f2d7e95b10b0e143833e2b59222fbf823c04ae440 | cf6626401b20ea5a0320471218a05b327e0598cfcd23b746d694de525b8c791a | 502c71caaa727bd8b02358f2fb27d87f2d4629e6e95863079add71a7047cdaf2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,898 | lcm_dvd_iff | Mathlib/Algebra/GCDMonoid/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases h : a = 0 ∨ b = 0 | α : Type u_1
inst✝¹ : CancelCommMonoidWithZero α
inst✝ : GCDMonoid α
a b c : α
⊢ lcm a b ∣ c ↔ a ∣ c ∧ b ∣ c | case pos
α : Type u_1
inst✝¹ : CancelCommMonoidWithZero α
inst✝ : GCDMonoid α
a b c : α
h : a = 0 ∨ b = 0
⊢ lcm a b ∣ c ↔ a ∣ c ∧ b ∣ c
case neg
α : Type u_1
inst✝¹ : CancelCommMonoidWithZero α
inst✝ : GCDMonoid α
a b c : α
h : ¬(a = 0 ∨ b = 0)
⊢ lcm a b ∣ c ↔ a ∣ c ∧ b ∣ c | ((:c Iff) ((:c Dvd.dvd) (:fv _uniq.86027) ((:c semigroupDvd) (:fv _uniq.86027) ((:c SemigroupWithZero.toSemigroup) (:fv _uniq.86027) ((:c MonoidWithZero.toSemigroupWithZero) (:fv _uniq.86027) ((:c CommMonoidWithZero.toMonoidWithZero) (:fv _uniq.86027) ((:c CancelCommMonoidWithZero.toCommMonoidWithZero) (:fv _uniq.86027... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CancelCommMonoidWithZero) (:fv _uniq.86027))"},{"name":"inst✝","sexp":"((:c GCDMonoid) (:fv _uniq.86027) (:fv _uniq.86030))"},{"name":"a","sexp":"(:fv _uniq.86027)"},{"name":"b","sexp":"(:fv _uniq.86027)"},{"name":"c","sexp":"(:fv _uniq.86027)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c GCDMonoid.lcm) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CancelCommMonoidWithZero) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86027","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.86030","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CancelCommMonoidWithZer... | {"children":[{"source":"by_cases","sourceEnd":32166,"sourceStart":32158,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":32168,"sourceStart":32167,"tag":"identifier"},{"source":":","sourceEnd":32170,"sourceStart":32169,"tag":"atom"}],"kind":"null","source":"h :","sourceEnd":32170,"sour... | [] | [{"source":"a = 0 ∨ b = 0","source_end":32186,"source_start":32171,"syntax_kind":"«term_∨_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86027","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.86030","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 196 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9ef81122ce5f357d988b20422965179571bb203efa4dad9958085b8747fccce3 | 562a90f0757a5d1af0e60fb218f4d5e61f809102e5a2f6c89b2103b979788ef2 | db86b3f2ea1b1b3a1254470885895c5ed1ff84b072eb3cf817e46415bfae2ff2 | 154f19246cafe7604a16c4e6306cbc5ab6030b3c476ed60e45fa3c53d4ee6958 |
cat-searcher/leandojo-benchmark-4-random | test | 1,899 | lcm_dvd_iff | Mathlib/Algebra/GCDMonoid/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases h with (rfl | rfl) <;> simp (config := { contextual := <a>Bool.true</a> }) only [<a>iff_def</a>, <a>GCDMonoid.lcm_zero_left</a>, <a>GCDMonoid.lcm_zero_right</a>, <a>zero_dvd_iff</a>, <a>dvd_zero</a>, <a>eq_self_iff_true</a>, <a>and_true_iff</a>, <a>imp_true_iff</a>] | case pos
α : Type u_1
inst✝¹ : CancelCommMonoidWithZero α
inst✝ : GCDMonoid α
a b c : α
h : a = 0 ∨ b = 0
⊢ lcm a b ∣ c ↔ a ∣ c ∧ b ∣ c | ((:c Iff) ((:c Dvd.dvd) (:fv _uniq.86027) ((:c semigroupDvd) (:fv _uniq.86027) ((:c SemigroupWithZero.toSemigroup) (:fv _uniq.86027) ((:c MonoidWithZero.toSemigroupWithZero) (:fv _uniq.86027) ((:c CommMonoidWithZero.toMonoidWithZero) (:fv _uniq.86027) ((:c CancelCommMonoidWithZero.toCommMonoidWithZero) (:fv _uniq.86027... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CancelCommMonoidWithZero) (:fv _uniq.86027))"},{"name":"inst✝","sexp":"((:c GCDMonoid) (:fv _uniq.86027) (:fv _uniq.86030))"},{"name":"a","sexp":"(:fv _uniq.86027)"},{"name":"b","sexp":"(:fv _uniq.86027)"},{"name":"c","sexp":"(:fv _uniq.86027)"},{"n... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c GCDMonoid.lcm) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CancelCommMonoidWithZero) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86027","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.86030","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CancelCommMonoidWithZer... | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"rcases","sourceEnd":32198,"sourceStart":32192,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":7,"semanticRole":"local","source":"h","sourceEnd":32200,"sourceStart":32199,"tag":"iden... | [] | [{"source":"h","source_end":32200,"source_start":32199,"syntax_kind":"ident"},{"source":"(rfl | rfl)","source_end":32217,"source_start":32206,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"},{"source":"{ contextual := true }","source_end":32266,"source_start":32244,"syntax_kind":"Lean.Parser.Term.structInst"},{"sour... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86027","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.86030","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 196 | 7 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2e7cd4da8876907cfa3f7a16026a692796dbe94ef3a31eeb4b33e6731d5a8892 | a2c6db2685e9651084ca311fe279644174768d627763bc99a8091bc752d68029 | 5628e6b0d92798e10fe3e02d00b21288bdc9e7fe1b8f7640922bbaf9d76bd288 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,900 | lcm_dvd_iff | Mathlib/Algebra/GCDMonoid/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨h1, h2⟩ := <a>not_or</a>.1 h | case neg
α : Type u_1
inst✝¹ : CancelCommMonoidWithZero α
inst✝ : GCDMonoid α
a b c : α
h : ¬(a = 0 ∨ b = 0)
⊢ lcm a b ∣ c ↔ a ∣ c ∧ b ∣ c | case neg.intro
α : Type u_1
inst✝¹ : CancelCommMonoidWithZero α
inst✝ : GCDMonoid α
a b c : α
h : ¬(a = 0 ∨ b = 0)
h1 : ¬a = 0
h2 : ¬b = 0
⊢ lcm a b ∣ c ↔ a ∣ c ∧ b ∣ c | ((:c Iff) ((:c Dvd.dvd) (:fv _uniq.86027) ((:c semigroupDvd) (:fv _uniq.86027) ((:c SemigroupWithZero.toSemigroup) (:fv _uniq.86027) ((:c MonoidWithZero.toSemigroupWithZero) (:fv _uniq.86027) ((:c CommMonoidWithZero.toMonoidWithZero) (:fv _uniq.86027) ((:c CancelCommMonoidWithZero.toCommMonoidWithZero) (:fv _uniq.86027... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CancelCommMonoidWithZero) (:fv _uniq.86027))"},{"name":"inst✝","sexp":"((:c GCDMonoid) (:fv _uniq.86027) (:fv _uniq.86030))"},{"name":"a","sexp":"(:fv _uniq.86027)"},{"name":"b","sexp":"(:fv _uniq.86027)"},{"name":"c","sexp":"(:fv _uniq.86027)"},{"n... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c GCDMonoid.lcm) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CancelCommMonoidWithZero) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86027","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.86030","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CancelCommMonoidWithZer... | {"children":[{"source":"obtain","sourceEnd":32403,"sourceStart":32397,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":32407,"sourceStart":32404,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h1","sourceE... | [] | [{"source":"not_or.1 h","source_end":32430,"source_start":32420,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨h1, h2⟩","source_end":32416,"source_start":32404,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86027","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.86030","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 196 | 18 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | caed11ee72649ed908aff5545818ffcad65097952c2e7bad6ae9d0d947ef1ee6 | 0f8febffeeb2f649bab4e3db41e18d7ab588c52153bf234d4ca8a4a64fd0857d | 64daef18edad4789de5df6c982fc30bc4faee5b4b77c9af645251519cd2ca17d | a81937342f92016ffc1efab47501bac7658d8e67dc743c62a19701370311235a |
cat-searcher/leandojo-benchmark-4-random | test | 1,901 | lcm_dvd_iff | Mathlib/Algebra/GCDMonoid/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h : <a>GCDMonoid.gcd</a> a b ≠ 0 := fun H => h1 ((<a>gcd_eq_zero_iff</a> _ _).1 H).1 | case neg.intro
α : Type u_1
inst✝¹ : CancelCommMonoidWithZero α
inst✝ : GCDMonoid α
a b c : α
h : ¬(a = 0 ∨ b = 0)
h1 : ¬a = 0
h2 : ¬b = 0
⊢ lcm a b ∣ c ↔ a ∣ c ∧ b ∣ c | case neg.intro
α : Type u_1
inst✝¹ : CancelCommMonoidWithZero α
inst✝ : GCDMonoid α
a b c : α
h✝ : ¬(a = 0 ∨ b = 0)
h1 : ¬a = 0
h2 : ¬b = 0
h : gcd a b ≠ 0
⊢ lcm a b ∣ c ↔ a ∣ c ∧ b ∣ c | ((:c Iff) ((:c Dvd.dvd) (:fv _uniq.86027) ((:c semigroupDvd) (:fv _uniq.86027) ((:c SemigroupWithZero.toSemigroup) (:fv _uniq.86027) ((:c MonoidWithZero.toSemigroupWithZero) (:fv _uniq.86027) ((:c CommMonoidWithZero.toMonoidWithZero) (:fv _uniq.86027) ((:c CancelCommMonoidWithZero.toCommMonoidWithZero) (:fv _uniq.86027... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CancelCommMonoidWithZero) (:fv _uniq.86027))"},{"name":"inst✝","sexp":"((:c GCDMonoid) (:fv _uniq.86027) (:fv _uniq.86030))"},{"name":"a","sexp":"(:fv _uniq.86027)"},{"name":"b","sexp":"(:fv _uniq.86027)"},{"name":"c","sexp":"(:fv _uniq.86027)"},{"n... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c GCDMonoid.lcm) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CancelCommMonoidWithZero) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86027","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.86030","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CancelCommMonoidWithZer... | {"children":[{"source":"have","sourceEnd":32439,"sourceStart":32435,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":32441,"sourceStart":32440,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":32441,"sourceStart":32440,"tag":"node"... | [] | [{"source":"gcd a b ≠ 0","source_end":32457,"source_start":32444,"syntax_kind":"«term_≠_»"},{"source":"fun H => h1 ((gcd_eq_zero_iff _ _).1 H).1","source_end":32502,"source_start":32461,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86027","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.86030","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 196 | 19 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4c5deeaf3c28c36127a0407979b2993377a8bae0a4158ff3b49eee9983026a21 | a81937342f92016ffc1efab47501bac7658d8e67dc743c62a19701370311235a | 38be271ce260784d9de3495d5d4df8f940cbe97e6ac478546e4f102055ddd66d | 4e949b72336fa37b3661c356eccdf8b054d7ed2abc13229123b50085a51ecfb4 |
cat-searcher/leandojo-benchmark-4-random | test | 1,902 | lcm_dvd_iff | Mathlib/Algebra/GCDMonoid/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>mul_dvd_mul_iff_left</a> h, (<a>gcd_mul_lcm</a> a b).<a>Associated.dvd_iff_dvd_left</a>, ← (<a>gcd_mul_right'</a> c a b).<a>Associated.dvd_iff_dvd_right</a>, <a>dvd_gcd_iff</a>, <a>mul_comm</a> b c, <a>mul_dvd_mul_iff_left</a> h1, <a>mul_dvd_mul_iff_right</a> h2, <a>and_comm</a>] | case neg.intro
α : Type u_1
inst✝¹ : CancelCommMonoidWithZero α
inst✝ : GCDMonoid α
a b c : α
h✝ : ¬(a = 0 ∨ b = 0)
h1 : ¬a = 0
h2 : ¬b = 0
h : gcd a b ≠ 0
⊢ lcm a b ∣ c ↔ a ∣ c ∧ b ∣ c | ((:c Iff) ((:c Dvd.dvd) (:fv _uniq.86027) ((:c semigroupDvd) (:fv _uniq.86027) ((:c SemigroupWithZero.toSemigroup) (:fv _uniq.86027) ((:c MonoidWithZero.toSemigroupWithZero) (:fv _uniq.86027) ((:c CommMonoidWithZero.toMonoidWithZero) (:fv _uniq.86027) ((:c CancelCommMonoidWithZero.toCommMonoidWithZero) (:fv _uniq.86027... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CancelCommMonoidWithZero) (:fv _uniq.86027))"},{"name":"inst✝","sexp":"((:c GCDMonoid) (:fv _uniq.86027) (:fv _uniq.86030))"},{"name":"a","sexp":"(:fv _uniq.86027)"},{"name":"b","sexp":"(:fv _uniq.86027)"},{"name":"c","sexp":"(:fv _uniq.86027)"},{"n... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c GCDMonoid.lcm) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CancelCommMonoidWithZero) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86027","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.86030","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CancelCommMonoidWithZer... | {"children":[{"source":"rw","sourceEnd":32509,"sourceStart":32507,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32511,"sourceStart":32510,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":32514,"sourceSt... | [] | [{"source":"mul_dvd_mul_iff_left h","source_end":32537,"source_start":32515,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(gcd_mul_lcm a b).dvd_iff_dvd_left","source_end":32573,"source_start":32539,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"(gcd_mul_right' c a b).dvd_iff_dvd_right","source_end":32625,"source_... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86027","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.86030","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 196 | 20 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d5ec8fd9b7ed13997d7628244ea76a4ca299db3e18080ed950592ea23e193eba | 4e949b72336fa37b3661c356eccdf8b054d7ed2abc13229123b50085a51ecfb4 | 60167703d7f57178f2754fec6761cbb261b0fde9fa8dff244943742c9894cea5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,903 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨C, r, Cpos, rpos, ple⟩ : ∃ (C r : _) (_ : 0 < C) (_ : 0 < r), ∀ n : ℕ, ‖p n‖ ≤ C * r ^ n := <a>FormalMultilinearSeries.le_mul_pow_of_radius_pos</a> p hp | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
⊢ 0 < (p.rightInv i).radius | case intro.intro.intro.intro
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
pl... | ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c ENNReal)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"obtain","sourceEnd":25202,"sourceStart":25196,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":25206,"sourceStart":25203,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"C","sourceEn... | [] | [{"source":"∃ (C r : _) (_ : 0 < C) (_ : 0 < r), ∀ n : ℕ, ‖p n‖ ≤ C * r ^ n","source_end":25312,"source_start":25237,"syntax_kind":"«term∃_,_»"},{"source":"le_mul_pow_of_radius_pos p hp","source_end":25349,"source_start":25320,"syntax_kind":"Lean.Parser.Term.app"},{"source":"obtain","source_end":25202,"source_start":25... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d32911696eed471e4eb055fc8bc7ed54dcf33a36be346a30dc9cb067e353c35c | 10cb1ed4098dda35fc41219eb4450c3ab0f495293c75e1d4e0b7f9b1408ab820 | b0c5b2821342508d00ef9cb8f6b70bac161caddd3ee31f20df11d932de77d18a | b423459873ac623de648ed31eca334efbfe82d11765dbed14f45e1e43d6668bc |
cat-searcher/leandojo-benchmark-4-random | test | 1,904 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let I := ‖(i.symm : F →L[𝕜] E)‖ | case intro.intro.intro.intro
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
pl... | case intro.intro.intro.intro
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
pl... | ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c ENNReal)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"let","sourceEnd":25355,"sourceStart":25352,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"I","sourceEnd":25357,"sourceStart":25356,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{... | [] | [{"source":"‖(i.symm : F →L[𝕜] E)‖\n -- choose `a` small enough to make sure that `∑_{k ≤ n} aᵏ Qₖ` will be controllable by\n -- induction","source_end":25392,"source_start":25361,"syntax_kind":"«term‖_‖»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 5 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 424cc514e89485500e2f59019dbfcb981cc6a7b2e39c103a9bcbb894d45a7da9 | b423459873ac623de648ed31eca334efbfe82d11765dbed14f45e1e43d6668bc | ee954e21065a10bc945bfd0727f8d461f44554ca45fda92e98b0404dcc20ddba | 89e793fa627b1b9b8d907b359cbf7e9c8a4e338097872db85b7085cbd865e6f1 |
cat-searcher/leandojo-benchmark-4-random | test | 1,905 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨a, apos, ha1, ha2⟩ : ∃ (a : _) (apos : 0 < a), 2 * I * C * r ^ 2 * (I + 1) ^ 2 * a ≤ 1 ∧ r * (I + 1) * a ≤ 1 / 2 := by have : <a>Filter.Tendsto</a> (fun a => 2 * I * C * r ^ 2 * (I + 1) ^ 2 * a) (𝓝 0) (𝓝 (2 * I * C * r ^ 2 * (I + 1) ^ 2 * 0)) := tendsto_const_nhds.mul <a>Filter.tendsto_id</a> have A : ∀ᶠ a in... | case intro.intro.intro.intro
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
pl... | case intro.intro.intro.intro.intro.intro.intro
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 <... | ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c ENNReal)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"obtain","sourceEnd":25513,"sourceStart":25507,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":25517,"sourceStart":25514,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEn... | [] | [{"source":"∃ (a : _) (apos : 0 < a),\n 2 * I * C * r ^ 2 * (I + 1) ^ 2 * a ≤ 1 ∧ r * (I + 1) * a ≤ 1 / 2","source_end":25649,"source_start":25544,"syntax_kind":"«term∃_,_»"},{"source":"Tendsto (fun a => 2 * I * C * r ^ 2 * (I + 1) ^ 2 * a) (𝓝 0)\n (𝓝 (2 * I * C * r ^ 2 * (I + 1) ^ 2 * 0))","source_end":2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 6 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 710144dccf2c5858080c75d02d540e7afd1dab7f2a8bdfc8b3f925f484cbbedd | 89e793fa627b1b9b8d907b359cbf7e9c8a4e338097872db85b7085cbd865e6f1 | 5a44642310e74c9cf550fb114d0ef42fc49dde791667d7a3efe892e5035721d9 | 55321a855ef98d54438ba80d0d952a1397d17fb3464edd03e2aed1218c750d30 |
cat-searcher/leandojo-benchmark-4-random | test | 1,906 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let S n := ∑ k ∈ <a>Finset.Ico</a> 1 n, a ^ k * ‖p.rightInv i k‖ | case intro.intro.intro.intro.intro.intro.intro
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 <... | case intro.intro.intro.intro.intro.intro.intro
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 <... | ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c ENNReal)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"let","sourceEnd":26644,"sourceStart":26641,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"S","sourceEnd":26646,"sourceStart":26645,"tag":"identifier"},{"children":[{"semanticRole":"scoped_local","source":"n","sourceEnd":26648,"sourceStart":26647,"tag":"identifie... | [] | [{"source":"∑ k ∈ Ico 1 n, a ^ k * ‖p.rightInv i k‖","source_end":26699,"source_start":26652,"syntax_kind":"BigOperators.bigsum"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 28 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3613cdf325f46284c3ff6226432bf1c47749b974d23dbd61551e6f7cc76440b1 | 55321a855ef98d54438ba80d0d952a1397d17fb3464edd03e2aed1218c750d30 | c4ff544c30eaa91e6250def0229bf16f53d6f6e623e8c1a5c3615546ec6f0821 | 58e3068bfff08c7df2d37225c22869cab045baec36d1cef26c01837b1c641ef9 |
cat-searcher/leandojo-benchmark-4-random | test | 1,907 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let a' : <a>NNReal</a> := ⟨a, apos.le⟩ | case intro.intro.intro.intro.intro.intro.intro
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 <... | case intro.intro.intro.intro.intro.intro.intro
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 <... | ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c ENNReal)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"let","sourceEnd":28002,"sourceStart":27999,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"a'","sourceEnd":28005,"sourceStart":28003,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":280... | [] | [{"source":"NNReal","source_end":28014,"source_start":28008,"syntax_kind":"ident"},{"source":"⟨a, apos.le⟩","source_end":28034,"source_start":28018,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 114 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4a82adfa19d1923450b94493b751fc7afec375e940a1f1bccfd79a3eaae7753c | f545d3a2802b25c793957c8f1ccae30338af95f0eddc484fef167a5093f7cba7 | 2440cef0f699ca3330cbed5e7d2ad727d55ae7dcc4ab4aef53a15ddf1c003ff3 | 2d97af821f2a47ece1b2e171279dc31a9cbd01ea5de21c95a8a690e0bbad6637 |
cat-searcher/leandojo-benchmark-4-random | test | 1,909 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>FormalMultilinearSeries.le_radius_of_bound</a> _ ((I + 1) * a) fun n => ?_ | case intro.intro.intro.intro.intro.intro.intro
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 <... | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((: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":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 ENNReal.ofNNReal) (:arg :explicit 0 (:fv FV24)))) (:arg :explicit 3 (:app (:c FormalMultilinearSeries.radius) (:arg :implicit-type 0 (:fv FV0)) (:arg :implic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"apply","sourceEnd":28234,"sourceStart":28229,"tag":"atom"},{"children":[{"name":"FormalMultilinearSeries.le_radius_of_bound","semanticRole":"global","source":"le_radius_of_bound","sourceEnd":28253,"sourceStart":28235,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":28255,"... | [] | [{"source":"le_radius_of_bound _ ((I + 1) * a) fun n => ?_","source_end":28281,"source_start":28235,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 120 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4e90f6f4bdc6e509d3112762a9cc3c1b641ca354f9d08b8fbd2921b904386528 | 74b76a0a14ff4248d6e7a1e19f2b13827091f1c1e9aaca60c2c874e8622a7860 | 8d77ed7b7e4c345957d937d513801f4acd9b21ba2d321605b476109cbfb8554b | 488129856a3245a1e9a9937e3f4630f97e2b83135b392206c1a352c81ba02ea2 |
cat-searcher/leandojo-benchmark-4-random | test | 1,910 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases hn : n = 0 | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | case pos
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c Norm.norm) ((:c ContinuousMultilinearMap) (:fv _uniq.490204) ((:c Fin) (:fv _uniq.622104)) (:lambda _ ((:c Fin) (:fv _uniq.622104)) (:fv _uniq.490324)) (:fv _uniq.490210) ((:c Ring.toSem... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"by_cases","sourceEnd":28292,"sourceStart":28284,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hn","sourceEnd":28295,"sourceStart":28293,"tag":"identifier"},{"source":":","sourceEnd":28297,"sourceStart":28296,"tag":"atom"}],"kind":"null","source":"hn :","sourceEnd":28297,"so... | [] | [{"source":"n = 0","source_end":28303,"source_start":28298,"syntax_kind":"«term_=_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 121 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f6f2874d5a39d28b7920fad8fa2e6a76ec8fd0787faf62b545a7c478ffc28b2c | 488129856a3245a1e9a9937e3f4630f97e2b83135b392206c1a352c81ba02ea2 | cbfea943ffcc71f35656e6d8db2246b58487d289951f7624827d3fae9964c4bb | 7fa8d299bf05bb1e9972f49fe9146b5e323855d8279ee2d94366c4dc82e24ab2 |
cat-searcher/leandojo-benchmark-4-random | test | 1,911 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>Filter.Tendsto</a> (fun a => 2 * I * C * r ^ 2 * (I + 1) ^ 2 * a) (𝓝 0) (𝓝 (2 * I * C * r ^ 2 * (I + 1) ^ 2 * 0)) := tendsto_const_nhds.mul <a>Filter.tendsto_id</a> | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c Exists) (:c Real) (:lambda a (:c Real) ((:c Exists) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) 0) (:lambda apos ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.inst... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda a :explicit (:c Real) (:app (:c Exists) (:arg :implicit-type 0 (: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 :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"have","sourceEnd":25664,"sourceStart":25660,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":25665,"sourceStart":25665,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":25665,"sourceStart":25665,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"Tendsto (fun a => 2 * I * C * r ^ 2 * (I + 1) ^ 2 * a) (𝓝 0)\n (𝓝 (2 * I * C * r ^ 2 * (I + 1) ^ 2 * 0))","source_end":25789,"source_start":25673,"syntax_kind":"Lean.Parser.Term.app"},{"source":"tendsto_const_nhds.mul tendsto_id","source_end":25832,"source_start":25799,"syntax_kind":"Lean.Parser.Te... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 11 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6f56ab3751f7587f20aef9c6c55c6b134429ae49031db9f7f6164aaa5466ede9 | 852ccf2753b9923541b195ccd3fab9fdf2482ffa7bf325f0c26f7f9ca5ca7736 | de730b1566024466e82322fb56703b6f7f1481320923f094e4ce4b0a0bc10bd8 | 294b4e38ef87fa2bb6f898d7b79b15be681e343a518ce5e8759d83ad2a9434c9 |
cat-searcher/leandojo-benchmark-4-random | test | 1,912 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have A : ∀ᶠ a in 𝓝 0, 2 * I * C * r ^ 2 * (I + 1) ^ 2 * a < 1 := by apply (<a>tendsto_order</a>.1 this).2; simp [<a>zero_lt_one</a>] | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c Exists) (:c Real) (:lambda a (:c Real) ((:c Exists) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) 0) (:lambda apos ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.inst... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda a :explicit (:c Real) (:app (:c Exists) (:arg :implicit-type 0 (: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 :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"have","sourceEnd":25841,"sourceStart":25837,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"A","sourceEnd":25843,"sourceStart":25842,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"A","sourceEnd":25843,"sourceStart":25842,"tag":"node"... | [] | [{"source":"∀ᶠ a in 𝓝 0, 2 * I * C * r ^ 2 * (I + 1) ^ 2 * a < 1","source_end":25905,"source_start":25846,"syntax_kind":"Filter.«term∀ᶠ_In_,_»"},{"source":"(tendsto_order.1 this).2","source_end":25948,"source_start":25924,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"zero_lt_one","source_end":25967,"source_start":... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 12 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0e232b9a9334fb28b435966a87df8bf7c718aeeb5826c8ab5a227f66d9727547 | 294b4e38ef87fa2bb6f898d7b79b15be681e343a518ce5e8759d83ad2a9434c9 | 077562ff3d53e419fa71e30c3108777f1f82418b1be00ae227f9cfec0a52d809 | 5508e7d99b6497327f8f836119ef2b61e478bb3a51ae91b62e1163f2d5e336c9 |
cat-searcher/leandojo-benchmark-4-random | test | 1,913 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>Filter.Tendsto</a> (fun a => r * (I + 1) * a) (𝓝 0) (𝓝 (r * (I + 1) * 0)) := tendsto_const_nhds.mul <a>Filter.tendsto_id</a> | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c Exists) (:c Real) (:lambda a (:c Real) ((:c Exists) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) 0) (:lambda apos ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.inst... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda a :explicit (:c Real) (:app (:c Exists) (:arg :implicit-type 0 (: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 :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"have","sourceEnd":25977,"sourceStart":25973,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":25978,"sourceStart":25978,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":25978,"sourceStart":25978,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"Tendsto (fun a => r * (I + 1) * a) (𝓝 0) (𝓝 (r * (I + 1) * 0))","source_end":26048,"source_start":25980,"syntax_kind":"Lean.Parser.Term.app"},{"source":"tendsto_const_nhds.mul tendsto_id","source_end":26091,"source_start":26058,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 17 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 07d93565acd0fb6830e8b21e9771eea98f9b000c5b3d5c5103655035d7cf5300 | 5508e7d99b6497327f8f836119ef2b61e478bb3a51ae91b62e1163f2d5e336c9 | ef4949814966692cd4ed91a0a84cf2b19a94b2bd9a2998538ce6c07027efce95 | a7d7763a2ef71a1b1ad2e7f057e05423853563a75e26ef6458685f33a67277c9 |
cat-searcher/leandojo-benchmark-4-random | test | 1,914 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have B : ∀ᶠ a in 𝓝 0, r * (I + 1) * a < 1 / 2 := by apply (<a>tendsto_order</a>.1 this).2; simp [<a>zero_lt_one</a>] | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c Exists) (:c Real) (:lambda a (:c Real) ((:c Exists) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) 0) (:lambda apos ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.inst... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda a :explicit (:c Real) (:app (:c Exists) (:arg :implicit-type 0 (: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 :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"have","sourceEnd":26100,"sourceStart":26096,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"B","sourceEnd":26102,"sourceStart":26101,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"B","sourceEnd":26102,"sourceStart":26101,"tag":"node"... | [] | [{"source":"∀ᶠ a in 𝓝 0, r * (I + 1) * a < 1 / 2","source_end":26148,"source_start":26105,"syntax_kind":"Filter.«term∀ᶠ_In_,_»"},{"source":"(tendsto_order.1 this).2","source_end":26191,"source_start":26167,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"zero_lt_one","source_end":26210,"source_start":26199,"syntax_ki... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 18 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 023989f09985d1940a69b56959e2107c31dfeda8a9242c02ed1b1e1eebdc16fe | a7d7763a2ef71a1b1ad2e7f057e05423853563a75e26ef6458685f33a67277c9 | c87eab52c42e97ed2720776a908d7549d29cbc1dca1b921f26004de52a93504c | 11fc6e65add60aaa2b88be0edff24829d75feec3e5eafedf755ea0c1d4221aea |
cat-searcher/leandojo-benchmark-4-random | test | 1,915 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have C : ∀ᶠ a in 𝓝[>] (0 : ℝ), (0 : ℝ) < a := by filter_upwards [<a>self_mem_nhdsWithin</a>] with _ ha using ha | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C✝ r : ℝ
Cpos : 0 < C✝
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C✝ *... | ((:c Exists) (:c Real) (:lambda a (:c Real) ((:c Exists) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) 0) (:lambda apos ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.inst... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda a :explicit (:c Real) (:app (:c Exists) (:arg :implicit-type 0 (: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 :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"have","sourceEnd":26220,"sourceStart":26216,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"C","sourceEnd":26222,"sourceStart":26221,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"C","sourceEnd":26222,"sourceStart":26221,"tag":"node"... | [] | [{"source":"∀ᶠ a in 𝓝[>] (0 : ℝ), (0 : ℝ) < a","source_end":26269,"source_start":26225,"syntax_kind":"Filter.«term∀ᶠ_In_,_»"},{"source":"self_mem_nhdsWithin","source_end":26317,"source_start":26298,"syntax_kind":"ident"},{"source":"ha","source_end":26337,"source_start":26335,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 23 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6a6a46bfb0199c173370f054f447038c16f740532684243888e816909b3fa248 | 11fc6e65add60aaa2b88be0edff24829d75feec3e5eafedf755ea0c1d4221aea | b895e8e13c6f5be875afdf02048f612455e8672d7b643a1a72f06f5e18ccd4ba | d2337f2fa941561ccf662b03c9639b991ad7e10193c405887957a68612dde7b0 |
cat-searcher/leandojo-benchmark-4-random | test | 1,916 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases (C.and ((A.and B).<a>Filter.Eventually.filter_mono</a> <a>inf_le_left</a>)).<a>Filter.Eventually.exists</a> with ⟨a, ha⟩ | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C✝ r : ℝ
Cpos : 0 < C✝
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C✝ *... | case intro
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C✝ r : ℝ
Cpos : 0 < C✝
rpos : 0 < r
ple : ∀ (n : ℕ), ‖... | ((:c Exists) (:c Real) (:lambda a (:c Real) ((:c Exists) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) 0) (:lambda apos ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.inst... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda a :explicit (:c Real) (:app (:c Exists) (:arg :implicit-type 0 (: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 :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"rcases","sourceEnd":26348,"sourceStart":26342,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":"(","sourceEnd":26350,"sourceStart":26349,"tag":"atom"},{"children":[{"source":"C.and","sourceEnd":26355,"sourceStart":... | [] | [{"source":"(C.and ((A.and B).filter_mono inf_le_left)).exists","source_end":26399,"source_start":26349,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"⟨a, ha⟩","source_end":26416,"source_start":26405,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 26 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7104ddf587fb20e77b1755785e871eb7c9f1614a887c4e42997760a3cb6f4963 | d2337f2fa941561ccf662b03c9639b991ad7e10193c405887957a68612dde7b0 | a2d673e3f1e1842a7ce8f4a81cda43134d59df2b6fb0ad3230880c19b79aae3f | 3e33710e406882eb93035e32d26cffe70169b842f3344bd8bef9cb16ccf2b4ae |
cat-searcher/leandojo-benchmark-4-random | test | 1,917 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨a, ha.1, ha.2.1.<a>LT.lt.le</a>, ha.2.2.<a>LT.lt.le</a>⟩ | case intro
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C✝ r : ℝ
Cpos : 0 < C✝
rpos : 0 < r
ple : ∀ (n : ℕ), ‖... | ((:c Exists) (:c Real) (:lambda a (:c Real) ((:c Exists) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) 0) (:lambda apos ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.inst... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda a :explicit (:c Real) (:app (:c Exists) (:arg :implicit-type 0 (: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 :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"exact","sourceEnd":26426,"sourceStart":26421,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":26430,"sourceStart":26427,"tag":"atom"},{"children":[{"contextIndex":23,"semanticRole":"local","source":"a","sourceEnd":26431,"sourceStart":26430,"tag":"identifier"},{"source":",","sourceEnd":26432,... | [] | [{"source":"⟨a, ha.1, ha.2.1.le, ha.2.2.le⟩\n -- check by induction that the partial sums are suitably bounded, using the choice of `a` and the\n -- inductive control from Lemma `radius_rightInv_pos_of_radius_pos_aux2`.","source_end":26462,"source_start":26427,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 27 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5ee7cd1f91473502aa56ec7261619f87f79372cacebcdd2d714bcdf58d7cbc08 | 3e33710e406882eb93035e32d26cffe70169b842f3344bd8bef9cb16ccf2b4ae | 7c8c7196533c73252d008ecb6257eab2bbdad2dd7055a9d6edd4422560b31200 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,918 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply (<a>tendsto_order</a>.1 this).2 | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | case a
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤... | ((:c Filter.Eventually) (:c Real) (:lambda a (:c Real) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda a :explicit (:c Real) (: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 HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"apply","sourceEnd":25923,"sourceStart":25918,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":25925,"sourceStart":25924,"tag":"atom"},{"children":[{"children":[{"name":"tendsto_order","semanticRole":"global","source":"tendsto_order","sourceEnd":25938,"sourceStart":25925,"tag":"i... | [] | [{"source":"(tendsto_order.1 this).2","source_end":25948,"source_start":25924,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 14 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d6155801f16ba143f0535ebd7e09c3d329f97a0f5b60f41ff3541b8623b47ef3 | 2aa681ca6d4d88c251257b863199df2780ff88c01e4a35d53311e821f3275ec2 | ca3e99c8ba4c80759c519254b1303cb5dfe7f702a96a8b332587a3bdcf4c066d | 022a398e70864ee07592901689bd1cf2928017143d316c9f76b1fe63eac86c34 |
cat-searcher/leandojo-benchmark-4-random | test | 1,919 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>zero_lt_one</a>] | case a
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤... | ((:c GT.gt) (:c Real) ((:c Preorder.toLT) (:c Real) (:c Real.instPreorder)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Rea... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c GT.gt) (: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 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"simp","sourceEnd":25954,"sourceStart":25950,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":25956,"sourceStart":25955,"tag":"a... | [] | [{"source":"zero_lt_one","source_end":25967,"source_start":25956,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 16 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1492fa1afb1b915d2c091d3b0c77f9ef1c6879cdbc722c04267deacb619102c9 | 022a398e70864ee07592901689bd1cf2928017143d316c9f76b1fe63eac86c34 | ff9876982e3146a3cf1e6a3ff6994a0e91c42beeb89a1902869e142e74c8bae9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,920 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply (<a>tendsto_order</a>.1 this).2 | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | case a
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤... | ((:c Filter.Eventually) (:c Real) (:lambda a (:c Real) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.496122) ((:c HAdd.hAdd) (:c Real) (... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda a :explicit (:c Real) (: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 HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"apply","sourceEnd":26166,"sourceStart":26161,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":26168,"sourceStart":26167,"tag":"atom"},{"children":[{"children":[{"name":"tendsto_order","semanticRole":"global","source":"tendsto_order","sourceEnd":26181,"sourceStart":26168,"tag":"i... | [] | [{"source":"(tendsto_order.1 this).2","source_end":26191,"source_start":26167,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 20 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0209814b3de124b4b68b3d706ccb787428a2b06da7ac5fc267b6dc81e55a72e5 | 76dd0cf9eb19c9336d5e98be5b16c89124c0a70cdcd7f90fd86f21592ea549a8 | ca3e99c8ba4c80759c519254b1303cb5dfe7f702a96a8b332587a3bdcf4c066d | af3ea365cb17ed2b4acdd509ce809fe702e19e08f00e67e5a7c1fb8b926d2847 |
cat-searcher/leandojo-benchmark-4-random | test | 1,921 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>zero_lt_one</a>] | case a
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤... | ((:c GT.gt) (:c Real) ((:c Preorder.toLT) (:c Real) (:c Real.instPreorder)) ((: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.toOfNat1) (:c Real) (:c Real.instOne))) ((:c OfNat.... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c GT.gt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"simp","sourceEnd":26197,"sourceStart":26193,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":26199,"sourceStart":26198,"tag":"a... | [] | [{"source":"zero_lt_one","source_end":26210,"source_start":26199,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 22 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 96357beedbd4be337abe5330b6752a26a8a3a07932bae875853ee8060f4d9e29 | af3ea365cb17ed2b4acdd509ce809fe702e19e08f00e67e5a7c1fb8b926d2847 | ff9876982e3146a3cf1e6a3ff6994a0e91c42beeb89a1902869e142e74c8bae9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,922 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards [<a>self_mem_nhdsWithin</a>] with _ ha using ha | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c Filter.Eventually) (:c Real) (:lambda a (:c Real) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) 0)) ((:c nhdsWithin) (:c Real) ((:c UniformSpace.toTopologicalSpace) (:c Real) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.p... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda a :explicit (:c Real) (: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)) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"filter_upwards","sourceEnd":26296,"sourceStart":26282,"tag":"atom"},{"children":[{"source":"[","sourceEnd":26298,"sourceStart":26297,"tag":"atom"},{"children":[{"name":"self_mem_nhdsWithin","semanticRole":"global","source":"self_mem_nhdsWithin","sourceEnd":26317,"sourceStart":26298,"tag":"identi... | [] | [{"source":"self_mem_nhdsWithin","source_end":26317,"source_start":26298,"syntax_kind":"ident"},{"source":"ha","source_end":26337,"source_start":26335,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 25 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 65a8dd5802a109cad21b9b65a0bd111a3bc581fa4b8207c4269bc3fe3ff93338 | 25710b782f39de8ceccf602dba45b860ba3f3cc797080b527243227876898ab2 | ed816277d99c5a05482149cbfe38a8bfe8a77b49d457c831b0f1531704c0737a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,923 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Nat.le_induction</a> | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | case base
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n... | (:forall n (:c Nat) (:forall _ ((:c LE.le) (:c Nat) (:c instLENat) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))) 0) ((:c LE.le) (:c Real) (:c Real.instLE) ((:fv _uniq.506747) 1) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HAdd.hAdd) (:c Real) (:c Re... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:forall n :explicit (:c Nat) (:forall _ :explicit (: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 OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"apply","sourceEnd":26768,"sourceStart":26763,"tag":"atom"},{"name":"Nat.le_induction","semanticRole":"global","source":"Nat.le_induction","sourceEnd":26785,"sourceStart":26769,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Nat.le_induction","sourceEnd":26785,"sourceStart"... | [] | [{"source":"Nat.le_induction","source_end":26785,"source_start":26769,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 31 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d8dfcab06f8b51946de029a61a81048b259a3f0daed48af18962384d7dbd96f4 | dca55e7b5160d8e85e73ab06205490a310a3623a8d34cfaed7ad933948d94a23 | 72780d453004d357a00aecac87a75b126cd9280bade00333eb175ee4e92cb5b7 | 5d5151d0ee64b6e94ebc82ba9c2be9f6a59bfd58f60be5bc488598efcd3a90da |
cat-searcher/leandojo-benchmark-4-random | test | 1,924 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [S] | case base
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n... | case base
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:fv _uniq.506747) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) (:fv _uniq.496... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 (:fv FV22) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"simp","sourceEnd":26797,"sourceStart":26793,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":26802,"sourceStart":26798,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":268... | [] | [{"source":"S","source_end":26805,"source_start":26804,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 36 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ef0af8337935ec002c12c09c4f715cdbb30f9c71e471dd6e92389eb75a8ce21f | 59df0e3320c03664604e2e8f69927b08c2ea28c60fea12ad7cf33f69868f479d | bffca996e80d5f8b8ce4c773e5f398bd06e22cb0ea30aa301d55cd604bcc4767 | cae4b64f1316537f011aa098d7f4a58ccb59ad021f9c4febcab9b78253eeb757 |
cat-searcher/leandojo-benchmark-4-random | test | 1,925 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.Ico_eq_empty_of_le</a> (<a>le_refl</a> 1), <a>Finset.sum_empty</a>] | case base
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n... | case base
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Finset.sum) (:c Nat) (:c Real) (:c Real.instAddCommMonoid) ((:c Finset.Ico) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))) (:c Nat.instLocallyFiniteOrder) ((:c OfNat.ofNat) (:c Nat) (:li... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 Finset.sum) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Real)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"rw","sourceEnd":26815,"sourceStart":26813,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":26817,"sourceStart":26816,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Fin... | [] | [{"source":"Ico_eq_empty_of_le (le_refl 1)","source_end":26847,"source_start":26817,"syntax_kind":"Lean.Parser.Term.app"},{"source":"sum_empty","source_end":26858,"source_start":26849,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 37 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f67314c6fee4c5830ca66ff3b0ccabef2c253b0207f77caeca9e067248f745b5 | cae4b64f1316537f011aa098d7f4a58ccb59ad021f9c4febcab9b78253eeb757 | 2740fec065dc0950bfab42cfe9816152812e5b6af34bb0be49175b1430d9c495 | b60824115c79baf9a0aa1379f149198d14f495f1edb8dd8fdfc9c8d29f634b9c |
cat-searcher/leandojo-benchmark-4-random | test | 1,926 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>mul_nonneg</a> (<a>add_nonneg</a> (<a>norm_nonneg</a> _) <a>zero_le_one</a>) apos.le | case base
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) ((:c AddMonoid.toZero) (:c Real) ((:c AddCommMonoid.toAddMonoid) (:c Real) (:c Real.instAddCommMonoid))))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HAdd.hAdd) (... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"exact","sourceEnd":26871,"sourceStart":26866,"tag":"atom"},{"children":[{"name":"mul_nonneg","semanticRole":"global","source":"mul_nonneg","sourceEnd":26882,"sourceStart":26872,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":26884,"sourceStart":26883,"tag":"atom"},{"child... | [] | [{"source":"mul_nonneg (add_nonneg (norm_nonneg _) zero_le_one) apos.le","source_end":26931,"source_start":26872,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 41 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 67f5911f448d772bbd4ba9ac2b7d653613a92c7054d30c4e5846259ea5099a52 | b60824115c79baf9a0aa1379f149198d14f495f1edb8dd8fdfc9c8d29f634b9c | 3380f1f70ba3a7aeb0b4956725b61aa4bad7cba58e8ff8ff1390b7022e4b94d1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,927 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro n one_le_n hn | case succ
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n... | case succ
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n... | (:forall n (:c Nat) (:forall hmn ((:c LE.le) (:c Nat) (:c instLENat) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))) 0) (:forall _ ((:c LE.le) (:c Real) (:c Real.instLE) ((:fv _uniq.506747) 1) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HAdd.hAdd) (:c... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:forall n :explicit (:c Nat) (:forall hmn :explicit (: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 OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"intro","sourceEnd":26944,"sourceStart":26939,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"n","sourceEnd":26946,"sourceStart":26945,"tag":"identifier"},{"semanticRole":"scoped_local","source":"one_le_n","sourceEnd":26955,"sourceStart":26947,"tag":"identifier"},{"semanticRol... | [{"role":"fresh_name","source":"n","source_end":26946,"source_start":26945,"syntax_kind":"ident"},{"role":"fresh_name","source":"one_le_n","source_end":26955,"source_start":26947,"syntax_kind":"ident"},{"role":"fresh_name","source":"hn","source_end":26958,"source_start":26956,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 46 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 575fb682edd2e385b56b8daf60a7d21dd8d7d939eff777016ca76480c4bfc8dd | 537e3e485658211584e3bd21d7c93b552271014e0625df877fe0223d91582455 | 14b048d47a766103b126d136d1b67896c682fe6741c27a02194b7444e8c8246a | 19102d6407c9695bb3af30c2488c58ef16313d2e4843f55659bb051bdb1ace72 |
cat-searcher/leandojo-benchmark-4-random | test | 1,928 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have In : 2 ≤ n + 1 := by linarith only [one_le_n] | case succ
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n... | case succ
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:fv _uniq.506747) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.509448) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 (:fv FV22) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"have","sourceEnd":26969,"sourceStart":26965,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"In","sourceEnd":26972,"sourceStart":26970,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"In","sourceEnd":26972,"sourceStart":26970,"tag":"nod... | [] | [{"source":"2 ≤ n + 1","source_end":26986,"source_start":26975,"syntax_kind":"«term_≤_»"},{"source":"one_le_n","source_end":27016,"source_start":27008,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 47 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7a0642ea3b8d00fca5aad29906f24717145153a7925fca183510fb2b7b633e3a | 19102d6407c9695bb3af30c2488c58ef16313d2e4843f55659bb051bdb1ace72 | 2bfd7e09480b4d08c2a40d26bf3ec9ce47b7d92a5ab3da35b9309c8d89ce9b71 | 344987e92a57530ca38eb9c11dd054b57044912e5e9aab802d05412b4ce97af7 |
cat-searcher/leandojo-benchmark-4-random | test | 1,929 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have rSn : r * S n ≤ 1 / 2 := calc r * S n ≤ r * ((I + 1) * a) := by gcongr _ ≤ 1 / 2 := by rwa [← <a>mul_assoc</a>] | case succ
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n... | case succ
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:fv _uniq.506747) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.509448) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 (:fv FV22) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"have","sourceEnd":27028,"sourceStart":27024,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rSn","sourceEnd":27032,"sourceStart":27029,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"rSn","sourceEnd":27032,"sourceStart":27029,"tag":"n... | [] | [{"source":"r * S n ≤ 1 / 2","source_end":27052,"source_start":27035,"syntax_kind":"«term_≤_»"},{"source":"calc\n r * S n ≤ r * ((I + 1) * a) := by gcongr\n _ ≤ 1 / 2 := by rwa [← mul_assoc]","source_end":27169,"source_start":27064,"syntax_kind":"Lean.calc"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 50 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ef1e25b9b50a717343f7fa600f1e04b4170173ada31d01cad3797c9555c8bd23 | 344987e92a57530ca38eb9c11dd054b57044912e5e9aab802d05412b4ce97af7 | a7803c4d0ee7bc3bc73352814228a0d37ab47f2745937405e59a3f3f4324037c | 1f3f32c20ae6d4aafac25865fe689f8e97999f3ba3e2b2a97b3a979a4e7ae24e |
cat-searcher/leandojo-benchmark-4-random | test | 1,930 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith only [one_le_n] | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c LE.le) (:c Nat) (:c instLENat) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2))) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.509448) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 2)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Nat)) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"linarith","sourceEnd":27001,"sourceStart":26993,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":27006,"sourceStart":27002,"tag":"atom"}],"kind":"null","source":"only... | [] | [{"source":"one_le_n","source_end":27016,"source_start":27008,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 49 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fffa7677639c706c5d300911d3f9638a9ca33f29148156294b53362871d48a56 | f364e6b44cc1e3a5607a87f3ea736fac15b0b89c8ab7b7ba87580c2b7e5d1c02 | 6ad13626698f85e84cdb4d8eae1797ba890d16cc95c81e9225cbae9cc7a983d6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,931 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.496122) ((:fv _uniq.506747) (:fv _uniq.509448))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.496122) ((:c HMul.hMul) (:c Re... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"children":[{"children":[{"children":[{"source":"gcongr","sourceEnd":27121,"sourceStart":27115,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":2712... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 53 | exact | true | 1 | 26 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 81edbbd64d01499ee8c9a65a4e00570bed85b769f9350ca4f6dc2785db5ae91a | 4127c28e54ef42bf56e93083310bdd66cb21fdb705f4a06aa5b9e7340682a3a0 | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,932 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [← <a>mul_assoc</a>] | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.496122) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.in... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":27153,"sourceStart":27150,"tag":"atom"},{"children":[{"source":"[","sourceEnd":27155,"sourceStart":27154,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":27158,"sourceStart":27155,"tag... | [] | [{"source":"mul_assoc","source_end":27168,"source_start":27159,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 58 | exact | true | 1 | 26 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fefeefa87a1550ed576eafa3907187bf4f1193c071cbd1fec45c388776e12c1d | 154aa54b1a57e8e4c5b7da298393c9760c7fc4302a78a653221609d3141ccb0c | ad0ca3b871ae0259cd5ce779255503227a7a8c83487e66555e67e3140b28ae35 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,933 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>geom_sum_Ico'</a> _ In] | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c Eq) (:c Real) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.496525) (:fv _uniq.505818)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.in... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"rw","sourceEnd":27447,"sourceStart":27445,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27449,"sourceStart":27448,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"geo... | [] | [{"source":"geom_sum_Ico' _ In","source_end":27467,"source_start":27449,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 68 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | de05b59ccb2757c1e888e4779c7073fc3e45a56841c96f42b8daaf70d81edb44 | 25fe1ddbb1169a75ec3be331b90e6bf3c0e87a89218b46f88f9ff325e2993f9c | cb9203b470cc067f0f06b279d11b7432daf0a5360832f1fc504beb88cb1633db | 00a4e20618dafc6e281a106e3186447520cc05068279ca415a36f4cfb476ba78 |
cat-searcher/leandojo-benchmark-4-random | test | 1,934 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>ne_of_lt</a> (rSn.trans_lt (by norm_num)) | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c Ne) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.496122) ((:fv _uniq.506747) (:fv _uniq.509448))) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) ((:c Semiring.toOne) (:c Real) ((:c DivisionSemiring.toSemiring) (:c Real) ((:c Divis... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c Ne) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"exact","sourceEnd":27475,"sourceStart":27470,"tag":"atom"},{"children":[{"name":"ne_of_lt","semanticRole":"global","source":"ne_of_lt","sourceEnd":27484,"sourceStart":27476,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":27486,"sourceStart":27485,"tag":"atom"},{"children"... | [] | [{"source":"ne_of_lt (rSn.trans_lt (by norm_num))","source_end":27513,"source_start":27476,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 72 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e2b74f0367b079d5d40cb345efbe0220b23ddad8ed0e53b186a4b7d2249fbf66 | 00a4e20618dafc6e281a106e3186447520cc05068279ca415a36f4cfb476ba78 | ea8e4c6e9fc62eb8cafe66670d9083ea1e01a64550a5029fde74c42508a97449 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,935 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_num | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) (:c Real.instPreorder)) ((: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.toOfNat1) (:c Real) (:c Real.instOne))) ((:c OfNat.... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 HDiv.hDiv) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"children":[{"children":[{"children":[{"source":"norm_num","sourceEnd":27511,"sourceStart":27503,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 75 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5a6fbb921104700faf558f0bfb9b5420680d75a463aaf445f01998a20ab7a415 | f5f08077f91859c5144bce24bf8fe990970785ff434e070a97c1316ebb187e13 | 7c64df8336d5a348b5f037e1d91facb19224fdef00e798d5c48c07a184602a59 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,936 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | case bc.h.hac
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.496525) (:fv _uniq.505818)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 HAdd.hAdd) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"gcongr","sourceEnd":27592,"sourceStart":27586,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":27592,"sourceStart":27586,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 82 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b64cdcb42cd4dc21b9056181d0444c7cc9faa4b0dae319e5151490e627175b87 | 382d0d9a0e7c4e1e32ad7424e79014598bfd1ee2ac31432bd4bf420cceaa66be | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | 0fac9c1f77a68d91dc1dd2119678a4a5d4e4047fc48704b9b298748922bf1b46 |
cat-searcher/leandojo-benchmark-4-random | test | 1,937 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>sub_le_self_iff</a>] | case bc.h.hac
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ... | case bc.h.hac
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) ((:c LinearOrderedSemifield.toLinearOrderedComm... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 HSub.hSub) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HSub) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"simp","sourceEnd":27610,"sourceStart":27606,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":27615,"sourceStart":27611,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":276... | [] | [{"source":"sub_le_self_iff","source_end":27632,"source_start":27617,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 87 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | acb8076f1f7949ddd18b4d01699f86d63ecf192856ca83a9595cc20d7d402405 | cdc45a185cfa6b251c141e64a70606da1e37143c7190a55afbc38553cd67ba8c | b19c63efc2cfc4525f02fc1959dba1538793d6aa343c2f75ed09360a81da86ad | 1e9b1c82f8c3d0c57e770146a36acb0afb87d32bf51fc00e37e798a3dad7791b |
cat-searcher/leandojo-benchmark-4-random | test | 1,938 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | case bc.h.hac
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) ((:c LinearOrderedSemifield.toLinearOrderedComm... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"positivity","sourceEnd":27656,"sourceStart":27646,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":27656,"sourceStart":27646,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 88 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 12f0106e75a2ca825f3811563d217de537c3994229da45a852eb6d5606e5b6f3 | 1e9b1c82f8c3d0c57e770146a36acb0afb87d32bf51fc00e37e798a3dad7791b | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,939 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith only [rSn] | case bc.h.hbd
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) ((:c LinearOrderedSemifield.toLinearOrderedComm... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 HDiv.hDiv) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"children":[{"children":[{"children":[{"source":"linarith","sourceEnd":27678,"sourceStart":27670,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":27683,"sourceStart":27679,"tag... | [] | [{"source":"rSn","source_end":27688,"source_start":27685,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 91 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 824297665cbc4ae3a19f699d4d8a9139231f6d21a741db0316ed43cd452794af | 0eeb11b9ea963c7b8c4355097aa0be9cc669971701009954de3a3fbcc381198c | 5c1396b6617c57f267c1ae7b1da07da09e57aac111f92eefe3e34d7338d92a0c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,940 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c Eq) (:c Real) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.496525) (:fv _uniq.505818)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.in... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"children":[{"children":[{"children":[{"source":"ring","sourceEnd":27746,"sourceStart":27742,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":27746,"sourceStart":27742,"tag":"node"}],"kind":"null","source":"ring","sourceEnd":27746,"sourceStart":27742,"tag":"node"}],"kind":"Le... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 96 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 163e60855c23d4f8e09afe6b07dfc92eaa0ec4b25b16721835d1ce4e9301d071 | 28b606f589cca5c23985269d70062a3c7cee12e6925d18da214f2ee7ffb3aa27 | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,941 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.496525) (:fv _uniq.505818)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 HAdd.hAdd) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"children":[{"children":[{"children":[{"source":"gcongr","sourceEnd":27817,"sourceStart":27811,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":2781... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 101 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8461252b387b907d238e6e007fae866aa40eeaea28b7653df93e32222fc8733c | a77a8f00fe9c6b0364f3929d7d48883df5e80cb54cb6a650717dbc899e6bd84f | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,942 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c Eq) (:c Real) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.496525) (:fv _uniq.505818)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.in... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"children":[{"children":[{"children":[{"source":"ring","sourceEnd":27886,"sourceStart":27882,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":27886,"sourceStart":27882,"tag":"node"}],"kind":"null","source":"ring","sourceEnd":27886,"sourceStart":27882,"tag":"node"}],"kind":"Le... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 106 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e2d594029a9936a95d27e591f87ddee66a1c32d76e4fa3c54382f816e740f9d3 | 75f6f1f35236520364221c29dae274144082b7d2f6462262f3249e792162c40f | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,943 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) (:fv _uniq.496525) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.in... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"children":[{"children":[{"children":[{"source":"gcongr","sourceEnd":27925,"sourceStart":27919,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr\n -- conclude th... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 111 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ecd847f8f760ba2aef37c190e58a290cae0574df6c17cf2ca9b8ccfca0b972e1 | fe109c3b10f7ae8428fe2529d4a373decbbc89e652eb28fa05670a1a47e4a6c6 | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,944 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>lt_of_lt_of_le</a> _ H | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c ENNReal)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"apply","sourceEnd":28103,"sourceStart":28098,"tag":"atom"},{"children":[{"name":"lt_of_lt_of_le","semanticRole":"global","source":"lt_of_lt_of_le","sourceEnd":28118,"sourceStart":28104,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":28120,"sourceStart":28119,"tag":"atom"}... | [] | [{"source":"lt_of_lt_of_le _ H\n -- Prior to leanprover/lean4#2734, this was `exact_mod_cast apos`.","source_end":28122,"source_start":28104,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 118 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a4f43181d118aa3e5d14407c37ee89c180b16f457413bd634c0320d8d64775c9 | 1f31a7884929fdb7603ea5774b8450f3ee466f46284882df1d6b3135d302cc27 | 0e8b59c01f96941cf0caddc96fd2867adb200bc5d62f22525739952cc701fba3 | 17d64e2a25051eb87abd68838749f5205342e2512d576ff2a23b6ad768addf79 |
cat-searcher/leandojo-benchmark-4-random | test | 1,945 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>ENNReal.coe_pos</a>] | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c ENNReal)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"simpa","sourceEnd":28203,"sourceStart":28198,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"ch... | [] | [{"source":"ENNReal.coe_pos","source_end":28225,"source_start":28210,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 119 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4db9fc8d86cbf81bd0326c0305f46f0bf0dd889c49eeb2ac0a6ddd55d1fcec58 | 17d64e2a25051eb87abd68838749f5205342e2512d576ff2a23b6ad768addf79 | 090b34d8386d6bc465c1e2339399b54088fccc1927c3726c0bbb4dc1c1bad484 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,946 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : ‖p.rightInv i n‖ = ‖p.rightInv i 0‖ := by congr <;> try rw [hn] | case pos
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖... | case pos
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c Norm.norm) ((:c ContinuousMultilinearMap) (:fv _uniq.490204) ((:c Fin) (:fv _uniq.622104)) (:lambda _ ((:c Fin) (:fv _uniq.622104)) (:fv _uniq.490324)) (:fv _uniq.490210) ((:c Ring.toSem... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"have","sourceEnd":28313,"sourceStart":28309,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":28314,"sourceStart":28314,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":28314,"sourceStart":28314,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"‖p.rightInv i n‖ = ‖p.rightInv i 0‖","source_end":28359,"source_start":28316,"syntax_kind":"«term_=_»"},{"source":"hn","source_end":28386,"source_start":28384,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 126 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5addc271de204c24a7f795f3e65a2975e6af36e327afe540714f6a7224059041 | 6f3277cafa0553a4d6cc6377d594a5cca19b91027a6b3f29941f817f7266f904 | 963d843d670c7626b69694fe5727a28875d9c9da1bee4d2334d724ea3b28cb05 | eabffdf346b7f38aea28843c87cc1d488d644cab11a750640651408ad147a3ad |
cat-searcher/leandojo-benchmark-4-random | test | 1,947 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [this, <a>norm_zero</a>, <a>MulZeroClass.zero_mul</a>, <a>FormalMultilinearSeries.rightInv_coeff_zero</a>] | case pos
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖... | case pos
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c Norm.norm) ((:c ContinuousMultilinearMap) (:fv _uniq.490204) ((:c Fin) (:fv _uniq.622104)) (:lambda _ ((:c Fin) (:fv _uniq.622104)) (:fv _uniq.490324)) (:fv _uniq.490210) ((:c Ring.toSem... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"simp","sourceEnd":28396,"sourceStart":28392,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":28401,"sourceStart":28397,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":284... | [] | [{"source":"this","source_end":28407,"source_start":28403,"syntax_kind":"ident"},{"source":"norm_zero","source_end":28418,"source_start":28409,"syntax_kind":"ident"},{"source":"zero_mul","source_end":28428,"source_start":28420,"syntax_kind":"ident"},{"source":"rightInv_coeff_zero","source_end":28449,"source_start":2843... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 155 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f8f7e4e905d3de79abedb23f216342cc7b5f521366c1d969778c4f253b7c5262 | eabffdf346b7f38aea28843c87cc1d488d644cab11a750640651408ad147a3ad | fc10c7aac5d373408c8cd4c7f1a4f4dabe393be1b451ee1d4d29688db16f7d35 | 0ae7bea5d6a4ff809ac946bc01303a7ff8867957d23dd40940d72985f9a0b8f8 |
cat-searcher/leandojo-benchmark-4-random | test | 1,948 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | case pos
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) ((:c MulZeroClass.toZero) (:c Real) ((:c NonUnitalNonAssocSemiring.toMulZeroClass) (:c Real) ((:c NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring) (:c Real) ((:c NonUnitalNonAssocCommRing.toNonUnitalNonAs... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"positivity","sourceEnd":28465,"sourceStart":28455,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":28465,"sourceStart":28455,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 156 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 834662b21dd10b3dd2254b623aa4da40ac6e61d865050bed7a7116653796fa9d | 0ae7bea5d6a4ff809ac946bc01303a7ff8867957d23dd40940d72985f9a0b8f8 | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,949 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr <;> try rw [hn] | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c Eq) (:c Real) ((:c Norm.norm) ((:c ContinuousMultilinearMap) (:fv _uniq.490204) ((:c Fin) (:fv _uniq.622104)) (:lambda _ ((:c Fin) (:fv _uniq.622104)) (:fv _uniq.490324)) (:fv _uniq.490210) ((:c Ring.toSemiring) (:fv _uniq.490204) ((:c NormedRing.toRing) (:fv _uniq.490204) ((:c NormedCommRing.toNormedRing) (:fv _u... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c ContinuousMultilinearMap) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Fin) (:arg :explicit 0 (:fv FV25)))) (:arg :explicit 2 (:lambda _ :explicit (:app (:c Fin) (:arg :explicit 0 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"children":[{"source":"congr","sourceEnd":28371,"sourceStart":28366,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.congr","source":"congr","sourceEnd":28371,"sourceStart":28366,"tag":"node"},{"source":"<;>","sourceEnd":28375,"sourceStart":28372,"tag":"atom... | [] | [{"source":"hn","source_end":28386,"source_start":28384,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 128 | exact | true | 1 | 26 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | df3f8007304763ae81af11a219c45d7690d8ef7a7e57e350022da0d874b55960 | 0bc9e239b85e258c51f13c710a71dce08c44adf88c98bb5a3d69fc046ccea8d0 | 4ac3d473a2aa39727980f644b9cc84f4af3d0306b92a9756936332d37f795f6a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,950 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hn] | case h.e_1.h.e_10
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ... | ((:c HEq) (:forall i ((:c Fin) (:fv _uniq.622104)) ((:c TopologicalSpace) (:fv _uniq.490324))) (:lambda i ((:c Fin) (:fv _uniq.622104)) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.490324) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.490324) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:fv _uniq.490324) (... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c HEq) (:arg :implicit-type 0 (:forall i :explicit (:app (:c Fin) (:arg :explicit 0 (:fv FV25))) (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 1 (:lambda i :explicit (:app (:c Fin) (:arg :explicit 0 (:fv FV25))) (:app (:c UniformSpace.toTopologicalSpace) (:arg :implicit-type 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":28382,"sourceStart":28380,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28384,"sourceStart":28383,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"hn","source_end":28386,"source_start":28384,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 150 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0914bbf494fdbff55cf5f8a82f036c9e4b92e959c4ada97941abeea35351ba18 | 4e9a5ba4629c372710ed2e3d339611217bc674601e00783095432335729a96c6 | 1b11c658e1ff95c2fb1f9fdaa7f8057c2998fa1d2540104594499d6ef908b09b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,951 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have one_le_n : 1 ≤ n := <a>bot_lt_iff_ne_bot</a>.2 hn | case neg
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖... | case neg
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c Norm.norm) ((:c ContinuousMultilinearMap) (:fv _uniq.490204) ((:c Fin) (:fv _uniq.622104)) (:lambda _ ((:c Fin) (:fv _uniq.622104)) (:fv _uniq.490324)) (:fv _uniq.490210) ((:c Ring.toSem... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"have","sourceEnd":28475,"sourceStart":28471,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"one_le_n","sourceEnd":28484,"sourceStart":28476,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"one_le_n","sourceEnd":28484,"sourceStart":2847... | [] | [{"source":"1 ≤ n","source_end":28494,"source_start":28487,"syntax_kind":"«term_≤_»"},{"source":"bot_lt_iff_ne_bot.2 hn","source_end":28520,"source_start":28498,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 161 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 12382b082df99f32ca5312ea8e1df34938f932f633e6961217efdc2e08fd22fe | 6e268a80ba98939e9781e71c74b2a3d70853f3af95875d5fc3eb9ee88706e2e8 | 83337970c4f26421b082bc5c1537e488f04e2bd42d0b2068077d863ad4c143a7 | 08e9cf0bd135903f4632c149007995f2ea471b11a73cff10ffbf90e50d6f48c2 |
cat-searcher/leandojo-benchmark-4-random | test | 1,952 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | calc ‖p.rightInv i n‖ * (a' : ℝ) ^ n = a ^ n * ‖p.rightInv i n‖ := <a>mul_comm</a> _ _ _ ≤ ∑ k ∈ <a>Finset.Ico</a> 1 (n + 1), a ^ k * ‖p.rightInv i k‖ := (haveI : ∀ k ∈ <a>Finset.Ico</a> 1 (n + 1), 0 ≤ a ^ k * ‖p.rightInv i k‖ := fun k _ => by positivity <a>Finset.single_le_sum</a> this (by simp [one_le_n])) _ ≤ (I + 1... | case neg
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c Norm.norm) ((:c ContinuousMultilinearMap) (:fv _uniq.490204) ((:c Fin) (:fv _uniq.622104)) (:lambda _ ((:c Fin) (:fv _uniq.622104)) (:fv _uniq.490324)) (:fv _uniq.490210) ((:c Ring.toSem... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"calc","sourceEnd":28529,"sourceStart":28525,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"‖","sourceEnd":28539,"sourceStart":28536,"tag":"atom"},{"children":[{"source":"p.rightInv","sourceEnd":28549,"sourceStart":28539,"tag":"identifier"},{"children":[... | [] | [{"source":"‖p.rightInv i n‖ * (a' : ℝ) ^ n = a ^ n * ‖p.rightInv i n‖","source_end":28604,"source_start":28536,"syntax_kind":"«term_=_»"},{"source":"mul_comm _ _","source_end":28620,"source_start":28608,"syntax_kind":"Lean.Parser.Term.app"},{"source":"_","source_end":28628,"source_start":28627,"syntax_kind":"Lean.Pars... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 162 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 02637de9ed5edd1d0491b7c2ac3d0b437495d7e0934b77a1e55255f2c6fc9414 | 08e9cf0bd135903f4632c149007995f2ea471b11a73cff10ffbf90e50d6f48c2 | de7e51510d5949da34cc1df70f02cc3a7e522fe46577b31142dc9a8510941ec1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,953 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNatPow) (:... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"children":[{"children":[{"children":[{"source":"positivity","sourceEnd":28794,"sourceStart":28784,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":28794,"sourceStart":28784,"tag":"node"}],"kind":"null","source":"positivity","sourceEnd":28794,"sourceStart":287... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 165 | exact | true | 1 | 29 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b37ecf6076dc17fc01878bfb7d1de591040587d195586421f59f37dfe8d241b4 | 667cbc934d1f12e0799e420f8b496760fa0d77f298e57b759f941a1247e3d82e | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,954 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [one_le_n] | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c Membership.mem) (:c Nat) ((:c Finset) (:c Nat)) ((:c Finset.instMembership) (:c Nat)) (:fv _uniq.622104) ((:c Finset.Ico) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))) (:c Nat.instLocallyFiniteOrder) ((:c OfNat.ofNat) (:c Na... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:c Nat)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 3 (:fv FV25)) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":28830,"sourceStart":28826,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"one_le_n","source_end":28840,"source_start":28832,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 170 | exact | true | 1 | 28 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0599f7b6777a2279dc3a0f0a18932c0e8579fec000fa56a83be269236fa60cf0 | 051bce279e13b9bfb1907a1fc7598a498620a6a5a5c3fe236b08b65087c09265 | 7532f9518f3f7104b6a56f78408a56ab62f7c2361ff21540b92053df83d060c2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,955 | FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_num | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
p : FormalMultilinearSeries 𝕜 E F
i : E ≃L[𝕜] F
hp : 0 < p.radius
C r : ℝ
Cpos : 0 < C
rpos : 0 < r
ple : ∀ (n : ℕ), ‖p n‖ ≤ C * r ... | ((:c LE.le) (:c Nat) (:c instLENat) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.622104) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.490204))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.490210))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.490204) (:fv _uniq.490210) ((:c Non... | (: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 OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Nat)) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"children":[{"children":[{"children":[{"source":"norm_num","sourceEnd":28896,"sourceStart":28888,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.490204","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.490207","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 43 | 175 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 04b7ddf36902a0ab72df98be9859a16575e5d898ac706a14d24bd2f7b0e5ddba | 9f7319ad4fb272b2f3e3510de218961a19bbda650fb91d4e51ca755ff9c213c8 | 7c64df8336d5a348b5f037e1d91facb19224fdef00e798d5c48c07a184602a59 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,956 | tprod_eq_mul_tprod_ite' | Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split_ifs with h <;> simp [<a>Function.update_apply</a>, h] | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
inst✝⁴ : CommMonoid α
inst✝³ : TopologicalSpace α
f✝ g : β → α
a a₁ a₂ : α
inst✝² : T2Space α
inst✝¹ : ContinuousMul α
inst✝ : DecidableEq β
f : β → α
b : β
hf : Multipliable (update f b 1)
n : β
⊢ f n = (if n = b then f n else 1) * update f b 1 n | ((:c Eq) (:fv _uniq.149183) ((:fv _uniq.151209) (:fv _uniq.152482)) ((:c HMul.hMul) (:fv _uniq.149183) (:fv _uniq.149183) (:fv _uniq.149183) ((:c instHMul) (:fv _uniq.149183) ((:c MulOneClass.toMul) (:fv _uniq.149183) ((:c Monoid.toMulOneClass) (:fv _uniq.149183) ((:c CommMonoid.toMonoid) (:fv _uniq.149183) (:fv _uniq.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁴","sexp":"((:c CommMonoid) (:fv _uniq.149183))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.149183))"},{"name":"f✝","sexp":"(:fo... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:fv FV15) (:arg :explicit 0 (:fv FV18)))) (:arg :explicit 2 (: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 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.149183","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.149186","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"split_ifs","sourceEnd":29055,"sourceStart":29046,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"with","sourceEnd":29060,"sourceStart":29056,"tag":"atom"},{"children":[{"children":[{"source":"h","sou... | [] | [{"source":"update_apply","source_end":29085,"source_start":29073,"syntax_kind":"ident"},{"source":"h","source_end":29088,"source_start":29087,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.149183","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.149186","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 171 | 2 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d03fbed7112c4c235f0396f7635bd40ba8088a9252b57edb73ec882228710e8e | 6eb731459d33e7d7ff648071128bde25579b22fd3a795c10bbf5cfe7b4bcf825 | 4b4fd7a4e7fcb1708b66b46231782449c31330395ac597313efa3ee9095cc9dd | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,957 | tprod_eq_mul_tprod_ite' | Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
inst✝⁴ : CommMonoid α
inst✝³ : TopologicalSpace α
f✝ g : β → α
a a₁ a₂ : α
inst✝² : T2Space α
inst✝¹ : ContinuousMul α
inst✝ : DecidableEq β
f : β → α
b : β
hf : Multipliable (update f b 1)
⊢ (∏' (x : β), if x = b then f x else 1) * ∏' (x : β), update f b 1 x =
(i... | case e_a
α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
inst✝⁴ : CommMonoid α
inst✝³ : TopologicalSpace α
f✝ g : β → α
a a₁ a₂ : α
inst✝² : T2Space α
inst✝¹ : ContinuousMul α
inst✝ : DecidableEq β
f : β → α
b : β
hf : Multipliable (update f b 1)
⊢ (∏' (x : β), if x = b then f x else 1) = if b = b then f b else 1 | ((:c Eq) (:fv _uniq.149183) ((:c HMul.hMul) (:fv _uniq.149183) (:fv _uniq.149183) (:fv _uniq.149183) ((:c instHMul) (:fv _uniq.149183) ((:c MulOneClass.toMul) (:fv _uniq.149183) ((:c Monoid.toMulOneClass) (:fv _uniq.149183) ((:c CommMonoid.toMonoid) (:fv _uniq.149183) (:fv _uniq.149195))))) ((:c tprod) (:fv _uniq.14918... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁴","sexp":"((:c CommMonoid) (:fv _uniq.149183))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.149183))"},{"name":"f✝","sexp":"(:fo... | (:app (:c Eq) (: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.149183","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.149186","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"congr","sourceEnd":29312,"sourceStart":29307,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.congr","source":"congr","sourceEnd":29312,"sourceStart":29307,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.149183","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.149186","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 171 | 13 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0fd7256bed2517c39780fe35a9c55664eae5a3f55fa561f28703554d4777d41a | 3b3023bee0f6badbc3b054f2383e1448de9cd9077d60fe79c6f7d77e067bcd60 | 092b163cac48997cb6cc327c63cda260e694055f56ff3698a70cdfda80ffbb2b | e2b00ad7b6bc53d5ab2fe38e842cb3a0d94c8d3f3878573972f161290da632b2 |
cat-searcher/leandojo-benchmark-4-random | test | 1,958 | tprod_eq_mul_tprod_ite' | Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>tprod_eq_mulSingle</a> b fun b' hb' ↦ <a>if_neg</a> hb' | case e_a
α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
inst✝⁴ : CommMonoid α
inst✝³ : TopologicalSpace α
f✝ g : β → α
a a₁ a₂ : α
inst✝² : T2Space α
inst✝¹ : ContinuousMul α
inst✝ : DecidableEq β
f : β → α
b : β
hf : Multipliable (update f b 1)
⊢ (∏' (x : β), if x = b then f x else 1) = if b = b then f b else 1 | ((:c Eq) (:fv _uniq.149183) ((:c tprod) (:fv _uniq.149183) (:fv _uniq.149195) (:fv _uniq.149198) (:fv _uniq.149186) (:lambda x (:fv _uniq.149186) ((:c ite) (:fv _uniq.149183) ((:c Eq) (:fv _uniq.149186) 0 (:fv _uniq.151210)) ((:fv _uniq.151208) 0 (:fv _uniq.151210)) ((:fv _uniq.151209) 0) ((:c OfNat.ofNat) (:fv _uniq.1... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁴","sexp":"((:c CommMonoid) (:fv _uniq.149183))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.149183))"},{"name":"f✝","sexp":"(:fo... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c tprod) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommMonoid) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 3 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.149183","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.149186","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":29324,"sourceStart":29319,"tag":"atom"},{"children":[{"name":"tprod_eq_mulSingle","semanticRole":"global","source":"tprod_eq_mulSingle","sourceEnd":29343,"sourceStart":29325,"tag":"identifier"},{"children":[{"contextIndex":16,"semanticRole":"local","source":"b","sourceEnd":293... | [] | [{"source":"tprod_eq_mulSingle b fun b' hb' ↦ if_neg hb'","source_end":29371,"source_start":29325,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.149183","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.149186","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 171 | 14 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73e17baed0b38abf5db727ad119fbaf04b4163efcc9cb787e16277d7eceb9ba9 | e2b00ad7b6bc53d5ab2fe38e842cb3a0d94c8d3f3878573972f161290da632b2 | 81fb7f10a24ead838abda5d6a7e74f29fb7288e4cd5012ae0c4945d9f54504d5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,959 | tprod_eq_mul_tprod_ite' | Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Function.update</a>, <a>eq_self_iff_true</a>, <a>if_true</a>, <a>eq_rec_constant</a>, <a>dite_eq_ite</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
inst✝⁴ : CommMonoid α
inst✝³ : TopologicalSpace α
f✝ g : β → α
a a₁ a₂ : α
inst✝² : T2Space α
inst✝¹ : ContinuousMul α
inst✝ : DecidableEq β
f : β → α
b : β
hf : Multipliable (update f b 1)
⊢ (if b = b then f b else 1) * ∏' (x : β), update f b 1 x = f b * ∏' (x : β), ... | ((:c Eq) (:fv _uniq.149183) ((:c HMul.hMul) (:fv _uniq.149183) (:fv _uniq.149183) (:fv _uniq.149183) ((:c instHMul) (:fv _uniq.149183) ((:c MulOneClass.toMul) (:fv _uniq.149183) ((:c Monoid.toMulOneClass) (:fv _uniq.149183) ((:c CommMonoid.toMonoid) (:fv _uniq.149183) (:fv _uniq.149195))))) ((:c ite) (:fv _uniq.149183)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁴","sexp":"((:c CommMonoid) (:fv _uniq.149183))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.149183))"},{"name":"f✝","sexp":"(:fo... | (:app (:c Eq) (: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.149183","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.149186","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":29430,"sourceStart":29426,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":29435,"sourceStart":29431,"tag":"atom"}],"kind"... | [] | [{"source":"update","source_end":29443,"source_start":29437,"syntax_kind":"ident"},{"source":"eq_self_iff_true","source_end":29461,"source_start":29445,"syntax_kind":"ident"},{"source":"if_true","source_end":29470,"source_start":29463,"syntax_kind":"ident"},{"source":"eq_rec_constant","source_end":29487,"source_start":... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.149183","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.149186","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 171 | 17 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0e7f3f29ad410c5d8209bac9005445ae88a122f47b7d98778691176596a5ef1c | 9af4d29e006aac3224a752037bade717a110ccf03b39a58007145745b34fbd79 | 831490939dcd06e8c899da8cf5645919251c6c3fa2f6db40b2d5e088101acc2f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 |
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