dataset stringclasses 1
value | split stringclasses 1
value | row_index int64 0 4.5k | theorem stringlengths 7 81 | file_path stringclasses 723
values | repo_url stringclasses 1
value | repo_commit stringclasses 1
value | tactic stringlengths 3 2.13k | text_state stringlengths 7 2.31k | text_target_state stringlengths 0 4.07k | raw_goal_sexp stringlengths 10 11.8M | raw_hyp_sexps stringlengths 2 15.6M | model_goal_sexp stringlengths 10 2.68M | model_hyp_sexps stringlengths 2 3.62M | source_syntax stringlengths 179 164k | syntax_args stringclasses 256
values | term_ranges stringlengths 2 6.01k | local_context stringlengths 2 10.3k | unit_index int64 3 1.26k | invocation_index int64 0 357 | alignment_kind stringclasses 2
values | target_state_matches_invocation bool 2
classes | pending_goal_count int64 1 1 | hypothesis_count int64 0 77 | hypothesis_names_match bool 2
classes | raw_schema_version int64 4 4 | raw_extractor_version stringclasses 1
value | model_schema_version int64 2 2 | model_normalization stringclasses 1
value | trace_schema_version int64 3 3 | trace_extractor_version stringclasses 1
value | pantograph_commit stringclasses 1
value | model_pantograph_commit stringclasses 1
value | raw_record_sha256 stringlengths 64 64 | state_sha256 stringlengths 64 64 | tactic_sha256 stringlengths 64 64 | target_state_sha256 stringlengths 64 64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
cat-searcher/leandojo-benchmark-4-random | test | 207 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | infer_instance | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | ((:c CategoryTheory.TwoSquare.GuitartExact) (:fv _uniq.68741) (:fv _uniq.68750) (:fv _uniq.68744) (:fv _uniq.68753) (:fv _uniq.68760) (:fv _uniq.68772) (:fv _uniq.68764) (:fv _uniq.68776) (:fv _uniq.68808) (:fv _uniq.68835) (:fv _uniq.68862) (:fv _uniq.68888) ((:c CategoryTheory.TwoSquare.vComp') (:fv _uniq.68741) (:fv... | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:app (:c CategoryTheory.TwoSquare.GuitartExact) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV1)) (:arg :implicit-type 3 (:fv FV4)) (:arg :instance 4 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 5 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"infer_instance","sourceEnd":6397,"sourceStart":6383,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticInfer_instance","source":"infer_instance","sourceEnd":6397,"sourceStart":6383,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 38 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 68464fea2e0d0b54541e958413123ce075c7e2fae30613d94830281cfef4346f | e361a50350ec8823fc1670482b8b5ba8a84926499e20320343e3748210427ebd | 1be023dbb859162463cfcba2e9fc80f1c85bab9d31edeb816d1518206e2b70fa | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 208 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext X₁ | C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ⥤ D₂
H₂ ... | case h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ⥤... | ((:c Eq) ((:c CategoryTheory.TwoSquare) (:fv _uniq.68741) (:fv _uniq.68750) (:fv _uniq.68744) (:fv _uniq.68753) (:fv _uniq.68760) (:fv _uniq.68772) (:fv _uniq.68764) (:fv _uniq.68776) (:fv _uniq.68808) (:fv _uniq.68835) (:fv _uniq.68862) (:fv _uniq.68888)) (:fv _uniq.69398) ((:c CategoryTheory.TwoSquare.vComp') (:fv _u... | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.TwoSquare) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV1)) (:arg :implicit-type 3 (:fv FV4)) (:arg :instance 4 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :insta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"ext","sourceEnd":5617,"sourceStart":5614,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"X₁","sourceEnd":5622,"sourceStart":5618,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"X₁","sourceEnd":5622,"sourceStart":5618,"tag":"n... | [{"role":"fresh_name","source":"X₁","source_end":5622,"source_start":5618,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 18 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1fe6e7b2d47eb05389d2e1e77e61f11f6fa9b889664472c1128aa1a2ca192265 | cf416369de2cc09b033850d5b10ad4049bdd57e928f33b534dc6d102ff7afc57 | 5ba57f8e121ce0b711e7ce565cc4693b267f1f1460dad8c9f988d7fd5711511f | 909ece0516074055fcb363d9f627a7e84676bb2e13cadf0cea8b0be73a3b54ee |
cat-searcher/leandojo-benchmark-4-random | test | 209 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp? [w'', β, α] says simp only [<a>CategoryTheory.TwoSquare.vComp'_app</a>, <a>CategoryTheory.Functor.comp_obj</a>, <a>CategoryTheory.Iso.trans_inv</a>, <a>CategoryTheory.isoWhiskerLeft_inv</a>, <a>CategoryTheory.Iso.symm_inv</a>, <a>CategoryTheory.Category.assoc</a>, <a>CategoryTheory.NatTrans.comp_app</a>, <a>Categ... | case h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ⥤... | case h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ⥤... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.68753) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.68753) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.68753) (:fv _uniq.68776))) ((:c Prefunctor.obj) (:fv _uniq.68750) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.68750) ((:c CategoryTheory.Catego... | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"source":"simp?","sourceEnd":5646,"sourceStart":5641,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"... | [] | [{"source":"vComp'_app","source_end":5695,"source_start":5685,"syntax_kind":"ident"},{"source":"Functor.comp_obj","source_end":5713,"source_start":5697,"syntax_kind":"ident"},{"source":"Iso.trans_inv","source_end":5728,"source_start":5715,"syntax_kind":"ident"},{"source":"isoWhiskerLeft_inv","source_end":5748,"source_s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 20 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 481f00c542146429c5a2412460c8b4ec3535a40065e1dcf464b658fdee94128d | 909ece0516074055fcb363d9f627a7e84676bb2e13cadf0cea8b0be73a3b54ee | 79ca1c9146f22c21596c7e8d9801c68fa26dd90eb667f126ba7a922fdb5f2ae8 | 348b1aa2e4aef336f4711e68800300eeea12b2c89bf033b35f650dc94e397d6d |
cat-searcher/leandojo-benchmark-4-random | test | 210 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | erw [<a>CategoryTheory.CatCommSq.vInv_iso'_hom_app</a>] | case h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ⥤... | case h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ⥤... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.68753) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.68753) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.68753) (:fv _uniq.68776))) ((:c Prefunctor.obj) (:fv _uniq.68750) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.68750) ((:c CategoryTheory.Catego... | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"erw","sourceEnd":6156,"sourceStart":6153,"tag":"atom"},{"children":[{"source":"[","sourceEnd":6158,"sourceStart":6157,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"CategoryTheory.CatCommSq.vInv_iso'_hom_app","semanticRole":"global","sourc... | [] | [{"source":"CatCommSq.vInv_iso'_hom_app","source_end":6185,"source_start":6158,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 24 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 30343d9aa7ee8ada19cd46182b26bf7545e9e7aaf0c0d2661d1c9074aec10263 | 348b1aa2e4aef336f4711e68800300eeea12b2c89bf033b35f650dc94e397d6d | a9a51ec3c261cfc28c7c5b9e28ab2d4a3a6261e0e4519284ffe93a99d7e40257 | c2dfeb5c96dbcacb864898a903370f1a254125fd39dc18d0596214242d3d25e9 |
cat-searcher/leandojo-benchmark-4-random | test | 211 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [hw', <a>CategoryTheory.Category.assoc</a>, ← eR.inverse.map_comp_assoc] | case h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ⥤... | case h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ⥤... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.68753) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.68753) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.68753) (:fv _uniq.68776))) ((:c Prefunctor.obj) (:fv _uniq.68750) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.68750) ((:c CategoryTheory.Catego... | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":6197,"sourceStart":6193,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":6202,"sourceStart":6198,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":6202,"s... | [] | [{"source":"hw'","source_end":6207,"source_start":6204,"syntax_kind":"ident"},{"source":"assoc","source_end":6214,"source_start":6209,"syntax_kind":"ident"},{"source":"eR.inverse.map_comp_assoc","source_end":6245,"source_start":6220,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 27 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7cea922ad423557786bb0e8ce2fc609c6b5712a9036f15a472b9b119931d5ef4 | c2dfeb5c96dbcacb864898a903370f1a254125fd39dc18d0596214242d3d25e9 | d8bb7040f6568f5f0db5fc94061445ece55cc3cdadcde389d1cc697b53fdfb88 | fac960b91396b09dc52fdc65d88aead497f4a203600c1e1cb54f47c87c01ef72 |
cat-searcher/leandojo-benchmark-4-random | test | 212 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>CategoryTheory.Equivalence.counitInv_app_functor</a>] | case h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ⥤... | case h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ⥤... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.68753) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.68753) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.68753) (:fv _uniq.68776))) ((:c Prefunctor.obj) (:fv _uniq.68750) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.68750) ((:c CategoryTheory.Catego... | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":6255,"sourceStart":6253,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6257,"sourceStart":6256,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"CategoryTheory.Equiv... | [] | [{"source":"Equivalence.counitInv_app_functor","source_end":6290,"source_start":6257,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 28 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3e78a0c6fadcc4b2cbe9c54444cb2e30ba0c822c83ccfd79171df759c4e62f8a | fac960b91396b09dc52fdc65d88aead497f4a203600c1e1cb54f47c87c01ef72 | 29d0fafaebdcd19cb7d1865adc7c8edfc0dbe1de4a35216691afeaad507b2e35 | 3b9303cd60395f412da526738ef58a851fbb04ed24f49de56c5092105f475bb2 |
cat-searcher/leandojo-benchmark-4-random | test | 213 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | erw [← <a>CategoryTheory.NatTrans.naturality_assoc</a>] | case h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ⥤... | case h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ⥤... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.68753) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.68753) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.68753) (:fv _uniq.68776))) ((:c Prefunctor.obj) (:fv _uniq.68750) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.68750) ((:c CategoryTheory.Catego... | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"erw","sourceEnd":6301,"sourceStart":6298,"tag":"atom"},{"children":[{"source":"[","sourceEnd":6303,"sourceStart":6302,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":6306,"sourceStart":6303,"tag":"atom"}],"kind":"token.«← »","source":"←","... | [] | [{"source":"NatTrans.naturality_assoc","source_end":6332,"source_start":6307,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 31 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c26acc8ab0be4233a93147e4dafe94e3ba81f0414b39576d70c5948b0802729a | 3b9303cd60395f412da526738ef58a851fbb04ed24f49de56c5092105f475bb2 | 874569d7b7ba1d7a8bc17fe75fdc1ff4531a67e792c3331649e78506d775c594 | 59dc6dbe671011ed00c9e71573081ffe2b6fa83cba30948bf69ef309ad72d7f8 |
cat-searcher/leandojo-benchmark-4-random | test | 214 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [← H₂.map_comp] | case h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ⥤... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.68753) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.68753) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.68753) (:fv _uniq.68776))) ((:c Prefunctor.obj) (:fv _uniq.68750) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.68750) ((:c CategoryTheory.Catego... | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":6344,"sourceStart":6340,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6346,"sourceStart":6345,"tag":"atom"... | [] | [{"source":"H₂.map_comp","source_end":6363,"source_start":6350,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 34 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bdfe8ab6379ece18c6b0cdfe9692e2e8ad3f35d2405575b0fd93b4059b0d8b3d | 59dc6dbe671011ed00c9e71573081ffe2b6fa83cba30948bf69ef309ad72d7f8 | 594d01fdb9dda40186a43b55faa9f89033c2158e74e5bc3f66fb73be7671ff9b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 215 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>CategoryTheory.TwoSquare.vComp'_app</a>, <a>CategoryTheory.Functor.comp_obj</a>, <a>CategoryTheory.Iso.trans_inv</a>, <a>CategoryTheory.isoWhiskerLeft_inv</a>, <a>CategoryTheory.Iso.symm_inv</a>, <a>CategoryTheory.Category.assoc</a>, <a>CategoryTheory.NatTrans.comp_app</a>, <a>CategoryTheory.Functor.id_ob... | case h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ⥤... | case h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ⥤... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.68753) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.68753) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.68753) (:fv _uniq.68776))) ((:c Prefunctor.obj) (:fv _uniq.68750) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.68750) ((:c CategoryTheory.Catego... | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":5678,"sourceStart":5674,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":5683,"sourceStart":5679,"tag":"atom"}],"kind":"nu... | [] | [{"source":"vComp'_app","source_end":5695,"source_start":5685,"syntax_kind":"ident"},{"source":"Functor.comp_obj","source_end":5713,"source_start":5697,"syntax_kind":"ident"},{"source":"Iso.trans_inv","source_end":5728,"source_start":5715,"syntax_kind":"ident"},{"source":"isoWhiskerLeft_inv","source_end":5748,"source_s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 21 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3becd1271a3ac9e2500e0fc4ef7d9c4571c422f030aa19e9616018ca8442f627 | 909ece0516074055fcb363d9f627a7e84676bb2e13cadf0cea8b0be73a3b54ee | 6fb3ee930336dd74cef14eff819088c5c62633cbaac5f9d98c78873f08860835 | 348b1aa2e4aef336f4711e68800300eeea12b2c89bf033b35f650dc94e397d6d |
cat-searcher/leandojo-benchmark-4-random | test | 216 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro | case mpr
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁... | case mpr
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁... | (:forall _ ((:c CategoryTheory.TwoSquare.GuitartExact) (:fv _uniq.68741) (:fv _uniq.68750) (:fv _uniq.68744) (:fv _uniq.68753) (:fv _uniq.68760) (:fv _uniq.68772) (:fv _uniq.68764) (:fv _uniq.68776) (:fv _uniq.68808) (:fv _uniq.68835) (:fv _uniq.68862) (:fv _uniq.68888) (:fv _uniq.69398)) ((:c CategoryTheory.TwoSquare.... | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:forall _ :explicit (:app (:c CategoryTheory.TwoSquare.GuitartExact) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV1)) (:arg :implicit-type 3 (:fv FV4)) (:arg :instance 4 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"intro","sourceEnd":6408,"sourceStart":6403,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source":"intro","sourceEnd":6408,"sourceStart":6403,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 43 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5c935db76697c4a73661218f22089e4ee9cb6c17ca7fc80d7a0355d020c51d19 | 3e2b5b9a9a13b8346570d18ffe62a58bab444663416fa671c83ec0bb0afa5946 | c432b372e0e30267e65e26a12a42c7957ab52e25dfe3c6d4b929213d88965e45 | 737a2c7160a97fa1fc09f9583da527fbc05d2de2c05154fbd59ff6d0f74b38c9 |
cat-searcher/leandojo-benchmark-4-random | test | 217 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>CategoryTheory.TwoSquare.GuitartExact.vComp</a> w w'.hom | case mpr
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁... | ((:c CategoryTheory.TwoSquare.GuitartExact) (:fv _uniq.68741) (:fv _uniq.68750) (:fv _uniq.68747) (:fv _uniq.68756) (:fv _uniq.68760) (:fv _uniq.68772) (:fv _uniq.68768) (:fv _uniq.68780) (:fv _uniq.68808) ((:c CategoryTheory.Functor.comp) (:fv _uniq.68741) (:fv _uniq.68760) (:fv _uniq.68744) (:fv _uniq.68764) (:fv _un... | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:app (:c CategoryTheory.TwoSquare.GuitartExact) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV2)) (:arg :implicit-type 3 (:fv FV5)) (:arg :instance 4 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 5 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":6418,"sourceStart":6413,"tag":"atom"},{"children":[{"name":"CategoryTheory.TwoSquare.GuitartExact.vComp","semanticRole":"global","source":"vComp","sourceEnd":6424,"sourceStart":6419,"tag":"identifier"},{"children":[{"contextIndex":16,"semanticRole":"local","source":"w","source... | [] | [{"source":"vComp w w'.hom","source_end":6433,"source_start":6419,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 44 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5609b6d5b835b3a3191faae860989c0deb191fb32e8aa0abc2df80339c7d92c4 | 737a2c7160a97fa1fc09f9583da527fbc05d2de2c05154fbd59ff6d0f74b38c9 | 3442514a85e455e19e9691034fa6f889031aff3e3ee680366ff40c06accc9c63 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 218 | Polynomial.mkDerivation_X | Mathlib/Algebra/Polynomial/Derivation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Polynomial.mkDerivation_apply</a>] | R : Type u_1
A : Type u_2
inst✝⁴ : CommSemiring R
inst✝³ : AddCommMonoid A
inst✝² : Module R A
inst✝¹ : Module R[X] A
inst✝ : IsScalarTower R R[X] A
a : A
⊢ ((mkDerivation R) a) X = a | ((:c Eq) (:fv _uniq.55962) ((:c DFunLike.coe) ((:c Derivation) (:fv _uniq.55959) ((:c Polynomial) (:fv _uniq.55959) ((:c CommSemiring.toSemiring) (:fv _uniq.55959) (:fv _uniq.55965))) (:fv _uniq.55962) (:fv _uniq.55965) ((:c Polynomial.commSemiring) (:fv _uniq.55959) (:fv _uniq.55965)) (:fv _uniq.55968) ((:c Polynomial... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.55959))"},{"name":"inst✝³","sexp":"((:c AddCommMonoid) (:fv _uniq.55962))"},{"name":"inst✝²","sexp":"((:c Module) (:fv _uniq.55959) (:fv _uniq.55962) ((:c CommSemiring.toSemiring) (:fv... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Derivation) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.55959","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55962","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":2223,"sourceStart":2219,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"mkDerivation_apply","source_end":2243,"source_start":2225,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.55959","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55962","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 14 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2df8ff3add901225cf1721a685cde49e065bf6d5e346d0e947b6ba60e411d8ec | 29bd4de9c7a66fe5df58cf310e0b95007046719bfe2cbfeb4f57bf3cd77e83ee | 68009c56365ad9b8b91c568dc2517b1ff6da19faff8eb0cc4271521dd32bae88 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 219 | Filter.principal_singleton | Mathlib/Order/Filter/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Filter.mem_pure</a>, <a>Filter.mem_principal</a>, <a>Set.singleton_subset_iff</a>] | α : Type u
β : Type v
γ : Type w
δ : Type u_1
ι : Sort x
l : Filter α
a : α
s : Set α
⊢ s ∈ 𝓟 {a} ↔ s ∈ pure a | ((:c Iff) ((:c Membership.mem) ((:c Set) (:fv _uniq.148255)) ((:c Filter) (:fv _uniq.148255)) ((:c instMembershipSetFilter) (:fv _uniq.148255)) (:fv _uniq.148348) ((:c Filter.principal) (:fv _uniq.148255) ((:c Singleton.singleton) (:fv _uniq.148255) ((:c Set) (:fv _uniq.148255)) ((:c Set.instSingletonSet) (:fv _uniq.14... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"δ","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort x)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.148255))"},{"name":"a","sexp":"(:fv _uniq.148255)"},{"name":"s","sexp":"((:c Set) (:fv _u... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Filter) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148255","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148257","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":97680,"sourceStart":97676,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":97685,"sourceStart":97681,"tag":"atom"}],"kind"... | [] | [{"source":"mem_pure","source_end":97695,"source_start":97687,"syntax_kind":"ident"},{"source":"mem_principal","source_end":97710,"source_start":97697,"syntax_kind":"ident"},{"source":"singleton_subset_iff","source_end":97732,"source_start":97712,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148255","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148257","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 715 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1b6aa4386e68f2baec1c74290018b32c2494e1005df8dfe2425f6b74dd3b0a45 | a2d5278d79f41acf95b6fa43039fa5934866d7d33cf3c2b35ea9a45a30ecc793 | a1b6589aab2d34599b1ef653a592b8c3f216c6de8f9d87f2fb0653f7186be3b7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 220 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨by simp [hf.1, hg.1], ?_⟩ | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
⊢ (f * g).IsMultiplicative | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
⊢ ∀ {m n : ℕ}, m.Coprime n → (f * g) (m * n) = (f * g) m * (f * g) n | ((:c ArithmeticFunction.IsMultiplicative) (:fv _uniq.310078) ((:c Semiring.toMonoidWithZero) (:fv _uniq.310078) ((:c CommSemiring.toSemiring) (:fv _uniq.310078) (:fv _uniq.310718))) ((:c HMul.hMul) ((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMon... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c ArithmeticFunction.IsMultiplicative) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MonoidWithZero) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c ArithmeticFunction) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"refine","sourceEnd":25775,"sourceStart":25769,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":25779,"sourceStart":25776,"tag":"atom"},{"children":[{"children":[{"source":"by","sourceEnd":25781,"sourceStart":25779,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"s... | [] | [{"source":"⟨by simp [hf.1, hg.1], ?_⟩","source_end":25806,"source_start":25776,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f7fe571764100d3dc1883337336254f45fe9324167b3b2b75649808d3e22a416 | 21cb221048bee0bdba15fc6f2ec739fa7d6d8c44d341cde7bdb1c35ebe39c1c3 | 7ff06a19541d645a5b55faa71c465d38a1f18dad2928a74a4546ce43a28a799a | b1840fba8ae32c211c029aeaddd6a173c427cbd88c5209b27ee613e601d98c27 |
cat-searcher/leandojo-benchmark-4-random | test | 221 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>ArithmeticFunction.mul_apply</a>] | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
⊢ ∀ {m n : ℕ}, m.Coprime n → (f * g) (m * n) = (f * g) m * (f * g) n | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
⊢ ∀ {m n : ℕ},
m.Coprime n →
∑ x ∈ (m * n).divisorsAntidiagonal, f x.1 * g x.2 =
(∑ x ∈ m.divisorsAntidiagonal, f x.1 * g x.2) * ∑ x ∈ n.divisorsAntidiagonal, f x.1 * g x.2 | (:forall m (:c Nat) (:forall n (:c Nat) (:forall _ ((:c Nat.Coprime) 1 0) ((:c Eq) (:fv _uniq.310078) ((:c DFunLike.coe) ((:c ArithmeticFunction) (:fv _uniq.310078) ((:c MonoidWithZero.toZero) (:fv _uniq.310078) ((:c Semiring.toMonoidWithZero) (:fv _uniq.310078) ((:c CommSemiring.toSemiring) (:fv _uniq.310078) (:fv _un... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:forall m :implicit (:c Nat) (:forall n :implicit (:c Nat) (:forall _ :explicit (:app (:c Nat.Coprime) (:arg :explicit 0 1) (:arg :explicit 1 0)) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c ArithmeticFunction) (:arg :explicit 0 (:fv FV0)) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"simp","sourceEnd":25813,"sourceStart":25809,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":25818,"sourceStart":25814,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":258... | [] | [{"source":"mul_apply","source_end":25829,"source_start":25820,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 10 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 812c586043c83dd3fa3c0c78ac2e924072696631c9e1000d05648b9d498e9ca0 | b1840fba8ae32c211c029aeaddd6a173c427cbd88c5209b27ee613e601d98c27 | 07ae7782d6eb1b74ef7e88551570548f2f746f190e73829208e2faaafcec8af2 | e14025cb3b1927b109d20cd02f79fd99875f631ff180ebeba6a62b9bfab8f25a |
cat-searcher/leandojo-benchmark-4-random | test | 222 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro m n cop | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
⊢ ∀ {m n : ℕ},
m.Coprime n →
∑ x ∈ (m * n).divisorsAntidiagonal, f x.1 * g x.2 =
(∑ x ∈ m.divisorsAntidiagonal, f x.1 * g x.2) * ∑ x ∈ n.divisorsAntidiagonal, f x.1 * g x.2 | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
⊢ ∑ x ∈ (m * n).divisorsAntidiagonal, f x.1 * g x.2 =
(∑ x ∈ m.divisorsAntidiagonal, f x.1 * g x.2) * ∑ x ∈ n.divisorsAntidiagonal, f x.1 * g x.2 | (:forall m (:c Nat) (:forall n (:c Nat) (:forall _ ((:c Nat.Coprime) 1 0) ((:c Eq) (:fv _uniq.310078) ((:c Finset.sum) ((:c Prod) (:c Nat) (:c Nat)) (:fv _uniq.310078) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.310078) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.310078) ((:c Semiring.t... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:forall m :implicit (:c Nat) (:forall n :implicit (:c Nat) (:forall _ :explicit (:app (:c Nat.Coprime) (:arg :explicit 0 1) (:arg :explicit 1 0)) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset.sum) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"intro","sourceEnd":25838,"sourceStart":25833,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"m","sourceEnd":25840,"sourceStart":25839,"tag":"identifier"},{"semanticRole":"scoped_local","source":"n","sourceEnd":25842,"sourceStart":25841,"tag":"identifier"},{"semanticRole":"sco... | [{"role":"fresh_name","source":"m","source_end":25840,"source_start":25839,"syntax_kind":"ident"},{"role":"fresh_name","source":"n","source_end":25842,"source_start":25841,"syntax_kind":"ident"},{"role":"fresh_name","source":"cop","source_end":25846,"source_start":25843,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 11 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e80db2f6bf58d8bcb13f25edf7ed26bba5c392768f2670e605193b1a345b5fa9 | e14025cb3b1927b109d20cd02f79fd99875f631ff180ebeba6a62b9bfab8f25a | b5529aa5dc8aac59188d0ca5a149504d50c32377aebd0d5a69a234727c3a839f | e14bc14c1fff8f25307b51965d2238ad2ffec0e3aa9937f764c4069b3cb41a22 |
cat-searcher/leandojo-benchmark-4-random | test | 223 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.sum_mul_sum</a>, ← <a>Finset.sum_product'</a>] | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
⊢ ∑ x ∈ (m * n).divisorsAntidiagonal, f x.1 * g x.2 =
(∑ x ∈ m.divisorsAntidiagonal, f x.1 * g x.2) * ∑ x ∈ n.divisorsAntidiagonal, f x.1 * g x.2 | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
⊢ ∑ x ∈ (m * n).divisorsAntidiagonal, f x.1 * g x.2 =
∑ x ∈ m.divisorsAntidiagonal ×ˢ n.divisorsAntidiagonal, f x.1.1 * g x.1.2 * (f x.2.1 * g x.2.2) | ((:c Eq) (:fv _uniq.310078) ((:c Finset.sum) ((:c Prod) (:c Nat) (:c Nat)) (:fv _uniq.310078) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.310078) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.310078) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.310078) ((:c CommSemiring.toSemiring) (:fv _... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset.sum) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV0))))) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"rw","sourceEnd":25851,"sourceStart":25849,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":25853,"sourceStart":25852,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.sum_mul_s... | [] | [{"source":"sum_mul_sum","source_end":25864,"source_start":25853,"syntax_kind":"ident"},{"source":"sum_product'","source_end":25882,"source_start":25870,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 12 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d8306dcbeaaf4092c4fee4edcd715ed0981d0ef8e09f2d383441414301dc13f8 | e14bc14c1fff8f25307b51965d2238ad2ffec0e3aa9937f764c4069b3cb41a22 | f88c284b88da2cab1ee525e6662bd4ed39459afec4ea3b3427b01a839786b3cc | b669149a0129ca32be377b6465800ca6cd4a310a4aaa9c92b12dcd836e63850a |
cat-searcher/leandojo-benchmark-4-random | test | 224 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | symm | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
⊢ ∑ x ∈ (m * n).divisorsAntidiagonal, f x.1 * g x.2 =
∑ x ∈ m.divisorsAntidiagonal ×ˢ n.divisorsAntidiagonal, f x.1.1 * g x.1.2 * (f x.2.1 * g x.2.2) | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
⊢ ∑ x ∈ m.divisorsAntidiagonal ×ˢ n.divisorsAntidiagonal, f x.1.1 * g x.1.2 * (f x.2.1 * g x.2.2) =
∑ x ∈ (m * n).divisorsAntidiagonal, f x.1 * g x.2 | ((:c Eq) (:fv _uniq.310078) ((:c Finset.sum) ((:c Prod) (:c Nat) (:c Nat)) (:fv _uniq.310078) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.310078) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.310078) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.310078) ((:c CommSemiring.toSemiring) (:fv _... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset.sum) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV0))))) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"symm","sourceEnd":25890,"sourceStart":25886,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.symm","source":"symm","sourceEnd":25890,"sourceStart":25886,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 16 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 321435caf7c10e1a229294063f02fa0b46cea6385edeca294ed75b738ba5d74c | b669149a0129ca32be377b6465800ca6cd4a310a4aaa9c92b12dcd836e63850a | f97373c83b943be1711d624ac8176e49b7c19e0f5ce55ad3a0ad56d8d1aae1fa | 446a1c9546d9a98137f0ab6eb6d774cf7286f8c749cc05a9fcfd9ecbdc38a76a |
cat-searcher/leandojo-benchmark-4-random | test | 225 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Finset.sum_nbij</a> fun ((i, j), k, l) ↦ (i * k, j * l) | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
⊢ ∑ x ∈ m.divisorsAntidiagonal ×ˢ n.divisorsAntidiagonal, f x.1.1 * g x.1.2 * (f x.2.1 * g x.2.2) =
∑ x ∈ (m * n).divisorsAntidiagonal, f x.1 * g x.2 | case hi
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
⊢ ∀ a ∈ m.divisorsAntidiagonal ×ˢ n.divisorsAntidiagonal,
(match a with
| ((i, j), k, l) => (i * k, j * l)) ∈
(m * n).divisorsAntidiagonal
case i_inj
R : Type ... | ((:c Eq) (:fv _uniq.310078) ((:c Finset.sum) ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) (:fv _uniq.310078) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.310078) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.310078) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.31... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset.sum) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"apply","sourceEnd":25898,"sourceStart":25893,"tag":"atom"},{"children":[{"name":"Finset.sum_nbij","semanticRole":"global","source":"sum_nbij","sourceEnd":25907,"sourceStart":25899,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":25911,"sourceStart":25908,"tag":"atom"},{"... | [] | [{"source":"sum_nbij fun ((i, j), k, l) ↦ (i * k, j * l)","source_end":25945,"source_start":25899,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 17 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3d7ae83868efa76ce9db9a3dd1165d69add9d20926e66d60a6f6387a67852dcf | 446a1c9546d9a98137f0ab6eb6d774cf7286f8c749cc05a9fcfd9ecbdc38a76a | 21453bfd5c95bcb63968dc0834824cc7e81612566441c7797a3774e48ca37e8b | 5b3566d6de551a667a44594d31fde6cc11a8f4e69ae4ce1459ce038547965b2a |
cat-searcher/leandojo-benchmark-4-random | test | 226 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [hf.1, hg.1] | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
⊢ (f * g) 1 = 1 | ((:c Eq) (:fv _uniq.310078) ((:c DFunLike.coe) ((:c ArithmeticFunction) (:fv _uniq.310078) ((:c MonoidWithZero.toZero) (:fv _uniq.310078) ((:c Semiring.toMonoidWithZero) (:fv _uniq.310078) ((:c CommSemiring.toSemiring) (:fv _uniq.310078) (:fv _uniq.310718))))) (:c Nat) (:lambda _ (:c Nat) (:fv _uniq.310078)) ((:c Arith... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c ArithmeticFunction) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:fv FV0))))))) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit 2) (:arg :instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":25786,"sourceStart":25782,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"hf.1","source_end":25792,"source_start":25788,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"hg.1","source_end":25798,"source_start":25794,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 7 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8a7d24de69f0f3364a07b95c2c30e87c2c7d1b6656e92329d96476a38027fca2 | b73d008eaa2b447aca534305ea4349f35ca248b654f539d50e21982d34c0433b | 687f69de6531480f5ddfe6662f269f3625c118e42a5e3e5d1aaddbd520810a1a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 227 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨⟨a1, a2⟩, ⟨b1, b2⟩⟩ h | case hi
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
⊢ ∀ a ∈ m.divisorsAntidiagonal ×ˢ n.divisorsAntidiagonal,
(match a with
| ((i, j), k, l) => (i * k, j * l)) ∈
(m * n).divisorsAntidiagonal | case hi.mk.mk.mk
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
a1 a2 b1 b2 : ℕ
h : ((a1, a2), b1, b2) ∈ m.divisorsAntidiagonal ×ˢ n.divisorsAntidiagonal
⊢ (match ((a1, a2), b1, b2) with
| ((i, j), k, l) => (i * k, j * l)) ∈
... | (:forall a ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) (:forall _ ((:c Membership.mem) ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) ((:c Finset) ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat)))) ((:c Finset.instMembership) ((:c Prod) ((:c Pro... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:forall a :explicit (:app (:c Prod) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat))))) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"rintro","sourceEnd":25957,"sourceStart":25951,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":25961,"sourceStart":25958,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":25964,"sourceStart":25961,"tag":"atom"},... | [{"role":"fresh_name","source":"a1","source_end":25966,"source_start":25964,"syntax_kind":"ident"},{"role":"fresh_name","source":"a2","source_end":25970,"source_start":25968,"syntax_kind":"ident"},{"role":"fresh_name","source":"b1","source_end":25980,"source_start":25978,"syntax_kind":"ident"},{"role":"fresh_name","sou... | [{"source":"⟨⟨a1, a2⟩, ⟨b1, b2⟩⟩","source_end":25990,"source_start":25958,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 22 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f2fbcb0d3820f240d93f72255c39e886b9eaf06c2f6a7ff162caec9259f9594e | 328061c8bf791d793fd4af4b692bce15b5f9075ede86040571a06d3429fca978 | 47a23e7325fa8d84c92235c71a93f539aa06c026707987e11bb59bd0ecb097c4 | e5a0668aab9ebade91d9b42ce1d89782c82487eed210a0fb4dc74791c8b5ee69 |
cat-searcher/leandojo-benchmark-4-random | test | 228 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Nat.mem_divisorsAntidiagonal</a>, <a>Ne</a>, <a>Finset.mem_product</a>] at h | case hi.mk.mk.mk
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
a1 a2 b1 b2 : ℕ
h : ((a1, a2), b1, b2) ∈ m.divisorsAntidiagonal ×ˢ n.divisorsAntidiagonal
⊢ (match ((a1, a2), b1, b2) with
| ((i, j), k, l) => (i * k, j * l)) ∈
... | case hi.mk.mk.mk
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
a1 a2 b1 b2 : ℕ
h : (a1 * a2 = m ∧ ¬m = 0) ∧ b1 * b2 = n ∧ ¬n = 0
⊢ (match ((a1, a2), b1, b2) with
| ((i, j), k, l) => (i * k, j * l)) ∈
(m * n).divisorsAntid... | ((:c Membership.mem) ((:c Prod) (:c Nat) (:c Nat)) ((:c Finset) ((:c Prod) (:c Nat) (:c Nat))) ((:c Finset.instMembership) ((:c Prod) (:c Nat) (:c Nat))) ((:c ArithmeticFunction.IsMultiplicative.mul.match_1) (:lambda _ ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) ((:c Prod) (:c Nat) (:c Nat))... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"simp","sourceEnd":26001,"sourceStart":25997,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":26006,"sourceStart":26002,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":260... | [] | [{"source":"mem_divisorsAntidiagonal","source_end":26032,"source_start":26008,"syntax_kind":"ident"},{"source":"Ne","source_end":26036,"source_start":26034,"syntax_kind":"ident"},{"source":"mem_product","source_end":26049,"source_start":26038,"syntax_kind":"ident"},{"source":"h","source_end":26055,"source_start":26054,... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 23 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a206ec6ecebb2de64f34ea4f1f209ce9604721a870d0bdd4e1ff8501dc473b63 | e5a0668aab9ebade91d9b42ce1d89782c82487eed210a0fb4dc74791c8b5ee69 | 369fada08148bf5662ae145f86f5eddb506bf8b7247dba0f30b2372a93549ca9 | 9c45af0de88d4eabb34c652edd36d99b46b31db58d347c3fc77c5895f01b7c5d |
cat-searcher/leandojo-benchmark-4-random | test | 229 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases h with ⟨⟨rfl, ha⟩, ⟨rfl, hb⟩⟩ | case hi.mk.mk.mk
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
a1 a2 b1 b2 : ℕ
h : (a1 * a2 = m ∧ ¬m = 0) ∧ b1 * b2 = n ∧ ¬n = 0
⊢ (match ((a1, a2), b1, b2) with
| ((i, j), k, l) => (i * k, j * l)) ∈
(m * n).divisorsAntid... | case hi.mk.mk.mk.intro.intro.intro
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬a1 * a2 = 0
cop : (a1 * a2).Coprime (b1 * b2)
hb : ¬b1 * b2 = 0
⊢ (match ((a1, a2), b1, b2) with
| ((i, j), k, l) => (i * k, j * l)) ∈
(a1 * a2 ... | ((:c Membership.mem) ((:c Prod) (:c Nat) (:c Nat)) ((:c Finset) ((:c Prod) (:c Nat) (:c Nat))) ((:c Finset.instMembership) ((:c Prod) (:c Nat) (:c Nat))) ((:c ArithmeticFunction.IsMultiplicative.mul.match_1) (:lambda _ ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) ((:c Prod) (:c Nat) (:c Nat))... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"rcases","sourceEnd":26066,"sourceStart":26060,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":14,"semanticRole":"local","source":"h","sourceEnd":26068,"sourceStart":26067,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","... | [] | [{"source":"h","source_end":26068,"source_start":26067,"syntax_kind":"ident"},{"source":"⟨⟨rfl, ha⟩, ⟨rfl, hb⟩⟩","source_end":26108,"source_start":26074,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 24 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2a8f5b014cccce9907100ae9cd6e642302a5fe6f80c3f5344262978880eebf5b | 9c45af0de88d4eabb34c652edd36d99b46b31db58d347c3fc77c5895f01b7c5d | 1d64516217d1899e47199242f90676d303026e84f7a8f16e85ff2008b9f8861d | 195e92ff7bc87e0b92173a8e621036b7f4201348d0a99258edc6733b2ff48949 |
cat-searcher/leandojo-benchmark-4-random | test | 230 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Nat.mem_divisorsAntidiagonal</a>, <a>Nat.mul_eq_zero</a>, <a>Ne</a>] | case hi.mk.mk.mk.intro.intro.intro
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬a1 * a2 = 0
cop : (a1 * a2).Coprime (b1 * b2)
hb : ¬b1 * b2 = 0
⊢ (match ((a1, a2), b1, b2) with
| ((i, j), k, l) => (i * k, j * l)) ∈
(a1 * a2 ... | case hi.mk.mk.mk.intro.intro.intro
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬a1 * a2 = 0
cop : (a1 * a2).Coprime (b1 * b2)
hb : ¬b1 * b2 = 0
⊢ a1 * b1 * (a2 * b2) = a1 * a2 * (b1 * b2) ∧ ¬((a1 = 0 ∨ a2 = 0) ∨ b1 = 0 ∨ b2 = 0) | ((:c Membership.mem) ((:c Prod) (:c Nat) (:c Nat)) ((:c Finset) ((:c Prod) (:c Nat) (:c Nat))) ((:c Finset.instMembership) ((:c Prod) (:c Nat) (:c Nat))) ((:c ArithmeticFunction.IsMultiplicative.mul.match_1) (:lambda _ ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) ((:c Prod) (:c Nat) (:c Nat))... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"simp","sourceEnd":26117,"sourceStart":26113,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":26122,"sourceStart":26118,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":261... | [] | [{"source":"mem_divisorsAntidiagonal","source_end":26148,"source_start":26124,"syntax_kind":"ident"},{"source":"Nat.mul_eq_zero","source_end":26165,"source_start":26150,"syntax_kind":"ident"},{"source":"Ne","source_end":26169,"source_start":26167,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 25 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5918b0246540190a198a6c69bdd39245a3bddf407fbfc3e50db1e9e79897fb24 | 195e92ff7bc87e0b92173a8e621036b7f4201348d0a99258edc6733b2ff48949 | e93d94a913cad2286dd37546d48a10ed7913349ebd02f2878a1cf5df86de1ad6 | f13d6d4812db08e4a280d3fcd92bda9705ae93b099345f373ecb7cdabe42c9c1 |
cat-searcher/leandojo-benchmark-4-random | test | 231 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | case hi.mk.mk.mk.intro.intro.intro
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬a1 * a2 = 0
cop : (a1 * a2).Coprime (b1 * b2)
hb : ¬b1 * b2 = 0
⊢ a1 * b1 * (a2 * b2) = a1 * a2 * (b1 * b2) ∧ ¬((a1 = 0 ∨ a2 = 0) ∨ b1 = 0 ∨ b2 = 0) | case hi.mk.mk.mk.intro.intro.intro.left
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬a1 * a2 = 0
cop : (a1 * a2).Coprime (b1 * b2)
hb : ¬b1 * b2 = 0
⊢ a1 * b1 * (a2 * b2) = a1 * a2 * (b1 * b2)
case hi.mk.mk.mk.intro.intro.intro.righ... | ((:c And) ((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.316176) (:fv _uniq.316195)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HMul.hMul) (: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 HMul) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"constructor","sourceEnd":26186,"sourceStart":26175,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":26186,"sourceStart":26175,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 26 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 030b867f000438db8ab79d13923492c2e75893844ef5027fb04080b955abf911 | f13d6d4812db08e4a280d3fcd92bda9705ae93b099345f373ecb7cdabe42c9c1 | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | 4f32f7af3a99a5bf85439aff466caa272ff79504ab9643d5d86abf59b51ba984 |
cat-searcher/leandojo-benchmark-4-random | test | 232 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Nat.mul_eq_zero</a>] at * | case hi.mk.mk.mk.intro.intro.intro.right
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬a1 * a2 = 0
cop : (a1 * a2).Coprime (b1 * b2)
hb : ¬b1 * b2 = 0
⊢ ¬((a1 = 0 ∨ a2 = 0) ∨ b1 = 0 ∨ b2 = 0) | case hi.mk.mk.mk.intro.intro.intro.right
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬(a1 = 0 ∨ a2 = 0)
cop : (a1 * a2).Coprime (b1 * b2)
hb : ¬(b1 = 0 ∨ b2 = 0)
⊢ ¬((a1 = 0 ∨ a2 = 0) ∨ b1 = 0 ∨ b2 = 0) | ((:c Not) ((:c Or) ((:c Or) ((:c Eq) (:c Nat) (:fv _uniq.316176) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) ((:c Eq) (:c Nat) (:fv _uniq.316177) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))) ((:c Or) ((:c Eq) (:c Nat) (:fv _uniq.316195) ((:c OfNat.ofNat) (:c Nat) (:lit 0) (... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Not) (:arg :explicit 0 (:app (:c Or) (:arg :explicit 0 (:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfN... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"rw","sourceEnd":26205,"sourceStart":26203,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":26207,"sourceStart":26206,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Nat.mul_eq_zero"... | [] | [{"source":"Nat.mul_eq_zero","source_end":26222,"source_start":26207,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 32 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8a187aae51569198c7c2886c1ad880844b45f74732e40ed385ebdcb835596edc | 3153af69aab4b2f6ef64d5ad3cd8640f538f53fcd3002a097efb1c99360763b3 | 19b648e65f020c1e7c23c0179f565e769772d7c9391a9de8aa46d5ff7a0224c6 | 69c835741a6cc3201b4540d6c28dedda81d42fb197d48d3fcae870dbedf80966 |
cat-searcher/leandojo-benchmark-4-random | test | 233 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>not_or_of_not</a> ha hb | case hi.mk.mk.mk.intro.intro.intro.right
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬(a1 = 0 ∨ a2 = 0)
cop : (a1 * a2).Coprime (b1 * b2)
hb : ¬(b1 = 0 ∨ b2 = 0)
⊢ ¬((a1 = 0 ∨ a2 = 0) ∨ b1 = 0 ∨ b2 = 0) | ((:c Not) ((:c Or) ((:c Or) ((:c Eq) (:c Nat) (:fv _uniq.316176) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) ((:c Eq) (:c Nat) (:fv _uniq.316177) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))) ((:c Or) ((:c Eq) (:c Nat) (:fv _uniq.316195) ((:c OfNat.ofNat) (:c Nat) (:lit 0) (... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Not) (:arg :explicit 0 (:app (:c Or) (:arg :explicit 0 (:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfN... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"apply","sourceEnd":26238,"sourceStart":26233,"tag":"atom"},{"children":[{"name":"not_or_of_not","semanticRole":"global","source":"not_or_of_not","sourceEnd":26252,"sourceStart":26239,"tag":"identifier"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"ha","sourceEnd":26255,"sourc... | [] | [{"source":"not_or_of_not ha hb","source_end":26258,"source_start":26239,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 35 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2907ecd998278bc6484767c9e81516f2752863993ad170e74ab58682c18b0116 | 69c835741a6cc3201b4540d6c28dedda81d42fb197d48d3fcae870dbedf80966 | 446269ea7167a7fe1f2fbc7f9b9847b146d776d668ac4510de482f1ea74d7251 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 234 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | case hi.mk.mk.mk.intro.intro.intro.left
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬a1 * a2 = 0
cop : (a1 * a2).Coprime (b1 * b2)
hb : ¬b1 * b2 = 0
⊢ a1 * b1 * (a2 * b2) = a1 * a2 * (b1 * b2) | ((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.316176) (:fv _uniq.316195)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HMul.hMul) (: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 HMul) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"children":[{"children":[{"children":[{"source":"ring","sourceEnd":26198,"sourceStart":26194,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":26198,"sourceStart":26194,"tag":"node"}],"kind":"null","source":"ring","sourceEnd":26198,"sourceStart":26194,"tag":"node"}],"kind":"Le... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 29 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 675423b930da4ea33e54a461a67345c2dcece8fee0db392e60eda651bd691744 | 3a22f335c4d9593419d4e86ec1c5bb49c79f9ba326cff9a7e64764a3f3bf391f | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 235 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.InjOn</a>, <a>Finset.mem_coe</a>, <a>Nat.mem_divisorsAntidiagonal</a>, <a>Ne</a>, <a>Finset.mem_product</a>, <a>Prod.mk.inj_iff</a>] | case i_inj
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
⊢ Set.InjOn
(fun x =>
match x with
| ((i, j), k, l) => (i * k, j * l))
↑(m.divisorsAntidiagonal ×ˢ n.divisorsAntidiagonal) | case i_inj
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
⊢ ∀ ⦃x₁ : (ℕ × ℕ) × ℕ × ℕ⦄,
(x₁.1.1 * x₁.1.2 = m ∧ ¬m = 0) ∧ x₁.2.1 * x₁.2.2 = n ∧ ¬n = 0 →
∀ ⦃x₂ : (ℕ × ℕ) × ℕ × ℕ⦄,
(x₂.1.1 * x₂.1.2 = m ∧ ¬m = 0) ∧ x₂.... | ((:c Set.InjOn) ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) ((:c Prod) (:c Nat) (:c Nat)) (:lambda _ ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) ((:c ArithmeticFunction.IsMultiplicative.mul.match_1) (:lambda _ ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Set.InjOn) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))))) (:arg :implicit-type 1 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"simp","sourceEnd":26268,"sourceStart":26264,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":26273,"sourceStart":26269,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":262... | [] | [{"source":"Set.InjOn","source_end":26284,"source_start":26275,"syntax_kind":"ident"},{"source":"mem_coe","source_end":26293,"source_start":26286,"syntax_kind":"ident"},{"source":"mem_divisorsAntidiagonal","source_end":26319,"source_start":26295,"syntax_kind":"ident"},{"source":"Ne","source_end":26323,"source_start":26... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 40 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7438a00b7d11758b2443cee6b30db388b93ac43f6afd9186a76d9a6f1a2fbe6b | 90da406004f68fb106b9fa1491f38fedf1b2aa7b0967e8e93c30cd00651190ea | 1bdbca12055d450500d42c3c71bc084f6525c26b0e523bfc9889cc7254e6cb42 | fa1a5efbd588d9adc540b13a998207d6f9eb313070b0089646c1ed74d491becf |
cat-searcher/leandojo-benchmark-4-random | test | 236 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨⟨a1, a2⟩, ⟨b1, b2⟩⟩ ⟨⟨rfl, ha⟩, ⟨rfl, hb⟩⟩ ⟨⟨c1, c2⟩, ⟨d1, d2⟩⟩ hcd h | case i_inj
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
⊢ ∀ ⦃x₁ : (ℕ × ℕ) × ℕ × ℕ⦄,
(x₁.1.1 * x₁.1.2 = m ∧ ¬m = 0) ∧ x₁.2.1 * x₁.2.2 = n ∧ ¬n = 0 →
∀ ⦃x₂ : (ℕ × ℕ) × ℕ × ℕ⦄,
(x₂.1.1 * x₂.1.2 = m ∧ ¬m = 0) ∧ x₂.... | case i_inj.mk.mk.mk.intro.intro.intro.mk.mk.mk
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 ... | (:forall x₁ ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) (:forall _ ((:c And) ((:c And) ((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) ((:c Prod.fst) (:c Nat) (:c Nat) ((:c Prod.fst) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c N... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:forall x₁ :strict-implicit (:app (:c Prod) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat))))) (:forall _ :explicit (:app (:c And) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"rintro","sourceEnd":26365,"sourceStart":26359,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":26369,"sourceStart":26366,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":26372,"sourceStart":26369,"tag":"atom"},... | [{"role":"fresh_name","source":"a1","source_end":26374,"source_start":26372,"syntax_kind":"ident"},{"role":"fresh_name","source":"a2","source_end":26378,"source_start":26376,"syntax_kind":"ident"},{"role":"fresh_name","source":"b1","source_end":26388,"source_start":26386,"syntax_kind":"ident"},{"role":"fresh_name","sou... | [{"source":"⟨⟨a1, a2⟩, ⟨b1, b2⟩⟩","source_end":26398,"source_start":26366,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"},{"source":"⟨⟨rfl, ha⟩, ⟨rfl, hb⟩⟩","source_end":26433,"source_start":26399,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"},{"source":"⟨⟨c1, c2⟩, ⟨d1, d2⟩⟩","source_end":26466,"source_start":... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 41 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a475928b7872cf8ee706d8779ca42f15d1ec6bd96c96c96f4860c04df94cdf37 | fa1a5efbd588d9adc540b13a998207d6f9eb313070b0089646c1ed74d491becf | baabd49b98e9188afa51908ac4b618a61946f3f8e9b13896ee84d72e6e761059 | fb241bb12d2e3b47367aed1f828d73e0a278803982ea70a5881837c3e9bc47bd |
cat-searcher/leandojo-benchmark-4-random | test | 237 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Prod.mk.inj_iff</a>] at h | case i_inj.mk.mk.mk.intro.intro.intro.mk.mk.mk
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 ... | case i_inj.mk.mk.mk.intro.intro.intro.mk.mk.mk
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 ... | ((:c Eq) ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) ((:c Prod.mk) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod.mk) (:c Nat) (:c Nat) (:fv _uniq.317836) (:fv _uniq.317837)) ((:c Prod.mk) (:c Nat) (:c Nat) (:fv _uniq.317858) (:fv _uniq.317859))) ((:c Prod.mk) ((:c Pro... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))))) (:arg :explicit 1 (:app (:c Prod.mk) (:arg :implicit-type 0 (:app (:c Prod) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"simp","sourceEnd":26481,"sourceStart":26477,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":26486,"sourceStart":26482,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":264... | [] | [{"source":"Prod.mk.inj_iff","source_end":26503,"source_start":26488,"syntax_kind":"ident"},{"source":"h","source_end":26509,"source_start":26508,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 42 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 76c73cf949279b310a5865ea02d1c400efb82ecd37c7a4b431282c8c04bc8a28 | fb241bb12d2e3b47367aed1f828d73e0a278803982ea70a5881837c3e9bc47bd | beabd90936dbcb147092594652717ee0bf952de2857f9c759bed96a613879a38 | 57d1a5bf7c86a3060d5db47370fd88d9fa427bb553ca07e0504878033336993b |
cat-searcher/leandojo-benchmark-4-random | test | 238 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext <;> dsimp only | case i_inj.mk.mk.mk.intro.intro.intro.mk.mk.mk
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 ... | case i_inj.mk.mk.mk.intro.intro.intro.mk.mk.mk.a.a
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).... | ((:c Eq) ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) ((:c Prod.mk) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod.mk) (:c Nat) (:c Nat) (:fv _uniq.317836) (:fv _uniq.317837)) ((:c Prod.mk) (:c Nat) (:c Nat) (:fv _uniq.317858) (:fv _uniq.317859))) ((:c Prod.mk) ((:c Pro... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))))) (:arg :explicit 1 (:app (:c Prod.mk) (:arg :implicit-type 0 (:app (:c Prod) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"children":[{"source":"ext","sourceEnd":26517,"sourceStart":26514,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":26517,"sourceStart":26514,"tag":"node"},{"source":"<;>... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 43 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aebaf28a6f6eec76b812f450872dc4b07e58343860cbe0f4c7f678ab1d6fe7b6 | 57d1a5bf7c86a3060d5db47370fd88d9fa427bb553ca07e0504878033336993b | ee615a0d235986f1bbe4fbeb89d2e66ad7c148584c0f8c24e22ce5f736a6b8e1 | a19d55adc2a9391d52f36a0c25d22b064d97fc61b7389f3f67dbff189dcbac63 |
cat-searcher/leandojo-benchmark-4-random | test | 239 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | trans <a>Nat.gcd</a> (a1 * a2) (a1 * b1) | case i_inj.mk.mk.mk.intro.intro.intro.mk.mk.mk.a.a
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).... | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2)
hb : ¬((a1, a2), b1, ... | ((:c Eq) (:c Nat) (:fv _uniq.317836) (:fv _uniq.318004)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:fv FV14))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"trans","sourceEnd":26545,"sourceStart":26540,"tag":"atom"},{"children":[{"children":[{"name":"Nat.gcd","semanticRole":"global","source":"Nat.gcd","sourceEnd":26553,"sourceStart":26546,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":26555,"sourceStart":26554,"tag":"atom"},... | [] | [{"source":"Nat.gcd (a1 * a2) (a1 * b1)","source_end":26573,"source_start":26546,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 54 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 630264c7af842a9af0f0d2dff2ffa2675bd665f81bddf079c2b60627bffc81cc | 3396c42ece6a0ea21498835b21e46f079e137fdbcf24b90607252258b3e434fe | f2f54f641e46ada4362cbb0ad2a27dd4417c01d1dbc8753fbca87aaae61ba5d8 | c7f3ee440fc8976ddbb9bc006230a2004c7849bff7faacd82b89f35d7deaefd1 |
cat-searcher/leandojo-benchmark-4-random | test | 240 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Nat.gcd_mul_left</a>, cop.coprime_mul_left.coprime_mul_right_right.gcd_eq_one, <a>mul_one</a>] | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2)
hb : ¬((a1, a2), b1, ... | ((:c Eq) (:c Nat) (:fv _uniq.317836) ((:c Nat.gcd) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317836) (:fv _uniq.317837)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317836) (:fv _uniq.317858)))) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:app (:c Nat.gcd) (:arg :explicit 0 (:app (:c HMul.hMul) (: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 HMul) (:arg :explicit 0 (:c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":26585,"sourceStart":26583,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":26587,"sourceStart":26586,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"Nat.gcd_mul_left","source_end":26603,"source_start":26587,"syntax_kind":"ident"},{"source":"cop.coprime_mul_left.coprime_mul_right_right.gcd_eq_one","source_end":26660,"source_start":26605,"syntax_kind":"ident"},{"source":"mul_one","source_end":26669,"source_start":26662,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 57 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c673d705b281724533bce01a7229d8bbc36b445412d19d3a972d93102bc5ea8e | dd716287c14629e93a3fe58398d94b5436f82d9c8ed64ac0e877fadf3a406512 | 06f850d661021a66b63812f3e5567ddfaf4ebd12e40734a2aef6f76ad48f7476 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 241 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hcd.1.1, ← hcd.2.1] at cop | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2)
hb : ¬((a1, a2), b1, ... | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
hb : ¬((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2 = 0
c1 c2 d1 d2 : ℕ
cop : (((c1, c2), d1, d2).1.1 * ((c1, c2), d1, d2).1.2).Copri... | ((:c Eq) (:c Nat) ((:c Nat.gcd) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317836) (:fv _uniq.317837)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317836) (:fv _uniq.317858))) (:fv _uniq.318004)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.gcd) (:arg :explicit 0 (:app (:c HMul.hMul) (: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 HMul) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"rw","sourceEnd":26682,"sourceStart":26680,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":26684,"sourceStart":26683,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":26687,"sourceSt... | [] | [{"source":"cop","source_end":26716,"source_start":26713,"syntax_kind":"ident"},{"source":"hcd.1.1","source_end":26695,"source_start":26688,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"hcd.2.1","source_end":26708,"source_start":26701,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 68 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7d80d066e4970d5153ab460d81bd6974a6ca8f3f4b133cac0035d65a13ba9ee7 | 3ab133ff5d46607eaeb0d03e73682e81eb34ddc4ff093de7338e499d8ca28be1 | 83c23e8f1648e8421582fba68d59016d9bec7702f6a046d896a813c5c7a79fb8 | 4cc9f35d4dd5e0f40489c627cfcfa94b55f959e4f6efc944d057f67a2f43e8ca |
cat-searcher/leandojo-benchmark-4-random | test | 242 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hcd.1.1, h.1, <a>Nat.gcd_mul_left</a>, cop.coprime_mul_left.coprime_mul_right_right.gcd_eq_one, <a>mul_one</a>] | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
hb : ¬((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2 = 0
c1 c2 d1 d2 : ℕ
cop : (((c1, c2), d1, d2).1.1 * ((c1, c2), d1, d2).1.2).Copri... | ((:c Eq) (:c Nat) ((:c Nat.gcd) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317836) (:fv _uniq.317837)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317836) (:fv _uniq.317858))) (:fv _uniq.318004)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.gcd) (:arg :explicit 0 (:app (:c HMul.hMul) (: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 HMul) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"rw","sourceEnd":26727,"sourceStart":26725,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":26729,"sourceStart":26728,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":26732,"sourceSt... | [] | [{"source":"hcd.1.1","source_end":26740,"source_start":26733,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"h.1","source_end":26745,"source_start":26742,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"Nat.gcd_mul_left","source_end":26763,"source_start":26747,"syntax_kind":"ident"},{"source":"cop.coprime_mul_left.c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 72 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 50e28e7f38442a0bbb0e5cac74d8c94d66170fcb6a546becdca1a411f235f9fb | 4cc9f35d4dd5e0f40489c627cfcfa94b55f959e4f6efc944d057f67a2f43e8ca | ef9035b3ddd9a6bef40c2a1b02d7de183f74b2d1e820b92ccc662bb2bafbd81c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 243 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | trans <a>Nat.gcd</a> (a1 * a2) (a2 * b2) | case i_inj.mk.mk.mk.intro.intro.intro.mk.mk.mk.a.a
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).... | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2)
hb : ¬((a1, a2), b1, ... | ((:c Eq) (:c Nat) (:fv _uniq.317837) (:fv _uniq.318005)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV8)) (:arg :explicit 2 (:fv FV15))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"trans","sourceEnd":26853,"sourceStart":26848,"tag":"atom"},{"children":[{"children":[{"name":"Nat.gcd","semanticRole":"global","source":"Nat.gcd","sourceEnd":26861,"sourceStart":26854,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":26863,"sourceStart":26862,"tag":"atom"},... | [] | [{"source":"Nat.gcd (a1 * a2) (a2 * b2)","source_end":26881,"source_start":26854,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 83 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1b1dbf68bfbd9826fbe5d5f1e879ea496082a063f87522a29fc90f8b7896743b | 4a216ebc0ea0156e2551873020118900de223a6f2219817cab7fda3fe612b25f | 79c02628ae010a3ff2a9aa21652eb6ea3b39b2bedc9f5c7d76a7f1731b55c406 | 1f5fe80efa69acf3840c313b2b2417f5ee91d981ba537850cc1717981faaa35b |
cat-searcher/leandojo-benchmark-4-random | test | 244 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>mul_comm</a>, <a>Nat.gcd_mul_left</a>, cop.coprime_mul_right.coprime_mul_left_right.gcd_eq_one, <a>mul_one</a>] | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2)
hb : ¬((a1, a2), b1, ... | ((:c Eq) (:c Nat) (:fv _uniq.317837) ((:c Nat.gcd) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317836) (:fv _uniq.317837)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317837) (:fv _uniq.317859)))) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV8)) (:arg :explicit 2 (:app (:c Nat.gcd) (:arg :explicit 0 (:app (:c HMul.hMul) (: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 HMul) (:arg :explicit 0 (:c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":26893,"sourceStart":26891,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":26895,"sourceStart":26894,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"mul_comm","source_end":26903,"source_start":26895,"syntax_kind":"ident"},{"source":"Nat.gcd_mul_left","source_end":26921,"source_start":26905,"syntax_kind":"ident"},{"source":"cop.coprime_mul_right.coprime_mul_left_right.gcd_eq_one","source_end":26978,"source_start":26923,"syntax_kind":"ident"},{"source":"m... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 86 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8aa22074fcf83302dc3f6f16d149080d08050c5bed5c848ccd2f495ce76c80a6 | b36cd039f598fc72c9474cfaf40946ecbda57162c7416dd0c0bf1417ecfd3526 | 10f69231c234b89bfc63bf3fe7fad915e8449cbabab8ac0f20adfd0fccbc6aff | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 245 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hcd.1.1, ← hcd.2.1] at cop | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2)
hb : ¬((a1, a2), b1, ... | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
hb : ¬((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2 = 0
c1 c2 d1 d2 : ℕ
cop : (((c1, c2), d1, d2).1.1 * ((c1, c2), d1, d2).1.2).Copri... | ((:c Eq) (:c Nat) ((:c Nat.gcd) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317836) (:fv _uniq.317837)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317837) (:fv _uniq.317859))) (:fv _uniq.318005)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.gcd) (:arg :explicit 0 (:app (:c HMul.hMul) (: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 HMul) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"rw","sourceEnd":27010,"sourceStart":27008,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27012,"sourceStart":27011,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":27015,"sourceSt... | [] | [{"source":"cop","source_end":27044,"source_start":27041,"syntax_kind":"ident"},{"source":"hcd.1.1","source_end":27023,"source_start":27016,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"hcd.2.1","source_end":27036,"source_start":27029,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 98 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 651407dd63ed0f5b3b7332b3077ec1aaaa90e540f6f8208fb7c3ef0cd2e2480b | 76c0ba82b36b53590655c4e17bf8f8ee25179786303d03216f61d980afa55445 | 83c23e8f1648e8421582fba68d59016d9bec7702f6a046d896a813c5c7a79fb8 | 4e6a2287a64b5a6376d0a56b55a229e76a4e4b9cc747e1126d55cb5dc47864af |
cat-searcher/leandojo-benchmark-4-random | test | 246 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hcd.1.1, h.2, <a>mul_comm</a>, <a>Nat.gcd_mul_left</a>, cop.coprime_mul_right.coprime_mul_left_right.gcd_eq_one, <a>mul_one</a>] | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
hb : ¬((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2 = 0
c1 c2 d1 d2 : ℕ
cop : (((c1, c2), d1, d2).1.1 * ((c1, c2), d1, d2).1.2).Copri... | ((:c Eq) (:c Nat) ((:c Nat.gcd) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317836) (:fv _uniq.317837)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317837) (:fv _uniq.317859))) (:fv _uniq.318005)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.gcd) (:arg :explicit 0 (:app (:c HMul.hMul) (: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 HMul) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"rw","sourceEnd":27055,"sourceStart":27053,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27057,"sourceStart":27056,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":27060,"sourceSt... | [] | [{"source":"hcd.1.1","source_end":27068,"source_start":27061,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"h.2","source_end":27073,"source_start":27070,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"mul_comm","source_end":27083,"source_start":27075,"syntax_kind":"ident"},{"source":"Nat.gcd_mul_left","source_end"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 102 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fdddd6501165ee895bd68f74e33318fd69050140abd0891f23f8f5ae927c3ba4 | 4e6a2287a64b5a6376d0a56b55a229e76a4e4b9cc747e1126d55cb5dc47864af | 3a5a7d992ae04e9a1e729e7aa4d7c6ca350040dd4de47752a9553a21cf8cc1db | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 247 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | trans <a>Nat.gcd</a> (b1 * b2) (a1 * b1) | case i_inj.mk.mk.mk.intro.intro.intro.mk.mk.mk.a.a
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).... | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2)
hb : ¬((a1, a2), b1, ... | ((:c Eq) (:c Nat) (:fv _uniq.317858) (:fv _uniq.318024)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV9)) (:arg :explicit 2 (:fv FV16))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"trans","sourceEnd":27191,"sourceStart":27186,"tag":"atom"},{"children":[{"children":[{"name":"Nat.gcd","semanticRole":"global","source":"Nat.gcd","sourceEnd":27199,"sourceStart":27192,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":27201,"sourceStart":27200,"tag":"atom"},... | [] | [{"source":"Nat.gcd (b1 * b2) (a1 * b1)","source_end":27219,"source_start":27192,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 114 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2b8d3d6de924715e6e171810fe500215c2c88bf7cf5e23bbd88209c282f45011 | 23744aab071ecf04bcc74aad85b08a82f40b23ab60684726c597dfbf1475ce98 | 0fb3a7c90e93fd95d86a5fbd71844901c2ed0921231716eb24a513eec3429c43 | 4193958e2421058cbcb3926246a933882c15e0f5c310a35770b9a9fb36cf8193 |
cat-searcher/leandojo-benchmark-4-random | test | 248 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>mul_comm</a>, <a>Nat.gcd_mul_right</a>, cop.coprime_mul_right.coprime_mul_left_right.symm.gcd_eq_one, <a>one_mul</a>] | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2)
hb : ¬((a1, a2), b1, ... | ((:c Eq) (:c Nat) (:fv _uniq.317858) ((:c Nat.gcd) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317858) (:fv _uniq.317859)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317836) (:fv _uniq.317858)))) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV9)) (:arg :explicit 2 (:app (:c Nat.gcd) (:arg :explicit 0 (:app (:c HMul.hMul) (: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 HMul) (:arg :explicit 0 (:c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":27231,"sourceStart":27229,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27233,"sourceStart":27232,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"mul_comm","source_end":27241,"source_start":27233,"syntax_kind":"ident"},{"source":"Nat.gcd_mul_right","source_end":27260,"source_start":27243,"syntax_kind":"ident"},{"source":"cop.coprime_mul_right.coprime_mul_left_right.symm.gcd_eq_one","source_end":27332,"source_start":27272,"syntax_kind":"ident"},{"sour... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 117 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d42082ca8cb531922c030a8d48111a115fb4670991396d2737f30007f17bc052 | e4b49e96bcb68f56c03156830f7e371d4a1afc7632f043ef21430fb6ee85eb78 | 5c55e5fe15c76f2b4b4ef35bbcfac6744ae20aa792200114cf5a59488fc4d9c1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 249 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hcd.1.1, ← hcd.2.1] at cop | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2)
hb : ¬((a1, a2), b1, ... | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
hb : ¬((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2 = 0
c1 c2 d1 d2 : ℕ
cop : (((c1, c2), d1, d2).1.1 * ((c1, c2), d1, d2).1.2).Copri... | ((:c Eq) (:c Nat) ((:c Nat.gcd) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317858) (:fv _uniq.317859)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317836) (:fv _uniq.317858))) (:fv _uniq.318024)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.gcd) (:arg :explicit 0 (:app (:c HMul.hMul) (: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 HMul) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"rw","sourceEnd":27354,"sourceStart":27352,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27356,"sourceStart":27355,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":27359,"sourceSt... | [] | [{"source":"cop","source_end":27388,"source_start":27385,"syntax_kind":"ident"},{"source":"hcd.1.1","source_end":27367,"source_start":27360,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"hcd.2.1","source_end":27380,"source_start":27373,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 129 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ee167ce34e0709580b7b3ce5169a54c8574be58429b1a05bd36a6ad9831631f7 | 16a8f55d9aaa7e53846cba4743958f1f7be408c812887684e54fce5d86d70c29 | 83c23e8f1648e8421582fba68d59016d9bec7702f6a046d896a813c5c7a79fb8 | 9ad1c4b411f9b512800c797f6110bf47302c25399df8cca5c4219b207d85e9d8 |
cat-searcher/leandojo-benchmark-4-random | test | 250 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hcd.2.1, h.1, <a>mul_comm</a> c1 d1, <a>Nat.gcd_mul_left</a>, cop.coprime_mul_right.coprime_mul_left_right.symm.gcd_eq_one, <a>mul_one</a>] | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
hb : ¬((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2 = 0
c1 c2 d1 d2 : ℕ
cop : (((c1, c2), d1, d2).1.1 * ((c1, c2), d1, d2).1.2).Copri... | ((:c Eq) (:c Nat) ((:c Nat.gcd) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317858) (:fv _uniq.317859)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317836) (:fv _uniq.317858))) (:fv _uniq.318024)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.gcd) (:arg :explicit 0 (:app (:c HMul.hMul) (: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 HMul) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"rw","sourceEnd":27399,"sourceStart":27397,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27401,"sourceStart":27400,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":27404,"sourceSt... | [] | [{"source":"hcd.2.1","source_end":27412,"source_start":27405,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"h.1","source_end":27417,"source_start":27414,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"mul_comm c1 d1","source_end":27433,"source_start":27419,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Nat.gcd_m... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 133 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ebedbf6cf0a50f30b21a8ba5fc7fb1f57a55f225279fae2cac7bd506d183d892 | 9ad1c4b411f9b512800c797f6110bf47302c25399df8cca5c4219b207d85e9d8 | cb26f4b0d4c83a3a2371dcf48512607408cbbd0c6bcc2d1f66601e8e6a0b25c6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 251 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | trans <a>Nat.gcd</a> (b1 * b2) (a2 * b2) | case i_inj.mk.mk.mk.intro.intro.intro.mk.mk.mk.a.a
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).... | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2)
hb : ¬((a1, a2), b1, ... | ((:c Eq) (:c Nat) (:fv _uniq.317859) (:fv _uniq.318025)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV10)) (:arg :explicit 2 (:fv FV17))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"trans","sourceEnd":27546,"sourceStart":27541,"tag":"atom"},{"children":[{"children":[{"name":"Nat.gcd","semanticRole":"global","source":"Nat.gcd","sourceEnd":27554,"sourceStart":27547,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":27556,"sourceStart":27555,"tag":"atom"},... | [] | [{"source":"Nat.gcd (b1 * b2) (a2 * b2)","source_end":27574,"source_start":27547,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 145 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8b4a91ece1fcffc5b398c4ae71128867889d87c1dfe0a6a3973037af5e1863cd | 26f44dc212dc1f70e720d9e43e2e53dcecca07cbc8bee1e39a34eb039d08c27f | 97cd84e679993d2b93e65291d8d2705067e7f26d87815a713b60d924c093f015 | 399203d90fcd9efb6284d402e96b6bbd028ef98d3b8a3754ff3b1465823951c8 |
cat-searcher/leandojo-benchmark-4-random | test | 252 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Nat.gcd_mul_right</a>, cop.coprime_mul_left.coprime_mul_right_right.symm.gcd_eq_one, <a>one_mul</a>] | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2)
hb : ¬((a1, a2), b1, ... | ((:c Eq) (:c Nat) (:fv _uniq.317859) ((:c Nat.gcd) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317858) (:fv _uniq.317859)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317837) (:fv _uniq.317859)))) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV10)) (:arg :explicit 2 (:app (:c Nat.gcd) (:arg :explicit 0 (:app (:c HMul.hMul) (: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 HMul) (:arg :explicit 0 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":27586,"sourceStart":27584,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27588,"sourceStart":27587,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"Nat.gcd_mul_right","source_end":27605,"source_start":27588,"syntax_kind":"ident"},{"source":"cop.coprime_mul_left.coprime_mul_right_right.symm.gcd_eq_one","source_end":27667,"source_start":27607,"syntax_kind":"ident"},{"source":"one_mul","source_end":27686,"source_start":27679,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 148 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 453a4d399e1268290d8de87dd23255aca2715203ecf80eff693ef6d86ecd2c97 | 47c8604e1df0bf3c9b8c2a731e372023880fec4068c7754908f0ea8963d8464b | 380db364e1fc7920def5fb116bb6f347a381b38c8d5bd172c91a7c1fb84b8db7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 253 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hcd.1.1, ← hcd.2.1] at cop | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2)
hb : ¬((a1, a2), b1, ... | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
hb : ¬((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2 = 0
c1 c2 d1 d2 : ℕ
cop : (((c1, c2), d1, d2).1.1 * ((c1, c2), d1, d2).1.2).Copri... | ((:c Eq) (:c Nat) ((:c Nat.gcd) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317858) (:fv _uniq.317859)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317837) (:fv _uniq.317859))) (:fv _uniq.318025)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.gcd) (:arg :explicit 0 (:app (:c HMul.hMul) (: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 HMul) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"rw","sourceEnd":27699,"sourceStart":27697,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27701,"sourceStart":27700,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":27704,"sourceSt... | [] | [{"source":"cop","source_end":27733,"source_start":27730,"syntax_kind":"ident"},{"source":"hcd.1.1","source_end":27712,"source_start":27705,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"hcd.2.1","source_end":27725,"source_start":27718,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 159 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a1894064127062c5e8c21b68245673cb64e35cd048252230081c98919953ff46 | 781b0637aadd16c8bb50addabd5f451005fcde6dcee6238c845725405c9e09cd | 83c23e8f1648e8421582fba68d59016d9bec7702f6a046d896a813c5c7a79fb8 | ea4e096705656d28c51627e8b436e79604bf4d202dce40f9116a342bd527a80c |
cat-searcher/leandojo-benchmark-4-random | test | 254 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hcd.2.1, h.2, <a>Nat.gcd_mul_right</a>, cop.coprime_mul_left.coprime_mul_right_right.symm.gcd_eq_one, <a>one_mul</a>] | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
hb : ¬((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2 = 0
c1 c2 d1 d2 : ℕ
cop : (((c1, c2), d1, d2).1.1 * ((c1, c2), d1, d2).1.2).Copri... | ((:c Eq) (:c Nat) ((:c Nat.gcd) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317858) (:fv _uniq.317859)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317837) (:fv _uniq.317859))) (:fv _uniq.318025)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.gcd) (:arg :explicit 0 (:app (:c HMul.hMul) (: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 HMul) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"rw","sourceEnd":27744,"sourceStart":27742,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27746,"sourceStart":27745,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":27749,"sourceSt... | [] | [{"source":"hcd.2.1","source_end":27757,"source_start":27750,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"h.2","source_end":27762,"source_start":27759,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"Nat.gcd_mul_right","source_end":27781,"source_start":27764,"syntax_kind":"ident"},{"source":"cop.coprime_mul_left.... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 163 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b77148e830f2727c24d10448e6cd611b3dd958f91687bbd088312cf38cdb6299 | ea4e096705656d28c51627e8b436e79604bf4d202dce40f9116a342bd527a80c | a6a861ba2a2ac5bb5b4a2ac5329d3e5f91697c66c31b888922b41b744e60bf7d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 255 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.SurjOn</a>, <a>Set.subset_def</a>, <a>Finset.mem_coe</a>, <a>Nat.mem_divisorsAntidiagonal</a>, <a>Ne</a>, <a>Finset.mem_product</a>, <a>Set.mem_image</a>, <a>exists_prop</a>, <a>Prod.mk.inj_iff</a>] | case i_surj
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
⊢ Set.SurjOn
(fun x =>
match x with
| ((i, j), k, l) => (i * k, j * l))
↑(m.divisorsAntidiagonal ×ˢ n.divisorsAntidiagonal) ↑(m * n).divisorsAntidiagon... | case i_surj
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
⊢ ∀ (x : ℕ × ℕ),
x.1 * x.2 = m * n ∧ ¬m * n = 0 →
∃ x_1,
((x_1.1.1 * x_1.1.2 = m ∧ ¬m = 0) ∧ x_1.2.1 * x_1.2.2 = n ∧ ¬n = 0) ∧ (x_1.1.1 * x_1.2.1, x_1.1.... | ((:c Set.SurjOn) ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) ((:c Prod) (:c Nat) (:c Nat)) (:lambda _ ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) ((:c ArithmeticFunction.IsMultiplicative.mul.match_1) (:lambda _ ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Set.SurjOn) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))))) (:arg :implicit-type 1 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"simp","sourceEnd":27873,"sourceStart":27869,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":27878,"sourceStart":27874,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":278... | [] | [{"source":"Set.SurjOn","source_end":27890,"source_start":27880,"syntax_kind":"ident"},{"source":"Set.subset_def","source_end":27906,"source_start":27892,"syntax_kind":"ident"},{"source":"mem_coe","source_end":27915,"source_start":27908,"syntax_kind":"ident"},{"source":"mem_divisorsAntidiagonal","source_end":27941,"sou... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 174 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a69f6a44ae8c5cddf408540b2215a9af73cfc18219a07ed0aeb1303a89e71c7b | d86150bee23dca4701683971a9eb0ea101c54cbc48e6161888e921131a63580c | d17ba315b62a95ea8c4d921683b7a2ecc388853c7ea6a78d4d78b3ea6cd2634b | 37a5bbfc858c5cfaffd6483cfeaf4a9657ada68e7a60afc847feeaf393e4509a |
cat-searcher/leandojo-benchmark-4-random | test | 256 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨b1, b2⟩ h | case i_surj
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
⊢ ∀ (x : ℕ × ℕ),
x.1 * x.2 = m * n ∧ ¬m * n = 0 →
∃ x_1,
((x_1.1.1 * x_1.1.2 = m ∧ ¬m = 0) ∧ x_1.2.1 * x_1.2.2 = n ∧ ¬n = 0) ∧ (x_1.1.1 * x_1.2.1, x_1.1.... | case i_surj.mk
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
b1 b2 : ℕ
h : (b1, b2).1 * (b1, b2).2 = m * n ∧ ¬m * n = 0
⊢ ∃ x, ((x.1.1 * x.1.2 = m ∧ ¬m = 0) ∧ x.2.1 * x.2.2 = n ∧ ¬n = 0) ∧ (x.1.1 * x.2.1, x.1.2 * x.2.2) = (b1, b2... | (:forall x ((:c Prod) (:c Nat) (:c Nat)) (:forall _ ((:c And) ((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) ((:c Prod.fst) (:c Nat) (:c Nat) 0) ((:c Prod.snd) (:c Nat) (:c Nat) 0)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat))... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:forall x :explicit (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat))) (:forall _ :explicit (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"rintro","sourceEnd":28021,"sourceStart":28015,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":28025,"sourceStart":28022,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"b1","sourceEnd":28027,"so... | [{"role":"fresh_name","source":"b1","source_end":28027,"source_start":28025,"syntax_kind":"ident"},{"role":"fresh_name","source":"b2","source_end":28031,"source_start":28029,"syntax_kind":"ident"},{"role":"fresh_name","source":"h","source_end":28036,"source_start":28035,"syntax_kind":"ident"}] | [{"source":"⟨b1, b2⟩","source_end":28034,"source_start":28022,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 175 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9abdf65d2d1864c7c996a94cea42a706943d5e601552c65f1118a25bf052dbd5 | 37a5bbfc858c5cfaffd6483cfeaf4a9657ada68e7a60afc847feeaf393e4509a | a610b7bf49cef65238da8ab6b7fc5301f076cebecf07cf64fd43b9bec2a9fbe9 | c6977a9d0fd548941b5322096f86927776fb04418262ec7b97506be5e2821354 |
cat-searcher/leandojo-benchmark-4-random | test | 257 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp at h | case i_surj.mk
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
b1 b2 : ℕ
h : (b1, b2).1 * (b1, b2).2 = m * n ∧ ¬m * n = 0
⊢ ∃ x, ((x.1.1 * x.1.2 = m ∧ ¬m = 0) ∧ x.2.1 * x.2.2 = n ∧ ¬n = 0) ∧ (x.1.1 * x.2.1, x.1.2 * x.2.2) = (b1, b2... | case i_surj.mk
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
b1 b2 : ℕ
h : b1 * b2 = m * n ∧ ¬m * n = 0
⊢ ∃ x, ((x.1.1 * x.1.2 = m ∧ ¬m = 0) ∧ x.2.1 * x.2.2 = n ∧ ¬n = 0) ∧ (x.1.1 * x.2.1, x.1.2 * x.2.2) = (b1, b2) | ((:c Exists) ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) (:lambda x ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) ((:c And) ((:c And) ((:c And) ((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) ((:c Prod.fst) (:c N... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))))) (:arg :explicit 1 (:lambda x :explicit (:app (:c Prod) (:arg :explicit 0 (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"dsimp","sourceEnd":28046,"sourceStart":28041,"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":[{"ch... | [] | [{"source":"h","source_end":28051,"source_start":28050,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 176 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fc3c4d3a21b6543f8767f83548abffefc5c9ed7237fc8f290f979f551962ca56 | c6977a9d0fd548941b5322096f86927776fb04418262ec7b97506be5e2821354 | 77a3f35897bdf6b787da21ef08ddf8dafef80050e286f9c04243531c1e998d85 | a7024c3286e156f339e30ec7bfa87e0f1a42d6e61c8b48b48c096ecfff9fc654 |
cat-searcher/leandojo-benchmark-4-random | test | 258 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | use ((b1.gcd m, b2.gcd m), (b1.gcd n, b2.gcd n)) | case i_surj.mk
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
b1 b2 : ℕ
h : b1 * b2 = m * n ∧ ¬m * n = 0
⊢ ∃ x, ((x.1.1 * x.1.2 = m ∧ ¬m = 0) ∧ x.2.1 * x.2.2 = n ∧ ¬n = 0) ∧ (x.1.1 * x.2.1, x.1.2 * x.2.2) = (b1, b2) | case h
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
b1 b2 : ℕ
h : b1 * b2 = m * n ∧ ¬m * n = 0
⊢ ((((b1.gcd m, b2.gcd m), b1.gcd n, b2.gcd n).1.1 * ((b1.gcd m, b2.gcd m), b1.gcd n, b2.gcd n).1.2 = m ∧ ¬m = 0) ∧
((b1.gcd m,... | ((:c Exists) ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) (:lambda x ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) ((:c And) ((:c And) ((:c And) ((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) ((:c Prod.fst) (:c N... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))))) (:arg :explicit 1 (:lambda x :explicit (:app (:c Prod) (:arg :explicit 0 (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"use","sourceEnd":28059,"sourceStart":28056,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"children":[{"source":"(","sourceEnd":28061,"sourceStart":28060,"tag":"atom"},{"children":[{"children":[{"source":... | [] | [{"source":"((b1.gcd m, b2.gcd m), (b1.gcd n, b2.gcd n))","source_end":28104,"source_start":28060,"syntax_kind":"Lean.Parser.Term.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 177 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ae0711e8777690d10b2610e2d9c97126776ffddcce9097a115ab4c2075b18872 | a7024c3286e156f339e30ec7bfa87e0f1a42d6e61c8b48b48c096ecfff9fc654 | edea50e09f792a987eae27b983109eefaefad65d4cbb6180e292222b51da349f | 4dfecb310ffdaa788321859fae6f0cbe66ab8c93bed67c0be5cee2d92abf816e |
cat-searcher/leandojo-benchmark-4-random | test | 259 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← cop.gcd_mul _, ← cop.gcd_mul _, ← h.1, <a>Nat.gcd_mul_gcd_of_coprime_of_mul_eq_mul</a> cop h.1, <a>Nat.gcd_mul_gcd_of_coprime_of_mul_eq_mul</a> cop.symm _] | case h
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
b1 b2 : ℕ
h : b1 * b2 = m * n ∧ ¬m * n = 0
⊢ ((((b1.gcd m, b2.gcd m), b1.gcd n, b2.gcd n).1.1 * ((b1.gcd m, b2.gcd m), b1.gcd n, b2.gcd n).1.2 = m ∧ ¬m = 0) ∧
((b1.gcd m,... | case h
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
b1 b2 : ℕ
h : b1 * b2 = m * n ∧ ¬m * n = 0
⊢ ((m = m ∧ ¬m = 0) ∧ n = n ∧ ¬n = 0) ∧ (b1.gcd (b1 * b2), b2.gcd (b1 * b2)) = (b1, b2)
R : Type u_1
inst✝ : CommSemiring R
f g : Ari... | ((:c And) ((:c And) ((:c And) ((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) ((:c Prod.fst) (:c Nat) (:c Nat) ((:c Prod.fst) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod.mk) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat)) ((:c P... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c And) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"rw","sourceEnd":28111,"sourceStart":28109,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28113,"sourceStart":28112,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":28116,"sourceSt... | [] | [{"source":"cop.gcd_mul _","source_end":28130,"source_start":28117,"syntax_kind":"Lean.Parser.Term.app"},{"source":"cop.gcd_mul _","source_end":28149,"source_start":28136,"syntax_kind":"Lean.Parser.Term.app"},{"source":"h.1","source_end":28158,"source_start":28155,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"Nat.g... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 178 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a7f478219dcf48c4a06bb2964e9bd16b3b9b5085933fc84b92012701d9a7b0dc | 4dfecb310ffdaa788321859fae6f0cbe66ab8c93bed67c0be5cee2d92abf816e | d20e61d6d8bf77c42fe65f32aa19b701bea5f77cf90d0aacec8498de1a369a4f | 0eb669873c7783805df3cc7de4b548aae5d89a2033683a01cd052fda896369ac |
cat-searcher/leandojo-benchmark-4-random | test | 260 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>mul_comm</a> n m, h.1] | R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
b1 b2 : ℕ
h : b1 * b2 = m * n ∧ ¬m * n = 0
⊢ b1 * b2 = n * m | ((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.320753) (:fv _uniq.320754)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.314627) (:fv _uniq.314624))) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HMul.hMul) (: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 HMul) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"rw","sourceEnd":28342,"sourceStart":28340,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28344,"sourceStart":28343,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"mul... | [] | [{"source":"mul_comm n m","source_end":28356,"source_start":28344,"syntax_kind":"Lean.Parser.Term.app"},{"source":"h.1","source_end":28361,"source_start":28358,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 194 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2db71c11dc4f915d8990adba2028d6bd5fa88c91b134051d5a408a280a7a2133 | c15778a6f91c2b474e7ecff1622dad162abced6cb54ea269a06ab3ab6bbf1a70 | b0644a721fed52b2421d97b7741f7c24f7dab995801da866481d40cc023feca1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 261 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Nat.mul_eq_zero</a>, <a>not_or</a>] at h | case h
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
b1 b2 : ℕ
h : b1 * b2 = m * n ∧ ¬m * n = 0
⊢ ((m = m ∧ ¬m = 0) ∧ n = n ∧ ¬n = 0) ∧ (b1.gcd (b1 * b2), b2.gcd (b1 * b2)) = (b1, b2) | case h
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
b1 b2 : ℕ
h : b1 * b2 = m * n ∧ ¬m = 0 ∧ ¬n = 0
⊢ ((m = m ∧ ¬m = 0) ∧ n = n ∧ ¬n = 0) ∧ (b1.gcd (b1 * b2), b2.gcd (b1 * b2)) = (b1, b2) | ((:c And) ((:c And) ((:c And) ((:c Eq) (:c Nat) (:fv _uniq.314624) (:fv _uniq.314624)) ((:c Not) ((:c Eq) (:c Nat) (:fv _uniq.314624) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))))) ((:c And) ((:c Eq) (:c Nat) (:fv _uniq.314627) (:fv _uniq.314627)) ((:c Not) ((:c Eq) (:c Nat) (:fv _uniq.314627) ((:... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c And) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:fv FV7)))) (:arg :explicit 1 (:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"rw","sourceEnd":28278,"sourceStart":28276,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28280,"sourceStart":28279,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Nat.mul_eq_zero"... | [] | [{"source":"Nat.mul_eq_zero","source_end":28295,"source_start":28280,"syntax_kind":"ident"},{"source":"h","source_end":28309,"source_start":28308,"syntax_kind":"ident"},{"source":"not_or","source_end":28303,"source_start":28297,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 189 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5970e2b93a610bf6260dc70463b2b51d3f3159363623787753f9178afd1409a9 | 3d5169d8e028e24ed13e09875de51ae4ae120985c230e0f8ecaa972a03012372 | 8dc78afdf39cba64fcca20fdafa865bca7f3f9dea3d7a3c158427fe4fc45e7e2 | 5bfe36cea59d280c7dfd815bbf307b02a7f1f49f29c0dc33f411f163fc770bf5 |
cat-searcher/leandojo-benchmark-4-random | test | 262 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [h.2.1, h.2.2] | case h
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
b1 b2 : ℕ
h : b1 * b2 = m * n ∧ ¬m = 0 ∧ ¬n = 0
⊢ ((m = m ∧ ¬m = 0) ∧ n = n ∧ ¬n = 0) ∧ (b1.gcd (b1 * b2), b2.gcd (b1 * b2)) = (b1, b2) | ((:c And) ((:c And) ((:c And) ((:c Eq) (:c Nat) (:fv _uniq.314624) (:fv _uniq.314624)) ((:c Not) ((:c Eq) (:c Nat) (:fv _uniq.314624) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))))) ((:c And) ((:c Eq) (:c Nat) (:fv _uniq.314627) (:fv _uniq.314627)) ((:c Not) ((:c Eq) (:c Nat) (:fv _uniq.314627) ((:... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:app (:c And) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:fv FV7)))) (:arg :explicit 1 (:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"simp","sourceEnd":28320,"sourceStart":28316,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28322,"sourceStart":28321,"tag":"a... | [] | [{"source":"h.2.1","source_end":28327,"source_start":28322,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"h.2.2","source_end":28334,"source_start":28329,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 193 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7c64d24371a8df92b0c20b10a7a6fce8bccbffbe1594d0ca88ae6500e2706463 | 5bfe36cea59d280c7dfd815bbf307b02a7f1f49f29c0dc33f411f163fc770bf5 | bc0fd1e97f42431ab838c6b268e1332dcc99244e697d44eed34f3d32e184dab1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 263 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Nat.mem_divisorsAntidiagonal</a>, <a>Ne</a>, <a>Finset.mem_product</a>] | case h
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
⊢ ∀ a ∈ m.divisorsAntidiagonal ×ˢ n.divisorsAntidiagonal,
f a.1.1 * g a.1.2 * (f a.2.1 * g a.2.2) =
f
(match a with
| ((i, j), k, l) => (i * k, ... | case h
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
⊢ ∀ (a : (ℕ × ℕ) × ℕ × ℕ),
(a.1.1 * a.1.2 = m ∧ ¬m = 0) ∧ a.2.1 * a.2.2 = n ∧ ¬n = 0 →
f a.1.1 * g a.1.2 * (f a.2.1 * g a.2.2) = f (a.1.1 * a.2.1) * g (a.1.2 * a.2.2) | (:forall a ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) (:forall _ ((:c Membership.mem) ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) ((:c Finset) ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat)))) ((:c Finset.instMembership) ((:c Prod) ((:c Pro... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:forall a :explicit (:app (:c Prod) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat))))) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"simp","sourceEnd":28372,"sourceStart":28368,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":28377,"sourceStart":28373,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":283... | [] | [{"source":"mem_divisorsAntidiagonal","source_end":28403,"source_start":28379,"syntax_kind":"ident"},{"source":"Ne","source_end":28407,"source_start":28405,"syntax_kind":"ident"},{"source":"mem_product","source_end":28420,"source_start":28409,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 202 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e9da492a29d7e42e4fd4e192d9bcb7be7eba916480b5efba1aa3ce3843ddd4ab | 4dbdfc95a493663387f75215751c578d6c581ed81082d58adebde6187935dca3 | 851d41f8b956c726ff056265397dc1d2eb7482189f0d94f9292af364236f797f | cbcf9785a33501e7e875306d49d29ea589784023bf33964523ddfa3e693b15cc |
cat-searcher/leandojo-benchmark-4-random | test | 264 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨⟨a1, a2⟩, ⟨b1, b2⟩⟩ ⟨⟨rfl, ha⟩, ⟨rfl, hb⟩⟩ | case h
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
m n : ℕ
cop : m.Coprime n
⊢ ∀ (a : (ℕ × ℕ) × ℕ × ℕ),
(a.1.1 * a.1.2 = m ∧ ¬m = 0) ∧ a.2.1 * a.2.2 = n ∧ ¬n = 0 →
f a.1.1 * g a.1.2 * (f a.2.1 * g a.2.2) = f (a.1.1 * a.2.1) * g (a.1.2 * a.2.2) | case h.mk.mk.mk.intro.intro.intro
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), ... | (:forall a ((:c Prod) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Nat))) (:forall _ ((:c And) ((:c And) ((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) ((:c Prod.fst) (:c Nat) (:c Nat) ((:c Prod.fst) ((:c Prod) (:c Nat) (:c Nat)) ((:c Prod) (:c Nat) (:c Na... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (:forall a :explicit (:app (:c Prod) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat))))) (:forall _ :explicit (:app (:c And) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c E... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"rintro","sourceEnd":28432,"sourceStart":28426,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":28436,"sourceStart":28433,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":28439,"sourceStart":28436,"tag":"atom"},... | [{"role":"fresh_name","source":"a1","source_end":28441,"source_start":28439,"syntax_kind":"ident"},{"role":"fresh_name","source":"a2","source_end":28445,"source_start":28443,"syntax_kind":"ident"},{"role":"fresh_name","source":"b1","source_end":28455,"source_start":28453,"syntax_kind":"ident"},{"role":"fresh_name","sou... | [{"source":"⟨⟨a1, a2⟩, ⟨b1, b2⟩⟩","source_end":28465,"source_start":28433,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"},{"source":"⟨⟨rfl, ha⟩, ⟨rfl, hb⟩⟩","source_end":28500,"source_start":28466,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 203 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4f28e83f966d34e39edfc019c312575ca437544ce36ea795c88d86a4febcbd7b | cbcf9785a33501e7e875306d49d29ea589784023bf33964523ddfa3e693b15cc | 6bfb85263e69f7db8479fec4869522d7ee2cf869a2dc8ca1fd1d4172f4b4cac5 | 5a57f50a1b63d30bfe5cb5a9e08c09a45087f56c05d8af86c629bed8a7e79e47 |
cat-searcher/leandojo-benchmark-4-random | test | 265 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp only | case h.mk.mk.mk.intro.intro.intro
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), ... | case h.mk.mk.mk.intro.intro.intro
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), ... | ((:c Eq) (:fv _uniq.310078) ((:c HMul.hMul) (:fv _uniq.310078) (:fv _uniq.310078) (:fv _uniq.310078) ((:c instHMul) (:fv _uniq.310078) ((:c NonUnitalNonAssocSemiring.toMul) (:fv _uniq.310078) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.310078) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.310078) ((:c ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (: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.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"dsimp","sourceEnd":28510,"sourceStart":28505,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":28515,"sourceStart":28511,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":28... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 204 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | df24e0fef6e64ad7e23824f654b7a4519d040857b45a7222b134b49bf4859622 | 5a57f50a1b63d30bfe5cb5a9e08c09a45087f56c05d8af86c629bed8a7e79e47 | a4e0c85d6bda4413b7728099944a8f316bd66db76d368a5fb7af15b2a8905273 | 0af98387ad1f17d95779bfbcc2c5d5fec654a2805cbe6292d898b94724913c13 |
cat-searcher/leandojo-benchmark-4-random | test | 266 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hf.map_mul_of_coprime cop.coprime_mul_right.coprime_mul_right_right, hg.map_mul_of_coprime cop.coprime_mul_left.coprime_mul_left_right] | case h.mk.mk.mk.intro.intro.intro
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), ... | case h.mk.mk.mk.intro.intro.intro
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), ... | ((:c Eq) (:fv _uniq.310078) ((:c HMul.hMul) (:fv _uniq.310078) (:fv _uniq.310078) (:fv _uniq.310078) ((:c instHMul) (:fv _uniq.310078) ((:c NonUnitalNonAssocSemiring.toMul) (:fv _uniq.310078) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.310078) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.310078) ((:c ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (: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.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"rw","sourceEnd":28522,"sourceStart":28520,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28524,"sourceStart":28523,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"h... | [] | [{"source":"hf.map_mul_of_coprime cop.coprime_mul_right.coprime_mul_right_right","source_end":28591,"source_start":28524,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hg.map_mul_of_coprime cop.coprime_mul_left.coprime_mul_left_right","source_end":28664,"source_start":28599,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 205 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 832931d9ed38909ddf90dce42c33e22a99410504fad7a1bb970e61617ea5cc83 | 0af98387ad1f17d95779bfbcc2c5d5fec654a2805cbe6292d898b94724913c13 | 91c06bed0e60685666f67183cbaf97cc906bcaf6b5c5edc952ac6ebb9f3d51d1 | 388761a81b08d541783a699c007b298f3325573410203992213cf1259ea335a6 |
cat-searcher/leandojo-benchmark-4-random | test | 267 | ArithmeticFunction.IsMultiplicative.mul | Mathlib/NumberTheory/ArithmeticFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | case h.mk.mk.mk.intro.intro.intro
R : Type u_1
inst✝ : CommSemiring R
f g : ArithmeticFunction R
hf : f.IsMultiplicative
hg : g.IsMultiplicative
a1 a2 b1 b2 : ℕ
ha : ¬((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 = 0
cop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), ... | ((:c Eq) (:fv _uniq.310078) ((:c HMul.hMul) (:fv _uniq.310078) (:fv _uniq.310078) (:fv _uniq.310078) ((:c instHMul) (:fv _uniq.310078) ((:c NonUnitalNonAssocSemiring.toMul) (:fv _uniq.310078) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.310078) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.310078) ((:c ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.310078))"},{"name":"f","sexp":"((:c ArithmeticFunction) (:fv _uniq.310078) ((:c CommMonoidWithZero.toZero) (:fv _uniq.310078) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.310078) (:fv _uniq.310718))))"},{"name":"g","sex... | (: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.310078","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommSemiring) (:arg :e... | {"children":[{"source":"ring","sourceEnd":28674,"sourceStart":28670,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":28674,"sourceStart":28670,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.310078","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.310718","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 184 | 209 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5b7ea7c751d03f8f522bf7a9f5cb2642a0dc79019e051356ae88c7aed5794ea6 | 388761a81b08d541783a699c007b298f3325573410203992213cf1259ea335a6 | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 268 | LinearMap.range_inl | Mathlib/LinearAlgebra/Prod.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext x | R : Type u
K : Type u'
M : Type v
V : Type v'
M₂ : Type w
V₂ : Type w'
M₃ : Type y
V₃ : Type y'
M₄ : Type z
ι : Type x
M₅ : Type u_1
M₆ : Type u_2
S : Type u_3
inst✝¹³ : Semiring R
inst✝¹² : Semiring S
inst✝¹¹ : AddCommMonoid M
inst✝¹⁰ : AddCommMonoid M₂
inst✝⁹ : AddCommMonoid M₃
inst✝⁸ : AddCommMonoid M₄
inst✝⁷ : AddC... | case h
R : Type u
K : Type u'
M : Type v
V : Type v'
M₂ : Type w
V₂ : Type w'
M₃ : Type y
V₃ : Type y'
M₄ : Type z
ι : Type x
M₅ : Type u_1
M₆ : Type u_2
S : Type u_3
inst✝¹³ : Semiring R
inst✝¹² : Semiring S
inst✝¹¹ : AddCommMonoid M
inst✝¹⁰ : AddCommMonoid M₂
inst✝⁹ : AddCommMonoid M₃
inst✝⁸ : AddCommMonoid M₄
inst✝⁷... | ((:c Eq) ((:c Submodule) (:fv _uniq.29124) ((:c Prod) (:fv _uniq.29128) (:fv _uniq.29132)) (:fv _uniq.29154) ((:c Prod.instAddCommMonoid) (:fv _uniq.29128) (:fv _uniq.29132) (:fv _uniq.29160) (:fv _uniq.29163)) ((:c Prod.instModule) (:fv _uniq.29124) (:fv _uniq.29128) (:fv _uniq.29132) (:fv _uniq.29154) (:fv _uniq.2916... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"K","sexp":"(:sort (+ u' 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"V","sexp":"(:sort (+ v' 1))"},{"name":"M₂","sexp":"(:sort (+ w 1))"},{"name":"V₂","sexp":"(:sort (+ w' 1))"},{"name":"M₃","sexp":"(:sort (+ y 1))"},{"name":"V₃","sexp":"(:sort (+ y' 1))"},{"name"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV4)))) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29124","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29126","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","con... | {"children":[{"source":"ext","sourceEnd":4839,"sourceStart":4836,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":4841,"sourceStart":4840,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":4841,"sourceStart":4840,"tag":"nod... | [{"role":"fresh_name","source":"x","source_end":4841,"source_start":4840,"syntax_kind":"ident"}] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29124","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29126","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":2,"internal_name":"_un... | 48 | 4 | exact | true | 1 | 28 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7baa0f709376fdeddb1a63dd808c21b2b6cb1908623940412bcb8a02003f9e9b | afd0995bbeb0e985738ce050ce27f4ca69a9de15a05f13fbc6c7ba8899038263 | ee522618587c4a8062e9541e92fad69d5c6e7dbdf5366e9d82c63ebe3c1e08c5 | 745f7e38d8777888877759110e1c444dc27c6fb2464177018b62954813a81b43 |
cat-searcher/leandojo-benchmark-4-random | test | 269 | LinearMap.range_inl | Mathlib/LinearAlgebra/Prod.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>LinearMap.mem_ker</a>, <a>LinearMap.mem_range</a>] | case h
R : Type u
K : Type u'
M : Type v
V : Type v'
M₂ : Type w
V₂ : Type w'
M₃ : Type y
V₃ : Type y'
M₄ : Type z
ι : Type x
M₅ : Type u_1
M₆ : Type u_2
S : Type u_3
inst✝¹³ : Semiring R
inst✝¹² : Semiring S
inst✝¹¹ : AddCommMonoid M
inst✝¹⁰ : AddCommMonoid M₂
inst✝⁹ : AddCommMonoid M₃
inst✝⁸ : AddCommMonoid M₄
inst✝⁷... | case h
R : Type u
K : Type u'
M : Type v
V : Type v'
M₂ : Type w
V₂ : Type w'
M₃ : Type y
V₃ : Type y'
M₄ : Type z
ι : Type x
M₅ : Type u_1
M₆ : Type u_2
S : Type u_3
inst✝¹³ : Semiring R
inst✝¹² : Semiring S
inst✝¹¹ : AddCommMonoid M
inst✝¹⁰ : AddCommMonoid M₂
inst✝⁹ : AddCommMonoid M₃
inst✝⁸ : AddCommMonoid M₄
inst✝⁷... | ((:c Iff) ((:c Membership.mem) ((:c Prod) (:fv _uniq.29128) (:fv _uniq.29132)) ((:c Submodule) (:fv _uniq.29124) ((:c Prod) (:fv _uniq.29128) (:fv _uniq.29132)) (:fv _uniq.29154) ((:c Prod.instAddCommMonoid) (:fv _uniq.29128) (:fv _uniq.29132) (:fv _uniq.29160) (:fv _uniq.29163)) ((:c Prod.instModule) (:fv _uniq.29124)... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"K","sexp":"(:sort (+ u' 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"V","sexp":"(:sort (+ v' 1))"},{"name":"M₂","sexp":"(:sort (+ w 1))"},{"name":"V₂","sexp":"(:sort (+ w' 1))"},{"name":"M₃","sexp":"(:sort (+ y 1))"},{"name":"V₃","sexp":"(:sort (+ y' 1))"},{"name"... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV4)))) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV4... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29124","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29126","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","con... | {"children":[{"source":"simp","sourceEnd":4848,"sourceStart":4844,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":4853,"sourceStart":4849,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":4853,"s... | [] | [{"source":"mem_ker","source_end":4862,"source_start":4855,"syntax_kind":"ident"},{"source":"mem_range","source_end":4873,"source_start":4864,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29124","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29126","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":2,"internal_name":"_un... | 48 | 5 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5f43d1eb0db9a4897d76511fb4b8c5e9cd1c7dcdd8acbd3ce51646db44fa48ac | 745f7e38d8777888877759110e1c444dc27c6fb2464177018b62954813a81b43 | b2f64949e5456949dc2b36d6d0d4f38f25db1fa5f94f6b329e89206b88883d86 | 9cf6a4aa561af8e56f85d0e72e8d3c12a5b43384c1b49e5111ec26ab104b7635 |
cat-searcher/leandojo-benchmark-4-random | test | 270 | LinearMap.range_inl | Mathlib/LinearAlgebra/Prod.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | case h
R : Type u
K : Type u'
M : Type v
V : Type v'
M₂ : Type w
V₂ : Type w'
M₃ : Type y
V₃ : Type y'
M₄ : Type z
ι : Type x
M₅ : Type u_1
M₆ : Type u_2
S : Type u_3
inst✝¹³ : Semiring R
inst✝¹² : Semiring S
inst✝¹¹ : AddCommMonoid M
inst✝¹⁰ : AddCommMonoid M₂
inst✝⁹ : AddCommMonoid M₃
inst✝⁸ : AddCommMonoid M₄
inst✝⁷... | case h.mp
R : Type u
K : Type u'
M : Type v
V : Type v'
M₂ : Type w
V₂ : Type w'
M₃ : Type y
V₃ : Type y'
M₄ : Type z
ι : Type x
M₅ : Type u_1
M₆ : Type u_2
S : Type u_3
inst✝¹³ : Semiring R
inst✝¹² : Semiring S
inst✝¹¹ : AddCommMonoid M
inst✝¹⁰ : AddCommMonoid M₂
inst✝⁹ : AddCommMonoid M₃
inst✝⁸ : AddCommMonoid M₄
ins... | ((:c Iff) ((:c Exists) (:fv _uniq.29128) (:lambda y (:fv _uniq.29128) ((:c Eq) ((:c Prod) (:fv _uniq.29128) (:fv _uniq.29132)) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.29124) (:fv _uniq.29124) (:fv _uniq.29154) (:fv _uniq.29154) ((:c RingHom.id) (:fv _uniq.29124) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.29124)... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"K","sexp":"(:sort (+ u' 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"V","sexp":"(:sort (+ v' 1))"},{"name":"M₂","sexp":"(:sort (+ w 1))"},{"name":"V₂","sexp":"(:sort (+ w' 1))"},{"name":"M₃","sexp":"(:sort (+ y 1))"},{"name":"V₃","sexp":"(:sort (+ y' 1))"},{"name"... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Exists) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda y :explicit (:fv FV2) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV4)))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29124","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29126","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","con... | {"children":[{"source":"constructor","sourceEnd":4888,"sourceStart":4877,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":4888,"sourceStart":4877,"tag":"node"} | [] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29124","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29126","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":2,"internal_name":"_un... | 48 | 6 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d63c8e4378037f86422623256223e1fe25517a46683d3ccd0bebd700f4fb6e1e | 9cf6a4aa561af8e56f85d0e72e8d3c12a5b43384c1b49e5111ec26ab104b7635 | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | 951c305caac71de12dc3d2ad61ff4a1a68bfb1cd08d0881dd24dfb04cddee562 |
cat-searcher/leandojo-benchmark-4-random | test | 271 | LinearMap.range_inl | Mathlib/LinearAlgebra/Prod.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨y, rfl⟩ | case h.mp
R : Type u
K : Type u'
M : Type v
V : Type v'
M₂ : Type w
V₂ : Type w'
M₃ : Type y
V₃ : Type y'
M₄ : Type z
ι : Type x
M₅ : Type u_1
M₆ : Type u_2
S : Type u_3
inst✝¹³ : Semiring R
inst✝¹² : Semiring S
inst✝¹¹ : AddCommMonoid M
inst✝¹⁰ : AddCommMonoid M₂
inst✝⁹ : AddCommMonoid M₃
inst✝⁸ : AddCommMonoid M₄
ins... | case h.mp.intro
R : Type u
K : Type u'
M : Type v
V : Type v'
M₂ : Type w
V₂ : Type w'
M₃ : Type y
V₃ : Type y'
M₄ : Type z
ι : Type x
M₅ : Type u_1
M₆ : Type u_2
S : Type u_3
inst✝¹³ : Semiring R
inst✝¹² : Semiring S
inst✝¹¹ : AddCommMonoid M
inst✝¹⁰ : AddCommMonoid M₂
inst✝⁹ : AddCommMonoid M₃
inst✝⁸ : AddCommMonoid ... | (:forall _ ((:c Exists) (:fv _uniq.29128) (:lambda y (:fv _uniq.29128) ((:c Eq) ((:c Prod) (:fv _uniq.29128) (:fv _uniq.29132)) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.29124) (:fv _uniq.29124) (:fv _uniq.29154) (:fv _uniq.29154) ((:c RingHom.id) (:fv _uniq.29124) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.29124... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"K","sexp":"(:sort (+ u' 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"V","sexp":"(:sort (+ v' 1))"},{"name":"M₂","sexp":"(:sort (+ w 1))"},{"name":"V₂","sexp":"(:sort (+ w' 1))"},{"name":"M₃","sexp":"(:sort (+ y 1))"},{"name":"V₃","sexp":"(:sort (+ y' 1))"},{"name"... | (:forall _ :explicit (:app (:c Exists) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda y :explicit (:fv FV2) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV4)))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap)... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29124","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29126","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","con... | {"children":[{"source":"rintro","sourceEnd":4900,"sourceStart":4894,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":4904,"sourceStart":4901,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":4905,"sourceSt... | [{"role":"fresh_name","source":"y","source_end":4905,"source_start":4904,"syntax_kind":"ident"}] | [{"source":"⟨y, rfl⟩","source_end":4913,"source_start":4901,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29124","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29126","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":2,"internal_name":"_un... | 48 | 11 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fb016749e74a2ce4d9d25a4d5cb79b5c518a4d71c3b3fdad57729f8b519f093a | 1d422a770261362bb88020c20f43125098266b7148ece45c3c3a2ee0f4484c2e | f8e70510d1e10f6e294735ec5506753ca0c17491b8ace5591037eec2acc7844b | 20627f9a36beb10a43ba0d6c41cf7297678801b9089f7c77a497ce9912f7eb5a |
cat-searcher/leandojo-benchmark-4-random | test | 272 | LinearMap.range_inl | Mathlib/LinearAlgebra/Prod.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case h.mp.intro
R : Type u
K : Type u'
M : Type v
V : Type v'
M₂ : Type w
V₂ : Type w'
M₃ : Type y
V₃ : Type y'
M₄ : Type z
ι : Type x
M₅ : Type u_1
M₆ : Type u_2
S : Type u_3
inst✝¹³ : Semiring R
inst✝¹² : Semiring S
inst✝¹¹ : AddCommMonoid M
inst✝¹⁰ : AddCommMonoid M₂
inst✝⁹ : AddCommMonoid M₃
inst✝⁸ : AddCommMonoid ... | ((:c Eq) (:fv _uniq.29132) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.29124) (:fv _uniq.29124) (:fv _uniq.29154) (:fv _uniq.29154) ((:c RingHom.id) (:fv _uniq.29124) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.29124) (:fv _uniq.29154))) ((:c Prod) (:fv _uniq.29128) (:fv _uniq.29132)) (:fv _uniq.29132) ((:c Prod.ins... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"K","sexp":"(:sort (+ u' 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"V","sexp":"(:sort (+ v' 1))"},{"name":"M₂","sexp":"(:sort (+ w 1))"},{"name":"V₂","sexp":"(:sort (+ w' 1))"},{"name":"M₃","sexp":"(:sort (+ y 1))"},{"name":"V₃","sexp":"(:sort (+ y' 1))"},{"name"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29124","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29126","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","con... | {"children":[{"source":"rfl","sourceEnd":4921,"sourceStart":4918,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":4921,"sourceStart":4918,"tag":"node"} | [] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29124","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29126","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":2,"internal_name":"_un... | 48 | 12 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1323c34151192b839c1cad9c38ae9eb8a09a87dd348d099a0995889dd7bdc547 | 20627f9a36beb10a43ba0d6c41cf7297678801b9089f7c77a497ce9912f7eb5a | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 273 | LinearMap.range_inl | Mathlib/LinearAlgebra/Prod.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro h | case h.mpr
R : Type u
K : Type u'
M : Type v
V : Type v'
M₂ : Type w
V₂ : Type w'
M₃ : Type y
V₃ : Type y'
M₄ : Type z
ι : Type x
M₅ : Type u_1
M₆ : Type u_2
S : Type u_3
inst✝¹³ : Semiring R
inst✝¹² : Semiring S
inst✝¹¹ : AddCommMonoid M
inst✝¹⁰ : AddCommMonoid M₂
inst✝⁹ : AddCommMonoid M₃
inst✝⁸ : AddCommMonoid M₄
in... | case h.mpr
R : Type u
K : Type u'
M : Type v
V : Type v'
M₂ : Type w
V₂ : Type w'
M₃ : Type y
V₃ : Type y'
M₄ : Type z
ι : Type x
M₅ : Type u_1
M₆ : Type u_2
S : Type u_3
inst✝¹³ : Semiring R
inst✝¹² : Semiring S
inst✝¹¹ : AddCommMonoid M
inst✝¹⁰ : AddCommMonoid M₂
inst✝⁹ : AddCommMonoid M₃
inst✝⁸ : AddCommMonoid M₄
in... | (:forall _ ((:c Eq) (:fv _uniq.29132) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.29124) (:fv _uniq.29124) (:fv _uniq.29154) (:fv _uniq.29154) ((:c RingHom.id) (:fv _uniq.29124) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.29124) (:fv _uniq.29154))) ((:c Prod) (:fv _uniq.29128) (:fv _uniq.29132)) (:fv _uniq.29132) ((... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"K","sexp":"(:sort (+ u' 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"V","sexp":"(:sort (+ v' 1))"},{"name":"M₂","sexp":"(:sort (+ w 1))"},{"name":"V₂","sexp":"(:sort (+ w' 1))"},{"name":"M₃","sexp":"(:sort (+ y 1))"},{"name":"V₃","sexp":"(:sort (+ y' 1))"},{"name"... | (:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instan... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29124","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29126","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","con... | {"children":[{"source":"intro","sourceEnd":4932,"sourceStart":4927,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":4934,"sourceStart":4933,"tag":"identifier"}],"kind":"null","source":"h","sourceEnd":4934,"sourceStart":4933,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source":"int... | [{"role":"fresh_name","source":"h","source_end":4934,"source_start":4933,"syntax_kind":"ident"}] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29124","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29126","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":2,"internal_name":"_un... | 48 | 17 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 01f0dfe8653f97f43ca6aa7bc2bc51b384fe8affa2e8d2f897a2800aaba2165d | 049be163c00227d86bede34ce0acc8ce2f8407923692990b0fc59f98438565a0 | 5cf42e5c5e9faf9804f4b8005e32168f3a46b38347377087a457c72b727740cb | c68e0553a0b927e59511f3d05e16364dff65a2f9403aafe881e0099704bcbab9 |
cat-searcher/leandojo-benchmark-4-random | test | 274 | LinearMap.range_inl | Mathlib/LinearAlgebra/Prod.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨x.fst, <a>Prod.ext</a> <a>rfl</a> h.symm⟩ | case h.mpr
R : Type u
K : Type u'
M : Type v
V : Type v'
M₂ : Type w
V₂ : Type w'
M₃ : Type y
V₃ : Type y'
M₄ : Type z
ι : Type x
M₅ : Type u_1
M₆ : Type u_2
S : Type u_3
inst✝¹³ : Semiring R
inst✝¹² : Semiring S
inst✝¹¹ : AddCommMonoid M
inst✝¹⁰ : AddCommMonoid M₂
inst✝⁹ : AddCommMonoid M₃
inst✝⁸ : AddCommMonoid M₄
in... | ((:c Exists) (:fv _uniq.29128) (:lambda y (:fv _uniq.29128) ((:c Eq) ((:c Prod) (:fv _uniq.29128) (:fv _uniq.29132)) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.29124) (:fv _uniq.29124) (:fv _uniq.29154) (:fv _uniq.29154) ((:c RingHom.id) (:fv _uniq.29124) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.29124) (:fv _uni... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"K","sexp":"(:sort (+ u' 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"V","sexp":"(:sort (+ v' 1))"},{"name":"M₂","sexp":"(:sort (+ w 1))"},{"name":"V₂","sexp":"(:sort (+ w' 1))"},{"name":"M₃","sexp":"(:sort (+ y 1))"},{"name":"V₃","sexp":"(:sort (+ y' 1))"},{"name"... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda y :explicit (:fv FV2) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV4)))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29124","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29126","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","con... | {"children":[{"source":"exact","sourceEnd":4944,"sourceStart":4939,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":4948,"sourceStart":4945,"tag":"atom"},{"children":[{"name":"Prod.fst","semanticRole":"global","source":"x.fst","sourceEnd":4953,"sourceStart":4948,"tag":"identifier"},{"source":",","sourceEnd":4954,"s... | [] | [{"source":"⟨x.fst, Prod.ext rfl h.symm⟩","source_end":4977,"source_start":4945,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29124","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29126","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":2,"internal_name":"_un... | 48 | 18 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3787a8ecc1ae540fc9c2e66c1d3e7e39cb6279271317b9b50d2179fd3d1d7609 | c68e0553a0b927e59511f3d05e16364dff65a2f9403aafe881e0099704bcbab9 | a9faf7c6b5040735aa33105b4ecb98bb6ed7e8d0f5a9e0346cf480f03e2aad57 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 275 | LowerSet.coe_iSup₂ | Mathlib/Order/UpperLower/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>LowerSet.coe_iSup</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
κ : ι → Sort u_5
inst✝ : LE α
S : Set (LowerSet α)
s t : LowerSet α
a : α
f : (i : ι) → κ i → LowerSet α
⊢ ↑(⨆ i, ⨆ j, f i j) = ⋃ i, ⋃ j, ↑(f i j) | ((:c Eq) ((:c Set) (:fv _uniq.606137)) ((:c SetLike.coe) ((:c LowerSet) (:fv _uniq.606137) (:fv _uniq.606154)) (:fv _uniq.606137) ((:c LowerSet.instSetLike) (:fv _uniq.606137) (:fv _uniq.606154)) ((:c iSup) ((:c LowerSet) (:fv _uniq.606137) (:fv _uniq.606154)) (:fv _uniq.606146) ((:c LowerSet.instSupSet) (:fv _uniq.606... | [{"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":"κ","sexp":"(:forall _ (:fv _uniq.606146) (:sort u_5))"},{"name":"inst✝","sexp":"((:c LE) (:fv _uniq.606137))"},{"name":"S","sexp":"((:c Set) ((:c LowerSet) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c SetLike.coe) (:arg :implicit-type 0 (:app (:c LowerSet) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV0))))))) (:arg :implicit-type 1 (:fv FV0)) (:arg :ins... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.606137","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.606140","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":28604,"sourceStart":28597,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28606,"sourceStart":28605,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source... | [] | [{"source":"coe_iSup","source_end":28614,"source_start":28606,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.606137","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.606140","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 318 | 2 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d49f1a127d647df131ce4007814302895609f8546554f31765f992b12a62dfcb | 8b1e88c55ea49346f28aa28acf6140110479c3cff55e42770b56e6f632ec5a8c | 0f33fecb245c3c62c19eb4a053510d467bd53921a1c787d08df1ec7a8248cc2f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 276 | List.kreplace_nodupKeys | Mathlib/Data/List/Sigma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>List.NodupKeys</a>, <a>List.keys_kreplace</a>] | α : Type u
β : α → Type v
l✝ l₁ l₂ : List (Sigma β)
inst✝ : DecidableEq α
a : α
b : β a
l : List (Sigma β)
⊢ (kreplace a b l).NodupKeys ↔ l.NodupKeys | ((:c Iff) ((:c List.NodupKeys) (:fv _uniq.63524) (:fv _uniq.63528) ((:c List.kreplace) (:fv _uniq.63524) (:fv _uniq.63528) (:fv _uniq.63562) (:fv _uniq.63629) (:fv _uniq.63630) (:fv _uniq.63631))) ((:c List.NodupKeys) (:fv _uniq.63524) (:fv _uniq.63528) (:fv _uniq.63631))) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:forall _ (:fv _uniq.63524) (:sort (+ v 1)))"},{"name":"l✝","sexp":"((:c List) ((:c Sigma) (:fv _uniq.63524) (:fv _uniq.63528)))"},{"name":"l₁","sexp":"((:c List) ((:c Sigma) (:fv _uniq.63524) (:fv _uniq.63528)))"},{"name":"l₂","sexp":"((:c List) ((:c Sigma) (... | (:app (:c Iff) (:arg :explicit 0 (:app (:c List.NodupKeys) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c List.kreplace) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :instance 2 (:instance-of (:app (:c DecidableEq) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 3 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.63524","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.63528","is_instance":false,"is_let":false,"name":"β","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"}... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":14654,"sourceStart":14650,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"NodupKeys","source_end":14665,"source_start":14656,"syntax_kind":"ident"},{"source":"keys_kreplace","source_end":14680,"source_start":14667,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.63524","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.63528","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 115 | 2 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8e60fb87570f3e96ea64ecea9e2bb82a8fcbc52c18a78a4bc659644624db1f05 | 514c2df7ec24fd7707c5992ad84290a06c65d2c4be249a6af86e1907e40903c0 | f1796d7f88fdcf7cb5fc739af59bf4d44de86b3e555d2cff313049619f044962 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 277 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨c₁, hc₁_mem, hc₁⟩ := R.exists_eventually_const_mul_le_r | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
⊢ ∃ c > 0, ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c * g ↑n ≤ sumTransform (p a b) g (r i n) n | case intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
⊢ ∃ c > 0, ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c * g ↑n ≤ sumTransform (p a b) g (r i... | ((:c Exists) (:c Real) (:lambda c (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c Filter.Eventually) (:c Nat) (:lambda n (:c Nat) (:forall i (:fv _uniq.672300) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (: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 0) (:arg :explicit 3 (:app (:c OfNat.of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"obtain","sourceEnd":34373,"sourceStart":34367,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":34377,"sourceStart":34374,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"c₁","sourceE... | [] | [{"source":"R.exists_eventually_const_mul_le_r","source_end":34440,"source_start":34406,"syntax_kind":"ident"},{"source":"⟨c₁, hc₁_mem, hc₁⟩","source_end":34402,"source_start":34374,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a582815cb793430cfb4ffaa464a8a7258a2fea354b94c8931b644329ffcc9a17 | caf613db43f8fd7d141c913bd52ac2d93bd418733a14743a08b7e758b5795569 | 7148b91503d2f3ce0737498474df6fbfc07dcabe3d473ffc678ef490b45b0c54 | 67c71085c9c9ff3cc1971eb6c58c40f6078c66363bf8b25dfb6938a561905771 |
cat-searcher/leandojo-benchmark-4-random | test | 278 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨c₂, hc₂_mem, hc₂⟩ := R.g_grows_poly.eventually_atTop_ge_nat hc₁_mem | case intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
⊢ ∃ c > 0, ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c * g ↑n ≤ sumTransform (p a b) g (r i... | case intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ ... | ((:c Exists) (:c Real) (:lambda c (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c Filter.Eventually) (:c Nat) (:lambda n (:c Nat) (:forall i (:fv _uniq.672300) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (: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 0) (:arg :explicit 3 (:app (:c OfNat.of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"obtain","sourceEnd":34449,"sourceStart":34443,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":34453,"sourceStart":34450,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"c₂","sourceE... | [] | [{"source":"R.g_grows_poly.eventually_atTop_ge_nat hc₁_mem","source_end":34530,"source_start":34482,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨c₂, hc₂_mem, hc₂⟩","source_end":34478,"source_start":34450,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 5 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a0a15dd94fd98cb4f23d15c769c1efea30d0f3550ed9d9968ad66f0e6870cf22 | 67c71085c9c9ff3cc1971eb6c58c40f6078c66363bf8b25dfb6938a561905771 | bfc357a9e6a92d508cd15e0b72845ea695ddf639c20eaf0295fb994accd58cd9 | 9cce3a811b8d042c52d5c97abe4adb93f8d83b930ab8a977ae4ff66c24f9a5a4 |
cat-searcher/leandojo-benchmark-4-random | test | 279 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨c₃, hc₃_mem, hc₃⟩ := R.exists_eventually_r_le_const_mul | case intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ ... | case intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ ... | ((:c Exists) (:c Real) (:lambda c (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c Filter.Eventually) (:c Nat) (:lambda n (:c Nat) (:forall i (:fv _uniq.672300) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (: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 0) (:arg :explicit 3 (:app (:c OfNat.of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"obtain","sourceEnd":34539,"sourceStart":34533,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":34543,"sourceStart":34540,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"c₃","sourceE... | [] | [{"source":"R.exists_eventually_r_le_const_mul","source_end":34606,"source_start":34572,"syntax_kind":"ident"},{"source":"⟨c₃, hc₃_mem, hc₃⟩","source_end":34568,"source_start":34540,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 6 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fc12a5d16fb6252427f7f9505f84b964f5b3bbc2288a40e613772aa2eb369a7b | 9cce3a811b8d042c52d5c97abe4adb93f8d83b930ab8a977ae4ff66c24f9a5a4 | 1c7d995529f72106af8514f3a94cd3b5f4d375002b5fc656254b506c62a411d5 | 1a8f972d85fb17e9af609605a500a2cc3842325d9067b53042fad0ace7c4773f |
cat-searcher/leandojo-benchmark-4-random | test | 280 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hc₁_pos : 0 < c₁ := hc₁_mem.1 | case intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ ... | case intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ ... | ((:c Exists) (:c Real) (:lambda c (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c Filter.Eventually) (:c Nat) (:lambda n (:c Nat) (:forall i (:fv _uniq.672300) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (: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 0) (:arg :explicit 3 (:app (:c OfNat.of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"have","sourceEnd":34613,"sourceStart":34609,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hc₁_pos","sourceEnd":34623,"sourceStart":34614,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hc₁_pos","sourceEnd":34623,"sourceStart":34614,... | [] | [{"source":"0 < c₁","source_end":34634,"source_start":34626,"syntax_kind":"«term_<_»"},{"source":"hc₁_mem.1","source_end":34649,"source_start":34638,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 7 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8bfd5a7bd11db53cfcac320032b517bf18d88330e8978cc178845dcebf94e562 | 1a8f972d85fb17e9af609605a500a2cc3842325d9067b53042fad0ace7c4773f | 2da89dd2d0e36dfc61fbcd7f0539a5b9f18b63065177a76b55fcfb979c4bdc86 | 2ea522ec57a2d1c626012defcb51bf008ad4e0d85806aeea205bfb7e897b070c |
cat-searcher/leandojo-benchmark-4-random | test | 281 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hc₃' : 0 < (1 - c₃) := by have := hc₃_mem.2; linarith | case intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ ... | case intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ ... | ((:c Exists) (:c Real) (:lambda c (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c Filter.Eventually) (:c Nat) (:lambda n (:c Nat) (:forall i (:fv _uniq.672300) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (: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 0) (:arg :explicit 3 (:app (:c OfNat.of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"have","sourceEnd":34656,"sourceStart":34652,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hc₃'","sourceEnd":34663,"sourceStart":34657,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hc₃'","sourceEnd":34663,"sourceStart":34657,"tag":... | [] | [{"source":"0 < (1 - c₃)","source_end":34680,"source_start":34666,"syntax_kind":"«term_<_»"},{"source":"hc₃_mem.2","source_end":34706,"source_start":34695,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 8 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 06caf0bdd5a69d842bdee0e9b5863c95384df76c4fb56baca35fcbbc534f19d5 | 2ea522ec57a2d1c626012defcb51bf008ad4e0d85806aeea205bfb7e897b070c | ea21804b1dd5ab326b1a6011946a7359c3e4fa636897e22ebc25cbf262818d07 | 80a80239cf37f4ea9b42d0c00e1923ec8d8e1781084ae2c80032a74ea28f6bc7 |
cat-searcher/leandojo-benchmark-4-random | test | 282 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨<a>Min.min</a> (c₂ * (1 - c₃)) ((1 - c₃) * c₂ / c₁^((<a>AkraBazziRecurrence.p</a> a b) + 1)), by positivity, ?_⟩ | case intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ ... | case intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ ... | ((:c Exists) (:c Real) (:lambda c (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c Filter.Eventually) (:c Nat) (:lambda n (:c Nat) (:forall i (:fv _uniq.672300) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (: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 0) (:arg :explicit 3 (:app (:c OfNat.of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"refine","sourceEnd":34725,"sourceStart":34719,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":34729,"sourceStart":34726,"tag":"atom"},{"children":[{"children":[{"name":"Min.min","semanticRole":"global","source":"min","sourceEnd":34732,"sourceStart":34729,"tag":"identifier"},{"children":[{"c... | [] | [{"source":"⟨min (c₂ * (1 - c₃)) ((1 - c₃) * c₂ / c₁^((p a b) + 1)), by positivity, ?_⟩","source_end":34815,"source_start":34726,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 13 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7832d660a2d445727b9fe3c5d67fbddba0e401754e677be5127ae294f97283b3 | 80a80239cf37f4ea9b42d0c00e1923ec8d8e1781084ae2c80032a74ea28f6bc7 | 8a7d7b1e649475bf4bd5276bbbbf2edcee135142529880f63f8a62309a057fab | 0f355a328a3aa8503b9d241e1cd7d7830fbe8ea39f991dcb9732a8c8dc14dc97 |
cat-searcher/leandojo-benchmark-4-random | test | 283 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards [hc₁, hc₂, hc₃, R.eventually_r_pos, R.eventually_r_lt_n, <a>Filter.eventually_gt_atTop</a> 0] with n hn₁ hn₂ hn₃ hrpos hr_lt_n hn_pos | case intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ ... | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ ... | ((:c Filter.Eventually) (:c Nat) (:lambda n (:c Nat) (:forall i (:fv _uniq.672300) ((: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 Min.min) (:c Real) ((:c LinearOrderedRing.toMin) (:c Real) (:c Real.instLinearOrderedRing)) ((:c HMul.h... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:forall i :explicit (:fv FV0) (: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 :impl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"filter_upwards","sourceEnd":34832,"sourceStart":34818,"tag":"atom"},{"children":[{"source":"[","sourceEnd":34834,"sourceStart":34833,"tag":"atom"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"hc₁","sourceEnd":34839,"sourceStart":34834,"tag":"identifier"},{"source":",","source... | [] | [{"source":"eventually_gt_atTop 0","source_end":34917,"source_start":34896,"syntax_kind":"Lean.Parser.Term.app"},{"source":"R.eventually_r_lt_n","source_end":34894,"source_start":34875,"syntax_kind":"ident"},{"source":"R.eventually_r_pos","source_end":34873,"source_start":34855,"syntax_kind":"ident"},{"source":"hc₃","s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 19 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7edd7ea8a91445a0dbdb9c8fe68f8dee02f2f77d634be47112207280a3af611d | 0f355a328a3aa8503b9d241e1cd7d7830fbe8ea39f991dcb9732a8c8dc14dc97 | 2d84e11fe8ae3bfed1f67a72b1df13bdc3496d018cd61482e34d1c466f3e992d | cba4e02d5a4934dec30075f33f6dc8c90f82c2a4456349fdafca9030def9f0ae |
cat-searcher/leandojo-benchmark-4-random | test | 284 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro i | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ ... | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ ... | (:forall i (:fv _uniq.672300) ((: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 Min.min) (:c Real) ((:c LinearOrderedRing.toMin) (:c Real) (:c Real.instLinearOrderedRing)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:forall i :explicit (:fv FV0) (: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 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"intro","sourceEnd":34976,"sourceStart":34971,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"i","sourceEnd":34978,"sourceStart":34977,"tag":"identifier"}],"kind":"null","source":"i","sourceEnd":34978,"sourceStart":34977,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"i","source_end":34978,"source_start":34977,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 20 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f906d42a3f318b4c5f9dd93ea59d23691414fdfaca36dfa73e4ff06b739c26a9 | cba4e02d5a4934dec30075f33f6dc8c90f82c2a4456349fdafca9030def9f0ae | dbbb5bd97a735e823e818f7e277169eb5193225c74d8cc1ad07622a04037f7c3 | 48469a4eeaa01069d78de474b65e5bfc31b5c035d3daa75d34aa0f5bf8be8f9d |
cat-searcher/leandojo-benchmark-4-random | test | 285 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hrpos_i := hrpos i | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ ... | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑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 Min.min) (:c Real) ((:c LinearOrderedRing.toMin) (:c Real) (:c Real.instLinearOrderedRing)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"have","sourceEnd":34985,"sourceStart":34981,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hrpos_i","sourceEnd":34993,"sourceStart":34986,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hrpos_i","sourceEnd":34993,"sourceStart":34986,... | [] | [{"source":"hrpos i","source_end":35004,"source_start":34997,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 21 | exact | true | 1 | 28 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b4dbcf29b84487c61d1d8dc388b7ffcf12ece0b693d431dca67274069c648771 | 48469a4eeaa01069d78de474b65e5bfc31b5c035d3daa75d34aa0f5bf8be8f9d | 8b545640ebec9d6bb2a5df5c9d083faf52be607ff1cf17e1e0925c67e0e93c8a | 5d5742f0c12f8e0b1684cba603fcbc415a96315c1011f8d8184fbd75dac82b7f |
cat-searcher/leandojo-benchmark-4-random | test | 286 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have g_nonneg : 0 ≤ g n := R.g_nonneg n (by positivity) | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ ... | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑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 Min.min) (:c Real) ((:c LinearOrderedRing.toMin) (:c Real) (:c Real.instLinearOrderedRing)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"have","sourceEnd":35011,"sourceStart":35007,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"g_nonneg","sourceEnd":35020,"sourceStart":35012,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"g_nonneg","sourceEnd":35020,"sourceStart":3501... | [] | [{"source":"0 ≤ g n","source_end":35032,"source_start":35023,"syntax_kind":"«term_≤_»"},{"source":"R.g_nonneg n (by positivity)","source_end":35064,"source_start":35036,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 22 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 27725c5a57c72da3069015a29ba7198ffb9b8efd84d075fe764823728ce5017c | 5d5742f0c12f8e0b1684cba603fcbc415a96315c1011f8d8184fbd75dac82b7f | d5a1c045b60241c5f1d33882f69c90c1d7be83fe22d682a72331c6ffd55a886a | 43b3b08859220b555a683748aa8cf8cc89664dbbb745757c6b87a9954b2ce8e6 |
cat-searcher/leandojo-benchmark-4-random | test | 287 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have := hc₃_mem.2 | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) (:fv _uniq.673438... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"have","sourceEnd":34691,"sourceStart":34687,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":34692,"sourceStart":34692,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":34692,"sourceStart":34692,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"hc₃_mem.2","source_end":34706,"source_start":34695,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 10 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fda401c3eac69f919de993af5716d4cf96662656d0927f5ebdb7da90afa7cac5 | f8d244d9c816e066b8f4a5ce2e81e85d32e7cacf28f677378b663accfd436e4c | dd196182bca2b7146f6cd4a490275aa75790f767210fe3fa516953947a035903 | 82e0f71f1b45988d2ffb90160ba1d47752efb18da7482593fe9dfc3a4cdb6de8 |
cat-searcher/leandojo-benchmark-4-random | test | 288 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) (:fv _uniq.673438... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"linarith","sourceEnd":34716,"sourceStart":34708,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 12 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 776657728ea303bc19d3f1935856a3cfd0d60008efd8138884f69beab1af6a13 | 82e0f71f1b45988d2ffb90160ba1d47752efb18da7482593fe9dfc3a4cdb6de8 | 2c587e2f140ae41533b8e0551e8c940d4f70fbd4b1f4245ea1c9efcde110c9af | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 289 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c GT.gt) (:c Real) (:c Real.instLT) ((:c Min.min) (:c Real) ((:c LinearOrderedRing.toMin) (:c Real) (:c Real.instLinearOrderedRing)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.673364) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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 Min.min) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Min) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"positivity","sourceEnd":34808,"sourceStart":34798,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":34808,"sourceStart":34798,"tag":"node"}],"kind":"null","source":"positivity","sourceEnd":34808,"sourceStart":347... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 16 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a4f4ac0727f3d45ce00216824334d084bb752fb1e1432b28f280a4978a115038 | e0620e8f2322a817f2efdcc175d58bffba6f757272e9c9876e0c00681ab52a1f | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 290 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c GE.ge) (:c Real) (:c Real.instLE) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c GE.ge) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV21)))) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"positivity","sourceEnd":35063,"sourceStart":35053,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":35063,"sourceStart":35053,"tag":"node"}],"kind":"null","source":"positivity","sourceEnd":35063,"sourceStart":350... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 25 | exact | true | 1 | 29 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f9159a52b19a6e6cca783a7a819fe4f54f73c6bf2ee404ba270748e25e716488 | dea5875d940296eb02e9e4ed7eb27502d30f36da35cbbb6b07f2947ccc01b36a | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 291 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c Eq) (:c Real) ((:c AkraBazziRecurrence.sumTransform) ((:c AkraBazziRecurrence.p) (:fv _uniq.672300) (:fv _uniq.672303) (:fv _uniq.672318) (:fv _uniq.672322)) (:fv _uniq.672314) ((:fv _uniq.672328) (:fv _uniq.685884) (:fv _uniq.685857)) (:fv _uniq.685857)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c AkraBazziRecurrence.sumTransform) (:arg :explicit 0 (:app (:c AkraBazziRecurrence.p) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Fintype) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV5)) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"rfl","sourceEnd":35276,"sourceStart":35273,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":35276,"sourceStart":35273,"tag":"node"}],"kind":"null","source":"rfl","sourceEnd":35276,"sourceStart":35273,"tag":"node"}],"kind":"Lea... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 36 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fa775aa01653609def1863f7e32cfd841865d52ddda7080639fa053c60c8020b | c8c893e581a63cd423c75c7ffff55eba9d384dc152d6d0feb40309005c5686ff | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 292 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr with u hu | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | ((:c GE.ge) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857)) ((:c AkraBazziRecurrence... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c GE.ge) (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"gcongr","sourceEnd":35397,"sourceStart":35391,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"with","sourceEnd":35402,"sourceStart":35398,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"u","sourceEnd":35404,"sourceStar... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 43 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9a678001969ca2d6ea9c511111bcf45f0fc0d20abecf75f2a75abcefc123bf1e | 34eabc5b053c2233076f5202e8a23cd6fcdde2359743d13ad9eeb1e84d8e6646 | e1ea6cbd757ecb01d4c26fae2d34b3e0eb9712d2944f09cef170e96a3fc37fb8 | 210d3135607d14fb82805fcc842d1436db91a2e8211669de54f47228736cd4a1 |
cat-searcher/leandojo-benchmark-4-random | test | 293 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.mem_Ico</a>] at hu | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | ((: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":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"rw","sourceEnd":35426,"sourceStart":35424,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":35428,"sourceStart":35427,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.mem_Ico",... | [] | [{"source":"Finset.mem_Ico","source_end":35442,"source_start":35428,"syntax_kind":"ident"},{"source":"hu","source_end":35449,"source_start":35447,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 44 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c9e4de6a118675b44fd1cd58ee12d688de25d9eb376b6247e5306ccab279b02d | 210d3135607d14fb82805fcc842d1436db91a2e8211669de54f47228736cd4a1 | e03ca1855f111f96df0ca3325cc611848b6b63c7d70640ceb137c2cbcd41fce3 | 22876da4f83392f9be0189f11291b927e6b5d5f3b71b4a4d468027356eb20d2e |
cat-searcher/leandojo-benchmark-4-random | test | 294 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hu' : u ∈ <a>Set.Icc</a> (r i n) n := ⟨hu.1, by omega⟩ | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | ((: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":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"have","sourceEnd":35470,"sourceStart":35466,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hu'","sourceEnd":35474,"sourceStart":35471,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hu'","sourceEnd":35474,"sourceStart":35471,"tag":"n... | [] | [{"source":"u ∈ Set.Icc (r i n) n","source_end":35500,"source_start":35477,"syntax_kind":"«term_∈_»"},{"source":"⟨hu.1, by omega⟩","source_end":35524,"source_start":35504,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 47 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4dd63448fb09233b742382320f8b64adc62fd436e77894e9debecbb203dc9d0d | 22876da4f83392f9be0189f11291b927e6b5d5f3b71b4a4d468027356eb20d2e | 34ee9d553bf40589f62d039cfa083e7551133cc008253c89b99e8052030099e4 | 8caaae02d31ddb75e462c28f96ec819189522dad4a508a86a06ae1419289753b |
cat-searcher/leandojo-benchmark-4-random | test | 295 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine hn₂ u ?_ | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | ((: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":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"refine","sourceEnd":35547,"sourceStart":35541,"tag":"atom"},{"children":[{"contextIndex":23,"semanticRole":"local","source":"hn₂","sourceEnd":35553,"sourceStart":35548,"tag":"identifier"},{"children":[{"contextIndex":32,"semanticRole":"local","source":"u","sourceEnd":35555,"sourceStart":35554,"t... | [] | [{"source":"hn₂ u ?_","source_end":35558,"source_start":35548,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 53 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d6a2427de36f7bcd7f8de1fd6e6190c894e88ae0b611d744213503512252e9e2 | 8caaae02d31ddb75e462c28f96ec819189522dad4a508a86a06ae1419289753b | 49a91b5362fdc92f75a9c65a12820be4cd55d1861edbadf2fc036501814b3fa7 | 2418293cfe064f45e21f88c962c23f4a8fffced353b8f93d37220b34c5b78824 |
cat-searcher/leandojo-benchmark-4-random | test | 296 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.mem_Icc</a>] | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.699044)) ((:c Set.Icc) (:c Real) (:c Real.instPreorder) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.673278) ((:c Nat.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 3 (:app (:c Nat.cast) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"rw","sourceEnd":35577,"sourceStart":35575,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":35579,"sourceStart":35578,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.mem_Icc","se... | [] | [{"source":"Set.mem_Icc","source_end":35590,"source_start":35579,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 54 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 657ecf74f927c35a339be50a395d0c763e1defb4ee9235925a010d98bf5b70e1 | 2418293cfe064f45e21f88c962c23f4a8fffced353b8f93d37220b34c5b78824 | 7860e98a80f38e7bc18c1fe77ce3f4ad43754d2b1aac472b17191699e19eba20 | 6ba0fa8c51fe3b82dfec6980b7f6abdee449ef7b5485fd7216c5c95e2dcabe3d |
cat-searcher/leandojo-benchmark-4-random | test | 297 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨?_, by norm_cast; omega⟩ | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | ((:c And) ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.673278) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857))) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c And) (:arg :explicit 0 (: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... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"refine","sourceEnd":35614,"sourceStart":35608,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":35618,"sourceStart":35615,"tag":"atom"},{"children":[{"children":[{"source":"?","sourceEnd":35619,"sourceStart":35618,"tag":"atom"},{"children":[{"source":"_","sourceEnd":35620,"sourceStart":35619,... | [] | [{"source":"⟨?_, by norm_cast; omega⟩","source_end":35644,"source_start":35615,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 57 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 918564c3d230b1051ff970234e62aaa4db2a81066f1c4ae30755db00586fe6e3 | 6ba0fa8c51fe3b82dfec6980b7f6abdee449ef7b5485fd7216c5c95e2dcabe3d | f9f28c7ff323c57081f0986fcf931274387da7f2dc085f339fc9b7b60ccf07b1 | 29017db9afbe547bd180cb59f751d492c4ba495d97694599b13c88c4680df240 |
cat-searcher/leandojo-benchmark-4-random | test | 298 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | calc c₁ * n ≤ r i n := by exact hn₁ i _ ≤ u := by exact_mod_cast hu'.1 | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.673278) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857))) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.699044))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"calc","sourceEnd":35665,"sourceStart":35661,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"contextIndex":10,"semanticRole":"local","source":"c₁","sourceEnd":35670,"sourceStart":35666,"tag":"identifier"},{"source":"*","sourceEnd":35672,"sourceStart":35671,"tag":"atom"},{"cont... | [] | [{"source":"c₁ * n ≤ r i n","source_end":35684,"source_start":35666,"syntax_kind":"«term_≤_»"},{"source":"hn₁ i","source_end":35709,"source_start":35702,"syntax_kind":"Lean.Parser.Term.app"},{"source":"_","source_end":35737,"source_start":35736,"syntax_kind":"Lean.Parser.Term.hole"},{"source":"u","source_end":35743,"so... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 65 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 72be146e3df0411e4157ded07dff61e3f93e8c32a8bc4b56b2a9520c511c44ce | 29017db9afbe547bd180cb59f751d492c4ba495d97694599b13c88c4680df240 | 78a9b87523d43682844003a3cbd796ef057f3f88725881b1a5f5cd2ec5fad5e6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 299 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | omega | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c LE.le) (:c Nat) ((:c Preorder.toLE) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring)))) (:fv _uniq.699044) (:fv _uniq.685857)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:fv FV32)) (:arg :explicit 3 (:fv FV21))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"omega","sourceEnd":35521,"sourceStart":35516,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.omega","source":"omega","sourceEnd":35521,"sourceStart":35516,"tag":"node"}],"kind":"null","source":"omega","source... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 50 | exact | true | 1 | 33 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b327fc0552f14c55632d4a71a02bae88c5d7160ab946609a8c9539ed72898dcc | 15fde91385bf1047ad6ca07d24b171b2269262cab49444b3d050b50d10046ca6 | 304b4a90a76a1cbe4c112e074b30e75181f54df43d60f883597457844293b341 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 300 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_cast | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.699044)) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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 Nat.cast) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV32)))) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"norm_cast","sourceEnd":35634,"sourceStart":35625,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.tacticNorm_cast_","source":"norm_cast","sourceEnd":35634,"sourceStart":35625,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 62 | exact | true | 1 | 34 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 25c1febcb788d6e855e02db822e62f3d660f1247dba25625d2a209d0d4b39366 | 1db859dd2b60d0df6505e553b29bd9410ab0907f957d006333c05b5206a66ad6 | 4526560ee387a60af0a3f42ddce7258b27dc8bd6782a63271dc2d5aa462e81b2 | 92c006f1d836081e991e73fcdc14ea64ae3e6c24ab58c18f7042517723f2ad04 |
cat-searcher/leandojo-benchmark-4-random | test | 301 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | omega | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c LE.le) (:c Nat) (:c instLENat) (:fv _uniq.699044) (:fv _uniq.685857)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:fv FV32)) (:arg :explicit 3 (:fv FV21))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"omega","sourceEnd":35641,"sourceStart":35636,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.omega","source":"omega","sourceEnd":35641,"sourceStart":35636,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 64 | exact | true | 1 | 34 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f5d2bd8e90d1bf811d957c84d80b7ab2dcbd1154205ff389abe8589682df75b6 | 92c006f1d836081e991e73fcdc14ea64ae3e6c24ab58c18f7042517723f2ad04 | 304b4a90a76a1cbe4c112e074b30e75181f54df43d60f883597457844293b341 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 302 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hn₁ i | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((: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.673278) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857))) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) ((:fv _uniq.672328) (:fv _uniq.685884) (:fv _uniq.685857)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":35701,"sourceStart":35696,"tag":"atom"},{"children":[{"contextIndex":22,"semanticRole":"local","source":"hn₁","sourceEnd":35707,"sourceStart":35702,"tag":"identifier"},{"children":[{"contextIndex":28,"semanticRole":"local","source":"i","s... | [] | [{"source":"hn₁ i","source_end":35709,"source_start":35702,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 68 | exact | true | 1 | 34 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 37593b62cf0944ca5141e400c51be198d752504c018ed47a908fb2f09b42848d | 5376d76b7d4ea30358a14bde07ff6c0ad5b078aa94fe9e74ae07ab371ec19407 | 65a0a6bcd04186e53972f1fd101d4c2c248fb48cee7e38510af9cf4f66a8cc03 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 303 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact_mod_cast hu'.1 | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) ((:fv _uniq.672328) (:fv _uniq.685884) (:fv _uniq.685857))) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.699044))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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 Nat.cast) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:fv FV7) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"exact_mod_cast","sourceEnd":35775,"sourceStart":35761,"tag":"atom"},{"children":[{"contextIndex":34,"semanticRole":"local","source":"hu'","sourceEnd":35779,"sourceStart":35776,"tag":"identifier"},{"source":".","sourceEnd":35780,"sourceStart":35779,"tag":"at... | [] | [{"source":"hu'.1","source_end":35781,"source_start":35776,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 73 | exact | true | 1 | 34 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9b9cb42216f9c604d7fa645b0cd34e4ed2ad663d5d802b9c343238f2077e275f | ce9a38be63ae3c22706b170ea46b25099d3677c77fb7a28348875ea24302bc11 | d6baa19933f6e4b56dc8be40f5cae3e2068344ecde60d74e2fde8fe2b99c35b7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 304 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr with u hu | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | case h.h.hc
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ... | ((:c GE.ge) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857)) ((:c AkraBazziRecurrence... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c GE.ge) (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"gcongr","sourceEnd":35905,"sourceStart":35899,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"with","sourceEnd":35910,"sourceStart":35906,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"u","sourceEnd":35912,"sourceStar... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 80 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 270c27ea1e02264d586000f53a9f25a6aa53fc1df8817ad6c770e2ff9295af0f | ace65998a61187ba405e1abc49c6d33163e399d0d4dbd4d73794d53751761c52 | e1ea6cbd757ecb01d4c26fae2d34b3e0eb9712d2944f09cef170e96a3fc37fb8 | 2ef813d033721141956191937544d2b185acca31a88f06976b4e29bf7444fa5c |
cat-searcher/leandojo-benchmark-4-random | test | 305 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.mem_Ico</a>] at hu | case h.h.hc
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ... | case h.h.hc
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ... | ((:c LT.lt) (:c Real) ((:c Preorder.toLT) (: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":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"rw","sourceEnd":35937,"sourceStart":35935,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":35939,"sourceStart":35938,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.mem_Ico",... | [] | [{"source":"Finset.mem_Ico","source_end":35953,"source_start":35939,"syntax_kind":"ident"},{"source":"hu","source_end":35960,"source_start":35958,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 85 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5b2b84da7c589394adc2c11f942049e37220e4ad75400508e6e87b95b34bf85d | df42f17403feb32faa432857675d84dd97bb0c671f209b5711ffe25a5ffcfe5a | e03ca1855f111f96df0ca3325cc611848b6b63c7d70640ceb137c2cbcd41fce3 | 87749da179dc2413461ac42ecc068b41fc3839ba077b680c27432ad909581df4 |
cat-searcher/leandojo-benchmark-4-random | test | 306 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have := calc 0 < r i n := hrpos_i _ ≤ u := hu.1 | case h.h.hc
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ... | case h.h.hc
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ... | ((:c LT.lt) (:c Real) ((:c Preorder.toLT) (: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":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"have","sourceEnd":35983,"sourceStart":35979,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":35984,"sourceStart":35984,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":35984,"sourceStart":35984,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"calc 0 < r i n := hrpos_i\n _ ≤ u := hu.1","source_end":36058,"source_start":35987,"syntax_kind":"Lean.calc"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 88 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 85588f69ea2bac2b618121d26e47489f8ceb8103baa3d37f7273439400159865 | 87749da179dc2413461ac42ecc068b41fc3839ba077b680c27432ad909581df4 | 462b645665503a04f21475c45538d1d18d71544cbf0b328442e8e0cfae0d4e32 | 5a515267bd1765a26401b614296f0ab5ace2c6598befd91fdf8b98fa4cb8b8f9 |
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