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 | 1,456 | CategoryTheory.CatCommSq.hInv_hInv | Mathlib/CategoryTheory/CatCommSq.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext X | C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
C₄ : Type u_4
C₅ : Type u_5
C₆ : Type u_6
inst✝⁵ : Category.{u_8, u_1} C₁
inst✝⁴ : Category.{u_9, u_2} C₂
inst✝³ : Category.{u_10, u_3} C₃
inst✝² : Category.{u_7, u_4} C₄
inst✝¹ : Category.{?u.17460, u_5} C₅
inst✝ : Category.{?u.17464, u_6} C₆
T✝ : C₁ ⥤ C₂
L✝ : C₁ ⥤ C₃
R✝ : C₂ ... | case iso'.w.w.h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
C₄ : Type u_4
C₅ : Type u_5
C₆ : Type u_6
inst✝⁵ : Category.{u_8, u_1} C₁
inst✝⁴ : Category.{u_9, u_2} C₂
inst✝³ : Category.{u_10, u_3} C₃
inst✝² : Category.{u_7, u_4} C₄
inst✝¹ : Category.{?u.17460, u_5} C₅
inst✝ : Category.{?u.17464, u_6} C₆
T✝ : C₁ ⥤ C₂
L✝ : ... | ((:c Eq) ((:c CategoryTheory.CatCommSq) (:fv _uniq.17426) (:fv _uniq.17429) (:fv _uniq.17432) (:fv _uniq.17435) (:fv _uniq.17445) (:fv _uniq.17449) (:fv _uniq.17453) (:fv _uniq.17457) ((:c CategoryTheory.Equivalence.inverse) (:fv _uniq.17429) (:fv _uniq.17426) (:fv _uniq.17449) (:fv _uniq.17445) ((:c CategoryTheory.Equ... | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"C₄","sexp":"(:sort (+ u_4 1))"},{"name":"C₅","sexp":"(:sort (+ u_5 1))"},{"name":"C₆","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.17426))... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.CatCommSq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV2)) (:arg :implicit-type 3 (:fv FV3)) (: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.17426","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17429","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"ext","sourceEnd":3484,"sourceStart":3481,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"X","sourceEnd":3486,"sourceStart":3485,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"X","sourceEnd":3486,"sourceStart":3485,"tag":"nod... | [{"role":"fresh_name","source":"X","source_end":3486,"source_start":3485,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17426","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17429","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 12 | 4 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f6af0f11e7303f927ae0f48601895a8a505cfac71c0db990fc26c8df9e6b6928 | 4161a59d0e92ac89ac0ee76d30b2ccf9bf55d5fcfbd401be1a5749e1ada7e1d1 | b9fd42f0337fc2601ad1a536450feb3363c42f98fd2367a477dfb38b60f321cd | 64cccd05d508667ee7d5019d722084149e4c6425e69fa16d329d02004b6b99a1 |
cat-searcher/leandojo-benchmark-4-random | test | 1,457 | CategoryTheory.CatCommSq.hInv_hInv | Mathlib/CategoryTheory/CatCommSq.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | erw [← <a>CategoryTheory.cancel_mono</a> (B.functor.map (L.map (T.unitIso.hom.app X))), ← h.iso'.hom.naturality (T.unitIso.hom.app X), <a>CategoryTheory.CatCommSq.hInv_iso'_hom_app</a>, <a>CategoryTheory.CatCommSq.hInv_iso'_inv_app</a>] | case iso'.w.w.h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
C₄ : Type u_4
C₅ : Type u_5
C₆ : Type u_6
inst✝⁵ : Category.{u_8, u_1} C₁
inst✝⁴ : Category.{u_9, u_2} C₂
inst✝³ : Category.{u_10, u_3} C₃
inst✝² : Category.{u_7, u_4} C₄
inst✝¹ : Category.{?u.17460, u_5} C₅
inst✝ : Category.{?u.17464, u_6} C₆
T✝ : C₁ ⥤ C₂
L✝ : ... | case iso'.w.w.h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
C₄ : Type u_4
C₅ : Type u_5
C₆ : Type u_6
inst✝⁵ : Category.{u_8, u_1} C₁
inst✝⁴ : Category.{u_9, u_2} C₂
inst✝³ : Category.{u_10, u_3} C₃
inst✝² : Category.{u_7, u_4} C₄
inst✝¹ : Category.{?u.17460, u_5} C₅
inst✝ : Category.{?u.17464, u_6} C₆
T✝ : C₁ ⥤ C₂
L✝ : ... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.17435) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.17435) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.17435) (:fv _uniq.17457))) ((:c Prefunctor.obj) (:fv _uniq.17426) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.17426) ((: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":"C₄","sexp":"(:sort (+ u_4 1))"},{"name":"C₅","sexp":"(:sort (+ u_5 1))"},{"name":"C₆","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.17426))... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17426","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17429","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"erw","sourceEnd":3492,"sourceStart":3489,"tag":"atom"},{"children":[{"source":"[","sourceEnd":3494,"sourceStart":3493,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":3497,"sourceStart":3494,"tag":"atom"}],"kind":"token.«← »","source":"←","... | [] | [{"source":"cancel_mono (B.functor.map (L.map (T.unitIso.hom.app X)))","source_end":3555,"source_start":3498,"syntax_kind":"Lean.Parser.Term.app"},{"source":"h.iso'.hom.naturality (T.unitIso.hom.app X)","source_end":3608,"source_start":3565,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hInv_iso'_hom_app","source_end... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17426","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17429","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 12 | 5 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f5d08e6fc8bb318b4660c267f402f19db88095f8e3b88723effec7dfe35e335e | 64cccd05d508667ee7d5019d722084149e4c6425e69fa16d329d02004b6b99a1 | aa493f655c0a4df0e88b5051fced405b1f80d83bd913d51bdf337297532ddfa4 | ba1782e7d00ce82ed508ce98ec7d1621e3806b85093d5677007001a8ce50f84e |
cat-searcher/leandojo-benchmark-4-random | test | 1,458 | CategoryTheory.CatCommSq.hInv_hInv | Mathlib/CategoryTheory/CatCommSq.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp | case iso'.w.w.h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
C₄ : Type u_4
C₅ : Type u_5
C₆ : Type u_6
inst✝⁵ : Category.{u_8, u_1} C₁
inst✝⁴ : Category.{u_9, u_2} C₂
inst✝³ : Category.{u_10, u_3} C₃
inst✝² : Category.{u_7, u_4} C₄
inst✝¹ : Category.{?u.17460, u_5} C₅
inst✝ : Category.{?u.17464, u_6} C₆
T✝ : C₁ ⥤ C₂
L✝ : ... | case iso'.w.w.h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
C₄ : Type u_4
C₅ : Type u_5
C₆ : Type u_6
inst✝⁵ : Category.{u_8, u_1} C₁
inst✝⁴ : Category.{u_9, u_2} C₂
inst✝³ : Category.{u_10, u_3} C₃
inst✝² : Category.{u_7, u_4} C₄
inst✝¹ : Category.{?u.17460, u_5} C₅
inst✝ : Category.{?u.17464, u_6} C₆
T✝ : C₁ ⥤ C₂
L✝ : ... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.17435) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.17435) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.17435) (:fv _uniq.17457))) ((:c Prefunctor.obj) (:fv _uniq.17426) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.17426) ((: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":"C₄","sexp":"(:sort (+ u_4 1))"},{"name":"C₅","sexp":"(:sort (+ u_5 1))"},{"name":"C₆","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.17426))... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17426","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17429","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"dsimp","sourceEnd":3655,"sourceStart":3650,"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":[],"kin... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17426","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17429","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 12 | 11 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 03fdd3e462d471db7e44618f9eb453ba218ea0477268255c9b2fc9cd19f9d39c | ba1782e7d00ce82ed508ce98ec7d1621e3806b85093d5677007001a8ce50f84e | 7854eab90b5d1f0eed9d2f7f6b885100cc44bc732b41c876b3af083c01260845 | 404155422b9c6282d95dfcd7966c32f7e88012f6cad414d0517c7f9ba9a64475 |
cat-searcher/leandojo-benchmark-4-random | test | 1,459 | CategoryTheory.CatCommSq.hInv_hInv | Mathlib/CategoryTheory/CatCommSq.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>CategoryTheory.Functor.comp_obj</a>, <a>CategoryTheory.Category.assoc</a>, ← <a>CategoryTheory.Functor.map_comp</a>, <a>CategoryTheory.Iso.inv_hom_id_app</a>, <a>CategoryTheory.Equivalence.counitInv_app_functor</a>, <a>CategoryTheory.Functor.map_id</a>] | case iso'.w.w.h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
C₄ : Type u_4
C₅ : Type u_5
C₆ : Type u_6
inst✝⁵ : Category.{u_8, u_1} C₁
inst✝⁴ : Category.{u_9, u_2} C₂
inst✝³ : Category.{u_10, u_3} C₃
inst✝² : Category.{u_7, u_4} C₄
inst✝¹ : Category.{?u.17460, u_5} C₅
inst✝ : Category.{?u.17464, u_6} C₆
T✝ : C₁ ⥤ C₂
L✝ : ... | case iso'.w.w.h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
C₄ : Type u_4
C₅ : Type u_5
C₆ : Type u_6
inst✝⁵ : Category.{u_8, u_1} C₁
inst✝⁴ : Category.{u_9, u_2} C₂
inst✝³ : Category.{u_10, u_3} C₃
inst✝² : Category.{u_7, u_4} C₄
inst✝¹ : Category.{?u.17460, u_5} C₅
inst✝ : Category.{?u.17464, u_6} C₆
T✝ : C₁ ⥤ C₂
L✝ : ... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.17435) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.17435) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.17435) (:fv _uniq.17457))) ((:c Prefunctor.obj) (:fv _uniq.17429) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.17429) ((: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":"C₄","sexp":"(:sort (+ u_4 1))"},{"name":"C₅","sexp":"(:sort (+ u_5 1))"},{"name":"C₆","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.17426))... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17426","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17429","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":3662,"sourceStart":3658,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":3667,"sourceStart":3663,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":3667,"s... | [] | [{"source":"Functor.comp_obj","source_end":3685,"source_start":3669,"syntax_kind":"ident"},{"source":"assoc","source_end":3692,"source_start":3687,"syntax_kind":"ident"},{"source":"Functor.map_comp","source_end":3714,"source_start":3698,"syntax_kind":"ident"},{"source":"Iso.inv_hom_id_app","source_end":3734,"source_sta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17426","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17429","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 12 | 12 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4646c4409fce828ff3f68bc9dfe4108ddfc29e059920ff8e87b1aeaad267b9a9 | 404155422b9c6282d95dfcd7966c32f7e88012f6cad414d0517c7f9ba9a64475 | 05a3bfa180ced5a577fee328e88bbbcdb2219ab9ed9dd2a9e6079415f7378d43 | 4bdb59830b2562b4719e108215934a7f4430c9cdbc86fbcb3f046ae558dfd646 |
cat-searcher/leandojo-benchmark-4-random | test | 1,460 | CategoryTheory.CatCommSq.hInv_hInv | Mathlib/CategoryTheory/CatCommSq.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>CategoryTheory.Functor.map_comp</a>, <a>CategoryTheory.Equivalence.fun_inv_map</a>, <a>CategoryTheory.Category.assoc</a>, <a>CategoryTheory.Equivalence.counitInv_functor_comp</a>, <a>CategoryTheory.Category.comp_id</a>, <a>CategoryTheory.Iso.inv_hom_id_app_assoc</a>] | case iso'.w.w.h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
C₄ : Type u_4
C₅ : Type u_5
C₆ : Type u_6
inst✝⁵ : Category.{u_8, u_1} C₁
inst✝⁴ : Category.{u_9, u_2} C₂
inst✝³ : Category.{u_10, u_3} C₃
inst✝² : Category.{u_7, u_4} C₄
inst✝¹ : Category.{?u.17460, u_5} C₅
inst✝ : Category.{?u.17464, u_6} C₆
T✝ : C₁ ⥤ C₂
L✝ : ... | case iso'.w.w.h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
C₄ : Type u_4
C₅ : Type u_5
C₆ : Type u_6
inst✝⁵ : Category.{u_8, u_1} C₁
inst✝⁴ : Category.{u_9, u_2} C₂
inst✝³ : Category.{u_10, u_3} C₃
inst✝² : Category.{u_7, u_4} C₄
inst✝¹ : Category.{?u.17460, u_5} C₅
inst✝ : Category.{?u.17464, u_6} C₆
T✝ : C₁ ⥤ C₂
L✝ : ... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.17435) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.17435) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.17435) (:fv _uniq.17457))) ((:c Prefunctor.obj) (:fv _uniq.17429) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.17429) ((: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":"C₄","sexp":"(:sort (+ u_4 1))"},{"name":"C₅","sexp":"(:sort (+ u_5 1))"},{"name":"C₆","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.17426))... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17426","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17429","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":3797,"sourceStart":3793,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":3802,"sourceStart":3798,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":3802,"s... | [] | [{"source":"Functor.map_comp","source_end":3820,"source_start":3804,"syntax_kind":"ident"},{"source":"Equivalence.fun_inv_map","source_end":3845,"source_start":3822,"syntax_kind":"ident"},{"source":"assoc","source_end":3852,"source_start":3847,"syntax_kind":"ident"},{"source":"Equivalence.counitInv_functor_comp","sourc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17426","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17429","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 12 | 13 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d564b67c4fe945b7f3e51d712e2b2fff7c7c18e0cdee98ca4b15ee5231ea1d34 | 4bdb59830b2562b4719e108215934a7f4430c9cdbc86fbcb3f046ae558dfd646 | bb0983fcdf42a3ae9f0a68b5bc21c16c49c2edd330917efad83ddb95ccd2d068 | de2c6fd510a81596d934c4017a3323af7315c2983a8f077373f84f0e04edaf95 |
cat-searcher/leandojo-benchmark-4-random | test | 1,461 | CategoryTheory.CatCommSq.hInv_hInv | Mathlib/CategoryTheory/CatCommSq.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case iso'.w.w.h
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
C₄ : Type u_4
C₅ : Type u_5
C₆ : Type u_6
inst✝⁵ : Category.{u_8, u_1} C₁
inst✝⁴ : Category.{u_9, u_2} C₂
inst✝³ : Category.{u_10, u_3} C₃
inst✝² : Category.{u_7, u_4} C₄
inst✝¹ : Category.{?u.17460, u_5} C₅
inst✝ : Category.{?u.17464, u_6} C₆
T✝ : C₁ ⥤ C₂
L✝ : ... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.17435) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.17435) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.17435) (:fv _uniq.17457))) ((:c Prefunctor.obj) (:fv _uniq.17429) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.17429) ((: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":"C₄","sexp":"(:sort (+ u_4 1))"},{"name":"C₅","sexp":"(:sort (+ u_5 1))"},{"name":"C₆","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.17426))... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17426","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17429","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rfl","sourceEnd":3934,"sourceStart":3931,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":3934,"sourceStart":3931,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17426","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17429","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 12 | 14 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0c135d89fac7571c04c6f8931b93057abd36b01c93c9f0ecf90d54944a5e3683 | de2c6fd510a81596d934c4017a3323af7315c2983a8f077373f84f0e04edaf95 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,462 | Matrix.charmatrix_apply_natDegree | Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases h : i = j <;> simp [h, ← <a>Polynomial.degree_eq_iff_natDegree_eq_of_pos</a> (<a>Nat.succ_pos</a> 0)] | R : Type u
inst✝⁴ : CommRing R
n G : Type v
inst✝³ : DecidableEq n
inst✝² : Fintype n
α β : Type v
inst✝¹ : DecidableEq α
M : Matrix n n R
inst✝ : Nontrivial R
i j : n
⊢ (M.charmatrix i j).natDegree = if i = j then 1 else 0 | ((:c Eq) (:c Nat) ((:c Polynomial.natDegree) (:fv _uniq.101) ((:c CommSemiring.toSemiring) (:fv _uniq.101) ((:c CommRing.toCommSemiring) (:fv _uniq.101) (:fv _uniq.104))) ((:c Matrix.charmatrix) (:fv _uniq.101) (:fv _uniq.104) (:fv _uniq.106) (:fv _uniq.115) (:fv _uniq.120) (:fv _uniq.138) (:fv _uniq.463) (:fv _uniq.46... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.101))"},{"name":"n","sexp":"(:sort (+ v 1))"},{"name":"G","sexp":"(:sort (+ v 1))"},{"name":"inst✝³","sexp":"((:c DecidableEq) (:fv _uniq.106))"},{"name":"inst✝²","sexp":"((:c Fintype) (:fv _uniq.106))"},{"name":"α","sexp":"(:sort... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Polynomial.natDegree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Matrix.charmatrix) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.101","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.104","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :explicit 0... | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"by_cases","sourceEnd":1914,"sourceStart":1906,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":1916,"sourceStart":1915,"tag":"identifier"},{"source":":","sourceEnd":1918,"sourceStart":1917,"tag":"atom"}],"kind"... | [] | [{"source":"i = j","source_end":1924,"source_start":1919,"syntax_kind":"«term_=_»"},{"source":"h","source_end":1936,"source_start":1935,"syntax_kind":"ident"},{"source":"degree_eq_iff_natDegree_eq_of_pos (Nat.succ_pos 0)","source_end":1992,"source_start":1942,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.101","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.104","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"internal_n... | 10 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fa24a7f6ea77f30bceb635aba3be729e4ca5fa8a954a7eb9a6320a60f8706635 | 5507457963a026a7282fe4ecbc2f68fab0b3f7d0604d19777109e1e38c1b18b6 | 8212debe5be291f780044eb7a0abc8f72a4b625359129a20b0bc952489398452 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,463 | ModelWithCorners.extChartAt_transDiffeomorph_target | Mathlib/Geometry/Manifold/Diffeomorph.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [e.range_comp, <a>Set.preimage_preimage</a>, mfld_simps] | 𝕜 : Type u_1
inst✝¹⁸ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁷ : NormedAddCommGroup E
inst✝¹⁶ : NormedSpace 𝕜 E
E' : Type u_3
inst✝¹⁵ : NormedAddCommGroup E'
inst✝¹⁴ : NormedSpace 𝕜 E'
F : Type u_4
inst✝¹³ : NormedAddCommGroup F
inst✝¹² : NormedSpace 𝕜 F
H : Type u_5
inst✝¹¹ : TopologicalSpace H
H' : Type u... | 𝕜 : Type u_1
inst✝¹⁸ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁷ : NormedAddCommGroup E
inst✝¹⁶ : NormedSpace 𝕜 E
E' : Type u_3
inst✝¹⁵ : NormedAddCommGroup E'
inst✝¹⁴ : NormedSpace 𝕜 E'
F : Type u_4
inst✝¹³ : NormedAddCommGroup F
inst✝¹² : NormedSpace 𝕜 F
H : Type u_5
inst✝¹¹ : TopologicalSpace H
H' : Type u... | ((:c Eq) ((:c Set) (:fv _uniq.220025)) ((:c PartialEquiv.target) (:fv _uniq.220382) (:fv _uniq.220025) ((:c extChartAt) (:fv _uniq.219900) (:fv _uniq.220025) (:fv _uniq.220382) (:fv _uniq.220253) (:fv _uniq.219903) (:fv _uniq.220028) (:fv _uniq.220136) (:fv _uniq.220256) (:fv _uniq.220385) ((:c ModelWithCorners.transDi... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.219900))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁷","sexp":"((:c NormedAddCommGroup) (:fv _uniq.219906))"},{"name":"inst✝¹⁶","sexp":"((:c NormedSpace) (:fv _uniq.219900) (:fv _uniq.219906) ((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :explicit 1 (:app (:c PartialEquiv.target) (:arg :implicit-type 0 (:fv FV23)) (:arg :implicit-type 1 (:fv FV5)) (:arg :explicit 2 (:app (:c extChartAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV5)) (:arg :impl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.219900","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.219903","is_instance":true,"is_let":false,"name":"inst✝¹⁸","sexp":"(:app (:c NontriviallyNormedF... | {"children":[{"source":"simp","sourceEnd":22891,"sourceStart":22887,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":22896,"sourceStart":22892,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":228... | [] | [{"source":"e.range_comp","source_end":22910,"source_start":22898,"syntax_kind":"ident"},{"source":"preimage_preimage","source_end":22929,"source_start":22912,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.219900","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.219903","is_instance":true,"is_let":false,"user_name":"inst✝¹⁸"},{"binder_role":":implicit","context_index":2,"in... | 177 | 4 | exact | true | 1 | 38 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aae12a3c1f01b7f8b746e485bcd97eb01c6ad2a32c50981348f9e16cffa299d9 | c005285e400dd5cd93e9c1b8efb4a71b8f617469781ac31ceb8c8b66a9253b16 | a2e118afde71dcda1c4e71d7dca6e6d27e52b4a12af98c5754aadaf2c4abb345 | bac056052cd0c0183dadcda05ff3c72363b316ef18434f4a5a65d5c8cd7b1dfd |
cat-searcher/leandojo-benchmark-4-random | test | 1,464 | ModelWithCorners.extChartAt_transDiffeomorph_target | Mathlib/Geometry/Manifold/Diffeomorph.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | 𝕜 : Type u_1
inst✝¹⁸ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁷ : NormedAddCommGroup E
inst✝¹⁶ : NormedSpace 𝕜 E
E' : Type u_3
inst✝¹⁵ : NormedAddCommGroup E'
inst✝¹⁴ : NormedSpace 𝕜 E'
F : Type u_4
inst✝¹³ : NormedAddCommGroup F
inst✝¹² : NormedSpace 𝕜 F
H : Type u_5
inst✝¹¹ : TopologicalSpace H
H' : Type u... | ((:c Eq) ((:c Set) (:fv _uniq.220025)) ((:c Inter.inter) ((:c Set) (:fv _uniq.220025)) ((:c Set.instInter) (:fv _uniq.220025)) ((:c Set.preimage) (:fv _uniq.220025) (:fv _uniq.219906) ((:c DFunLike.coe) ((:c Diffeomorph) (:fv _uniq.219900) (:fv _uniq.219903) (:fv _uniq.220025) (:fv _uniq.220028) (:fv _uniq.220136) (:fv... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.219900))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁷","sexp":"((:c NormedAddCommGroup) (:fv _uniq.219906))"},{"name":"inst✝¹⁶","sexp":"((:c NormedSpace) (:fv _uniq.219900) (:fv _uniq.219906) ((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :explicit 1 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :instance 1 (:instance-of (:app (:c Inter) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV5))))))) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.219900","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.219903","is_instance":true,"is_let":false,"name":"inst✝¹⁸","sexp":"(:app (:c NontriviallyNormedF... | {"children":[{"source":"rfl","sourceEnd":22947,"sourceStart":22944,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":22947,"sourceStart":22944,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.219900","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.219903","is_instance":true,"is_let":false,"user_name":"inst✝¹⁸"},{"binder_role":":implicit","context_index":2,"in... | 177 | 6 | exact | true | 1 | 38 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7d15b653478a5b36afeb15b327790ddccc7ef3dc59777ca7880bf307ec122629 | bac056052cd0c0183dadcda05ff3c72363b316ef18434f4a5a65d5c8cd7b1dfd | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,465 | MeasureTheory.Measure.measurePreserving_div_left | Mathlib/MeasureTheory/Group/Measure.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>div_eq_mul_inv</a>] | 𝕜 : Type u_1
G : Type u_2
H : Type u_3
inst✝⁶ : MeasurableSpace G
inst✝⁵ : MeasurableSpace H
inst✝⁴ : DivisionMonoid G
inst✝³ : MeasurableMul G
inst✝² : MeasurableInv G
μ✝ μ : Measure G
inst✝¹ : μ.IsInvInvariant
inst✝ : μ.IsMulLeftInvariant
g : G
⊢ MeasurePreserving (fun t => g / t) μ μ | 𝕜 : Type u_1
G : Type u_2
H : Type u_3
inst✝⁶ : MeasurableSpace G
inst✝⁵ : MeasurableSpace H
inst✝⁴ : DivisionMonoid G
inst✝³ : MeasurableMul G
inst✝² : MeasurableInv G
μ✝ μ : Measure G
inst✝¹ : μ.IsInvInvariant
inst✝ : μ.IsMulLeftInvariant
g : G
⊢ MeasurePreserving (fun t => g * t⁻¹) μ μ | ((:c MeasureTheory.MeasurePreserving) (:fv _uniq.110237) (:fv _uniq.110237) (:fv _uniq.110243) (:fv _uniq.110243) (:lambda t (:fv _uniq.110237) ((:c HDiv.hDiv) (:fv _uniq.110237) (:fv _uniq.110237) (:fv _uniq.110237) ((:c instHDiv) (:fv _uniq.110237) ((:c DivInvMonoid.toDiv) (:fv _uniq.110237) ((:c DivisionMonoid.toDiv... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"H","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁶","sexp":"((:c MeasurableSpace) (:fv _uniq.110237))"},{"name":"inst✝⁵","sexp":"((:c MeasurableSpace) (:fv _uniq.110240))"},{"name":"inst✝⁴","sexp":"((:c DivisionMonoid) (:fv _uniq.110... | (:app (:c MeasureTheory.MeasurePreserving) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 4 (:lambda ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110234","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110237","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"simp_rw","sourceEnd":25677,"sourceStart":25670,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":25679,"sourceStart":25678,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"div_eq_mul_... | [] | [{"source":"div_eq_mul_inv","source_end":25693,"source_start":25679,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110234","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110237","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 176 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eb0fa71902ad85c32913572f04d55fb676f9de536481037e6afdbcac046f5720 | 0423b2382c4ec4c96408834bb12bc94d3196aa6dc23aee2569524e8192eb55b2 | f2459fa46a6d6794a4d416313cac6dba747691047eb307f61c444343b4700dea | 753d461901a0f19a6cc6a37ea5ac7f36e148f4063abd228f5fbcea96a4420b65 |
cat-searcher/leandojo-benchmark-4-random | test | 1,466 | MeasureTheory.Measure.measurePreserving_div_left | Mathlib/MeasureTheory/Group/Measure.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>MeasureTheory.measurePreserving_mul_left</a> μ g).<a>MeasureTheory.MeasurePreserving.comp</a> (<a>MeasureTheory.Measure.measurePreserving_inv</a> μ) | 𝕜 : Type u_1
G : Type u_2
H : Type u_3
inst✝⁶ : MeasurableSpace G
inst✝⁵ : MeasurableSpace H
inst✝⁴ : DivisionMonoid G
inst✝³ : MeasurableMul G
inst✝² : MeasurableInv G
μ✝ μ : Measure G
inst✝¹ : μ.IsInvInvariant
inst✝ : μ.IsMulLeftInvariant
g : G
⊢ MeasurePreserving (fun t => g * t⁻¹) μ μ | ((:c MeasureTheory.MeasurePreserving) (:fv _uniq.110237) (:fv _uniq.110237) (:fv _uniq.110243) (:fv _uniq.110243) (:lambda t (:fv _uniq.110237) ((:c HMul.hMul) (:fv _uniq.110237) (:fv _uniq.110237) (:fv _uniq.110237) ((:c instHMul) (:fv _uniq.110237) ((:c MulOneClass.toMul) (:fv _uniq.110237) ((:c Monoid.toMulOneClass)... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"H","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁶","sexp":"((:c MeasurableSpace) (:fv _uniq.110237))"},{"name":"inst✝⁵","sexp":"((:c MeasurableSpace) (:fv _uniq.110240))"},{"name":"inst✝⁴","sexp":"((:c DivisionMonoid) (:fv _uniq.110... | (:app (:c MeasureTheory.MeasurePreserving) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 4 (:lambda ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110234","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110237","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"exact","sourceEnd":25702,"sourceStart":25697,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":25704,"sourceStart":25703,"tag":"atom"},{"children":[{"name":"MeasureTheory.measurePreserving_mul_left","semanticRole":"global","source":"measurePreserving_mul_left","sourc... | [] | [{"source":"(measurePreserving_mul_left μ g).comp (measurePreserving_inv μ)","source_end":25768,"source_start":25703,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110234","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110237","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 176 | 7 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0e9218f64cd7a6d24124fcc6fe8a2af02598e751d94a954dd0c8b97effd60f07 | 753d461901a0f19a6cc6a37ea5ac7f36e148f4063abd228f5fbcea96a4420b65 | dc863b56b47cbc6165efd386d28498069ff61f710db0756f631ea7a406ab98f0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,467 | CochainComplex.HomComplex.Cochain.congr_v | Mathlib/Algebra/Homology/HomotopyCategory/HomComplex.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | subst h | C : Type u
inst✝³ : Category.{v, u} C
inst✝² : Preadditive C
R : Type u_1
inst✝¹ : Ring R
inst✝ : Linear R C
F G K L : CochainComplex C ℤ
n m : ℤ
z₁ z₂ : Cochain F G n
h : z₁ = z₂
p q : ℤ
hpq : p + n = q
⊢ z₁.v p q hpq = z₂.v p q hpq | C : Type u
inst✝³ : Category.{v, u} C
inst✝² : Preadditive C
R : Type u_1
inst✝¹ : Ring R
inst✝ : Linear R C
F G K L : CochainComplex C ℤ
n m : ℤ
z₁ : Cochain F G n
p q : ℤ
hpq : p + n = q
⊢ z₁.v p q hpq = z₁.v p q hpq | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.8860) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.8860) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.8860) (:fv _uniq.8863))) ((:c HomologicalComplex.X) (:c Int) (:fv _uniq.8860) (:fv _uniq.8863) ((:c CategoryTheory.Preadditive.preadditiveHasZeroMorphisms) (... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.8860))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Preadditive) (:fv _uniq.8860) (:fv _uniq.8863))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.8881))"},{"name":"inst✝"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HomologicalComplex.X) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8860","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.8863","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Category) ... | {"children":[{"source":"subst","sourceEnd":3131,"sourceStart":3126,"tag":"atom"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"h","sourceEnd":3133,"sourceStart":3132,"tag":"identifier"}],"kind":"null","source":"h","sourceEnd":3133,"sourceStart":3132,"tag":"node"}],"kind":"Lean.Parser.Tactic.subst","s... | [] | [{"source":"h","source_end":3133,"source_start":3132,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8860","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.8863","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":2,... | 17 | 4 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6a504b3efed3ec833b671cd46bc8cadaf14fc0bce8ae755c401982f43a227378 | 1fcf7cef1637b12dff61cc9ef9442597d322510a8e6afc0281e4681490b56887 | 831cd1e16045cc06861f8cf3670f78a5450740dc3de3f30710e86d17a4b036b3 | 2edd0c5d12deba5b8861cd16a99828f8a39d079040ddd7aa017feebb3a19e644 |
cat-searcher/leandojo-benchmark-4-random | test | 1,468 | CochainComplex.HomComplex.Cochain.congr_v | Mathlib/Algebra/Homology/HomotopyCategory/HomComplex.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | C : Type u
inst✝³ : Category.{v, u} C
inst✝² : Preadditive C
R : Type u_1
inst✝¹ : Ring R
inst✝ : Linear R C
F G K L : CochainComplex C ℤ
n m : ℤ
z₁ : Cochain F G n
p q : ℤ
hpq : p + n = q
⊢ z₁.v p q hpq = z₁.v p q hpq | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.8860) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.8860) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.8860) (:fv _uniq.8863))) ((:c HomologicalComplex.X) (:c Int) (:fv _uniq.8860) (:fv _uniq.8863) ((:c CategoryTheory.Preadditive.preadditiveHasZeroMorphisms) (... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.8860))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Preadditive) (:fv _uniq.8860) (:fv _uniq.8863))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.8881))"},{"name":"inst✝"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HomologicalComplex.X) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8860","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.8863","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Category) ... | {"children":[{"source":"rfl","sourceEnd":3138,"sourceStart":3135,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":3138,"sourceStart":3135,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8860","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.8863","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":2,... | 17 | 6 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7692adb5c6e7c49c6fdfaa4731de0a56ecfc0bed9070cc0532e7abce31639c50 | 2edd0c5d12deba5b8861cd16a99828f8a39d079040ddd7aa017feebb3a19e644 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,469 | IsClosed.vadd_right_of_isCompact | Mathlib/Analysis/Normed/Group/AddTorsor.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>IsSeqClosed.isClosed</a> (fun u p husv hup ↦ ?_) | α : Type u_1
V : Type u_2
P : Type u_3
W : Type u_4
Q : Type u_5
inst✝⁵ : SeminormedAddCommGroup V
inst✝⁴ : PseudoMetricSpace P
inst✝³ : NormedAddTorsor V P
inst✝² : NormedAddCommGroup W
inst✝¹ : MetricSpace Q
inst✝ : NormedAddTorsor W Q
s : Set V
t : Set P
hs : IsClosed s
ht : IsCompact t
⊢ IsClosed (s +ᵥ t) | α : Type u_1
V : Type u_2
P : Type u_3
W : Type u_4
Q : Type u_5
inst✝⁵ : SeminormedAddCommGroup V
inst✝⁴ : PseudoMetricSpace P
inst✝³ : NormedAddTorsor V P
inst✝² : NormedAddCommGroup W
inst✝¹ : MetricSpace Q
inst✝ : NormedAddTorsor W Q
s : Set V
t : Set P
hs : IsClosed s
ht : IsCompact t
u : ℕ → P
p : P
husv : ∀ (n :... | ((:c IsClosed) (:fv _uniq.60117) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.60117) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.60117) (:fv _uniq.60129))) ((:c HVAdd.hVAdd) ((:c Set) (:fv _uniq.60114)) ((:c Set) (:fv _uniq.60117)) ((:c Set) (:fv _uniq.60117)) ((:c instHVAdd) ((:c Set) (:fv _uniq.60114)) ((:c... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"W","sexp":"(:sort (+ u_4 1))"},{"name":"Q","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁵","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.60114))"},{"name":"inst✝⁴","sexp":"((:c PseudoMetricSp... | (:app (:c IsClosed) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 (:app (:c HVAdd.hVAdd) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60111","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60114","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":14417,"sourceStart":14411,"tag":"atom"},{"children":[{"name":"IsSeqClosed.isClosed","semanticRole":"global","source":"IsSeqClosed.isClosed","sourceEnd":14438,"sourceStart":14418,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":14440,"sourceStart":14439,... | [] | [{"source":"IsSeqClosed.isClosed (fun u p husv hup ↦ ?_)","source_end":14464,"source_start":14418,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60111","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60114","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 102 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 062c09a22ca5ef1e8bab6d9b83cf2b841721f4b505694fb823d5fbe279176455 | 9c20dc9d775351729b692900e07c7c4b0c66750db9f934e8310acf4573dbcaad | 8f219298ad7bfd1d318a6c29a9ad607cc76f4befc03a4248d5be238884c27284 | 2d5dc53533eefa8e0d6de856673a2cc0035d1f2c6797b26950eea3451b388f35 |
cat-searcher/leandojo-benchmark-4-random | test | 1,470 | IsClosed.vadd_right_of_isCompact | Mathlib/Analysis/Normed/Group/AddTorsor.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | choose! a ha v hv hav using husv | α : Type u_1
V : Type u_2
P : Type u_3
W : Type u_4
Q : Type u_5
inst✝⁵ : SeminormedAddCommGroup V
inst✝⁴ : PseudoMetricSpace P
inst✝³ : NormedAddTorsor V P
inst✝² : NormedAddCommGroup W
inst✝¹ : MetricSpace Q
inst✝ : NormedAddTorsor W Q
s : Set V
t : Set P
hs : IsClosed s
ht : IsCompact t
u : ℕ → P
p : P
husv : ∀ (n :... | α : Type u_1
V : Type u_2
P : Type u_3
W : Type u_4
Q : Type u_5
inst✝⁵ : SeminormedAddCommGroup V
inst✝⁴ : PseudoMetricSpace P
inst✝³ : NormedAddTorsor V P
inst✝² : NormedAddCommGroup W
inst✝¹ : MetricSpace Q
inst✝ : NormedAddTorsor W Q
s : Set V
t : Set P
hs : IsClosed s
ht : IsCompact t
u : ℕ → P
p : P
hup : Tendsto... | ((:c Membership.mem) (:fv _uniq.60117) ((:c Set) (:fv _uniq.60117)) ((:c Set.instMembership) (:fv _uniq.60117)) (:fv _uniq.60881) ((:c HVAdd.hVAdd) ((:c Set) (:fv _uniq.60114)) ((:c Set) (:fv _uniq.60117)) ((:c Set) (:fv _uniq.60117)) ((:c instHVAdd) ((:c Set) (:fv _uniq.60114)) ((:c Set) (:fv _uniq.60117)) ((:c Set.va... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"W","sexp":"(:sort (+ u_4 1))"},{"name":"Q","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁵","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.60114))"},{"name":"inst✝⁴","sexp":"((:c PseudoMetricSp... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 3 (:fv FV17)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60111","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60114","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"choose!","sourceEnd":14474,"sourceStart":14467,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":14476,"sourceStart":14475,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"a","sourceEnd":14476,"sourceStart":14475,"tag":"node"},{"children":[{"... | [] | [{"source":"husv","source_end":14499,"source_start":14495,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60111","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60114","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 102 | 5 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d3675d761087df48cab37e82a51f5e8941a8d523244e13e1b875211a13ba6e4a | 2d5dc53533eefa8e0d6de856673a2cc0035d1f2c6797b26950eea3451b388f35 | f9874960fe4181a2c7f1755abd58ccfc6b965438f5d237117148f23c11b5baf3 | b12099552843935a602d496e43e181f7115bf153b0a5c7d43e344f1a8294283e |
cat-searcher/leandojo-benchmark-4-random | test | 1,471 | IsClosed.vadd_right_of_isCompact | Mathlib/Analysis/Normed/Group/AddTorsor.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases ht.isSeqCompact hv with ⟨q, hqt, φ, φ_mono, hφq⟩ | α : Type u_1
V : Type u_2
P : Type u_3
W : Type u_4
Q : Type u_5
inst✝⁵ : SeminormedAddCommGroup V
inst✝⁴ : PseudoMetricSpace P
inst✝³ : NormedAddTorsor V P
inst✝² : NormedAddCommGroup W
inst✝¹ : MetricSpace Q
inst✝ : NormedAddTorsor W Q
s : Set V
t : Set P
hs : IsClosed s
ht : IsCompact t
u : ℕ → P
p : P
hup : Tendsto... | case intro.intro.intro.intro
α : Type u_1
V : Type u_2
P : Type u_3
W : Type u_4
Q : Type u_5
inst✝⁵ : SeminormedAddCommGroup V
inst✝⁴ : PseudoMetricSpace P
inst✝³ : NormedAddTorsor V P
inst✝² : NormedAddCommGroup W
inst✝¹ : MetricSpace Q
inst✝ : NormedAddTorsor W Q
s : Set V
t : Set P
hs : IsClosed s
ht : IsCompact t
... | ((:c Membership.mem) (:fv _uniq.60117) ((:c Set) (:fv _uniq.60117)) ((:c Set.instMembership) (:fv _uniq.60117)) (:fv _uniq.60881) ((:c HVAdd.hVAdd) ((:c Set) (:fv _uniq.60114)) ((:c Set) (:fv _uniq.60117)) ((:c Set) (:fv _uniq.60117)) ((:c instHVAdd) ((:c Set) (:fv _uniq.60114)) ((:c Set) (:fv _uniq.60117)) ((:c Set.va... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"W","sexp":"(:sort (+ u_4 1))"},{"name":"Q","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁵","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.60114))"},{"name":"inst✝⁴","sexp":"((:c PseudoMetricSp... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 3 (:fv FV17)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60111","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60114","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rcases","sourceEnd":14508,"sourceStart":14502,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"ht.isSeqCompact","sourceEnd":14524,"sourceStart":14509,"tag":"identifier"},{"children":[{"contextIndex":22,"semanticRole":"local","... | [] | [{"source":"ht.isSeqCompact hv","source_end":14527,"source_start":14509,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨q, hqt, φ, φ_mono, hφq⟩","source_end":14564,"source_start":14533,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60111","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60114","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 102 | 6 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 04cac9105fe159a07a47070186630c795e2e92e3876cea7738518d0559909a76 | b12099552843935a602d496e43e181f7115bf153b0a5c7d43e344f1a8294283e | b66e4d9866389d19aa5d28f072f58eb645a0a977d101de1fb4ad54799c3ea0cb | cec2593c274918e89a3d173895f55c09e4374e9160891df40c31b035e02c27e7 |
cat-searcher/leandojo-benchmark-4-random | test | 1,472 | IsClosed.vadd_right_of_isCompact | Mathlib/Analysis/Normed/Group/AddTorsor.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨p -ᵥ q, hs.mem_of_tendsto ((hup.comp φ_mono.tendsto_atTop).<a>Filter.Tendsto.vsub</a> hφq) (<a>Filter.eventually_of_forall</a> fun n ↦ ?_), q, hqt, <a>vsub_vadd</a> _ _⟩ | case intro.intro.intro.intro
α : Type u_1
V : Type u_2
P : Type u_3
W : Type u_4
Q : Type u_5
inst✝⁵ : SeminormedAddCommGroup V
inst✝⁴ : PseudoMetricSpace P
inst✝³ : NormedAddTorsor V P
inst✝² : NormedAddCommGroup W
inst✝¹ : MetricSpace Q
inst✝ : NormedAddTorsor W Q
s : Set V
t : Set P
hs : IsClosed s
ht : IsCompact t
... | case intro.intro.intro.intro
α : Type u_1
V : Type u_2
P : Type u_3
W : Type u_4
Q : Type u_5
inst✝⁵ : SeminormedAddCommGroup V
inst✝⁴ : PseudoMetricSpace P
inst✝³ : NormedAddTorsor V P
inst✝² : NormedAddCommGroup W
inst✝¹ : MetricSpace Q
inst✝ : NormedAddTorsor W Q
s : Set V
t : Set P
hs : IsClosed s
ht : IsCompact t
... | ((:c Membership.mem) (:fv _uniq.60117) ((:c Set) (:fv _uniq.60117)) ((:c Set.instMembership) (:fv _uniq.60117)) (:fv _uniq.60881) ((:c HVAdd.hVAdd) ((:c Set) (:fv _uniq.60114)) ((:c Set) (:fv _uniq.60117)) ((:c Set) (:fv _uniq.60117)) ((:c instHVAdd) ((:c Set) (:fv _uniq.60114)) ((:c Set) (:fv _uniq.60117)) ((:c Set.va... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"W","sexp":"(:sort (+ u_4 1))"},{"name":"Q","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁵","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.60114))"},{"name":"inst✝⁴","sexp":"((:c PseudoMetricSp... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 3 (:fv FV17)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60111","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60114","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":14573,"sourceStart":14567,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":14577,"sourceStart":14574,"tag":"atom"},{"children":[{"children":[{"contextIndex":17,"semanticRole":"local","source":"p","sourceEnd":14578,"sourceStart":14577,"tag":"identifier"},{"source":"-ᵥ","so... | [] | [{"source":"⟨p -ᵥ q, hs.mem_of_tendsto ((hup.comp φ_mono.tendsto_atTop).vsub hφq)\n (eventually_of_forall fun n ↦ ?_), q, hqt, vsub_vadd _ _⟩","source_end":14715,"source_start":14574,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60111","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60114","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 102 | 7 | exact | true | 1 | 28 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 21b00627b2b253779efa427c12fed8cb946f97fb4cb874ad17ecfc92675ba692 | cec2593c274918e89a3d173895f55c09e4374e9160891df40c31b035e02c27e7 | c152538d27017667bba11b3161337b327a12df909f8fd572fd66f60f9863de10 | 15dab37fd1c41c7bef00a38247bb78a9d43166bfbdf813680bc6ca2ef01e901a |
cat-searcher/leandojo-benchmark-4-random | test | 1,473 | IsClosed.vadd_right_of_isCompact | Mathlib/Analysis/Normed/Group/AddTorsor.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert ha (φ n) using 1 | case intro.intro.intro.intro
α : Type u_1
V : Type u_2
P : Type u_3
W : Type u_4
Q : Type u_5
inst✝⁵ : SeminormedAddCommGroup V
inst✝⁴ : PseudoMetricSpace P
inst✝³ : NormedAddTorsor V P
inst✝² : NormedAddCommGroup W
inst✝¹ : MetricSpace Q
inst✝ : NormedAddTorsor W Q
s : Set V
t : Set P
hs : IsClosed s
ht : IsCompact t
... | case h.e'_4
α : Type u_1
V : Type u_2
P : Type u_3
W : Type u_4
Q : Type u_5
inst✝⁵ : SeminormedAddCommGroup V
inst✝⁴ : PseudoMetricSpace P
inst✝³ : NormedAddTorsor V P
inst✝² : NormedAddCommGroup W
inst✝¹ : MetricSpace Q
inst✝ : NormedAddTorsor W Q
s : Set V
t : Set P
hs : IsClosed s
ht : IsCompact t
u : ℕ → P
p : P
h... | ((:c Membership.mem) (:fv _uniq.60114) ((:c Set) (:fv _uniq.60114)) ((:c Set.instMembership) (:fv _uniq.60114)) ((:c VSub.vsub) (:forall i (:c Nat) (:fv _uniq.60114)) (:forall _ (:c Nat) (:fv _uniq.60117)) ((:c AddTorsor.toVSub) (:forall i (:c Nat) (:fv _uniq.60114)) (:forall _ (:c Nat) (:fv _uniq.60117)) ((:c Pi.addGr... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"W","sexp":"(:sort (+ u_4 1))"},{"name":"Q","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁵","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.60114))"},{"name":"inst✝⁴","sexp":"((:c PseudoMetricSp... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:app (:c VSub.vsub) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60111","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60114","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"convert","sourceEnd":14725,"sourceStart":14718,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"contextIndex":20,"semanticRole":"local","source":"ha","sourceEnd":14728,"sourceStart":14726,"tag":"identifier"... | [] | [{"source":"ha (φ n)","source_end":14735,"source_start":14726,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60111","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60114","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 102 | 8 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | de6728c2241a121aef3e3c04eff04869017c7547aa4332054caa17ad4fdc9ba1 | 15dab37fd1c41c7bef00a38247bb78a9d43166bfbdf813680bc6ca2ef01e901a | c2aa2cb8349ded42c5112016b6006673f6b06fd621dde6e6decf3b728e3b8ade | 6b37a756e6b9d635f1f05c12a9c18012320217a9cda8ebb134556d5337bf7db8 |
cat-searcher/leandojo-benchmark-4-random | test | 1,474 | IsClosed.vadd_right_of_isCompact | Mathlib/Analysis/Normed/Group/AddTorsor.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>eq_vadd_iff_vsub_eq</a> _ _ _).<a>Iff.mp</a> (hav (φ n)).<a>Eq.symm</a> | case h.e'_4
α : Type u_1
V : Type u_2
P : Type u_3
W : Type u_4
Q : Type u_5
inst✝⁵ : SeminormedAddCommGroup V
inst✝⁴ : PseudoMetricSpace P
inst✝³ : NormedAddTorsor V P
inst✝² : NormedAddCommGroup W
inst✝¹ : MetricSpace Q
inst✝ : NormedAddTorsor W Q
s : Set V
t : Set P
hs : IsClosed s
ht : IsCompact t
u : ℕ → P
p : P
h... | ((:c Eq) (:fv _uniq.60114) ((:c VSub.vsub) (:forall i (:c Nat) (:fv _uniq.60114)) (:forall _ (:c Nat) (:fv _uniq.60117)) ((:c AddTorsor.toVSub) (:forall i (:c Nat) (:fv _uniq.60114)) (:forall _ (:c Nat) (:fv _uniq.60117)) ((:c Pi.addGroup) (:c Nat) (:lambda i (:c Nat) (:fv _uniq.60114)) (:lambda i (:c Nat) ((:c Seminor... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"W","sexp":"(:sort (+ u_4 1))"},{"name":"Q","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁵","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.60114))"},{"name":"inst✝⁴","sexp":"((:c PseudoMetricSp... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c VSub.vsub) (:arg :implicit-type 0 (:forall i :explicit (:c Nat) (:fv FV1))) (:arg :implicit-type 1 (:forall _ :explicit (:c Nat) (:fv FV2))) (:arg :instance 2 (:instance-of (:app (:c VSub) (:arg :explicit 0 (:forall i :explicit (:c Nat) (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60111","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60114","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":14751,"sourceStart":14746,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":14753,"sourceStart":14752,"tag":"atom"},{"children":[{"name":"eq_vadd_iff_vsub_eq","semanticRole":"global","source":"eq_vadd_iff_vsub_eq","sourceEnd":14772,"sourceStart":14... | [] | [{"source":"(eq_vadd_iff_vsub_eq _ _ _).mp (hav (φ n)).symm","source_end":14800,"source_start":14752,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60111","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60114","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 102 | 9 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 250fa1937be50ffb0aee50a2cbdb2617a5d2b6efe240737b85e270b166aaceea | 6b37a756e6b9d635f1f05c12a9c18012320217a9cda8ebb134556d5337bf7db8 | 4e5c7b9e3b2342d9386851e747059abf5d4663aa3a147304bfc738c66a51bf20 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,475 | geom_sum_eq | Mathlib/Algebra/GeomSum.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : x - 1 ≠ 0 := by simp_all [<a>sub_eq_iff_eq_add</a>] | α : Type u
inst✝ : DivisionRing α
x : α
h : x ≠ 1
n : ℕ
⊢ ∑ i ∈ range n, x ^ i = (x ^ n - 1) / (x - 1) | α : Type u
inst✝ : DivisionRing α
x : α
h : x ≠ 1
n : ℕ
this : x - 1 ≠ 0
⊢ ∑ i ∈ range n, x ^ i = (x ^ n - 1) / (x - 1) | ((:c Eq) (:fv _uniq.85468) ((:c Finset.sum) (:c Nat) (:fv _uniq.85468) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.85468) ((:c NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring) (:fv _uniq.85468) ((:c NonAssocRing.toNonUnitalNonAssocRing) (:fv _uniq.85468) ((:c Ring.toNonAssocRing) (:fv _uniq.85468) ((:c... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c DivisionRing) (:fv _uniq.85468))"},{"name":"x","sexp":"(:fv _uniq.85468)"},{"name":"h","sexp":"((:c Ne) (:fv _uniq.85468) (:fv _uniq.86054) ((:c OfNat.ofNat) (:fv _uniq.85468) (:lit 1) ((:c One.toOfNat1) (:fv _uniq.85468) ((:c Semiring.toOne) (:fv _uni... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset.sum) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 3 (:app (:c Finset.range) (:arg :explicit 0 (:fv FV5)))) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.85468","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.86053","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DivisionRing) (:arg :exp... | {"children":[{"source":"have","sourceEnd":12099,"sourceStart":12095,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":12100,"sourceStart":12100,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":12100,"sourceStart":12100,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"x - 1 ≠ 0","source_end":12113,"source_start":12102,"syntax_kind":"«term_≠_»"},{"source":"sub_eq_iff_eq_add","source_end":12147,"source_start":12130,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.85468","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.86053","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna... | 73 | 4 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9102a880dff70370b77fab290eaa7b4289ea74bd62b1d63c715d1f9ba41f15e7 | 340681992653a178a0c36638dd70ccfe7478bb54347c873708c4dfc4de7d6ad2 | 22fa2f9e4a30e52f211335084498a1db8a9a6a4aef73c4c1b274f872ef703e3c | 787c98c3e0192fadecf4595d7d8461adc4600eac76814afae20dd344fe4c5f1b |
cat-searcher/leandojo-benchmark-4-random | test | 1,476 | geom_sum_eq | Mathlib/Algebra/GeomSum.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>geom_sum_mul</a>, <a>mul_div_cancel_right₀</a> _ this] | α : Type u
inst✝ : DivisionRing α
x : α
h : x ≠ 1
n : ℕ
this : x - 1 ≠ 0
⊢ ∑ i ∈ range n, x ^ i = (x ^ n - 1) / (x - 1) | ((:c Eq) (:fv _uniq.85468) ((:c Finset.sum) (:c Nat) (:fv _uniq.85468) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.85468) ((:c NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring) (:fv _uniq.85468) ((:c NonAssocRing.toNonUnitalNonAssocRing) (:fv _uniq.85468) ((:c Ring.toNonAssocRing) (:fv _uniq.85468) ((:c... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c DivisionRing) (:fv _uniq.85468))"},{"name":"x","sexp":"(:fv _uniq.85468)"},{"name":"h","sexp":"((:c Ne) (:fv _uniq.85468) (:fv _uniq.86054) ((:c OfNat.ofNat) (:fv _uniq.85468) (:lit 1) ((:c One.toOfNat1) (:fv _uniq.85468) ((:c Semiring.toOne) (:fv _uni... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset.sum) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 3 (:app (:c Finset.range) (:arg :explicit 0 (:fv FV5)))) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.85468","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.86053","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DivisionRing) (:arg :exp... | {"children":[{"source":"rw","sourceEnd":12153,"sourceStart":12151,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12155,"sourceStart":12154,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":12158,"sourceSt... | [] | [{"source":"geom_sum_mul","source_end":12171,"source_start":12159,"syntax_kind":"ident"},{"source":"mul_div_cancel_right₀ _ this","source_end":12203,"source_start":12173,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.85468","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.86053","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna... | 73 | 7 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7c03488e2ac05494fbb60b4d234bd8762746c95ab1fb7e29fd95216a939cc563 | 787c98c3e0192fadecf4595d7d8461adc4600eac76814afae20dd344fe4c5f1b | 7a2eb6392a74f3261a107496618073b800dd34d7158edbff246af285475d6d1e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,477 | geom_sum_eq | Mathlib/Algebra/GeomSum.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_all [<a>sub_eq_iff_eq_add</a>] | α : Type u
inst✝ : DivisionRing α
x : α
h : x ≠ 1
n : ℕ
⊢ x - 1 ≠ 0 | ((:c Ne) (:fv _uniq.85468) ((:c HSub.hSub) (:fv _uniq.85468) (:fv _uniq.85468) (:fv _uniq.85468) ((:c instHSub) (:fv _uniq.85468) ((:c Ring.toSub) (:fv _uniq.85468) ((:c DivisionRing.toRing) (:fv _uniq.85468) (:fv _uniq.86053)))) (:fv _uniq.86054) ((:c OfNat.ofNat) (:fv _uniq.85468) (:lit 1) ((:c One.toOfNat1) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c DivisionRing) (:fv _uniq.85468))"},{"name":"x","sexp":"(:fv _uniq.85468)"},{"name":"h","sexp":"((:c Ne) (:fv _uniq.85468) (:fv _uniq.86054) ((:c OfNat.ofNat) (:fv _uniq.85468) (:lit 1) ((:c One.toOfNat1) (:fv _uniq.85468) ((:c Semiring.toOne) (:fv _uni... | (:app (:c Ne) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HSub) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.85468","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.86053","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DivisionRing) (:arg :exp... | {"children":[{"source":"simp_all","sourceEnd":12128,"sourceStart":12120,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12130,"sourceStart":12129,"tag... | [] | [{"source":"sub_eq_iff_eq_add","source_end":12147,"source_start":12130,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.85468","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.86053","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna... | 73 | 6 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b767e6030cf70fd484aa6fdf1e902b54695753d0460e68cf4033d4a5022f09fc | 50474f981729603ef8b104e18a0e49cedef6cc5e140541f99127a8e420402868 | 6aad26f7c63aedc8a3edcb461333b5dbfd21e421ddc749c58ca5ba988f4e730f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,478 | iteratedDerivWithin_sub | Mathlib/Analysis/Calculus/IteratedDeriv/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>sub_eq_add_neg</a>, <a>sub_eq_add_neg</a>, <a>Pi.neg_def</a>, <a>iteratedDerivWithin_add</a> hx h hf hg.neg, <a>iteratedDerivWithin_neg'</a> hx h] | 𝕜 : Type u_1
inst✝⁶ : NontriviallyNormedField 𝕜
F : Type u_2
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
R : Type u_3
inst✝³ : Semiring R
inst✝² : Module R F
inst✝¹ : SMulCommClass 𝕜 R F
inst✝ : ContinuousConstSMul R F
n : ℕ
x : 𝕜
s : Set 𝕜
hx : x ∈ s
h : UniqueDiffOn 𝕜 s
f g : 𝕜 → F
hf : ContDiffOn ... | ((:c Eq) (:fv _uniq.63685) ((:c iteratedDerivWithin) (:fv _uniq.63679) (:fv _uniq.63682) (:fv _uniq.63685) (:fv _uniq.63688) (:fv _uniq.63801) (:fv _uniq.67563) ((:c HSub.hSub) (:forall _ (:fv _uniq.63679) (:fv _uniq.63685)) (:forall _ (:fv _uniq.63679) (:fv _uniq.63685)) (:forall _ (:fv _uniq.63679) (:fv _uniq.63685))... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁶","sexp":"((:c NontriviallyNormedField) (:fv _uniq.63679))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.63685))"},{"name":"inst✝⁴","sexp":"((:c NormedSpace) (:fv _uniq.63679) (:fv _uniq.63685) ((:c Nontriv... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c iteratedDerivWithin) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommG... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.63679","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.63682","is_instance":true,"is_let":false,"name":"inst✝⁶","sexp":"(:app (:c NontriviallyNormedFiel... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":3676,"sourceStart":3674,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3678,"sourceStart":3677,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"sub_eq_add_neg","source_end":3692,"source_start":3678,"syntax_kind":"ident"},{"source":"sub_eq_add_neg","source_end":3708,"source_start":3694,"syntax_kind":"ident"},{"source":"Pi.neg_def","source_end":3720,"source_start":3710,"syntax_kind":"ident"},{"source":"iteratedDerivWithin_add hx h hf hg.neg","source_... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.63679","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.63682","is_instance":true,"is_let":false,"user_name":"inst✝⁶"},{"binder_role":":implicit","context_index":2,"inter... | 10 | 2 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 681e7b8cbd602bd771ed88894224a31642d9101471282cb90360ab5657a130c6 | 859ea03c303da912a12d92a7fa77d1e6042ef45bc0d8f9865783f65d6f39f72f | a94f315c9bbbb1faa0dc332f169426e1668c2a31cf47c0af77127f62f41e29b6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,479 | PartialHomeomorph.map_extend_symm_nhdsWithin_range | Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>nhdsWithin_univ</a>, ← <a>PartialHomeomorph.map_extend_symm_nhdsWithin</a> f I hy, <a>Set.preimage_univ</a>, <a>Set.univ_inter</a>] | 𝕜 : Type u_1
E : Type u_2
M : Type u_3
H : Type u_4
E' : Type u_5
M' : Type u_6
H' : Type u_7
inst✝⁸ : NontriviallyNormedField 𝕜
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : TopologicalSpace H
inst✝⁴ : TopologicalSpace M
f f' : PartialHomeomorph M H
I : ModelWithCorners 𝕜 E H
inst✝³ : NormedAddCo... | ((:c Eq) ((:c Filter) (:fv _uniq.123986)) ((:c Filter.map) (:fv _uniq.123983) (:fv _uniq.123986) ((:c PartialEquiv.toFun) (:fv _uniq.123983) (:fv _uniq.123986) ((:c PartialEquiv.symm) (:fv _uniq.123986) (:fv _uniq.123983) ((:c PartialHomeomorph.extend) (:fv _uniq.123980) (:fv _uniq.123983) (:fv _uniq.123986) (:fv _uniq... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"H","sexp":"(:sort (+ u_4 1))"},{"name":"E'","sexp":"(:sort (+ u_5 1))"},{"name":"M'","sexp":"(:sort (+ u_6 1))"},{"name":"H'","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁸","sexp":"((:c Nontr... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:app (:c Filter.map) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :explicit 2 (:app (:c PartialEquiv.toFun) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.123980","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.123983","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":49741,"sourceStart":49739,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":49743,"sourceStart":49742,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"nhdsWithin_univ","source_end":49762,"source_start":49747,"syntax_kind":"ident"},{"source":"map_extend_symm_nhdsWithin f I hy","source_end":49801,"source_start":49768,"syntax_kind":"Lean.Parser.Term.app"},{"source":"preimage_univ","source_end":49816,"source_start":49803,"syntax_kind":"ident"},{"source":"univ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.123980","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.123983","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 257 | 2 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8b95cf0736fe002c812df4663be5928d639fe1a19f4956139fae41338967d761 | 640f141a34772e65259c2734dd041e0b70e158b56496f37b94e548db5538b632 | 33c086dc843ab5acdb6eef957cb0a602239f7553b7a76338016597512d426117 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,480 | CategoryTheory.factorThruImage_comp_imageUnopOp_inv | Mathlib/CategoryTheory/Abelian/Opposite.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>CategoryTheory.Iso.comp_inv_eq</a>, <a>CategoryTheory.image_ι_op_comp_imageUnopOp_hom</a>] | C : Type u_1
inst✝¹ : Category.{u_2, u_1} C
inst✝ : Abelian C
X Y : C
f : X ⟶ Y
A B : Cᵒᵖ
g : A ⟶ B
⊢ factorThruImage g ≫ (imageUnopOp g).inv = (image.ι g.unop).op | ((:c Eq) ((:c Quiver.Hom) ((:c Opposite) (:fv _uniq.51096)) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c Opposite) (:fv _uniq.51096)) ((:c CategoryTheory.Category.toCategoryStruct) ((:c Opposite) (:fv _uniq.51096)) ((:c CategoryTheory.Category.opposite) (:fv _uniq.51096) (:fv _uniq.51100)))) (:fv _uniq.51175) ((:c... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.51096))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Abelian) (:fv _uniq.51096) (:fv _uniq.51100))"},{"name":"X","sexp":"(:fv _uniq.51096)"},{"name":"Y","sexp":"(:fv _uniq.51096)"},{"name":"f","sexp":"((:c Quiver... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:app (:c Opposite) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:app (:c Opposite) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:fv FV6)) (:arg :explicit 3 (:app (:c Opposite... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.51096","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.51100","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":7206,"sourceStart":7204,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7208,"sourceStart":7207,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"Iso.comp_inv_eq","source_end":7223,"source_start":7208,"syntax_kind":"ident"},{"source":"image_ι_op_comp_imageUnopOp_hom","source_end":7257,"source_start":7225,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.51096","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.51100","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 46 | 2 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2e7266f2c340b3a6683f14bbb48cb74c3946afd921d89d2f9fd805d8a221f3ae | 64949c0c67ceaaeafd9c3e6eb12ae64cd5a02ce11d3589b47b6fdd00ff6815a2 | 079a0e7d49adef59010d6b8bf397cfb1e4c2d52de05b3df915c2f1a8fc206aa2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,481 | affineIndependent_equiv | Mathlib/LinearAlgebra/AffineSpace/Independent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨?_, <a>AffineIndependent.comp_embedding</a> e.toEmbedding⟩ | k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
ι' : Type u_5
e : ι ≃ ι'
p : ι' → P
⊢ AffineIndependent k (p ∘ ⇑e) ↔ AffineIndependent k p | k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
ι' : Type u_5
e : ι ≃ ι'
p : ι' → P
⊢ AffineIndependent k (p ∘ ⇑e) → AffineIndependent k p | ((:c Iff) ((:c AffineIndependent) (:fv _uniq.86896) (:fv _uniq.86899) (:fv _uniq.86902) (:fv _uniq.86905) (:fv _uniq.86908) (:fv _uniq.87495) (:fv _uniq.87584) (:fv _uniq.87587) ((:c Function.comp) (:fv _uniq.87587) (:fv _uniq.88052) (:fv _uniq.86902) (:fv _uniq.88054) ((:c DFunLike.coe) ((:c Equiv) (:fv _uniq.87587) (... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.86896))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.86899))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.86896) (:fv _uniq.86899) ((:... | (:app (:c Iff) (:arg :explicit 0 (:app (:c AffineIndependent) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86896","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.86899","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":16833,"sourceStart":16827,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":16837,"sourceStart":16834,"tag":"atom"},{"children":[{"children":[{"source":"?","sourceEnd":16838,"sourceStart":16837,"tag":"atom"},{"children":[{"source":"_","sourceEnd":16839,"sourceStart":16838,... | [] | [{"source":"⟨?_, AffineIndependent.comp_embedding e.toEmbedding⟩","source_end":16890,"source_start":16834,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86896","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.86899","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 39 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3e4ef4a86e802a04a9c6c91d8a3f40f123527b4de59bb38307cd0f46ecb16009 | 61ccf8b0bd17a726d307adc4176bf2522e3df8c77575290e6e9f96dae369f3e2 | c808433c0da3f71ee89d5288f0085979bc8c2e66f2402aca333438e00e9e81ea | c11f22f3b319e81d496b7c05f554a824d07bfa1952389d96ffce469df909854f |
cat-searcher/leandojo-benchmark-4-random | test | 1,482 | affineIndependent_equiv | Mathlib/LinearAlgebra/AffineSpace/Independent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro h | k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
ι' : Type u_5
e : ι ≃ ι'
p : ι' → P
⊢ AffineIndependent k (p ∘ ⇑e) → AffineIndependent k p | k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
ι' : Type u_5
e : ι ≃ ι'
p : ι' → P
h : AffineIndependent k (p ∘ ⇑e)
⊢ AffineIndependent k p | (:forall _ ((:c AffineIndependent) (:fv _uniq.86896) (:fv _uniq.86899) (:fv _uniq.86902) (:fv _uniq.86905) (:fv _uniq.86908) (:fv _uniq.87495) (:fv _uniq.87584) (:fv _uniq.87587) ((:c Function.comp) (:fv _uniq.87587) (:fv _uniq.88052) (:fv _uniq.86902) (:fv _uniq.88054) ((:c DFunLike.coe) ((:c Equiv) (:fv _uniq.87587) ... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.86896))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.86899))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.86896) (:fv _uniq.86899) ((:... | (:forall _ :explicit (:app (:c AffineIndependent) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86896","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.86899","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"intro","sourceEnd":16898,"sourceStart":16893,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":16900,"sourceStart":16899,"tag":"identifier"}],"kind":"null","source":"h","sourceEnd":16900,"sourceStart":16899,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"h","source_end":16900,"source_start":16899,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86896","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.86899","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 39 | 5 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aeb04620a1ee066e419d1cf1adf069c60cbd3f2c7587a0e211110fb2d438e961 | c11f22f3b319e81d496b7c05f554a824d07bfa1952389d96ffce469df909854f | 5cf42e5c5e9faf9804f4b8005e32168f3a46b38347377087a457c72b727740cb | f4688298efc057a7c253428accd6d9f10046e160fbc8f47639e064155b7ecd1a |
cat-searcher/leandojo-benchmark-4-random | test | 1,483 | affineIndependent_equiv | Mathlib/LinearAlgebra/AffineSpace/Independent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : p = p ∘ e ∘ e.symm.toEmbedding := by ext simp | k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
ι' : Type u_5
e : ι ≃ ι'
p : ι' → P
h : AffineIndependent k (p ∘ ⇑e)
⊢ AffineIndependent k p | k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
ι' : Type u_5
e : ι ≃ ι'
p : ι' → P
h : AffineIndependent k (p ∘ ⇑e)
this : p = p ∘ ⇑e ∘ ⇑e.symm.toEmbedding
⊢ AffineIndependent k p | ((:c AffineIndependent) (:fv _uniq.86896) (:fv _uniq.86899) (:fv _uniq.86902) (:fv _uniq.86905) (:fv _uniq.86908) (:fv _uniq.87495) (:fv _uniq.87584) (:fv _uniq.88052) (:fv _uniq.88054)) | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.86896))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.86899))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.86896) (:fv _uniq.86899) ((:... | (:app (:c AffineIndependent) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 5 (:instan... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86896","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.86899","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":16907,"sourceStart":16903,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":16908,"sourceStart":16908,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":16908,"sourceStart":16908,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"p = p ∘ e ∘ e.symm.toEmbedding","source_end":16944,"source_start":16910,"syntax_kind":"«term_=_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86896","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.86899","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 39 | 6 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 568e6ac0aa341d56025a8b988cdcdd89338f8bc76b5e06622c92e4e7b1b88b04 | f4688298efc057a7c253428accd6d9f10046e160fbc8f47639e064155b7ecd1a | 0a53825a766b7f93c522c3aa59cf90c4f3063c0031a1a58d86a6310214604344 | 50d85bacf4566fe8f09645bbdde620545609ef043000fa929e9b828ce5f227fe |
cat-searcher/leandojo-benchmark-4-random | test | 1,484 | affineIndependent_equiv | Mathlib/LinearAlgebra/AffineSpace/Independent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [this] | k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
ι' : Type u_5
e : ι ≃ ι'
p : ι' → P
h : AffineIndependent k (p ∘ ⇑e)
this : p = p ∘ ⇑e ∘ ⇑e.symm.toEmbedding
⊢ AffineIndependent k p | k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
ι' : Type u_5
e : ι ≃ ι'
p : ι' → P
h : AffineIndependent k (p ∘ ⇑e)
this : p = p ∘ ⇑e ∘ ⇑e.symm.toEmbedding
⊢ AffineIndependent k (p ∘ ⇑e ∘ ⇑e.symm.toEmbedding) | ((:c AffineIndependent) (:fv _uniq.86896) (:fv _uniq.86899) (:fv _uniq.86902) (:fv _uniq.86905) (:fv _uniq.86908) (:fv _uniq.87495) (:fv _uniq.87584) (:fv _uniq.88052) (:fv _uniq.88054)) | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.86896))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.86899))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.86896) (:fv _uniq.86899) ((:... | (:app (:c AffineIndependent) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 5 (:instan... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86896","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.86899","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":16972,"sourceStart":16970,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16974,"sourceStart":16973,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":13,"seman... | [] | [{"source":"this","source_end":16978,"source_start":16974,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86896","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.86899","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 39 | 10 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fcd046159ab93b880745f40230a545ce6f8188f67972f66566def6a30484a4ab | 50d85bacf4566fe8f09645bbdde620545609ef043000fa929e9b828ce5f227fe | 65e47f2d4a9bfabc21e1664a0b073b87e8fee657aeade999395c39aa954c5bad | d1ae2ed4fe64b282d842fa445cceee7961acf3cd180d3bbbbcb5a1ba4fee6f15 |
cat-searcher/leandojo-benchmark-4-random | test | 1,485 | affineIndependent_equiv | Mathlib/LinearAlgebra/AffineSpace/Independent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact h.comp_embedding e.symm.toEmbedding | k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
ι' : Type u_5
e : ι ≃ ι'
p : ι' → P
h : AffineIndependent k (p ∘ ⇑e)
this : p = p ∘ ⇑e ∘ ⇑e.symm.toEmbedding
⊢ AffineIndependent k (p ∘ ⇑e ∘ ⇑e.symm.toEmbedding) | ((:c AffineIndependent) (:fv _uniq.86896) (:fv _uniq.86899) (:fv _uniq.86902) (:fv _uniq.86905) (:fv _uniq.86908) (:fv _uniq.87495) (:fv _uniq.87584) (:fv _uniq.88052) ((:c Function.comp) (:fv _uniq.88052) (:fv _uniq.88052) (:fv _uniq.86902) (:fv _uniq.88054) ((:c Function.comp) (:fv _uniq.88052) (:fv _uniq.87587) (:fv... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.86896))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.86899))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.86896) (:fv _uniq.86899) ((:... | (:app (:c AffineIndependent) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 5 (:instan... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86896","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.86899","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":16987,"sourceStart":16982,"tag":"atom"},{"children":[{"source":"h.comp_embedding","sourceEnd":17004,"sourceStart":16988,"tag":"identifier"},{"children":[{"name":"Equiv.toEmbedding","semanticRole":"global","source":"e.symm.toEmbedding","sourceEnd":17023,"sourceStart":17005,"tag... | [] | [{"source":"h.comp_embedding e.symm.toEmbedding","source_end":17023,"source_start":16988,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86896","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.86899","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 39 | 13 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 89ebab4cf66cd298a805e4e4d84192c4f52c49e5075c19dccb893df82d339420 | d1ae2ed4fe64b282d842fa445cceee7961acf3cd180d3bbbbcb5a1ba4fee6f15 | 7ab415119524671837e83adfa0dfdc5a85d5fddd58bb92797ce3428b3cf86f79 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,486 | affineIndependent_equiv | Mathlib/LinearAlgebra/AffineSpace/Independent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext | k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
ι' : Type u_5
e : ι ≃ ι'
p : ι' → P
h : AffineIndependent k (p ∘ ⇑e)
⊢ p = p ∘ ⇑e ∘ ⇑e.symm.toEmbedding | case h
k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
ι' : Type u_5
e : ι ≃ ι'
p : ι' → P
h : AffineIndependent k (p ∘ ⇑e)
x✝ : ι'
⊢ p x✝ = (p ∘ ⇑e ∘ ⇑e.symm.toEmbedding) x✝ | ((:c Eq) (:forall _ (:fv _uniq.88052) (:fv _uniq.86902)) (:fv _uniq.88054) ((:c Function.comp) (:fv _uniq.88052) (:fv _uniq.88052) (:fv _uniq.86902) (:fv _uniq.88054) ((:c Function.comp) (:fv _uniq.88052) (:fv _uniq.87587) (:fv _uniq.88052) ((:c DFunLike.coe) ((:c Equiv) (:fv _uniq.87587) (:fv _uniq.88052)) (:fv _uniq.... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.86896))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.86899))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.86896) (:fv _uniq.86899) ((:... | (:app (:c Eq) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV9) (:fv FV2))) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:app (:c Function.comp) (:arg :implicit-type 0 (:fv FV9)) (:arg :implicit-type 1 (:fv FV9)) (:arg :implicit-type 2 (:fv FV2)) (:arg :explicit 3 (:fv FV11)) (:arg :explicit 4 (:app (:c Functio... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86896","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.86899","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"ext","sourceEnd":16958,"sourceStart":16955,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":16958,"sourceStart":16955,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86896","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.86899","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 39 | 8 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3ac797e2e05527a90b99198164eec4765ef59859981ab7ac424f70ca69c4ca43 | 4e76b96d0e824ecf675d7bf74c5f6d38ee240104773d7174555db3b9978d905d | a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de | f5ecfcac485d1dba3d7a53628f5860c298294d677703688e2250b6ce718db854 |
cat-searcher/leandojo-benchmark-4-random | test | 1,487 | affineIndependent_equiv | Mathlib/LinearAlgebra/AffineSpace/Independent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case h
k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
ι' : Type u_5
e : ι ≃ ι'
p : ι' → P
h : AffineIndependent k (p ∘ ⇑e)
x✝ : ι'
⊢ p x✝ = (p ∘ ⇑e ∘ ⇑e.symm.toEmbedding) x✝ | ((:c Eq) (:fv _uniq.86902) ((:fv _uniq.88054) (:fv _uniq.88535)) ((:c Function.comp) (:fv _uniq.88052) (:fv _uniq.88052) (:fv _uniq.86902) (:fv _uniq.88054) ((:c Function.comp) (:fv _uniq.88052) (:fv _uniq.87587) (:fv _uniq.88052) ((:c DFunLike.coe) ((:c Equiv) (:fv _uniq.87587) (:fv _uniq.88052)) (:fv _uniq.87587) (:l... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.86896))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.86899))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.86896) (:fv _uniq.86899) ((:... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:fv FV11) (:arg :explicit 0 (:fv FV13)))) (:arg :explicit 2 (:app (:c Function.comp) (:arg :implicit-type 0 (:fv FV9)) (:arg :implicit-type 1 (:fv FV9)) (:arg :implicit-type 2 (:fv FV2)) (:arg :explicit 3 (:fv FV11)) (:arg :explicit 4 (:app (:c Fu... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86896","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.86899","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":16967,"sourceStart":16963,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"ki... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.86896","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.86899","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 39 | 9 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ca49e66fc17a4244b23461c202c553530cf1512ce20941d47b05a11526764f95 | f5ecfcac485d1dba3d7a53628f5860c298294d677703688e2250b6ce718db854 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,488 | List.Ico.eq_nil_of_le | Mathlib/Data/List/Intervals.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>List.Ico</a>, Nat.sub_eq_zero_iff_le.mpr h] | n m : ℕ
h : m ≤ n
⊢ Ico n m = [] | ((:c Eq) ((:c List) (:c Nat)) ((:c List.Ico) (:fv _uniq.2404) (:fv _uniq.2405)) ((:c List.nil) (:c Nat))) | [{"name":"n","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c LE.le) (:c Nat) (:c instLENat) (:fv _uniq.2405) (:fv _uniq.2404))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c List.Ico) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))) (:arg :explicit 2 (:app (:c List.nil) (:arg :implicit-type 0 (:c Nat))))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2404","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.2405","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":2422,"sourceStart":2418,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"Ico","source_end":2427,"source_start":2424,"syntax_kind":"ident"},{"source":"Nat.sub_eq_zero_iff_le.mpr h","source_end":2457,"source_start":2429,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2404","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.2405","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 17 | 2 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cbcb5628bc6de643909fa319f9757d11ce02fc129cbe56ff3f8b1ecfcf1f35cb | df495ef9364cf7335bcbcc2e907c581e85510a0b98bbef6531e7d3fb3477c5a3 | 0e7122130d57f9dc4f84edb2f7d07eb94a5ae00e285ae3302900afcadb02521b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,489 | Polynomial.natSepDegree_X | Mathlib/FieldTheory/SeparableDegree.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Polynomial.natSepDegree</a>, <a>Polynomial.aroots_X</a>, <a>Multiset.toFinset_singleton</a>, <a>Finset.card_singleton</a>] | F : Type u
E : Type v
inst✝⁴ : Field F
inst✝³ : Field E
inst✝² : Algebra F E
K : Type w
inst✝¹ : Field K
inst✝ : Algebra F K
f : F[X]
⊢ X.natSepDegree = 1 | ((:c Eq) (:c Nat) ((:c Polynomial.natSepDegree) (:fv _uniq.33471) (:fv _uniq.33476) ((:c Polynomial.X) (:fv _uniq.33471) ((:c DivisionSemiring.toSemiring) (:fv _uniq.33471) ((:c Semifield.toDivisionSemiring) (:fv _uniq.33471) ((:c Field.toSemifield) (:fv _uniq.33471) (:fv _uniq.33476)))))) ((:c OfNat.ofNat) (:c Nat) (:... | [{"name":"F","sexp":"(:sort (+ u 1))"},{"name":"E","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.33471))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.33473))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.33471) (:fv _uniq.33473) ((:c Semifield.toCommSemiring) (:fv _uniq.33471) ((:... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Polynomial.natSepDegree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Polynomial.X) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33471","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33473","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":13511,"sourceStart":13507,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":13516,"sourceStart":13512,"tag":"atom"}],"kind"... | [] | [{"source":"natSepDegree","source_end":13530,"source_start":13518,"syntax_kind":"ident"},{"source":"aroots_X","source_end":13540,"source_start":13532,"syntax_kind":"ident"},{"source":"Multiset.toFinset_singleton","source_end":13569,"source_start":13542,"syntax_kind":"ident"},{"source":"Finset.card_singleton","source_en... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33471","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33473","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 39 | 2 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0751653715c3098b3a5ccb268f45818c5f0c642b3d6a77bc8e2d0952631bfc3c | 5eeaabfa7fe1a05afc9c3e452a90a21812aae6c25c8fc2a0cb3b50254aa23ca7 | 102b59649e2a71ddf040011339b6c5f63c81e65e803f7fc6bef5d901df420fae | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,490 | Polynomial.isUnit_of_self_mul_dvd_separable | Mathlib/FieldTheory/Separable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨p, rfl⟩ := hq | R : Type u
inst✝¹ : CommSemiring R
S : Type v
inst✝ : CommSemiring S
p✝ q✝ : ℕ
p q : R[X]
hp : p.Separable
hq : q * q ∣ p
⊢ IsUnit q | case intro
R : Type u
inst✝¹ : CommSemiring R
S : Type v
inst✝ : CommSemiring S
p✝ q✝ : ℕ
q p : R[X]
hp : (q * q * p).Separable
⊢ IsUnit q | ((:c IsUnit) ((:c Polynomial) (:fv _uniq.31551) ((:c CommSemiring.toSemiring) (:fv _uniq.31551) (:fv _uniq.31554))) ((:c MonoidWithZero.toMonoid) ((:c Polynomial) (:fv _uniq.31551) ((:c CommSemiring.toSemiring) (:fv _uniq.31551) (:fv _uniq.31554))) ((:c Semiring.toMonoidWithZero) ((:c Polynomial) (:fv _uniq.31551) ((:c... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommSemiring) (:fv _uniq.31551))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.31556))"},{"name":"p✝","sexp":"(:c Nat)"},{"name":"q✝","sexp":"(:c Nat)"},{"name":"p","sexp":"((:c Polynomial) (:fv _uniq.31... | (:app (:c IsUnit) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:ins... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31551","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31554","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CommSemiring) (:arg :ex... | {"children":[{"source":"obtain","sourceEnd":7116,"sourceStart":7110,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":7120,"sourceStart":7117,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"p","sourceEnd":7... | [] | [{"source":"hq","source_end":7135,"source_start":7133,"syntax_kind":"ident"},{"source":"⟨p, rfl⟩","source_end":7129,"source_start":7117,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31551","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31554","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 52 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9fbd3bcbf9cb77b8d6fe00f90a1820c8f4646f019e9d46bde24287716b1e9c23 | ac5b0a76ca3c735d9b33767cc492e3071b6c46b783711d53640c538ae08c7ce3 | dd15974d427710057eeb67c520c12f172158186cb414b2766c1f02d800ce4fa2 | 8f12330cad25d0c99e04d4f0e208edc370d26c281686ac2155fc869a702ff7f6 |
cat-searcher/leandojo-benchmark-4-random | test | 1,491 | Polynomial.isUnit_of_self_mul_dvd_separable | Mathlib/FieldTheory/Separable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply isCoprime_self.mp | case intro
R : Type u
inst✝¹ : CommSemiring R
S : Type v
inst✝ : CommSemiring S
p✝ q✝ : ℕ
q p : R[X]
hp : (q * q * p).Separable
⊢ IsUnit q | case intro
R : Type u
inst✝¹ : CommSemiring R
S : Type v
inst✝ : CommSemiring S
p✝ q✝ : ℕ
q p : R[X]
hp : (q * q * p).Separable
⊢ IsCoprime q q | ((:c IsUnit) ((:c Polynomial) (:fv _uniq.31551) ((:c CommSemiring.toSemiring) (:fv _uniq.31551) (:fv _uniq.31554))) ((:c MonoidWithZero.toMonoid) ((:c Polynomial) (:fv _uniq.31551) ((:c CommSemiring.toSemiring) (:fv _uniq.31551) (:fv _uniq.31554))) ((:c Semiring.toMonoidWithZero) ((:c Polynomial) (:fv _uniq.31551) ((:c... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommSemiring) (:fv _uniq.31551))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.31556))"},{"name":"p✝","sexp":"(:c Nat)"},{"name":"q✝","sexp":"(:c Nat)"},{"name":"q","sexp":"((:c Polynomial) (:fv _uniq.31... | (:app (:c IsUnit) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:ins... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31551","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31554","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CommSemiring) (:arg :ex... | {"children":[{"source":"apply","sourceEnd":7143,"sourceStart":7138,"tag":"atom"},{"name":"Iff.mp","semanticRole":"global","source":"isCoprime_self.mp","sourceEnd":7161,"sourceStart":7144,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply isCoprime_self.mp","sourceEnd":7161,"sourceStart":7138,"tag":"... | [] | [{"source":"isCoprime_self.mp","source_end":7161,"source_start":7144,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31551","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31554","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 52 | 5 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 80212e9560f76466f58ea11004223e78fc969e3287850e8967224ef51f84ee0e | 8f12330cad25d0c99e04d4f0e208edc370d26c281686ac2155fc869a702ff7f6 | db49ec21634c0e31811a1659d2d52bb63df9155580ed6cd04c5daf1527cd2a9c | f7f304bb921942d7162b2044e40e5e3b64dbb3f1066a5d1ae2456190aab39f16 |
cat-searcher/leandojo-benchmark-4-random | test | 1,492 | Polynomial.isUnit_of_self_mul_dvd_separable | Mathlib/FieldTheory/Separable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>IsCoprime</a> (q * (q * p)) (q * (<a>Polynomial.derivative</a> q * p + <a>Polynomial.derivative</a> q * p + q * <a>Polynomial.derivative</a> p)) := by simp only [← <a>mul_assoc</a>, <a>mul_add</a>] dsimp only [<a>Polynomial.Separable</a>] at hp convert hp using 1 rw [<a>Polynomial.derivative_mul</a>, <a>Polyn... | case intro
R : Type u
inst✝¹ : CommSemiring R
S : Type v
inst✝ : CommSemiring S
p✝ q✝ : ℕ
q p : R[X]
hp : (q * q * p).Separable
⊢ IsCoprime q q | case intro
R : Type u
inst✝¹ : CommSemiring R
S : Type v
inst✝ : CommSemiring S
p✝ q✝ : ℕ
q p : R[X]
hp : (q * q * p).Separable
this : IsCoprime (q * (q * p)) (q * (derivative q * p + derivative q * p + q * derivative p))
⊢ IsCoprime q q | ((:c IsCoprime) ((:c Polynomial) (:fv _uniq.31551) ((:c CommSemiring.toSemiring) (:fv _uniq.31551) (:fv _uniq.31554))) ((:c Polynomial.commSemiring) (:fv _uniq.31551) (:fv _uniq.31554)) (:fv _uniq.32039) (:fv _uniq.32039)) | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommSemiring) (:fv _uniq.31551))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.31556))"},{"name":"p✝","sexp":"(:c Nat)"},{"name":"q✝","sexp":"(:c Nat)"},{"name":"q","sexp":"((:c Polynomial) (:fv _uniq.31... | (:app (:c IsCoprime) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31551","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31554","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CommSemiring) (:arg :ex... | {"children":[{"source":"have","sourceEnd":7168,"sourceStart":7164,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":7169,"sourceStart":7169,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":7169,"sourceStart":7169,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"IsCoprime (q * (q * p))\n (q * (derivative q * p + derivative q * p + q * derivative p))","source_end":7263,"source_start":7171,"syntax_kind":"Lean.Parser.Term.app"},{"source":"mul_assoc","source_end":7298,"source_start":7289,"syntax_kind":"ident"},{"source":"mul_add","source_end":7307,"source_start":7... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31551","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31554","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 52 | 6 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8c4cdb2de609bd6fe73377a6057f1db1145b90e4bda69834e5640b28f1ba63e8 | f7f304bb921942d7162b2044e40e5e3b64dbb3f1066a5d1ae2456190aab39f16 | 8b14db2b5d23c9cbd64e55130a61859d8c6db6afed363b088a37b85ea912b95e | 90c6a6137841a551ebda1b4d1686109450760cedfa2df593e8a05b6ca0fd2a7c |
cat-searcher/leandojo-benchmark-4-random | test | 1,493 | Polynomial.isUnit_of_self_mul_dvd_separable | Mathlib/FieldTheory/Separable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>IsCoprime.of_mul_right_left</a> (<a>IsCoprime.of_mul_left_left</a> this) | case intro
R : Type u
inst✝¹ : CommSemiring R
S : Type v
inst✝ : CommSemiring S
p✝ q✝ : ℕ
q p : R[X]
hp : (q * q * p).Separable
this : IsCoprime (q * (q * p)) (q * (derivative q * p + derivative q * p + q * derivative p))
⊢ IsCoprime q q | ((:c IsCoprime) ((:c Polynomial) (:fv _uniq.31551) ((:c CommSemiring.toSemiring) (:fv _uniq.31551) (:fv _uniq.31554))) ((:c Polynomial.commSemiring) (:fv _uniq.31551) (:fv _uniq.31554)) (:fv _uniq.32039) (:fv _uniq.32039)) | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommSemiring) (:fv _uniq.31551))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.31556))"},{"name":"p✝","sexp":"(:c Nat)"},{"name":"q✝","sexp":"(:c Nat)"},{"name":"q","sexp":"((:c Polynomial) (:fv _uniq.31... | (:app (:c IsCoprime) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31551","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31554","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CommSemiring) (:arg :ex... | {"children":[{"source":"exact","sourceEnd":7421,"sourceStart":7416,"tag":"atom"},{"children":[{"name":"IsCoprime.of_mul_right_left","semanticRole":"global","source":"IsCoprime.of_mul_right_left","sourceEnd":7449,"sourceStart":7422,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":7451,"sourceStart... | [] | [{"source":"IsCoprime.of_mul_right_left (IsCoprime.of_mul_left_left this)","source_end":7483,"source_start":7422,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31551","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31554","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 52 | 16 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4cb9d792981d65ed983aa17a34d030dab017f80bdbcb2578268559b2794c8a3d | 90c6a6137841a551ebda1b4d1686109450760cedfa2df593e8a05b6ca0fd2a7c | bf853cfab2b8b394974f009dc78dec61fa51c4237f7aaa7363db3478b430bc75 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,494 | Polynomial.isUnit_of_self_mul_dvd_separable | Mathlib/FieldTheory/Separable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [← <a>mul_assoc</a>, <a>mul_add</a>] | R : Type u
inst✝¹ : CommSemiring R
S : Type v
inst✝ : CommSemiring S
p✝ q✝ : ℕ
q p : R[X]
hp : (q * q * p).Separable
⊢ IsCoprime (q * (q * p)) (q * (derivative q * p + derivative q * p + q * derivative p)) | R : Type u
inst✝¹ : CommSemiring R
S : Type v
inst✝ : CommSemiring S
p✝ q✝ : ℕ
q p : R[X]
hp : (q * q * p).Separable
⊢ IsCoprime (q * q * p) (q * derivative q * p + q * derivative q * p + q * q * derivative p) | ((:c IsCoprime) ((:c Polynomial) (:fv _uniq.31551) ((:c CommSemiring.toSemiring) (:fv _uniq.31551) (:fv _uniq.31554))) ((:c Polynomial.commSemiring) (:fv _uniq.31551) (:fv _uniq.31554)) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.31551) ((:c CommSemiring.toSemiring) (:fv _uniq.31551) (:fv _uniq.31554))) ((:c Polynomial... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommSemiring) (:fv _uniq.31551))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.31556))"},{"name":"p✝","sexp":"(:c Nat)"},{"name":"q✝","sexp":"(:c Nat)"},{"name":"q","sexp":"((:c Polynomial) (:fv _uniq.31... | (:app (:c IsCoprime) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31551","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31554","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CommSemiring) (:arg :ex... | {"children":[{"source":"simp","sourceEnd":7278,"sourceStart":7274,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":7283,"sourceStart":7279,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":7283,"s... | [] | [{"source":"mul_assoc","source_end":7298,"source_start":7289,"syntax_kind":"ident"},{"source":"mul_add","source_end":7307,"source_start":7300,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31551","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31554","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 52 | 8 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 77ac0d0a92a814dca5a3e7060e1eac8f190fb57e7453751f28260c59f01700d5 | 0ac41857fe571751b786634cec625627084e920acc3726c95f394e7a3e7c45d6 | 44ac071efed8f8bf7c9b88b023a450b2ea1cf7586b693292f8ae11cbc189460c | ff921f6a7d5308611a92cbefa9a36b29b78b87173e7f3b7bf22aada194e04a1e |
cat-searcher/leandojo-benchmark-4-random | test | 1,495 | Polynomial.isUnit_of_self_mul_dvd_separable | Mathlib/FieldTheory/Separable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp only [<a>Polynomial.Separable</a>] at hp | R : Type u
inst✝¹ : CommSemiring R
S : Type v
inst✝ : CommSemiring S
p✝ q✝ : ℕ
q p : R[X]
hp : (q * q * p).Separable
⊢ IsCoprime (q * q * p) (q * derivative q * p + q * derivative q * p + q * q * derivative p) | R : Type u
inst✝¹ : CommSemiring R
S : Type v
inst✝ : CommSemiring S
p✝ q✝ : ℕ
q p : R[X]
hp : IsCoprime (q * q * p) (derivative (q * q * p))
⊢ IsCoprime (q * q * p) (q * derivative q * p + q * derivative q * p + q * q * derivative p) | ((:c IsCoprime) ((:c Polynomial) (:fv _uniq.31551) ((:c CommSemiring.toSemiring) (:fv _uniq.31551) (:fv _uniq.31554))) ((:c Polynomial.commSemiring) (:fv _uniq.31551) (:fv _uniq.31554)) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.31551) ((:c CommSemiring.toSemiring) (:fv _uniq.31551) (:fv _uniq.31554))) ((:c Polynomial... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommSemiring) (:fv _uniq.31551))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.31556))"},{"name":"p✝","sexp":"(:c Nat)"},{"name":"q✝","sexp":"(:c Nat)"},{"name":"q","sexp":"((:c Polynomial) (:fv _uniq.31... | (:app (:c IsCoprime) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31551","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31554","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CommSemiring) (:arg :ex... | {"children":[{"source":"dsimp","sourceEnd":7318,"sourceStart":7313,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":7323,"sourceStart":7319,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":7323,"... | [] | [{"source":"Separable","source_end":7334,"source_start":7325,"syntax_kind":"ident"},{"source":"hp","source_end":7341,"source_start":7339,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31551","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31554","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 52 | 9 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f3172d121560dc096f9eff23730c904f3a8890835f87963bf63eefb67d896907 | ff921f6a7d5308611a92cbefa9a36b29b78b87173e7f3b7bf22aada194e04a1e | f48bb9748a918d7dc5f331b1e17ae87b0c8ee405ced415b0649272b19d81dae1 | 4af7deae61f41f50b5c89dc725a4ebef627117dd161c7c388d330c768dde2180 |
cat-searcher/leandojo-benchmark-4-random | test | 1,496 | Polynomial.isUnit_of_self_mul_dvd_separable | Mathlib/FieldTheory/Separable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert hp using 1 | R : Type u
inst✝¹ : CommSemiring R
S : Type v
inst✝ : CommSemiring S
p✝ q✝ : ℕ
q p : R[X]
hp : IsCoprime (q * q * p) (derivative (q * q * p))
⊢ IsCoprime (q * q * p) (q * derivative q * p + q * derivative q * p + q * q * derivative p) | case h.e'_4
R : Type u
inst✝¹ : CommSemiring R
S : Type v
inst✝ : CommSemiring S
p✝ q✝ : ℕ
q p : R[X]
hp : IsCoprime (q * q * p) (derivative (q * q * p))
⊢ q * derivative q * p + q * derivative q * p + q * q * derivative p = derivative (q * q * p) | ((:c IsCoprime) ((:c Polynomial) (:fv _uniq.31551) ((:c CommSemiring.toSemiring) (:fv _uniq.31551) (:fv _uniq.31554))) ((:c Polynomial.commSemiring) (:fv _uniq.31551) (:fv _uniq.31554)) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.31551) ((:c CommSemiring.toSemiring) (:fv _uniq.31551) (:fv _uniq.31554))) ((:c Polynomial... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommSemiring) (:fv _uniq.31551))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.31556))"},{"name":"p✝","sexp":"(:c Nat)"},{"name":"q✝","sexp":"(:c Nat)"},{"name":"q","sexp":"((:c Polynomial) (:fv _uniq.31... | (:app (:c IsCoprime) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31551","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31554","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CommSemiring) (:arg :ex... | {"children":[{"source":"convert","sourceEnd":7353,"sourceStart":7346,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":9,"semanticRole":"local","source":"hp","sourceEnd":7356,"sourceStart":7354,"tag":"identifier"},{"children":[{"s... | [] | [{"source":"hp","source_end":7356,"source_start":7354,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31551","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31554","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 52 | 10 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e9c962019c4222af19f3fcf8a088cc26db0e1b94e7878d81d1d0410ddd8651ba | 4af7deae61f41f50b5c89dc725a4ebef627117dd161c7c388d330c768dde2180 | b384601cf5fcffa2b1d9b5be9be70b8312b05ff30db261a8ba21f81f460855fc | 15b411e8b30fa498d12e1c0a88b068366fdbab18f742dcb6c8e42b3e9cc2de49 |
cat-searcher/leandojo-benchmark-4-random | test | 1,497 | Polynomial.isUnit_of_self_mul_dvd_separable | Mathlib/FieldTheory/Separable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Polynomial.derivative_mul</a>, <a>Polynomial.derivative_mul</a>] | case h.e'_4
R : Type u
inst✝¹ : CommSemiring R
S : Type v
inst✝ : CommSemiring S
p✝ q✝ : ℕ
q p : R[X]
hp : IsCoprime (q * q * p) (derivative (q * q * p))
⊢ q * derivative q * p + q * derivative q * p + q * q * derivative p = derivative (q * q * p) | case h.e'_4
R : Type u
inst✝¹ : CommSemiring R
S : Type v
inst✝ : CommSemiring S
p✝ q✝ : ℕ
q p : R[X]
hp : IsCoprime (q * q * p) (derivative (q * q * p))
⊢ q * derivative q * p + q * derivative q * p + q * q * derivative p =
(derivative q * q + q * derivative q) * p + q * q * derivative p | ((:c Eq) ((:c Polynomial) (:fv _uniq.31551) ((:c CommSemiring.toSemiring) (:fv _uniq.31551) (:fv _uniq.31554))) ((:c HAdd.hAdd) ((:c Polynomial) (:fv _uniq.31551) ((:c CommSemiring.toSemiring) (:fv _uniq.31551) (:fv _uniq.31554))) ((:c Polynomial) (:fv _uniq.31551) ((:c CommSemiring.toSemiring) (:fv _uniq.31551) (:fv _... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommSemiring) (:fv _uniq.31551))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.31556))"},{"name":"p✝","sexp":"(:c Nat)"},{"name":"q✝","sexp":"(:c Nat)"},{"name":"q","sexp":"((:c Polynomial) (:fv _uniq.31... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31551","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31554","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CommSemiring) (:arg :ex... | {"children":[{"source":"rw","sourceEnd":7371,"sourceStart":7369,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7373,"sourceStart":7372,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Polynomial.derivativ... | [] | [{"source":"derivative_mul","source_end":7387,"source_start":7373,"syntax_kind":"ident"},{"source":"derivative_mul","source_end":7403,"source_start":7389,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31551","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31554","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 52 | 11 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | de6a4d718391ba1e8bfce862d18f4b48dda2993c2cb1419565905b80f20646e7 | 15b411e8b30fa498d12e1c0a88b068366fdbab18f742dcb6c8e42b3e9cc2de49 | 0201605681416c15952d0352eff0d5116b16ca2481e90837f13ceeccdfbf0230 | 66bab0a0e5cbc5d99842859da460763ee3a8334d441daded9be0d06908444c98 |
cat-searcher/leandojo-benchmark-4-random | test | 1,498 | Polynomial.isUnit_of_self_mul_dvd_separable | Mathlib/FieldTheory/Separable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | case h.e'_4
R : Type u
inst✝¹ : CommSemiring R
S : Type v
inst✝ : CommSemiring S
p✝ q✝ : ℕ
q p : R[X]
hp : IsCoprime (q * q * p) (derivative (q * q * p))
⊢ q * derivative q * p + q * derivative q * p + q * q * derivative p =
(derivative q * q + q * derivative q) * p + q * q * derivative p | ((:c Eq) ((:c Polynomial) (:fv _uniq.31551) ((:c CommSemiring.toSemiring) (:fv _uniq.31551) (:fv _uniq.31554))) ((:c HAdd.hAdd) ((:c Polynomial) (:fv _uniq.31551) ((:c CommSemiring.toSemiring) (:fv _uniq.31551) (:fv _uniq.31554))) ((:c Polynomial) (:fv _uniq.31551) ((:c CommSemiring.toSemiring) (:fv _uniq.31551) (:fv _... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommSemiring) (:fv _uniq.31551))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.31556))"},{"name":"p✝","sexp":"(:c Nat)"},{"name":"q✝","sexp":"(:c Nat)"},{"name":"q","sexp":"((:c Polynomial) (:fv _uniq.31... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31551","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31554","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CommSemiring) (:arg :ex... | {"children":[{"source":"ring","sourceEnd":7413,"sourceStart":7409,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":7413,"sourceStart":7409,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31551","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31554","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 52 | 15 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2aa89feb43b1da3a215ec6f09f86cbe2f4640ea48b66c116ad6b0f2f7112f8c3 | 66bab0a0e5cbc5d99842859da460763ee3a8334d441daded9be0d06908444c98 | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,499 | Disjoint.le_of_codisjoint | Mathlib/Order/Disjoint.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← @<a>inf_top_eq</a> _ _ _ a, ← @<a>bot_sup_eq</a> _ _ _ c, ← hab.eq_bot, ← hbc.eq_top, <a>sup_inf_right</a>] | α : Type u_1
inst✝¹ : DistribLattice α
inst✝ : BoundedOrder α
a b c : α
hab : Disjoint a b
hbc : Codisjoint b c
⊢ a ≤ c | α : Type u_1
inst✝¹ : DistribLattice α
inst✝ : BoundedOrder α
a b c : α
hab : Disjoint a b
hbc : Codisjoint b c
⊢ a ⊓ (b ⊔ c) ≤ (a ⊔ c) ⊓ (b ⊔ c) | ((:c LE.le) (:fv _uniq.21613) ((:c Preorder.toLE) (:fv _uniq.21613) ((:c PartialOrder.toPreorder) (:fv _uniq.21613) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.21613) ((:c Lattice.toSemilatticeInf) (:fv _uniq.21613) ((:c DistribLattice.toLattice) (:fv _uniq.21613) (:fv _uniq.21616)))))) (:fv _uniq.21655) (:fv _uniq.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c DistribLattice) (:fv _uniq.21613))"},{"name":"inst✝","sexp":"((:c BoundedOrder) (:fv _uniq.21613) ((:c Preorder.toLE) (:fv _uniq.21613) ((:c PartialOrder.toPreorder) (:fv _uniq.21613) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.21613) ((:c Lattic... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:fv FV5))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21613","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21616","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c DistribLattice) (:arg :... | {"children":[{"source":"rw","sourceEnd":16665,"sourceStart":16663,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16667,"sourceStart":16666,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":16670,"sourceSt... | [] | [{"source":"@inf_top_eq _ _ _ a","source_end":16690,"source_start":16671,"syntax_kind":"Lean.Parser.Term.app"},{"source":"@bot_sup_eq _ _ _ c","source_end":16715,"source_start":16696,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hab.eq_bot","source_end":16731,"source_start":16721,"syntax_kind":"ident"},{"source":"hb... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21613","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21616","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 198 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ca7d776203991daa963c024d3a7b5a68a17074109de61eb1aa84678abf9ef3ee | 84437a1a756f4ebcbc7e798be3f534c576e1d515372d2ab27ebcc87ca2d0876b | 3d49bee5bba6b263e7e9792dbfdc31509fd343163b3593ceb83d5b5e905deff4 | 8b47aee13bd0f6c28fe9d5dc7464391216ea47f631cc524aefbf76bc1e92d24c |
cat-searcher/leandojo-benchmark-4-random | test | 1,500 | Disjoint.le_of_codisjoint | Mathlib/Order/Disjoint.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>inf_le_inf_right</a> _ <a>le_sup_left</a> | α : Type u_1
inst✝¹ : DistribLattice α
inst✝ : BoundedOrder α
a b c : α
hab : Disjoint a b
hbc : Codisjoint b c
⊢ a ⊓ (b ⊔ c) ≤ (a ⊔ c) ⊓ (b ⊔ c) | ((:c LE.le) (:fv _uniq.21613) ((:c Preorder.toLE) (:fv _uniq.21613) ((:c PartialOrder.toPreorder) (:fv _uniq.21613) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.21613) ((:c Lattice.toSemilatticeInf) (:fv _uniq.21613) ((:c DistribLattice.toLattice) (:fv _uniq.21613) (:fv _uniq.21616)))))) ((:c Inf.inf) (:fv _uniq.2161... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c DistribLattice) (:fv _uniq.21613))"},{"name":"inst✝","sexp":"((:c BoundedOrder) (:fv _uniq.21613) ((:c Preorder.toLE) (:fv _uniq.21613) ((:c PartialOrder.toPreorder) (:fv _uniq.21613) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.21613) ((:c Lattic... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Inf.inf) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Inf) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV3)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21613","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21616","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c DistribLattice) (:arg :... | {"children":[{"source":"exact","sourceEnd":16771,"sourceStart":16766,"tag":"atom"},{"children":[{"name":"inf_le_inf_right","semanticRole":"global","source":"inf_le_inf_right","sourceEnd":16788,"sourceStart":16772,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":16790,"sourceStart":16789,"tag":"at... | [] | [{"source":"inf_le_inf_right _ le_sup_left","source_end":16802,"source_start":16772,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21613","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21616","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 198 | 11 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fb74251dadcf6843ae581b00a931991d621d18cb674590c0eb1288064cab3f1c | 8b47aee13bd0f6c28fe9d5dc7464391216ea47f631cc524aefbf76bc1e92d24c | 734aa6b5346c0466ded4b44d9c264f049c4fb4222545365fa8fc82312789f2ac | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,501 | MvPolynomial.totalDegree_finset_prod | Mathlib/Algebra/MvPolynomial/Degrees.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>le_trans</a> (<a>MvPolynomial.totalDegree_multiset_prod</a> _) ?_ | R : Type u
S : Type v
σ : Type u_1
τ : Type u_2
r : R
e : ℕ
n m : σ
s✝ : σ →₀ ℕ
inst✝ : CommSemiring R
p q : MvPolynomial σ R
ι : Type u_3
s : Finset ι
f : ι → MvPolynomial σ R
⊢ (s.prod f).totalDegree ≤ ∑ i ∈ s, (f i).totalDegree | R : Type u
S : Type v
σ : Type u_1
τ : Type u_2
r : R
e : ℕ
n m : σ
s✝ : σ →₀ ℕ
inst✝ : CommSemiring R
p q : MvPolynomial σ R
ι : Type u_3
s : Finset ι
f : ι → MvPolynomial σ R
⊢ (Multiset.map totalDegree (Multiset.map f s.val)).sum ≤ ∑ i ∈ s, (f i).totalDegree | ((:c LE.le) (:c Nat) (:c instLENat) ((:c MvPolynomial.totalDegree) (:fv _uniq.108700) (:fv _uniq.108705) (:fv _uniq.108744) ((:c Finset.prod) (:fv _uniq.108919) ((:c MvPolynomial) (:fv _uniq.108705) (:fv _uniq.108700) (:fv _uniq.108744)) ((:c CommSemiring.toCommMonoid) ((:c MvPolynomial) (:fv _uniq.108705) (:fv _uniq.1... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"σ","sexp":"(:sort (+ u_1 1))"},{"name":"τ","sexp":"(:sort (+ u_2 1))"},{"name":"r","sexp":"(:fv _uniq.108700)"},{"name":"e","sexp":"(:c Nat)"},{"name":"n","sexp":"(:fv _uniq.108705)"},{"name":"m","sexp":"(:fv _uniq.108705)"},{"name":"... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c MvPolynomial.totalDegree) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.108700","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.108702","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":20115,"sourceStart":20109,"tag":"atom"},{"children":[{"name":"le_trans","semanticRole":"global","source":"le_trans","sourceEnd":20124,"sourceStart":20116,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":20126,"sourceStart":20125,"tag":"atom"},{"children... | [] | [{"source":"le_trans (totalDegree_multiset_prod _) ?_","source_end":20157,"source_start":20116,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.108700","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.108702","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 126 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 807be706f60160def05add20629c246c333b3de42b052dcf2492dd9a03678aa4 | 1c613386bd737eefc1644be72505c9553f1dadff258b97123909c60e23523477 | ed0cd2c0cd492aa96d68b3c438b76fa705d983f877cf46d2e0d2b1ae2a4df6b8 | 2b6b93ef551a93f5e85e6ff56763a5ec1cfbe8b193d81caf7729a63bef8fa8e3 |
cat-searcher/leandojo-benchmark-4-random | test | 1,502 | MvPolynomial.totalDegree_finset_prod | Mathlib/Algebra/MvPolynomial/Degrees.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Multiset.map_map</a>] | R : Type u
S : Type v
σ : Type u_1
τ : Type u_2
r : R
e : ℕ
n m : σ
s✝ : σ →₀ ℕ
inst✝ : CommSemiring R
p q : MvPolynomial σ R
ι : Type u_3
s : Finset ι
f : ι → MvPolynomial σ R
⊢ (Multiset.map totalDegree (Multiset.map f s.val)).sum ≤ ∑ i ∈ s, (f i).totalDegree | R : Type u
S : Type v
σ : Type u_1
τ : Type u_2
r : R
e : ℕ
n m : σ
s✝ : σ →₀ ℕ
inst✝ : CommSemiring R
p q : MvPolynomial σ R
ι : Type u_3
s : Finset ι
f : ι → MvPolynomial σ R
⊢ (Multiset.map (totalDegree ∘ f) s.val).sum ≤ ∑ i ∈ s, (f i).totalDegree | ((:c LE.le) (:c Nat) ((:c Preorder.toLE) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring)))) ((:c Multiset.sum) (:c Nat) (:c Nat.instAddCommMonoid) ((:c Multiset.map) ((:c MvPolynomial) (:fv _uniq.108705) (:fv _uniq.108700) (:fv _uniq... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"σ","sexp":"(:sort (+ u_1 1))"},{"name":"τ","sexp":"(:sort (+ u_2 1))"},{"name":"r","sexp":"(:fv _uniq.108700)"},{"name":"e","sexp":"(:c Nat)"},{"name":"n","sexp":"(:fv _uniq.108705)"},{"name":"m","sexp":"(:fv _uniq.108705)"},{"name":"... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Multiset.sum) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Mu... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.108700","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.108702","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":20162,"sourceStart":20160,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":20164,"sourceStart":20163,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Multiset.map_map... | [] | [{"source":"Multiset.map_map","source_end":20180,"source_start":20164,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.108700","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.108702","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 126 | 5 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 748dc6246c01b7e58efd5cd1d31801ea001e60b34f4839a20b04f078452c8e0f | 2b6b93ef551a93f5e85e6ff56763a5ec1cfbe8b193d81caf7729a63bef8fa8e3 | b52466db650d3d80546ee0a0053723029b8fa2c2d80a302ca4ea49d200852eb5 | c53a88104c40cd0032c853b790006662fc7e3c469539d47be0f884d05fe8c87c |
cat-searcher/leandojo-benchmark-4-random | test | 1,503 | MvPolynomial.totalDegree_finset_prod | Mathlib/Algebra/MvPolynomial/Degrees.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | R : Type u
S : Type v
σ : Type u_1
τ : Type u_2
r : R
e : ℕ
n m : σ
s✝ : σ →₀ ℕ
inst✝ : CommSemiring R
p q : MvPolynomial σ R
ι : Type u_3
s : Finset ι
f : ι → MvPolynomial σ R
⊢ (Multiset.map (totalDegree ∘ f) s.val).sum ≤ ∑ i ∈ s, (f i).totalDegree | ((:c LE.le) (:c Nat) ((:c Preorder.toLE) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring)))) ((:c Multiset.sum) (:c Nat) (:c Nat.instAddCommMonoid) ((:c Multiset.map) (:fv _uniq.108919) (:c Nat) ((:c Function.comp) (:fv _uniq.108919) ... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"σ","sexp":"(:sort (+ u_1 1))"},{"name":"τ","sexp":"(:sort (+ u_2 1))"},{"name":"r","sexp":"(:fv _uniq.108700)"},{"name":"e","sexp":"(:c Nat)"},{"name":"n","sexp":"(:fv _uniq.108705)"},{"name":"m","sexp":"(:fv _uniq.108705)"},{"name":"... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Multiset.sum) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Mu... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.108700","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.108702","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rfl","sourceEnd":20187,"sourceStart":20184,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":20187,"sourceStart":20184,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.108700","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.108702","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 126 | 8 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0ec3f84b52931a0ef179e613d97d53a3ffb4c065f1b403704b8ffe4697f483f2 | c53a88104c40cd0032c853b790006662fc7e3c469539d47be0f884d05fe8c87c | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,504 | Set.directedOn_iUnion | Mathlib/Data/Set/Lattice.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>DirectedOn</a>, <a>exists_prop</a>, <a>Set.mem_iUnion</a>, <a>exists_imp</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
ι₂ : Sort u_6
κ : ι → Sort u_7
κ₁ : ι → Sort u_8
κ₂ : ι → Sort u_9
κ' : ι' → Sort u_10
r : α → α → Prop
f : ι → Set α
hd : Directed (fun x x_1 => x ⊆ x_1) f
h : ∀ (x : ι), DirectedOn r (f x)
⊢ DirectedOn r (⋃ x, f x) | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
ι₂ : Sort u_6
κ : ι → Sort u_7
κ₁ : ι → Sort u_8
κ₂ : ι → Sort u_9
κ' : ι' → Sort u_10
r : α → α → Prop
f : ι → Set α
hd : Directed (fun x x_1 => x ⊆ x_1) f
h : ∀ (x : ι), DirectedOn r (f x)
⊢ ∀ (x : α) (x_1 : ι), x ∈ f x_1 → ∀ (y : α) (x_2 : ι), y ∈ f x... | ((:c DirectedOn) (:fv _uniq.218151) (:fv _uniq.218282) ((:c Set.iUnion) (:fv _uniq.218151) (:fv _uniq.218160) (:lambda x (:fv _uniq.218160) ((:fv _uniq.218283) 0)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort u_4)"},{"name":"ι'","sexp":"(:sort u_5)"},{"name":"ι₂","sexp":"(:sort u_6)"},{"name":"κ","sexp":"(:forall _ (:fv _uniq.218160) (:sort u_7))"},{"name":"κ₁","sexp":"(:forall ... | (:app (:c DirectedOn) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:app (:c Set.iUnion) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV3)) (:arg :explicit 2 (:lambda x :explicit (:fv FV3) (:app (:fv FV12) (:arg :explicit 0 0))))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.218151","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.218154","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":89102,"sourceStart":89098,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":89107,"sourceStart":89103,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":891... | [] | [{"source":"DirectedOn","source_end":89119,"source_start":89109,"syntax_kind":"ident"},{"source":"exists_prop","source_end":89132,"source_start":89121,"syntax_kind":"ident"},{"source":"mem_iUnion","source_end":89144,"source_start":89134,"syntax_kind":"ident"},{"source":"exists_imp","source_end":89156,"source_start":891... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.218151","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.218154","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 731 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a8c04f93544e7fe258832087349c54d25cefb87a6f9991cb63de5d7e576040fe | d1927aa0d8fa9f4b2f5eaedd38d07b7c5427e8b44e8ad6a9bc47fd0dacb7dfe0 | 15b4758e0737855062c1ca6b6e18d4bba66a59739a90348d542b66b0c70d3103 | 69bf5fa3b4cf49bca9e99b769bb2f32fba6071cad2e98fe2895deaa24afb733e |
cat-searcher/leandojo-benchmark-4-random | test | 1,505 | Set.directedOn_iUnion | Mathlib/Data/Set/Lattice.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun a₁ b₁ fb₁ a₂ b₂ fb₂ => let ⟨z, zb₁, zb₂⟩ := hd b₁ b₂ let ⟨x, xf, xa₁, xa₂⟩ := h z a₁ (zb₁ fb₁) a₂ (zb₂ fb₂) ⟨x, ⟨z, xf⟩, xa₁, xa₂⟩ | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
ι₂ : Sort u_6
κ : ι → Sort u_7
κ₁ : ι → Sort u_8
κ₂ : ι → Sort u_9
κ' : ι' → Sort u_10
r : α → α → Prop
f : ι → Set α
hd : Directed (fun x x_1 => x ⊆ x_1) f
h : ∀ (x : ι), DirectedOn r (f x)
⊢ ∀ (x : α) (x_1 : ι), x ∈ f x_1 → ∀ (y : α) (x_2 : ι), y ∈ f x... | (:forall x (:fv _uniq.218151) (:forall x (:fv _uniq.218160) (:forall _ ((:c Membership.mem) (:fv _uniq.218151) ((:c Set) (:fv _uniq.218151)) ((:c Set.instMembership) (:fv _uniq.218151)) 1 ((:fv _uniq.218283) 0)) (:forall y (:fv _uniq.218151) (:forall x (:fv _uniq.218160) (:forall _ ((:c Membership.mem) (:fv _uniq.21815... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort u_4)"},{"name":"ι'","sexp":"(:sort u_5)"},{"name":"ι₂","sexp":"(:sort u_6)"},{"name":"κ","sexp":"(:forall _ (:fv _uniq.218160) (:sort u_7))"},{"name":"κ₁","sexp":"(:forall ... | (:forall x :explicit (:fv FV0) (:forall x :explicit (:fv FV3) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.218151","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.218154","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":89165,"sourceStart":89160,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":89169,"sourceStart":89166,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"a₁","sourceEnd":89174,"sourceStart":89170,"tag":"identifier"},{"semanticRole":"scoped_loc... | [] | [{"source":"fun a₁ b₁ fb₁ a₂ b₂ fb₂ =>\n let ⟨z, zb₁, zb₂⟩ := hd b₁ b₂\n let ⟨x, xf, xa₁, xa₂⟩ := h z a₁ (zb₁ fb₁) a₂ (zb₂ fb₂)\n ⟨x, ⟨z, xf⟩, xa₁, xa₂⟩","source_end":89368,"source_start":89166,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.218151","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.218154","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 731 | 5 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 324447a7abcf16710043db255406da36a62e2e0f517743a8722356c9bf406dc1 | 69bf5fa3b4cf49bca9e99b769bb2f32fba6071cad2e98fe2895deaa24afb733e | 7eda088d02655cef2e82f455010f376e7b84fe8c7c9905fe28ef261c0824b9fa | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,506 | CategoryTheory.ShortComplex.HomologyMapData.congr_left_φH | Mathlib/Algebra/Homology/ShortComplex/Homology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [eq] | C : Type u
inst✝¹ : Category.{v, u} C
inst✝ : HasZeroMorphisms C
S S₁ S₂ S₃ S₄ : ShortComplex C
φ : S₁ ⟶ S₂
h₁ : S₁.HomologyData
h₂ : S₂.HomologyData
γ₁ γ₂ : HomologyMapData φ h₁ h₂
eq : γ₁ = γ₂
⊢ γ₁.left.φH = γ₂.left.φH | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.9544) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.9544) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.9544) (:fv _uniq.9547))) ((:c CategoryTheory.ShortComplex.LeftHomologyData.H) (:fv _uniq.9544) (:fv _uniq.9547) (:fv _uniq.9562) (:fv _uniq.9597) ((:c Catego... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.9544))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Limits.HasZeroMorphisms) (:fv _uniq.9544) (:fv _uniq.9547))"},{"name":"S","sexp":"((:c CategoryTheory.ShortComplex) (:fv _uniq.9544) (:fv _uniq.9547) (:fv _uniq.9... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c CategoryTheory.ShortComplex.LeftHomologyData.H) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9544","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.9547","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category) ... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":4110,"sourceStart":4108,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4112,"sourceStart":4111,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"eq","source_end":4114,"source_start":4112,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9544","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.9547","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":2,... | 20 | 2 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8ee4b20ea7ec7e1b43cceb477106c178c25351f93483b0d5fdd3ab26d7911e76 | 37d995d28ac7dc6a321105e1b88f4d93a6ab2f845c7d91b088520dcb5aab0782 | e5546e9c84981a9d89bde641a1dacab6d2d7c8c4f2c4a2825fcc86d385317bb5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,507 | TrivSqZeroExt.hasSum_expSeries_of_smul_comm | Mathlib/Analysis/NormedSpace/TrivSqZeroExt.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>HasSum</a> (fun n => <a>TrivSqZeroExt.fst</a> (<a>NormedSpace.expSeries</a> 𝕜 (tsze R M) n fun _ => x)) e := by simpa [<a>TrivSqZeroExt.fst_expSeries</a>] using h | 𝕜 : Type u_1
S : Type u_2
R : Type u_3
M : Type u_4
inst✝¹⁶ : Field 𝕜
inst✝¹⁵ : CharZero 𝕜
inst✝¹⁴ : Ring R
inst✝¹³ : AddCommGroup M
inst✝¹² : Algebra 𝕜 R
inst✝¹¹ : Module 𝕜 M
inst✝¹⁰ : Module R M
inst✝⁹ : Module Rᵐᵒᵖ M
inst✝⁸ : SMulCommClass R Rᵐᵒᵖ M
inst✝⁷ : IsScalarTower 𝕜 R M
inst✝⁶ : IsScalarTower 𝕜 Rᵐᵒᵖ M
... | 𝕜 : Type u_1
S : Type u_2
R : Type u_3
M : Type u_4
inst✝¹⁶ : Field 𝕜
inst✝¹⁵ : CharZero 𝕜
inst✝¹⁴ : Ring R
inst✝¹³ : AddCommGroup M
inst✝¹² : Algebra 𝕜 R
inst✝¹¹ : Module 𝕜 M
inst✝¹⁰ : Module R M
inst✝⁹ : Module Rᵐᵒᵖ M
inst✝⁸ : SMulCommClass R Rᵐᵒᵖ M
inst✝⁷ : IsScalarTower 𝕜 R M
inst✝⁶ : IsScalarTower 𝕜 Rᵐᵒᵖ M
... | ((:c HasSum) ((:c TrivSqZeroExt) (:fv _uniq.103171) (:fv _uniq.103174)) (:c Nat) ((:c TrivSqZeroExt.addCommMonoid) (:fv _uniq.103171) (:fv _uniq.103174) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.103171) ((:c NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring) (:fv _uniq.103171) ((:c NonAssocRing.toNonUn... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹⁶","sexp":"((:c Field) (:fv _uniq.103165))"},{"name":"inst✝¹⁵","sexp":"((:c CharZero) (:fv _uniq.103165) ((:c AddGroupWithOne.toAddMonoidWithOn... | (:app (:c HasSum) (:arg :implicit-type 0 (:app (:c TrivSqZeroExt) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV3)))) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:app (:c TrivSqZeroExt) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV3))))))... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.103165","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.103168","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"have","sourceEnd":4641,"sourceStart":4637,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":4642,"sourceStart":4642,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":4642,"sourceStart":4642,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"HasSum (fun n => fst (expSeries 𝕜 (tsze R M) n fun _ => x)) e","source_end":4708,"source_start":4644,"syntax_kind":"Lean.Parser.Term.app"},{"source":"fst_expSeries","source_end":4739,"source_start":4726,"syntax_kind":"ident"},{"source":"h","source_end":4748,"source_start":4747,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.103165","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.103168","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 16 | 4 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e0067f1e48a41ff9428262bab7e227f6d795a377c9a04a309c5835375c0aa2d9 | f22a0452f95c86af20ea904585104ccbbaacc629e1b4c8126d3efd0176be4c90 | fee8e34717c2ccbae6bb6b8deedc80b8f9c7be962dce351a023737ea1fa21b4f | 9a362b8ade21b17f4b3290c39bc3e7670d2c060c1270efc27e4744f9fa346a18 |
cat-searcher/leandojo-benchmark-4-random | test | 1,508 | TrivSqZeroExt.hasSum_expSeries_of_smul_comm | Mathlib/Analysis/NormedSpace/TrivSqZeroExt.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>TrivSqZeroExt.inl_fst_add_inr_snd_eq</a>] using (<a>TrivSqZeroExt.hasSum_inl</a> _ <| this).<a>HasSum.add</a> (<a>TrivSqZeroExt.hasSum_inr</a> _ <| <a>TrivSqZeroExt.hasSum_snd_expSeries_of_smul_comm</a> 𝕜 x hx h) | 𝕜 : Type u_1
S : Type u_2
R : Type u_3
M : Type u_4
inst✝¹⁶ : Field 𝕜
inst✝¹⁵ : CharZero 𝕜
inst✝¹⁴ : Ring R
inst✝¹³ : AddCommGroup M
inst✝¹² : Algebra 𝕜 R
inst✝¹¹ : Module 𝕜 M
inst✝¹⁰ : Module R M
inst✝⁹ : Module Rᵐᵒᵖ M
inst✝⁸ : SMulCommClass R Rᵐᵒᵖ M
inst✝⁷ : IsScalarTower 𝕜 R M
inst✝⁶ : IsScalarTower 𝕜 Rᵐᵒᵖ M
... | ((:c HasSum) ((:c TrivSqZeroExt) (:fv _uniq.103171) (:fv _uniq.103174)) (:c Nat) ((:c TrivSqZeroExt.addCommMonoid) (:fv _uniq.103171) (:fv _uniq.103174) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.103171) ((:c NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring) (:fv _uniq.103171) ((:c NonAssocRing.toNonUn... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹⁶","sexp":"((:c Field) (:fv _uniq.103165))"},{"name":"inst✝¹⁵","sexp":"((:c CharZero) (:fv _uniq.103165) ((:c AddGroupWithOne.toAddMonoidWithOn... | (:app (:c HasSum) (:arg :implicit-type 0 (:app (:c TrivSqZeroExt) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV3)))) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:app (:c TrivSqZeroExt) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV3))))))... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.103165","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.103168","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"simpa","sourceEnd":4756,"sourceStart":4751,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"chil... | [] | [{"source":"inl_fst_add_inr_snd_eq","source_end":4785,"source_start":4763,"syntax_kind":"ident"},{"source":"(hasSum_inl _ <| this).add (hasSum_inr _ <| hasSum_snd_expSeries_of_smul_comm 𝕜 x hx h)","source_end":4887,"source_start":4797,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.103165","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.103168","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 16 | 7 | exact | true | 1 | 26 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eb0980e083094f2d78e61d3c777e211184684442a02a7902261a01ce05ec211e | 9a362b8ade21b17f4b3290c39bc3e7670d2c060c1270efc27e4744f9fa346a18 | bf128445907fe235bdc4263fc7f8930ae1e6fc9ecc77651cc4becd9895a4e6b7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,509 | TrivSqZeroExt.hasSum_expSeries_of_smul_comm | Mathlib/Analysis/NormedSpace/TrivSqZeroExt.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [<a>TrivSqZeroExt.fst_expSeries</a>] using h | 𝕜 : Type u_1
S : Type u_2
R : Type u_3
M : Type u_4
inst✝¹⁶ : Field 𝕜
inst✝¹⁵ : CharZero 𝕜
inst✝¹⁴ : Ring R
inst✝¹³ : AddCommGroup M
inst✝¹² : Algebra 𝕜 R
inst✝¹¹ : Module 𝕜 M
inst✝¹⁰ : Module R M
inst✝⁹ : Module Rᵐᵒᵖ M
inst✝⁸ : SMulCommClass R Rᵐᵒᵖ M
inst✝⁷ : IsScalarTower 𝕜 R M
inst✝⁶ : IsScalarTower 𝕜 Rᵐᵒᵖ M
... | ((:c HasSum) (:fv _uniq.103171) (:c Nat) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.103171) ((:c NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring) (:fv _uniq.103171) ((:c NonAssocRing.toNonUnitalNonAssocRing) (:fv _uniq.103171) ((:c Ring.toNonAssocRing) (:fv _uniq.103171) (:fv _uniq.103313))))) (:fv _u... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹⁶","sexp":"((:c Field) (:fv _uniq.103165))"},{"name":"inst✝¹⁵","sexp":"((:c CharZero) (:fv _uniq.103165) ((:c AddGroupWithOne.toAddMonoidWithOn... | (:app (:c HasSum) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 4 (:lambda n :explicit (:c Nat) (:app ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.103165","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.103168","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"simpa","sourceEnd":4724,"sourceStart":4719,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"chil... | [] | [{"source":"fst_expSeries","source_end":4739,"source_start":4726,"syntax_kind":"ident"},{"source":"h","source_end":4748,"source_start":4747,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.103165","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.103168","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 16 | 6 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fc5ad908a10f1bdfe9e97e35ac99e13afacb5672bbe39ef0807fa9a2b1f57190 | 7aa79e310b109784bef3e771a9e54fa11a0de3d280f3a21b1055827fca5fb3b6 | a55db0f5884970d7d0763d54f3deff6a5bbe7efd83f62be865d5aca831a889c1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,510 | one_lt_finprod' | Mathlib/Algebra/BigOperators/Finprod.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases h' with ⟨i, hi⟩ | α : Type u_1
β : Type u_2
ι : Type u_3
G : Type u_4
M✝ : Type u_5
N : Type u_6
inst✝² : CommMonoid M✝
inst✝¹ : CommMonoid N
f✝ g : α → M✝
a b : α
s t : Set α
M : Type u_7
inst✝ : OrderedCancelCommMonoid M
f : ι → M
h : ∀ (i : ι), 1 ≤ f i
h' : ∃ i, 1 < f i
hf : (mulSupport f).Finite
⊢ 1 < ∏ᶠ (i : ι), f i | case intro
α : Type u_1
β : Type u_2
ι : Type u_3
G : Type u_4
M✝ : Type u_5
N : Type u_6
inst✝² : CommMonoid M✝
inst✝¹ : CommMonoid N
f✝ g : α → M✝
a b : α
s t : Set α
M : Type u_7
inst✝ : OrderedCancelCommMonoid M
f : ι → M
h : ∀ (i : ι), 1 ≤ f i
hf : (mulSupport f).Finite
i : ι
hi : 1 < f i
⊢ 1 < ∏ᶠ (i : ι), f i | ((:c LT.lt) (:fv _uniq.83979) ((:c Preorder.toLT) (:fv _uniq.83979) ((:c PartialOrder.toPreorder) (:fv _uniq.83979) ((:c OrderedCommMonoid.toPartialOrder) (:fv _uniq.83979) ((:c OrderedCancelCommMonoid.toOrderedCommMonoid) (:fv _uniq.83979) (:fv _uniq.83980))))) ((:c OfNat.ofNat) (:fv _uniq.83979) (:lit 1) ((:c One.toO... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"M✝","sexp":"(:sort (+ u_5 1))"},{"name":"N","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝²","sexp":"((:c CommMonoid) (:fv _uniq.82699))"},{"name":"inst✝¹... | (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV15)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV15))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV15)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV15)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.82687","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.82690","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rcases","sourceEnd":27410,"sourceStart":27404,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":19,"semanticRole":"local","source":"h'","sourceEnd":27413,"sourceStart":27411,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget",... | [] | [{"source":"h'","source_end":27413,"source_start":27411,"syntax_kind":"ident"},{"source":"⟨i, hi⟩","source_end":27430,"source_start":27419,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.82687","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.82690","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 171 | 4 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 53bbe9a49e367776afbbcc2d076aaa0173c2e2f611c71f6b20b4a2b90f203775 | 53e7cfc16a1522070396732a0572ee6a861cae23d4bec1d6db1da15643175f80 | a9cdb9d8180b53656853e26a401d92977710a2ae1ce3d292fc40435b995dbe1d | b7ea80552189090e3b0a8b9a5a9f496538e1ac8076b3e1933febb0e66ca987a2 |
cat-searcher/leandojo-benchmark-4-random | test | 1,511 | one_lt_finprod' | Mathlib/Algebra/BigOperators/Finprod.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>finprod_eq_prod</a> _ hf] | case intro
α : Type u_1
β : Type u_2
ι : Type u_3
G : Type u_4
M✝ : Type u_5
N : Type u_6
inst✝² : CommMonoid M✝
inst✝¹ : CommMonoid N
f✝ g : α → M✝
a b : α
s t : Set α
M : Type u_7
inst✝ : OrderedCancelCommMonoid M
f : ι → M
h : ∀ (i : ι), 1 ≤ f i
hf : (mulSupport f).Finite
i : ι
hi : 1 < f i
⊢ 1 < ∏ᶠ (i : ι), f i | case intro
α : Type u_1
β : Type u_2
ι : Type u_3
G : Type u_4
M✝ : Type u_5
N : Type u_6
inst✝² : CommMonoid M✝
inst✝¹ : CommMonoid N
f✝ g : α → M✝
a b : α
s t : Set α
M : Type u_7
inst✝ : OrderedCancelCommMonoid M
f : ι → M
h : ∀ (i : ι), 1 ≤ f i
hf : (mulSupport f).Finite
i : ι
hi : 1 < f i
⊢ 1 < ∏ i ∈ hf.toFinset, ... | ((:c LT.lt) (:fv _uniq.83979) ((:c Preorder.toLT) (:fv _uniq.83979) ((:c PartialOrder.toPreorder) (:fv _uniq.83979) ((:c OrderedCommMonoid.toPartialOrder) (:fv _uniq.83979) ((:c OrderedCancelCommMonoid.toOrderedCommMonoid) (:fv _uniq.83979) (:fv _uniq.83980))))) ((:c OfNat.ofNat) (:fv _uniq.83979) (:lit 1) ((:c One.toO... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"M✝","sexp":"(:sort (+ u_5 1))"},{"name":"N","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝²","sexp":"((:c CommMonoid) (:fv _uniq.82699))"},{"name":"inst✝¹... | (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV15)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV15))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV15)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV15)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.82687","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.82690","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":27435,"sourceStart":27433,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27437,"sourceStart":27436,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"fin... | [] | [{"source":"finprod_eq_prod _ hf","source_end":27457,"source_start":27437,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.82687","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.82690","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 171 | 5 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ac02eb042680070362adee7c4d45aa7cef1d1dc4e68e3604d85b325bf8bc23c9 | b7ea80552189090e3b0a8b9a5a9f496538e1ac8076b3e1933febb0e66ca987a2 | 433603a54da6f6260658db2b68d37d3bbad4c0752dcff63ba3f0195beee8531e | be58fbb26490f8efb95f50699e489c9b130291fa18f187a8de574f059aa2a498 |
cat-searcher/leandojo-benchmark-4-random | test | 1,512 | one_lt_finprod' | Mathlib/Algebra/BigOperators/Finprod.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Finset.one_lt_prod'</a> (fun i _ ↦ h i) ⟨i, ?_, hi⟩ | case intro
α : Type u_1
β : Type u_2
ι : Type u_3
G : Type u_4
M✝ : Type u_5
N : Type u_6
inst✝² : CommMonoid M✝
inst✝¹ : CommMonoid N
f✝ g : α → M✝
a b : α
s t : Set α
M : Type u_7
inst✝ : OrderedCancelCommMonoid M
f : ι → M
h : ∀ (i : ι), 1 ≤ f i
hf : (mulSupport f).Finite
i : ι
hi : 1 < f i
⊢ 1 < ∏ i ∈ hf.toFinset, ... | case intro
α : Type u_1
β : Type u_2
ι : Type u_3
G : Type u_4
M✝ : Type u_5
N : Type u_6
inst✝² : CommMonoid M✝
inst✝¹ : CommMonoid N
f✝ g : α → M✝
a b : α
s t : Set α
M : Type u_7
inst✝ : OrderedCancelCommMonoid M
f : ι → M
h : ∀ (i : ι), 1 ≤ f i
hf : (mulSupport f).Finite
i : ι
hi : 1 < f i
⊢ i ∈ hf.toFinset | ((:c LT.lt) (:fv _uniq.83979) ((:c Preorder.toLT) (:fv _uniq.83979) ((:c PartialOrder.toPreorder) (:fv _uniq.83979) ((:c OrderedCommMonoid.toPartialOrder) (:fv _uniq.83979) ((:c OrderedCancelCommMonoid.toOrderedCommMonoid) (:fv _uniq.83979) (:fv _uniq.83980))))) ((:c OfNat.ofNat) (:fv _uniq.83979) (:lit 1) ((:c One.toO... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"M✝","sexp":"(:sort (+ u_5 1))"},{"name":"N","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝²","sexp":"((:c CommMonoid) (:fv _uniq.82699))"},{"name":"inst✝¹... | (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV15)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV15))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV15)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV15)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.82687","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.82690","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":27467,"sourceStart":27461,"tag":"atom"},{"children":[{"name":"Finset.one_lt_prod'","semanticRole":"global","source":"Finset.one_lt_prod'","sourceEnd":27487,"sourceStart":27468,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":27489,"sourceStart":27488,"t... | [] | [{"source":"Finset.one_lt_prod' (fun i _ ↦ h i) ⟨i, ?_, hi⟩","source_end":27521,"source_start":27468,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.82687","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.82690","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 171 | 8 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b17f09351000b504dd4a4b4346cc95d5739c3644f24c251f8a886dd264ec056e | be58fbb26490f8efb95f50699e489c9b130291fa18f187a8de574f059aa2a498 | 44e6dcee1d26f411ff6a20184facdfb7b6b153167aff06dd19e99e06d0f3af0b | abd5a4ca873f95723aad1eb570af23988e9861159cedd3651866fcee3d827ffc |
cat-searcher/leandojo-benchmark-4-random | test | 1,513 | one_lt_finprod' | Mathlib/Algebra/BigOperators/Finprod.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>Set.Finite.mem_toFinset</a>, <a>Function.mem_mulSupport</a>] using <a>ne_of_gt</a> hi | case intro
α : Type u_1
β : Type u_2
ι : Type u_3
G : Type u_4
M✝ : Type u_5
N : Type u_6
inst✝² : CommMonoid M✝
inst✝¹ : CommMonoid N
f✝ g : α → M✝
a b : α
s t : Set α
M : Type u_7
inst✝ : OrderedCancelCommMonoid M
f : ι → M
h : ∀ (i : ι), 1 ≤ f i
hf : (mulSupport f).Finite
i : ι
hi : 1 < f i
⊢ i ∈ hf.toFinset | ((:c Membership.mem) (:fv _uniq.82693) ((:c Finset) (:fv _uniq.82693)) ((:c Finset.instMembership) (:fv _uniq.82693)) (:fv _uniq.84009) ((:c Set.Finite.toFinset) (:fv _uniq.82693) ((:c Function.mulSupport) (:fv _uniq.82693) (:fv _uniq.83979) ((:c Monoid.toOne) (:fv _uniq.83979) ((:c CommMonoid.toMonoid) (:fv _uniq.8397... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"M✝","sexp":"(:sort (+ u_5 1))"},{"name":"N","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝²","sexp":"((:c CommMonoid) (:fv _uniq.82699))"},{"name":"inst✝¹... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 3 (:fv FV20)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.82687","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.82690","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simpa","sourceEnd":27529,"sourceStart":27524,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"ch... | [] | [{"source":"Finite.mem_toFinset","source_end":27555,"source_start":27536,"syntax_kind":"ident"},{"source":"mem_mulSupport","source_end":27571,"source_start":27557,"syntax_kind":"ident"},{"source":"ne_of_gt hi","source_end":27590,"source_start":27579,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.82687","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.82690","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 171 | 9 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8c5ebcf71b0587211c375baf2312a92c0c65ef919c714f6a193cb0d1064949a2 | abd5a4ca873f95723aad1eb570af23988e9861159cedd3651866fcee3d827ffc | bb43dfd59ca99d8288742af6632a79cd8dc4a47b86c499d8723fc39dba483a55 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,514 | Seminorm.closedBall_smul_closedBall | Mathlib/Analysis/Seminorm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.smul_subset_iff</a>, <a>Seminorm.mem_closedBall_zero</a>, <a>mem_closedBall_zero_iff</a>, <a>SeminormClass.map_smul_eq_mul</a>] | R : Type u_1
R' : Type u_2
𝕜 : Type u_3
𝕜₂ : Type u_4
𝕜₃ : Type u_5
𝕝 : Type u_6
E : Type u_7
E₂ : Type u_8
E₃ : Type u_9
F : Type u_10
G : Type u_11
ι : Type u_12
inst✝⁶ : SeminormedRing 𝕜
inst✝⁵ : AddCommGroup E
inst✝⁴ : Module 𝕜 E
inst✝³ : SeminormedRing 𝕜₂
inst✝² : AddCommGroup E₂
inst✝¹ : Module 𝕜₂ E₂
σ₁₂ ... | R : Type u_1
R' : Type u_2
𝕜 : Type u_3
𝕜₂ : Type u_4
𝕜₃ : Type u_5
𝕝 : Type u_6
E : Type u_7
E₂ : Type u_8
E₃ : Type u_9
F : Type u_10
G : Type u_11
ι : Type u_12
inst✝⁶ : SeminormedRing 𝕜
inst✝⁵ : AddCommGroup E
inst✝⁴ : Module 𝕜 E
inst✝³ : SeminormedRing 𝕜₂
inst✝² : AddCommGroup E₂
inst✝¹ : Module 𝕜₂ E₂
σ₁₂ ... | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.771460)) ((:c Set.instHasSubset) (:fv _uniq.771460)) ((:c HSMul.hSMul) ((:c Set) (:fv _uniq.771448)) ((:c Set) (:fv _uniq.771460)) ((:c Set) (:fv _uniq.771460)) ((:c instHSMul) ((:c Set) (:fv _uniq.771448)) ((:c Set) (:fv _uniq.771460)) ((:c Set.smul) (:fv _uniq.771448) (:fv ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R'","sexp":"(:sort (+ u_2 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜₂","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜₃","sexp":"(:sort (+ u_5 1))"},{"name":"𝕝","sexp":"(:sort (+ u_6 1))"},{"name":"E","sexp":"(:sort (+ u_7 1))"},{"name":"E₂","sexp":"(:sort (+ u... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV6))))))) (:arg :explicit 2 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.771442","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.771445","is_instance":false,"is_let":false,"name":"R'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"simp","sourceEnd":40570,"sourceStart":40566,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":40575,"sourceStart":40571,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":405... | [] | [{"source":"smul_subset_iff","source_end":40592,"source_start":40577,"syntax_kind":"ident"},{"source":"mem_closedBall_zero","source_end":40613,"source_start":40594,"syntax_kind":"ident"},{"source":"mem_closedBall_zero_iff","source_end":40638,"source_start":40615,"syntax_kind":"ident"},{"source":"map_smul_eq_mul","sourc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.771442","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.771445","is_instance":false,"is_let":false,"user_name":"R'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 280 | 4 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9d9b562a4833b0a7f8268d1cce42b56beb8e2c452fc3484fae90d0c4434becf4 | d40fde7cdd646431182c53d475d954cf6d23f6b22f263ff188d600712c1a7e7c | e9b18044628cfd6dc1d3388b5f344e07ecfc54c948bf49f54c7fa6dc7b8d6032 | 999f589bed2ecd71326eb321d9f83dd9f7559e54e65c6a02837433f16241c0af |
cat-searcher/leandojo-benchmark-4-random | test | 1,515 | Seminorm.closedBall_smul_closedBall | Mathlib/Analysis/Seminorm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro a ha b hb | R : Type u_1
R' : Type u_2
𝕜 : Type u_3
𝕜₂ : Type u_4
𝕜₃ : Type u_5
𝕝 : Type u_6
E : Type u_7
E₂ : Type u_8
E₃ : Type u_9
F : Type u_10
G : Type u_11
ι : Type u_12
inst✝⁶ : SeminormedRing 𝕜
inst✝⁵ : AddCommGroup E
inst✝⁴ : Module 𝕜 E
inst✝³ : SeminormedRing 𝕜₂
inst✝² : AddCommGroup E₂
inst✝¹ : Module 𝕜₂ E₂
σ₁₂ ... | R : Type u_1
R' : Type u_2
𝕜 : Type u_3
𝕜₂ : Type u_4
𝕜₃ : Type u_5
𝕝 : Type u_6
E : Type u_7
E₂ : Type u_8
E₃ : Type u_9
F : Type u_10
G : Type u_11
ι : Type u_12
inst✝⁶ : SeminormedRing 𝕜
inst✝⁵ : AddCommGroup E
inst✝⁴ : Module 𝕜 E
inst✝³ : SeminormedRing 𝕜₂
inst✝² : AddCommGroup E₂
inst✝¹ : Module 𝕜₂ E₂
σ₁₂ ... | (:forall a (:fv _uniq.771448) (:forall _ ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.771448) ((:c SeminormedAddGroup.toNorm) (:fv _uniq.771448) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) (:fv _uniq.771448) ((:c NonUnitalSeminormedRing.toSeminormedAddCommGroup) (:fv _uniq.771448) ((:c Semino... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R'","sexp":"(:sort (+ u_2 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜₂","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜₃","sexp":"(:sort (+ u_5 1))"},{"name":"𝕝","sexp":"(:sort (+ u_6 1))"},{"name":"E","sexp":"(:sort (+ u_7 1))"},{"name":"E₂","sexp":"(:sort (+ u... | (:forall a :explicit (:fv FV2) (:forall _ :explicit (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.771442","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.771445","is_instance":false,"is_let":false,"name":"R'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"intro","sourceEnd":40664,"sourceStart":40659,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":40666,"sourceStart":40665,"tag":"identifier"},{"semanticRole":"scoped_local","source":"ha","sourceEnd":40669,"sourceStart":40667,"tag":"identifier"},{"semanticRole":"sc... | [{"role":"fresh_name","source":"a","source_end":40666,"source_start":40665,"syntax_kind":"ident"},{"role":"fresh_name","source":"ha","source_end":40669,"source_start":40667,"syntax_kind":"ident"},{"role":"fresh_name","source":"b","source_end":40671,"source_start":40670,"syntax_kind":"ident"},{"role":"fresh_name","sourc... | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.771442","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.771445","is_instance":false,"is_let":false,"user_name":"R'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 280 | 5 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d3d2661c46a3da3255e38e8f80c8ee83f66e66b04ea88864ec6ac7d2ad6ca15e | 999f589bed2ecd71326eb321d9f83dd9f7559e54e65c6a02837433f16241c0af | 880e79bbd1cd41c63d694b3bc245eda77a1892ff28a5514c86a17b1d7b08d04a | eec5771a9b2734cbca6e772dbf988e8a27084fd4048b0720e7b10c7a95c85f80 |
cat-searcher/leandojo-benchmark-4-random | test | 1,516 | Seminorm.closedBall_smul_closedBall | Mathlib/Analysis/Seminorm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | R : Type u_1
R' : Type u_2
𝕜 : Type u_3
𝕜₂ : Type u_4
𝕜₃ : Type u_5
𝕝 : Type u_6
E : Type u_7
E₂ : Type u_8
E₃ : Type u_9
F : Type u_10
G : Type u_11
ι : Type u_12
inst✝⁶ : SeminormedRing 𝕜
inst✝⁵ : AddCommGroup E
inst✝⁴ : Module 𝕜 E
inst✝³ : SeminormedRing 𝕜₂
inst✝² : AddCommGroup E₂
inst✝¹ : Module 𝕜₂ E₂
σ₁₂ ... | case b0
R : Type u_1
R' : Type u_2
𝕜 : Type u_3
𝕜₂ : Type u_4
𝕜₃ : Type u_5
𝕝 : Type u_6
E : Type u_7
E₂ : Type u_8
E₃ : Type u_9
F : Type u_10
G : Type u_11
ι : Type u_12
inst✝⁶ : SeminormedRing 𝕜
inst✝⁵ : AddCommGroup E
inst✝⁴ : Module 𝕜 E
inst✝³ : SeminormedRing 𝕜₂
inst✝² : AddCommGroup E₂
inst✝¹ : Module 𝕜₂... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c Norm.norm) (:fv _uniq.771448) ((:c SeminormedRing.toNorm) (:fv _uniq.771448) (:fv _uniq.771478)) (:fv _uniq.779794)) ((:c DFunLike.coe) ((:c Seminorm) (:fv _uniq.771448) (:fv _uniq.77146... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R'","sexp":"(:sort (+ u_2 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜₂","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜₃","sexp":"(:sort (+ u_5 1))"},{"name":"𝕝","sexp":"(:sort (+ u_6 1))"},{"name":"E","sexp":"(:sort (+ u_7 1))"},{"name":"E₂","sexp":"(:sort (+ u... | (: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.771442","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.771445","is_instance":false,"is_let":false,"name":"R'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"gcongr","sourceEnd":40683,"sourceStart":40677,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":40683,"sourceStart":40677,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.771442","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.771445","is_instance":false,"is_let":false,"user_name":"R'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 280 | 6 | exact | true | 1 | 28 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fd2d19277c5cab406a64b1e7e2bfe85f1a59606e5ba86fe20ae0e6208e066021 | eec5771a9b2734cbca6e772dbf988e8a27084fd4048b0720e7b10c7a95c85f80 | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | 8117cc38e2a8f984804ef330858a17fab57480abdc7101aa50f1ad1c4ebf8dbb |
cat-searcher/leandojo-benchmark-4-random | test | 1,517 | Seminorm.closedBall_smul_closedBall | Mathlib/Analysis/Seminorm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>norm_nonneg</a> _).<a>LE.le.trans</a> ha | case b0
R : Type u_1
R' : Type u_2
𝕜 : Type u_3
𝕜₂ : Type u_4
𝕜₃ : Type u_5
𝕝 : Type u_6
E : Type u_7
E₂ : Type u_8
E₃ : Type u_9
F : Type u_10
G : Type u_11
ι : Type u_12
inst✝⁶ : SeminormedRing 𝕜
inst✝⁵ : AddCommGroup E
inst✝⁴ : Module 𝕜 E
inst✝³ : SeminormedRing 𝕜₂
inst✝² : AddCommGroup E₂
inst✝¹ : Module 𝕜₂... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) ((:c MulZeroClass.toZero) (:c Real) ((:c NonUnitalNonAssocSemiring.toMulZeroClass) (:c Real) ((:c NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring) (:c Real) ((:c NonUn... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R'","sexp":"(:sort (+ u_2 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜₂","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜₃","sexp":"(:sort (+ u_5 1))"},{"name":"𝕝","sexp":"(:sort (+ u_6 1))"},{"name":"E","sexp":"(:sort (+ u_7 1))"},{"name":"E₂","sexp":"(:sort (+ u... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.771442","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.771445","is_instance":false,"is_let":false,"name":"R'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"exact","sourceEnd":40691,"sourceStart":40686,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":40693,"sourceStart":40692,"tag":"atom"},{"children":[{"name":"norm_nonneg","semanticRole":"global","source":"norm_nonneg","sourceEnd":40704,"sourceStart":40693,"tag":"ident... | [] | [{"source":"(norm_nonneg _).trans ha","source_end":40716,"source_start":40692,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.771442","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.771445","is_instance":false,"is_let":false,"user_name":"R'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 280 | 7 | exact | true | 1 | 28 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 009e4f6c5db886e860c2187544607c1ee534340804ce5084090e72fc9e4d2f57 | 8117cc38e2a8f984804ef330858a17fab57480abdc7101aa50f1ad1c4ebf8dbb | 2d5d2fea06e6155738d6370fe601324dd05ffaac9ba241f6af579290d1ab0410 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,518 | Mon_.Mon_tensor_one_mul | Mathlib/CategoryTheory/Monoidal/Mon_.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>CategoryTheory.MonoidalCategory.comp_whiskerRight_assoc</a>] | C : Type u₁
inst✝² : Category.{v₁, u₁} C
inst✝¹ : MonoidalCategory C
inst✝ : BraidedCategory C
M N : Mon_ C
⊢ ((λ_ (𝟙_ C)).inv ≫ (M.one ⊗ N.one)) ▷ (M.X ⊗ N.X) ≫ tensor_μ C (M.X, N.X) (M.X, N.X) ≫ (M.mul ⊗ N.mul) =
(λ_ (M.X ⊗ N.X)).hom | C : Type u₁
inst✝² : Category.{v₁, u₁} C
inst✝¹ : MonoidalCategory C
inst✝ : BraidedCategory C
M N : Mon_ C
⊢ (λ_ (𝟙_ C)).inv ▷ (M.X ⊗ N.X) ≫ (M.one ⊗ N.one) ▷ (M.X ⊗ N.X) ≫ tensor_μ C (M.X, N.X) (M.X, N.X) ≫ (M.mul ⊗ N.mul) =
(λ_ (M.X ⊗ N.X)).hom | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.154409) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.154409) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.154409) (:fv _uniq.154412))) ((:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:fv _uniq.154409) (:fv _uniq.154412) ((:c CategoryTheory.MonoidalCate... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.154409))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.MonoidalCategory) (:fv _uniq.154409) (:fv _uniq.154412))"},{"name":"inst✝","sexp":"((:c CategoryTheory.BraidedCategory) (:fv _uniq.154409) (:fv _uniq.154412) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154409","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.154412","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Catego... | {"children":[{"source":"simp","sourceEnd":14009,"sourceStart":14005,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":14014,"sourceStart":14010,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":140... | [] | [{"source":"comp_whiskerRight_assoc","source_end":14039,"source_start":14016,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154409","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.154412","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 92 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 876649068980f1840558f4dbb981d80aadc5daf442806460fc64a4a61b54213a | 0f004cffe1a2222f226ba6fa473545e511c98740ac6786ee20bdd12d0b6a0022 | 204a9050cfd9bbd8b0c04cf924ecd2524afa58728fff1f131f7086e6200a922c | 65350a1ef458620370d1a31d9fd0479b29f91716869a57ee8c8ec2631aa5fff3 |
cat-searcher/leandojo-benchmark-4-random | test | 1,519 | Mon_.Mon_tensor_one_mul | Mathlib/CategoryTheory/Monoidal/Mon_.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | slice_lhs 2 3 => rw [<a>CategoryTheory.tensor_μ_natural_left</a>] | C : Type u₁
inst✝² : Category.{v₁, u₁} C
inst✝¹ : MonoidalCategory C
inst✝ : BraidedCategory C
M N : Mon_ C
⊢ (λ_ (𝟙_ C)).inv ▷ (M.X ⊗ N.X) ≫ (M.one ⊗ N.one) ▷ (M.X ⊗ N.X) ≫ tensor_μ C (M.X, N.X) (M.X, N.X) ≫ (M.mul ⊗ N.mul) =
(λ_ (M.X ⊗ N.X)).hom | C : Type u₁
inst✝² : Category.{v₁, u₁} C
inst✝¹ : MonoidalCategory C
inst✝ : BraidedCategory C
M N : Mon_ C
⊢ (λ_ (𝟙_ C)).inv ▷ (M.X ⊗ N.X) ≫ (tensor_μ C (𝟙_ C, 𝟙_ C) (M.X, N.X) ≫ (M.one ▷ M.X ⊗ N.one ▷ N.X)) ≫ (M.mul ⊗ N.mul) =
(λ_ (M.X ⊗ N.X)).hom | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.154409) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.154409) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.154409) (:fv _uniq.154412))) ((:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:fv _uniq.154409) (:fv _uniq.154412) ((:c CategoryTheory.MonoidalCate... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.154409))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.MonoidalCategory) (:fv _uniq.154409) (:fv _uniq.154412))"},{"name":"inst✝","sexp":"((:c CategoryTheory.BraidedCategory) (:fv _uniq.154409) (:fv _uniq.154412) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154409","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.154412","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Catego... | {"children":[{"source":"slice_lhs","sourceEnd":14052,"sourceStart":14043,"tag":"atom"},{"children":[{"source":"2","sourceEnd":14054,"sourceStart":14053,"tag":"atom"}],"kind":"num","source":"2","sourceEnd":14054,"sourceStart":14053,"tag":"node"},{"children":[{"source":"3","sourceEnd":14056,"sourceStart":14055,"tag":"ato... | [] | [{"source":"tensor_μ_natural_left","source_end":14086,"source_start":14064,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154409","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.154412","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 92 | 5 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4757a4fd20279b2b25d73b0b6c3fbdecd082263bbfb0300de0f61cb37071b5b3 | 65350a1ef458620370d1a31d9fd0479b29f91716869a57ee8c8ec2631aa5fff3 | 9690ed3c1e0928e9e968b02261f5da2934f5761bce3cb440d16b6f0caccf9712 | 54c0a7a6db2640269f5272abc23ad9563034e73ce88a1e4868d6a90cd794871c |
cat-searcher/leandojo-benchmark-4-random | test | 1,520 | Mon_.Mon_tensor_one_mul | Mathlib/CategoryTheory/Monoidal/Mon_.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | slice_lhs 3 4 => rw [← <a>CategoryTheory.MonoidalCategory.tensor_comp</a>, <a>Mon_.one_mul</a> M, <a>Mon_.one_mul</a> N] | C : Type u₁
inst✝² : Category.{v₁, u₁} C
inst✝¹ : MonoidalCategory C
inst✝ : BraidedCategory C
M N : Mon_ C
⊢ (λ_ (𝟙_ C)).inv ▷ (M.X ⊗ N.X) ≫ (tensor_μ C (𝟙_ C, 𝟙_ C) (M.X, N.X) ≫ (M.one ▷ M.X ⊗ N.one ▷ N.X)) ≫ (M.mul ⊗ N.mul) =
(λ_ (M.X ⊗ N.X)).hom | C : Type u₁
inst✝² : Category.{v₁, u₁} C
inst✝¹ : MonoidalCategory C
inst✝ : BraidedCategory C
M N : Mon_ C
⊢ (λ_ (𝟙_ C)).inv ▷ (M.X ⊗ N.X) ≫ tensor_μ C (𝟙_ C, 𝟙_ C) (M.X, N.X) ≫ ((λ_ M.X).hom ⊗ (λ_ N.X).hom) =
(λ_ (M.X ⊗ N.X)).hom | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.154409) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.154409) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.154409) (:fv _uniq.154412))) ((:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:fv _uniq.154409) (:fv _uniq.154412) ((:c CategoryTheory.MonoidalCate... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.154409))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.MonoidalCategory) (:fv _uniq.154409) (:fv _uniq.154412))"},{"name":"inst✝","sexp":"((:c CategoryTheory.BraidedCategory) (:fv _uniq.154409) (:fv _uniq.154412) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154409","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.154412","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Catego... | {"children":[{"source":"slice_lhs","sourceEnd":14099,"sourceStart":14090,"tag":"atom"},{"children":[{"source":"3","sourceEnd":14101,"sourceStart":14100,"tag":"atom"}],"kind":"num","source":"3","sourceEnd":14101,"sourceStart":14100,"tag":"node"},{"children":[{"source":"4","sourceEnd":14103,"sourceStart":14102,"tag":"ato... | [] | [{"source":"tensor_comp","source_end":14126,"source_start":14115,"syntax_kind":"ident"},{"source":"one_mul M","source_end":14137,"source_start":14128,"syntax_kind":"Lean.Parser.Term.app"},{"source":"one_mul N","source_end":14148,"source_start":14139,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154409","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.154412","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 92 | 10 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 111e5d4942e374796109a6779ed8217bb8c0c302e41967c5edc9538e250807a9 | 54c0a7a6db2640269f5272abc23ad9563034e73ce88a1e4868d6a90cd794871c | b60fa370c7d396f3688ca272c1354dccfdc603b4ebb190a6970bfda9e2a2cfd1 | ade0bdbcba9da27105290db70440394579dd93f85593eb29209856e39fa9afa4 |
cat-searcher/leandojo-benchmark-4-random | test | 1,521 | Mon_.Mon_tensor_one_mul | Mathlib/CategoryTheory/Monoidal/Mon_.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | symm | C : Type u₁
inst✝² : Category.{v₁, u₁} C
inst✝¹ : MonoidalCategory C
inst✝ : BraidedCategory C
M N : Mon_ C
⊢ (λ_ (𝟙_ C)).inv ▷ (M.X ⊗ N.X) ≫ tensor_μ C (𝟙_ C, 𝟙_ C) (M.X, N.X) ≫ ((λ_ M.X).hom ⊗ (λ_ N.X).hom) =
(λ_ (M.X ⊗ N.X)).hom | C : Type u₁
inst✝² : Category.{v₁, u₁} C
inst✝¹ : MonoidalCategory C
inst✝ : BraidedCategory C
M N : Mon_ C
⊢ (λ_ (M.X ⊗ N.X)).hom =
(λ_ (𝟙_ C)).inv ▷ (M.X ⊗ N.X) ≫ tensor_μ C (𝟙_ C, 𝟙_ C) (M.X, N.X) ≫ ((λ_ M.X).hom ⊗ (λ_ N.X).hom) | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.154409) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.154409) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.154409) (:fv _uniq.154412))) ((:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:fv _uniq.154409) (:fv _uniq.154412) ((:c CategoryTheory.MonoidalCate... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.154409))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.MonoidalCategory) (:fv _uniq.154409) (:fv _uniq.154412))"},{"name":"inst✝","sexp":"((:c CategoryTheory.BraidedCategory) (:fv _uniq.154409) (:fv _uniq.154412) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154409","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.154412","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Catego... | {"children":[{"source":"symm","sourceEnd":14156,"sourceStart":14152,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.symm","source":"symm","sourceEnd":14156,"sourceStart":14152,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154409","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.154412","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 92 | 17 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d94ea7b4980ed13257a1f05bc3d6bb49c9377a8bbfb6c3796527ae0a92e91a83 | ade0bdbcba9da27105290db70440394579dd93f85593eb29209856e39fa9afa4 | f97373c83b943be1711d624ac8176e49b7c19e0f5ce55ad3a0ad56d8d1aae1fa | 5989a97e854d8a28b02b06f4495b763d735a0c38487ac89df680399bc42f25cd |
cat-searcher/leandojo-benchmark-4-random | test | 1,522 | Mon_.Mon_tensor_one_mul | Mathlib/CategoryTheory/Monoidal/Mon_.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>CategoryTheory.tensor_left_unitality</a> C M.X N.X | C : Type u₁
inst✝² : Category.{v₁, u₁} C
inst✝¹ : MonoidalCategory C
inst✝ : BraidedCategory C
M N : Mon_ C
⊢ (λ_ (M.X ⊗ N.X)).hom =
(λ_ (𝟙_ C)).inv ▷ (M.X ⊗ N.X) ≫ tensor_μ C (𝟙_ C, 𝟙_ C) (M.X, N.X) ≫ ((λ_ M.X).hom ⊗ (λ_ N.X).hom) | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.154409) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.154409) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.154409) (:fv _uniq.154412))) ((:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:fv _uniq.154409) (:fv _uniq.154412) ((:c CategoryTheory.MonoidalCate... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.154409))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.MonoidalCategory) (:fv _uniq.154409) (:fv _uniq.154412))"},{"name":"inst✝","sexp":"((:c CategoryTheory.BraidedCategory) (:fv _uniq.154409) (:fv _uniq.154412) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154409","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.154412","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Catego... | {"children":[{"source":"exact","sourceEnd":14164,"sourceStart":14159,"tag":"atom"},{"children":[{"name":"CategoryTheory.tensor_left_unitality","semanticRole":"global","source":"tensor_left_unitality","sourceEnd":14186,"sourceStart":14165,"tag":"identifier"},{"children":[{"contextIndex":0,"semanticRole":"local","source"... | [] | [{"source":"tensor_left_unitality C M.X N.X","source_end":14196,"source_start":14165,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154409","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.154412","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 92 | 18 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dfe0dcba5854b90edb5342a28983823cdc92a0bf12c2933fd66e60b98bfb8f88 | 5989a97e854d8a28b02b06f4495b763d735a0c38487ac89df680399bc42f25cd | ce053c624f0496ac4880fc42154c283c1d86d8843943665eff2a1abd47dded3e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,523 | Int.toNat_add_toNat_neg_eq_nnnorm | Mathlib/Analysis/NormedSpace/Int.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Nat.cast_add</a>, <a>Int.toNat_add_toNat_neg_eq_natAbs</a>, <a>NNReal.natCast_natAbs</a>] | n : ℤ
⊢ ↑n.toNat + ↑(-n).toNat = ‖n‖₊ | ((:c Eq) (:c NNReal) ((:c HAdd.hAdd) (:c NNReal) (:c NNReal) (:c NNReal) ((:c instHAdd) (:c NNReal) ((:c Distrib.toAdd) (:c NNReal) ((:c NonUnitalNonAssocSemiring.toDistrib) (:c NNReal) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:c NNReal) ((:c Semiring.toNonAssocSemiring) (:c NNReal) (:c instNNRealSemiring)))... | [{"name":"n","sexp":"(:c Int)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c NNReal)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c NNReal)) (:arg :implicit-type 1 (:c NNReal)) (:arg :implicit-type 2 (:c NNReal)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c NNReal)) (:arg :explicit 1 (:c NNReal)) (:arg :explic... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.1846","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Int)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":1443,"sourceStart":1441,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1445,"sourceStart":1444,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"sour... | [] | [{"source":"Nat.cast_add","source_end":1461,"source_start":1449,"syntax_kind":"ident"},{"source":"toNat_add_toNat_neg_eq_natAbs","source_end":1492,"source_start":1463,"syntax_kind":"ident"},{"source":"NNReal.natCast_natAbs","source_end":1515,"source_start":1494,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.1846","is_instance":false,"is_let":false,"user_name":"n"}] | 10 | 2 | exact | true | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ba80e8c0f3c538ae770ed3566b8f557092df1768479330372fc90cf08220e74b | 31ed37ff9053abc9f8709993e7cec38bfc7043be77fc782ff8024e8f155b345b | ca8aab7ee50c9e56f9a7b8e5022f37e480d2c0272a81343c9319975ee1a3094b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,524 | Sym2.out_snd_mem | Mathlib/Data/Sym/Sym2.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Sym2.eq_swap</a>, <a>Sym2.mk</a>, e.out_eq] | α : Type u_1
β : Type u_2
γ : Type u_3
e : Sym2 α
⊢ e = s((Quot.out e).2, (Quot.out e).1) | ((:c Eq) ((:c Sym2) (:fv _uniq.20145)) (:fv _uniq.20211) ((:c Sym2.mk) (:fv _uniq.20145) ((:c Prod.mk) (:fv _uniq.20145) (:fv _uniq.20145) ((:c Prod.snd) (:fv _uniq.20145) (:fv _uniq.20145) ((:c Quot.out) ((:c Prod) (:fv _uniq.20145) (:fv _uniq.20145)) ((:c Sym2.Rel) (:fv _uniq.20145)) (:fv _uniq.20211))) ((:c Prod.fst... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"e","sexp":"((:c Sym2) (:fv _uniq.20145))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Sym2) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:fv FV4)) (:arg :explicit 2 (:app (:c Sym2.mk) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Prod.mk) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:app (:c Pro... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20145","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20148","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":12770,"sourceStart":12768,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12772,"sourceStart":12771,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"eq_swap","source_end":12779,"source_start":12772,"syntax_kind":"ident"},{"source":"Sym2.mk","source_end":12788,"source_start":12781,"syntax_kind":"ident"},{"source":"e.out_eq","source_end":12798,"source_start":12790,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20145","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20148","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 101 | 2 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f9949f0f7610aeebe8429c8234e452518258f99d73bde8c783b4acf1914673f8 | f61bbb6aa2f0f2b92feab36d2b320a5eae6a0959ee315ff24ba4db94eb279fc9 | f6de8a499d8c476e299b13fdf536d44f5869fc5f1264b9abefe9b7432829d302 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,525 | AlgebraicGeometry.Spec.map_eqToHom | Mathlib/AlgebraicGeometry/Scheme.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | subst e | R S : CommRingCat
e : R = S
⊢ map (eqToHom e) = eqToHom ⋯ | R : CommRingCat
⊢ map (eqToHom ⋯) = eqToHom ⋯ | ((:c Eq) ((:c Quiver.Hom) (:c AlgebraicGeometry.Scheme) ((:c CategoryTheory.CategoryStruct.toQuiver) (:c AlgebraicGeometry.Scheme) ((:c CategoryTheory.Category.toCategoryStruct) (:c AlgebraicGeometry.Scheme) (:c AlgebraicGeometry.Scheme.instCategory))) ((:c AlgebraicGeometry.Spec) (:fv _uniq.61934)) ((:c AlgebraicGeome... | [{"name":"R","sexp":"(:c CommRingCat)"},{"name":"S","sexp":"(:c CommRingCat)"},{"name":"e","sexp":"((:c Eq) (:c CommRingCat) (:fv _uniq.61933) (:fv _uniq.61934))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:c AlgebraicGeometry.Scheme)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:c AlgebraicGeometry.Scheme))))) (:arg :explicit 2 (:app (:c AlgebraicGeometry.Spec) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 3 (:ap... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61933","is_instance":false,"is_let":false,"name":"R","sexp":"(:c CommRingCat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.61934","is_instance":false,"is_let":false,"name":"S","sexp":"(:c CommRingCat)"},{"binder_role":":explic... | {"children":[{"source":"subst","sourceEnd":13103,"sourceStart":13098,"tag":"atom"},{"children":[{"contextIndex":3,"semanticRole":"local","source":"e","sourceEnd":13105,"sourceStart":13104,"tag":"identifier"}],"kind":"null","source":"e","sourceEnd":13105,"sourceStart":13104,"tag":"node"}],"kind":"Lean.Parser.Tactic.subs... | [] | [{"source":"e","source_end":13105,"source_start":13104,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61933","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.61934","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 90 | 4 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aeadb8fd310abeb4c96d276df581b64cd0802a25d8765bc52ff2a45d0ad03ad1 | 49629db5edce7e9c8b7b08ad1097e3af3c98731dbf20e52e312dd98319f07a20 | 9f87dce166543dae54bdf0d93e7bf67fad5e58e02009c37a2d8eb8b1f30b1ce7 | b9755da78072f21dd9f27f9d4869634f054a507bb375ac6841820ba2d24c54c3 |
cat-searcher/leandojo-benchmark-4-random | test | 1,526 | AlgebraicGeometry.Spec.map_eqToHom | Mathlib/AlgebraicGeometry/Scheme.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>AlgebraicGeometry.Spec.map_id</a> _ | R : CommRingCat
⊢ map (eqToHom ⋯) = eqToHom ⋯ | ((:c Eq) ((:c Quiver.Hom) (:c AlgebraicGeometry.Scheme) ((:c CategoryTheory.CategoryStruct.toQuiver) (:c AlgebraicGeometry.Scheme) ((:c CategoryTheory.Category.toCategoryStruct) (:c AlgebraicGeometry.Scheme) (:c AlgebraicGeometry.Scheme.instCategory))) ((:c AlgebraicGeometry.Spec) (:fv _uniq.61933)) ((:c AlgebraicGeome... | [{"name":"R","sexp":"(:c CommRingCat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:c AlgebraicGeometry.Scheme)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:c AlgebraicGeometry.Scheme))))) (:arg :explicit 2 (:app (:c AlgebraicGeometry.Spec) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 3 (:ap... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61933","is_instance":false,"is_let":false,"name":"R","sexp":"(:c CommRingCat)"}] | {"children":[{"source":"exact","sourceEnd":13112,"sourceStart":13107,"tag":"atom"},{"children":[{"name":"AlgebraicGeometry.Spec.map_id","semanticRole":"global","source":"Spec.map_id","sourceEnd":13124,"sourceStart":13113,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":13126,"sourceStart":13125,"... | [] | [{"source":"Spec.map_id _","source_end":13126,"source_start":13113,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61933","is_instance":false,"is_let":false,"user_name":"R"}] | 90 | 6 | exact | true | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8502c00d52d8419c6b1df125cfd855933c691806c49a2c346a4bb758437e830a | b9755da78072f21dd9f27f9d4869634f054a507bb375ac6841820ba2d24c54c3 | 55e38992d8c201eccc70036ffd96604be6e3d755ce6e8dc416b961f029bd5f8c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,527 | Complex.isTheta_cpow_rpow | Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Complex.ofReal_one</a>, <a>div_one</a>] | α : Type u_1
l : Filter α
f g : α → ℂ
hl_im : IsBoundedUnder (fun x x_1 => x ≤ x_1) l fun x => |(g x).im|
hl : ∀ᶠ (x : α) in l, f x = 0 → (g x).re = 0 → g x = 0
⊢ (let_fun this := fun x => abs (f x) ^ (g x).re / 1;
this) =ᶠ[l]
let_fun this := fun x => abs (f x) ^ (g x).re;
this | α : Type u_1
l : Filter α
f g : α → ℂ
hl_im : IsBoundedUnder (fun x x_1 => x ≤ x_1) l fun x => |(g x).im|
hl : ∀ᶠ (x : α) in l, f x = 0 → (g x).re = 0 → g x = 0
⊢ (fun x => abs (f x) ^ (g x).re) =ᶠ[l] fun x => abs (f x) ^ (g x).re | ((:c Filter.EventuallyEq) (:fv _uniq.38187) (:c Real) (:fv _uniq.38190) ((:c letFun) (:forall _ (:fv _uniq.38187) (:c Real)) (:lambda this (:forall _ (:fv _uniq.38187) (:c Real)) (:forall _ (:fv _uniq.38187) (:c Real))) (:lambda x (:fv _uniq.38187) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.38187))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.38187) (:c Complex))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.38187) (:c Complex))"},{"name":"hl_im","sexp":"((:c Filter.IsBoundedUnder) (:c Real) (:fv _uniq.38187) (:lambda _ (:c ... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c Real)) (:arg :explicit 2 (:fv FV1)) (:arg :explicit 3 (:app (:c letFun) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:c Real))) (:arg :implicit 1) (:arg :explicit 2 (:lambda x :explicit (:fv FV0) (:app (:c HDiv.hDiv) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38187","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38190","is_instance":false,"is_let":false,"name":"l","sexp":"(:app (:c Filter) (:arg :explicit 0 (:fv FV0))... | {"children":[{"source":"simp","sourceEnd":10331,"sourceStart":10327,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":10336,"sourceStart":10332,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":103... | [] | [{"source":"ofReal_one","source_end":10348,"source_start":10338,"syntax_kind":"ident"},{"source":"div_one","source_end":10357,"source_start":10350,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38187","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38190","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 44 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4c5913babb6224ab041c8829ae7fb39457012b9f3295ab3eae2d0f8af4cf6b92 | 0ba59510f1c71b8590a5d978d75ea81b2844fafcd70ba0c7f64a0d3fa8de91f4 | 7702511191279f82510dcb744a4e5af192aad878c911a73373a36dd8d1f718f1 | 5d6a6c52105b691ed049f92401555c0bb2bed0b307a5a26de69543081fa65871 |
cat-searcher/leandojo-benchmark-4-random | test | 1,528 | Complex.isTheta_cpow_rpow | Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | α : Type u_1
l : Filter α
f g : α → ℂ
hl_im : IsBoundedUnder (fun x x_1 => x ≤ x_1) l fun x => |(g x).im|
hl : ∀ᶠ (x : α) in l, f x = 0 → (g x).re = 0 → g x = 0
⊢ (fun x => abs (f x) ^ (g x).re) =ᶠ[l] fun x => abs (f x) ^ (g x).re | ((:c Filter.EventuallyEq) (:fv _uniq.38187) (:c Real) (:fv _uniq.38190) (:lambda x (:fv _uniq.38187) ((:c HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) ((:c DFunLike.coe) ((:c AbsoluteValue) (:c Complex) (:c Real) (:c Complex.instSemiring) (:c Real.orderedSemiring)) (:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.38187))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.38187) (:c Complex))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.38187) (:c Complex))"},{"name":"hl_im","sexp":"((:c Filter.IsBoundedUnder) (:c Real) (:fv _uniq.38187) (:lambda _ (:c ... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c Real)) (:arg :explicit 2 (:fv FV1)) (:arg :explicit 3 (:lambda x :explicit (:fv FV0) (:app (:c HPow.hPow) (: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.38187","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38190","is_instance":false,"is_let":false,"name":"l","sexp":"(:app (:c Filter) (:arg :explicit 0 (:fv FV0))... | {"children":[{"source":"rfl","sourceEnd":10368,"sourceStart":10365,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":10368,"sourceStart":10365,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38187","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38190","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 44 | 5 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d24ef0a11ab44bc4fc35b31fc77eb9f8706806d79fe818efcc26bcb4b14eb5c8 | 5d6a6c52105b691ed049f92401555c0bb2bed0b307a5a26de69543081fa65871 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,529 | MeasurableEmbedding.absolutelyContinuous_map | Mathlib/MeasureTheory/Measure/MeasureSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro t ht | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Type u_5
R : Type u_6
R' : Type u_7
m0 : MeasurableSpace α
m1 : MeasurableSpace β
f : α → β
μ ν : Measure α
hf : MeasurableEmbedding f
hμν : μ ≪ ν
⊢ Measure.map f μ ≪ Measure.map f ν | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Type u_5
R : Type u_6
R' : Type u_7
m0 : MeasurableSpace α
m1 : MeasurableSpace β
f : α → β
μ ν : Measure α
hf : MeasurableEmbedding f
hμν : μ ≪ ν
t : Set β
ht : (Measure.map f ν) t = 0
⊢ (Measure.map f μ) t = 0 | ((:c MeasureTheory.Measure.AbsolutelyContinuous) (:fv _uniq.566223) (:fv _uniq.566244) ((:c MeasureTheory.Measure.map) (:fv _uniq.566220) (:fv _uniq.566223) (:fv _uniq.566244) (:fv _uniq.566241) (:fv _uniq.566248) (:fv _uniq.566256)) ((:c MeasureTheory.Measure.map) (:fv _uniq.566220) (:fv _uniq.566223) (:fv _uniq.56624... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"R","sexp":"(:sort (+ u_6 1))"},{"name":"R'","sexp":"(:sort (+ u_7 1))"},{"name":"m0","sexp":"((:c MeasurableSp... | (:app (:c MeasureTheory.Measure.AbsolutelyContinuous) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure.map) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV1)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.566220","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.566223","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"intro","sourceEnd":114399,"sourceStart":114394,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"t","sourceEnd":114401,"sourceStart":114400,"tag":"identifier"},{"semanticRole":"scoped_local","source":"ht","sourceEnd":114404,"sourceStart":114402,"tag":"identifier"}],"kind":"null... | [{"role":"fresh_name","source":"t","source_end":114401,"source_start":114400,"syntax_kind":"ident"},{"role":"fresh_name","source":"ht","source_end":114404,"source_start":114402,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.566220","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.566223","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 603 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fc92e4304a495464c352550b86ab2ab8fe9f2588f2386304c1ef98dd06caaf0a | 3fe346b8d86c3e2914cdaab0d2505640848c063036f72efbfe5d2b83e9608b5c | 0739bfdcdc031efb63257ff4b2cf0a312c689994658859969f8eae6b2c78c652 | bbae98f0cf090f345b2f9da234e3a84b3fc92daba37f8e34b7a30b431c4cdd58 |
cat-searcher/leandojo-benchmark-4-random | test | 1,530 | MeasurableEmbedding.absolutelyContinuous_map | Mathlib/MeasureTheory/Measure/MeasureSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hf.map_apply] at ht ⊢ | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Type u_5
R : Type u_6
R' : Type u_7
m0 : MeasurableSpace α
m1 : MeasurableSpace β
f : α → β
μ ν : Measure α
hf : MeasurableEmbedding f
hμν : μ ≪ ν
t : Set β
ht : (Measure.map f ν) t = 0
⊢ (Measure.map f μ) t = 0 | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Type u_5
R : Type u_6
R' : Type u_7
m0 : MeasurableSpace α
m1 : MeasurableSpace β
f : α → β
μ ν : Measure α
hf : MeasurableEmbedding f
hμν : μ ≪ ν
t : Set β
ht : ν (f ⁻¹' t) = 0
⊢ μ (f ⁻¹' t) = 0 | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.566223) (:fv _uniq.566244)) ((:c Set) (:fv _uniq.566223)) (:lambda _ ((:c Set) (:fv _uniq.566223)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.566223) (:fv _uniq.566244)) ((:c MeasureTheory.Measure.map) (:fv _uniq.56622... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"R","sexp":"(:sort (+ u_6 1))"},{"name":"R'","sexp":"(:sort (+ u_7 1))"},{"name":"m0","sexp":"((:c MeasurableSp... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV1))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.566220","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.566223","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":114409,"sourceStart":114407,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":114411,"sourceStart":114410,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MeasurableEm... | [] | [{"source":"hf.map_apply","source_end":114423,"source_start":114411,"syntax_kind":"ident"},{"source":"ht","source_end":114430,"source_start":114428,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.566220","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.566223","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 603 | 5 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 49f35f3981c0ee1dbf46c306a543c1f646fb412367b059c6379d56c513fc3f17 | bbae98f0cf090f345b2f9da234e3a84b3fc92daba37f8e34b7a30b431c4cdd58 | af29607e09db20adf01862ca6041f8b846da7518d65a75ceaf81369885ba9c01 | 5a220692da7eac19a82b40f305d2916765946d053f33d56a347dd72a0aa85a42 |
cat-searcher/leandojo-benchmark-4-random | test | 1,531 | MeasurableEmbedding.absolutelyContinuous_map | Mathlib/MeasureTheory/Measure/MeasureSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hμν ht | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Type u_5
R : Type u_6
R' : Type u_7
m0 : MeasurableSpace α
m1 : MeasurableSpace β
f : α → β
μ ν : Measure α
hf : MeasurableEmbedding f
hμν : μ ≪ ν
t : Set β
ht : ν (f ⁻¹' t) = 0
⊢ μ (f ⁻¹' t) = 0 | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.566220) (:fv _uniq.566241)) ((:c Set) (:fv _uniq.566220)) (:lambda _ ((:c Set) (:fv _uniq.566220)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.566220) (:fv _uniq.566241)) (:fv _uniq.566256) ((:c Set.preimage) (:fv _uniq... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"R","sexp":"(:sort (+ u_6 1))"},{"name":"R'","sexp":"(:sort (+ u_7 1))"},{"name":"m0","sexp":"((:c MeasurableSp... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.566220","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.566223","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":114442,"sourceStart":114437,"tag":"atom"},{"children":[{"contextIndex":14,"semanticRole":"local","source":"hμν","sourceEnd":114448,"sourceStart":114443,"tag":"identifier"},{"children":[{"contextIndex":16,"semanticRole":"local","source":"ht","sourceEnd":114451,"sourceStart":114... | [] | [{"source":"hμν ht","source_end":114451,"source_start":114443,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.566220","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.566223","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 603 | 8 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d0fc25d99c8cfab82c3ca77d1f929734e04a8503f379519113441a1394ea28b0 | 5a220692da7eac19a82b40f305d2916765946d053f33d56a347dd72a0aa85a42 | 8502231d8eeb884bb84445b9b659f8b559cd1a60d6b5bad2dbabb9d6cbc9be50 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,532 | MeasureTheory.OuterMeasure.sup_apply | Mathlib/MeasureTheory/OuterMeasure/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have := <a>MeasureTheory.OuterMeasure.iSup_apply</a> (fun b => <a>cond</a> b m₁ m₂) s | α : Type u_1
β : Type u_2
m m₁ m₂ : OuterMeasure α
s : Set α
⊢ (m₁ ⊔ m₂) s = m₁ s ⊔ m₂ s | α : Type u_1
β : Type u_2
m m₁ m₂ : OuterMeasure α
s : Set α
this : (⨆ i, bif i then m₁ else m₂) s = ⨆ i, (bif i then m₁ else m₂) s
⊢ (m₁ ⊔ m₂) s = m₁ s ⊔ m₂ s | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.OuterMeasure) (:fv _uniq.40877)) ((:c Set) (:fv _uniq.40877)) (:lambda _ ((:c Set) (:fv _uniq.40877)) (:c ENNReal)) ((:c MeasureTheory.OuterMeasure.instFunLikeSetENNReal) (:fv _uniq.40877)) ((:c Sup.sup) ((:c MeasureTheory.OuterMeasure) (:fv _uniq.40877)) ((:c... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.40877))"},{"name":"m₁","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.40877))"},{"name":"m₂","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.40877))"},{"name":"s","se... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.OuterMeasure) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c FunLi... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40877","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40880","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":8747,"sourceStart":8743,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":8748,"sourceStart":8748,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":8748,"sourceStart":8748,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"iSup_apply (fun b => cond b m₁ m₂) s","source_end":8791,"source_start":8751,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40877","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40880","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 67 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 33bb4f6e07cfad1bee011b6f179dfc17a036f6f7017022f6653caaf365259ad7 | 2cec66819c542d5e15b00f9074fbb252aba8eba19e029eecf5d8a98d990af8f9 | 7e5a1768bf8477e16c4c122befe7d1e41569c4891ed4fa71a721b217e16fa3fc | 2712ab3f1fcaaf66ef988a77482a0bf76e0e4376c9f1efb24394311ed9c427bb |
cat-searcher/leandojo-benchmark-4-random | test | 1,533 | MeasureTheory.OuterMeasure.sup_apply | Mathlib/MeasureTheory/OuterMeasure/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>iSup_bool_eq</a>, <a>iSup_bool_eq</a>] at this | α : Type u_1
β : Type u_2
m m₁ m₂ : OuterMeasure α
s : Set α
this : (⨆ i, bif i then m₁ else m₂) s = ⨆ i, (bif i then m₁ else m₂) s
⊢ (m₁ ⊔ m₂) s = m₁ s ⊔ m₂ s | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.OuterMeasure) (:fv _uniq.40877)) ((:c Set) (:fv _uniq.40877)) (:lambda _ ((:c Set) (:fv _uniq.40877)) (:c ENNReal)) ((:c MeasureTheory.OuterMeasure.instFunLikeSetENNReal) (:fv _uniq.40877)) ((:c Sup.sup) ((:c MeasureTheory.OuterMeasure) (:fv _uniq.40877)) ((:c... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.40877))"},{"name":"m₁","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.40877))"},{"name":"m₂","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.40877))"},{"name":"s","se... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.OuterMeasure) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c FunLi... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40877","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40880","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rwa","sourceEnd":8796,"sourceStart":8793,"tag":"atom"},{"children":[{"source":"[","sourceEnd":8798,"sourceStart":8797,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"iSup_bool_eq","semanticRole":"global","source":"iSup_bool_eq","sourceEnd":... | [] | [{"source":"iSup_bool_eq","source_end":8810,"source_start":8798,"syntax_kind":"ident"},{"source":"this","source_end":8833,"source_start":8829,"syntax_kind":"ident"},{"source":"iSup_bool_eq","source_end":8824,"source_start":8812,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40877","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40880","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 67 | 6 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5d94893d9bba673e432244b44db4d125809b36cdd2e565fc2483ff7304930085 | 2712ab3f1fcaaf66ef988a77482a0bf76e0e4376c9f1efb24394311ed9c427bb | 9dc494fdacdf5686abddb273622a449022d492d065cb5a3ff239da9b8db05b1a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,534 | LieModuleEquiv.symm_symm | Mathlib/Algebra/Lie/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | R : Type u
L : Type v
M : Type w
N : Type w₁
P : Type w₂
inst✝¹⁴ : CommRing R
inst✝¹³ : LieRing L
inst✝¹² : LieAlgebra R L
inst✝¹¹ : AddCommGroup M
inst✝¹⁰ : AddCommGroup N
inst✝⁹ : AddCommGroup P
inst✝⁸ : Module R M
inst✝⁷ : Module R N
inst✝⁶ : Module R P
inst✝⁵ : LieRingModule L M
inst✝⁴ : LieRingModule L N
inst✝³ : ... | ((:c Eq) ((:c LieModuleEquiv) (:fv _uniq.511384) (:fv _uniq.511386) (:fv _uniq.511388) (:fv _uniq.511390) (:fv _uniq.511395) (:fv _uniq.511398) (:fv _uniq.511416) (:fv _uniq.511419) (:fv _uniq.511931) (:fv _uniq.512407) (:fv _uniq.512896) (:fv _uniq.512909)) ((:c LieModuleEquiv.symm) (:fv _uniq.511384) (:fv _uniq.51138... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"L","sexp":"(:sort (+ v 1))"},{"name":"M","sexp":"(:sort (+ w 1))"},{"name":"N","sexp":"(:sort (+ w₁ 1))"},{"name":"P","sexp":"(:sort (+ w₂ 1))"},{"name":"inst✝¹⁴","sexp":"((:c CommRing) (:fv _uniq.511384))"},{"name":"inst✝¹³","sexp":"((:c LieRing) (:fv _uniq.511386))"},{"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LieModuleEquiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 5 (:instance-of (:app (:c LieRing) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.511384","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.511386","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rfl","sourceEnd":40769,"sourceStart":40766,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":40769,"sourceStart":40766,"tag":"node"}],"kind":"null","source":"rfl","sourceEnd":40769,"sourceStart":40766,"tag":"node"}],"kind":"Lea... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.511384","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.511386","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 371 | 2 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 985a93a749be578fc28abd7e383f510d3d596e57107d4d8930679c5542d1fc17 | 9ddd76080a6dbaa951b192e83b929f9c805283d92de31046c64c2693634bf7ba | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,535 | LinearMap.polyCharpolyAux_map_eq_charpoly | Mathlib/Algebra/Module/LinearMap/Polynomial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | nontriviality R | R : Type u_1
L : Type u_2
M : Type u_3
n : Type u_4
ι : Type u_5
ι' : Type u_6
ιM : Type u_7
inst✝¹² : CommRing R
inst✝¹¹ : AddCommGroup L
inst✝¹⁰ : Module R L
inst✝⁹ : AddCommGroup M
inst✝⁸ : Module R M
φ : L →ₗ[R] Module.End R M
inst✝⁷ : Fintype ι
inst✝⁶ : Fintype ι'
inst✝⁵ : Fintype ιM
inst✝⁴ : DecidableEq ι
inst✝³ ... | R : Type u_1
L : Type u_2
M : Type u_3
n : Type u_4
ι : Type u_5
ι' : Type u_6
ιM : Type u_7
inst✝¹² : CommRing R
inst✝¹¹ : AddCommGroup L
inst✝¹⁰ : Module R L
inst✝⁹ : AddCommGroup M
inst✝⁸ : Module R M
φ : L →ₗ[R] Module.End R M
inst✝⁷ : Fintype ι
inst✝⁶ : Fintype ι'
inst✝⁵ : Fintype ιM
inst✝⁴ : DecidableEq ι
inst✝³ ... | ((:c Eq) ((:c Polynomial) (:fv _uniq.354798) ((:c CommSemiring.toSemiring) (:fv _uniq.354798) ((:c CommRing.toCommSemiring) (:fv _uniq.354798) (:fv _uniq.354819)))) ((:c Polynomial.map) ((:c MvPolynomial) (:fv _uniq.354810) (:fv _uniq.354798) ((:c CommRing.toCommSemiring) (:fv _uniq.354798) (:fv _uniq.354819))) (:fv _u... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"n","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"ι'","sexp":"(:sort (+ u_6 1))"},{"name":"ιM","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝¹²","sexp":"((:c CommRi... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c Polynomial.map) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:fv FV4)) (:arg :explicit 1 (:fv FV0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.354798","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.354801","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"nontriviality","sourceEnd":13188,"sourceStart":13175,"tag":"atom"},{"children":[{"contextIndex":0,"semanticRole":"local","source":"R","sourceEnd":13190,"sourceStart":13189,"tag":"identifier"}],"kind":"null","source":"R","sourceEnd":13190,"sourceStart":13189,"tag":"node"},{"children":[],"kind":"n... | [] | [{"source":"R","source_end":13190,"source_start":13189,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.354798","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.354801","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 56 | 4 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6443c710be7a350a5cdc207c4e02027b1c334ef737415fdf07d28575fbb820b9 | e486d98df90927d18d01da102000b8586aee5ebea274697645b72893697b1031 | 5382e3598f2f95a9b47c72cede0853cde729cfb3288670190a447baa9ed65849 | 503a2100b56fdae1c45c7c96d704d8fc7bab9871ca4f5d65f2cba6f0aab417d2 |
cat-searcher/leandojo-benchmark-4-random | test | 1,536 | LinearMap.polyCharpolyAux_map_eq_charpoly | Mathlib/Algebra/Module/LinearMap/Polynomial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>LinearMap.polyCharpolyAux_map_eq_toMatrix_charpoly</a>, <a>LinearMap.charpoly_toMatrix</a>] | R : Type u_1
L : Type u_2
M : Type u_3
n : Type u_4
ι : Type u_5
ι' : Type u_6
ιM : Type u_7
inst✝¹² : CommRing R
inst✝¹¹ : AddCommGroup L
inst✝¹⁰ : Module R L
inst✝⁹ : AddCommGroup M
inst✝⁸ : Module R M
φ : L →ₗ[R] Module.End R M
inst✝⁷ : Fintype ι
inst✝⁶ : Fintype ι'
inst✝⁵ : Fintype ιM
inst✝⁴ : DecidableEq ι
inst✝³ ... | ((:c Eq) ((:c Polynomial) (:fv _uniq.354798) ((:c CommSemiring.toSemiring) (:fv _uniq.354798) ((:c CommRing.toCommSemiring) (:fv _uniq.354798) (:fv _uniq.354819)))) ((:c Polynomial.map) ((:c MvPolynomial) (:fv _uniq.354810) (:fv _uniq.354798) ((:c CommRing.toCommSemiring) (:fv _uniq.354798) (:fv _uniq.354819))) (:fv _u... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"n","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"ι'","sexp":"(:sort (+ u_6 1))"},{"name":"ιM","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝¹²","sexp":"((:c CommRi... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c Polynomial.map) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:fv FV4)) (:arg :explicit 1 (:fv FV0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.354798","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.354801","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":13195,"sourceStart":13193,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13197,"sourceStart":13196,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"LinearMap.polyCh... | [] | [{"source":"polyCharpolyAux_map_eq_toMatrix_charpoly","source_end":13237,"source_start":13197,"syntax_kind":"ident"},{"source":"LinearMap.charpoly_toMatrix","source_end":13266,"source_start":13239,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.354798","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.354801","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 56 | 5 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8dd780c6a194fa04312fb15de6a194f806c33d27c9799cbe2b8faa1a7bfebee2 | 503a2100b56fdae1c45c7c96d704d8fc7bab9871ca4f5d65f2cba6f0aab417d2 | d3f764ded2bad3c389efb1c895b4daef6315f22504404d2b50878e23b7119e85 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,537 | Fin.castOrderIso_toEquiv | Mathlib/Order/Fin.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | subst h | m n : ℕ
p : Fin (n + 1)
i j : Fin n
h : n = m
⊢ (castOrderIso h).toEquiv = Equiv.cast ⋯ | n : ℕ
p : Fin (n + 1)
i j : Fin n
⊢ (castOrderIso ⋯).toEquiv = Equiv.cast ⋯ | ((:c Eq) ((:c Equiv) ((:c Fin) (:fv _uniq.15106)) ((:c Fin) (:fv _uniq.15104))) ((:c RelIso.toEquiv) ((:c Fin) (:fv _uniq.15106)) ((:c Fin) (:fv _uniq.15104)) (:lambda _ ((:c Fin) (:fv _uniq.15106)) (:lambda _ ((:c Fin) (:fv _uniq.15106)) ((:c LE.le) ((:c Fin) (:fv _uniq.15106)) ((:c instLEFin) (:fv _uniq.15106)) 1 0))... | [{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"p","sexp":"((:c Fin) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.15106) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"i","sexp":"((:c Fin) (:fv _uniq.15106))"},{"na... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Equiv) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Fin) (:arg :explicit 0 (:fv FV0)))))) (:arg :explicit 1 (:app (:c RelIso.toEquiv) (:arg :implicit-type 0 (:app (:c Fin) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15104","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15106","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_ind... | {"children":[{"source":"subst","sourceEnd":9367,"sourceStart":9362,"tag":"atom"},{"children":[{"contextIndex":6,"semanticRole":"local","source":"h","sourceEnd":9369,"sourceStart":9368,"tag":"identifier"}],"kind":"null","source":"h","sourceEnd":9369,"sourceStart":9368,"tag":"node"}],"kind":"Lean.Parser.Tactic.subst","so... | [] | [{"source":"h","source_end":9369,"source_start":9368,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15104","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15106","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 72 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f5e0e7aef135485b5886ddb8acef4850b945cfcf7a260ca9eaf278a87da63eed | 4c876c13201844e58aa3bf48157c3889344f604c636a811e60b8e3cfc30b6545 | 831cd1e16045cc06861f8cf3670f78a5450740dc3de3f30710e86d17a4b036b3 | d704c6b9ff4ed66000e77c0216a452cc7e83b37dc3ed5b8a6c83d3ae66c35a35 |
cat-searcher/leandojo-benchmark-4-random | test | 1,538 | Fin.castOrderIso_toEquiv | Mathlib/Order/Fin.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | n : ℕ
p : Fin (n + 1)
i j : Fin n
⊢ (castOrderIso ⋯).toEquiv = Equiv.cast ⋯ | ((:c Eq) ((:c Equiv) ((:c Fin) (:fv _uniq.15106)) ((:c Fin) (:fv _uniq.15106))) ((:c RelIso.toEquiv) ((:c Fin) (:fv _uniq.15106)) ((:c Fin) (:fv _uniq.15106)) (:lambda _ ((:c Fin) (:fv _uniq.15106)) (:lambda _ ((:c Fin) (:fv _uniq.15106)) ((:c LE.le) ((:c Fin) (:fv _uniq.15106)) ((:c instLEFin) (:fv _uniq.15106)) 1 0))... | [{"name":"n","sexp":"(:c Nat)"},{"name":"p","sexp":"((:c Fin) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.15106) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"i","sexp":"((:c Fin) (:fv _uniq.15106))"},{"name":"j","sexp":"((:c Fin) (:fv ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Equiv) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Fin) (:arg :explicit 0 (:fv FV0)))))) (:arg :explicit 1 (:app (:c RelIso.toEquiv) (:arg :implicit-type 0 (:app (:c Fin) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15106","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15156","is_instance":false,"is_let":false,"name":"p","sexp":"(:app (:c Fin) (:arg :explicit 0 (:app (:c HAdd.hA... | {"children":[{"source":"rfl","sourceEnd":9374,"sourceStart":9371,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":9374,"sourceStart":9371,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15106","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15156","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 72 | 6 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ebb4f00fc9268729b75b82a55d80f5efb0550d0b3da2b480ca16b2bc6cdcc31f | d704c6b9ff4ed66000e77c0216a452cc7e83b37dc3ed5b8a6c83d3ae66c35a35 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,539 | MeasurableSpace.generateFrom_iUnion_countablePartition | Mathlib/MeasureTheory/MeasurableSpace/CountablyGenerated.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasurableSpace.countablePartition</a>, <a>MeasurableSpace.generateFrom_iUnion_memPartition</a>, <a>Set.range_enumerateCountable_of_mem</a> _ <a>MeasurableSpace.empty_mem_countableGeneratingSet</a>, <a>MeasurableSpace.generateFrom_countableGeneratingSet</a>] | α✝ : Type u_1
β : Type u_2
m✝ : MeasurableSpace α✝
h : CountablyGenerated α✝
α : Type u_3
m : MeasurableSpace α
inst✝ : CountablyGenerated α
⊢ generateFrom (⋃ n, countablePartition α n) = m | ((:c Eq) ((:c MeasurableSpace) (:fv _uniq.51435)) ((:c MeasurableSpace.generateFrom) (:fv _uniq.51435) ((:c Set.iUnion) ((:c Set) (:fv _uniq.51435)) (:c Nat) (:lambda n (:c Nat) ((:c MeasurableSpace.countablePartition) (:fv _uniq.51435) (:fv _uniq.51436) (:fv _uniq.51437) 0)))) (:fv _uniq.51436)) | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m✝","sexp":"((:c MeasurableSpace) (:fv _uniq.51377))"},{"name":"h","sexp":"((:c MeasurableSpace.CountablyGenerated) (:fv _uniq.51377) (:fv _uniq.51383))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"m","sexp":"((:c Measurabl... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV5)))) (:arg :explicit 1 (:app (:c MeasurableSpace.generateFrom) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:app (:c Set.iUnion) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :implicit-type 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.51377","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.51380","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impl... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":22181,"sourceStart":22179,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":22183,"sourceStart":22182,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"countablePartition","source_end":22201,"source_start":22183,"syntax_kind":"ident"},{"source":"generateFrom_iUnion_memPartition","source_end":22235,"source_start":22203,"syntax_kind":"ident"},{"source":"range_enumerateCountable_of_mem _ empty_mem_countableGeneratingSet","source_end":22307,"source_start":2224... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.51377","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.51380","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_... | 73 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 90281ca8955977f382575a1b4bee634a90c1a22660fe6716a1f11c5769e0feda | ce06bf3b00d5b77a7c80c511ad4ba884bca0f8dcd7d23745ccefad4b15ad6fdb | 8a57f07f77d1d0bc3264340e4ad7638cfa64efe1dafd47e5b8e634f021e7c115 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,540 | IsLUB.exists_seq_monotone_tendsto | Mathlib/Topology/Order/IsLUB.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases h : x ∈ t | α : Type u_1
β : Type u_2
γ : Type u_3
inst✝⁶ : TopologicalSpace α
inst✝⁵ : TopologicalSpace β
inst✝⁴ : LinearOrder α
inst✝³ : LinearOrder β
inst✝² : OrderTopology α
inst✝¹ : OrderTopology β
t : Set α
x : α
inst✝ : (𝓝 x).IsCountablyGenerated
htx : IsLUB t x
ht : t.Nonempty
⊢ ∃ u, Monotone u ∧ (∀ (n : ℕ), u n ≤ x) ∧ Te... | case pos
α : Type u_1
β : Type u_2
γ : Type u_3
inst✝⁶ : TopologicalSpace α
inst✝⁵ : TopologicalSpace β
inst✝⁴ : LinearOrder α
inst✝³ : LinearOrder β
inst✝² : OrderTopology α
inst✝¹ : OrderTopology β
t : Set α
x : α
inst✝ : (𝓝 x).IsCountablyGenerated
htx : IsLUB t x
ht : t.Nonempty
h : x ∈ t
⊢ ∃ u, Monotone u ∧ (∀ (n ... | ((:c Exists) (:forall _ (:c Nat) (:fv _uniq.52526)) (:lambda u (:forall _ (:c Nat) (:fv _uniq.52526)) ((:c And) ((:c Monotone) (:c Nat) (:fv _uniq.52526) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))) ((:c PartialOrder.toPreorder) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁶","sexp":"((:c TopologicalSpace) (:fv _uniq.52526))"},{"name":"inst✝⁵","sexp":"((:c TopologicalSpace) (:fv _uniq.52529))"},{"name":"inst✝⁴","sexp":"((:c LinearOrder) (:fv _uniq.52526))... | (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:c Nat) (:fv FV0))) (:arg :explicit 1 (:lambda u :explicit (:forall _ :explicit (:c Nat) (:fv FV0)) (:app (:c And) (:arg :explicit 0 (:app (:c Monotone) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52526","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52529","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"by_cases","sourceEnd":9688,"sourceStart":9680,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":9690,"sourceStart":9689,"tag":"identifier"},{"source":":","sourceEnd":9692,"sourceStart":9691,"tag":"atom"}],"kind":"null","source":"h :","sourceEnd":9692,"sourceStart... | [] | [{"source":"x ∈ t","source_end":9700,"source_start":9693,"syntax_kind":"«term_∈_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52526","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52529","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 57 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 367d759caccefddfb4996145599d90e8915eeef6c981520b4e52eeb11a7caeab | ef2ab09f794d1d43a86f9c3df9e58f98f2a959a7f7d7375531e1bb9f83a5e818 | 97dda878044b58792e002725dbd61063fbe9e8102dd80be4a5059caf6545bc07 | 92ed450326a7cbcdb7b7c3f592a7ace3a2ac11c8df46419ffa86d17ee4503f10 |
cat-searcher/leandojo-benchmark-4-random | test | 1,541 | IsLUB.exists_seq_monotone_tendsto | Mathlib/Topology/Order/IsLUB.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨fun _ => x, <a>monotone_const</a>, fun n => <a>le_rfl</a>, <a>tendsto_const_nhds</a>, fun _ => h⟩ | case pos
α : Type u_1
β : Type u_2
γ : Type u_3
inst✝⁶ : TopologicalSpace α
inst✝⁵ : TopologicalSpace β
inst✝⁴ : LinearOrder α
inst✝³ : LinearOrder β
inst✝² : OrderTopology α
inst✝¹ : OrderTopology β
t : Set α
x : α
inst✝ : (𝓝 x).IsCountablyGenerated
htx : IsLUB t x
ht : t.Nonempty
h : x ∈ t
⊢ ∃ u, Monotone u ∧ (∀ (n ... | ((:c Exists) (:forall _ (:c Nat) (:fv _uniq.52526)) (:lambda u (:forall _ (:c Nat) (:fv _uniq.52526)) ((:c And) ((:c Monotone) (:c Nat) (:fv _uniq.52526) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))) ((:c PartialOrder.toPreorder) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁶","sexp":"((:c TopologicalSpace) (:fv _uniq.52526))"},{"name":"inst✝⁵","sexp":"((:c TopologicalSpace) (:fv _uniq.52529))"},{"name":"inst✝⁴","sexp":"((:c LinearOrder) (:fv _uniq.52526))... | (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:c Nat) (:fv FV0))) (:arg :explicit 1 (:lambda u :explicit (:forall _ :explicit (:c Nat) (:fv FV0)) (:app (:c And) (:arg :explicit 0 (:app (:c Monotone) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52526","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52529","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":9711,"sourceStart":9706,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":9715,"sourceStart":9712,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":9718,"sourceStart":9715,"tag":"atom"},{"children":[{"children":[{"chi... | [] | [{"source":"⟨fun _ => x, monotone_const, fun n => le_rfl, tendsto_const_nhds, fun _ => h⟩","source_end":9793,"source_start":9712,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52526","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52529","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 57 | 7 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fb8031a10a8ca1423957bf7755228f67bb94764208cf323b54ea69d5c9612e83 | bef6dec4a33fd44191528cdd37b9eed5679e839f27f9dc41c44b9a542952ba9b | 3b403372b84c647b2353c67dafcf37d2657d9ff6be82737a54d6a1071a5f6874 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,542 | IsLUB.exists_seq_monotone_tendsto | Mathlib/Topology/Order/IsLUB.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases htx.exists_seq_strictMono_tendsto_of_not_mem h ht with ⟨u, hu⟩ | case neg
α : Type u_1
β : Type u_2
γ : Type u_3
inst✝⁶ : TopologicalSpace α
inst✝⁵ : TopologicalSpace β
inst✝⁴ : LinearOrder α
inst✝³ : LinearOrder β
inst✝² : OrderTopology α
inst✝¹ : OrderTopology β
t : Set α
x : α
inst✝ : (𝓝 x).IsCountablyGenerated
htx : IsLUB t x
ht : t.Nonempty
h : x ∉ t
⊢ ∃ u, Monotone u ∧ (∀ (n ... | case neg.intro
α : Type u_1
β : Type u_2
γ : Type u_3
inst✝⁶ : TopologicalSpace α
inst✝⁵ : TopologicalSpace β
inst✝⁴ : LinearOrder α
inst✝³ : LinearOrder β
inst✝² : OrderTopology α
inst✝¹ : OrderTopology β
t : Set α
x : α
inst✝ : (𝓝 x).IsCountablyGenerated
htx : IsLUB t x
ht : t.Nonempty
h : x ∉ t
u : ℕ → α
hu : Stric... | ((:c Exists) (:forall _ (:c Nat) (:fv _uniq.52526)) (:lambda u (:forall _ (:c Nat) (:fv _uniq.52526)) ((:c And) ((:c Monotone) (:c Nat) (:fv _uniq.52526) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))) ((:c PartialOrder.toPreorder) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁶","sexp":"((:c TopologicalSpace) (:fv _uniq.52526))"},{"name":"inst✝⁵","sexp":"((:c TopologicalSpace) (:fv _uniq.52529))"},{"name":"inst✝⁴","sexp":"((:c LinearOrder) (:fv _uniq.52526))... | (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:c Nat) (:fv FV0))) (:arg :explicit 1 (:lambda u :explicit (:forall _ :explicit (:c Nat) (:fv FV0)) (:app (:c And) (:arg :explicit 0 (:app (:c Monotone) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52526","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52529","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rcases","sourceEnd":9805,"sourceStart":9799,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"htx.exists_seq_strictMono_tendsto_of_not_mem","sourceEnd":9850,"sourceStart":9806,"tag":"identifier"},{"children":[{"contextIndex":15... | [] | [{"source":"htx.exists_seq_strictMono_tendsto_of_not_mem h ht","source_end":9855,"source_start":9806,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨u, hu⟩","source_end":9872,"source_start":9861,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52526","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52529","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 57 | 14 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b62303e7e94a1609cd1b3c00864acd63573f3c8c1a6c2bb15a04ed51eaf55a1a | 29d224ac9ef4104c21733f48fe372419503c31e24928b03890ae8e170a6383f1 | 0bd877b66e39879a79cc316165e464f92f84953b8302043b9a155ce9660c58e6 | 59e82c109ea5638941e1e015ab5efe8c433e3fc403f718efee331f1a09adb33e |
cat-searcher/leandojo-benchmark-4-random | test | 1,543 | IsLUB.exists_seq_monotone_tendsto | Mathlib/Topology/Order/IsLUB.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨u, hu.1.<a>StrictMono.monotone</a>, fun n => (hu.2.1 n).<a>LT.lt.le</a>, hu.2.2⟩ | case neg.intro
α : Type u_1
β : Type u_2
γ : Type u_3
inst✝⁶ : TopologicalSpace α
inst✝⁵ : TopologicalSpace β
inst✝⁴ : LinearOrder α
inst✝³ : LinearOrder β
inst✝² : OrderTopology α
inst✝¹ : OrderTopology β
t : Set α
x : α
inst✝ : (𝓝 x).IsCountablyGenerated
htx : IsLUB t x
ht : t.Nonempty
h : x ∉ t
u : ℕ → α
hu : Stric... | ((:c Exists) (:forall _ (:c Nat) (:fv _uniq.52526)) (:lambda u (:forall _ (:c Nat) (:fv _uniq.52526)) ((:c And) ((:c Monotone) (:c Nat) (:fv _uniq.52526) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))) ((:c PartialOrder.toPreorder) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁶","sexp":"((:c TopologicalSpace) (:fv _uniq.52526))"},{"name":"inst✝⁵","sexp":"((:c TopologicalSpace) (:fv _uniq.52529))"},{"name":"inst✝⁴","sexp":"((:c LinearOrder) (:fv _uniq.52526))... | (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:c Nat) (:fv FV0))) (:arg :explicit 1 (:lambda u :explicit (:forall _ :explicit (:c Nat) (:fv FV0)) (:app (:c And) (:arg :explicit 0 (:app (:c Monotone) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52526","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52529","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":9882,"sourceStart":9877,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":9886,"sourceStart":9883,"tag":"atom"},{"children":[{"contextIndex":16,"semanticRole":"local","source":"u","sourceEnd":9887,"sourceStart":9886,"tag":"identifier"},{"source":",","sourceEnd":9888,"source... | [] | [{"source":"⟨u, hu.1.monotone, fun n => (hu.2.1 n).le, hu.2.2⟩","source_end":9937,"source_start":9883,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52526","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52529","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 57 | 15 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 46eb11d72077f150d0be0a66140180836ca12b1e36e03f39504e7527a529d143 | 59e82c109ea5638941e1e015ab5efe8c433e3fc403f718efee331f1a09adb33e | a3852173a8a11a5c087df1ee3d65f6b9417f23ff8dc2ee5c8607186850cba77a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,544 | integral_exp_neg_mul_rpow | Mathlib/MeasureTheory/Integral/Gamma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert (<a>integral_rpow_mul_exp_neg_mul_rpow</a> hp <a>neg_one_lt_zero</a> hb) using 1 | p b : ℝ
hp : 0 < p
hb : 0 < b
⊢ ∫ (x : ℝ) in Ioi 0, rexp (-b * x ^ p) = b ^ (-1 / p) * Gamma (1 / p + 1) | case h.e'_2
p b : ℝ
hp : 0 < p
hb : 0 < b
⊢ ∫ (x : ℝ) in Ioi 0, rexp (-b * x ^ p) = ∫ (x : ℝ) in Ioi 0, x ^ 0 * rexp (-b * x ^ p)
case h.e'_3
p b : ℝ
hp : 0 < p
hb : 0 < b
⊢ b ^ (-1 / p) * Gamma (1 / p + 1) = b ^ (-(0 + 1) / p) * (1 / p) * Gamma ((0 + 1) / p) | ((:c Eq) (:c Real) ((:c MeasureTheory.integral) (:c Real) (:c Real) (:c Real.normedAddCommGroup) ((:c InnerProductSpace.toNormedSpace) (:c Real) (:c Real) (:c Real.RCLike) (:c Real.normedAddCommGroup) ((:c RCLike.innerProductSpace) (:c Real) (:c Real.RCLike))) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real... | [{"name":"p","sexp":"(:c Real)"},{"name":"b","sexp":"(:c Real)"},{"name":"hp","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.35556))"},{"name":"hb","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c MeasureTheory.integral) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c NormedSpace) (:a... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35556","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.35557","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Real)"},{"binder_role":":explicit","context_i... | {"children":[{"source":"convert","sourceEnd":3194,"sourceStart":3187,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"(","sourceEnd":3196,"sourceStart":3195,"tag":"atom"},{"children":[{"name":"integral_rpow_mul_exp_neg_mu... | [] | [{"source":"(integral_rpow_mul_exp_neg_mul_rpow hp neg_one_lt_zero hb)","source_end":3253,"source_start":3195,"syntax_kind":"Lean.Parser.Term.paren"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35556","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.35557","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 6 | 4 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e8054c73c5fffd4b08a8b6633841b349cee5003fe0a639470d7c4a8a28a205fa | 2b32e6d0e4e4694ec8454f1d2ad9c38332d2d56faaf81d77b886c5c22b95883c | 9e8e235727b01dd458b75e6be8abb1b0b5cbe98786ff5eb5c1ff8d3afead8d00 | cd239699c902f5462352c9cac669b0e3093b099f88d4a2310b41926921d3c625 |
cat-searcher/leandojo-benchmark-4-random | test | 1,545 | integral_exp_neg_mul_rpow | Mathlib/MeasureTheory/Integral/Gamma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>Real.rpow_zero</a>, <a>one_mul</a>] | case h.e'_2
p b : ℝ
hp : 0 < p
hb : 0 < b
⊢ ∫ (x : ℝ) in Ioi 0, rexp (-b * x ^ p) = ∫ (x : ℝ) in Ioi 0, x ^ 0 * rexp (-b * x ^ p) | ((:c Eq) (:c Real) ((:c MeasureTheory.integral) (:c Real) (:c Real) (:c Real.normedAddCommGroup) ((:c InnerProductSpace.toNormedSpace) (:c Real) (:c Real) (:c Real.RCLike) (:c Real.normedAddCommGroup) ((:c RCLike.innerProductSpace) (:c Real) (:c Real.RCLike))) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real... | [{"name":"p","sexp":"(:c Real)"},{"name":"b","sexp":"(:c Real)"},{"name":"hp","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.35556))"},{"name":"hb","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c MeasureTheory.integral) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c NormedSpace) (:a... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35556","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.35557","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Real)"},{"binder_role":":explicit","context_i... | {"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":3274,"sourceStart":3267,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3276,"sourceStart":3275,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":""... | [] | [{"source":"rpow_zero","source_end":3285,"source_start":3276,"syntax_kind":"ident"},{"source":"one_mul","source_end":3294,"source_start":3287,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35556","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.35557","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 6 | 7 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 26728e8732bd24760c8969a51edcf6d8216925a128189293a5517eb8af54556d | d8f28cb0327df73465da947025deaa726cbd0eea69ad6b2efb854254b7324c28 | 730f8de4445b462c88931064549d0527c462e8346f8757cfabfedcb95a933eca | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,546 | integral_exp_neg_mul_rpow | Mathlib/MeasureTheory/Integral/Gamma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>zero_add</a>, <a>Real.Gamma_add_one</a> (<a>one_div_ne_zero</a> (<a>ne_of_gt</a> hp)), <a>mul_assoc</a>] | case h.e'_3
p b : ℝ
hp : 0 < p
hb : 0 < b
⊢ b ^ (-1 / p) * Gamma (1 / p + 1) = b ^ (-(0 + 1) / p) * (1 / p) * Gamma ((0 + 1) / p) | ((:c Eq) (:c Real) ((: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)) (:fv _uniq.35557) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedFiel... | [{"name":"p","sexp":"(:c Real)"},{"name":"b","sexp":"(:c Real)"},{"name":"hp","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.35556))"},{"name":"hb","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35556","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.35557","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Real)"},{"binder_role":":explicit","context_i... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":3303,"sourceStart":3301,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3305,"sourceStart":3304,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"zero_add","source_end":3313,"source_start":3305,"syntax_kind":"ident"},{"source":"Gamma_add_one (one_div_ne_zero (ne_of_gt hp))","source_end":3360,"source_start":3315,"syntax_kind":"Lean.Parser.Term.app"},{"source":"mul_assoc","source_end":3371,"source_start":3362,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35556","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.35557","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 6 | 15 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5fdf9352d47824699cefb6c102977191f669f0800806baf3877eec6e681857de | 1093060f2bd29eb762121d65cc3ce558806e8e07ee92836218cd4eed235f7b3e | c8bdf1fd1c09838ba8cf59259d91a89b2d68ff5b9e0d5362945a310698e80705 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,547 | AlgebraCat.forget₂_map_associator_hom | Mathlib/Algebra/Category/AlgebraCat/Monoidal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | R : Type u
inst✝ : CommRing R
X Y Z : AlgebraCat R
⊢ (forget₂ (AlgebraCat R) (ModuleCat R)).map (α_ X Y Z).hom =
(α_ ((forget₂ (AlgebraCat R) (ModuleCat R)).obj X) ((forget₂ (AlgebraCat R) (ModuleCat R)).obj Y)
((forget₂ (AlgebraCat R) (ModuleCat R)).obj Z)).hom | ((:c Eq) ((:c Quiver.Hom) ((:c ModuleCat) (:fv _uniq.10024) ((:c CommRing.toRing) (:fv _uniq.10024) (:fv _uniq.10027))) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c ModuleCat) (:fv _uniq.10024) ((:c CommRing.toRing) (:fv _uniq.10024) (:fv _uniq.10027))) ((:c CategoryTheory.Category.toCategoryStruct) ((:c ModuleCat... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.10024))"},{"name":"X","sexp":"((:c AlgebraCat) (:fv _uniq.10024) (:fv _uniq.10027))"},{"name":"Y","sexp":"((:c AlgebraCat) (:fv _uniq.10024) (:fv _uniq.10027))"},{"name":"Z","sexp":"((:c AlgebraCat) (:fv _uniq.10024) (:fv _uniq.100... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:app (:c ModuleCat) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:app (:c ModuleCat) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10024","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.10027","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CommRing) (:arg :explici... | {"children":[{"children":[{"children":[{"children":[{"source":"rfl","sourceEnd":1929,"sourceStart":1926,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":1929,"sourceStart":1926,"tag":"node"}],"kind":"null","source":"rfl","sourceEnd":1929,"sourceStart":1926,"tag":"node"}],"kind":"Lean.Pars... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10024","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.10027","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":3,"interna... | 15 | 2 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d330b6c3745956405a5cf81b6dc3e27254cd2328231bdd331a57b222bc438630 | 2a2cee0a1e0697b6abfaec83b395ddc8dffb2b6692121af9edaf0da3f67fdfd8 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,548 | CategoryTheory.HasLiftingProperty.iff_of_arrow_iso_right | Mathlib/CategoryTheory/LiftingProperties/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor <;> intro | C : Type u_1
inst✝ : Category.{u_2, u_1} C
A✝ B✝ B' X✝ Y✝ Y'✝ : C
i✝ : A✝ ⟶ B✝
i' : B✝ ⟶ B'
p✝ : X✝ ⟶ Y✝
p'✝ : Y✝ ⟶ Y'✝
A B X Y X' Y' : C
i : A ⟶ B
p : X ⟶ Y
p' : X' ⟶ Y'
e : Arrow.mk p ≅ Arrow.mk p'
⊢ HasLiftingProperty i p ↔ HasLiftingProperty i p' | case mp
C : Type u_1
inst✝ : Category.{u_2, u_1} C
A✝ B✝ B' X✝ Y✝ Y'✝ : C
i✝ : A✝ ⟶ B✝
i' : B✝ ⟶ B'
p✝ : X✝ ⟶ Y✝
p'✝ : Y✝ ⟶ Y'✝
A B X Y X' Y' : C
i : A ⟶ B
p : X ⟶ Y
p' : X' ⟶ Y'
e : Arrow.mk p ≅ Arrow.mk p'
a✝ : HasLiftingProperty i p
⊢ HasLiftingProperty i p'
case mpr
C : Type u_1
inst✝ : Category.{u_2, u_1} C
A✝ B✝ ... | ((:c Iff) ((:c CategoryTheory.HasLiftingProperty) (:fv _uniq.10716) (:fv _uniq.10720) (:fv _uniq.11129) (:fv _uniq.11130) (:fv _uniq.11131) (:fv _uniq.11132) (:fv _uniq.11135) (:fv _uniq.11136)) ((:c CategoryTheory.HasLiftingProperty) (:fv _uniq.10716) (:fv _uniq.10720) (:fv _uniq.11129) (:fv _uniq.11130) (:fv _uniq.11... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.10716))"},{"name":"A✝","sexp":"(:fv _uniq.10716)"},{"name":"B✝","sexp":"(:fv _uniq.10716)"},{"name":"B'","sexp":"(:fv _uniq.10716)"},{"name":"X✝","sexp":"(:fv _uniq.10716)"},{"name":"Y✝","sexp":"(:fv _uniq.10716)"}... | (:app (:c Iff) (:arg :explicit 0 (:app (:c CategoryTheory.HasLiftingProperty) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit 2) (:arg :implicit 3) (:arg :implicit 4) (:arg :implicit 5) (:arg :explicit 6 (:fv FV19)) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10716","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.10720","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Category)... | {"children":[{"children":[{"source":"constructor","sourceEnd":6035,"sourceStart":6024,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":6035,"sourceStart":6024,"tag":"node"},{"source":"<;>","sourceEnd":6039,"sourceStart":6036,"tag":"atom"},{"children":[{"source":"intro","sourceEn... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10716","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.10720","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 36 | 4 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 25dc0c148b584dd416f1b9385b17f6d333478b98555b88e932d219af452b8d3c | abd059fd27e2da30dcecf35d1af69479b048a72ff11e8ed2895bd6b68f47397f | c4ace24b1b5fd392cc08967e0632cc0ff3858a14102e7d3c0ab591cb2d19d266 | 88582b16d7788827fcb4613147e536c8d2383fc15774d947ca679696aa91a087 |
cat-searcher/leandojo-benchmark-4-random | test | 1,550 | SimpleGraph.singletonSubgraph_le_iff | Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨fun h ↦ h.1 (<a>Set.mem_singleton</a> v), ?_⟩ | ι : Sort u_1
V : Type u
W : Type v
G : SimpleGraph V
G' : SimpleGraph W
v : V
H : G.Subgraph
⊢ G.singletonSubgraph v ≤ H ↔ v ∈ H.verts | ι : Sort u_1
V : Type u
W : Type v
G : SimpleGraph V
G' : SimpleGraph W
v : V
H : G.Subgraph
⊢ v ∈ H.verts → G.singletonSubgraph v ≤ H | ((:c Iff) ((:c LE.le) ((:c SimpleGraph.Subgraph) (:fv _uniq.97973) (:fv _uniq.97978)) ((:c Preorder.toLE) ((:c SimpleGraph.Subgraph) (:fv _uniq.97973) (:fv _uniq.97978)) ((:c PartialOrder.toPreorder) ((:c SimpleGraph.Subgraph) (:fv _uniq.97973) (:fv _uniq.97978)) ((:c CompleteSemilatticeInf.toPartialOrder) ((:c SimpleG... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"W","sexp":"(:sort (+ v 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.97973))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.97975))"},{"name":"v","sexp":"(:fv _uniq.97973)"},{"name":"H","sexp":"((:c SimpleGraph.Subgraph) (:f... | (:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c SimpleGraph.Subgraph) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV3)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c SimpleGraph.Subgraph) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.97971","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.97973","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":35155,"sourceStart":35149,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":35159,"sourceStart":35156,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":35162,"sourceStart":35159,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","sourc... | [] | [{"source":"⟨fun h ↦ h.1 (Set.mem_singleton v), ?_⟩","source_end":35201,"source_start":35156,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.97971","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.97973","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 244 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 59441b4f75ec6a4f56aa031e39407d74bb4cca9ad5f006109587c2c88518c165 | b8ae9e1e20443cb6c8e95610507914176329fbe9aa1651da106b4ac372c05888 | 80d7e55887a3fb9490c6bfcea18757c40b2e0b841c4f0bd203fe40c47be50270 | 767c0477fef0e8028f968782d85fb1f2534fe53c7a2dcd2b6c097129281f4260 |
cat-searcher/leandojo-benchmark-4-random | test | 1,551 | SimpleGraph.singletonSubgraph_le_iff | Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro h | ι : Sort u_1
V : Type u
W : Type v
G : SimpleGraph V
G' : SimpleGraph W
v : V
H : G.Subgraph
⊢ v ∈ H.verts → G.singletonSubgraph v ≤ H | ι : Sort u_1
V : Type u
W : Type v
G : SimpleGraph V
G' : SimpleGraph W
v : V
H : G.Subgraph
h : v ∈ H.verts
⊢ G.singletonSubgraph v ≤ H | (:forall _ ((:c Membership.mem) (:fv _uniq.97973) ((:c Set) (:fv _uniq.97973)) ((:c Set.instMembership) (:fv _uniq.97973)) (:fv _uniq.98077) ((:c SimpleGraph.Subgraph.verts) (:fv _uniq.97973) (:fv _uniq.97978) (:fv _uniq.98078))) ((:c LE.le) ((:c SimpleGraph.Subgraph) (:fv _uniq.97973) (:fv _uniq.97978)) ((:c Preorder.... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"W","sexp":"(:sort (+ v 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.97973))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.97975))"},{"name":"v","sexp":"(:fv _uniq.97973)"},{"name":"H","sexp":"((:c SimpleGraph.Subgraph) (:f... | (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.97971","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.97973","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"intro","sourceEnd":35209,"sourceStart":35204,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":35211,"sourceStart":35210,"tag":"identifier"}],"kind":"null","source":"h","sourceEnd":35211,"sourceStart":35210,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"h","source_end":35211,"source_start":35210,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.97971","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.97973","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 244 | 5 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0015b5003b1ab2aa2a60cf5e7b60d3e0fcf7d7be13b4321c46b226ab42f74851 | 767c0477fef0e8028f968782d85fb1f2534fe53c7a2dcd2b6c097129281f4260 | 5cf42e5c5e9faf9804f4b8005e32168f3a46b38347377087a457c72b727740cb | d4df9a5826e4a8c2f0d897f87aa6dc6e8aba8b884ae7cec77c0a2b4e6c6f8203 |
cat-searcher/leandojo-benchmark-4-random | test | 1,552 | SimpleGraph.singletonSubgraph_le_iff | Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | ι : Sort u_1
V : Type u
W : Type v
G : SimpleGraph V
G' : SimpleGraph W
v : V
H : G.Subgraph
h : v ∈ H.verts
⊢ G.singletonSubgraph v ≤ H | case left
ι : Sort u_1
V : Type u
W : Type v
G : SimpleGraph V
G' : SimpleGraph W
v : V
H : G.Subgraph
h : v ∈ H.verts
⊢ (G.singletonSubgraph v).verts ⊆ H.verts
case right
ι : Sort u_1
V : Type u
W : Type v
G : SimpleGraph V
G' : SimpleGraph W
v : V
H : G.Subgraph
h : v ∈ H.verts
⊢ ∀ ⦃v_1 w : V⦄, (G.singletonSubgraph v... | ((:c LE.le) ((:c SimpleGraph.Subgraph) (:fv _uniq.97973) (:fv _uniq.97978)) ((:c Preorder.toLE) ((:c SimpleGraph.Subgraph) (:fv _uniq.97973) (:fv _uniq.97978)) ((:c PartialOrder.toPreorder) ((:c SimpleGraph.Subgraph) (:fv _uniq.97973) (:fv _uniq.97978)) ((:c CompleteSemilatticeInf.toPartialOrder) ((:c SimpleGraph.Subgr... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"W","sexp":"(:sort (+ v 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.97973))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.97975))"},{"name":"v","sexp":"(:fv _uniq.97973)"},{"name":"H","sexp":"((:c SimpleGraph.Subgraph) (:f... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c SimpleGraph.Subgraph) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV3)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c SimpleGraph.Subgraph) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV3))))))) (:arg :explicit 2 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.97971","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.97973","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"constructor","sourceEnd":35225,"sourceStart":35214,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":35225,"sourceStart":35214,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.97971","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.97973","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 244 | 6 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 37c01fe938b23bb60ae4f85feb174411aaeef4d1c2264ee0f0c3eb1bc16f2130 | d4df9a5826e4a8c2f0d897f87aa6dc6e8aba8b884ae7cec77c0a2b4e6c6f8203 | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | f35ec78473b5eaee8c6773481d478281a20cba3750cd223c5665f94fdc78067f |
cat-searcher/leandojo-benchmark-4-random | test | 1,553 | SimpleGraph.singletonSubgraph_le_iff | Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>SimpleGraph.singletonSubgraph_verts</a>, <a>Set.singleton_subset_iff</a>] | case left
ι : Sort u_1
V : Type u
W : Type v
G : SimpleGraph V
G' : SimpleGraph W
v : V
H : G.Subgraph
h : v ∈ H.verts
⊢ (G.singletonSubgraph v).verts ⊆ H.verts | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.97973)) ((:c Set.instHasSubset) (:fv _uniq.97973)) ((:c SimpleGraph.Subgraph.verts) (:fv _uniq.97973) (:fv _uniq.97978) ((:c SimpleGraph.singletonSubgraph) (:fv _uniq.97973) (:fv _uniq.97978) (:fv _uniq.98077))) ((:c SimpleGraph.Subgraph.verts) (:fv _uniq.97973) (:fv _uniq.97... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"W","sexp":"(:sort (+ v 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.97973))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.97975))"},{"name":"v","sexp":"(:fv _uniq.97973)"},{"name":"H","sexp":"((:c SimpleGraph.Subgraph) (:f... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 2 (:app (:c SimpleGraph.Subgraph.verts) (:arg :implicit-type 0 (:fv FV1)) (:arg :implic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.97971","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.97973","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":35234,"sourceStart":35231,"tag":"atom"},{"children":[{"source":"[","sourceEnd":35236,"sourceStart":35235,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"SimpleGraph.singletonSubgraph_v... | [] | [{"source":"singletonSubgraph_verts","source_end":35259,"source_start":35236,"syntax_kind":"ident"},{"source":"Set.singleton_subset_iff","source_end":35285,"source_start":35261,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.97971","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.97973","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 244 | 9 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b89b5f90d77894b488daa08bfe75655e277b14dd7b634f5bd0158733636377df | 2a138af0ae1ef564a7bb5c4537f2127d65e6ef26529c41520ad25ca45343827b | 94b736168766a048386f4461f2f5a0c05cce5adc56e1b4de67c406e53716ec5b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,554 | SimpleGraph.singletonSubgraph_le_iff | Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun _ _ ↦ <a>False.elim</a> | case right
ι : Sort u_1
V : Type u
W : Type v
G : SimpleGraph V
G' : SimpleGraph W
v : V
H : G.Subgraph
h : v ∈ H.verts
⊢ ∀ ⦃v_1 w : V⦄, (G.singletonSubgraph v).Adj v_1 w → H.Adj v_1 w | (:forall v (:fv _uniq.97973) (:forall w (:fv _uniq.97973) (:forall _ ((:c SimpleGraph.Subgraph.Adj) (:fv _uniq.97973) (:fv _uniq.97978) ((:c SimpleGraph.singletonSubgraph) (:fv _uniq.97973) (:fv _uniq.97978) (:fv _uniq.98077)) 1 0) ((:c SimpleGraph.Subgraph.Adj) (:fv _uniq.97973) (:fv _uniq.97978) (:fv _uniq.98078) 2 1... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"W","sexp":"(:sort (+ v 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.97973))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.97975))"},{"name":"v","sexp":"(:fv _uniq.97973)"},{"name":"H","sexp":"((:c SimpleGraph.Subgraph) (:f... | (:forall v :strict-implicit (:fv FV1) (:forall w :strict-implicit (:fv FV1) (:forall _ :explicit (:app (:c SimpleGraph.Subgraph.Adj) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c SimpleGraph.singletonSubgraph) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV3)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.97971","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.97973","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":35297,"sourceStart":35292,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":35301,"sourceStart":35298,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"_","sourceEnd":35303,"sourceStart":35302,"tag":"atom"}],"kind":"Lea... | [] | [{"source":"fun _ _ ↦ False.elim","source_end":35320,"source_start":35298,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.97971","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.97973","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 244 | 17 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dc0b6bcd31938cf1e10635482ab5dab7ae41a633f1231fb54ecb588a053ceb2f | e2b1b168f662421d1202a85d5b557565541f962898ea4a581bf72b304a495bb5 | 3230c21c3acd4500afddbbd5316a9dbd9f703dab090760326c8fa60930ca4e03 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,555 | Multiset.le_iff_count | Mathlib/Data/Multiset/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← (<a>Multiset.ext</a>.2 fun a => by simp [<a>max_eq_right</a> (al a)] : s ∪ t = t)] | α : Type u_1
β : Type v
γ : Type u_2
inst✝ : DecidableEq α
s✝ s t : Multiset α
al : ∀ (a : α), count a s ≤ count a t
⊢ s ≤ t | α : Type u_1
β : Type v
γ : Type u_2
inst✝ : DecidableEq α
s✝ s t : Multiset α
al : ∀ (a : α), count a s ≤ count a t
⊢ s ≤ s ∪ t | ((:c LE.le) ((:c Multiset) (:fv _uniq.275410)) ((:c Preorder.toLE) ((:c Multiset) (:fv _uniq.275410)) ((:c PartialOrder.toPreorder) ((:c Multiset) (:fv _uniq.275410)) ((:c Multiset.instPartialOrder) (:fv _uniq.275410)))) (:fv _uniq.275504) (:fv _uniq.275505)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.275410))"},{"name":"s✝","sexp":"((:c Multiset) (:fv _uniq.275410))"},{"name":"s","sexp":"((:c Multiset) (:fv _uniq.275410))"},{"name":"t","sexp":"((... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:fv FV6)) (:arg :explicit 3 (:fv FV7))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.275410","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.275412","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":108490,"sourceStart":108488,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":108492,"sourceStart":108491,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":108495,"sou... | [] | [{"source":"(ext.2 fun a => by simp [max_eq_right (al a)] : s ∪ t = t)","source_end":108556,"source_start":108496,"syntax_kind":"Lean.Parser.Term.typeAscription"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.275410","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.275412","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 931 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1ce0dbf5a437fb5f9225b4243db7ca9541d805dd9195d433154e535a03657f9d | 4c54317f2166d0a5023d235a64296d0fe86fca943906826278d8910758b98a23 | 03614e098dd044ba82ee3939dbdfbcd961611d566ea882f34b79ee5fb62609c5 | 120bec51dd3e7267cf092f263d602b5c499e33ac8d160a1e19f01e4a568f7836 |
cat-searcher/leandojo-benchmark-4-random | test | 1,556 | Multiset.le_iff_count | Mathlib/Data/Multiset/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Multiset.le_union_left</a> | α : Type u_1
β : Type v
γ : Type u_2
inst✝ : DecidableEq α
s✝ s t : Multiset α
al : ∀ (a : α), count a s ≤ count a t
⊢ s ≤ s ∪ t | ((:c LE.le) ((:c Multiset) (:fv _uniq.275410)) ((:c Preorder.toLE) ((:c Multiset) (:fv _uniq.275410)) ((:c PartialOrder.toPreorder) ((:c Multiset) (:fv _uniq.275410)) ((:c Multiset.instPartialOrder) (:fv _uniq.275410)))) (:fv _uniq.275504) ((:c Union.union) ((:c Multiset) (:fv _uniq.275410)) ((:c Multiset.instUnion) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.275410))"},{"name":"s✝","sexp":"((:c Multiset) (:fv _uniq.275410))"},{"name":"s","sexp":"((:c Multiset) (:fv _uniq.275410))"},{"name":"t","sexp":"((... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:fv FV6)) (:arg :explicit 3 (:app (:c Union.union) (:arg :implicit-type 0 (:app (:c Multiset... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.275410","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.275412","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"apply","sourceEnd":108564,"sourceStart":108559,"tag":"atom"},{"name":"Multiset.le_union_left","semanticRole":"global","source":"le_union_left","sourceEnd":108578,"sourceStart":108565,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply le_union_left","sourceEnd":108578,"sourceS... | [] | [{"source":"le_union_left","source_end":108578,"source_start":108565,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.275410","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.275412","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 931 | 13 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6166dda2553ca6a4b7879c5e037219f2193ecddea0ae277abb934e2abe037e5b | 120bec51dd3e7267cf092f263d602b5c499e33ac8d160a1e19f01e4a568f7836 | 7128a9a227232d2d1e37c357846212d4e684711002260bd8464c931bf4335ebc | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 |
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