Datasets:
iCogLabs-Dev
/
Mathlib-Normalized-Sexpr

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cat-searcher/leandojo-benchmark-4-random
test
1,759
LinearMap.injective_domRestrict_iff
Mathlib/Algebra/Module/Submodule/Ker.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [h] at this
case refine_1 R : Type u_1 R₁ : Type u_2 R₂ : Type u_3 R₃ : Type u_4 K : Type u_5 M : Type u_6 M₁ : Type u_7 M₂ : Type u_8 M₃ : Type u_9 V : Type u_10 V₂ : Type u_11 inst✝¹¹ : Ring R inst✝¹⁰ : Ring R₂ inst✝⁹ : Ring R₃ inst✝⁸ : AddCommGroup M inst✝⁷ : AddCommGroup M₂ inst✝⁶ : AddCommGroup M₃ inst✝⁵ : Module R M inst✝⁴ :...
case refine_1 R : Type u_1 R₁ : Type u_2 R₂ : Type u_3 R₃ : Type u_4 K : Type u_5 M : Type u_6 M₁ : Type u_7 M₂ : Type u_8 M₃ : Type u_9 V : Type u_10 V₂ : Type u_11 inst✝¹¹ : Ring R inst✝¹⁰ : Ring R₂ inst✝⁹ : Ring R₃ inst✝⁸ : AddCommGroup M inst✝⁷ : AddCommGroup M₂ inst✝⁶ : AddCommGroup M₃ inst✝⁵ : Module R M inst✝⁴ :...
((:c Membership.mem) (:fv _uniq.141918) ((:c Submodule) (:fv _uniq.141903) (:fv _uniq.141918) ((:c Ring.toSemiring) (:fv _uniq.141903) (:fv _uniq.141936)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.141918) (:fv _uniq.141945)) (:fv _uniq.142475)) ((:c SetLike.instMembership) ((:c Submodule) (:fv _uniq.141903) (:fv _u...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₁","sexp":"(:sort (+ u_2 1))"},{"name":"R₂","sexp":"(:sort (+ u_3 1))"},{"name":"R₃","sexp":"(:sort (+ u_4 1))"},{"name":"K","sexp":"(:sort (+ u_5 1))"},{"name":"M","sexp":"(:sort (+ u_6 1))"},{"name":"M₁","sexp":"(:sort (+ u_7 1))"},{"name":"M₂","sexp":"(:sort (+ u_8 ...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"rw","sourceEnd":8916,"sourceStart":8914,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8918,"sourceStart":8917,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":31,"semanticR...
[]
[{"source":"h","source_end":8919,"source_start":8918,"syntax_kind":"ident"},{"source":"this","source_end":8928,"source_start":8924,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":2,"internal_name":"...
83
16
exact
true
1
35
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
801bedbaf257bc5439b51443249c2cfc6b7bed2219c7b72f78cee395fdd08b97
353d2983cea27bace3da0deac34232472558faf153ad04495100efaffbcb8ff5
85b3a18b2e150bbc8333274648dd15c3e2895a5836b200efc85dd695faa43109
80f95a3ad8cd1f4fcb43722762beffaa9d415971fa8433292a568af3a6a25358
cat-searcher/leandojo-benchmark-4-random
test
1,760
LinearMap.injective_domRestrict_iff
Mathlib/Algebra/Module/Submodule/Ker.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simpa using this
case refine_1 R : Type u_1 R₁ : Type u_2 R₂ : Type u_3 R₃ : Type u_4 K : Type u_5 M : Type u_6 M₁ : Type u_7 M₂ : Type u_8 M₃ : Type u_9 V : Type u_10 V₂ : Type u_11 inst✝¹¹ : Ring R inst✝¹⁰ : Ring R₂ inst✝⁹ : Ring R₃ inst✝⁸ : AddCommGroup M inst✝⁷ : AddCommGroup M₂ inst✝⁶ : AddCommGroup M₃ inst✝⁵ : Module R M inst✝⁴ :...
((:c Membership.mem) (:fv _uniq.141918) ((:c Submodule) (:fv _uniq.141903) (:fv _uniq.141918) ((:c Ring.toSemiring) (:fv _uniq.141903) (:fv _uniq.141936)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.141918) (:fv _uniq.141945)) (:fv _uniq.142475)) ((:c SetLike.instMembership) ((:c Submodule) (:fv _uniq.141903) (:fv _u...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₁","sexp":"(:sort (+ u_2 1))"},{"name":"R₂","sexp":"(:sort (+ u_3 1))"},{"name":"R₃","sexp":"(:sort (+ u_4 1))"},{"name":"K","sexp":"(:sort (+ u_5 1))"},{"name":"M","sexp":"(:sort (+ u_6 1))"},{"name":"M₁","sexp":"(:sort (+ u_7 1))"},{"name":"M₂","sexp":"(:sort (+ u_8 ...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"simpa","sourceEnd":8938,"sourceStart":8933,"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":"this","source_end":8949,"source_start":8945,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":2,"internal_name":"...
83
19
exact
true
1
35
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4a469c56778099abacfa44f3a66cfc3ae464f04eada8825b4ff2595bed45f262
80f95a3ad8cd1f4fcb43722762beffaa9d415971fa8433292a568af3a6a25358
0b3921c44845605e252e1bd356fd2f4a7a040ada5f0a7969881a98444ae0243c
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,761
LinearMap.injective_domRestrict_iff
Mathlib/Algebra/Module/Submodule/Ker.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simpa using h'x
R : Type u_1 R₁ : Type u_2 R₂ : Type u_3 R₃ : Type u_4 K : Type u_5 M : Type u_6 M₁ : Type u_7 M₂ : Type u_8 M₃ : Type u_9 V : Type u_10 V₂ : Type u_11 inst✝¹¹ : Ring R inst✝¹⁰ : Ring R₂ inst✝⁹ : Ring R₃ inst✝⁸ : AddCommGroup M inst✝⁷ : AddCommGroup M₂ inst✝⁶ : AddCommGroup M₃ inst✝⁵ : Module R M inst✝⁴ : Module R₂ M₂ ...
((:c Membership.mem) ((:c Subtype) (:fv _uniq.141918) (:lambda x (:fv _uniq.141918) ((:c Membership.mem) (:fv _uniq.141918) ((:c Submodule) (:fv _uniq.141903) (:fv _uniq.141918) ((:c Ring.toSemiring) (:fv _uniq.141903) (:fv _uniq.141936)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.141918) (:fv _uniq.141945)) (:fv _u...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₁","sexp":"(:sort (+ u_2 1))"},{"name":"R₂","sexp":"(:sort (+ u_3 1))"},{"name":"R₃","sexp":"(:sort (+ u_4 1))"},{"name":"K","sexp":"(:sort (+ u_5 1))"},{"name":"M","sexp":"(:sort (+ u_6 1))"},{"name":"M₁","sexp":"(:sort (+ u_7 1))"},{"name":"M₂","sexp":"(:sort (+ u_8 ...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:lambda x :explicit (:fv FV5) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)) (:arg :...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"simpa","sourceEnd":8899,"sourceStart":8894,"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":"h'x","source_end":8909,"source_start":8906,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":2,"internal_name":"...
83
15
exact
true
1
34
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
eacf30dd487ad6051fa42900e300f8acdb2d6a540483ec6f8a537926c9be02db
c28c6be0f03da630dd1b47d1b6a3232eabd6db9ad6cd74a917c0cc777787799d
e7f990dcade4a65721dad4e0c9882ac4c9a7eb621266d047cda4f8aeab1dd81d
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,762
LinearMap.injective_domRestrict_iff
Mathlib/Algebra/Module/Submodule/Ker.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro ⟨x, hx⟩ h'x
case refine_2 R : Type u_1 R₁ : Type u_2 R₂ : Type u_3 R₃ : Type u_4 K : Type u_5 M : Type u_6 M₁ : Type u_7 M₂ : Type u_8 M₃ : Type u_9 V : Type u_10 V₂ : Type u_11 inst✝¹¹ : Ring R inst✝¹⁰ : Ring R₂ inst✝⁹ : Ring R₃ inst✝⁸ : AddCommGroup M inst✝⁷ : AddCommGroup M₂ inst✝⁶ : AddCommGroup M₃ inst✝⁵ : Module R M inst✝⁴ :...
case refine_2.mk R : Type u_1 R₁ : Type u_2 R₂ : Type u_3 R₃ : Type u_4 K : Type u_5 M : Type u_6 M₁ : Type u_7 M₂ : Type u_8 M₃ : Type u_9 V : Type u_10 V₂ : Type u_11 inst✝¹¹ : Ring R inst✝¹⁰ : Ring R₂ inst✝⁹ : Ring R₃ inst✝⁸ : AddCommGroup M inst✝⁷ : AddCommGroup M₂ inst✝⁶ : AddCommGroup M₃ inst✝⁵ : Module R M inst✝...
((:c LE.le) ((:c Submodule) (:fv _uniq.141903) ((:c Subtype) (:fv _uniq.141918) (:lambda x (:fv _uniq.141918) ((:c Membership.mem) (:fv _uniq.141918) ((:c Submodule) (:fv _uniq.141903) (:fv _uniq.141918) ((:c Ring.toSemiring) (:fv _uniq.141903) (:fv _uniq.141936)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.141918) (...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₁","sexp":"(:sort (+ u_2 1))"},{"name":"R₂","sexp":"(:sort (+ u_3 1))"},{"name":"R₃","sexp":"(:sort (+ u_4 1))"},{"name":"K","sexp":"(:sort (+ u_5 1))"},{"name":"M","sexp":"(:sort (+ u_6 1))"},{"name":"M₁","sexp":"(:sort (+ u_7 1))"},{"name":"M₂","sexp":"(:sort (+ u_8 ...
(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:lambda x :explicit (:fv FV5) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"rintro","sourceEnd":8961,"sourceStart":8955,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":8965,"sourceStart":8962,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":8966,"sourceSt...
[{"role":"fresh_name","source":"x","source_end":8966,"source_start":8965,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":8970,"source_start":8968,"syntax_kind":"ident"},{"role":"fresh_name","source":"h'x","source_end":8977,"source_start":8974,"syntax_kind":"ident"}]
[{"source":"⟨x, hx⟩","source_end":8973,"source_start":8962,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":2,"internal_name":"...
83
24
exact
true
1
31
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
84b02d78d20a9f540850acb784a4da963474e4e9e4591362ea38173ab1117797
36e61449d2c7b82d7a0d25e6064be009a7d59ff6f817de998ea704e9c568ab39
bc1bfdabb2e2f3bb99e774de0b613c4b82b01379fd3dc14529c77bbdddaf6aa1
06ac7a3570d56260558db64aa152593c0d06b860495f29e5c7b0fe101459283a
cat-searcher/leandojo-benchmark-4-random
test
1,763
LinearMap.injective_domRestrict_iff
Mathlib/Algebra/Module/Submodule/Ker.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have : x ∈ S ⊓ <a>LinearMap.ker</a> f := ⟨hx, h'x⟩
case refine_2.mk R : Type u_1 R₁ : Type u_2 R₂ : Type u_3 R₃ : Type u_4 K : Type u_5 M : Type u_6 M₁ : Type u_7 M₂ : Type u_8 M₃ : Type u_9 V : Type u_10 V₂ : Type u_11 inst✝¹¹ : Ring R inst✝¹⁰ : Ring R₂ inst✝⁹ : Ring R₃ inst✝⁸ : AddCommGroup M inst✝⁷ : AddCommGroup M₂ inst✝⁶ : AddCommGroup M₃ inst✝⁵ : Module R M inst✝...
case refine_2.mk R : Type u_1 R₁ : Type u_2 R₂ : Type u_3 R₃ : Type u_4 K : Type u_5 M : Type u_6 M₁ : Type u_7 M₂ : Type u_8 M₃ : Type u_9 V : Type u_10 V₂ : Type u_11 inst✝¹¹ : Ring R inst✝¹⁰ : Ring R₂ inst✝⁹ : Ring R₃ inst✝⁸ : AddCommGroup M inst✝⁷ : AddCommGroup M₂ inst✝⁶ : AddCommGroup M₃ inst✝⁵ : Module R M inst✝...
((:c Membership.mem) ((:c Subtype) (:fv _uniq.141918) (:lambda x (:fv _uniq.141918) ((:c Membership.mem) (:fv _uniq.141918) ((:c Submodule) (:fv _uniq.141903) (:fv _uniq.141918) ((:c Ring.toSemiring) (:fv _uniq.141903) (:fv _uniq.141936)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.141918) (:fv _uniq.141945)) (:fv _u...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₁","sexp":"(:sort (+ u_2 1))"},{"name":"R₂","sexp":"(:sort (+ u_3 1))"},{"name":"R₃","sexp":"(:sort (+ u_4 1))"},{"name":"K","sexp":"(:sort (+ u_5 1))"},{"name":"M","sexp":"(:sort (+ u_6 1))"},{"name":"M₁","sexp":"(:sort (+ u_7 1))"},{"name":"M₂","sexp":"(:sort (+ u_8 ...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:lambda x :explicit (:fv FV5) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)) (:arg :...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"have","sourceEnd":8986,"sourceStart":8982,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":8987,"sourceStart":8987,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":8987,"sourceStart":8987,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","...
[]
[{"source":"x ∈ S ⊓ LinearMap.ker f","source_end":9016,"source_start":8989,"syntax_kind":"«term_∈_»"},{"source":"⟨hx, h'x⟩","source_end":9033,"source_start":9020,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":2,"internal_name":"...
83
25
exact
true
1
34
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5f5eb49e8b936fee43845095049e52fa5ade8411e1e2ca1ed46038a4156a5eea
06ac7a3570d56260558db64aa152593c0d06b860495f29e5c7b0fe101459283a
10b6e0489fe865804bed048efe1b8c204d6ddef8103ad3b6b8b1765d996bec1b
8dfa6f5c556db7aeeadb91008ad5f55e347f360a3e0cec027bc497e4f9346969
cat-searcher/leandojo-benchmark-4-random
test
1,764
LinearMap.injective_domRestrict_iff
Mathlib/Algebra/Module/Submodule/Ker.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [h] at this
case refine_2.mk R : Type u_1 R₁ : Type u_2 R₂ : Type u_3 R₃ : Type u_4 K : Type u_5 M : Type u_6 M₁ : Type u_7 M₂ : Type u_8 M₃ : Type u_9 V : Type u_10 V₂ : Type u_11 inst✝¹¹ : Ring R inst✝¹⁰ : Ring R₂ inst✝⁹ : Ring R₃ inst✝⁸ : AddCommGroup M inst✝⁷ : AddCommGroup M₂ inst✝⁶ : AddCommGroup M₃ inst✝⁵ : Module R M inst✝...
case refine_2.mk R : Type u_1 R₁ : Type u_2 R₂ : Type u_3 R₃ : Type u_4 K : Type u_5 M : Type u_6 M₁ : Type u_7 M₂ : Type u_8 M₃ : Type u_9 V : Type u_10 V₂ : Type u_11 inst✝¹¹ : Ring R inst✝¹⁰ : Ring R₂ inst✝⁹ : Ring R₃ inst✝⁸ : AddCommGroup M inst✝⁷ : AddCommGroup M₂ inst✝⁶ : AddCommGroup M₃ inst✝⁵ : Module R M inst✝...
((:c Membership.mem) ((:c Subtype) (:fv _uniq.141918) (:lambda x (:fv _uniq.141918) ((:c Membership.mem) (:fv _uniq.141918) ((:c Submodule) (:fv _uniq.141903) (:fv _uniq.141918) ((:c Ring.toSemiring) (:fv _uniq.141903) (:fv _uniq.141936)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.141918) (:fv _uniq.141945)) (:fv _u...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₁","sexp":"(:sort (+ u_2 1))"},{"name":"R₂","sexp":"(:sort (+ u_3 1))"},{"name":"R₃","sexp":"(:sort (+ u_4 1))"},{"name":"K","sexp":"(:sort (+ u_5 1))"},{"name":"M","sexp":"(:sort (+ u_6 1))"},{"name":"M₁","sexp":"(:sort (+ u_7 1))"},{"name":"M₂","sexp":"(:sort (+ u_8 ...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:lambda x :explicit (:fv FV5) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)) (:arg :...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"rw","sourceEnd":9040,"sourceStart":9038,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9042,"sourceStart":9041,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":31,"semanticR...
[]
[{"source":"h","source_end":9043,"source_start":9042,"syntax_kind":"ident"},{"source":"this","source_end":9052,"source_start":9048,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":2,"internal_name":"...
83
26
exact
true
1
35
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
49e397bf0e36fdbaee3934f103f4032cd61c33bbf3a55a1d13e7f44366a53644
8dfa6f5c556db7aeeadb91008ad5f55e347f360a3e0cec027bc497e4f9346969
85b3a18b2e150bbc8333274648dd15c3e2895a5836b200efc85dd695faa43109
1818f12839f3725e725cfc8a14f997527c24843c9290d56398a4b4df68e062bd
cat-searcher/leandojo-benchmark-4-random
test
1,765
LinearMap.injective_domRestrict_iff
Mathlib/Algebra/Module/Submodule/Ker.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simpa using this
case refine_2.mk R : Type u_1 R₁ : Type u_2 R₂ : Type u_3 R₃ : Type u_4 K : Type u_5 M : Type u_6 M₁ : Type u_7 M₂ : Type u_8 M₃ : Type u_9 V : Type u_10 V₂ : Type u_11 inst✝¹¹ : Ring R inst✝¹⁰ : Ring R₂ inst✝⁹ : Ring R₃ inst✝⁸ : AddCommGroup M inst✝⁷ : AddCommGroup M₂ inst✝⁶ : AddCommGroup M₃ inst✝⁵ : Module R M inst✝...
((:c Membership.mem) ((:c Subtype) (:fv _uniq.141918) (:lambda x (:fv _uniq.141918) ((:c Membership.mem) (:fv _uniq.141918) ((:c Submodule) (:fv _uniq.141903) (:fv _uniq.141918) ((:c Ring.toSemiring) (:fv _uniq.141903) (:fv _uniq.141936)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.141918) (:fv _uniq.141945)) (:fv _u...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₁","sexp":"(:sort (+ u_2 1))"},{"name":"R₂","sexp":"(:sort (+ u_3 1))"},{"name":"R₃","sexp":"(:sort (+ u_4 1))"},{"name":"K","sexp":"(:sort (+ u_5 1))"},{"name":"M","sexp":"(:sort (+ u_6 1))"},{"name":"M₁","sexp":"(:sort (+ u_7 1))"},{"name":"M₂","sexp":"(:sort (+ u_8 ...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:lambda x :explicit (:fv FV5) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)) (:arg :...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"simpa","sourceEnd":9062,"sourceStart":9057,"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":"this","source_end":9073,"source_start":9069,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":2,"internal_name":"...
83
29
exact
true
1
35
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ab3a014f49422e6b98d89809e5892d1fa35b65f6e82a9e6bec033c9cbcc3614e
1818f12839f3725e725cfc8a14f997527c24843c9290d56398a4b4df68e062bd
0b3921c44845605e252e1bd356fd2f4a7a040ada5f0a7969881a98444ae0243c
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,766
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
cases' n with n
p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n : ℕ IH : ∀ m < n, (map (Int.castRingHom ℚ)) (wittStructureInt p Φ m) = wittStructureRat p ((map (Int.castRingHom ℚ)) Φ) m ⊢ C ↑(p ^ n) ∣ (bind₁ fun b => (rename fun i => (b, i)) (W_ ℤ n)) Φ - ∑ i ∈ Finset.ran...
case zero p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ IH : ∀ m < 0, (map (Int.castRingHom ℚ)) (wittStructureInt p Φ m) = wittStructureRat p ((map (Int.castRingHom ℚ)) Φ) m ⊢ C ↑(p ^ 0) ∣ (bind₁ fun b => (rename fun i => (b, i)) (W_ ℤ 0)) Φ - ∑ i ∈ Finset...
((:c Dvd.dvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c semigroupDvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c SemigroupWithZero.toSemigroup) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c I...
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:c Int)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:c Int))))))) (:arg :instance 1 (:instance-of (:app (:c Dv...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"cases'","sourceEnd":11110,"sourceStart":11104,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":7,"semanticRole":"local","source":"n","sourceEnd":11112,"sourceStart":11111,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","s...
[]
[{"source":"n","source_end":11112,"source_start":11111,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
4
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8eed9bd4ec134eda4cbe1c54b9444f6bc917643e4057d8b065ffe15c95d97327
14e46781e9802934a62d2c870c3d2722356482edec3ad3b8d71eb48771c15505
c7832e8177f0f48d1a93433f6da916304dc6877192de4506d57a7af16e576bdd
2f4785a10fb323e5a0a52745b0a79f403f89782388bb550c0e9d1d7d266de33d
cat-searcher/leandojo-benchmark-4-random
test
1,767
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have key := <a>bind₁_rename_expand_wittPolynomial</a> Φ n IH
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n : ℕ IH : ∀ m < n + 1, (map (Int.castRingHom ℚ)) (wittStructureInt p Φ m) = wittStructureRat p ((map (Int.castRingHom ℚ)) Φ) m ⊢ C ↑(p ^ (n + 1)) ∣ (bind₁ fun b => (rename fun i => (b, i)) (W_ ℤ (n + 1))...
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n : ℕ IH : ∀ m < n + 1, (map (Int.castRingHom ℚ)) (wittStructureInt p Φ m) = wittStructureRat p ((map (Int.castRingHom ℚ)) Φ) m key : (bind₁ fun b => (rename fun i => (b, i)) ((expand p) (W_ ℤ n))) Φ = ...
((:c Dvd.dvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c semigroupDvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c SemigroupWithZero.toSemigroup) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c I...
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:c Int)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:c Int))))))) (:arg :instance 1 (:instance-of (:app (:c Dv...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"have","sourceEnd":11301,"sourceStart":11297,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"key","sourceEnd":11305,"sourceStart":11302,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"key","sourceEnd":11305,"sourceStart":11302,"tag":"n...
[]
[{"source":"bind₁_rename_expand_wittPolynomial Φ n IH","source_end":11353,"source_start":11309,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
10
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c5adbbf0c7aff4d5773bbea667ec60c5619af9f670f394e610ddc826aa3cec8b
fd288e8fb981d4874a04d7acaaeacab05cd24c6d6fb54844256e1131fd1bee63
068ccac8e49d38fa46cadbb1b5ac9dc83b2621218b8f690c162f2e21db95ee62
b87d700127b60af23dea7a92af8f7ed20f16fea4bb5bf7d7cda43718a5707052
cat-searcher/leandojo-benchmark-4-random
test
1,768
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply_fun <a>MvPolynomial.map</a> (<a>Int.castRingHom</a> (<a>ZMod</a> (p ^ (n + 1)))) at key
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n : ℕ IH : ∀ m < n + 1, (map (Int.castRingHom ℚ)) (wittStructureInt p Φ m) = wittStructureRat p ((map (Int.castRingHom ℚ)) Φ) m key : (bind₁ fun b => (rename fun i => (b, i)) ((expand p) (W_ ℤ n))) Φ = ...
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n : ℕ IH : ∀ m < n + 1, (map (Int.castRingHom ℚ)) (wittStructureInt p Φ m) = wittStructureRat p ((map (Int.castRingHom ℚ)) Φ) m key : (map (Int.castRingHom (ZMod (p ^ (n + 1))))) ((bind₁ fun b => (rename fu...
((:c Dvd.dvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c semigroupDvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c SemigroupWithZero.toSemigroup) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c I...
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:c Int)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:c Int))))))) (:arg :instance 1 (:instance-of (:app (:c Dv...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"apply_fun","sourceEnd":11365,"sourceStart":11356,"tag":"atom"},{"children":[{"name":"MvPolynomial.map","semanticRole":"global","source":"map","sourceEnd":11369,"sourceStart":11366,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":11371,"sourceStart":11370,"tag":"atom"},{"ch...
[]
[{"source":"key","source_end":11415,"source_start":11412,"syntax_kind":"ident"},{"source":"map (Int.castRingHom (ZMod (p ^ (n + 1))))","source_end":11408,"source_start":11366,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
11
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1b80636c6a8737f78d6edbe00c32bc2abb028dd2ce87661e39e40714389fbf4d
b87d700127b60af23dea7a92af8f7ed20f16fea4bb5bf7d7cda43718a5707052
02ac1b8254369858bf1b113ff40a268613633cb183339f094c8394a97cd938da
094074931323810333cfbefbff18e3fb91edde49a8ab0628755a8ba19e78335f
cat-searcher/leandojo-benchmark-4-random
test
1,769
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
conv_lhs at key => simp only [<a>MvPolynomial.map_bind₁</a>, <a>MvPolynomial.map_rename</a>, <a>MvPolynomial.map_expand</a>, <a>map_wittPolynomial</a>]
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n : ℕ IH : ∀ m < n + 1, (map (Int.castRingHom ℚ)) (wittStructureInt p Φ m) = wittStructureRat p ((map (Int.castRingHom ℚ)) Φ) m key : (map (Int.castRingHom (ZMod (p ^ (n + 1))))) ((bind₁ fun b => (rename fu...
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n : ℕ IH : ∀ m < n + 1, (map (Int.castRingHom ℚ)) (wittStructureInt p Φ m) = wittStructureRat p ((map (Int.castRingHom ℚ)) Φ) m key : (bind₁ fun i => (rename fun i_1 => (i, i_1)) ((expand p) (W_ (ZMod (p ^ ...
((:c Dvd.dvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c semigroupDvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c SemigroupWithZero.toSemigroup) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c I...
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:c Int)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:c Int))))))) (:arg :instance 1 (:instance-of (:app (:c Dv...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"conv_lhs","sourceEnd":11426,"sourceStart":11418,"tag":"atom"},{"children":[{"source":"at","sourceEnd":11429,"sourceStart":11427,"tag":"atom"},{"source":"key","sourceEnd":11433,"sourceStart":11430,"tag":"identifier"}],"kind":"null","source":"at key","sourceEnd":11433,"sourceStart":11427,"tag":"no...
[]
[{"source":"map_bind₁","source_end":11459,"source_start":11448,"syntax_kind":"ident"},{"source":"map_rename","source_end":11471,"source_start":11461,"syntax_kind":"ident"},{"source":"map_expand","source_end":11483,"source_start":11473,"syntax_kind":"ident"},{"source":"map_wittPolynomial","source_end":11503,"source_star...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
12
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f62b84390d0b8d7b0b911116d4122a19e44711f274c3198a7a51e4ed9cc3f026
094074931323810333cfbefbff18e3fb91edde49a8ab0628755a8ba19e78335f
cec083618c76432d0c5f3ae20b5d6ef375afa139c2673c0476023a72315dc07f
f06d8e6846f97fe1cf35777e1452fcc15f100fa22ac0e017cb1390e673e43f98
cat-searcher/leandojo-benchmark-4-random
test
1,770
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>MvPolynomial.C_dvd_iff_zmod</a>, <a>RingHom.map_sub</a>, <a>sub_eq_zero</a>, <a>MvPolynomial.map_bind₁</a>]
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n : ℕ IH : ∀ m < n + 1, (map (Int.castRingHom ℚ)) (wittStructureInt p Φ m) = wittStructureRat p ((map (Int.castRingHom ℚ)) Φ) m key : (bind₁ fun i => (rename fun i_1 => (i, i_1)) ((expand p) (W_ (ZMod (p ^ ...
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n : ℕ IH : ∀ m < n + 1, (map (Int.castRingHom ℚ)) (wittStructureInt p Φ m) = wittStructureRat p ((map (Int.castRingHom ℚ)) Φ) m key : (bind₁ fun i => (rename fun i_1 => (i, i_1)) ((expand p) (W_ (ZMod (p ^ ...
((:c Dvd.dvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c semigroupDvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c SemigroupWithZero.toSemigroup) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c I...
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:c Int)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:c Int))))))) (:arg :instance 1 (:instance-of (:app (:c Dv...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"rw","sourceEnd":11535,"sourceStart":11533,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11537,"sourceStart":11536,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MvPolynomial.C_d...
[]
[{"source":"C_dvd_iff_zmod","source_end":11551,"source_start":11537,"syntax_kind":"ident"},{"source":"RingHom.map_sub","source_end":11568,"source_start":11553,"syntax_kind":"ident"},{"source":"sub_eq_zero","source_end":11581,"source_start":11570,"syntax_kind":"ident"},{"source":"map_bind₁","source_end":11594,"source_st...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
16
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d3d48377d059b919cb966123afe42dd03468204a375686c72a7b863edc03d7f3
f06d8e6846f97fe1cf35777e1452fcc15f100fa22ac0e017cb1390e673e43f98
6d2564cc18e02ac5be95cb423ec177795b399235adf80ebda9a765ea424fae7c
c6475d76f76406c9e18f1f48eb9c96698b7fad2280b3ca91c1f3d458fcbd4445
cat-searcher/leandojo-benchmark-4-random
test
1,771
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>MvPolynomial.map_rename</a>, <a>map_wittPolynomial</a>, <a>wittPolynomial_zmod_self</a>]
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n : ℕ IH : ∀ m < n + 1, (map (Int.castRingHom ℚ)) (wittStructureInt p Φ m) = wittStructureRat p ((map (Int.castRingHom ℚ)) Φ) m key : (bind₁ fun i => (rename fun i_1 => (i, i_1)) ((expand p) (W_ (ZMod (p ^ ...
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n : ℕ IH : ∀ m < n + 1, (map (Int.castRingHom ℚ)) (wittStructureInt p Φ m) = wittStructureRat p ((map (Int.castRingHom ℚ)) Φ) m key : (bind₁ fun i => (rename fun i_1 => (i, i_1)) ((expand p) (W_ (ZMod (p ^ ...
((:c Eq) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) ((:c ZMod) ((:c HPow.hPow) (:c Nat) (:c Nat) (:c Nat) ((:c instHPow) (:c Nat) (:c Nat) ((:c Monoid.toNatPow) (:c Nat) (:c Nat.instMonoid))) (:fv _uniq.29858) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq....
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:app (:c ZMod) (:arg :explicit 0 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"simp","sourceEnd":11602,"sourceStart":11598,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":11607,"sourceStart":11603,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":116...
[]
[{"source":"map_rename","source_end":11619,"source_start":11609,"syntax_kind":"ident"},{"source":"map_wittPolynomial","source_end":11639,"source_start":11621,"syntax_kind":"ident"},{"source":"wittPolynomial_zmod_self","source_end":11665,"source_start":11641,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
22
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
cb7a7d1200e54c6f65bbdcec15f9e1b8c9e9c423736abf64c61dc1468246382b
c6475d76f76406c9e18f1f48eb9c96698b7fad2280b3ca91c1f3d458fcbd4445
335b8c8dddb1b2571a87ec18aad90ee547b7c900996c558f2882f9bf2df670cd
3476b86527cbbac339fdc17d22dfc944c0b1afc9c412db4994a2b32844457c5c
cat-searcher/leandojo-benchmark-4-random
test
1,772
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [key]
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n : ℕ IH : ∀ m < n + 1, (map (Int.castRingHom ℚ)) (wittStructureInt p Φ m) = wittStructureRat p ((map (Int.castRingHom ℚ)) Φ) m key : (bind₁ fun i => (rename fun i_1 => (i, i_1)) ((expand p) (W_ (ZMod (p ^ ...
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n : ℕ IH : ∀ m < n + 1, (map (Int.castRingHom ℚ)) (wittStructureInt p Φ m) = wittStructureRat p ((map (Int.castRingHom ℚ)) Φ) m key : (bind₁ fun i => (rename fun i_1 => (i, i_1)) ((expand p) (W_ (ZMod (p ^ ...
((:c Eq) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) ((:c ZMod) ((:c HPow.hPow) (:c Nat) (:c Nat) (:c Nat) ((:c instHPow) (:c Nat) (:c Nat) ((:c Monoid.toNatPow) (:c Nat) (:c Nat.instMonoid))) (:fv _uniq.29858) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq....
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:app (:c ZMod) (:arg :explicit 0 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"rw","sourceEnd":11671,"sourceStart":11669,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11673,"sourceStart":11672,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":9,"semant...
[]
[{"source":"key","source_end":11676,"source_start":11673,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
23
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ca7eadb7e659817710d333ef272654b93fc95ae17320aeffcffa2ba80048daae
3476b86527cbbac339fdc17d22dfc944c0b1afc9c412db4994a2b32844457c5c
ce111be035cfe5200afa7226c0fc12bfe35d45f2da43985ae2a9ce7cce303629
b0488ab3db3deff30373b09a44ce13147e6b9536ab990ee62be99800e0a0f1a6
cat-searcher/leandojo-benchmark-4-random
test
1,773
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
clear key IH
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n : ℕ IH : ∀ m < n + 1, (map (Int.castRingHom ℚ)) (wittStructureInt p Φ m) = wittStructureRat p ((map (Int.castRingHom ℚ)) Φ) m key : (bind₁ fun i => (rename fun i_1 => (i, i_1)) ((expand p) (W_ (ZMod (p ^ ...
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n : ℕ ⊢ (map (Int.castRingHom (ZMod (p ^ (n + 1))))) ((bind₁ fun i => (expand p) (wittStructureInt p Φ i)) (W_ ℤ n)) = (map (Int.castRingHom (ZMod (p ^ (n + 1))))) (∑ i ∈ Finset.range (n + 1), C (↑p ^...
((:c Eq) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) ((:c ZMod) ((:c HPow.hPow) (:c Nat) (:c Nat) (:c Nat) ((:c instHPow) (:c Nat) (:c Nat) ((:c Monoid.toNatPow) (:c Nat) (:c Nat.instMonoid))) (:fv _uniq.29858) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq....
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:app (:c ZMod) (:arg :explicit 0 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"clear","sourceEnd":11684,"sourceStart":11679,"tag":"atom"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"key","sourceEnd":11688,"sourceStart":11685,"tag":"identifier"},{"contextIndex":8,"semanticRole":"local","source":"IH","sourceEnd":11691,"sourceStart":11689,"tag":"identifier...
[]
[{"source":"key","source_end":11688,"source_start":11685,"syntax_kind":"ident"},{"source":"IH","source_end":11691,"source_start":11689,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
27
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7c8e1058c74d245639676b4c5ae70dc3a36e101664ced18617a400f800ec8ba4
b0488ab3db3deff30373b09a44ce13147e6b9536ab990ee62be99800e0a0f1a6
2943a790c996dc81f5cdd93305004817486d550ef6aaba3dd57d563d3519b478
eef8ae674707cce2a341158b949be7efc555c1db0893d3784e4b99ffbe1c4cb4
cat-searcher/leandojo-benchmark-4-random
test
1,774
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>MvPolynomial.bind₁</a>, <a>aeval_wittPolynomial</a>, <a>map_sum</a>, <a>map_sum</a>, <a>Finset.sum_congr</a> <a>rfl</a>]
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n : ℕ ⊢ (map (Int.castRingHom (ZMod (p ^ (n + 1))))) ((bind₁ fun i => (expand p) (wittStructureInt p Φ i)) (W_ ℤ n)) = (map (Int.castRingHom (ZMod (p ^ (n + 1))))) (∑ i ∈ Finset.range (n + 1), C (↑p ^...
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n : ℕ ⊢ ∀ x ∈ Finset.range (n + 1), (map (Int.castRingHom (ZMod (p ^ (n + 1))))) (↑p ^ x * (expand p) (wittStructureInt p Φ x) ^ p ^ (n - x)) = (map (Int.castRingHom (ZMod (p ^ (n + 1))))) (C (↑p ^ x)...
((:c Eq) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) ((:c ZMod) ((:c HPow.hPow) (:c Nat) (:c Nat) (:c Nat) ((:c instHPow) (:c Nat) (:c Nat) ((:c Monoid.toNatPow) (:c Nat) (:c Nat.instMonoid))) (:fv _uniq.29858) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq....
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:app (:c ZMod) (:arg :explicit 0 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"rw","sourceEnd":11696,"sourceStart":11694,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11698,"sourceStart":11697,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MvPolynomial.bin...
[]
[{"source":"bind₁","source_end":11705,"source_start":11698,"syntax_kind":"ident"},{"source":"aeval_wittPolynomial","source_end":11727,"source_start":11707,"syntax_kind":"ident"},{"source":"map_sum","source_end":11736,"source_start":11729,"syntax_kind":"ident"},{"source":"map_sum","source_end":11745,"source_start":11738...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
28
exact
true
1
7
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4fead68dc101746d1d190df1fe74996e6a184eda0f0facd91e2787d062d7c310
eef8ae674707cce2a341158b949be7efc555c1db0893d3784e4b99ffbe1c4cb4
e59bd68cb31dae643f7dd940b92b42eb93765bfdea0bd3958adada000d61919c
2dfdc7072f3a7d3a0df24c992008332f967dc0b507979805d2dd57ec797003c9
cat-searcher/leandojo-benchmark-4-random
test
1,775
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro k hk
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n : ℕ ⊢ ∀ x ∈ Finset.range (n + 1), (map (Int.castRingHom (ZMod (p ^ (n + 1))))) (↑p ^ x * (expand p) (wittStructureInt p Φ x) ^ p ^ (n - x)) = (map (Int.castRingHom (ZMod (p ^ (n + 1))))) (C (↑p ^ x)...
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ∈ Finset.range (n + 1) ⊢ (map (Int.castRingHom (ZMod (p ^ (n + 1))))) (↑p ^ k * (expand p) (wittStructureInt p Φ k) ^ p ^ (n - k)) = (map (Int.castRingHom (ZMod (p ^ (n + 1))))) (C (↑p ^ k) *...
(:forall x (:c Nat) (:forall _ ((:c Membership.mem) (:c Nat) ((:c Finset) (:c Nat)) ((:c Finset.instMembership) (:c Nat)) 0 ((:c Finset.range) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.33102) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))) ((:c E...
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:forall x :explicit (:c Nat) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:c Nat)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:c...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"intro","sourceEnd":11776,"sourceStart":11771,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"k","sourceEnd":11778,"sourceStart":11777,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hk","sourceEnd":11781,"sourceStart":11779,"tag":"identifier"}],"kind":"null","sou...
[{"role":"fresh_name","source":"k","source_end":11778,"source_start":11777,"syntax_kind":"ident"},{"role":"fresh_name","source":"hk","source_end":11781,"source_start":11779,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
35
exact
true
1
7
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
dee5eacc046f45c0b1e2434f1592873c922e01636669a652401d9e83c82b6fcc
2dfdc7072f3a7d3a0df24c992008332f967dc0b507979805d2dd57ec797003c9
a501ea6d8debc22e584386e1b6aeb3177f2f0ff35003119d15c8e6cd400ca34d
fbfe4c6d91e25f478b63f1e0ad26dbbae5c630e0cb0874c9d53c7799b8946e78
cat-searcher/leandojo-benchmark-4-random
test
1,776
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Finset.mem_range</a>, <a>Nat.lt_succ_iff</a>] at hk
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ∈ Finset.range (n + 1) ⊢ (map (Int.castRingHom (ZMod (p ^ (n + 1))))) (↑p ^ k * (expand p) (wittStructureInt p Φ k) ^ p ^ (n - k)) = (map (Int.castRingHom (ZMod (p ^ (n + 1))))) (C (↑p ^ k) *...
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n ⊢ (map (Int.castRingHom (ZMod (p ^ (n + 1))))) (↑p ^ k * (expand p) (wittStructureInt p Φ k) ^ p ^ (n - k)) = (map (Int.castRingHom (ZMod (p ^ (n + 1))))) (C (↑p ^ k) * wittStructureInt p...
((:c Eq) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) ((:c ZMod) ((:c HPow.hPow) (:c Nat) (:c Nat) (:c Nat) ((:c instHPow) (:c Nat) (:c Nat) ((:c Monoid.toNatPow) (:c Nat) (:c Nat.instMonoid))) (:fv _uniq.29858) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq....
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:app (:c ZMod) (:arg :explicit 0 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"rw","sourceEnd":11786,"sourceStart":11784,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11788,"sourceStart":11787,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.mem_range...
[]
[{"source":"Finset.mem_range","source_end":11804,"source_start":11788,"syntax_kind":"ident"},{"source":"hk\n -- Porting note (#11083): was much slower\n -- simp only [← sub_eq_zero, ← RingHom.map_sub, ← C_dvd_iff_zmod, C_eq_coe_nat, ← mul_sub, ←\n -- Nat.cast_pow]","source_end":11828,"source_start":11826,"syntax_k...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
36
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
884550899e755993f455cadaf9f8a4cc24c80be54e50d2fd82c5aed3c8ea16fe
fbfe4c6d91e25f478b63f1e0ad26dbbae5c630e0cb0874c9d53c7799b8946e78
091c95b540d1eaa96869d6b840448296ea5b08abae8dca1802668edf8194a806
9237f265a5eb5c1cb4f88a7f867353018e75ef45f0778d49cd2af2235e80b5bf
cat-searcher/leandojo-benchmark-4-random
test
1,777
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>sub_eq_zero</a>, ← <a>RingHom.map_sub</a>, ← <a>MvPolynomial.C_dvd_iff_zmod</a>, <a>MvPolynomial.C_eq_coe_nat</a>, ← <a>Nat.cast_pow</a>, ← <a>Nat.cast_pow</a>, <a>MvPolynomial.C_eq_coe_nat</a>, ← <a>mul_sub</a>]
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n ⊢ (map (Int.castRingHom (ZMod (p ^ (n + 1))))) (↑p ^ k * (expand p) (wittStructureInt p Φ k) ^ p ^ (n - k)) = (map (Int.castRingHom (ZMod (p ^ (n + 1))))) (C (↑p ^ k) * wittStructureInt p...
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n ⊢ ↑(p ^ (n + 1)) ∣ ↑(p ^ k) * ((expand p) (wittStructureInt p Φ k) ^ p ^ (n - k) - wittStructureInt p Φ k ^ p ^ (n + 1 - k))
((:c Eq) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) ((:c ZMod) ((:c HPow.hPow) (:c Nat) (:c Nat) (:c Nat) ((:c instHPow) (:c Nat) (:c Nat) ((:c Monoid.toNatPow) (:c Nat) (:c Nat.instMonoid))) (:fv _uniq.29858) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq....
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:app (:c ZMod) (:arg :explicit 0 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"rw","sourceEnd":12003,"sourceStart":12001,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12005,"sourceStart":12004,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":12008,"sourceSt...
[]
[{"source":"sub_eq_zero","source_end":12020,"source_start":12009,"syntax_kind":"ident"},{"source":"RingHom.map_sub","source_end":12041,"source_start":12026,"syntax_kind":"ident"},{"source":"C_dvd_iff_zmod","source_end":12061,"source_start":12047,"syntax_kind":"ident"},{"source":"C_eq_coe_nat","source_end":12075,"source...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
40
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a3c9b60979385cd4484423ee830520533db4c41061a61843e6003d7222d6cdfa
9237f265a5eb5c1cb4f88a7f867353018e75ef45f0778d49cd2af2235e80b5bf
daad127cc0f2b5d65cd79ce74d38d0d6aed0729b7f0f8f7b0947e88e141890ae
da109f9115c051cec06361212911b19c7face7a8329163e98e1669a95961b7d6
cat-searcher/leandojo-benchmark-4-random
test
1,778
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have : p ^ (n + 1) = p ^ k * p ^ (n - k + 1) := by rw [← <a>pow_add</a>, ← <a>add_assoc</a>]; congr 2; rw [<a>add_comm</a>, ← <a>tsub_eq_iff_eq_add_of_le</a> hk]
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n ⊢ ↑(p ^ (n + 1)) ∣ ↑(p ^ k) * ((expand p) (wittStructureInt p Φ k) ^ p ^ (n - k) - wittStructureInt p Φ k ^ p ^ (n + 1 - k))
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n this : p ^ (n + 1) = p ^ k * p ^ (n - k + 1) ⊢ ↑(p ^ (n + 1)) ∣ ↑(p ^ k) * ((expand p) (wittStructureInt p Φ k) ^ p ^ (n - k) - wittStructureInt p Φ k ^ p ^ (n + 1 - k))
((:c Dvd.dvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c semigroupDvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c SemigroupWithZero.toSemigroup) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c I...
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:c Int)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:c Int))))))) (:arg :instance 1 (:instance-of (:app (:c Dv...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"have","sourceEnd":12150,"sourceStart":12146,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":12151,"sourceStart":12151,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":12151,"sourceStart":12151,"tag":"node"}],"kind":"Lean.Parser.Term.hav...
[]
[{"source":"p ^ (n + 1) = p ^ k * p ^ (n - k + 1)","source_end":12190,"source_start":12153,"syntax_kind":"«term_=_»"},{"source":"pow_add","source_end":12216,"source_start":12209,"syntax_kind":"ident"},{"source":"add_assoc","source_end":12231,"source_start":12222,"syntax_kind":"ident"},{"source":"add_comm","source_end":...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
50
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
50cb1b73ae5259b4d60080942688faf66f7d240f17c102546e105f415b6581a5
da109f9115c051cec06361212911b19c7face7a8329163e98e1669a95961b7d6
fa747b610600ca6f20c034fa7ed851d8dd2cd90864e4196e84fd52bcdcb48847
16c5fd06ecfd8f6cc92c0e1f524bb35c44b78a9f2621bef81818fd0ae5f0e053
cat-searcher/leandojo-benchmark-4-random
test
1,779
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [this]
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n this : p ^ (n + 1) = p ^ k * p ^ (n - k + 1) ⊢ ↑(p ^ (n + 1)) ∣ ↑(p ^ k) * ((expand p) (wittStructureInt p Φ k) ^ p ^ (n - k) - wittStructureInt p Φ k ^ p ^ (n + 1 - k))
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n this : p ^ (n + 1) = p ^ k * p ^ (n - k + 1) ⊢ ↑(p ^ k * p ^ (n - k + 1)) ∣ ↑(p ^ k) * ((expand p) (wittStructureInt p Φ k) ^ p ^ (n - k) - wittStructureInt p Φ k ^ p ^ (n + 1 - k))
((:c Dvd.dvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c semigroupDvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c SemigroupWithZero.toSemigroup) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c I...
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:c Int)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:c Int))))))) (:arg :instance 1 (:instance-of (:app (:c Dv...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"rw","sourceEnd":12294,"sourceStart":12292,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12296,"sourceStart":12295,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":10,"seman...
[]
[{"source":"this","source_end":12300,"source_start":12296,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
63
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
cc5fe0f196c6f9ba3c96fc992913dec8d514378f6b485c945f7d95d6fc2f57f0
16c5fd06ecfd8f6cc92c0e1f524bb35c44b78a9f2621bef81818fd0ae5f0e053
65e47f2d4a9bfabc21e1664a0b073b87e8fee657aeade999395c39aa954c5bad
756ee27e636b2f467afe093a3b7606ae315e08886957016f5f10d5389fe4071d
cat-searcher/leandojo-benchmark-4-random
test
1,780
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Nat.cast_mul</a>, <a>Nat.cast_pow</a>, <a>Nat.cast_pow</a>]
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n this : p ^ (n + 1) = p ^ k * p ^ (n - k + 1) ⊢ ↑(p ^ k * p ^ (n - k + 1)) ∣ ↑(p ^ k) * ((expand p) (wittStructureInt p Φ k) ^ p ^ (n - k) - wittStructureInt p Φ k ^ p ^ (n + 1 - k))
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n this : p ^ (n + 1) = p ^ k * p ^ (n - k + 1) ⊢ ↑p ^ k * ↑p ^ (n - k + 1) ∣ ↑p ^ k * ((expand p) (wittStructureInt p Φ k) ^ p ^ (n - k) - wittStructureInt p Φ k ^ p ^ (n + 1 - k))
((:c Dvd.dvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c semigroupDvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c SemigroupWithZero.toSemigroup) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c I...
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:c Int)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:c Int))))))) (:arg :instance 1 (:instance-of (:app (:c Dv...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"rw","sourceEnd":12306,"sourceStart":12304,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12308,"sourceStart":12307,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Nat.cast_mul","s...
[]
[{"source":"Nat.cast_mul","source_end":12320,"source_start":12308,"syntax_kind":"ident"},{"source":"Nat.cast_pow","source_end":12334,"source_start":12322,"syntax_kind":"ident"},{"source":"Nat.cast_pow","source_end":12348,"source_start":12336,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
66
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ad46ebf58760f748147c39b534fd028140fae406241058ad04d6bebb5f84ef56
756ee27e636b2f467afe093a3b7606ae315e08886957016f5f10d5389fe4071d
567146f31e3c431386764c9759cbb626b71efd51a58f75d7b484c3a4eda904be
d6f261e8ea1e7420777cd6d1e5be8d5576dbdc01c3ecfad9774be8c2c10dd59b
cat-searcher/leandojo-benchmark-4-random
test
1,781
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>mul_dvd_mul_left</a> ((p : <a>MvPolynomial</a> (idx × ℕ) ℤ) ^ k)
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n this : p ^ (n + 1) = p ^ k * p ^ (n - k + 1) ⊢ ↑p ^ k * ↑p ^ (n - k + 1) ∣ ↑p ^ k * ((expand p) (wittStructureInt p Φ k) ^ p ^ (n - k) - wittStructureInt p Φ k ^ p ^ (n + 1 - k))
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n this : p ^ (n + 1) = p ^ k * p ^ (n - k + 1) ⊢ ↑p ^ (n - k + 1) ∣ (expand p) (wittStructureInt p Φ k) ^ p ^ (n - k) - wittStructureInt p Φ k ^ p ^ (n + 1 - k)
((:c Dvd.dvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c semigroupDvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c SemigroupWithZero.toSemigroup) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c I...
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:c Int)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:c Int))))))) (:arg :instance 1 (:instance-of (:app (:c Dv...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"apply","sourceEnd":12357,"sourceStart":12352,"tag":"atom"},{"children":[{"name":"mul_dvd_mul_left","semanticRole":"global","source":"mul_dvd_mul_left","sourceEnd":12374,"sourceStart":12358,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":12376,"sourceStart":12375,"tag":"at...
[]
[{"source":"mul_dvd_mul_left ((p : MvPolynomial (idx × ℕ) ℤ) ^ k)","source_end":12416,"source_start":12358,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
71
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f1af0fb3098ad8bb4944d3cfa2e2299795cc1e5b0a384e0679d917b6e1c989bb
d6f261e8ea1e7420777cd6d1e5be8d5576dbdc01c3ecfad9774be8c2c10dd59b
72f02c65d65d811516e1e276118641952313a42df7edcd06f7d8f5bd5c65967d
9dfe5d9f69829e4135fbd87c39204ada6c89690e6bb03465934a437c06610a08
cat-searcher/leandojo-benchmark-4-random
test
1,782
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [show p ^ (n + 1 - k) = p * p ^ (n - k) by rw [← <a>pow_succ'</a>, ← <a>tsub_add_eq_add_tsub</a> hk]]
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n this : p ^ (n + 1) = p ^ k * p ^ (n - k + 1) ⊢ ↑p ^ (n - k + 1) ∣ (expand p) (wittStructureInt p Φ k) ^ p ^ (n - k) - wittStructureInt p Φ k ^ p ^ (n + 1 - k)
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n this : p ^ (n + 1) = p ^ k * p ^ (n - k + 1) ⊢ ↑p ^ (n - k + 1) ∣ (expand p) (wittStructureInt p Φ k) ^ p ^ (n - k) - wittStructureInt p Φ k ^ (p * p ^ (n - k))
((:c Dvd.dvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c semigroupDvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c Monoid.toSemigroup) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int...
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:c Int)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:c Int))))))) (:arg :instance 1 (:instance-of (:app (:c Dv...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"rw","sourceEnd":12421,"sourceStart":12419,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12423,"sourceStart":12422,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"s...
[]
[{"source":"show p ^ (n + 1 - k) = p * p ^ (n - k) by rw [← pow_succ', ← tsub_add_eq_add_tsub hk]","source_end":12512,"source_start":12423,"syntax_kind":"Lean.Parser.Term.show"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
72
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
59be25c8edf452230a093198a07d00467b2973c039d225861fe54d569191f1bf
9dfe5d9f69829e4135fbd87c39204ada6c89690e6bb03465934a437c06610a08
097e1c5116a1918d87a43c36ef336058f45702f0898d78a3eca19a60070cecf9
c3cbab0edf33894e6d4156f8bc8f6bedc2363622327844d23726b4cf94ededa1
cat-searcher/leandojo-benchmark-4-random
test
1,783
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>pow_mul</a>]
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n this : p ^ (n + 1) = p ^ k * p ^ (n - k + 1) ⊢ ↑p ^ (n - k + 1) ∣ (expand p) (wittStructureInt p Φ k) ^ p ^ (n - k) - wittStructureInt p Φ k ^ (p * p ^ (n - k))
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n this : p ^ (n + 1) = p ^ k * p ^ (n - k + 1) ⊢ ↑p ^ (n - k + 1) ∣ (expand p) (wittStructureInt p Φ k) ^ p ^ (n - k) - (wittStructureInt p Φ k ^ p) ^ p ^ (n - k)
((:c Dvd.dvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c semigroupDvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c Monoid.toSemigroup) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int...
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:c Int)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:c Int))))))) (:arg :instance 1 (:instance-of (:app (:c Dv...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"rw","sourceEnd":12518,"sourceStart":12516,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12520,"sourceStart":12519,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"pow_mul","semant...
[]
[{"source":"pow_mul","source_end":12527,"source_start":12520,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
81
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9a5532e5b78e0b4d81b0bf545ca513c6999cf55b5dbbd8052647c79e88d8dd4e
c3cbab0edf33894e6d4156f8bc8f6bedc2363622327844d23726b4cf94ededa1
5440438b9415b509cd3c8476b6e8608a48e095b5cf95925d1af84ca844737e9c
8d38f4e9797d2ff4854bba82c24d585c3c8ef74101c824041a9ad02672dbbb59
cat-searcher/leandojo-benchmark-4-random
test
1,784
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>dvd_sub_pow_of_dvd_sub</a>
case succ p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n this : p ^ (n + 1) = p ^ k * p ^ (n - k + 1) ⊢ ↑p ^ (n - k + 1) ∣ (expand p) (wittStructureInt p Φ k) ^ p ^ (n - k) - (wittStructureInt p Φ k ^ p) ^ p ^ (n - k)
case succ.h p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n this : p ^ (n + 1) = p ^ k * p ^ (n - k + 1) ⊢ ↑p ∣ (expand p) (wittStructureInt p Φ k) - wittStructureInt p Φ k ^ p
((:c Dvd.dvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c semigroupDvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c Monoid.toSemigroup) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int...
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:c Int)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:c Int))))))) (:arg :instance 1 (:instance-of (:app (:c Dv...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"apply","sourceEnd":12554,"sourceStart":12549,"tag":"atom"},{"name":"dvd_sub_pow_of_dvd_sub","semanticRole":"global","source":"dvd_sub_pow_of_dvd_sub","sourceEnd":12577,"sourceStart":12555,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply dvd_sub_pow_of_dvd_sub","sourceEnd":1...
[]
[{"source":"dvd_sub_pow_of_dvd_sub","source_end":12577,"source_start":12555,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
84
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
fe1c0ef3576ffb11cec6b32db51e5d87165c95498ff96c52aee972ad2e698ef0
8d38f4e9797d2ff4854bba82c24d585c3c8ef74101c824041a9ad02672dbbb59
6859920eb3ce0c2ab99a9d6e018718625c6feb86cd27fb6746101ac671654411
1f1dba8488d914ea6103c39b9a3c3e04ccc271c9e35c1d610dfef82bdcf1752d
cat-searcher/leandojo-benchmark-4-random
test
1,785
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>MvPolynomial.C_eq_coe_nat</a>, <a>MvPolynomial.C_dvd_iff_zmod</a>, <a>RingHom.map_sub</a>, <a>sub_eq_zero</a>, <a>MvPolynomial.map_expand</a>, <a>RingHom.map_pow</a>, <a>MvPolynomial.expand_zmod</a>]
case succ.h p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n this : p ^ (n + 1) = p ^ k * p ^ (n - k + 1) ⊢ ↑p ∣ (expand p) (wittStructureInt p Φ k) - wittStructureInt p Φ k ^ p
((:c Dvd.dvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c semigroupDvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c SemigroupWithZero.toSemigroup) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c I...
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:c Int)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:c Int))))))) (:arg :instance 1 (:instance-of (:app (:c Dv...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"rw","sourceEnd":12582,"sourceStart":12580,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12584,"sourceStart":12583,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":12587,"sourceSt...
[]
[{"source":"C_eq_coe_nat","source_end":12600,"source_start":12588,"syntax_kind":"ident"},{"source":"C_dvd_iff_zmod","source_end":12616,"source_start":12602,"syntax_kind":"ident"},{"source":"RingHom.map_sub","source_end":12633,"source_start":12618,"syntax_kind":"ident"},{"source":"sub_eq_zero","source_end":12646,"source...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
85
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2f367e7d6782af5a4dfb9ea79dd1f9d3b37fc2428d8312a41499d86b23131c05
1f1dba8488d914ea6103c39b9a3c3e04ccc271c9e35c1d610dfef82bdcf1752d
2209a3b18cf79382819c5b9feda8eacbc20e76734d13dad01183b2415ccda5a8
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,786
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>isUnit_one</a>, <a>Int.ofNat_zero</a>, <a>Int.ofNat_succ</a>, <a>zero_add</a>, <a>pow_zero</a>, <a>MvPolynomial.C_1</a>, <a>IsUnit.dvd</a>, <a>Nat.cast_one</a>, <a>Nat.zero_eq</a>]
case zero p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ IH : ∀ m < 0, (map (Int.castRingHom ℚ)) (wittStructureInt p Φ m) = wittStructureRat p ((map (Int.castRingHom ℚ)) Φ) m ⊢ C ↑(p ^ 0) ∣ (bind₁ fun b => (rename fun i => (b, i)) (W_ ℤ 0)) Φ - ∑ i ∈ Finset...
((:c Dvd.dvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c semigroupDvd) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c Int) (:c Int.instCommSemiring)) ((:c SemigroupWithZero.toSemigroup) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.29864) (:c Nat)) (:c I...
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:c Int)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:c Int))))))) (:arg :instance 1 (:instance-of (:app (:c Dv...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":11129,"sourceStart":11125,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":11134,"sourceStart":11130,"tag":"atom"}],"kind"...
[]
[{"source":"isUnit_one","source_end":11146,"source_start":11136,"syntax_kind":"ident"},{"source":"Int.ofNat_zero","source_end":11162,"source_start":11148,"syntax_kind":"ident"},{"source":"Int.ofNat_succ","source_end":11178,"source_start":11164,"syntax_kind":"ident"},{"source":"zero_add","source_end":11188,"source_start...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
7
exact
true
1
7
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
bb79d43c6cd9b91be35e6609e73bbef06591fd631c01439dd07cf35639b6d481
19328ddeba9392f799a80b12d3d5e1a3468569e17114ed5e15b2270247a3bc1c
6bf37c13a60077daf5a14db496c460804560799b76b71219324cc7980d267a97
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,787
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>pow_add</a>, ← <a>add_assoc</a>]
p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n ⊢ p ^ (n + 1) = p ^ k * p ^ (n - k + 1)
p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n ⊢ p ^ (n + 1) = p ^ (k + (n - k) + 1)
((:c Eq) (:c Nat) ((:c HPow.hPow) (:c Nat) (:c Nat) (:c Nat) ((:c instHPow) (:c Nat) (:c Nat) ((:c Monoid.toNatPow) (:c Nat) (:c Nat.instMonoid))) (:fv _uniq.29858) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.33102) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat...
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"rw","sourceEnd":12203,"sourceStart":12201,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12205,"sourceStart":12204,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":12208,"sourceSt...
[]
[{"source":"pow_add","source_end":12216,"source_start":12209,"syntax_kind":"ident"},{"source":"add_assoc","source_end":12231,"source_start":12222,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
52
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
457264face3f969be942df5b927fcc48b4562f22a592bd77e22961fa84773809
10fd692cf96ebc289c123a491d24628fdca919b702988e29c72140fd0a732d88
c87a0910ead3b4c9bb99802aba3800b83e277b9356504ae8132b8d176a19b440
f12236d466d123fa6659d26bfb556d46641c3f998d5e395ef6594c43c9c5d4b3
cat-searcher/leandojo-benchmark-4-random
test
1,788
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
congr 2
p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n ⊢ p ^ (n + 1) = p ^ (k + (n - k) + 1)
case e_a.e_a p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n ⊢ n = k + (n - k)
((:c Eq) (:c Nat) ((:c HPow.hPow) (:c Nat) (:c Nat) (:c Nat) ((:c instHPow) (:c Nat) (:c Nat) ((:c Monoid.toNatPow) (:c Nat) (:c Nat.instMonoid))) (:fv _uniq.29858) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.33102) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat...
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"congr","sourceEnd":12239,"sourceStart":12234,"tag":"atom"},{"children":[{"children":[{"source":"2","sourceEnd":12241,"sourceStart":12240,"tag":"atom"}],"kind":"num","source":"2","sourceEnd":12241,"sourceStart":12240,"tag":"node"}],"kind":"null","source":"2","sourceEnd":12241,"sourceStart":12240,...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
57
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7a3c6e518e28930a43c34a0ce3c203ec7b4d79a1d7c4701d4543d319004d4a9f
f12236d466d123fa6659d26bfb556d46641c3f998d5e395ef6594c43c9c5d4b3
216dbc98bbb24e1a0fab2dbe9996a78800e7e700a272495ba61387ecc465ca0e
76b26dad9dc4ecceb6940d81c75ff9d35c48812ecbf3a2c9021f7e5f82507d62
cat-searcher/leandojo-benchmark-4-random
test
1,789
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>add_comm</a>, ← <a>tsub_eq_iff_eq_add_of_le</a> hk]
case e_a.e_a p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n ⊢ n = k + (n - k)
((:c Eq) (:c Nat) (:fv _uniq.33102) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) ((:c AddSemigroup.toAdd) (:c Nat) (:c Nat.instAddSemigroup))) (:fv _uniq.43560) ((:c HSub.hSub) (:c Nat) (:c Nat) (:c Nat) ((:c instHSub) (:c Nat) (:c instSubNat)) (:fv _uniq.33102) (:fv _uniq.43560))))
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"source":"rw","sourceEnd":12245,"sourceStart":12243,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12247,"sourceStart":12246,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"add_comm","seman...
[]
[{"source":"add_comm","source_end":12255,"source_start":12247,"syntax_kind":"ident"},{"source":"tsub_eq_iff_eq_add_of_le hk","source_end":12288,"source_start":12261,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
59
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4d68762bfa2138e34f63e5a7bfaa745dd699111225a33412e125d5b617c18c5b
76b26dad9dc4ecceb6940d81c75ff9d35c48812ecbf3a2c9021f7e5f82507d62
81576232e46de46fd6170c15d347a54e136ec06bd957004f87771ad1bfb7eb27
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,790
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum
Mathlib/RingTheory/WittVector/StructurePolynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>pow_succ'</a>, ← <a>tsub_add_eq_add_tsub</a> hk]
p : ℕ R : Type u_1 idx : Type u_2 inst✝ : CommRing R hp : Fact (Nat.Prime p) Φ : MvPolynomial idx ℤ n k : ℕ hk : k ≤ n this : p ^ (n + 1) = p ^ k * p ^ (n - k + 1) ⊢ p ^ (n + 1 - k) = p * p ^ (n - k)
((:c Eq) (:c Nat) ((:c HPow.hPow) (:c Nat) (:c Nat) (:c Nat) ((:c instHPow) (:c Nat) (:c Nat) ((:c Monoid.toNatPow) (:c Nat) (:c Nat.instMonoid))) (:fv _uniq.29858) ((:c HSub.hSub) (:c Nat) (:c Nat) (:c Nat) ((:c instHSub) (:c Nat) (:c instSubNat)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c ...
[{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.29861))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.29858)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.29864) (:c Int) (:c Int.in...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":12467,"sourceStart":12465,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12469,"sourceStart":12468,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"...
[]
[{"source":"pow_succ'","source_end":12482,"source_start":12473,"syntax_kind":"ident"},{"source":"tsub_add_eq_add_tsub hk","source_end":12511,"source_start":12488,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29858","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29861","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
28
74
exact
true
1
10
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7260f5d60d93d2a8c137cc6c22c2efdc7cff8c85abd9d235e46dd7d0fbb3c5dc
3b19b70fb1f7d75015aafb61f6b6cc3e71f437b2b7d314dce425c31c6b0dc6c4
38c51ac05a319aaf44a71d321213884a89bfbec8adfef0c7890bae325f5eaf7f
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,791
SetTheory.PGame.Impartial.nonneg
Mathlib/SetTheory/Game/Impartial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have h' := <a>SetTheory.PGame.neg_lt_neg_iff</a>.2 h
G : PGame inst✝ : G.Impartial h : G < 0 ⊢ False
G : PGame inst✝ : G.Impartial h : G < 0 h' : -0 < -G ⊢ False
(:c False)
[{"name":"G","sexp":"(:c SetTheory.PGame)"},{"name":"inst✝","sexp":"((:c SetTheory.PGame.Impartial) (:fv _uniq.29129))"},{"name":"h","sexp":"((:c LT.lt) (:c SetTheory.PGame) ((:c Preorder.toLT) (:c SetTheory.PGame) (:c SetTheory.PGame.instPreorder)) (:fv _uniq.29129) ((:c OfNat.ofNat) (:c SetTheory.PGame) (:lit 0) ((:c...
(:c False)
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29129","is_instance":false,"is_let":false,"name":"G","sexp":"(:c SetTheory.PGame)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.29132","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c SetTheory.PGame....
{"children":[{"source":"have","sourceEnd":5114,"sourceStart":5110,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h'","sourceEnd":5117,"sourceStart":5115,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h'","sourceEnd":5117,"sourceStart":5115,"tag":"node"},{"...
[]
[{"source":"neg_lt_neg_iff.2 h","source_end":5139,"source_start":5121,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29129","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.29132","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":3,"interna...
38
4
exact
true
1
3
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4c11fc5c6f7c07417f0cff331082eac2f1d6cc898c8baec40269b50ad3563e86
cd34261ccc53fd8731538072068f8ff419618ef73bb8cfdb2d55600d3023f415
ce1346304d4d439860e06e32192d8026274677a62f2b322a489ecdabd2efccb4
e4e5a46765f32c6397a7ccb12ba9f767d311e1f4fd659fc41a52cc99f5dc37d9
cat-searcher/leandojo-benchmark-4-random
test
1,792
SetTheory.PGame.Impartial.nonneg
Mathlib/SetTheory/Game/Impartial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>neg_zero</a>, <a>SetTheory.PGame.lt_congr_right</a> (<a>SetTheory.PGame.Equiv.symm</a> (<a>SetTheory.PGame.Impartial.neg_equiv_self</a> G))] at h'
G : PGame inst✝ : G.Impartial h : G < 0 h' : -0 < -G ⊢ False
G : PGame inst✝ : G.Impartial h : G < 0 h' : 0 < G ⊢ False
(:c False)
[{"name":"G","sexp":"(:c SetTheory.PGame)"},{"name":"inst✝","sexp":"((:c SetTheory.PGame.Impartial) (:fv _uniq.29129))"},{"name":"h","sexp":"((:c LT.lt) (:c SetTheory.PGame) ((:c Preorder.toLT) (:c SetTheory.PGame) (:c SetTheory.PGame.instPreorder)) (:fv _uniq.29129) ((:c OfNat.ofNat) (:c SetTheory.PGame) (:lit 0) ((:c...
(:c False)
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29129","is_instance":false,"is_let":false,"name":"G","sexp":"(:c SetTheory.PGame)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.29132","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c SetTheory.PGame....
{"children":[{"source":"rw","sourceEnd":5144,"sourceStart":5142,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5146,"sourceStart":5145,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"neg_zero","semanticR...
[]
[{"source":"neg_zero","source_end":5154,"source_start":5146,"syntax_kind":"ident"},{"source":"h'","source_end":5209,"source_start":5207,"syntax_kind":"ident"},{"source":"lt_congr_right (Equiv.symm (neg_equiv_self G))","source_end":5202,"source_start":5156,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29129","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.29132","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":3,"interna...
38
5
exact
true
1
4
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
485d2353cb07c8f44a4607c3f5270c0f1f024da4c93c9ea48056ad7c8de57707
e4e5a46765f32c6397a7ccb12ba9f767d311e1f4fd659fc41a52cc99f5dc37d9
a15aeb5e15581c0b46f8fa11f7957bac484e3553d880ba204f16a550e6449133
75340f1abf8617441d9c01e5bb5d66ed116d77d9158a8e44c4243044007bc3da
cat-searcher/leandojo-benchmark-4-random
test
1,793
SetTheory.PGame.Impartial.nonneg
Mathlib/SetTheory/Game/Impartial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact (h.trans h').<a>LT.lt.false</a>
G : PGame inst✝ : G.Impartial h : G < 0 h' : 0 < G ⊢ False
(:c False)
[{"name":"G","sexp":"(:c SetTheory.PGame)"},{"name":"inst✝","sexp":"((:c SetTheory.PGame.Impartial) (:fv _uniq.29129))"},{"name":"h","sexp":"((:c LT.lt) (:c SetTheory.PGame) ((:c Preorder.toLT) (:c SetTheory.PGame) (:c SetTheory.PGame.instPreorder)) (:fv _uniq.29129) ((:c OfNat.ofNat) (:c SetTheory.PGame) (:lit 0) ((:c...
(:c False)
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29129","is_instance":false,"is_let":false,"name":"G","sexp":"(:c SetTheory.PGame)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.29132","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c SetTheory.PGame....
{"children":[{"source":"exact","sourceEnd":5217,"sourceStart":5212,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":5219,"sourceStart":5218,"tag":"atom"},{"children":[{"source":"h.trans","sourceEnd":5226,"sourceStart":5219,"tag":"identifier"},{"children":[{"contextIndex":4,"semanticRole":"local","sourc...
[]
[{"source":"(h.trans h').false","source_end":5236,"source_start":5218,"syntax_kind":"Lean.Parser.Term.proj"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.29129","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.29132","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":3,"interna...
38
9
exact
true
1
4
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7aa27fa05c8928d37d4311cccaeda622aa14aab6c0affbdb940d8c92b0cf2dbf
75340f1abf8617441d9c01e5bb5d66ed116d77d9158a8e44c4243044007bc3da
91cc0a9d2ef67c978db605461e05c2fd0f17ce905a6e19603bd69e3e8eef3a31
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,794
NNReal.ball_zero_eq_Ico'
Mathlib/Topology/MetricSpace/Pseudo/Constructions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
ext x
α : Type u_1 β : Type u_2 inst✝ : PseudoMetricSpace α c : ℝ≥0 ⊢ ball 0 ↑c = Ico 0 c
case h α : Type u_1 β : Type u_2 inst✝ : PseudoMetricSpace α c x : ℝ≥0 ⊢ x ∈ ball 0 ↑c ↔ x ∈ Ico 0 c
((:c Eq) ((:c Set) (:c NNReal)) ((:c Metric.ball) (:c NNReal) (:c instPseudoMetricSpaceNNReal) ((:c OfNat.ofNat) (:c NNReal) (:lit 0) ((:c Zero.toOfNat0) (:c NNReal) (:c instNNRealZero))) ((:c NNReal.toReal) (:fv _uniq.6566))) ((:c Set.Ico) (:c NNReal) ((:c PartialOrder.toPreorder) (:c NNReal) ((:c StrictOrderedSemirin...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c PseudoMetricSpace) (:fv _uniq.6447))"},{"name":"c","sexp":"(:c NNReal)"}]
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:c NNReal)))) (:arg :explicit 1 (:app (:c Metric.ball) (:arg :implicit-type 0 (:c NNReal)) (:arg :instance 1 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c NNReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6447","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6450","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"ext","sourceEnd":5184,"sourceStart":5181,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":5186,"sourceStart":5185,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":5186,"sourceStart":5185,"tag":"nod...
[{"role":"fresh_name","source":"x","source_end":5186,"source_start":5185,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6447","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6450","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
43
4
exact
true
1
4
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
881a3e918221c7eaa4c4b05c1c74285b88a819cf4be1561c13356b7ad4f98c7c
82d5e3bdb341b87789a2910ad5a4ba639d2e5595f4e60ba34fd2d2443effb585
ee522618587c4a8062e9541e92fad69d5c6e7dbdf5366e9d82c63ebe3c1e08c5
d9c379be78dca807644a5c3d7e53573f15194179a841fff805e8e3ff04e93c80
cat-searcher/leandojo-benchmark-4-random
test
1,795
NNReal.ball_zero_eq_Ico'
Mathlib/Topology/MetricSpace/Pseudo/Constructions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
case h α : Type u_1 β : Type u_2 inst✝ : PseudoMetricSpace α c x : ℝ≥0 ⊢ x ∈ ball 0 ↑c ↔ x ∈ Ico 0 c
((:c Iff) ((:c Membership.mem) (:c NNReal) ((:c Set) (:c NNReal)) ((:c Set.instMembership) (:c NNReal)) (:fv _uniq.6590) ((:c Metric.ball) (:c NNReal) (:c instPseudoMetricSpaceNNReal) ((:c OfNat.ofNat) (:c NNReal) (:lit 0) ((:c Zero.toOfNat0) (:c NNReal) (:c instNNRealZero))) ((:c NNReal.toReal) (:fv _uniq.6566)))) ((:...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c PseudoMetricSpace) (:fv _uniq.6447))"},{"name":"c","sexp":"(:c NNReal)"},{"name":"x","sexp":"(:c NNReal)"}]
(:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:c NNReal)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c NNReal)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c NNReal)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c NNReal))))))) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6447","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6450","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"simp","sourceEnd":5192,"sourceStart":5188,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6447","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6450","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
43
6
exact
true
1
5
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0813119f18cd858122208f78318a0e6fa8c07d2321fedaceab4ae77785b4a22e
d9c379be78dca807644a5c3d7e53573f15194179a841fff805e8e3ff04e93c80
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,796
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
let Eu : Type max uE uF uG := <a>ULift</a>.{max uF uG} E
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c ContDiffOn) (:fv _uniq.502218) (:fv _uniq.502221) (:fv _uniq.502341) (:fv _uniq.502344) (:fv _uniq.502452) (:fv _uniq.502567) (:fv _uniq.502570) (:fv _uniq.502678) (:fv _uniq.502832) ((:c Function.comp) (:fv _uniq.502341) (:fv _uniq.502454) (:fv _uniq.502567) (:fv _uniq.506409) (:fv _uniq.506410)) (:fv _uniq.50640...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c ContDiffOn) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-of (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"let","sourceEnd":35199,"sourceStart":35196,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"Eu","sourceEnd":35202,"sourceStart":35200,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":352...
[]
[{"source":"Type max uE uF uG","source_end":35222,"source_start":35205,"syntax_kind":"Lean.Parser.Term.type"},{"source":"ULift.{max uF uG} E","source_end":35245,"source_start":35226,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
4
exact
true
1
38
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
34df2040253c24fe346737e0b49e433fa612fd6e2ce228af9ae7f410f5dce296
ecfd45e7d8e05ae0df446f10ba675ddd558ccd9fbfce9fa3a4a33e3ff9651865
6eba3218655b69b821244118ec4d8f6f1a3378fff599097d6f8953c8c7387664
c50696dbf1ed60afd1a7a197c9550d488c9b6e6b0ea25dee48bc7e647dcc92e5
cat-searcher/leandojo-benchmark-4-random
test
1,797
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
let Fu : Type max uE uF uG := <a>ULift</a>.{max uE uG} F
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c ContDiffOn) (:fv _uniq.502218) (:fv _uniq.502221) (:fv _uniq.502341) (:fv _uniq.502344) (:fv _uniq.502452) (:fv _uniq.502567) (:fv _uniq.502570) (:fv _uniq.502678) (:fv _uniq.502832) ((:c Function.comp) (:fv _uniq.502341) (:fv _uniq.502454) (:fv _uniq.502567) (:fv _uniq.506409) (:fv _uniq.506410)) (:fv _uniq.50640...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c ContDiffOn) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-of (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"let","sourceEnd":35251,"sourceStart":35248,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"Fu","sourceEnd":35254,"sourceStart":35252,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":352...
[]
[{"source":"Type max uE uF uG","source_end":35274,"source_start":35257,"syntax_kind":"Lean.Parser.Term.type"},{"source":"ULift.{max uE uG} F","source_end":35297,"source_start":35278,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
5
exact
true
1
39
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5a9957f46c1d17111edae10a4b4d825b9faa8208e4bde9d94039994f1f143c9b
c50696dbf1ed60afd1a7a197c9550d488c9b6e6b0ea25dee48bc7e647dcc92e5
1877a452061c0350db9ae08684543170d258544535fc0e084a9c7b0289a1082a
5893b80237d902a065269cf12d5122fa9a5eb2fe7ab76160626dab2dc48a032c
cat-searcher/leandojo-benchmark-4-random
test
1,798
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
let Gu : Type max uE uF uG := <a>ULift</a>.{max uE uF} G
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c ContDiffOn) (:fv _uniq.502218) (:fv _uniq.502221) (:fv _uniq.502341) (:fv _uniq.502344) (:fv _uniq.502452) (:fv _uniq.502567) (:fv _uniq.502570) (:fv _uniq.502678) (:fv _uniq.502832) ((:c Function.comp) (:fv _uniq.502341) (:fv _uniq.502454) (:fv _uniq.502567) (:fv _uniq.506409) (:fv _uniq.506410)) (:fv _uniq.50640...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c ContDiffOn) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-of (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"let","sourceEnd":35303,"sourceStart":35300,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"Gu","sourceEnd":35306,"sourceStart":35304,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":353...
[]
[{"source":"Type max uE uF uG","source_end":35326,"source_start":35309,"syntax_kind":"Lean.Parser.Term.type"},{"source":"ULift.{max uE uF} G\n -- declare the isomorphisms","source_end":35349,"source_start":35330,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
6
exact
true
1
40
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
856fa8204efe0837124b865b762e92d539a66c688cd1ab7a09441048f01acd81
5893b80237d902a065269cf12d5122fa9a5eb2fe7ab76160626dab2dc48a032c
afbcf4d6af1d84f008df8ef124968b8a863a3449aea21819eae4df6631df1567
63ccb299602baab2a6039e03cb70836d25ddaa6fb54fd178b157fd7cc78a8938
cat-searcher/leandojo-benchmark-4-random
test
1,799
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have isoE : Eu ≃L[𝕜] E := <a>ContinuousLinearEquiv.ulift</a>
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c ContDiffOn) (:fv _uniq.502218) (:fv _uniq.502221) (:fv _uniq.502341) (:fv _uniq.502344) (:fv _uniq.502452) (:fv _uniq.502567) (:fv _uniq.502570) (:fv _uniq.502678) (:fv _uniq.502832) ((:c Function.comp) (:fv _uniq.502341) (:fv _uniq.502454) (:fv _uniq.502567) (:fv _uniq.506409) (:fv _uniq.506410)) (:fv _uniq.50640...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c ContDiffOn) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-of (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"have","sourceEnd":35386,"sourceStart":35382,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"isoE","sourceEnd":35391,"sourceStart":35387,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"isoE","sourceEnd":35391,"sourceStart":35387,"tag":...
[]
[{"source":"Eu ≃L[𝕜] E","source_end":35409,"source_start":35394,"syntax_kind":"«term_≃L[_]_»"},{"source":"ContinuousLinearEquiv.ulift","source_end":35440,"source_start":35413,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
7
exact
true
1
41
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1aa3f694d05c1414a06f663c5578d050280f7535841454ce0f4f611e79a137e2
63ccb299602baab2a6039e03cb70836d25ddaa6fb54fd178b157fd7cc78a8938
ead86f07c14dc085c1a779471520565a6ffda47316c17f5b29bd9ab1ffdba212
b076fc53365eef8f54e26c891945a57a012874cc7562d49e0a79ef9d19c1afd4
cat-searcher/leandojo-benchmark-4-random
test
1,800
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have isoF : Fu ≃L[𝕜] F := <a>ContinuousLinearEquiv.ulift</a>
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c ContDiffOn) (:fv _uniq.502218) (:fv _uniq.502221) (:fv _uniq.502341) (:fv _uniq.502344) (:fv _uniq.502452) (:fv _uniq.502567) (:fv _uniq.502570) (:fv _uniq.502678) (:fv _uniq.502832) ((:c Function.comp) (:fv _uniq.502341) (:fv _uniq.502454) (:fv _uniq.502567) (:fv _uniq.506409) (:fv _uniq.506410)) (:fv _uniq.50640...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c ContDiffOn) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-of (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"have","sourceEnd":35447,"sourceStart":35443,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"isoF","sourceEnd":35452,"sourceStart":35448,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"isoF","sourceEnd":35452,"sourceStart":35448,"tag":...
[]
[{"source":"Fu ≃L[𝕜] F","source_end":35470,"source_start":35455,"syntax_kind":"«term_≃L[_]_»"},{"source":"ContinuousLinearEquiv.ulift","source_end":35501,"source_start":35474,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
8
exact
true
1
42
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
922fc9591a3b218a0aebff903afe074ca9b51ba3db4b67b1fdf50bd68b018da2
b076fc53365eef8f54e26c891945a57a012874cc7562d49e0a79ef9d19c1afd4
da151aad36fa7dc3ff000799f6081d65e72b8fd5b44d4d00b05498b6d0f6fd79
20cd2b47201230b7c2f65ef748e86c8fccaa708ba5933b7902695d08fe689ea7
cat-searcher/leandojo-benchmark-4-random
test
1,801
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have isoG : Gu ≃L[𝕜] G := <a>ContinuousLinearEquiv.ulift</a>
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c ContDiffOn) (:fv _uniq.502218) (:fv _uniq.502221) (:fv _uniq.502341) (:fv _uniq.502344) (:fv _uniq.502452) (:fv _uniq.502567) (:fv _uniq.502570) (:fv _uniq.502678) (:fv _uniq.502832) ((:c Function.comp) (:fv _uniq.502341) (:fv _uniq.502454) (:fv _uniq.502567) (:fv _uniq.506409) (:fv _uniq.506410)) (:fv _uniq.50640...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c ContDiffOn) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-of (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"have","sourceEnd":35508,"sourceStart":35504,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"isoG","sourceEnd":35513,"sourceStart":35509,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"isoG","sourceEnd":35513,"sourceStart":35509,"tag":...
[]
[{"source":"Gu ≃L[𝕜] G","source_end":35531,"source_start":35516,"syntax_kind":"«term_≃L[_]_»"},{"source":"ContinuousLinearEquiv.ulift\n -- lift the functions to the new spaces, check smoothness there, and then go back.","source_end":35562,"source_start":35535,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
9
exact
true
1
43
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
26231471d174b67c60b3955c21c988cfffdbd53880bcd62aff18a43616329415
20cd2b47201230b7c2f65ef748e86c8fccaa708ba5933b7902695d08fe689ea7
d19f7bdddc6fb20233d492706d2e15765edfcb9a5b0ba06997482bdbd5a8a347
0a2818f4182b0652f50236b1f221502060d6e01d2709305f437ff29c4748fb2c
cat-searcher/leandojo-benchmark-4-random
test
1,802
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
let fu : Eu → Fu := (isoF.symm ∘ f) ∘ isoE
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c ContDiffOn) (:fv _uniq.502218) (:fv _uniq.502221) (:fv _uniq.502341) (:fv _uniq.502344) (:fv _uniq.502452) (:fv _uniq.502567) (:fv _uniq.502570) (:fv _uniq.502678) (:fv _uniq.502832) ((:c Function.comp) (:fv _uniq.502341) (:fv _uniq.502454) (:fv _uniq.502567) (:fv _uniq.506409) (:fv _uniq.506410)) (:fv _uniq.50640...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c ContDiffOn) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-of (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"let","sourceEnd":35653,"sourceStart":35650,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"fu","sourceEnd":35656,"sourceStart":35654,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":356...
[]
[{"source":"Eu → Fu","source_end":35668,"source_start":35659,"syntax_kind":"Lean.Parser.Term.arrow"},{"source":"(isoF.symm ∘ f) ∘ isoE","source_end":35698,"source_start":35672,"syntax_kind":"«term_∘_»"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
10
exact
true
1
44
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
dd2dcbdaa0308015806951ebaca717cc2399878ce560f4f092dfa48680d69dc8
0a2818f4182b0652f50236b1f221502060d6e01d2709305f437ff29c4748fb2c
b9220f155e52f7ac56ad4079c0a58f5232273ebc438bad2808deb1be12fc4e97
4739aaefebf24f88d14503ecacbfa7f25fcbed0a85c20358184ddd91b29f4cbe
cat-searcher/leandojo-benchmark-4-random
test
1,803
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have fu_diff : <a>ContDiffOn</a> 𝕜 n fu (isoE ⁻¹' s) := by rwa [isoE.contDiffOn_comp_iff, isoF.symm.comp_contDiffOn_iff]
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c ContDiffOn) (:fv _uniq.502218) (:fv _uniq.502221) (:fv _uniq.502341) (:fv _uniq.502344) (:fv _uniq.502452) (:fv _uniq.502567) (:fv _uniq.502570) (:fv _uniq.502678) (:fv _uniq.502832) ((:c Function.comp) (:fv _uniq.502341) (:fv _uniq.502454) (:fv _uniq.502567) (:fv _uniq.506409) (:fv _uniq.506410)) (:fv _uniq.50640...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c ContDiffOn) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-of (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"have","sourceEnd":35705,"sourceStart":35701,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"fu_diff","sourceEnd":35713,"sourceStart":35706,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"fu_diff","sourceEnd":35713,"sourceStart":35706,...
[]
[{"source":"ContDiffOn 𝕜 n fu (isoE ⁻¹' s)","source_end":35752,"source_start":35716,"syntax_kind":"Lean.Parser.Term.app"},{"source":"isoE.contDiffOn_comp_iff","source_end":35792,"source_start":35768,"syntax_kind":"ident"},{"source":"isoF.symm.comp_contDiffOn_iff","source_end":35823,"source_start":35794,"syntax_kind":"...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
11
exact
true
1
45
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
62b8b69c43e08a833354a9a90b9afb1415a056553cd288296db340ebe48acb06
4739aaefebf24f88d14503ecacbfa7f25fcbed0a85c20358184ddd91b29f4cbe
3f15d42216ed88eedfb07aa17497174777136626f417a979f3d7ebd11c2019af
5da80cc750d39d3a8713c76943397fb197e6f2b1ad45ac3207a8b2e6560add28
cat-searcher/leandojo-benchmark-4-random
test
1,804
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
let gu : Fu → Gu := (isoG.symm ∘ g) ∘ isoF
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c ContDiffOn) (:fv _uniq.502218) (:fv _uniq.502221) (:fv _uniq.502341) (:fv _uniq.502344) (:fv _uniq.502452) (:fv _uniq.502567) (:fv _uniq.502570) (:fv _uniq.502678) (:fv _uniq.502832) ((:c Function.comp) (:fv _uniq.502341) (:fv _uniq.502454) (:fv _uniq.502567) (:fv _uniq.506409) (:fv _uniq.506410)) (:fv _uniq.50640...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c ContDiffOn) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-of (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"let","sourceEnd":35830,"sourceStart":35827,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"gu","sourceEnd":35833,"sourceStart":35831,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":358...
[]
[{"source":"Fu → Gu","source_end":35845,"source_start":35836,"syntax_kind":"Lean.Parser.Term.arrow"},{"source":"(isoG.symm ∘ g) ∘ isoF","source_end":35875,"source_start":35849,"syntax_kind":"«term_∘_»"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
17
exact
true
1
46
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0ebf3b2ebda13dfd0753b94cc913ab3d3142d363166e9cfa4bc98bb8a87c48d9
5da80cc750d39d3a8713c76943397fb197e6f2b1ad45ac3207a8b2e6560add28
29b7541035932f024a49de21c1109687eac6d957803fef736d6547ddb9e4a636
f499cbcea474d4a2ca160b166c7b7835e9070822b09bfed21d8f21dc81895d9e
cat-searcher/leandojo-benchmark-4-random
test
1,805
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have gu_diff : <a>ContDiffOn</a> 𝕜 n gu (isoF ⁻¹' t) := by rwa [isoF.contDiffOn_comp_iff, isoG.symm.comp_contDiffOn_iff]
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c ContDiffOn) (:fv _uniq.502218) (:fv _uniq.502221) (:fv _uniq.502341) (:fv _uniq.502344) (:fv _uniq.502452) (:fv _uniq.502567) (:fv _uniq.502570) (:fv _uniq.502678) (:fv _uniq.502832) ((:c Function.comp) (:fv _uniq.502341) (:fv _uniq.502454) (:fv _uniq.502567) (:fv _uniq.506409) (:fv _uniq.506410)) (:fv _uniq.50640...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c ContDiffOn) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-of (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"have","sourceEnd":35882,"sourceStart":35878,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"gu_diff","sourceEnd":35890,"sourceStart":35883,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"gu_diff","sourceEnd":35890,"sourceStart":35883,...
[]
[{"source":"ContDiffOn 𝕜 n gu (isoF ⁻¹' t)","source_end":35929,"source_start":35893,"syntax_kind":"Lean.Parser.Term.app"},{"source":"isoF.contDiffOn_comp_iff","source_end":35969,"source_start":35945,"syntax_kind":"ident"},{"source":"isoG.symm.comp_contDiffOn_iff","source_end":36000,"source_start":35971,"syntax_kind":"...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
18
exact
true
1
47
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1028787d6c6a839b3b3dc13d0d80b82dcbe2ef8e9f48504c6dd4e84ac1a4db45
f499cbcea474d4a2ca160b166c7b7835e9070822b09bfed21d8f21dc81895d9e
2dfc06345b49e66a2227d61a6664d15c184f3e6f58d1afa9e0720ee322d00015
a9fa16a09c4853c61bec0f3fc6cdb7cc922d670e2c05ca8f1e88ef9a2a11a34e
cat-searcher/leandojo-benchmark-4-random
test
1,806
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have main : <a>ContDiffOn</a> 𝕜 n (gu ∘ fu) (isoE ⁻¹' s) := by apply <a>_private.Mathlib.Analysis.Calculus.ContDiff.Basic.0.ContDiffOn.comp_same_univ</a> gu_diff fu_diff intro y hy simp only [fu, <a>ContinuousLinearEquiv.coe_apply</a>, <a>Function.comp_apply</a>, <a>Set.mem_preimage</a>] rw [isoF.apply_symm_apply (f (...
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c ContDiffOn) (:fv _uniq.502218) (:fv _uniq.502221) (:fv _uniq.502341) (:fv _uniq.502344) (:fv _uniq.502452) (:fv _uniq.502567) (:fv _uniq.502570) (:fv _uniq.502678) (:fv _uniq.502832) ((:c Function.comp) (:fv _uniq.502341) (:fv _uniq.502454) (:fv _uniq.502567) (:fv _uniq.506409) (:fv _uniq.506410)) (:fv _uniq.50640...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c ContDiffOn) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-of (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"have","sourceEnd":36008,"sourceStart":36004,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"main","sourceEnd":36013,"sourceStart":36009,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"main","sourceEnd":36013,"sourceStart":36009,"tag":...
[]
[{"source":"ContDiffOn 𝕜 n (gu ∘ fu) (isoE ⁻¹' s)","source_end":36061,"source_start":36016,"syntax_kind":"Lean.Parser.Term.app"},{"source":"ContDiffOn.comp_same_univ gu_diff fu_diff","source_end":36119,"source_start":36078,"syntax_kind":"Lean.Parser.Term.app"},{"source":"fu","source_end":36152,"source_start":36150,"sy...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
24
exact
true
1
48
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9ba1090ea3042a5ef91d7d41c86a7c4dd3bdfb3439eed750650c2fb5ada51ecc
a9fa16a09c4853c61bec0f3fc6cdb7cc922d670e2c05ca8f1e88ef9a2a11a34e
1bc1ebb2b30c9ae9c618a86b260edbdcf344c2d8c843281ee0e199549843c95c
35a4c59a3c0cff167ceb7f2b2dc989bec78ef2f76ad202e3af9d262d9a4c031c
cat-searcher/leandojo-benchmark-4-random
test
1,807
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have : gu ∘ fu = (isoG.symm ∘ g ∘ f) ∘ isoE := by ext y simp only [fu, gu, <a>Function.comp_apply</a>] rw [isoF.apply_symm_apply (f (isoE y))]
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c ContDiffOn) (:fv _uniq.502218) (:fv _uniq.502221) (:fv _uniq.502341) (:fv _uniq.502344) (:fv _uniq.502452) (:fv _uniq.502567) (:fv _uniq.502570) (:fv _uniq.502678) (:fv _uniq.502832) ((:c Function.comp) (:fv _uniq.502341) (:fv _uniq.502454) (:fv _uniq.502567) (:fv _uniq.506409) (:fv _uniq.506410)) (:fv _uniq.50640...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c ContDiffOn) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-of (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"have","sourceEnd":36288,"sourceStart":36284,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":36289,"sourceStart":36289,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":36289,"sourceStart":36289,"tag":"node"}],"kind":"Lean.Parser.Term.hav...
[]
[{"source":"gu ∘ fu = (isoG.symm ∘ g ∘ f) ∘ isoE","source_end":36335,"source_start":36291,"syntax_kind":"«term_=_»"},{"source":"fu","source_end":36369,"source_start":36367,"syntax_kind":"ident"},{"source":"gu","source_end":36373,"source_start":36371,"syntax_kind":"ident"},{"source":"Function.comp_apply","source_end":36...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
33
exact
true
1
49
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
641fb248d9c5f644695cca308af42364052274689f73973864e92ac174194852
35a4c59a3c0cff167ceb7f2b2dc989bec78ef2f76ad202e3af9d262d9a4c031c
9f4dc81ba3ff75901d924b44a362d93105544a6104fdd0aeffb5f7bc314f3984
0045e642cfe646042904861eb7a163b0a933d324a7dcdfc762ef7f61f3c4654c
cat-searcher/leandojo-benchmark-4-random
test
1,808
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rwa [this, isoE.contDiffOn_comp_iff, isoG.symm.comp_contDiffOn_iff] at main
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c ContDiffOn) (:fv _uniq.502218) (:fv _uniq.502221) (:fv _uniq.502341) (:fv _uniq.502344) (:fv _uniq.502452) (:fv _uniq.502567) (:fv _uniq.502570) (:fv _uniq.502678) (:fv _uniq.502832) ((:c Function.comp) (:fv _uniq.502341) (:fv _uniq.502454) (:fv _uniq.502567) (:fv _uniq.506409) (:fv _uniq.506410)) (:fv _uniq.50640...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c ContDiffOn) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-of (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"rwa","sourceEnd":36445,"sourceStart":36442,"tag":"atom"},{"children":[{"source":"[","sourceEnd":36447,"sourceStart":36446,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":50,"semanticRole":"local","source":"this","sourceEnd":36451,"so...
[]
[{"source":"this","source_end":36451,"source_start":36447,"syntax_kind":"ident"},{"source":"main","source_end":36517,"source_start":36513,"syntax_kind":"ident"},{"source":"isoE.contDiffOn_comp_iff","source_end":36477,"source_start":36453,"syntax_kind":"ident"},{"source":"isoG.symm.comp_contDiffOn_iff","source_end":3650...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
40
exact
true
1
50
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5ebb05c774ef8f19079abde67345bc94e6c8a910b85e075fe430cd28d13eadc1
0045e642cfe646042904861eb7a163b0a933d324a7dcdfc762ef7f61f3c4654c
edaecb1bf29531387e8527615e293212d907d4e5d6590791374309867ac9b4e7
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,809
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rwa [isoE.contDiffOn_comp_iff, isoF.symm.comp_contDiffOn_iff]
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c ContDiffOn) (:fv _uniq.502218) (:fv _uniq.502221) (:fv _uniq.506417) ((:c ULift.normedAddCommGroup) (:fv _uniq.502341) (:fv _uniq.502344)) ((:c ULift.normedSpace) (:fv _uniq.502218) (:fv _uniq.502341) ((:c NontriviallyNormedField.toNormedField) (:fv _uniq.502218) (:fv _uniq.502221)) ((:c NormedAddCommGroup.toSemin...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c ContDiffOn) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV39)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:app (:c ULift) (:arg :explicit 0 (:fv FV5))))))) (:ar...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"rwa","sourceEnd":35766,"sourceStart":35763,"tag":"atom"},{"children":[{"source":"[","sourceEnd":35768,"sourceStart":35767,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"ContinuousLinearEquiv.contDiffOn_comp_iff","semanticRole":"global","so...
[]
[{"source":"isoE.contDiffOn_comp_iff","source_end":35792,"source_start":35768,"syntax_kind":"ident"},{"source":"isoF.symm.comp_contDiffOn_iff","source_end":35823,"source_start":35794,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
13
exact
true
1
45
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
27398fefa5a640f33445c49a7957e48d784f82390d0af95e973961d769c36f35
7fdfcdb0e81413ef23936c71df9a25ce4548ea77d574c773fb1a875873cdecdd
77ab42a654e26b418d6a07568a36ddb03082632365f2386034f3eed575a486f6
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,810
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rwa [isoF.contDiffOn_comp_iff, isoG.symm.comp_contDiffOn_iff]
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c ContDiffOn) (:fv _uniq.502218) (:fv _uniq.502221) (:fv _uniq.506423) ((:c ULift.normedAddCommGroup) (:fv _uniq.502454) (:fv _uniq.502457)) ((:c ULift.normedSpace) (:fv _uniq.502218) (:fv _uniq.502454) ((:c NontriviallyNormedField.toNormedField) (:fv _uniq.502218) (:fv _uniq.502221)) ((:c NormedAddCommGroup.toSemin...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c ContDiffOn) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV40)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:app (:c ULift) (:arg :explicit 0 (:fv FV8))))))) (:ar...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"rwa","sourceEnd":35943,"sourceStart":35940,"tag":"atom"},{"children":[{"source":"[","sourceEnd":35945,"sourceStart":35944,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"ContinuousLinearEquiv.contDiffOn_comp_iff","semanticRole":"global","so...
[]
[{"source":"isoF.contDiffOn_comp_iff","source_end":35969,"source_start":35945,"syntax_kind":"ident"},{"source":"isoG.symm.comp_contDiffOn_iff","source_end":36000,"source_start":35971,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
20
exact
true
1
47
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
bcab342832ca0a69983eb58eaf74d828367e8a722128bec97d887d646a7dcfb0
91e9d1312a0fa8c158ce6b651a2a942b935a0436d680146f8c61cec2a1e26c7f
eeb508b88c1d8c4c9f8c0e0d1e2c63afcf01f18c53ea3aee07f92aeafff8c6f9
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,811
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>_private.Mathlib.Analysis.Calculus.ContDiff.Basic.0.ContDiffOn.comp_same_univ</a> gu_diff fu_diff
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c ContDiffOn) (:fv _uniq.502218) (:fv _uniq.502221) (:fv _uniq.506417) ((:c ULift.normedAddCommGroup) (:fv _uniq.502341) (:fv _uniq.502344)) ((:c ULift.normedSpace) (:fv _uniq.502218) (:fv _uniq.502341) ((:c NontriviallyNormedField.toNormedField) (:fv _uniq.502218) (:fv _uniq.502221)) ((:c NormedAddCommGroup.toSemin...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c ContDiffOn) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV39)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:app (:c ULift) (:arg :explicit 0 (:fv FV5))))))) (:ar...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"apply","sourceEnd":36077,"sourceStart":36072,"tag":"atom"},{"children":[{"name":"_private.Mathlib.Analysis.Calculus.ContDiff.Basic.0.ContDiffOn.comp_same_univ","semanticRole":"global","source":"ContDiffOn.comp_same_univ","sourceEnd":36103,"sourceStart":36078,"tag":"identifier"},{"children":[{"co...
[]
[{"source":"ContDiffOn.comp_same_univ gu_diff fu_diff","source_end":36119,"source_start":36078,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
26
exact
true
1
48
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
350db0c9c5e7d49a26a775b379772c8629b7a03b4dfbd0def4b2c4161d212f41
1588458a888e7049b37c1bac0136ae939e9ae0569ad7474a1348897d4e172280
af15b30405a9b06cd7d88f05a0260f1f35e4f824caf8dbc14c48f7be10434618
c44b38ffafa7cfea57c7d5ff67093972ded0625e2214b0301096e1b47602b679
cat-searcher/leandojo-benchmark-4-random
test
1,812
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro y hy
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c HasSubset.Subset) ((:c Set) (:fv _uniq.506417)) ((:c Set.instHasSubset) (:fv _uniq.506417)) ((:c Set.preimage) (:fv _uniq.506417) (:fv _uniq.502341) ((:c DFunLike.coe) ((:c ContinuousLinearEquiv) (:fv _uniq.502218) (:fv _uniq.502218) ((:c DivisionSemiring.toSemiring) (:fv _uniq.502218) ((:c Semifield.toDivisionSem...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV39)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV39))))))) (:arg :explicit 2 (:app (:c Set.preimage) (:arg :implicit-type 0 (:fv FV39)) (:arg :implicit-type 1 (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"intro","sourceEnd":36129,"sourceStart":36124,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":36131,"sourceStart":36130,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hy","sourceEnd":36134,"sourceStart":36132,"tag":"identifier"}],"kind":"null","sou...
[{"role":"fresh_name","source":"y","source_end":36131,"source_start":36130,"syntax_kind":"ident"},{"role":"fresh_name","source":"hy","source_end":36134,"source_start":36132,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
27
exact
true
1
48
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
dd949d76a841346bb83bbd2d830040b7cd7300e0f1e34e27b595131df214a82f
c44b38ffafa7cfea57c7d5ff67093972ded0625e2214b0301096e1b47602b679
69ac7ac9f4300ee3290568559761b10f79f65930316d628484707cb4cb9d79dc
134d5d310afa47d0ea299a0a4f6f611f7e154df3228271e1826a04c0463ec5af
cat-searcher/leandojo-benchmark-4-random
test
1,813
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [fu, <a>ContinuousLinearEquiv.coe_apply</a>, <a>Function.comp_apply</a>, <a>Set.mem_preimage</a>]
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c Membership.mem) (:fv _uniq.506417) ((:c Set) (:fv _uniq.506417)) ((:c Set.instMembership) (:fv _uniq.506417)) (:fv _uniq.515566) ((:c Set.preimage) (:fv _uniq.506417) (:fv _uniq.506423) (:fv _uniq.511587) ((:c Set.preimage) (:fv _uniq.506423) (:fv _uniq.502454) ((:c DFunLike.coe) ((:c ContinuousLinearEquiv) (:fv _...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV39)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV39)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV39)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV39))))))) (:arg :explicit 3 (:fv FV49)) (:arg :...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"simp","sourceEnd":36143,"sourceStart":36139,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":36148,"sourceStart":36144,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":361...
[]
[{"source":"fu","source_end":36152,"source_start":36150,"syntax_kind":"ident"},{"source":"ContinuousLinearEquiv.coe_apply","source_end":36185,"source_start":36154,"syntax_kind":"ident"},{"source":"Function.comp_apply","source_end":36206,"source_start":36187,"syntax_kind":"ident"},{"source":"mem_preimage","source_end":3...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
28
exact
true
1
50
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7542c42996a0cffa93c7bcacc0965347c8fd2b56fea3ea558bcfaf0bc2580f50
134d5d310afa47d0ea299a0a4f6f611f7e154df3228271e1826a04c0463ec5af
5223255bf00fccde21451fab73a6b4152ac24b67afb7126ebd29921c75571ac2
d34b45fc79a44b365dca4752477cb18b4565d45126b7f6c770215787e2463604
cat-searcher/leandojo-benchmark-4-random
test
1,814
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [isoF.apply_symm_apply (f (isoE y))]
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c Membership.mem) (:fv _uniq.502454) ((:c Set) (:fv _uniq.502454)) ((:c Set.instMembership) (:fv _uniq.502454)) ((:c DFunLike.coe) ((:c ContinuousLinearEquiv) (:fv _uniq.502218) (:fv _uniq.502218) ((:c DivisionSemiring.toSemiring) (:fv _uniq.502218) ((:c Semifield.toDivisionSemiring) (:fv _uniq.502218) ((:c Field.to...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV8)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV8)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV8)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV8))))))) (:arg :explicit 3 (:app (:c DFunLike.coe)...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"rw","sourceEnd":36228,"sourceStart":36226,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":36230,"sourceStart":36229,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"i...
[]
[{"source":"isoF.apply_symm_apply (f (isoE y))","source_end":36264,"source_start":36230,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
29
exact
true
1
50
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5e44d2c2a4d39646ffc687e74f97cac7ddd9d918866900a224f81971954d666f
d34b45fc79a44b365dca4752477cb18b4565d45126b7f6c770215787e2463604
167dc9ce1258cfae47d975a7bc09177c510ce1615dfb46f6ef0be827f470fb2d
5bbf37d61f4f42eab34248e462240674ede6f9054cef9c220e847195ad895874
cat-searcher/leandojo-benchmark-4-random
test
1,815
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact st hy
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
((:c Membership.mem) (:fv _uniq.502454) ((:c Set) (:fv _uniq.502454)) ((:c Set.instMembership) (:fv _uniq.502454)) ((:fv _uniq.506410) ((:c DFunLike.coe) ((:c ContinuousLinearEquiv) (:fv _uniq.502218) (:fv _uniq.502218) ((:c DivisionSemiring.toSemiring) (:fv _uniq.502218) ((:c Semifield.toDivisionSemiring) (:fv _uniq.5...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV8)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV8)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV8)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV8))))))) (:arg :explicit 3 (:app (:fv FV35) (:arg ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"exact","sourceEnd":36275,"sourceStart":36270,"tag":"atom"},{"children":[{"contextIndex":38,"semanticRole":"local","source":"st","sourceEnd":36278,"sourceStart":36276,"tag":"identifier"},{"children":[{"contextIndex":50,"semanticRole":"local","source":"hy","sourceEnd":36281,"sourceStart":36279,"ta...
[]
[{"source":"st hy","source_end":36281,"source_start":36276,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
32
exact
true
1
50
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1c9226ef85d406f0e5186427a844786af6247244ab7006c1d545a719252c11b3
5bbf37d61f4f42eab34248e462240674ede6f9054cef9c220e847195ad895874
99644b67902bb4a2a0e1745ce2375bf23fc34ad647c62ff666441ed06a593d81
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,816
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
ext y
𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...
case h.h 𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : Norme...
((:c Eq) (:forall _ (:fv _uniq.506417) (:fv _uniq.506429)) ((:c Function.comp) (:fv _uniq.506417) (:fv _uniq.506423) (:fv _uniq.506429) (:fv _uniq.513634) (:fv _uniq.511587)) ((:c Function.comp) (:fv _uniq.506417) (:fv _uniq.502341) (:fv _uniq.506429) ((:c Function.comp) (:fv _uniq.502341) (:fv _uniq.502567) (:fv _uniq...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c Eq) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV39) (:fv FV41))) (:arg :explicit 1 (:app (:c Function.comp) (:arg :implicit-type 0 (:fv FV39)) (:arg :implicit-type 1 (:fv FV40)) (:arg :implicit-type 2 (:fv FV41)) (:arg :explicit 3 (:fv FV47)) (:arg :explicit 4 (:fv FV45)))) (:arg :explicit 2 (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"ext","sourceEnd":36349,"sourceStart":36346,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":36351,"sourceStart":36350,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"y","sourceEnd":36351,"sourceStart":36350,"tag...
[{"role":"fresh_name","source":"y","source_end":36351,"source_start":36350,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
35
exact
true
1
49
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
399795888f19f257b528070f01b15db13e37130933115aa594b4dcf1e3299625
154b53ba6ac3f1dd0e07b7399af539e71c5efc736abf5b3aae7126cc07c12ebc
37d49c45b1abbe86a4687a0eab685a29b148c16e65ed2a21b8d9a8fd1054d53a
52da9243df8dd8f43dd623d6c8d9684b313b69ceb8cb8ed16b4af652c92f1f91
cat-searcher/leandojo-benchmark-4-random
test
1,817
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [fu, gu, <a>Function.comp_apply</a>]
case h.h 𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : Norme...
case h.h 𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : Norme...
((:c Eq) (:fv _uniq.502567) ((:c ULift.down) (:fv _uniq.502567) ((:c Function.comp) (:fv _uniq.506417) (:fv _uniq.506423) (:fv _uniq.506429) (:fv _uniq.513634) (:fv _uniq.511587) (:fv _uniq.518792))) ((:c ULift.down) (:fv _uniq.502567) ((:c Function.comp) (:fv _uniq.506417) (:fv _uniq.502341) (:fv _uniq.506429) ((:c Fu...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV11)) (:arg :explicit 1 (:app (:c ULift.down) (:arg :implicit-type 0 (:fv FV11)) (:arg :explicit 1 (:app (:c Function.comp) (:arg :implicit-type 0 (:fv FV39)) (:arg :implicit-type 1 (:fv FV40)) (:arg :implicit-type 2 (:fv FV41)) (:arg :explicit 3 (:fv FV47)) (:arg :explicit 4 ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"simp","sourceEnd":36360,"sourceStart":36356,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":36365,"sourceStart":36361,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":363...
[]
[{"source":"fu","source_end":36369,"source_start":36367,"syntax_kind":"ident"},{"source":"gu","source_end":36373,"source_start":36371,"syntax_kind":"ident"},{"source":"Function.comp_apply","source_end":36394,"source_start":36375,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
36
exact
true
1
50
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5424926e696549540a7dc8bde41596ed281cfe95b337629e7deeccbcfe5e3ff9
52da9243df8dd8f43dd623d6c8d9684b313b69ceb8cb8ed16b4af652c92f1f91
38cdfd7893549a9ba374220b67ccc98b1aaa54b2d793809ba6b4dc143b1186de
c25e2d9a86af5aa975df2bf0ccdec3ba63a6ef8a2556ef3d42c0b6e3e558b280
cat-searcher/leandojo-benchmark-4-random
test
1,818
ContDiffOn.comp
Mathlib/Analysis/Calculus/ContDiff/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [isoF.apply_symm_apply (f (isoE y))]
case h.h 𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : Norme...
((:c Eq) (:fv _uniq.502567) ((:c ULift.down) (:fv _uniq.502567) ((:c DFunLike.coe) ((:c ContinuousLinearEquiv) (:fv _uniq.502218) (:fv _uniq.502218) ((:c DivisionSemiring.toSemiring) (:fv _uniq.502218) ((:c Semifield.toDivisionSemiring) (:fv _uniq.502218) ((:c Field.toSemifield) (:fv _uniq.502218) ((:c NormedField.toFi...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.502218))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.502223))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.502218) (:fv _uniq.502223) ((:c Non...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV11)) (:arg :explicit 1 (:app (:c ULift.down) (:arg :implicit-type 0 (:fv FV11)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c ContinuousLinearEquiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-o...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"source":"rw","sourceEnd":36402,"sourceStart":36400,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":36404,"sourceStart":36403,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"i...
[]
[{"source":"isoF.apply_symm_apply (f (isoE y))","source_end":36438,"source_start":36404,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.502218","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.502221","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
129
37
exact
true
1
50
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2dcf9aed2f08bad282b7764103a4003224bb91a1c231b61bb2f2dcfcaf0192fc
c25e2d9a86af5aa975df2bf0ccdec3ba63a6ef8a2556ef3d42c0b6e3e558b280
167dc9ce1258cfae47d975a7bc09177c510ce1615dfb46f6ef0be827f470fb2d
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,819
ProbabilityTheory.mgf_undef
Mathlib/Probability/Moments.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>ProbabilityTheory.mgf</a>, <a>MeasureTheory.integral_undef</a> hX]
Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ hX : ¬Integrable (fun ω => rexp (t * X ω)) μ ⊢ mgf X μ t = 0
((:c Eq) (:c Real) ((:c ProbabilityTheory.mgf) (:fv _uniq.12919) (:fv _uniq.12925) (:fv _uniq.12929) (:fv _uniq.12940) (:fv _uniq.12942)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.12919))"},{"name":"X","sexp":"(:forall _ (:fv _uniq.12919) (:c Real))"},{"name":"p","sexp":"(:c Nat)"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.12919) (:fv _uniq.12925)...
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c ProbabilityTheory.mgf) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:fv FV5)) (:arg :explicit 4 (:fv FV6)))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:ar...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12919","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12922","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":7783,"sourceStart":7779,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":7788,"sourceStart":7784,"tag":"atom"}],"kind":"nu...
[]
[{"source":"mgf","source_end":7793,"source_start":7790,"syntax_kind":"ident"},{"source":"integral_undef hX","source_end":7812,"source_start":7795,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12919","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12922","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
51
2
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
32ecc87fd23c0eccd391a2b8d391ab35cd3e972b5f5564b5b1ab1296736d1b32
883f9bd8fdf03d686d8b02ed94cabf9949618c6cc291eedf80819216ac7f2fd1
4f4e601d207e1eb0691289d9e46a8388e4a2b6441829ff3f821f189a61b614fe
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,820
Embedding.map_nhdsWithin_eq
Mathlib/Topology/ContinuousOn.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>nhdsWithin</a>, <a>Filter.map_inf</a> hf.inj, hf.map_nhds_eq, <a>Filter.map_principal</a>, ← <a>nhdsWithin_inter'</a>, <a>Set.inter_eq_self_of_subset_right</a> (<a>Set.image_subset_range</a> _ _)]
α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 inst✝⁴ : TopologicalSpace α ι : Type u_5 π : ι → Type u_6 inst✝³ : (i : ι) → TopologicalSpace (π i) inst✝² : TopologicalSpace β inst✝¹ : TopologicalSpace γ inst✝ : TopologicalSpace δ f : α → β hf : _root_.Embedding f s : Set α x : α ⊢ map f (𝓝[s] x) = 𝓝[f '' s] f x
((:c Eq) ((:c Filter) (:fv _uniq.137186)) ((:c Filter.map) (:fv _uniq.137183) (:fv _uniq.137186) (:fv _uniq.137841) ((:c nhdsWithin) (:fv _uniq.137183) (:fv _uniq.137195) (:fv _uniq.137844) (:fv _uniq.137843))) ((:c nhdsWithin) (:fv _uniq.137186) (:fv _uniq.137214) ((:fv _uniq.137841) (:fv _uniq.137844)) ((:c Set.image...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁴","sexp":"((:c TopologicalSpace) (:fv _uniq.137183))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.137198)...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Filter.map) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV12)) (:arg :explicit 3 (:app (:c nhdsWithin) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:in...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.137183","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.137186","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":62564,"sourceStart":62562,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":62566,"sourceStart":62565,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",...
[]
[{"source":"nhdsWithin","source_end":62576,"source_start":62566,"syntax_kind":"ident"},{"source":"Filter.map_inf hf.inj","source_end":62599,"source_start":62578,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hf.map_nhds_eq","source_end":62615,"source_start":62601,"syntax_kind":"ident"},{"source":"map_principal","sour...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.137183","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.137186","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
396
2
exact
true
1
15
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a7c6f0c3bf742a3d7c54da39e596161ccf52c9ff46ba368918fb90898a0a5723
cf4994a7b7fc49bde4f7edaf01f36c7ff06e8514fda5ba18925c2a8db246de33
231312bfe0189ac9fab155028d6abbac671c957fb69eaa98b54eb9c7914255a7
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,821
Polynomial.ker_mapRingHom
Mathlib/RingTheory/Polynomial/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
ext
R : Type u S : Type u_1 inst✝¹ : CommSemiring R inst✝ : Semiring S f : R →+* S ⊢ LinearMap.ker (mapRingHom f).toSemilinearMap = map C (RingHom.ker f)
case h R : Type u S : Type u_1 inst✝¹ : CommSemiring R inst✝ : Semiring S f : R →+* S x✝ : R[X] ⊢ x✝ ∈ LinearMap.ker (mapRingHom f).toSemilinearMap ↔ x✝ ∈ map C (RingHom.ker f)
((:c Eq) ((:c Submodule) ((:c Polynomial) (:fv _uniq.145361) ((:c CommSemiring.toSemiring) (:fv _uniq.145361) (:fv _uniq.145367))) ((:c Polynomial) (:fv _uniq.145361) ((:c CommSemiring.toSemiring) (:fv _uniq.145361) (:fv _uniq.145367))) ((:c Polynomial.semiring) (:fv _uniq.145361) ((:c CommSemiring.toSemiring) (:fv _un...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CommSemiring) (:fv _uniq.145361))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.145364))"},{"name":"f","sexp":"((:c RingHom) (:fv _uniq.145361) (:fv _uniq.145364) ((:c Semiring.toNonAssocSemiring) (:fv _un...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 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) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.145361","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.145364","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"ext","sourceEnd":25145,"sourceStart":25142,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":25145,"sourceStart":25142,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.145361","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.145364","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal...
158
4
exact
true
1
5
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
6b0f32a3844695033c4043360ad5031e63650eb531dabb2052c5149426a9ef0c
ea29d3bd949e59f12f5083a9adabf2a5341c1da9267c9e87ef90913d8d173cde
a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de
15321f3f5c317357a3fe0c82c4c8cf2163e70c7c7d4593987393bc4bd22b370b
cat-searcher/leandojo-benchmark-4-random
test
1,822
Polynomial.ker_mapRingHom
Mathlib/RingTheory/Polynomial/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>LinearMap.mem_ker</a>, <a>RingHom.toSemilinearMap_apply</a>, <a>Polynomial.coe_mapRingHom</a>]
case h R : Type u S : Type u_1 inst✝¹ : CommSemiring R inst✝ : Semiring S f : R →+* S x✝ : R[X] ⊢ x✝ ∈ LinearMap.ker (mapRingHom f).toSemilinearMap ↔ x✝ ∈ map C (RingHom.ker f)
case h R : Type u S : Type u_1 inst✝¹ : CommSemiring R inst✝ : Semiring S f : R →+* S x✝ : R[X] ⊢ (↑↑(mapRingHom f)).toFun x✝ = 0 ↔ x✝ ∈ map C (RingHom.ker f)
((:c Iff) ((:c Membership.mem) ((:c Polynomial) (:fv _uniq.145361) ((:c CommSemiring.toSemiring) (:fv _uniq.145361) (:fv _uniq.145367))) ((:c Ideal) ((:c Polynomial) (:fv _uniq.145361) ((:c CommSemiring.toSemiring) (:fv _uniq.145361) (:fv _uniq.145367))) ((:c Polynomial.semiring) (:fv _uniq.145361) ((:c CommSemiring.to...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CommSemiring) (:fv _uniq.145361))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.145364))"},{"name":"f","sexp":"((:c RingHom) (:fv _uniq.145361) (:fv _uniq.145364) ((:c Semiring.toNonAssocSemiring) (:fv _un...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (: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 :implicit-type 1 (:app (:c Ideal) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:f...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.145361","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.145364","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"simp","sourceEnd":25152,"sourceStart":25148,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":25157,"sourceStart":25153,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":251...
[]
[{"source":"LinearMap.mem_ker","source_end":25176,"source_start":25159,"syntax_kind":"ident"},{"source":"RingHom.toSemilinearMap_apply","source_end":25207,"source_start":25178,"syntax_kind":"ident"},{"source":"coe_mapRingHom","source_end":25223,"source_start":25209,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.145361","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.145364","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal...
158
5
exact
true
1
6
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b21851f46965914e631935f67333cebe191384761ef33465126555564e74e2d0
15321f3f5c317357a3fe0c82c4c8cf2163e70c7c7d4593987393bc4bd22b370b
90d7e9d88726c4fc86ed34e41d024dcad80cfa9b02cc23f90bb2800a4b13ade9
ac075e90d0d7d7be271bae032f65e76c743fb6b88ba7addc127f875d74e95f78
cat-searcher/leandojo-benchmark-4-random
test
1,823
Polynomial.ker_mapRingHom
Mathlib/RingTheory/Polynomial/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Ideal.mem_map_C_iff</a>, <a>Polynomial.ext_iff</a>]
case h R : Type u S : Type u_1 inst✝¹ : CommSemiring R inst✝ : Semiring S f : R →+* S x✝ : R[X] ⊢ (↑↑(mapRingHom f)).toFun x✝ = 0 ↔ x✝ ∈ map C (RingHom.ker f)
case h R : Type u S : Type u_1 inst✝¹ : CommSemiring R inst✝ : Semiring S f : R →+* S x✝ : R[X] ⊢ (∀ (n : ℕ), ((↑↑(mapRingHom f)).toFun x✝).coeff n = coeff 0 n) ↔ ∀ (n : ℕ), x✝.coeff n ∈ RingHom.ker f
((:c Iff) ((:c Eq) ((:c Polynomial) (:fv _uniq.145364) (:fv _uniq.145370)) ((:c OneHom.toFun) ((:c Polynomial) (:fv _uniq.145361) ((:c CommSemiring.toSemiring) (:fv _uniq.145361) (:fv _uniq.145367))) ((:c Polynomial) (:fv _uniq.145364) (:fv _uniq.145370)) ((:c MulOneClass.toOne) ((:c Polynomial) (:fv _uniq.145361) ((:c...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CommSemiring) (:fv _uniq.145361))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.145364))"},{"name":"f","sexp":"((:c RingHom) (:fv _uniq.145361) (:fv _uniq.145364) ((:c Semiring.toNonAssocSemiring) (:fv _un...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 1 (:app (:c OneHom.toFun) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.145361","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.145364","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"rw","sourceEnd":25229,"sourceStart":25227,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":25231,"sourceStart":25230,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Ideal.mem_map_C_...
[]
[{"source":"mem_map_C_iff","source_end":25244,"source_start":25231,"syntax_kind":"ident"},{"source":"Polynomial.ext_iff","source_end":25264,"source_start":25246,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.145361","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.145364","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal...
158
6
exact
true
1
6
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d670b1c79358f6db3e09abe4f0c2b5b75beed27ff82abf2d40e42f9bdb862591
ac075e90d0d7d7be271bae032f65e76c743fb6b88ba7addc127f875d74e95f78
06ae0f329f7b5524238263e35725af8ac0d620a083d33b961444dac78e0c53de
2fc9c5b84d0a1c77d5d7f76cbb18a2b1e37a0829bee877588b82c190b5e23bb3
cat-searcher/leandojo-benchmark-4-random
test
1,824
Polynomial.ker_mapRingHom
Mathlib/RingTheory/Polynomial/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp_rw [<a>RingHom.mem_ker</a> f]
case h R : Type u S : Type u_1 inst✝¹ : CommSemiring R inst✝ : Semiring S f : R →+* S x✝ : R[X] ⊢ (∀ (n : ℕ), ((↑↑(mapRingHom f)).toFun x✝).coeff n = coeff 0 n) ↔ ∀ (n : ℕ), x✝.coeff n ∈ RingHom.ker f
case h R : Type u S : Type u_1 inst✝¹ : CommSemiring R inst✝ : Semiring S f : R →+* S x✝ : R[X] ⊢ (∀ (n : ℕ), ((↑↑(mapRingHom f)).toFun x✝).coeff n = coeff 0 n) ↔ ∀ (n : ℕ), f (x✝.coeff n) = 0
((:c Iff) (:forall n (:c Nat) ((:c Eq) (:fv _uniq.145364) ((:c Polynomial.coeff) (:fv _uniq.145364) (:fv _uniq.145370) ((:c OneHom.toFun) ((:c Polynomial) (:fv _uniq.145361) ((:c CommSemiring.toSemiring) (:fv _uniq.145361) (:fv _uniq.145367))) ((:c Polynomial) (:fv _uniq.145364) (:fv _uniq.145370)) ((:c MulOneClass.toO...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CommSemiring) (:fv _uniq.145361))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.145364))"},{"name":"f","sexp":"((:c RingHom) (:fv _uniq.145361) (:fv _uniq.145364) ((:c Semiring.toNonAssocSemiring) (:fv _un...
(:app (:c Iff) (:arg :explicit 0 (:forall n :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Polynomial.coeff) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c OneHom.toFun) (:a...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.145361","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.145364","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"simp_rw","sourceEnd":25275,"sourceStart":25268,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":25277,"sourceStart":25276,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name"...
[]
[{"source":"RingHom.mem_ker f","source_end":25294,"source_start":25277,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.145361","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.145364","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal...
158
10
exact
true
1
6
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d16883117dff626347dba8ab8492bfe56c2594caf13a29a9861966f6a9de0463
2fc9c5b84d0a1c77d5d7f76cbb18a2b1e37a0829bee877588b82c190b5e23bb3
526b80676cbf33de679abba6200fe4136ed994d5eee4536029ca48ef2def7ba1
349a47c4fd5bc4e7043c6b1f1cc731b7ba38d6fb43250021163d5c31d329e114
cat-searcher/leandojo-benchmark-4-random
test
1,825
Polynomial.ker_mapRingHom
Mathlib/RingTheory/Polynomial/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
case h R : Type u S : Type u_1 inst✝¹ : CommSemiring R inst✝ : Semiring S f : R →+* S x✝ : R[X] ⊢ (∀ (n : ℕ), ((↑↑(mapRingHom f)).toFun x✝).coeff n = coeff 0 n) ↔ ∀ (n : ℕ), f (x✝.coeff n) = 0
((:c Iff) (:forall n (:c Nat) ((:c Eq) (:fv _uniq.145364) ((:c Polynomial.coeff) (:fv _uniq.145364) (:fv _uniq.145370) ((:c OneHom.toFun) ((:c Polynomial) (:fv _uniq.145361) ((:c CommSemiring.toSemiring) (:fv _uniq.145361) (:fv _uniq.145367))) ((:c Polynomial) (:fv _uniq.145364) (:fv _uniq.145370)) ((:c MulOneClass.toO...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CommSemiring) (:fv _uniq.145361))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.145364))"},{"name":"f","sexp":"((:c RingHom) (:fv _uniq.145361) (:fv _uniq.145364) ((:c Semiring.toNonAssocSemiring) (:fv _un...
(:app (:c Iff) (:arg :explicit 0 (:forall n :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Polynomial.coeff) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c OneHom.toFun) (:a...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.145361","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.145364","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"simp","sourceEnd":25302,"sourceStart":25298,"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.145361","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.145364","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal...
158
13
exact
true
1
6
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
24d6eaadb6fade28e1041b0f30442367553f09f3ee03769191458cf584609c34
349a47c4fd5bc4e7043c6b1f1cc731b7ba38d6fb43250021163d5c31d329e114
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,826
Seminorm.neg_ball
Mathlib/Analysis/Seminorm.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
ext
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 h 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 Eq) ((:c Set) (:fv _uniq.798946)) ((:c Neg.neg) ((:c Set) (:fv _uniq.798946)) ((:c Set.neg) (:fv _uniq.798946) ((:c NegZeroClass.toNeg) (:fv _uniq.798946) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.798946) ((:c SubtractionMonoid.toSubNegZeroMonoid) (:fv _uniq.798946) ((:c SubtractionCommMonoid.toSubtractionM...
[{"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 Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :explicit 1 (:app (:c Neg.neg) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV6))))))) (:arg :explicit 2...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.798928","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.798931","is_instance":false,"is_let":false,"name":"R'","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"ext","sourceEnd":41104,"sourceStart":41101,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":41104,"sourceStart":41101,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.798928","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.798931","is_instance":false,"is_let":false,"user_name":"R'"},{"binder_role":":implicit","context_index":2,"internal_name":"...
284
4
exact
true
1
24
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
11ec1d8179d12c9ae8951c31b32858526059e957b40af8ec36a4f92f2befeb4b
b71624ee4ca313301e07e5479dd7a21878ea5164b6e9a181714dfdc227efdf96
a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de
430ed73a5b3216a0b48456c39ed2308b9d914872e4d21397c9bc519a2f1f110d
cat-searcher/leandojo-benchmark-4-random
test
1,827
Seminorm.neg_ball
Mathlib/Analysis/Seminorm.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Set.mem_neg</a>, <a>Seminorm.mem_ball</a>, <a>Seminorm.mem_ball</a>, ← <a>neg_add'</a>, <a>sub_neg_eq_add</a>, <a>AddGroupSeminormClass.map_neg_eq_map</a>]
case h 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 Iff) ((:c Membership.mem) (:fv _uniq.798946) ((:c Set) (:fv _uniq.798946)) ((:c Set.instMembership) (:fv _uniq.798946)) (:fv _uniq.805378) ((:c Neg.neg) ((:c Set) (:fv _uniq.798946)) ((:c Set.neg) (:fv _uniq.798946) ((:c NegZeroClass.toNeg) (:fv _uniq.798946) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.798946...
[{"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 Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6))))))) (:arg :e...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.798928","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.798931","is_instance":false,"is_let":false,"name":"R'","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"rw","sourceEnd":41109,"sourceStart":41107,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":41111,"sourceStart":41110,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.mem_neg","se...
[]
[{"source":"Set.mem_neg","source_end":41122,"source_start":41111,"syntax_kind":"ident"},{"source":"mem_ball","source_end":41132,"source_start":41124,"syntax_kind":"ident"},{"source":"mem_ball","source_end":41142,"source_start":41134,"syntax_kind":"ident"},{"source":"neg_add'","source_end":41156,"source_start":41148,"sy...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.798928","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.798931","is_instance":false,"is_let":false,"user_name":"R'"},{"binder_role":":implicit","context_index":2,"internal_name":"...
284
5
exact
true
1
25
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1b1c0ecada78845582b8bbfc2aeaf2901c458db8dec273372c093534d7574378
430ed73a5b3216a0b48456c39ed2308b9d914872e4d21397c9bc519a2f1f110d
fd838eb70a6aef8c2e0ebe36749b1e95b7a8fd49970e2b0b66ff3f285a1f5ae4
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,828
Finset.sigmaLift_nonempty
Mathlib/Data/Finset/Sigma.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp_rw [<a>Finset.nonempty_iff_ne_empty</a>, <a>Finset.sigmaLift</a>]
ι : Type u_1 α : ι → Type u_2 β : ι → Type u_3 γ : ι → Type u_4 inst✝ : DecidableEq ι f g : ⦃i : ι⦄ → α i → β i → Finset (γ i) a : (i : ι) × α i b : (i : ι) × β i ⊢ (sigmaLift f a b).Nonempty ↔ ∃ (h : a.fst = b.fst), (f (h ▸ a.snd) b.snd).Nonempty
ι : Type u_1 α : ι → Type u_2 β : ι → Type u_3 γ : ι → Type u_4 inst✝ : DecidableEq ι f g : ⦃i : ι⦄ → α i → β i → Finset (γ i) a : (i : ι) × α i b : (i : ι) × β i ⊢ (if h : a.fst = b.fst then map (Embedding.sigmaMk b.fst) (f (h ▸ a.snd) b.snd) else ∅) ≠ ∅ ↔ ∃ (h : a.fst = b.fst), f (⋯ ▸ a.snd) b.snd ≠ ∅
((:c Iff) ((:c Finset.Nonempty) ((:c Sigma) (:fv _uniq.27959) (:fv _uniq.27974)) ((:c Finset.sigmaLift) (:fv _uniq.27959) (:fv _uniq.27964) (:fv _uniq.27969) (:fv _uniq.27974) (:fv _uniq.27981) (:fv _uniq.27994) (:fv _uniq.28015) (:fv _uniq.28025))) ((:c Exists) ((:c Eq) (:fv _uniq.27959) ((:c Sigma.fst) (:fv _uniq.279...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:forall _ (:fv _uniq.27959) (:sort (+ u_2 1)))"},{"name":"β","sexp":"(:forall _ (:fv _uniq.27959) (:sort (+ u_3 1)))"},{"name":"γ","sexp":"(:forall _ (:fv _uniq.27959) (:sort (+ u_4 1)))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.27959))"},{"name...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Finset.Nonempty) (:arg :implicit-type 0 (:app (:c Sigma) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)))) (:arg :explicit 1 (:app (:c Finset.sigmaLift) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :implicit 2) (:arg :implicit 3) (:arg :instance 4 ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27959","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27964","is_instance":false,"is_let":false,"name":"α","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"}...
{"children":[{"source":"simp_rw","sourceEnd":8485,"sourceStart":8478,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8487,"sourceStart":8486,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.nonempty...
[]
[{"source":"nonempty_iff_ne_empty","source_end":8508,"source_start":8487,"syntax_kind":"ident"},{"source":"sigmaLift","source_end":8519,"source_start":8510,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27959","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27964","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
53
4
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
51434c7b5058e35dc429a8cb0320211eeef739e3b2b5cb2968d1571637ea0f97
bdfc534d2dd5723f78192cd011d7b94e04ada4c75dba4b4c848a002c357dcf7d
d7d72ebb1467d372aecff619e268a141452346719cd8162b119659cbbd1c265a
c300c3996be99caab6f1daf3df7ded1a896d4895130ba13d7f229597e50dd223
cat-searcher/leandojo-benchmark-4-random
test
1,829
Finset.sigmaLift_nonempty
Mathlib/Data/Finset/Sigma.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
split_ifs with h <;> simp [h]
ι : Type u_1 α : ι → Type u_2 β : ι → Type u_3 γ : ι → Type u_4 inst✝ : DecidableEq ι f g : ⦃i : ι⦄ → α i → β i → Finset (γ i) a : (i : ι) × α i b : (i : ι) × β i ⊢ (if h : a.fst = b.fst then map (Embedding.sigmaMk b.fst) (f (h ▸ a.snd) b.snd) else ∅) ≠ ∅ ↔ ∃ (h : a.fst = b.fst), f (⋯ ▸ a.snd) b.snd ≠ ∅
((:c Iff) ((:c Ne) ((:c Finset) ((:c Sigma) (:fv _uniq.27959) (:fv _uniq.27974))) ((:c dite) ((:c Finset) ((:c Sigma) (:fv _uniq.27959) (:fv _uniq.27974))) ((:c Eq) (:fv _uniq.27959) ((:c Sigma.fst) (:fv _uniq.27959) (:fv _uniq.27964) (:fv _uniq.28015)) ((:c Sigma.fst) (:fv _uniq.27959) (:fv _uniq.27969) (:fv _uniq.280...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:forall _ (:fv _uniq.27959) (:sort (+ u_2 1)))"},{"name":"β","sexp":"(:forall _ (:fv _uniq.27959) (:sort (+ u_3 1)))"},{"name":"γ","sexp":"(:forall _ (:fv _uniq.27959) (:sort (+ u_4 1)))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.27959))"},{"name...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Ne) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:app (:c Sigma) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)))))) (:arg :explicit 1 (:app (:c dite) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:app (:c Sigma) (:arg :implicit-type...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27959","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27964","is_instance":false,"is_let":false,"name":"α","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"}...
{"children":[{"children":[{"source":"split_ifs","sourceEnd":8532,"sourceStart":8523,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"with","sourceEnd":8537,"sourceStart":8533,"tag":"atom"},{"children":[{"children":[{"source":"h","sourceEnd":8539,"sourceStart":8538,"tag":"iden...
[]
[{"source":"h","source_end":8551,"source_start":8550,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27959","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27964","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
53
8
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1492cb16e997e7596e25ba330c2e351a29b984f9a0ab73b2e29da58cada305cc
c300c3996be99caab6f1daf3df7ded1a896d4895130ba13d7f229597e50dd223
967de915a4bca2de7578bb7c1d71b707362e00ce57612b82ae6b17853f81e240
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,830
Affine.Simplex.circumsphere_reindex
Mathlib/Geometry/Euclidean/Circumcenter.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine s.circumsphere_unique_dist_eq.2 _ ⟨?_, ?_⟩ <;> rw [← s.reindex_range_points e]
V : Type u_1 P : Type u_2 inst✝³ : NormedAddCommGroup V inst✝² : InnerProductSpace ℝ V inst✝¹ : MetricSpace P inst✝ : NormedAddTorsor V P m n : ℕ s : Simplex ℝ P m e : Fin (m + 1) ≃ Fin (n + 1) ⊢ (s.reindex e).circumsphere = s.circumsphere
case refine_1 V : Type u_1 P : Type u_2 inst✝³ : NormedAddCommGroup V inst✝² : InnerProductSpace ℝ V inst✝¹ : MetricSpace P inst✝ : NormedAddTorsor V P m n : ℕ s : Simplex ℝ P m e : Fin (m + 1) ≃ Fin (n + 1) ⊢ (s.reindex e).circumsphere.center ∈ affineSpan ℝ (Set.range (s.reindex e).points) case refine_2 V : Type u_1 P...
((:c Eq) ((:c EuclideanGeometry.Sphere) (:fv _uniq.181672) (:fv _uniq.181691)) ((:c Affine.Simplex.circumsphere) (:fv _uniq.181669) (:fv _uniq.181672) (:fv _uniq.181675) (:fv _uniq.181688) (:fv _uniq.181691) (:fv _uniq.181979) (:fv _uniq.183198) ((:c Affine.Simplex.reindex) (:c Real) (:fv _uniq.181669) (:fv _uniq.18167...
[{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.181669))"},{"name":"inst✝²","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.181669) (:c Real.RCLike) (:fv _uniq.181675))"},{"name":"inst✝¹","sexp":"((:c MetricSpace) (:fv _u...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c EuclideanGeometry.Sphere) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c MetricSpace) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 1 (:app (:c Affine.Simplex.circumsphere) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:ar...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.181669","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.181672","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"children":[{"source":"refine","sourceEnd":19361,"sourceStart":19355,"tag":"atom"},{"children":[{"children":[{"source":"s.circumsphere_unique_dist_eq","sourceEnd":19391,"sourceStart":19362,"tag":"identifier"},{"source":".","sourceEnd":19392,"sourceStart":19391,"tag":"atom"},{"children":[{"source":"2","sou...
[]
[{"source":"s.circumsphere_unique_dist_eq.2 _ ⟨?_, ?_⟩","source_end":19408,"source_start":19362,"syntax_kind":"Lean.Parser.Term.app"},{"source":"s.reindex_range_points e","source_end":19445,"source_start":19421,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.181669","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.181672","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal...
55
4
exact
true
1
10
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0f2e9430a1f211d19970e6fbb49021ae315a8e292b4e14854a915e7987bea592
724b6efd29847d6bad11049b2993556beb9b2326770a905d438d5a3eabbe0cb4
5237006e3d4f3a2fc5fe027a1440c47077f0255ead4e266b5f5590ec1d2d6bda
5aa6cec18745e6295e07217b0145cce993412b5bf9290527aebc2d8b26d1ded5
cat-searcher/leandojo-benchmark-4-random
test
1,831
Affine.Simplex.circumsphere_reindex
Mathlib/Geometry/Euclidean/Circumcenter.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact (s.reindex e).<a>Affine.Simplex.circumsphere_unique_dist_eq</a>.1.1
case refine_1 V : Type u_1 P : Type u_2 inst✝³ : NormedAddCommGroup V inst✝² : InnerProductSpace ℝ V inst✝¹ : MetricSpace P inst✝ : NormedAddTorsor V P m n : ℕ s : Simplex ℝ P m e : Fin (m + 1) ≃ Fin (n + 1) ⊢ (s.reindex e).circumsphere.center ∈ affineSpan ℝ (Set.range (s.reindex e).points)
((:c Membership.mem) (:fv _uniq.181672) ((:c AffineSubspace) (:c Real) (:fv _uniq.181669) (:fv _uniq.181672) (:c Real.instRing) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.181669) (:fv _uniq.181675)) ((:c NormedSpace.toModule) (:c Real) (:fv _uniq.181669) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminorme...
[{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.181669))"},{"name":"inst✝²","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.181669) (:c Real.RCLike) (:fv _uniq.181675))"},{"name":"inst✝¹","sexp":"((:c MetricSpace) (:fv _u...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c AffineSubspace) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:c Real))))) (:arg :instance 4 (:instance-of (:app (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.181669","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.181672","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":19457,"sourceStart":19452,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"(","sourceEnd":19459,"sourceStart":19458,"tag":"atom"},{"children":[{"source":"s.reindex","sourceEnd":19468,"sourceStart":19459,"tag":"...
[]
[{"source":"(s.reindex e).circumsphere_unique_dist_eq.1.1","source_end":19503,"source_start":19458,"syntax_kind":"Lean.Parser.Term.proj"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.181669","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.181672","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal...
55
15
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0a6d51fcf149db8f4fea3481380ccde0b4e80cdda7cb9f65c14961c7d0c04da1
b35100d105c252122383e95f8fcd4574d75fe9112d6ba09476de4ab065cb187a
2c41da08567b64494faa0b63f70676071bba69f9a35a5ddf4128474707121294
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,832
Affine.Simplex.circumsphere_reindex
Mathlib/Geometry/Euclidean/Circumcenter.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact (s.reindex e).<a>Affine.Simplex.circumsphere_unique_dist_eq</a>.1.2
case refine_2 V : Type u_1 P : Type u_2 inst✝³ : NormedAddCommGroup V inst✝² : InnerProductSpace ℝ V inst✝¹ : MetricSpace P inst✝ : NormedAddTorsor V P m n : ℕ s : Simplex ℝ P m e : Fin (m + 1) ≃ Fin (n + 1) ⊢ Set.range (s.reindex e).points ⊆ Metric.sphere (s.reindex e).circumsphere.center (s.reindex e).circumsphere.ra...
((:c HasSubset.Subset) ((:c Set) (:fv _uniq.181672)) ((:c Set.instHasSubset) (:fv _uniq.181672)) ((:c Set.range) (:fv _uniq.181672) ((:c Fin) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.183198) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) ((:c Af...
[{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.181669))"},{"name":"inst✝²","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.181669) (:c Real.RCLike) (:fv _uniq.181675))"},{"name":"inst✝¹","sexp":"((:c MetricSpace) (:fv _u...
(:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 2 (:app (:c Set.range) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.181669","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.181672","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":19514,"sourceStart":19509,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"(","sourceEnd":19516,"sourceStart":19515,"tag":"atom"},{"children":[{"source":"s.reindex","sourceEnd":19525,"sourceStart":19516,"tag":"...
[]
[{"source":"(s.reindex e).circumsphere_unique_dist_eq.1.2","source_end":19560,"source_start":19515,"syntax_kind":"Lean.Parser.Term.proj"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.181669","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.181672","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal...
55
20
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
50edac9859ff9813d663a0df0f372c03e611ba24a39d8d30d6c2fb3fca4b8f97
570f4f4d64c0e67163d5c262f491670e0756243e1c6c3ed658a1ad996f08f61b
b243f903569d5e33e43be2718446e00e50c6d9ed95021cfdb14069105db98b86
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,833
Pi.basisFun_repr
Mathlib/LinearAlgebra/StdBasis.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>Pi.basisFun</a>]
R : Type u_1 η : Type u_2 ιs : η → Type u_3 Ms : η → Type u_4 inst✝³ : Semiring R inst✝² : (i : η) → AddCommMonoid (Ms i) inst✝¹ : (i : η) → Module R (Ms i) inst✝ : Finite η x : η → R i : η ⊢ ((basisFun R η).repr x) i = x i
((:c Eq) (:fv _uniq.96514) ((:c DFunLike.coe) ((:c Finsupp) (:fv _uniq.96517) (:fv _uniq.96514) ((:c MonoidWithZero.toZero) (:fv _uniq.96514) ((:c Semiring.toMonoidWithZero) (:fv _uniq.96514) (:fv _uniq.96530)))) (:fv _uniq.96517) (:lambda _ (:fv _uniq.96517) (:fv _uniq.96514)) ((:c Finsupp.instFunLike) (:fv _uniq.9651...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"η","sexp":"(:sort (+ u_2 1))"},{"name":"ιs","sexp":"(:forall _ (:fv _uniq.96517) (:sort (+ u_3 1)))"},{"name":"Ms","sexp":"(:forall _ (:fv _uniq.96517) (:sort (+ u_4 1)))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.96514))"},{"name":"inst✝²","sexp":"(:forall i ...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Finsupp) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:fv FV0))))))) (:arg :implicit-type 1 (:fv FV1)) (:arg :implici...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.96514","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.96517","is_instance":false,"is_let":false,"name":"η","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":11882,"sourceStart":11878,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...
[]
[{"source":"basisFun","source_end":11892,"source_start":11884,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.96514","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.96517","is_instance":false,"is_let":false,"user_name":"η"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
68
2
exact
true
1
10
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
6fe9abad9a6522bfa0c986c0201d8587a4b977a7eaff1be8946211b9be61ed46
7f1017a633709ac6ea7a67af55bc621802e5d317e1cef681c4efc47f0711cb4d
315d7c7a5d898abbc544e2ac38a350ab28ab828d291c33c965aa9e7bb156da56
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,834
Set.projIic_eq_self
Mathlib/Order/Interval/Set/ProjIcc.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>Set.projIic</a>, <a>Subtype.ext_iff</a>]
α : Type u_1 β : Type u_2 inst✝ : LinearOrder α a b : α h : a ≤ b x : α ⊢ projIic b x = ⟨b, ⋯⟩ ↔ b ≤ x
((:c Iff) ((:c Eq) ((:c Set.Elem) (:fv _uniq.7500) ((:c Set.Iic) (:fv _uniq.7500) ((:c PartialOrder.toPreorder) (:fv _uniq.7500) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.7500) ((:c Lattice.toSemilatticeInf) (:fv _uniq.7500) ((:c DistribLattice.toLattice) (:fv _uniq.7500) ((:c instDistribLatticeOfLinearOrder) (:fv...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.7500))"},{"name":"a","sexp":"(:fv _uniq.7500)"},{"name":"b","sexp":"(:fv _uniq.7500)"},{"name":"h","sexp":"((:c LE.le) (:fv _uniq.7500) ((:c Preorder.toLE) (:fv _uniq.7500) ((:c PartialO...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set.Iic) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV4)))))) (:arg :e...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7500","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7503","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":3864,"sourceStart":3860,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn...
[]
[{"source":"projIic","source_end":3873,"source_start":3866,"syntax_kind":"ident"},{"source":"Subtype.ext_iff","source_end":3890,"source_start":3875,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7500","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7503","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
36
2
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4b4ef66c581f2c9dabeb3369f39eecca35b01bf110c3722c423c36cf04d9aee0
23d748929f7877788383a2407508291f907f53a48e1475fa67a7e10ee2e5de3d
34a54a6dcf2b8be62a5822f11301d6124267821e03b04009d37686b344cc9322
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,835
MeasureTheory.SimpleFunc.nnnorm_approxOn_le
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have := <a>MeasureTheory.SimpleFunc.edist_approxOn_le</a> hf h₀ x n
α : Type u_1 β : Type u_2 ι : Type u_3 E : Type u_4 F : Type u_5 𝕜 : Type u_6 inst✝⁵ : MeasurableSpace β inst✝⁴ : MeasurableSpace E inst✝³ : NormedAddCommGroup E inst✝² : NormedAddCommGroup F q : ℝ p : ℝ≥0∞ inst✝¹ : OpensMeasurableSpace E f : β → E hf : Measurable f s : Set E y₀ : E h₀ : y₀ ∈ s inst✝ : SeparableSpace ...
α : Type u_1 β : Type u_2 ι : Type u_3 E : Type u_4 F : Type u_5 𝕜 : Type u_6 inst✝⁵ : MeasurableSpace β inst✝⁴ : MeasurableSpace E inst✝³ : NormedAddCommGroup E inst✝² : NormedAddCommGroup F q : ℝ p : ℝ≥0∞ inst✝¹ : OpensMeasurableSpace E f : β → E hf : Measurable f s : Set E y₀ : E h₀ : y₀ ∈ s inst✝ : SeparableSpace ...
((:c LE.le) (:c NNReal) ((:c Preorder.toLE) (:c NNReal) ((:c PartialOrder.toPreorder) (:c NNReal) ((:c StrictOrderedSemiring.toPartialOrder) (:c NNReal) (:c instNNRealStrictOrderedSemiring)))) ((:c NNNorm.nnnorm) (:fv _uniq.1614) ((:c SeminormedAddGroup.toNNNorm) (:fv _uniq.1614) ((:c SeminormedAddCommGroup.toSeminorme...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"E","sexp":"(:sort (+ u_4 1))"},{"name":"F","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c MeasurableSpace) (:fv _uniq.1608))"},{"name":"in...
(:app (:c LE.le) (:arg :implicit-type 0 (:c NNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c NNReal))))) (:arg :explicit 2 (:app (:c NNNorm.nnnorm) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c NNNorm) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1605","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1608","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte...
{"children":[{"source":"have","sourceEnd":2412,"sourceStart":2408,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":2413,"sourceStart":2413,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":2413,"sourceStart":2413,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","...
[]
[{"source":"edist_approxOn_le hf h₀ x n","source_end":2445,"source_start":2416,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1605","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1608","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq...
13
4
exact
true
1
21
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0fc9511ab1a3daafa26de35f8080e9bc985123338b0b74b647438db759a4bfa1
8fff18f89c0d561c758eec872be3423d38f18586cd30f431850cf5cf6b73b3d9
9bf7e57aaa968292326cb7328fdff484a37bc39d668117a99b8fd25c1c7431ba
760ec1372d4274305ea4726f9eced851e6388e05823698919e9100303f463cae
cat-searcher/leandojo-benchmark-4-random
test
1,836
MeasureTheory.SimpleFunc.nnnorm_approxOn_le
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>PseudoEMetricSpace.edist_comm</a> y₀] at this
α : Type u_1 β : Type u_2 ι : Type u_3 E : Type u_4 F : Type u_5 𝕜 : Type u_6 inst✝⁵ : MeasurableSpace β inst✝⁴ : MeasurableSpace E inst✝³ : NormedAddCommGroup E inst✝² : NormedAddCommGroup F q : ℝ p : ℝ≥0∞ inst✝¹ : OpensMeasurableSpace E f : β → E hf : Measurable f s : Set E y₀ : E h₀ : y₀ ∈ s inst✝ : SeparableSpace ...
α : Type u_1 β : Type u_2 ι : Type u_3 E : Type u_4 F : Type u_5 𝕜 : Type u_6 inst✝⁵ : MeasurableSpace β inst✝⁴ : MeasurableSpace E inst✝³ : NormedAddCommGroup E inst✝² : NormedAddCommGroup F q : ℝ p : ℝ≥0∞ inst✝¹ : OpensMeasurableSpace E f : β → E hf : Measurable f s : Set E y₀ : E h₀ : y₀ ∈ s inst✝ : SeparableSpace ...
((:c LE.le) (:c NNReal) ((:c Preorder.toLE) (:c NNReal) ((:c PartialOrder.toPreorder) (:c NNReal) ((:c StrictOrderedSemiring.toPartialOrder) (:c NNReal) (:c instNNRealStrictOrderedSemiring)))) ((:c NNNorm.nnnorm) (:fv _uniq.1614) ((:c SeminormedAddGroup.toNNNorm) (:fv _uniq.1614) ((:c SeminormedAddCommGroup.toSeminorme...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"E","sexp":"(:sort (+ u_4 1))"},{"name":"F","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c MeasurableSpace) (:fv _uniq.1608))"},{"name":"in...
(:app (:c LE.le) (:arg :implicit-type 0 (:c NNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c NNReal))))) (:arg :explicit 2 (:app (:c NNNorm.nnnorm) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c NNNorm) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1605","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1608","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte...
{"children":[{"source":"rw","sourceEnd":2450,"sourceStart":2448,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2452,"sourceStart":2451,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"PseudoE...
[]
[{"source":"this","source_end":2476,"source_start":2472,"syntax_kind":"ident"},{"source":"edist_comm y₀","source_end":2467,"source_start":2452,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1605","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1608","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq...
13
5
exact
true
1
22
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b65b909ca9b153ac638798446b96723a5d88db6f05fb2cbaf9d1685853ea60e5
760ec1372d4274305ea4726f9eced851e6388e05823698919e9100303f463cae
23ac43c99e02f32dfdc7587ea47bcdb3851497f636133be8f504d247ae9051d5
60a70c3ae1e41b94476fca706bde3b196f319dfd1a3c22b921eb7d5c2cfa4564
cat-searcher/leandojo-benchmark-4-random
test
1,837
MeasureTheory.SimpleFunc.nnnorm_approxOn_le
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>edist_nndist</a>, <a>nndist_eq_nnnorm</a>] at this
α : Type u_1 β : Type u_2 ι : Type u_3 E : Type u_4 F : Type u_5 𝕜 : Type u_6 inst✝⁵ : MeasurableSpace β inst✝⁴ : MeasurableSpace E inst✝³ : NormedAddCommGroup E inst✝² : NormedAddCommGroup F q : ℝ p : ℝ≥0∞ inst✝¹ : OpensMeasurableSpace E f : β → E hf : Measurable f s : Set E y₀ : E h₀ : y₀ ∈ s inst✝ : SeparableSpace ...
α : Type u_1 β : Type u_2 ι : Type u_3 E : Type u_4 F : Type u_5 𝕜 : Type u_6 inst✝⁵ : MeasurableSpace β inst✝⁴ : MeasurableSpace E inst✝³ : NormedAddCommGroup E inst✝² : NormedAddCommGroup F q : ℝ p : ℝ≥0∞ inst✝¹ : OpensMeasurableSpace E f : β → E hf : Measurable f s : Set E y₀ : E h₀ : y₀ ∈ s inst✝ : SeparableSpace ...
((:c LE.le) (:c NNReal) ((:c Preorder.toLE) (:c NNReal) ((:c PartialOrder.toPreorder) (:c NNReal) ((:c StrictOrderedSemiring.toPartialOrder) (:c NNReal) (:c instNNRealStrictOrderedSemiring)))) ((:c NNNorm.nnnorm) (:fv _uniq.1614) ((:c SeminormedAddGroup.toNNNorm) (:fv _uniq.1614) ((:c SeminormedAddCommGroup.toSeminorme...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"E","sexp":"(:sort (+ u_4 1))"},{"name":"F","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c MeasurableSpace) (:fv _uniq.1608))"},{"name":"in...
(:app (:c LE.le) (:arg :implicit-type 0 (:c NNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c NNReal))))) (:arg :explicit 2 (:app (:c NNNorm.nnnorm) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c NNNorm) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1605","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1608","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte...
{"children":[{"source":"simp","sourceEnd":2483,"sourceStart":2479,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":2488,"sourceStart":2484,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":2488,"s...
[]
[{"source":"edist_nndist","source_end":2502,"source_start":2490,"syntax_kind":"ident"},{"source":"nndist_eq_nnnorm","source_end":2520,"source_start":2504,"syntax_kind":"ident"},{"source":"this","source_end":2529,"source_start":2525,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1605","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1608","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq...
13
8
exact
true
1
22
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f3b1c084d87d870d6279811daab3a42ec66676f2c65985f50db1398e829dbb2a
60a70c3ae1e41b94476fca706bde3b196f319dfd1a3c22b921eb7d5c2cfa4564
fea2dd52f9c928d6096e76c73b115b8d41fb8ecbb6489da64f73dcec2a1ca617
3711abaeee30a0a0654844ead1ffc525c8220fa13b30f19369591daa51fba973
cat-searcher/leandojo-benchmark-4-random
test
1,838
MeasureTheory.SimpleFunc.nnnorm_approxOn_le
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact mod_cast this
α : Type u_1 β : Type u_2 ι : Type u_3 E : Type u_4 F : Type u_5 𝕜 : Type u_6 inst✝⁵ : MeasurableSpace β inst✝⁴ : MeasurableSpace E inst✝³ : NormedAddCommGroup E inst✝² : NormedAddCommGroup F q : ℝ p : ℝ≥0∞ inst✝¹ : OpensMeasurableSpace E f : β → E hf : Measurable f s : Set E y₀ : E h₀ : y₀ ∈ s inst✝ : SeparableSpace ...
((:c LE.le) (:c NNReal) ((:c Preorder.toLE) (:c NNReal) ((:c PartialOrder.toPreorder) (:c NNReal) ((:c StrictOrderedSemiring.toPartialOrder) (:c NNReal) (:c instNNRealStrictOrderedSemiring)))) ((:c NNNorm.nnnorm) (:fv _uniq.1614) ((:c SeminormedAddGroup.toNNNorm) (:fv _uniq.1614) ((:c SeminormedAddCommGroup.toSeminorme...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"E","sexp":"(:sort (+ u_4 1))"},{"name":"F","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c MeasurableSpace) (:fv _uniq.1608))"},{"name":"in...
(:app (:c LE.le) (:arg :implicit-type 0 (:c NNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c NNReal))))) (:arg :explicit 2 (:app (:c NNNorm.nnnorm) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c NNNorm) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1605","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1608","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte...
{"children":[{"source":"exact","sourceEnd":2537,"sourceStart":2532,"tag":"atom"},{"children":[{"source":"mod_cast","sourceEnd":2546,"sourceStart":2538,"tag":"atom"},{"contextIndex":22,"semanticRole":"local","source":"this","sourceEnd":2551,"sourceStart":2547,"tag":"identifier"}],"kind":"Lean.modCast","source":"mod_cast...
[]
[{"source":"mod_cast this","source_end":2551,"source_start":2538,"syntax_kind":"Lean.modCast"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1605","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1608","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq...
13
9
exact
true
1
22
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
eeb77055a453cd71d5012f7b4c195793bab4ef2cf72b46ef18f91d2fa93a101d
3711abaeee30a0a0654844ead1ffc525c8220fa13b30f19369591daa51fba973
e9f95273f233e6789fe850c2b1cb6f9e6f0c95fe3854c3b511336682f4da019f
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,839
Multiset.rel_refl_of_refl_on
Mathlib/Data/Multiset/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine m.induction_on ?_ ?_
α : Type u_1 β : Type v γ : Type u_2 δ : Type u_3 r✝ : α → β → Prop p : γ → δ → Prop m : Multiset α r : α → α → Prop ⊢ (∀ x ∈ m, r x x) → Rel r m m
case refine_1 α : Type u_1 β : Type v γ : Type u_2 δ : Type u_3 r✝ : α → β → Prop p : γ → δ → Prop m : Multiset α r : α → α → Prop ⊢ (∀ x ∈ 0, r x x) → Rel r 0 0 case refine_2 α : Type u_1 β : Type v γ : Type u_2 δ : Type u_3 r✝ : α → β → Prop p : γ → δ → Prop m : Multiset α r : α → α → Prop ⊢ ∀ (a : α) (s : Multiset α...
(:forall _ (:forall x (:fv _uniq.298103) (:forall _ ((:c Membership.mem) (:fv _uniq.298103) ((:c Multiset) (:fv _uniq.298103)) ((:c Multiset.instMembership) (:fv _uniq.298103)) 0 (:fv _uniq.298181)) ((:fv _uniq.298182) 1 1))) ((:c Multiset.Rel) (:fv _uniq.298103) (:fv _uniq.298103) (:fv _uniq.298182) (:fv _uniq.298181)...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"r✝","sexp":"(:forall _ (:fv _uniq.298103) (:forall _ (:fv _uniq.298105) (:sort 0)))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.298108) (:forall _ (:fv ...
(:forall _ :explicit (:forall x :explicit (:fv FV0) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Mu...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.298103","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.298105","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"refine","sourceEnd":115285,"sourceStart":115279,"tag":"atom"},{"children":[{"source":"m.induction_on","sourceEnd":115300,"sourceStart":115286,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":115302,"sourceStart":115301,"tag":"atom"},{"children":[{"source":"_","sourceEnd":1...
[]
[{"source":"m.induction_on ?_ ?_","source_end":115306,"source_start":115286,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.298103","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.298105","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
974
4
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
cd071ea9006fda77ca617862f3144e294e99fbf0e2d120bdbc696810039b9917
4bd20419a0d093ec49ed8970b5560e7fbe1e20aee5548fe53219cbf079c37601
3a26d0b9f6a22fba52a077437acb2495d01115c40b986c6bd7a56d342abcfce1
6714aadc61a8386b64c7e3d0b3655ab5ba8e2938940c1068eb1e7c3e781fd0af
cat-searcher/leandojo-benchmark-4-random
test
1,840
Multiset.rel_refl_of_refl_on
Mathlib/Data/Multiset/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intros
case refine_1 α : Type u_1 β : Type v γ : Type u_2 δ : Type u_3 r✝ : α → β → Prop p : γ → δ → Prop m : Multiset α r : α → α → Prop ⊢ (∀ x ∈ 0, r x x) → Rel r 0 0
case refine_1 α : Type u_1 β : Type v γ : Type u_2 δ : Type u_3 r✝ : α → β → Prop p : γ → δ → Prop m : Multiset α r : α → α → Prop a✝ : ∀ x ∈ 0, r x x ⊢ Rel r 0 0
(:forall _ (:forall x (:fv _uniq.298103) (:forall _ ((:c Membership.mem) (:fv _uniq.298103) ((:c Multiset) (:fv _uniq.298103)) ((:c Multiset.instMembership) (:fv _uniq.298103)) 0 ((:c OfNat.ofNat) ((:c Multiset) (:fv _uniq.298103)) (:lit 0) ((:c Zero.toOfNat0) ((:c Multiset) (:fv _uniq.298103)) ((:c Multiset.instZero) ...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"r✝","sexp":"(:forall _ (:fv _uniq.298103) (:forall _ (:fv _uniq.298105) (:sort 0)))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.298108) (:forall _ (:fv ...
(:forall _ :explicit (:forall x :explicit (:fv FV0) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Mu...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.298103","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.298105","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"intros","sourceEnd":115318,"sourceStart":115312,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.intros","source":"intros","sourceEnd":115318,"sourceStart":115312,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.298103","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.298105","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
974
9
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
159ae303662e12fb804c60c3b712bb05c4a9e31e55a02568993d9e6d325bc67c
e7ca098183151cfdf6af700161cc21ca6c3fdf114d7cd039378dd8fc66c55505
8a2c826875b67a30aac85e115b96c946e0338e1c0af119ef1ac259f27e74aee6
2e5b4e07b673913c7a24ca263267f80d753060429f9990da1473bb70d0351218
cat-searcher/leandojo-benchmark-4-random
test
1,841
Multiset.rel_refl_of_refl_on
Mathlib/Data/Multiset/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>Multiset.Rel.zero</a>
case refine_1 α : Type u_1 β : Type v γ : Type u_2 δ : Type u_3 r✝ : α → β → Prop p : γ → δ → Prop m : Multiset α r : α → α → Prop a✝ : ∀ x ∈ 0, r x x ⊢ Rel r 0 0
((:c Multiset.Rel) (:fv _uniq.298103) (:fv _uniq.298103) (:fv _uniq.298182) ((:c OfNat.ofNat) ((:c Multiset) (:fv _uniq.298103)) (:lit 0) ((:c Zero.toOfNat0) ((:c Multiset) (:fv _uniq.298103)) ((:c Multiset.instZero) (:fv _uniq.298103)))) ((:c OfNat.ofNat) ((:c Multiset) (:fv _uniq.298103)) (:lit 0) ((:c Zero.toOfNat0)...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"r✝","sexp":"(:forall _ (:fv _uniq.298103) (:forall _ (:fv _uniq.298105) (:sort 0)))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.298108) (:forall _ (:fv ...
(:app (:c Multiset.Rel) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.298103","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.298105","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"apply","sourceEnd":115328,"sourceStart":115323,"tag":"atom"},{"name":"Multiset.Rel.zero","semanticRole":"constructor","source":"Rel.zero","sourceEnd":115337,"sourceStart":115329,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Rel.zero","sourceEnd":115337,"sourceStart":1153...
[]
[{"source":"Rel.zero","source_end":115337,"source_start":115329,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.298103","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.298105","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
974
10
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
900d3fbf3582253f8bb344637dab3ee37d325010fc0e2ded00223147fb9b0645
2e5b4e07b673913c7a24ca263267f80d753060429f9990da1473bb70d0351218
5ce1c545efee864fb2325ce0148994657af39c7f6dc3bbc13bf750d85de9fc75
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,842
Multiset.rel_refl_of_refl_on
Mathlib/Data/Multiset/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro a m ih h
case refine_2 α : Type u_1 β : Type v γ : Type u_2 δ : Type u_3 r✝ : α → β → Prop p : γ → δ → Prop m : Multiset α r : α → α → Prop ⊢ ∀ (a : α) (s : Multiset α), ((∀ x ∈ s, r x x) → Rel r s s) → (∀ x ∈ a ::ₘ s, r x x) → Rel r (a ::ₘ s) (a ::ₘ s)
case refine_2 α : Type u_1 β : Type v γ : Type u_2 δ : Type u_3 r✝ : α → β → Prop p : γ → δ → Prop m✝ : Multiset α r : α → α → Prop a : α m : Multiset α ih : (∀ x ∈ m, r x x) → Rel r m m h : ∀ x ∈ a ::ₘ m, r x x ⊢ Rel r (a ::ₘ m) (a ::ₘ m)
(:forall a (:fv _uniq.298103) (:forall s ((:c Multiset) (:fv _uniq.298103)) (:forall _ (:forall _ (:forall x (:fv _uniq.298103) (:forall _ ((:c Membership.mem) (:fv _uniq.298103) ((:c Multiset) (:fv _uniq.298103)) ((:c Multiset.instMembership) (:fv _uniq.298103)) 0 1) ((:fv _uniq.298182) 1 1))) ((:c Multiset.Rel) (:fv ...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"r✝","sexp":"(:forall _ (:fv _uniq.298103) (:forall _ (:fv _uniq.298105) (:sort 0)))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.298108) (:forall _ (:fv ...
(:forall a :explicit (:fv FV0) (:forall s :explicit (:app (:c Multiset) (:arg :explicit 0 (:fv FV0))) (:forall _ :explicit (:forall _ :explicit (:forall x :explicit (:fv FV0) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Multiset) (:arg :explicit 0 (:f...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.298103","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.298105","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"intro","sourceEnd":115348,"sourceStart":115343,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":115350,"sourceStart":115349,"tag":"identifier"},{"semanticRole":"scoped_local","source":"m","sourceEnd":115352,"sourceStart":115351,"tag":"identifier"},{"semanticRole...
[{"role":"fresh_name","source":"a","source_end":115350,"source_start":115349,"syntax_kind":"ident"},{"role":"fresh_name","source":"m","source_end":115352,"source_start":115351,"syntax_kind":"ident"},{"role":"fresh_name","source":"ih","source_end":115355,"source_start":115353,"syntax_kind":"ident"},{"role":"fresh_name",...
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.298103","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.298105","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
974
15
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
136933c3bba739eb68b0901a204b8acf2efcf7861604e2a9b55453a691cd6278
33e088c9ce72ee7890067c2e85a90c595996a93ebc76bdc9ecc69a92f87ea4d2
9de929be52d8668227da4a3510e1953e7c7a6bd15c6068615f8a754ea6f143bd
209ce113f22be17ca64fc393041e49008dbd611a4b34f5d07dc8d43d9bb552d0
cat-searcher/leandojo-benchmark-4-random
test
1,843
Multiset.rel_refl_of_refl_on
Mathlib/Data/Multiset/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>Multiset.Rel.cons</a> (h _ (<a>Multiset.mem_cons_self</a> _ _)) (ih fun _ ha => h _ (<a>Multiset.mem_cons_of_mem</a> ha))
case refine_2 α : Type u_1 β : Type v γ : Type u_2 δ : Type u_3 r✝ : α → β → Prop p : γ → δ → Prop m✝ : Multiset α r : α → α → Prop a : α m : Multiset α ih : (∀ x ∈ m, r x x) → Rel r m m h : ∀ x ∈ a ::ₘ m, r x x ⊢ Rel r (a ::ₘ m) (a ::ₘ m)
((:c Multiset.Rel) (:fv _uniq.298103) (:fv _uniq.298103) (:fv _uniq.298182) ((:c Multiset.cons) (:fv _uniq.298103) (:fv _uniq.298238) (:fv _uniq.298241)) ((:c Multiset.cons) (:fv _uniq.298103) (:fv _uniq.298238) (:fv _uniq.298241)))
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"r✝","sexp":"(:forall _ (:fv _uniq.298103) (:forall _ (:fv _uniq.298105) (:sort 0)))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.298108) (:forall _ (:fv ...
(:app (:c Multiset.Rel) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:app (:c Multiset.cons) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV9)) (:arg :explicit 2 (:fv FV10)))) (:arg :explicit 4 (:app (:c Multiset.cons) (:arg :implicit-ty...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.298103","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.298105","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"exact","sourceEnd":115367,"sourceStart":115362,"tag":"atom"},{"children":[{"name":"Multiset.Rel.cons","semanticRole":"constructor","source":"Rel.cons","sourceEnd":115376,"sourceStart":115368,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":115378,"sourceStart":115377,"tag"...
[]
[{"source":"Rel.cons (h _ (mem_cons_self _ _)) (ih fun _ ha => h _ (mem_cons_of_mem ha))","source_end":115444,"source_start":115368,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.298103","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.298105","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
974
16
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
175165fa238d4bcc446c206fb1aab513dcdeadc8528059199a59334203092832
209ce113f22be17ca64fc393041e49008dbd611a4b34f5d07dc8d43d9bb552d0
3dcdd3df0f3de58f0426c8554fc157c486acf2248e11266ef91e6acbcffec33b
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,844
Real.cos_pi_div_four
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
trans <a>Real.cos</a> (π / 2 ^ 2)
x : ℝ ⊢ cos (π / 4) = √2 / 2
((:c Eq) (:c Real) ((:c Real.cos) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) (:c Real.pi) ((:c OfNat.ofNat) (:c Real) (:lit 4) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 4) (:c Real.instNatCast) ((:c instNatAtLeastTwo...
[{"name":"x","sexp":"(:c Real)"}]
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Real.cos) (:arg :explicit 0 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:c Real)) (:arg :explicit ...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.180085","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"}]
{"children":[{"children":[{"children":[{"children":[{"source":"trans","sourceEnd":32512,"sourceStart":32507,"tag":"atom"},{"children":[{"children":[{"name":"Real.cos","semanticRole":"global","source":"cos","sourceEnd":32516,"sourceStart":32513,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":3251...
[]
[{"source":"cos (π / 2 ^ 2)","source_end":32529,"source_start":32513,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.180085","is_instance":false,"is_let":false,"user_name":"x"}]
296
2
branch_opener
false
1
1
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a950d9957a987db0c9f2eeba1855f3cf378dd668e30f954715358591d9e1df88
a42a82f3bbba69b2ac3d5ff72363d2b3edb01122880dab6060cd9eaa51b29c48
c831606a980dc4afcd4c618dd2d1c2e86eb9188bb9ee10735e48d6f1bf79972c
254bcb4497d64a6fc4b16d7b88c0253a0d630b98c4c5651ed4415e1b67fbea7b
cat-searcher/leandojo-benchmark-4-random
test
1,845
Real.cos_pi_div_four
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
congr
x : ℝ ⊢ cos (π / 4) = cos (π / 2 ^ 2)
case e_x.e_a x : ℝ ⊢ 4 = 2 ^ 2
((:c Eq) (:c Real) ((:c Real.cos) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) (:c Real.pi) ((:c OfNat.ofNat) (:c Real) (:lit 4) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 4) (:c Real.instNatCast) ((:c instNatAtLeastTwo...
[{"name":"x","sexp":"(:c Real)"}]
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Real.cos) (:arg :explicit 0 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:c Real)) (:arg :explicit ...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.180085","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"}]
{"children":[{"source":"congr","sourceEnd":32540,"sourceStart":32535,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.congr","source":"congr","sourceEnd":32540,"sourceStart":32535,"tag":"node"}
[]
[]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.180085","is_instance":false,"is_let":false,"user_name":"x"}]
296
9
exact
true
1
1
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3d107486abd2c4137d3c437eeafbc49a8653f96ced74925e8569dd539ebdebcf
ee8df834feae6fc36129742b8f551923ca32a25cfe66998c654edcd6e5caecac
092b163cac48997cb6cc327c63cda260e694055f56ff3698a70cdfda80ffbb2b
12c6aa0a39c59ca6f7d9b30dba307b2ae1ac6a7e7999a51f407fa10287448171
cat-searcher/leandojo-benchmark-4-random
test
1,846
Real.cos_pi_div_four
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
norm_num
case e_x.e_a x : ℝ ⊢ 4 = 2 ^ 2
((:c Eq) (:c Real) ((:c OfNat.ofNat) (:c Real) (:lit 4) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 4) (:c Real.instNatCast) ((:c instNatAtLeastTwo) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNatPow) (:c...
[{"name":"x","sexp":"(:c Real)"}]
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 4)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:lit 4))))))) (:arg :explicit 2 (:app (:c HPow.hPow) (:arg :implicit-typ...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.180085","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"}]
{"children":[{"source":"norm_num","sourceEnd":32553,"sourceStart":32545,"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"}],"kind":"Mathl...
[]
[]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.180085","is_instance":false,"is_let":false,"user_name":"x"}]
296
10
exact
true
1
1
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b654cf3bc7ffb488e4f81a4385fa63d8cdc93a2f82a34125ac475f88faab8997
12c6aa0a39c59ca6f7d9b30dba307b2ae1ac6a7e7999a51f407fa10287448171
7c64df8336d5a348b5f037e1d91facb19224fdef00e798d5c48c07a184602a59
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,847
Real.cos_pi_div_four
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
x : ℝ ⊢ cos (π / 2 ^ 2) = √2 / 2
((:c Eq) (:c Real) ((:c Real.cos) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) (:c Real.pi) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNatPow) (:c Real) (:c Real.instMo...
[{"name":"x","sexp":"(:c Real)"}]
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Real.cos) (:arg :explicit 0 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:c Real)) (:arg :explicit ...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.180085","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"}]
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":32563,"sourceStart":32559,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","sour...
[]
[]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.180085","is_instance":false,"is_let":false,"user_name":"x"}]
296
13
exact
true
1
1
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ad0c26be3328d4d84580af60ad7cdc9aae563aea7eff0ad175acb5c5f6ab9c32
806c1c0164eabd8755c621a9ee0ce02dd2d37371ea44e95a44b7840317660283
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,848
zero_le_two
Mathlib/Algebra/Order/Monoid/NatCast.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>one_add_one_eq_two</a>]
α : Type u_1 inst✝³ : AddMonoidWithOne α inst✝² : Preorder α inst✝¹ : ZeroLEOneClass α inst✝ : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1 ⊢ 0 ≤ 2
α : Type u_1 inst✝³ : AddMonoidWithOne α inst✝² : Preorder α inst✝¹ : ZeroLEOneClass α inst✝ : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1 ⊢ 0 ≤ 1 + 1
((:c LE.le) (:fv _uniq.2770) ((:c Preorder.toLE) (:fv _uniq.2770) (:fv _uniq.3164)) ((:c OfNat.ofNat) (:fv _uniq.2770) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.2770) ((:c AddMonoid.toZero) (:fv _uniq.2770) ((:c AddMonoidWithOne.toAddMonoid) (:fv _uniq.2770) (:fv _uniq.2773))))) ((:c OfNat.ofNat) (:fv _uniq.2770) (:lit 2...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c AddMonoidWithOne) (:fv _uniq.2770))"},{"name":"inst✝²","sexp":"((:c Preorder) (:fv _uniq.2770))"},{"name":"inst✝¹","sexp":"((:c ZeroLEOneClass) (:fv _uniq.2770) ((:c AddMonoid.toZero) (:fv _uniq.2770) ((:c AddMonoidWithOne.toAddMonoid) (:fv _uniq.27...
(: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 OfNat.ofNat) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV0)) (:arg :exp...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2770","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2773","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c AddMonoidWithOne) (:arg :...
{"children":[{"source":"rw","sourceEnd":1187,"sourceStart":1185,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1189,"sourceStart":1188,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":1192,"sourceStart":...
[]
[{"source":"one_add_one_eq_two","source_end":1211,"source_start":1193,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2770","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2773","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":3,...
9
4
exact
true
1
5
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2a4b36712f1ac49dbc2196ba5ef2d353407799722774a715e8d127ca48b08c6b
93a825763b615c67696917d562999d60d9303199f6cf24430c0f31f122b298c2
416924c80b38138227816c8bc1acb1db1541fb23fbeff2c411606691cb13f47f
77d77cf2cc852973abba4248036c5dfccb6f7a784df3cbc478695a2262ec130e
cat-searcher/leandojo-benchmark-4-random
test
1,849
zero_le_two
Mathlib/Algebra/Order/Monoid/NatCast.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>add_nonneg</a> <a>zero_le_one</a> <a>zero_le_one</a>
α : Type u_1 inst✝³ : AddMonoidWithOne α inst✝² : Preorder α inst✝¹ : ZeroLEOneClass α inst✝ : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1 ⊢ 0 ≤ 1 + 1
((:c LE.le) (:fv _uniq.2770) ((:c Preorder.toLE) (:fv _uniq.2770) (:fv _uniq.3164)) ((:c OfNat.ofNat) (:fv _uniq.2770) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.2770) ((:c AddMonoid.toZero) (:fv _uniq.2770) ((:c AddMonoidWithOne.toAddMonoid) (:fv _uniq.2770) (:fv _uniq.2773))))) ((:c HAdd.hAdd) (:fv _uniq.2770) (:fv _uni...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c AddMonoidWithOne) (:fv _uniq.2770))"},{"name":"inst✝²","sexp":"((:c Preorder) (:fv _uniq.2770))"},{"name":"inst✝¹","sexp":"((:c ZeroLEOneClass) (:fv _uniq.2770) ((:c AddMonoid.toZero) (:fv _uniq.2770) ((:c AddMonoidWithOne.toAddMonoid) (:fv _uniq.27...
(: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 OfNat.ofNat) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV0)) (:arg :exp...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2770","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2773","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c AddMonoidWithOne) (:arg :...
{"children":[{"source":"exact","sourceEnd":1220,"sourceStart":1215,"tag":"atom"},{"children":[{"name":"add_nonneg","semanticRole":"global","source":"add_nonneg","sourceEnd":1231,"sourceStart":1221,"tag":"identifier"},{"children":[{"name":"zero_le_one","semanticRole":"global","source":"zero_le_one","sourceEnd":1243,"sou...
[]
[{"source":"add_nonneg zero_le_one zero_le_one","source_end":1255,"source_start":1221,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2770","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2773","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":3,...
9
7
exact
true
1
5
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
bd0fa21c6a6c8638deb1bd3ebda3bc4140bee371b7f256671618d5c03d48a1ff
77d77cf2cc852973abba4248036c5dfccb6f7a784df3cbc478695a2262ec130e
78dff1f9475530819f725bfa1366996a7f10e47b1b00c54a7941d2d93c8f0ff1
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,850
UpperHalfPlane.im_inv_neg_coe_pos
Mathlib/Analysis/Complex/UpperHalfPlane/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simpa using <a>div_pos</a> z.property (<a>UpperHalfPlane.normSq_pos</a> z)
z : ℍ ⊢ 0 < (-↑z)⁻¹.im
((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Complex.im) ((:c Inv.inv) (:c Complex) (:c Complex.instInv) ((:c Neg.neg) (:c Complex) (:c Complex.instNeg) ((:c UpperHalfPlane.coe) (:fv _uniq.14025))))))
[{"name":"z","sexp":"(:c UpperHalfPlane)"}]
(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.14025","is_instance":false,"is_let":false,"name":"z","sexp":"(:c UpperHalfPlane)"}]
{"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":6007,"sourceStart":6002,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":...
[]
[{"source":"div_pos z.property (normSq_pos z)","source_end":6047,"source_start":6014,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.14025","is_instance":false,"is_let":false,"user_name":"z"}]
65
2
exact
true
1
1
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
67cf02e5d26032a82b085367545bfdbf9db82dda1490b9058f7d1d3e77874783
d93f163db25e4b4238fab72736ff43df42f3bb43e046330b85eea6d59fdfb0f1
851b7df20cc8ec551cd045be4654098c47c9d8cad27ffdbba13948301ff43354
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,851
LieDerivation.coe_ad_apply_eq_ad_apply
Mathlib/Algebra/Lie/Derivation/AdjointAction.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
ext
R : Type u_1 L : Type u_2 inst✝² : CommRing R inst✝¹ : LieRing L inst✝ : LieAlgebra R L x : L ⊢ ↑((ad R L) x) = (LieAlgebra.ad R L) x
case h R : Type u_1 L : Type u_2 inst✝² : CommRing R inst✝¹ : LieRing L inst✝ : LieAlgebra R L x x✝ : L ⊢ ↑((ad R L) x) x✝ = ((LieAlgebra.ad R L) x) x✝
((:c Eq) ((:c LinearMap) (:fv _uniq.6136) (:fv _uniq.6136) ((:c CommSemiring.toSemiring) (:fv _uniq.6136) ((:c CommRing.toCommSemiring) (:fv _uniq.6136) (:fv _uniq.6142))) ((:c CommSemiring.toSemiring) (:fv _uniq.6136) ((:c CommRing.toCommSemiring) (:fv _uniq.6136) (:fv _uniq.6142))) ((:c RingHom.id) (:fv _uniq.6136) (...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CommRing) (:fv _uniq.6136))"},{"name":"inst✝¹","sexp":"((:c LieRing) (:fv _uniq.6139))"},{"name":"inst✝","sexp":"((:c LieAlgebra) (:fv _uniq.6136) (:fv _uniq.6139) (:fv _uniq.6142) (:fv _uniq.6145))"},{"name":...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 4 (:app (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6136","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6139","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"ext","sourceEnd":2051,"sourceStart":2048,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":2051,"sourceStart":2048,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6136","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6139","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
6
4
exact
true
1
6
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
567846b9ec9b57a2158e1b057423eb8d16dc50a60efa114bf3464dd62a115929
42938b52ad5dd3df6ff520a7c6376812a6a115e71a2cb52bd85cdf4b2786a9df
a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de
341b244205799be449b494ec1445ed97ecad83c2fb80c4caca7e644b55dc2ebf
cat-searcher/leandojo-benchmark-4-random
test
1,852
LieDerivation.coe_ad_apply_eq_ad_apply
Mathlib/Algebra/Lie/Derivation/AdjointAction.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
case h R : Type u_1 L : Type u_2 inst✝² : CommRing R inst✝¹ : LieRing L inst✝ : LieAlgebra R L x x✝ : L ⊢ ↑((ad R L) x) x✝ = ((LieAlgebra.ad R L) x) x✝
((:c Eq) (:fv _uniq.6139) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.6136) (:fv _uniq.6136) ((:c CommSemiring.toSemiring) (:fv _uniq.6136) ((:c CommRing.toCommSemiring) (:fv _uniq.6136) (:fv _uniq.6142))) ((:c CommSemiring.toSemiring) (:fv _uniq.6136) ((:c CommRing.toCommSemiring) (:fv _uniq.6136) (:fv _uniq.6142)))...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CommRing) (:fv _uniq.6136))"},{"name":"inst✝¹","sexp":"((:c LieRing) (:fv _uniq.6139))"},{"name":"inst✝","sexp":"((:c LieAlgebra) (:fv _uniq.6136) (:fv _uniq.6139) (:fv _uniq.6142) (:fv _uniq.6145))"},{"name":...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6136","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6139","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"simp","sourceEnd":2057,"sourceStart":2053,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6136","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6139","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
6
6
exact
true
1
7
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
43f8dfab4a0684fc635d99306e3bd7e21cfe34e36f1cb84721b31c526bcf00be
341b244205799be449b494ec1445ed97ecad83c2fb80c4caca7e644b55dc2ebf
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,853
newton_seq_dist
Mathlib/NumberTheory/Padics/Hensel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have hex : ∃ m, k = n + m := <a>Nat.exists_eq_add_of_le</a> hnk
p : ℕ inst✝ : Fact (Nat.Prime p) F : Polynomial ℤ_[p] a : ℤ_[p] hnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (Polynomial.derivative F)‖ ^ 2 hnsol : Polynomial.eval a F ≠ 0 n k : ℕ hnk : n ≤ k ⊢ ‖newton_seq k - newton_seq n‖ ≤ ‖Polynomial.eval a (Polynomial.derivative F)‖ * T_gen p F a ^ 2 ^ n
p : ℕ inst✝ : Fact (Nat.Prime p) F : Polynomial ℤ_[p] a : ℤ_[p] hnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (Polynomial.derivative F)‖ ^ 2 hnsol : Polynomial.eval a F ≠ 0 n k : ℕ hnk : n ≤ k hex : ∃ m, k = n + m ⊢ ‖newton_seq k - newton_seq n‖ ≤ ‖Polynomial.eval a (Polynomial.derivative F)‖ * T_gen p F a ^ 2 ^ n
((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c PadicInt.instNorm) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c HSub.hSub) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c PadicInt) (:fv _uni...
[{"name":"p","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.174701)))"},{"name":"F","sexp":"((:c Polynomial) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c CommSemiring.toSemiring) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c CommRing.toCommSemiring) ((:c Padi...
(: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 (:app (:c PadicInt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Fact) (:arg :explicit 0 (:app (:c Nat....
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.174701","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.174704","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Fact) (:arg :explicit 0 (:...
{"children":[{"source":"have","sourceEnd":14881,"sourceStart":14877,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hex","sourceEnd":14885,"sourceStart":14882,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hex","sourceEnd":14885,"sourceStart":14882,"tag":"n...
[]
[{"source":"∃ m, k = n + m","source_end":14904,"source_start":14888,"syntax_kind":"«term∃_,_»"},{"source":"Nat.exists_eq_add_of_le hnk","source_end":14935,"source_start":14908,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.174701","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.174704","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"inter...
56
4
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3b80ec128de457fc76a28115632e247e797b2b3042b27a2579045636cbfeb585
ad872c0448d65dd46ac8a2279245d8688230c9f163e6672e027ae85d46cbc87c
505ecc6deee886669e64842503bf0afec6f80d4d033b7c12c9d8c01c96865eb3
df9949784d478e4c5e3d281fc1fc9aaf20c5a4df8812f5068eb087c2742c0a1f
cat-searcher/leandojo-benchmark-4-random
test
1,854
newton_seq_dist
Mathlib/NumberTheory/Padics/Hensel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
let ⟨_, hex'⟩ := hex
p : ℕ inst✝ : Fact (Nat.Prime p) F : Polynomial ℤ_[p] a : ℤ_[p] hnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (Polynomial.derivative F)‖ ^ 2 hnsol : Polynomial.eval a F ≠ 0 n k : ℕ hnk : n ≤ k hex : ∃ m, k = n + m ⊢ ‖newton_seq k - newton_seq n‖ ≤ ‖Polynomial.eval a (Polynomial.derivative F)‖ * T_gen p F a ^ 2 ^ n
p : ℕ inst✝ : Fact (Nat.Prime p) F : Polynomial ℤ_[p] a : ℤ_[p] hnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (Polynomial.derivative F)‖ ^ 2 hnsol : Polynomial.eval a F ≠ 0 n k : ℕ hnk : n ≤ k hex : ∃ m, k = n + m w✝ : ℕ hex' : k = n + w✝ ⊢ ‖newton_seq k - newton_seq n‖ ≤ ‖Polynomial.eval a (Polynomial.derivative ...
((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c PadicInt.instNorm) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c HSub.hSub) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c PadicInt) (:fv _uni...
[{"name":"p","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.174701)))"},{"name":"F","sexp":"((:c Polynomial) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c CommSemiring.toSemiring) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c CommRing.toCommSemiring) ((:c Padi...
(: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 (:app (:c PadicInt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Fact) (:arg :explicit 0 (:app (:c Nat....
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{"children":[{"source":"let","sourceEnd":14941,"sourceStart":14938,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":14945,"sourceStart":14942,"tag":"atom"},{"children":[{"children":[{"source":"_","sourceEnd":14946,"sourceStart":14945,"tag":"atom"}],"kind":"Lean.Parser.Term.hole","source":"...
[]
[{"source":"hex","source_end":14962,"source_start":14959,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.174701","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.174704","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"inter...
56
5
exact
true
1
10
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
39f2e5768aa270c0d7aede57972a27807dc29a7956d1bd34e83ca649dd7deb12
df9949784d478e4c5e3d281fc1fc9aaf20c5a4df8812f5068eb087c2742c0a1f
7c36257a379d89ae58c3bdfe0f6d28d08d285670f2f5073b2f0865657670474a
c315222d394cea8653cb7772554b93103e7574ad747ee1ee53cbc561b2b79f23
cat-searcher/leandojo-benchmark-4-random
test
1,855
newton_seq_dist
Mathlib/NumberTheory/Padics/Hensel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [hex']
p : ℕ inst✝ : Fact (Nat.Prime p) F : Polynomial ℤ_[p] a : ℤ_[p] hnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (Polynomial.derivative F)‖ ^ 2 hnsol : Polynomial.eval a F ≠ 0 n k : ℕ hnk : n ≤ k hex : ∃ m, k = n + m w✝ : ℕ hex' : k = n + w✝ ⊢ ‖newton_seq k - newton_seq n‖ ≤ ‖Polynomial.eval a (Polynomial.derivative ...
p : ℕ inst✝ : Fact (Nat.Prime p) F : Polynomial ℤ_[p] a : ℤ_[p] hnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (Polynomial.derivative F)‖ ^ 2 hnsol : Polynomial.eval a F ≠ 0 n k : ℕ hnk : n ≤ k hex : ∃ m, k = n + m w✝ : ℕ hex' : k = n + w✝ ⊢ ‖newton_seq (n + w✝) - newton_seq n‖ ≤ ‖Polynomial.eval a (Polynomial.deri...
((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c PadicInt.instNorm) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c HSub.hSub) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c PadicInt) (:fv _uni...
[{"name":"p","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.174701)))"},{"name":"F","sexp":"((:c Polynomial) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c CommSemiring.toSemiring) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c CommRing.toCommSemiring) ((:c Padi...
(: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 (:app (:c PadicInt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Fact) (:arg :explicit 0 (:app (:c Nat....
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.174701","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.174704","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Fact) (:arg :explicit 0 (:...
{"children":[{"source":"rw","sourceEnd":14967,"sourceStart":14965,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":14969,"sourceStart":14968,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":12,"seman...
[]
[{"source":"hex'","source_end":14973,"source_start":14969,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.174701","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.174704","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"inter...
56
6
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
67f576b19ee0b3a7e9a93fbf53e4b05245188309f0c241b1e49b9afcea5c2b28
c315222d394cea8653cb7772554b93103e7574ad747ee1ee53cbc561b2b79f23
7818413381c9064b3e825969dc865d51c6ea3f76c1a256967ab3201ee2507eae
c232c51deea54edd827c93ac09bb18db290cfb40ba72e2d1d281a18636e33e10
cat-searcher/leandojo-benchmark-4-random
test
1,856
newton_seq_dist
Mathlib/NumberTheory/Padics/Hensel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>_private.Mathlib.NumberTheory.Padics.Hensel.0.newton_seq_dist_aux</a>
p : ℕ inst✝ : Fact (Nat.Prime p) F : Polynomial ℤ_[p] a : ℤ_[p] hnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (Polynomial.derivative F)‖ ^ 2 hnsol : Polynomial.eval a F ≠ 0 n k : ℕ hnk : n ≤ k hex : ∃ m, k = n + m w✝ : ℕ hex' : k = n + w✝ ⊢ ‖newton_seq (n + w✝) - newton_seq n‖ ≤ ‖Polynomial.eval a (Polynomial.deri...
((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c PadicInt.instNorm) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c HSub.hSub) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c PadicInt) (:fv _uni...
[{"name":"p","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.174701)))"},{"name":"F","sexp":"((:c Polynomial) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c CommSemiring.toSemiring) ((:c PadicInt) (:fv _uniq.174701) (:fv _uniq.174704)) ((:c CommRing.toCommSemiring) ((:c Padi...
(: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 (:app (:c PadicInt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Fact) (:arg :explicit 0 (:app (:c Nat....
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[]
[{"source":"newton_seq_dist_aux","source_end":15001,"source_start":14982,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.174701","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.174704","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"inter...
56
10
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
6fcf9f5c116985d7dac1f47c0b14b97a147727a27640514cf2f5952ccecff137
c232c51deea54edd827c93ac09bb18db290cfb40ba72e2d1d281a18636e33e10
993a25890525ac8ad3db550cb19db3b62bd250b25192585c356e74491090d934
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,857
CategoryTheory.EffectiveEpiFamily.transitive_of_finite
Mathlib/CategoryTheory/Sites/Coherent/CoherentTopology.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>CategoryTheory.Sieve.effectiveEpimorphic_family</a>]
C : Type u_1 inst✝³ : Category.{u_2, u_1} C inst✝² : Precoherent C X : C α : Type inst✝¹ : Finite α Y : α → C π : (a : α) → Y a ⟶ X h : EffectiveEpiFamily Y π β : α → Type inst✝ : ∀ (a : α), Finite (β a) Y_n : (a : α) → β a → C π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a H : ∀ (a : α), EffectiveEpiFamily (Y_n a) (π_n a) ...
C : Type u_1 inst✝³ : Category.{u_2, u_1} C inst✝² : Precoherent C X : C α : Type inst✝¹ : Finite α Y : α → C π : (a : α) → Y a ⟶ X h : EffectiveEpiFamily Y π β : α → Type inst✝ : ∀ (a : α), Finite (β a) Y_n : (a : α) → β a → C π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a H : ∀ (a : α), EffectiveEpiFamily (Y_n a) (π_n a) ...
((:c CategoryTheory.EffectiveEpiFamily) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1400) ((:c Sigma) (:fv _uniq.2126) (:lambda a (:fv _uniq.2126) ((:fv _uniq.2131) 0))) (:lambda c ((:c Sigma) (:fv _uniq.2126) (:lambda a (:fv _uniq.2126) ((:fv _uniq.2131) 0))) ((:fv _uniq.2133) ((:c Sigma.fst) (:fv _uniq.2126) (:lambd...
[{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1379))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Precoherent) (:fv _uniq.1379) (:fv _uniq.1383))"},{"name":"X","sexp":"(:fv _uniq.1379)"},{"name":"α","sexp":"(:sort 1)"},{"name":"inst✝¹","sexp":"((:c Finite) ...
(:app (:c CategoryTheory.EffectiveEpiFamily) (: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-type 3 (:app (:c Sigma) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:lambda a :explicit (:fv FV5) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Category) ...
{"children":[{"source":"rw","sourceEnd":2165,"sourceStart":2163,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2167,"sourceStart":2166,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":2170,"sourceStart":...
[]
[{"source":"Sieve.effectiveEpimorphic_family","source_end":2203,"source_start":2171,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":2,...
4
4
exact
true
1
14
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5a013c53dc7b870cb0884541eb8d1ce22a814fd2091fb6359b429f986496cd96
3304ae26c988bf6080683ea0eaefd8f9902a300ff4f1553f3bdfde3f4ca6d04a
cf5bcebfc85a96a8421d5487588ed3e39728d84f32889245b691d31ecb52e8c9
e43235f1f7cb8fad94ee376c596c8e80ad8bf46013bbe0a022a294c22fc3647a
cat-searcher/leandojo-benchmark-4-random
test
1,858
CategoryTheory.EffectiveEpiFamily.transitive_of_finite
Mathlib/CategoryTheory/Sites/Coherent/CoherentTopology.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
suffices h₂ : (<a>CategoryTheory.Sieve.generate</a> (<a>CategoryTheory.Presieve.ofArrows</a> (fun (⟨a, b⟩ : Σ _, β _) => Y_n a b) (fun ⟨a,b⟩ => π_n a b ≫ π a))) ∈ <a>CategoryTheory.GrothendieckTopology.sieves</a> (<a>CategoryTheory.coherentTopology</a> C) X by change <a>Nonempty</a> _ rw [← <a>CategoryTheory.Sieve.fora...
C : Type u_1 inst✝³ : Category.{u_2, u_1} C inst✝² : Precoherent C X : C α : Type inst✝¹ : Finite α Y : α → C π : (a : α) → Y a ⟶ X h : EffectiveEpiFamily Y π β : α → Type inst✝ : ∀ (a : α), Finite (β a) Y_n : (a : α) → β a → C π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a H : ∀ (a : α), EffectiveEpiFamily (Y_n a) (π_n a) ...
C : Type u_1 inst✝³ : Category.{u_2, u_1} C inst✝² : Precoherent C X : C α : Type inst✝¹ : Finite α Y : α → C π : (a : α) → Y a ⟶ X h : EffectiveEpiFamily Y π β : α → Type inst✝ : ∀ (a : α), Finite (β a) Y_n : (a : α) → β a → C π_n : (a : α) → (b : β a) → Y_n a b ⟶ Y a H : ∀ (a : α), EffectiveEpiFamily (Y_n a) (π_n a) ...
((:c CategoryTheory.Presieve.EffectiveEpimorphic) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1400) ((:c CategoryTheory.Presieve.ofArrows) (:fv _uniq.1379) (:fv _uniq.1383) (:fv _uniq.1400) ((:c Sigma) (:fv _uniq.2126) (:lambda a (:fv _uniq.2126) ((:fv _uniq.2131) 0))) (:lambda c ((:c Sigma) (:fv _uniq.2126) (:lambda ...
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(:app (:c CategoryTheory.Presieve.EffectiveEpimorphic) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit 2) (:arg :explicit 3 (:app (:c CategoryTheory.Presieve.ofArrows) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1...
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{"children":[{"source":"suffices","sourceEnd":2215,"sourceStart":2207,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"h₂","sourceEnd":2220,"sourceStart":2216,"tag":"identifier"},{"source":":","sourceEnd":2222,"sourceStart":2221,"tag":"atom"}],"kind":"group","source":"h₂ :","sourceEnd":2...
[]
[{"source":"(Sieve.generate (Presieve.ofArrows (fun (⟨a, b⟩ : Σ _, β _) => Y_n a b)\n (fun ⟨a,b⟩ => π_n a b ≫ π a))) ∈ GrothendieckTopology.sieves (coherentTopology C) X","source_end":2402,"source_start":2223,"syntax_kind":"«term_∈_»"},{"source":"Nonempty _","source_end":2427,"source_start":2417,"syntax_kind":"L...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1379","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1383","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":2,...
4
7
exact
true
1
14
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
6d8e55a5c0759383e65e008ae96a34e2f80933b0b7787c9696feaf85264618d6
e43235f1f7cb8fad94ee376c596c8e80ad8bf46013bbe0a022a294c22fc3647a
04c36dec61fbc368000d18758545be22fdd7f0c495a0a0dc40a19ea34a3bc741
5176c2d3399a9423d0de9d863e9a870fb70f06aed13efffb4aace9f15aa77800