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iCogLabs-Dev
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Mathlib-Normalized-Sexpr

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cat-searcher/leandojo-benchmark-4-random
test
4,412
Cardinal.cantor
Mathlib/SetTheory/Cardinal/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨⟨⟨<a>Singleton.singleton</a>, fun a b => <a>Set.singleton_eq_singleton_iff</a>.1⟩⟩, ?_⟩
case h α✝ β α : Type u ⊢ #α < #(Set α)
case h α✝ β α : Type u ⊢ ¬Quotient.liftOn₂ (#(Set α)) (#α) (fun α β => Nonempty (α ↪ β)) instLE.proof_1
((:c LT.lt) (:c Cardinal) ((:c Preorder.toLT) (:c Cardinal) ((:c PartialOrder.toPreorder) (:c Cardinal) (:c Cardinal.partialOrder))) ((:c Cardinal.mk) (:fv _uniq.39402)) ((:c Cardinal.mk) ((:c Set) (:fv _uniq.39402))))
[{"name":"α✝","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u 1))"},{"name":"α","sexp":"(:sort (+ u 1))"}]
(:app (:c LT.lt) (:arg :implicit-type 0 (:c Cardinal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Cardinal))))) (:arg :explicit 2 (:app (:c Cardinal.mk) (:arg :explicit 0 (:fv FV3)))) (:arg :explicit 3 (:app (:c Cardinal.mk) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3)))))))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.39281","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.39283","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":explicit","co...
{"children":[{"source":"refine","sourceEnd":29673,"sourceStart":29667,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":29677,"sourceStart":29674,"tag":"atom"},{"children":[{"children":[{"source":"⟨","sourceEnd":29680,"sourceStart":29677,"tag":"atom"},{"children":[{"children":[{"source":"⟨","sourceEnd":29683,"source...
[]
[{"source":"⟨⟨⟨singleton, fun a b => singleton_eq_singleton_iff.1⟩⟩, ?_⟩","source_end":29746,"source_start":29674,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.39281","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.39283","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":explicit","context_index":3,"internal_name":"_u...
225
8
exact
true
1
3
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9a616b26ac81cbd0623352be54bf8f8252f3a48f912eb7b761e67689aab579f0
be90314891384b9144804246516464305452ad36e3d47005cd5272039df94cd5
894d1f74afc8d38daa51aad0118d7058a37aa4967092d84f2724d20b4c787e53
12218690109b3617c468056992a41dacf23f3f9b06ce326a62b5952e22334cc6
cat-searcher/leandojo-benchmark-4-random
test
4,413
Cardinal.cantor
Mathlib/SetTheory/Cardinal/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro ⟨⟨f, hf⟩⟩
case h α✝ β α : Type u ⊢ ¬Quotient.liftOn₂ (#(Set α)) (#α) (fun α β => Nonempty (α ↪ β)) instLE.proof_1
case h.intro.mk α✝ β α : Type u f : Set α → α hf : Injective f ⊢ False
((:c Not) ((:c Quotient.liftOn₂) (:sort (+ u 1)) (:sort (+ u 1)) (:sort 0) (:c Cardinal.isEquivalent) (:c Cardinal.isEquivalent) ((:c Cardinal.mk) ((:c Set) (:fv _uniq.39402))) ((:c Cardinal.mk) (:fv _uniq.39402)) (:lambda α (:sort (+ u 1)) (:lambda β (:sort (+ u 1)) ((:c Nonempty) ((:c Function.Embedding) 1 0)))) (:c ...
[{"name":"α✝","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u 1))"},{"name":"α","sexp":"(:sort (+ u 1))"}]
(:app (:c Not) (:arg :explicit 0 (:app (:c Quotient.liftOn₂) (:arg :implicit-type 0 (:sort Type)) (:arg :implicit-type 1 (:sort Type)) (:arg :implicit-type 2 (:sort Prop)) (:arg :implicit 3) (:arg :implicit 4) (:arg :explicit 5 (:app (:c Cardinal.mk) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3)))))) (:a...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.39281","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.39283","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":explicit","co...
{"children":[{"source":"rintro","sourceEnd":29755,"sourceStart":29749,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":29759,"sourceStart":29756,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":29762,"sourceStart":29759,"tag":"atom"},...
[{"role":"fresh_name","source":"f","source_end":29763,"source_start":29762,"syntax_kind":"ident"},{"role":"fresh_name","source":"hf","source_end":29767,"source_start":29765,"syntax_kind":"ident"}]
[{"source":"⟨⟨f, hf⟩⟩","source_end":29773,"source_start":29756,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.39281","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.39283","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":explicit","context_index":3,"internal_name":"_u...
225
9
exact
true
1
3
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1cedde741fda0b125c1adff45059d68dad47ef0c82856403efda15930e15bc84
12218690109b3617c468056992a41dacf23f3f9b06ce326a62b5952e22334cc6
e8b16630a653ec6ad8504c68f17f3b525dd1e6303adc3be21b1ae6f4295083dd
4946385cf5aae93edd7aaad366622fa3899670fc98291fe525f54ea7d0d6f89a
cat-searcher/leandojo-benchmark-4-random
test
4,414
Cardinal.cantor
Mathlib/SetTheory/Cardinal/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>Function.cantor_injective</a> f hf
case h.intro.mk α✝ β α : Type u f : Set α → α hf : Injective f ⊢ False
(:c False)
[{"name":"α✝","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u 1))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"f","sexp":"(:forall _ ((:c Set) (:fv _uniq.39402)) (:fv _uniq.39402))"},{"name":"hf","sexp":"((:c Function.Injective) ((:c Set) (:fv _uniq.39402)) (:fv _uniq.39402) (:fv _uniq.39555))"}]
(:c False)
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.39281","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.39283","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":explicit","co...
{"children":[{"source":"exact","sourceEnd":29781,"sourceStart":29776,"tag":"atom"},{"children":[{"name":"Function.cantor_injective","semanticRole":"global","source":"cantor_injective","sourceEnd":29798,"sourceStart":29782,"tag":"identifier"},{"children":[{"contextIndex":4,"semanticRole":"local","source":"f","sourceEnd"...
[]
[{"source":"cantor_injective f hf","source_end":29803,"source_start":29782,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.39281","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.39283","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":explicit","context_index":3,"internal_name":"_u...
225
10
exact
true
1
5
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
11a16869098298eca1b3657d03ffc7eec9a0387164d646a2cd91d871b5688049
4946385cf5aae93edd7aaad366622fa3899670fc98291fe525f54ea7d0d6f89a
e4d076b1c851da65ded1095982acb8e2057e40d7126720b58a2ee7ccd12a1bad
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,415
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have := H.1.1
R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes ⊢ ∃ p', p'.IsPrime ∧ I ≤ p' ∧ comap f p' = p
R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this : p.IsPrime ⊢ ∃ p', p'.IsPrime ∧ I ≤ p' ∧ comap f p' = p
((:c Exists) ((:c Ideal) (:fv _uniq.26260) ((:c CommSemiring.toSemiring) (:fv _uniq.26260) ((:c CommRing.toCommSemiring) (:fv _uniq.26260) (:fv _uniq.26266)))) (:lambda p' ((:c Ideal) (:fv _uniq.26260) ((:c CommSemiring.toSemiring) (:fv _uniq.26260) ((:c CommRing.toCommSemiring) (:fv _uniq.26260) (:fv _uniq.26266)))) (...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 1 (:lambda p' :explicit (:app (:c Ideal) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :ex...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"have","sourceEnd":5642,"sourceStart":5638,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":5643,"sourceStart":5643,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":5643,"sourceStart":5643,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","...
[]
[{"source":"H.1.1","source_end":5651,"source_start":5646,"syntax_kind":"Lean.Parser.Term.proj"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
4
exact
true
1
10
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
bf45e8d0d494f52eff0a322c8fb8882579b2ec1f5b542055f7c454723850a661
522c5f9419467597de97aef46a7e1878e6f204de7fbb163334e3aa76f4c970a7
70fb94e7c47c36a3e2ac60bc9a38c8015b20c93822e963d94a1f8f6c0601f787
f388b93b9a2d39f84e1ee68195f9c879da47ea186db1454b8efdf53ada6fd7dc
cat-searcher/leandojo-benchmark-4-random
test
4,416
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
let f' := (<a>Ideal.Quotient.mk</a> I).<a>RingHom.comp</a> f
R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this : p.IsPrime ⊢ ∃ p', p'.IsPrime ∧ I ≤ p' ∧ comap f p' = p
R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f ⊢ ∃ p', p'.IsPrime ∧ I ≤ p' ∧ comap f p' = p
((:c Exists) ((:c Ideal) (:fv _uniq.26260) ((:c CommSemiring.toSemiring) (:fv _uniq.26260) ((:c CommRing.toCommSemiring) (:fv _uniq.26260) (:fv _uniq.26266)))) (:lambda p' ((:c Ideal) (:fv _uniq.26260) ((:c CommSemiring.toSemiring) (:fv _uniq.26260) ((:c CommRing.toCommSemiring) (:fv _uniq.26260) (:fv _uniq.26266)))) (...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 1 (:lambda p' :explicit (:app (:c Ideal) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :ex...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"let","sourceEnd":5657,"sourceStart":5654,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"f'","sourceEnd":5660,"sourceStart":5658,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"so...
[]
[{"source":"(Ideal.Quotient.mk I).comp f","source_end":5692,"source_start":5664,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
5
exact
true
1
11
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8f86af3482f07a4983af0e8d4e29395f5c0dc4526b27b856ef5d77c511cd9fd5
f388b93b9a2d39f84e1ee68195f9c879da47ea186db1454b8efdf53ada6fd7dc
ba068a72b9ed5e2bf9632c3360b93e1f1ab6b4dfcac3581e723bad229e933a83
5b06a02c026849d327dd174d0e7390a52b8c6a86c5455d5617cd9753a73ee02e
cat-searcher/leandojo-benchmark-4-random
test
4,417
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have e : <a>RingHom.ker</a> f' = I.comap f := by ext1 exact <a>Submodule.Quotient.mk_eq_zero</a> _
R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f ⊢ ∃ p', p'.IsPrime ∧ I ≤ p' ∧ comap f p' = p
R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I ⊢ ∃ p', p'.IsPrime ∧ I ≤ p' ∧ comap f p' = p
((:c Exists) ((:c Ideal) (:fv _uniq.26260) ((:c CommSemiring.toSemiring) (:fv _uniq.26260) ((:c CommRing.toCommSemiring) (:fv _uniq.26260) (:fv _uniq.26266)))) (:lambda p' ((:c Ideal) (:fv _uniq.26260) ((:c CommSemiring.toSemiring) (:fv _uniq.26260) ((:c CommRing.toCommSemiring) (:fv _uniq.26260) (:fv _uniq.26266)))) (...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 1 (:lambda p' :explicit (:app (:c Ideal) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :ex...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"have","sourceEnd":5699,"sourceStart":5695,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"e","sourceEnd":5701,"sourceStart":5700,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"e","sourceEnd":5701,"sourceStart":5700,"tag":"node"},{"ch...
[]
[{"source":"RingHom.ker f' = I.comap f","source_end":5730,"source_start":5704,"syntax_kind":"«term_=_»"},{"source":"Submodule.Quotient.mk_eq_zero _","source_end":5787,"source_start":5756,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
6
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3c566e755ae8a3191947a1972f2b98d86fb36a51c1195c5ab95e84e890d2c1bf
5b06a02c026849d327dd174d0e7390a52b8c6a86c5455d5617cd9753a73ee02e
5cd0d8dc5f58cb3f1e53ac9a50b40d7a38f5bfc2d436f846714695bd3cdb2ab4
dc668fef2f4950c4ad5c5013b85019eb88379cfd1ac2f1f827c1d8d21931fd7c
cat-searcher/leandojo-benchmark-4-random
test
4,418
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have : <a>RingHom.ker</a> (<a>Ideal.Quotient.mk</a> <| <a>RingHom.ker</a> f') ≤ p := by rw [<a>Ideal.mk_ker</a>, e] exact H.1.2
R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I ⊢ ∃ p', p'.IsPrime ∧ I ≤ p' ∧ comap f p' = p
R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p ⊢ ∃ p', p'.IsPrime ∧ I ≤...
((:c Exists) ((:c Ideal) (:fv _uniq.26260) ((:c CommSemiring.toSemiring) (:fv _uniq.26260) ((:c CommRing.toCommSemiring) (:fv _uniq.26260) (:fv _uniq.26266)))) (:lambda p' ((:c Ideal) (:fv _uniq.26260) ((:c CommSemiring.toSemiring) (:fv _uniq.26260) ((:c CommRing.toCommSemiring) (:fv _uniq.26260) (:fv _uniq.26266)))) (...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 1 (:lambda p' :explicit (:app (:c Ideal) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :ex...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"have","sourceEnd":5794,"sourceStart":5790,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":5795,"sourceStart":5795,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":5795,"sourceStart":5795,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","...
[]
[{"source":"RingHom.ker (Ideal.Quotient.mk <| RingHom.ker f') ≤ p","source_end":5852,"source_start":5797,"syntax_kind":"«term_≤_»"},{"source":"Ideal.mk_ker","source_end":5879,"source_start":5867,"syntax_kind":"ident"},{"source":"e","source_end":5882,"source_start":5881,"syntax_kind":"ident"},{"source":"H.1.2","source_e...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
10
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
fff0da2a7b9fe3b7a6e895e3ddd4349954ec3bca603b37ade752e072d6cf22f1
dc668fef2f4950c4ad5c5013b85019eb88379cfd1ac2f1f827c1d8d21931fd7c
2371340631a932caa88d2b0cab653bb77b541d177f540cc7ecd3b6dd5d386ab6
fe816dfdc0a31536181e8163663ca5c2285b0d14d69728e9b10348d84fe8e848
cat-searcher/leandojo-benchmark-4-random
test
4,419
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨⟨?_, <a>bot_le</a>⟩, ?_⟩
R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p ⊢ map (Quotient.mk (Ring...
case refine_1 R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p ⊢ (map (Qu...
((:c Membership.mem) ((:c Ideal) ((:c HasQuotient.Quotient) (:fv _uniq.26257) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.26263)))) ((:c Ideal.instHasQuotient) (:fv _uniq.26257) (:fv _uniq.26263)) ((:c RingHom.ker) (:fv _uniq.2...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:app (:c HasQuotient.Quotient) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 2 (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"refine","sourceEnd":6473,"sourceStart":6467,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":6477,"sourceStart":6474,"tag":"atom"},{"children":[{"children":[{"source":"⟨","sourceEnd":6480,"sourceStart":6477,"tag":"atom"},{"children":[{"children":[{"source":"?","sourceEnd":6481,"sourceStart":...
[]
[{"source":"⟨⟨?_, bot_le⟩, ?_⟩","source_end":6500,"source_start":6474,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
37
exact
true
1
14
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
731ace0fe2e121aec94f70261731c28ae0bf38060118d855ac7d923fbd94ee98
172a37aaa7e044e697df1937757bb67652fdef99075e5fa28f0abd33933b78aa
0665faa9611a6028dbd4b9e99a85ff570d3a2b03ab59082043a9de899e533d6d
f1a358b3124da276dc990430de4ded3f2049380340d99e50f659be9bcb264db1
cat-searcher/leandojo-benchmark-4-random
test
4,420
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
ext1
R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f ⊢ RingHom.ker f' = comap f I
case h R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f x✝ : R ⊢ x✝ ∈ RingHom.ker f' ↔ x✝ ∈ comap f I
((:c Eq) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.26263)))) ((:c RingHom.ker) (:fv _uniq.26257) ((:c HasQuotient.Quotient) (:fv _uniq.26260) ((:c Ideal) (:fv _uniq.26260) ((:c CommSemiring.toSemiring) (:fv _uniq.26260) ((:c ...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c RingHom.ker) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c HasQuotient.Quotient) (:arg :explicit 0 (:f...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"ext1","sourceEnd":5745,"sourceStart":5741,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.tacticExt1___","source":"ext1","sourceEnd":5745,"sourceStart":5741,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
8
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ca36601313df11a30848f0dab44334c4ea6f836178817e0364f92295a3548fca
96d96207cb8ac2b8cffb65257b54b2194f38af4151a42fee5d9b9f9a64560120
e7fe907b3287888acfd1b4783f3ce5b528593e6c60d4d7f2923662da6d41fe8b
3eb76173af49dcc5662fd04e1d00cf0af13f5e62b4b3416588e58e72c43a73b9
cat-searcher/leandojo-benchmark-4-random
test
4,421
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>Submodule.Quotient.mk_eq_zero</a> _
case h R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f x✝ : R ⊢ x✝ ∈ RingHom.ker f' ↔ x✝ ∈ comap f I
((:c Iff) ((:c Membership.mem) (:fv _uniq.26257) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.26263)))) ((:c SetLike.instMembership) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toC...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"exact","sourceEnd":5755,"sourceStart":5750,"tag":"atom"},{"children":[{"name":"Submodule.Quotient.mk_eq_zero","semanticRole":"global","source":"Submodule.Quotient.mk_eq_zero","sourceEnd":5785,"sourceStart":5756,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":5787,"sourceS...
[]
[{"source":"Submodule.Quotient.mk_eq_zero _","source_end":5787,"source_start":5756,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
9
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
85b83283ca0ebd5ebce722a16db32d6c189d54f934f426cacf8838dbef7feb24
3eb76173af49dcc5662fd04e1d00cf0af13f5e62b4b3416588e58e72c43a73b9
3d4a417f82c14d93064b179164f172f38830bfa2e86a58f5847ed13874548c0b
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,422
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Ideal.mk_ker</a>, e]
R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I ⊢ RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p
R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I ⊢ comap f I ≤ p
((:c LE.le) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.26263)))) ((:c Preorder.toLE) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.2626...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"rw","sourceEnd":5865,"sourceStart":5863,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5867,"sourceStart":5866,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Ideal.mk_ker","seman...
[]
[{"source":"Ideal.mk_ker","source_end":5879,"source_start":5867,"syntax_kind":"ident"},{"source":"e","source_end":5882,"source_start":5881,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
12
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c38a8a40ba8afcbe3af33fe12e83b3377466aadb8aa9e42691cec7e24d465100
21ed747819e70df5d80c3b46f40586b52b49084bb211a187906024c2de7f5731
9b9d50e09089440433178b2dd14a4a8cc182a117c42fa3d44c8a87582fdedcde
b86bf975b74491f91a360c5e387907c59e47514f8582008408e36bb2e0c475a7
cat-searcher/leandojo-benchmark-4-random
test
4,423
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact H.1.2
R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I ⊢ comap f I ≤ p
((:c LE.le) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.26263)))) ((:c Preorder.toLE) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.2626...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"exact","sourceEnd":5893,"sourceStart":5888,"tag":"atom"},{"children":[{"children":[{"contextIndex":10,"semanticRole":"local","source":"H","sourceEnd":5895,"sourceStart":5894,"tag":"identifier"},{"source":".","sourceEnd":5896,"sourceStart":5895,"tag":"atom"},{"children":[{"source":"1","sourceEnd"...
[]
[{"source":"H.1.2","source_end":5899,"source_start":5894,"syntax_kind":"Lean.Parser.Term.proj"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
16
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a135ec26dda31d238c6a7a92a4d8e97891c0a8cef5ab7eca2d8c4df7ece24869
b86bf975b74491f91a360c5e387907c59e47514f8582008408e36bb2e0c475a7
ec7f490a528780b6a04e8379e4b0655cd6db99980d7f0b2615f9e45b1cc7bf58
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,424
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have ⟨p', hp₁, hp₂⟩ := <a>Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective</a> (<a>RingHom.kerLift_injective</a> f') (p.map <| <a>Ideal.Quotient.mk</a> <| <a>RingHom.ker</a> f') this
R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝¹ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this✝ : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p this : ?m.29985 ⊢ ∃ p'...
R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝¹ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this✝ : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p this : map (Quotient.m...
((:c Exists) ((:c Ideal) (:fv _uniq.26260) ((:c CommSemiring.toSemiring) (:fv _uniq.26260) ((:c CommRing.toCommSemiring) (:fv _uniq.26260) (:fv _uniq.26266)))) (:lambda p' ((:c Ideal) (:fv _uniq.26260) ((:c CommSemiring.toSemiring) (:fv _uniq.26260) ((:c CommRing.toCommSemiring) (:fv _uniq.26260) (:fv _uniq.26266)))) (...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 1 (:lambda p' :explicit (:app (:c Ideal) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :ex...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"have","sourceEnd":5924,"sourceStart":5920,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":5928,"sourceStart":5925,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"p'","sourceEnd":5930,"sourceStart":5928,"tag":"identifier"},{"source":",","sourceEn...
[]
[{"source":"Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective\n (RingHom.kerLift_injective f') (p.map <| Ideal.Quotient.mk <| RingHom.ker f') this","source_end":6095,"source_start":5951,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
20
exact
true
1
15
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7212d4d7b4e6aef212feb51fd5fa2ad68addfa19717c456ee13c9bb85b7bdc50
e2074167cae41c9a9fa37717dc51c7703d59d960cfdd40df5350d448c9b82270
2bd44017eb3aa6e0ad2a1da3197b8b1456e671534a02250dc48418a159d159a2
a4f053e4dc8df32073212a1580b4d2653a7dd98a4a720614c1a576f232ac0c5a
cat-searcher/leandojo-benchmark-4-random
test
4,425
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨p'.comap <| <a>Ideal.Quotient.mk</a> I, <a>Ideal.IsPrime.comap</a> _, ?_, ?_⟩
R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝¹ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this✝ : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p this : map (Quotient.m...
case refine_1 R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝¹ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this✝ : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p this : m...
((:c Exists) ((:c Ideal) (:fv _uniq.26260) ((:c CommSemiring.toSemiring) (:fv _uniq.26260) ((:c CommRing.toCommSemiring) (:fv _uniq.26260) (:fv _uniq.26266)))) (:lambda p' ((:c Ideal) (:fv _uniq.26260) ((:c CommSemiring.toSemiring) (:fv _uniq.26260) ((:c CommRing.toCommSemiring) (:fv _uniq.26260) (:fv _uniq.26266)))) (...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 1 (:lambda p' :explicit (:app (:c Ideal) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :ex...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"refine","sourceEnd":6106,"sourceStart":6100,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":6110,"sourceStart":6107,"tag":"atom"},{"children":[{"children":[{"source":"p'.comap","sourceEnd":6118,"sourceStart":6110,"tag":"identifier"},{"source":"<|","sourceEnd":6121,"sourceStart":6119,"tag":"...
[]
[{"source":"⟨p'.comap <| Ideal.Quotient.mk I, Ideal.IsPrime.comap _, ?_, ?_⟩","source_end":6175,"source_start":6107,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
21
exact
true
1
18
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
20d697c57344b5e1c3c7117901e54a1341907c38e79eab77601324d340a39c85
a4f053e4dc8df32073212a1580b4d2653a7dd98a4a720614c1a576f232ac0c5a
5e7841fb9599092b28437fd6a755e65c6755784f7de424a753a2cf3b944eb95d
141bab400340bae85879bf5e6eea7beb724bd03d547d5a8b42d05c863ac00354
cat-searcher/leandojo-benchmark-4-random
test
4,426
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact Ideal.mk_ker.symm.trans_le (<a>Ideal.comap_mono</a> <a>bot_le</a>)
case refine_1 R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝¹ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this✝ : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p this : m...
((:c LE.le) ((:c Ideal) (:fv _uniq.26260) ((:c CommSemiring.toSemiring) (:fv _uniq.26260) ((:c CommRing.toCommSemiring) (:fv _uniq.26260) (:fv _uniq.26266)))) ((:c Preorder.toLE) ((:c Ideal) (:fv _uniq.26260) ((:c CommSemiring.toSemiring) (:fv _uniq.26260) ((:c CommRing.toCommSemiring) (:fv _uniq.26260) (:fv _uniq.2626...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":6188,"sourceStart":6183,"tag":"atom"},{"children":[{"source":"Ideal.mk_ker.symm.trans_le","sourceEnd":6215,"sourceStart":6189,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":6217,"sourceStart":6216,"tag":"atom"},{"...
[]
[{"source":"Ideal.mk_ker.symm.trans_le (Ideal.comap_mono bot_le)","source_end":6241,"source_start":6189,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
24
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
898da57bc6894a6e437ec59e23af9a61749bfe092059d45a1aefaa410b1cb456
53275b9c79bed5fa31b15453c4b93cfd00d13d16b6b1f67b8dd9150260664171
6f6f3196e1eafb3f1b531fc0622064e9049741558cbff5952119596ca87a10ab
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,427
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
convert <a>congr_arg</a> (<a>Ideal.comap</a> <| <a>Ideal.Quotient.mk</a> <| <a>RingHom.ker</a> f') hp₂
case refine_2 R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝¹ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this✝ : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p this : m...
case h.e'_3 R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝¹ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this✝ : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p this : map...
((:c Eq) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.26263)))) ((:c Ideal.comap) (:fv _uniq.26257) (:fv _uniq.26260) ((:c RingHom) (:fv _uniq.26257) (:fv _uniq.26260) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.26257) ((:c Com...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c Ideal.comap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:app (:c RingHom) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"convert","sourceEnd":6256,"sourceStart":6249,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"congr_arg","semanticRole":"global","source":"congr_arg","sourceEnd":6266,"sourceStart":6257,"tag":"identi...
[]
[{"source":"congr_arg (Ideal.comap <| Ideal.Quotient.mk <| RingHom.ker f') hp₂","source_end":6325,"source_start":6257,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
31
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
408a51f72ac56f16b15a8b1c38418d2efc9c144c35c8dfaea7ff1c00f6f9bac5
72a4b1254e20ec01f758a74c453620612438d7fe719574c91ce5706acc863a65
0c70fe938b8235b3035d9ed8a2741a8a4f007ff525e43da2663541f1391c6034
ca5ff9bbd3b673783c9ac4de17e8e5da73626cfec870afdcb57edc13a105f61d
cat-searcher/leandojo-benchmark-4-random
test
4,428
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rwa [<a>Ideal.comap_map_of_surjective</a> (<a>Ideal.Quotient.mk</a> <| <a>RingHom.ker</a> f') <a>Ideal.Quotient.mk_surjective</a>, <a>eq_comm</a>, <a>sup_eq_left</a>]
case h.e'_3 R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝¹ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this✝ : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p this : map...
((:c Eq) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.26263)))) (:fv _uniq.27683) ((:c Ideal.comap) (:fv _uniq.26257) ((:c HasQuotient.Quotient) (:fv _uniq.26257) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv ...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:fv FV9)) (:arg :explicit 2 (:app (:c Ideal.comap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c HasQuotient.Qu...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"rwa","sourceEnd":6335,"sourceStart":6332,"tag":"atom"},{"children":[{"source":"[","sourceEnd":6337,"sourceStart":6336,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Ideal.comap_map_of_surjective","semanticRole":"global","sourc...
[]
[{"source":"Ideal.comap_map_of_surjective (Ideal.Quotient.mk <| RingHom.ker f')\n Ideal.Quotient.mk_surjective","source_end":6441,"source_start":6337,"syntax_kind":"Lean.Parser.Term.app"},{"source":"eq_comm","source_end":6450,"source_start":6443,"syntax_kind":"ident"},{"source":"sup_eq_left","source_end":6463,"s...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
32
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
07e612d58fb0489717130e93a61d4c9cc37494e27eca724a99211b72b9ed65a9
ca5ff9bbd3b673783c9ac4de17e8e5da73626cfec870afdcb57edc13a105f61d
6fe61775af371ed3b459869b6ff631b9dd8e3ba9244f2682cfb36254e6738aa2
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,429
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>Ideal.map_isPrime_of_surjective</a> _ this
case refine_1 R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p ⊢ (map (Qu...
R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p ⊢ Function.Surjective ⇑(...
((:c Ideal.IsPrime) ((:c HasQuotient.Quotient) (:fv _uniq.26257) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.26263)))) ((:c Ideal.instHasQuotient) (:fv _uniq.26257) (:fv _uniq.26263)) ((:c RingHom.ker) (:fv _uniq.26257) ((:c Ha...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c Ideal.IsPrime) (:arg :implicit-type 0 (:app (:c HasQuotient.Quotient) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 2 (:instance-of (:app (:c HasQuotient) (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"apply","sourceEnd":6511,"sourceStart":6506,"tag":"atom"},{"children":[{"name":"Ideal.map_isPrime_of_surjective","semanticRole":"global","source":"Ideal.map_isPrime_of_surjective","sourceEnd":6543,"sourceStart":6512,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":6545,"sou...
[]
[{"source":"Ideal.map_isPrime_of_surjective _ this","source_end":6550,"source_start":6512,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
42
exact
true
1
14
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f4eb68e9347767bf478dffd18ae696d35293d1dcb36c0fa05d797cd8d45da8fd
8e71d7d82b1e693510fead084ddf4ef3d1bd0fad8d036a356ced5287eb407d94
309e82034b2d688f373136a1b4b605338a9d0abec2b1b997e5c523350af28b99
d1a3e0c0d737df95c341687224f06efde6be6732bcf4938e50f2ff3d7c32b6c5
cat-searcher/leandojo-benchmark-4-random
test
4,430
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>Ideal.Quotient.mk_surjective</a>
R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p ⊢ Function.Surjective ⇑(...
((:c Function.Surjective) (:fv _uniq.26257) ((:c HasQuotient.Quotient) (:fv _uniq.26257) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.26263)))) ((:c Ideal.instHasQuotient) (:fv _uniq.26257) (:fv _uniq.26263)) ((:c RingHom.ker) (...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c Function.Surjective) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c HasQuotient.Quotient) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"exact","sourceEnd":6560,"sourceStart":6555,"tag":"atom"},{"name":"Ideal.Quotient.mk_surjective","semanticRole":"global","source":"Ideal.Quotient.mk_surjective","sourceEnd":6589,"sourceStart":6561,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact Ideal.Quotient.mk_surjective"...
[]
[{"source":"Ideal.Quotient.mk_surjective","source_end":6589,"source_start":6561,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
43
exact
true
1
14
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
aac56ad95017bfbc8b2dfa65d78352ddb037fe8587a347510ae319d0b2637d63
d1a3e0c0d737df95c341687224f06efde6be6732bcf4938e50f2ff3d7c32b6c5
52c57126f156266dcda7b70fd76e47a2b1fdf0c4da5ad12a122ca2a6ff2e583e
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,431
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro q ⟨hq, -⟩ hq'
case refine_2 R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p ⊢ ∀ ⦃b : I...
case refine_2.intro R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p q : ...
(:forall b ((:c Ideal) ((:c HasQuotient.Quotient) (:fv _uniq.26257) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.26263)))) ((:c Ideal.instHasQuotient) (:fv _uniq.26257) (:fv _uniq.26263)) ((:c RingHom.ker) (:fv _uniq.26257) ((:c...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:forall b :strict-implicit (:app (:c Ideal) (:arg :explicit 0 (:app (:c HasQuotient.Quotient) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 2 (:instance-of (:app (:c...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"rintro","sourceEnd":6601,"sourceStart":6595,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"q","sourceEnd":6603,"sourceStart":6602,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"q","sourceEnd":6603,"sourceStart":6602,"tag":"...
[{"role":"fresh_name","source":"q","source_end":6603,"source_start":6602,"syntax_kind":"ident"},{"role":"fresh_name","source":"hq","source_end":6609,"source_start":6607,"syntax_kind":"ident"},{"role":"fresh_name","source":"hq'","source_end":6619,"source_start":6616,"syntax_kind":"ident"}]
[{"source":"⟨hq, -⟩","source_end":6615,"source_start":6604,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
48
exact
true
1
14
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
886dcc780b0fbc98e177390c8f6ea8048a75bf0900f91b502888c1d52384fe0d
c6da487508f3959e250839858d5af3ed4a77c1a2e69fac7994fcc31807fb75e9
2a41acf3673c94f96fc5c1733c05512f9a75d6b40c0d900bcef0be3d41c3882a
6a3edb558eb43c755b784fd1a2d2ac8942fc38920db1a58f55c01284c513ece8
cat-searcher/leandojo-benchmark-4-random
test
4,432
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>Ideal.map_comap_of_surjective</a> (<a>Ideal.Quotient.mk</a> (<a>RingHom.ker</a> ((<a>Ideal.Quotient.mk</a> I).<a>RingHom.comp</a> f))) <a>Ideal.Quotient.mk_surjective</a> q]
case refine_2.intro R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p q : ...
case refine_2.intro R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p q : ...
((:c LE.le) ((:c Ideal) ((:c HasQuotient.Quotient) (:fv _uniq.26257) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.26263)))) ((:c Ideal.instHasQuotient) (:fv _uniq.26257) (:fv _uniq.26263)) ((:c RingHom.ker) (:fv _uniq.26257) ((:...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:app (:c HasQuotient.Quotient) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 2 (:instance-...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"rw","sourceEnd":6626,"sourceStart":6624,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6628,"sourceStart":6627,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":6631,"sourceStart":...
[]
[{"source":"Ideal.map_comap_of_surjective\n (Ideal.Quotient.mk (RingHom.ker ((Ideal.Quotient.mk I).comp f)))\n Ideal.Quotient.mk_surjective q","source_end":6773,"source_start":6632,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
49
exact
true
1
17
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1a8e6d971b8f75daf08821cfa567326b9674d0f02070d5c87f01eb9281fde055
6a3edb558eb43c755b784fd1a2d2ac8942fc38920db1a58f55c01284c513ece8
cee7c3b1bdd7386725817420fa07ef7fbfbd9a8a05b9e6379cedf42ba8c20efa
aa7c41493dd2b21f3684cbf99598a4a1c83023865ccc1a6e9a85b35d21b1ae4b
cat-searcher/leandojo-benchmark-4-random
test
4,433
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>Ideal.map_mono</a>
case refine_2.intro R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p q : ...
case refine_2.intro.h R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p q ...
((:c LE.le) ((:c Ideal) ((:c HasQuotient.Quotient) (:fv _uniq.26257) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.26263)))) ((:c Ideal.instHasQuotient) (:fv _uniq.26257) (:fv _uniq.26263)) ((:c RingHom.ker) (:fv _uniq.26257) ((:...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:app (:c HasQuotient.Quotient) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 2 (:instance-...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"apply","sourceEnd":6784,"sourceStart":6779,"tag":"atom"},{"name":"Ideal.map_mono","semanticRole":"global","source":"Ideal.map_mono","sourceEnd":6799,"sourceStart":6785,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Ideal.map_mono","sourceEnd":6799,"sourceStart":6779,"tag"...
[]
[{"source":"Ideal.map_mono","source_end":6799,"source_start":6785,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
52
exact
true
1
17
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
95055a00cd2bffa59998df0021b17c1a3171fa177cfd76091326e8b4440c1d7d
aa7c41493dd2b21f3684cbf99598a4a1c83023865ccc1a6e9a85b35d21b1ae4b
fb1b019fbe60be8615d534d1390f25d08857ac2153652f81090d2e5878ea6c07
7154bd70e1c9b0876449ccd3258bc7c5b31bf5f8ac026452cf6c2f71cd5dc115
cat-searcher/leandojo-benchmark-4-random
test
4,434
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply H.2
case refine_2.intro.h R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p q ...
case refine_2.intro.h.a R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p ...
((:c LE.le) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.26263)))) ((:c Preorder.toLE) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.2626...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"apply","sourceEnd":6809,"sourceStart":6804,"tag":"atom"},{"children":[{"contextIndex":10,"semanticRole":"local","source":"H","sourceEnd":6811,"sourceStart":6810,"tag":"identifier"},{"source":".","sourceEnd":6812,"sourceStart":6811,"tag":"atom"},{"children":[{"source":"2","sourceEnd":6813,"source...
[]
[{"source":"H.2","source_end":6813,"source_start":6810,"syntax_kind":"Lean.Parser.Term.proj"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
53
exact
true
1
17
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4057a17a6213f305b809169cd91ed74abc8588d076e48a5b69ccdbd28069f1e2
7154bd70e1c9b0876449ccd3258bc7c5b31bf5f8ac026452cf6c2f71cd5dc115
0103b74c0e5f0755658577bd315ba844a662f133f87aa1e7afd16091d7f3fb15
b5494dd33ea021e4dc6313869d0fc32ba4349a3429187e662906107da8d7ced3
cat-searcher/leandojo-benchmark-4-random
test
4,435
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨<a>inferInstance</a>, (Ideal.mk_ker.trans e).symm.trans_le (<a>Ideal.comap_mono</a> <a>bot_le</a>)⟩
case refine_2.intro.h.a R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p ...
((:c Membership.mem) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.26263)))) ((:c Set) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.26263...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"children":[{"children":[{"children":[{"source":"refine","sourceEnd":6827,"sourceStart":6821,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":6831,"sourceStart":6828,"tag":"atom"},{"children":[{"name":"inferInstance","semanticRole":"global","source":"inferInstance","sourceEnd":6844,"sourceStart":6831,...
[]
[{"source":"⟨inferInstance, (Ideal.mk_ker.trans e).symm.trans_le (Ideal.comap_mono bot_le)⟩","source_end":6911,"source_start":6828,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
56
exact
true
1
17
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2801bde2d7606d2e1252b2ebf36b099dcf3c5b34222dad16ecdaf9aeb20d4309
0be028068893899e8f3011ca2f48f595fcbb91df9f8be7df99824419a8250462
f06de7d62ea86ce95ceb1de50dcdab28574e9466f1ada97079bea79d6fb789e9
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,436
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine (<a>Ideal.comap_mono</a> hq').<a>LE.le.trans</a> ?_
case refine_2.intro.h.a R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p ...
case refine_2.intro.h.a R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p ...
((:c LE.le) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.26263)))) ((:c Preorder.toLE) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.2626...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"refine","sourceEnd":6925,"sourceStart":6919,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":6927,"sourceStart":6926,"tag":"atom"},{"children":[{"name":"Ideal.comap_mono","semanticRole":"global","source":"Ideal.comap_mono","sourceEnd":6943,"sourceStart":6927,"tag":"...
[]
[{"source":"(Ideal.comap_mono hq').trans ?_","source_end":6957,"source_start":6926,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
63
exact
true
1
17
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e212cb131d428bd5f0b2c16ba1c5de5482815f37106ce36e70184b926b03a5b1
f6e4b1e698c8a21d5122d902e32aa79e4231f91462b1cd8e2d3f33294ff08a0a
89ce00a5b87ebe2bb6f09a22572220395b1972d6a549e6ad2cb6ada96068e66a
613abbd38325644bce171e960c2c5251fc8f9d847e342148152bc86878247027
cat-searcher/leandojo-benchmark-4-random
test
4,437
Ideal.exists_comap_eq_of_mem_minimalPrimes
Mathlib/RingTheory/Ideal/MinimalPrime.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Ideal.comap_map_of_surjective</a>]
case refine_2.intro.h.a R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p ...
case refine_2.intro.h.a R : Type u_1 S : Type u_2 inst✝¹ : CommRing R inst✝ : CommRing S I✝ J : Ideal R I : Ideal S f : R →+* S p : Ideal R H : p ∈ (comap f I).minimalPrimes this✝ : p.IsPrime f' : R →+* S ⧸ I := (Quotient.mk I).comp f e : RingHom.ker f' = comap f I this : RingHom.ker (Quotient.mk (RingHom.ker f')) ≤ p ...
((:c LE.le) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.26263)))) ((:c Preorder.toLE) ((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCommSemiring) (:fv _uniq.26257) (:fv _uniq.2626...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.26257))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.26260))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.26257) ((:c CommSemiring.toSemiring) (:fv _uniq.26257) ((:c CommRing.toCom...
(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"rw","sourceEnd":6966,"sourceStart":6964,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6968,"sourceStart":6967,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Ideal.comap_map_of_s...
[]
[{"source":"Ideal.comap_map_of_surjective","source_end":6997,"source_start":6968,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26257","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26260","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
21
64
exact
true
1
17
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5ee9e11c9958b8212fe2293eecbff3e73acbe035859b1ed27ac430be1031429d
613abbd38325644bce171e960c2c5251fc8f9d847e342148152bc86878247027
7c9945f4ca1139f6b1583cccbbc2584246e52182cca6f1b495ce0b1313df1f85
d54e18bdf5c1819879b2813b21eaaa8e6365f0956be00f1139f53a56e258c439
cat-searcher/leandojo-benchmark-4-random
test
4,439
Polynomial.leadingCoeff_prod
Mathlib/Algebra/Polynomial/BigOperators.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simpa using <a>Polynomial.leadingCoeff_multiset_prod</a> (s.1.<a>Multiset.map</a> f)
R : Type u ι : Type w s : Finset ι inst✝¹ : CommSemiring R inst✝ : NoZeroDivisors R f : ι → R[X] t : Multiset R[X] ⊢ (∏ i ∈ s, f i).leadingCoeff = ∏ i ∈ s, (f i).leadingCoeff
((:c Eq) (:fv _uniq.864903) ((:c Polynomial.leadingCoeff) (:fv _uniq.864903) ((:c CommSemiring.toSemiring) (:fv _uniq.864903) (:fv _uniq.864911)) ((:c Finset.prod) (:fv _uniq.864905) ((:c Polynomial) (:fv _uniq.864903) ((:c CommSemiring.toSemiring) (:fv _uniq.864903) (:fv _uniq.864911))) ((:c CommSemiring.toCommMonoid)...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"ι","sexp":"(:sort (+ w 1))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.864905))"},{"name":"inst✝¹","sexp":"((:c CommSemiring) (:fv _uniq.864903))"},{"name":"inst✝","sexp":"((:c NoZeroDivisors) (:fv _uniq.864903) ((:c NonUnitalNonAssocSemiring.toMul) (:fv _uniq.864903) (...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Polynomial.leadingCoeff) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Finset.prod) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:a...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.864903","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.864905","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":explicit","c...
{"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":16142,"sourceStart":16137,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind...
[]
[{"source":"leadingCoeff_multiset_prod (s.1.map f)","source_end":16187,"source_start":16149,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.864903","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.864905","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":explicit","context_index":2,"internal_name":"_...
88
2
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d5143bde4be739ea6f17d6cd437bca80d2aff2f7d0ba77623f9dde2e010f66e1
e30591ef410162021273df96794412086c14ce40c92e790ef2e3480b60371ac4
d2765d15a0244d042cda046ed4137afd76391d925e362324d4bd2881a1b03fc1
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,440
CochainComplex.mappingCone.ext_cochain_to_iff
Mathlib/Algebra/Homology/HomotopyCategory/MappingCone.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
constructor
C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ γ₂ : Cochain K (mappingCone φ) i ⊢ γ₁ = γ₂ ↔ γ₁.comp (↑(fst φ)) hij = γ₂.comp (↑(fst φ)) hij ∧ γ₁.comp (snd φ) ⋯ = γ₂.comp (snd φ) ⋯
case mp C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ γ₂ : Cochain K (mappingCone φ) i ⊢ γ₁ = γ₂ → γ₁.comp (↑(fst φ)) hij = γ₂.comp (↑(fst φ)) hij ∧ γ₁.comp (snd φ) ⋯ = γ₂.comp (snd φ) ...
((:c Iff) ((:c Eq) ((:c CochainComplex.HomComplex.Cochain) (:fv _uniq.66766) (:fv _uniq.66770) (:fv _uniq.66785) (:fv _uniq.68485) ((:c CochainComplex.mappingCone) (:fv _uniq.66766) (:fv _uniq.66770) (:fv _uniq.66785) (:fv _uniq.66882) (:fv _uniq.66900) (:fv _uniq.66969) (:fv _uniq.67194)) (:fv _uniq.68482)) (:fv _uniq...
[{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.66766))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Preadditive) (:fv _uniq.66766) (:fv _uniq.66770))"},{"name":"F","sexp":"((:c CochainComplex) (:fv _uniq.66766) (:fv _uniq.66770) ((:c CategoryTheory.Preadditi...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CochainComplex.HomComplex.Cochain) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c CategoryTheory.Preadditive) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Category...
{"children":[{"source":"constructor","sourceEnd":7714,"sourceStart":7703,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":7714,"sourceStart":7703,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
37
4
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
74e53b6255b4a962dc40d3b148de7575dc71bb692c68e46f38ba7b7ffc1d3817
adb0042874e55169b4d369712cd0cdc8db8076a848b00e4fa9d0511993051d97
e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068
623777b069ac7b67b29645fd523f59f20a4f4bb99f3c6766fccca1c1a953d0f7
cat-searcher/leandojo-benchmark-4-random
test
4,441
CochainComplex.mappingCone.ext_cochain_to_iff
Mathlib/Algebra/Homology/HomotopyCategory/MappingCone.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro rfl
case mp C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ γ₂ : Cochain K (mappingCone φ) i ⊢ γ₁ = γ₂ → γ₁.comp (↑(fst φ)) hij = γ₂.comp (↑(fst φ)) hij ∧ γ₁.comp (snd φ) ⋯ = γ₂.comp (snd φ) ...
case mp C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ : Cochain K (mappingCone φ) i ⊢ γ₁.comp (↑(fst φ)) hij = γ₁.comp (↑(fst φ)) hij ∧ γ₁.comp (snd φ) ⋯ = γ₁.comp (snd φ) ⋯
(:forall _ ((:c Eq) ((:c CochainComplex.HomComplex.Cochain) (:fv _uniq.66766) (:fv _uniq.66770) (:fv _uniq.66785) (:fv _uniq.68485) ((:c CochainComplex.mappingCone) (:fv _uniq.66766) (:fv _uniq.66770) (:fv _uniq.66785) (:fv _uniq.66882) (:fv _uniq.66900) (:fv _uniq.66969) (:fv _uniq.67194)) (:fv _uniq.68482)) (:fv _uni...
[{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.66766))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Preadditive) (:fv _uniq.66766) (:fv _uniq.66770))"},{"name":"F","sexp":"((:c CochainComplex) (:fv _uniq.66766) (:fv _uniq.66770) ((:c CategoryTheory.Preadditi...
(:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CochainComplex.HomComplex.Cochain) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c CategoryTheory.Preadditive) (:arg :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Category...
{"children":[{"source":"rintro","sourceEnd":7726,"sourceStart":7720,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":7730,"sourceStart":7727,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl","sourceEnd":7730,"sourceStart":7727,"ta...
[]
[{"source":"rfl","source_end":7730,"source_start":7727,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
37
9
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d7079784d5adfe09d4e79d8990b6b4c0e191d5f4c3eb39f0d0868095ee9edcab
6b31944b2068c96aff3bc6290d3caa1b2325bb3a6a7a957a20867498811be76e
09e128cd6787f35d3c063b643315aff1382388dafa4e55b6546fbf9dcecb02da
0ade1e6fd212b124bf9abc5c21600c38ed3389ea75230b3dc5459f54c4537a50
cat-searcher/leandojo-benchmark-4-random
test
4,442
CochainComplex.mappingCone.ext_cochain_to_iff
Mathlib/Algebra/Homology/HomotopyCategory/MappingCone.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
tauto
case mp C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ : Cochain K (mappingCone φ) i ⊢ γ₁.comp (↑(fst φ)) hij = γ₁.comp (↑(fst φ)) hij ∧ γ₁.comp (snd φ) ⋯ = γ₁.comp (snd φ) ⋯
((:c And) ((:c Eq) ((:c CochainComplex.HomComplex.Cochain) (:fv _uniq.66766) (:fv _uniq.66770) (:fv _uniq.66785) (:fv _uniq.68485) (:fv _uniq.66882) (:fv _uniq.68483)) ((:c CochainComplex.HomComplex.Cochain.comp) (:fv _uniq.66766) (:fv _uniq.66770) (:fv _uniq.66785) (:fv _uniq.68485) ((:c CochainComplex.mappingCone) (:...
[{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.66766))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Preadditive) (:fv _uniq.66766) (:fv _uniq.66770))"},{"name":"F","sexp":"((:c CochainComplex) (:fv _uniq.66766) (:fv _uniq.66770) ((:c CategoryTheory.Preadditi...
(:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CochainComplex.HomComplex.Cochain) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c CategoryTheory.Preadditive) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Category...
{"children":[{"source":"tauto","sourceEnd":7740,"sourceStart":7735,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.Tauto.tauto","source":"tauto","sourceEnd":7740,"sourceStart":7735,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
37
10
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7b1cbf825b330d6cf114264f66a336bf7b356cf02bbfcefee02b6cc8724bab11
0ade1e6fd212b124bf9abc5c21600c38ed3389ea75230b3dc5459f54c4537a50
78175d0e14580017b7abde3d46f7acc510808867e2ea0a22535e39b5dff68317
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,443
CochainComplex.mappingCone.ext_cochain_to_iff
Mathlib/Algebra/Homology/HomotopyCategory/MappingCone.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro ⟨h₁, h₂⟩
case mpr C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ γ₂ : Cochain K (mappingCone φ) i ⊢ γ₁.comp (↑(fst φ)) hij = γ₂.comp (↑(fst φ)) hij ∧ γ₁.comp (snd φ) ⋯ = γ₂.comp (snd φ) ⋯ → γ₁ = ...
case mpr.intro C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ γ₂ : Cochain K (mappingCone φ) i h₁ : γ₁.comp (↑(fst φ)) hij = γ₂.comp (↑(fst φ)) hij h₂ : γ₁.comp (snd φ) ⋯ = γ₂.comp (snd ...
(:forall _ ((:c And) ((:c Eq) ((:c CochainComplex.HomComplex.Cochain) (:fv _uniq.66766) (:fv _uniq.66770) (:fv _uniq.66785) (:fv _uniq.68485) (:fv _uniq.66882) (:fv _uniq.68483)) ((:c CochainComplex.HomComplex.Cochain.comp) (:fv _uniq.66766) (:fv _uniq.66770) (:fv _uniq.66785) (:fv _uniq.68485) ((:c CochainComplex.mapp...
[{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.66766))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Preadditive) (:fv _uniq.66766) (:fv _uniq.66770))"},{"name":"F","sexp":"((:c CochainComplex) (:fv _uniq.66766) (:fv _uniq.66770) ((:c CategoryTheory.Preadditi...
(:forall _ :explicit (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CochainComplex.HomComplex.Cochain) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c CategoryT...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Category...
{"children":[{"source":"rintro","sourceEnd":7752,"sourceStart":7746,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":7756,"sourceStart":7753,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h₁","sourceEnd":7760,"sourceS...
[{"role":"fresh_name","source":"h₁","source_end":7760,"source_start":7756,"syntax_kind":"ident"},{"role":"fresh_name","source":"h₂","source_end":7766,"source_start":7762,"syntax_kind":"ident"}]
[{"source":"⟨h₁, h₂⟩","source_end":7769,"source_start":7753,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
37
15
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
dda84b0cd44b1e1ef0bb1203eb370865762810db054ed6a5c498bb3644ab1303
c72463f38ad47e05185a36e10d49ae3d0ff435d76b14f2ffdfaaff51c2835b2f
fd8e7c266f2cbda01b20b6d19c51a338746a0de6fd85d9ae349b8d097a2b04e7
ccb3ae8326668c69d496b71594913ff4a5b181eb8cf0ad99cdc61f1a4fa1dd34
cat-searcher/leandojo-benchmark-4-random
test
4,444
CochainComplex.mappingCone.ext_cochain_to_iff
Mathlib/Algebra/Homology/HomotopyCategory/MappingCone.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
ext p q hpq
case mpr.intro C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ γ₂ : Cochain K (mappingCone φ) i h₁ : γ₁.comp (↑(fst φ)) hij = γ₂.comp (↑(fst φ)) hij h₂ : γ₁.comp (snd φ) ⋯ = γ₂.comp (snd ...
case mpr.intro.h C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ γ₂ : Cochain K (mappingCone φ) i h₁ : γ₁.comp (↑(fst φ)) hij = γ₂.comp (↑(fst φ)) hij h₂ : γ₁.comp (snd φ) ⋯ = γ₂.comp (sn...
((:c Eq) ((:c CochainComplex.HomComplex.Cochain) (:fv _uniq.66766) (:fv _uniq.66770) (:fv _uniq.66785) (:fv _uniq.68485) ((:c CochainComplex.mappingCone) (:fv _uniq.66766) (:fv _uniq.66770) (:fv _uniq.66785) (:fv _uniq.66882) (:fv _uniq.66900) (:fv _uniq.66969) (:fv _uniq.67194)) (:fv _uniq.68482)) (:fv _uniq.68486) (:...
[{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.66766))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Preadditive) (:fv _uniq.66766) (:fv _uniq.66770))"},{"name":"F","sexp":"((:c CochainComplex) (:fv _uniq.66766) (:fv _uniq.66770) ((:c CategoryTheory.Preadditi...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CochainComplex.HomComplex.Cochain) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c CategoryTheory.Preadditive) (:arg :explicit 0 (:fv FV0)) (:arg ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Category...
{"children":[{"source":"ext","sourceEnd":7777,"sourceStart":7774,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"p","sourceEnd":7779,"sourceStart":7778,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"p","sourceEnd":7779,"sourceStart":7778,"tag":"nod...
[{"role":"fresh_name","source":"p","source_end":7779,"source_start":7778,"syntax_kind":"ident"},{"role":"fresh_name","source":"q","source_end":7781,"source_start":7780,"syntax_kind":"ident"},{"role":"fresh_name","source":"hpq","source_end":7785,"source_start":7782,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
37
16
exact
true
1
15
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ee765fd43b4c26175ce5b77967b0ad5578ba26591cc52b4f235f0c09ad82b5b3
ccb3ae8326668c69d496b71594913ff4a5b181eb8cf0ad99cdc61f1a4fa1dd34
4b3e40fb12ab8bc2c1c809554097506a3191d9a2fe59a24ed76ccbb3c2eface9
fcca881d0cd23264ad49c2b498a949c45bb0839a0ec25ababd128bfc95279806
cat-searcher/leandojo-benchmark-4-random
test
4,445
CochainComplex.mappingCone.ext_cochain_to_iff
Mathlib/Algebra/Homology/HomotopyCategory/MappingCone.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>CochainComplex.mappingCone.ext_to_iff</a> φ q (q + 1) <a>rfl</a>]
case mpr.intro.h C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ γ₂ : Cochain K (mappingCone φ) i h₁ : γ₁.comp (↑(fst φ)) hij = γ₂.comp (↑(fst φ)) hij h₂ : γ₁.comp (snd φ) ⋯ = γ₂.comp (sn...
case mpr.intro.h C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ γ₂ : Cochain K (mappingCone φ) i h₁ : γ₁.comp (↑(fst φ)) hij = γ₂.comp (↑(fst φ)) hij h₂ : γ₁.comp (snd φ) ⋯ = γ₂.comp (sn...
((:c Eq) ((:c Quiver.Hom) (:fv _uniq.66766) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.66766) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.66766) (:fv _uniq.66770))) ((:c HomologicalComplex.X) (:c Int) (:fv _uniq.66766) (:fv _uniq.66770) ((:c CategoryTheory.Preadditive.preadditiveHasZeroMorphi...
[{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.66766))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Preadditive) (:fv _uniq.66766) (:fv _uniq.66770))"},{"name":"F","sexp":"((:c CochainComplex) (:fv _uniq.66766) (:fv _uniq.66770) ((:c CategoryTheory.Preadditi...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HomologicalComplex.X) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Category...
{"children":[{"source":"rw","sourceEnd":7792,"sourceStart":7790,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7794,"sourceStart":7793,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Cochain...
[]
[{"source":"ext_to_iff φ q (q + 1) rfl","source_end":7821,"source_start":7794,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
37
17
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9624c469435b38cf066bafb6ed5a4162d2799204655f242b36e6207a38d1edd9
fcca881d0cd23264ad49c2b498a949c45bb0839a0ec25ababd128bfc95279806
825938cf73356e5d26745b99f338208ade03325cdebee8119c60d6377bd905a0
43fc8fa572bf03a916589f1f1b019a95172c5550062c0ed906319594c0f7787a
cat-searcher/leandojo-benchmark-4-random
test
4,446
CochainComplex.mappingCone.ext_cochain_to_iff
Mathlib/Algebra/Homology/HomotopyCategory/MappingCone.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
replace h₁ := <a>CochainComplex.HomComplex.Cochain.congr_v</a> h₁ p (q + 1) (by omega)
case mpr.intro.h C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ γ₂ : Cochain K (mappingCone φ) i h₁ : γ₁.comp (↑(fst φ)) hij = γ₂.comp (↑(fst φ)) hij h₂ : γ₁.comp (snd φ) ⋯ = γ₂.comp (sn...
case mpr.intro.h C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ γ₂ : Cochain K (mappingCone φ) i h₂ : γ₁.comp (snd φ) ⋯ = γ₂.comp (snd φ) ⋯ p q : ℤ hpq : p + i = q h₁ : (γ₁.comp (↑(fst φ...
((:c And) ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.66766) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.66766) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.66766) (:fv _uniq.66770))) ((:c HomologicalComplex.X) (:c Int) (:fv _uniq.66766) (:fv _uniq.66770) ((:c CategoryTheory.Preadditive.preadditiveHas...
[{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.66766))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Preadditive) (:fv _uniq.66766) (:fv _uniq.66770))"},{"name":"F","sexp":"((:c CochainComplex) (:fv _uniq.66766) (:fv _uniq.66770) ((:c CategoryTheory.Preadditi...
(:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HomologicalComplex.X) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:fv F...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Category...
{"children":[{"source":"replace","sourceEnd":7834,"sourceStart":7827,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h₁","sourceEnd":7839,"sourceStart":7835,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h₁","sourceEnd":7839,"sourceStart":7835,"tag":"node"}...
[]
[{"source":"Cochain.congr_v h₁ p (q + 1) (by omega)","source_end":7884,"source_start":7843,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
37
20
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
03a27862e958b4c3509eb2b15e7121b16b7a76696bb25b5af99b0d2662b07ec6
43fc8fa572bf03a916589f1f1b019a95172c5550062c0ed906319594c0f7787a
f57dd5aeebc43cd3a65d97e1fdad7f6c74b3202c274f1b063700c1f8b47131c3
f2b359537f1c41a701fa646567ce25131ee8cdac92e0eeb7ab60f96b4b013313
cat-searcher/leandojo-benchmark-4-random
test
4,447
CochainComplex.mappingCone.ext_cochain_to_iff
Mathlib/Algebra/Homology/HomotopyCategory/MappingCone.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
replace h₂ := <a>CochainComplex.HomComplex.Cochain.congr_v</a> h₂ p q hpq
case mpr.intro.h C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ γ₂ : Cochain K (mappingCone φ) i h₂ : γ₁.comp (snd φ) ⋯ = γ₂.comp (snd φ) ⋯ p q : ℤ hpq : p + i = q h₁ : (γ₁.comp (↑(fst φ...
case mpr.intro.h C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ γ₂ : Cochain K (mappingCone φ) i p q : ℤ hpq : p + i = q h₁ : (γ₁.comp (↑(fst φ)) hij).v p (q + 1) ⋯ = (γ₂.comp (↑(fst φ))...
((:c And) ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.66766) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.66766) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.66766) (:fv _uniq.66770))) ((:c HomologicalComplex.X) (:c Int) (:fv _uniq.66766) (:fv _uniq.66770) ((:c CategoryTheory.Preadditive.preadditiveHas...
[{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.66766))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Preadditive) (:fv _uniq.66766) (:fv _uniq.66770))"},{"name":"F","sexp":"((:c CochainComplex) (:fv _uniq.66766) (:fv _uniq.66770) ((:c CategoryTheory.Preadditi...
(:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HomologicalComplex.X) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:fv F...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Category...
{"children":[{"source":"replace","sourceEnd":7896,"sourceStart":7889,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h₂","sourceEnd":7901,"sourceStart":7897,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h₂","sourceEnd":7901,"sourceStart":7897,"tag":"node"}...
[]
[{"source":"Cochain.congr_v h₂ p q hpq","source_end":7933,"source_start":7905,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
37
26
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a56cd048f522901bb58e8e4a69a392344688eb931265a9ced15e3e9f2240082f
f2b359537f1c41a701fa646567ce25131ee8cdac92e0eeb7ab60f96b4b013313
8b7b80c86493b1e0cee58bd4cefafc06f9a710f83dc81f8f90dd17b12f458b71
ab87bac069f5d8eb191faca180224de12a11d5e8223eda0a8841f7ffc95dee09
cat-searcher/leandojo-benchmark-4-random
test
4,448
CochainComplex.mappingCone.ext_cochain_to_iff
Mathlib/Algebra/Homology/HomotopyCategory/MappingCone.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>CochainComplex.HomComplex.Cochain.comp_v</a> _ _ _ p q (q + 1) hpq <a>rfl</a>] at h₁
case mpr.intro.h C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ γ₂ : Cochain K (mappingCone φ) i p q : ℤ hpq : p + i = q h₁ : (γ₁.comp (↑(fst φ)) hij).v p (q + 1) ⋯ = (γ₂.comp (↑(fst φ))...
case mpr.intro.h C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ γ₂ : Cochain K (mappingCone φ) i p q : ℤ hpq : p + i = q h₂ : (γ₁.comp (snd φ) ⋯).v p q hpq = (γ₂.comp (snd φ) ⋯).v p q hp...
((:c And) ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.66766) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.66766) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.66766) (:fv _uniq.66770))) ((:c HomologicalComplex.X) (:c Int) (:fv _uniq.66766) (:fv _uniq.66770) ((:c CategoryTheory.Preadditive.preadditiveHas...
[{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.66766))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Preadditive) (:fv _uniq.66766) (:fv _uniq.66770))"},{"name":"F","sexp":"((:c CochainComplex) (:fv _uniq.66766) (:fv _uniq.66770) ((:c CategoryTheory.Preadditi...
(:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HomologicalComplex.X) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:fv F...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Category...
{"children":[{"source":"simp","sourceEnd":7942,"sourceStart":7938,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":7947,"sourceStart":7943,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":7947,"s...
[]
[{"source":"Cochain.comp_v _ _ _ p q (q + 1) hpq rfl","source_end":7989,"source_start":7949,"syntax_kind":"Lean.Parser.Term.app"},{"source":"h₁","source_end":7998,"source_start":7994,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
37
27
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0534ea7b50f629a315b05d6a8394d528be27a254436e1e732fecd5cbe3d90945
ab87bac069f5d8eb191faca180224de12a11d5e8223eda0a8841f7ffc95dee09
25097bad4a94d781f6684feb3a1f22ff5767dc26b6cf7c919f51b3d23a331d8d
a340b44fe0789a2496717b9828136634cc8dfaeba74c7df3d5057d64f82b3741
cat-searcher/leandojo-benchmark-4-random
test
4,449
CochainComplex.mappingCone.ext_cochain_to_iff
Mathlib/Algebra/Homology/HomotopyCategory/MappingCone.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>CochainComplex.HomComplex.Cochain.comp_zero_cochain_v</a>] at h₂
case mpr.intro.h C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ γ₂ : Cochain K (mappingCone φ) i p q : ℤ hpq : p + i = q h₂ : (γ₁.comp (snd φ) ⋯).v p q hpq = (γ₂.comp (snd φ) ⋯).v p q hp...
case mpr.intro.h C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ γ₂ : Cochain K (mappingCone φ) i p q : ℤ hpq : p + i = q h₁ : γ₁.v p q hpq ≫ (↑(fst φ)).v q (q + 1) ⋯ = γ₂.v p q hpq ≫ (↑(...
((:c And) ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.66766) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.66766) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.66766) (:fv _uniq.66770))) ((:c HomologicalComplex.X) (:c Int) (:fv _uniq.66766) (:fv _uniq.66770) ((:c CategoryTheory.Preadditive.preadditiveHas...
[{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.66766))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Preadditive) (:fv _uniq.66766) (:fv _uniq.66770))"},{"name":"F","sexp":"((:c CochainComplex) (:fv _uniq.66766) (:fv _uniq.66770) ((:c CategoryTheory.Preadditi...
(:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HomologicalComplex.X) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:fv F...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Category...
{"children":[{"source":"simp","sourceEnd":8007,"sourceStart":8003,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":8012,"sourceStart":8008,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":8012,"s...
[]
[{"source":"Cochain.comp_zero_cochain_v","source_end":8041,"source_start":8014,"syntax_kind":"ident"},{"source":"h₂","source_end":8050,"source_start":8046,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
37
28
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c6d1a071559346704f1564e661adbb7644beb9db921582d679a36c3bcd6c087f
a340b44fe0789a2496717b9828136634cc8dfaeba74c7df3d5057d64f82b3741
342d1cf56584ba3ab72ee4e5866297340dfd19bfe06a517fe0d7b2d0f74fb0ce
bb9ed08b9946a7f6c74f203d118740f2870529dad36e8d0b7e1173a2175087d2
cat-searcher/leandojo-benchmark-4-random
test
4,450
CochainComplex.mappingCone.ext_cochain_to_iff
Mathlib/Algebra/Homology/HomotopyCategory/MappingCone.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact ⟨h₁, h₂⟩
case mpr.intro.h C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ γ₂ : Cochain K (mappingCone φ) i p q : ℤ hpq : p + i = q h₁ : γ₁.v p q hpq ≫ (↑(fst φ)).v q (q + 1) ⋯ = γ₂.v p q hpq ≫ (↑(...
((:c And) ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.66766) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.66766) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.66766) (:fv _uniq.66770))) ((:c HomologicalComplex.X) (:c Int) (:fv _uniq.66766) (:fv _uniq.66770) ((:c CategoryTheory.Preadditive.preadditiveHas...
[{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.66766))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Preadditive) (:fv _uniq.66766) (:fv _uniq.66770))"},{"name":"F","sexp":"((:c CochainComplex) (:fv _uniq.66766) (:fv _uniq.66770) ((:c CategoryTheory.Preadditi...
(:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HomologicalComplex.X) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:fv F...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Category...
{"children":[{"source":"exact","sourceEnd":8060,"sourceStart":8055,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":8064,"sourceStart":8061,"tag":"atom"},{"children":[{"contextIndex":17,"semanticRole":"local","source":"h₁","sourceEnd":8068,"sourceStart":8064,"tag":"identifier"},{"source":",","sourceEnd":8069,"sourc...
[]
[{"source":"⟨h₁, h₂⟩","source_end":8077,"source_start":8061,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
37
29
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f8de3e2f344cf72095833b12bd145bf9fd90436015b8338c286d81fe6c1cb8c6
bb9ed08b9946a7f6c74f203d118740f2870529dad36e8d0b7e1173a2175087d2
670540d40337bf003e3a0f3f46ae677ddcb0bcd51cec291294711ca5dc1c589b
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,451
CochainComplex.mappingCone.ext_cochain_to_iff
Mathlib/Algebra/Homology/HomotopyCategory/MappingCone.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
omega
C : Type u_1 inst✝² : Category.{u_2, u_1} C inst✝¹ : Preadditive C F G : CochainComplex C ℤ φ : F ⟶ G inst✝ : HasHomotopyCofiber φ i j : ℤ hij : i + 1 = j K : CochainComplex C ℤ γ₁ γ₂ : Cochain K (mappingCone φ) i h₁ : γ₁.comp (↑(fst φ)) hij = γ₂.comp (↑(fst φ)) hij h₂ : γ₁.comp (snd φ) ⋯ = γ₂.comp (snd φ) ⋯ p q : ℤ hp...
((:c Eq) (:c Int) ((:c HAdd.hAdd) (:c Int) (:c Int) (:c Int) ((:c instHAdd) (:c Int) (:c Int.instAdd)) (:fv _uniq.69308) (:fv _uniq.68483)) ((:c HAdd.hAdd) (:c Int) (:c Int) (:c Int) ((:c instHAdd) (:c Int) (:c Int.instAdd)) (:fv _uniq.69311) ((:c OfNat.ofNat) (:c Int) (:lit 1) ((:c instOfNat) (:lit 1)))))
[{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.66766))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Preadditive) (:fv _uniq.66766) (:fv _uniq.66770))"},{"name":"F","sexp":"((:c CochainComplex) (:fv _uniq.66766) (:fv _uniq.66770) ((:c CategoryTheory.Preadditi...
(:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:c Int)) (:arg :implicit-type 2 (:c Int)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Int)) (:arg :explicit 1 (:c Int)) (:arg :explicit 2 (:c Int))))) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Category...
{"children":[{"children":[{"children":[{"children":[{"source":"omega","sourceEnd":7883,"sourceStart":7878,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.omega","source":"omega","sourceEnd":7883,"sourceStart":7878,"tag":"node"}],"kind":"null","source":"omega","sourceEnd"...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66766","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.66770","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
37
23
exact
true
1
18
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4f16a1b358d782b19486d781428b7af299abfc4d204566d0dcc4246b2257a608
143352c6835706c773bf8fff240400ecf3fd1adf75aa4a25ac74c250605b24f0
304b4a90a76a1cbe4c112e074b30e75181f54df43d60f883597457844293b341
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,452
Batteries.HashMap.Imp.Buckets.WF.update
.lake/packages/batteries/Batteries/Data/HashMap/WF.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨fun l hl => ?_, fun i hi p hp => ?_⟩
α : Type u_1 β : Type u_2 inst✝¹ : BEq α inst✝ : Hashable α buckets : Buckets α β i : USize d : AssocList α β h : i.toNat < buckets.val.size H : buckets.WF h₁ : ∀ [inst : PartialEquivBEq α] [inst : LawfulHashable α], List.Pairwise (fun a b => ¬(a.fst == b.fst) = true) buckets.val[i].toList → List.Pairwise (...
case refine_1 α : Type u_1 β : Type u_2 inst✝³ : BEq α inst✝² : Hashable α buckets : Buckets α β i : USize d : AssocList α β h : i.toNat < buckets.val.size H : buckets.WF h₁ : ∀ [inst : PartialEquivBEq α] [inst : LawfulHashable α], List.Pairwise (fun a b => ¬(a.fst == b.fst) = true) buckets.val[i].toList → ...
((:c Batteries.HashMap.Imp.Buckets.WF) (:fv _uniq.5109) (:fv _uniq.5110) (:fv _uniq.5111) (:fv _uniq.5112) ((:c Batteries.HashMap.Imp.Buckets.update) (:fv _uniq.5109) (:fv _uniq.5110) (:fv _uniq.5113) (:fv _uniq.5114) (:fv _uniq.5115) (:fv _uniq.5116)))
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c BEq) (:fv _uniq.5109))"},{"name":"inst✝","sexp":"((:c Hashable) (:fv _uniq.5109))"},{"name":"buckets","sexp":"((:c Batteries.HashMap.Imp.Buckets) (:fv _uniq.5109) (:fv _uniq.5110))"},{"name":"i","sexp":"(:c US...
(:app (:c Batteries.HashMap.Imp.Buckets.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c BEq) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c Hashable) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 4 (:app (:c Batteries.HashMap...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5109","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.5110","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"refine","sourceEnd":2245,"sourceStart":2239,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":2249,"sourceStart":2246,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":2252,"sourceStart":2249,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"l"...
[]
[{"source":"⟨fun l hl => ?_, fun i hi p hp => ?_⟩","source_end":2287,"source_start":2246,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5109","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.5110","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":3,"internal_nam...
11
4
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
95029cd177f8a6bec26a4b9be92e1376b6ccb25c3d5f8e837457cf2a1d4a11c0
d970e62ef3ac7397e46be5b4f8db1faebb91ce3e74454f838414fc358400e52b
2d5571395d82b0f08f90b414a9d90ae9cc6a02d2b14666b589ec6914391742bb
9e8a39b112e74ef411700f2882e7b1739714fd95d90c2ceddb3217597155a6ad
cat-searcher/leandojo-benchmark-4-random
test
4,453
Batteries.HashMap.Imp.Buckets.WF.update
.lake/packages/batteries/Batteries/Data/HashMap/WF.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact match <a>List.mem_or_eq_of_mem_set</a> hl with | .inl hl => H.1 _ hl | .inr <a>rfl</a> => h₁ (H.1 _ (<a>Array.getElem_mem_data</a> ..))
case refine_1 α : Type u_1 β : Type u_2 inst✝³ : BEq α inst✝² : Hashable α buckets : Buckets α β i : USize d : AssocList α β h : i.toNat < buckets.val.size H : buckets.WF h₁ : ∀ [inst : PartialEquivBEq α] [inst : LawfulHashable α], List.Pairwise (fun a b => ¬(a.fst == b.fst) = true) buckets.val[i].toList → ...
((:c List.Pairwise) ((:c Prod) (:fv _uniq.5109) (:fv _uniq.5110)) (:lambda a ((:c Prod) (:fv _uniq.5109) (:fv _uniq.5110)) (:lambda b ((:c Prod) (:fv _uniq.5109) (:fv _uniq.5110)) ((:c Not) ((:c Eq) (:c Bool) ((:c BEq.beq) (:fv _uniq.5109) (:fv _uniq.5111) ((:c Prod.fst) (:fv _uniq.5109) (:fv _uniq.5110) 1) ((:c Prod.f...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c BEq) (:fv _uniq.5109))"},{"name":"inst✝²","sexp":"((:c Hashable) (:fv _uniq.5109))"},{"name":"buckets","sexp":"((:c Batteries.HashMap.Imp.Buckets) (:fv _uniq.5109) (:fv _uniq.5110))"},{"name":"i","sexp":"(:c U...
(:app (:c List.Pairwise) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))) (:arg :explicit 1 (:lambda a :explicit (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2))) (:lambda b :explicit (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit ...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5109","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.5110","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":2298,"sourceStart":2293,"tag":"atom"},{"children":[{"source":"match","sourceEnd":2304,"sourceStart":2299,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"childre...
[]
[{"source":"match List.mem_or_eq_of_mem_set hl with\n | .inl hl => H.1 _ hl\n | .inr rfl => h₁ (H.1 _ (Array.getElem_mem_data ..))","source_end":2423,"source_start":2299,"syntax_kind":"Lean.Parser.Term.match"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5109","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.5110","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":3,"internal_nam...
11
7
exact
true
1
15
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8e8d0f6fc73ebd7a1ca15b832b9e83967ac9c5bbeca0e11557079a7fb6df2060
d8d8935f4aef02d8a9c188e224a098c0e7b8b2b99b7623d1cda12c229e9e7600
59622bca04f7d67563fa2ab5c47328bd592eededa6aeaa978846483045c9d1fe
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,454
Batteries.HashMap.Imp.Buckets.WF.update
.lake/packages/batteries/Batteries/Data/HashMap/WF.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
revert hp
case refine_2 α : Type u_1 β : Type u_2 inst✝¹ : BEq α inst✝ : Hashable α buckets : Buckets α β i✝ : USize d : AssocList α β h : i✝.toNat < buckets.val.size H : buckets.WF h₁ : ∀ [inst : PartialEquivBEq α] [inst : LawfulHashable α], List.Pairwise (fun a b => ¬(a.fst == b.fst) = true) buckets.val[i✝].toList → ...
case refine_2 α : Type u_1 β : Type u_2 inst✝¹ : BEq α inst✝ : Hashable α buckets : Buckets α β i✝ : USize d : AssocList α β h : i✝.toNat < buckets.val.size H : buckets.WF h₁ : ∀ [inst : PartialEquivBEq α] [inst : LawfulHashable α], List.Pairwise (fun a b => ¬(a.fst == b.fst) = true) buckets.val[i✝].toList → ...
((:lambda k (:fv _uniq.5109) (:lambda _ (:fv _uniq.5110) ((:c Eq) (:c Nat) ((:c USize.toNat) ((:c HMod.hMod) (:c USize) (:c Nat) (:c USize) (:c instHModUSizeNat) ((:c UInt64.toUSize) ((:c Hashable.hash) (:fv _uniq.5109) (:fv _uniq.5112) 1)) ((:c Array.size) ((:c Batteries.AssocList) (:fv _uniq.5109) (:fv _uniq.5110)) (...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c BEq) (:fv _uniq.5109))"},{"name":"inst✝","sexp":"((:c Hashable) (:fv _uniq.5109))"},{"name":"buckets","sexp":"((:c Batteries.HashMap.Imp.Buckets) (:fv _uniq.5109) (:fv _uniq.5110))"},{"name":"i✝","sexp":"(:c U...
(:app (:lambda k :explicit (:fv FV1) (:lambda _ :explicit (:fv FV2) (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c USize.toNat) (:arg :explicit 0 (:app (:c HMod.hMod) (:arg :implicit-type 0 (:c USize)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c USize)) (:arg :instance 3 (:in...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5109","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.5110","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"revert","sourceEnd":2435,"sourceStart":2429,"tag":"atom"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"hp","sourceEnd":2438,"sourceStart":2436,"tag":"identifier"}],"kind":"null","source":"hp","sourceEnd":2438,"sourceStart":2436,"tag":"node"}],"kind":"Lean.Parser.Tactic.revert...
[]
[{"source":"hp","source_end":2438,"source_start":2436,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5109","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.5110","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":3,"internal_nam...
11
14
exact
true
1
15
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
33f67468af4a9b707b980bdbf0d23cdf568e7f44e51ba67de1adf6a0e7616a0f
62c3c1d42bafda3d545c2a82bc660897cb867f58e5ab5e5f450544651c9c4df1
49f8cba8941182eb92fb75f82e5919fa8588979e66af4fca76b18f0adb2329c5
a8f120edc7e08b028b1b90a55c531b5a4ebb21fb497c8ce805a269021e9c3339
cat-searcher/leandojo-benchmark-4-random
test
4,455
Batteries.HashMap.Imp.Buckets.WF.update
.lake/packages/batteries/Batteries/Data/HashMap/WF.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>Array.getElem_eq_data_getElem</a>, <a>Batteries.HashMap.Imp.Buckets.update_data</a>, <a>List.getElem_set</a>, <a>Array.data_length</a>, <a>Batteries.HashMap.Imp.Buckets.update_size</a>]
case refine_2 α : Type u_1 β : Type u_2 inst✝¹ : BEq α inst✝ : Hashable α buckets : Buckets α β i✝ : USize d : AssocList α β h : i✝.toNat < buckets.val.size H : buckets.WF h₁ : ∀ [inst : PartialEquivBEq α] [inst : LawfulHashable α], List.Pairwise (fun a b => ¬(a.fst == b.fst) = true) buckets.val[i✝].toList → ...
case refine_2 α : Type u_1 β : Type u_2 inst✝¹ : BEq α inst✝ : Hashable α buckets : Buckets α β i✝ : USize d : AssocList α β h : i✝.toNat < buckets.val.size H : buckets.WF h₁ : ∀ [inst : PartialEquivBEq α] [inst : LawfulHashable α], List.Pairwise (fun a b => ¬(a.fst == b.fst) = true) buckets.val[i✝].toList → ...
(:forall hp ((:c Membership.mem) ((:c Prod) (:fv _uniq.5109) (:fv _uniq.5110)) ((:c List) ((:c Prod) (:fv _uniq.5109) (:fv _uniq.5110))) ((:c List.instMembership) ((:c Prod) (:fv _uniq.5109) (:fv _uniq.5110))) (:fv _uniq.5218) ((:c Batteries.AssocList.toList) (:fv _uniq.5109) (:fv _uniq.5110) ((:c GetElem.getElem) ((:c...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c BEq) (:fv _uniq.5109))"},{"name":"inst✝","sexp":"((:c Hashable) (:fv _uniq.5109))"},{"name":"buckets","sexp":"((:c Batteries.HashMap.Imp.Buckets) (:fv _uniq.5109) (:fv _uniq.5110))"},{"name":"i✝","sexp":"(:c U...
(:forall hp :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))))) (:arg :instance 2 (:instance-of (:app ...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5109","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.5110","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"simp","sourceEnd":2447,"sourceStart":2443,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":2452,"sourceStart":2448,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":2452,"s...
[]
[{"source":"Array.getElem_eq_data_getElem","source_end":2483,"source_start":2454,"syntax_kind":"ident"},{"source":"update_data","source_end":2496,"source_start":2485,"syntax_kind":"ident"},{"source":"List.getElem_set","source_end":2514,"source_start":2498,"syntax_kind":"ident"},{"source":"Array.data_length","source_end...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5109","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.5110","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":3,"internal_nam...
11
15
exact
true
1
14
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
81d3659d5bc2c2ddb387419c1915dc7b70225e7f78a0c8aa44b0d0f468bbd3cb
a8f120edc7e08b028b1b90a55c531b5a4ebb21fb497c8ce805a269021e9c3339
76a80bbaf43c1d3381ebedc3b28dcb10d50c5ca159c10d6d193621fcc5a44413
2af0ee9bb6bf340f8b2f94a5c8c0a9a51d3a9f9b5963f32d16aa32e37acacd77
cat-searcher/leandojo-benchmark-4-random
test
4,456
Batteries.HashMap.Imp.Buckets.WF.update
.lake/packages/batteries/Batteries/Data/HashMap/WF.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
split <;> intro hp
case refine_2 α : Type u_1 β : Type u_2 inst✝¹ : BEq α inst✝ : Hashable α buckets : Buckets α β i✝ : USize d : AssocList α β h : i✝.toNat < buckets.val.size H : buckets.WF h₁ : ∀ [inst : PartialEquivBEq α] [inst : LawfulHashable α], List.Pairwise (fun a b => ¬(a.fst == b.fst) = true) buckets.val[i✝].toList → ...
case refine_2.isTrue α : Type u_1 β : Type u_2 inst✝¹ : BEq α inst✝ : Hashable α buckets : Buckets α β i✝ : USize d : AssocList α β h : i✝.toNat < buckets.val.size H : buckets.WF h₁ : ∀ [inst : PartialEquivBEq α] [inst : LawfulHashable α], List.Pairwise (fun a b => ¬(a.fst == b.fst) = true) buckets.val[i✝].toList...
(:forall hp ((:c Membership.mem) ((:c Prod) (:fv _uniq.5109) (:fv _uniq.5110)) ((:c List) ((:c Prod) (:fv _uniq.5109) (:fv _uniq.5110))) ((:c List.instMembership) ((:c Prod) (:fv _uniq.5109) (:fv _uniq.5110))) (:fv _uniq.5218) ((:c Batteries.AssocList.toList) (:fv _uniq.5109) (:fv _uniq.5110) ((:c ite) ((:c Batteries.A...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c BEq) (:fv _uniq.5109))"},{"name":"inst✝","sexp":"((:c Hashable) (:fv _uniq.5109))"},{"name":"buckets","sexp":"((:c Batteries.HashMap.Imp.Buckets) (:fv _uniq.5109) (:fv _uniq.5110))"},{"name":"i✝","sexp":"(:c U...
(:forall hp :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))))) (:arg :instance 2 (:instance-of (:app ...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5109","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.5110","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"children":[{"source":"split","sourceEnd":2563,"sourceStart":2558,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.split","source":"split","sourceEnd":2563,"sourceStart":2558,"tag":"node"},{"source":"<;>...
[]
[]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5109","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.5110","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":3,"internal_nam...
11
16
exact
true
1
14
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f165d889a427434f898bbc70a53da479a2ea4bfc373985feeb660ae5b19ad8df
2af0ee9bb6bf340f8b2f94a5c8c0a9a51d3a9f9b5963f32d16aa32e37acacd77
bee730bc095489f0822813f10991760b7a8549c85e27f75aa82d95ab469f0a44
df18f9cbcdc8fbea2ba5377a40858a152f2e99296d457811f15ad0c473c7c424
cat-searcher/leandojo-benchmark-4-random
test
4,457
Batteries.HashMap.Imp.Buckets.WF.update
.lake/packages/batteries/Batteries/Data/HashMap/WF.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
next eq => exact eq ▸ h₂ (H.2 _ _) _ hp
case refine_2.isTrue α : Type u_1 β : Type u_2 inst✝¹ : BEq α inst✝ : Hashable α buckets : Buckets α β i✝ : USize d : AssocList α β h : i✝.toNat < buckets.val.size H : buckets.WF h₁ : ∀ [inst : PartialEquivBEq α] [inst : LawfulHashable α], List.Pairwise (fun a b => ¬(a.fst == b.fst) = true) buckets.val[i✝].toList...
((:c Eq) (:c Nat) ((:c USize.toNat) ((:c HMod.hMod) (:c USize) (:c Nat) (:c USize) (:c instHModUSizeNat) ((:c UInt64.toUSize) ((:c Hashable.hash) (:fv _uniq.5109) (:fv _uniq.5112) ((:c Prod.fst) (:fv _uniq.5109) (:fv _uniq.5110) (:fv _uniq.5218)))) ((:c Array.size) ((:c Batteries.AssocList) (:fv _uniq.5109) (:fv _uniq....
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c BEq) (:fv _uniq.5109))"},{"name":"inst✝","sexp":"((:c Hashable) (:fv _uniq.5109))"},{"name":"buckets","sexp":"((:c Batteries.HashMap.Imp.Buckets) (:fv _uniq.5109) (:fv _uniq.5110))"},{"name":"i✝","sexp":"(:c U...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c USize.toNat) (:arg :explicit 0 (:app (:c HMod.hMod) (:arg :implicit-type 0 (:c USize)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c USize)) (:arg :instance 3 (:instance-of (:app (:c HMod) (:arg :explicit 0 (:c USize)) (:arg :expli...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5109","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.5110","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"children":[{"children":[{"children":[{"source":"next","sourceEnd":2588,"sourceStart":2584,"tag":"atom"},{"children":[{"children":[{"contextIndex":15,"semanticRole":"local","source":"eq","sourceEnd":2591,"sourceStart":2589,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"eq","sourceEnd":2591,"sour...
[]
[{"source":"eq ▸ h₂ (H.2 _ _) _ hp","source_end":2627,"source_start":2601,"syntax_kind":"Lean.Parser.Term.subst"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5109","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.5110","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":3,"internal_nam...
11
23
exact
true
1
16
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0c8418c59d8a54a799d4091470292206ae79290ae0aa2db443f00e2f12393db6
dffde92ce806623e957aeb870d35bf210fa8af079104dcc49112b0e9c316bbc0
2968b687775be0d7d3ecf0747c6461dbbcdd38917dbc1a6055e9354c38555bd7
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,458
Batteries.HashMap.Imp.Buckets.WF.update
.lake/packages/batteries/Batteries/Data/HashMap/WF.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact eq ▸ h₂ (H.2 _ _) _ hp
α : Type u_1 β : Type u_2 inst✝¹ : BEq α inst✝ : Hashable α buckets : Buckets α β i✝ : USize d : AssocList α β h : i✝.toNat < buckets.val.size H : buckets.WF h₁ : ∀ [inst : PartialEquivBEq α] [inst : LawfulHashable α], List.Pairwise (fun a b => ¬(a.fst == b.fst) = true) buckets.val[i✝].toList → List.Pairwis...
((:c Eq) (:c Nat) ((:c USize.toNat) ((:c HMod.hMod) (:c USize) (:c Nat) (:c USize) (:c instHModUSizeNat) ((:c UInt64.toUSize) ((:c Hashable.hash) (:fv _uniq.5109) (:fv _uniq.5112) ((:c Prod.fst) (:fv _uniq.5109) (:fv _uniq.5110) (:fv _uniq.5218)))) ((:c Array.size) ((:c Batteries.AssocList) (:fv _uniq.5109) (:fv _uniq....
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c BEq) (:fv _uniq.5109))"},{"name":"inst✝","sexp":"((:c Hashable) (:fv _uniq.5109))"},{"name":"buckets","sexp":"((:c Batteries.HashMap.Imp.Buckets) (:fv _uniq.5109) (:fv _uniq.5110))"},{"name":"i✝","sexp":"(:c U...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c USize.toNat) (:arg :explicit 0 (:app (:c HMod.hMod) (:arg :implicit-type 0 (:c USize)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c USize)) (:arg :instance 3 (:instance-of (:app (:c HMod) (:arg :explicit 0 (:c USize)) (:arg :expli...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5109","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.5110","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":2600,"sourceStart":2595,"tag":"atom"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"eq","sourceEnd":2603,"sourceStart":2601,"tag":"identifier"},{"source":"▸","sourceEnd":2607,"sourceStart":2604,"tag":"atom"},{"children"...
[]
[{"source":"eq ▸ h₂ (H.2 _ _) _ hp","source_end":2627,"source_start":2601,"syntax_kind":"Lean.Parser.Term.subst"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5109","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.5110","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":3,"internal_nam...
11
26
exact
true
1
16
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7f1bca338bd98e61325fd84dd0b62e64eb8370e4870468be8022bd92a97a15ad
523a6281eb15c7207e1046b43057f304c9aa57bf42bb42b76a6b3d67216042db
5951fd44ebe08197bdec5f9830b29be5fc9062aaff29894e98f137a71260f658
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,459
Batteries.HashMap.Imp.Buckets.WF.update
.lake/packages/batteries/Batteries/Data/HashMap/WF.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>Batteries.HashMap.Imp.Buckets.update_size</a>, <a>Array.data_length</a>] at hi
case refine_2.isFalse α : Type u_1 β : Type u_2 inst✝¹ : BEq α inst✝ : Hashable α buckets : Buckets α β i✝ : USize d : AssocList α β h : i✝.toNat < buckets.val.size H : buckets.WF h₁ : ∀ [inst : PartialEquivBEq α] [inst : LawfulHashable α], List.Pairwise (fun a b => ¬(a.fst == b.fst) = true) buckets.val[i✝].toLis...
case refine_2.isFalse α : Type u_1 β : Type u_2 inst✝¹ : BEq α inst✝ : Hashable α buckets : Buckets α β i✝ : USize d : AssocList α β h : i✝.toNat < buckets.val.size H : buckets.WF h₁ : ∀ [inst : PartialEquivBEq α] [inst : LawfulHashable α], List.Pairwise (fun a b => ¬(a.fst == b.fst) = true) buckets.val[i✝].toLis...
((:c Eq) (:c Nat) ((:c USize.toNat) ((:c HMod.hMod) (:c USize) (:c Nat) (:c USize) (:c instHModUSizeNat) ((:c UInt64.toUSize) ((:c Hashable.hash) (:fv _uniq.5109) (:fv _uniq.5112) ((:c Prod.fst) (:fv _uniq.5109) (:fv _uniq.5110) (:fv _uniq.5218)))) ((:c Array.size) ((:c Batteries.AssocList) (:fv _uniq.5109) (:fv _uniq....
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c BEq) (:fv _uniq.5109))"},{"name":"inst✝","sexp":"((:c Hashable) (:fv _uniq.5109))"},{"name":"buckets","sexp":"((:c Batteries.HashMap.Imp.Buckets) (:fv _uniq.5109) (:fv _uniq.5110))"},{"name":"i✝","sexp":"(:c U...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c USize.toNat) (:arg :explicit 0 (:app (:c HMod.hMod) (:arg :implicit-type 0 (:c USize)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c USize)) (:arg :instance 3 (:instance-of (:app (:c HMod) (:arg :explicit 0 (:c USize)) (:arg :expli...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5109","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.5110","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"simp","sourceEnd":2639,"sourceStart":2635,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":2644,"sourceStart":2640,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":2644,"s...
[]
[{"source":"update_size","source_end":2657,"source_start":2646,"syntax_kind":"ident"},{"source":"Array.data_length","source_end":2676,"source_start":2659,"syntax_kind":"ident"},{"source":"hi","source_end":2683,"source_start":2681,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5109","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.5110","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":3,"internal_nam...
11
33
exact
true
1
16
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
05affc913661f13169102f346ade3310f4de0a53cbceaca9ac3765a0e4a4d705
005ab7d265983ddfeb98fd73713eb47c6d26f79264b0ded185e2fb1ed3d415d4
cdb996dfa7c4e435cede29fd67e0053379593c3d61a79f2ee7b7e877dc898031
aab309b246f0c35538783d6b401cb5145b8d7828ee181aceb68de66128597a67
cat-searcher/leandojo-benchmark-4-random
test
4,460
Batteries.HashMap.Imp.Buckets.WF.update
.lake/packages/batteries/Batteries/Data/HashMap/WF.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact H.2 i hi _ hp
case refine_2.isFalse α : Type u_1 β : Type u_2 inst✝¹ : BEq α inst✝ : Hashable α buckets : Buckets α β i✝ : USize d : AssocList α β h : i✝.toNat < buckets.val.size H : buckets.WF h₁ : ∀ [inst : PartialEquivBEq α] [inst : LawfulHashable α], List.Pairwise (fun a b => ¬(a.fst == b.fst) = true) buckets.val[i✝].toLis...
((:c Eq) (:c Nat) ((:c USize.toNat) ((:c HMod.hMod) (:c USize) (:c Nat) (:c USize) (:c instHModUSizeNat) ((:c UInt64.toUSize) ((:c Hashable.hash) (:fv _uniq.5109) (:fv _uniq.5112) ((:c Prod.fst) (:fv _uniq.5109) (:fv _uniq.5110) (:fv _uniq.5218)))) ((:c Array.size) ((:c Batteries.AssocList) (:fv _uniq.5109) (:fv _uniq....
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c BEq) (:fv _uniq.5109))"},{"name":"inst✝","sexp":"((:c Hashable) (:fv _uniq.5109))"},{"name":"buckets","sexp":"((:c Batteries.HashMap.Imp.Buckets) (:fv _uniq.5109) (:fv _uniq.5110))"},{"name":"i✝","sexp":"(:c U...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c USize.toNat) (:arg :explicit 0 (:app (:c HMod.hMod) (:arg :implicit-type 0 (:c USize)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c USize)) (:arg :instance 3 (:instance-of (:app (:c HMod) (:arg :explicit 0 (:c USize)) (:arg :expli...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5109","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.5110","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"exact","sourceEnd":2695,"sourceStart":2690,"tag":"atom"},{"children":[{"children":[{"contextIndex":9,"semanticRole":"local","source":"H","sourceEnd":2697,"sourceStart":2696,"tag":"identifier"},{"source":".","sourceEnd":2698,"sourceStart":2697,"tag":"atom"},{"children":[{"source":"2","sourceEnd":...
[]
[{"source":"H.2 i hi _ hp","source_end":2709,"source_start":2696,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5109","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.5110","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":3,"internal_nam...
11
34
exact
true
1
17
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
71511a261a18663c7a2a86176a0e19b682a8d7daa239241b7cdab57c40ffe1d0
aab309b246f0c35538783d6b401cb5145b8d7828ee181aceb68de66128597a67
2f60444ba7cb6e295b166dc465466ca8047a60b892d67a2272ceb78b00dbb651
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,461
Prod.smul_mk_zero
Mathlib/GroupTheory/GroupAction/Prod.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Prod.smul_mk</a>, <a>smul_zero</a>]
M : Type u_1 N : Type u_2 P : Type u_3 E : Type u_4 α : Type u_5 β✝ : Type u_6 inst✝⁶ : SMul M α inst✝⁵ : SMul M β✝ inst✝⁴ : SMul N α inst✝³ : SMul N β✝ a✝ : M x : α × β✝ β : Type u_7 inst✝² : Monoid M inst✝¹ : AddMonoid β inst✝ : DistribMulAction M β a : M b : α ⊢ a • (b, 0) = (a • b, 0)
((:c Eq) ((:c Prod) (:fv _uniq.2440) (:fv _uniq.2876)) ((:c HSMul.hSMul) (:fv _uniq.2428) ((:c Prod) (:fv _uniq.2440) (:fv _uniq.2876)) ((:c Prod) (:fv _uniq.2440) (:fv _uniq.2876)) ((:c instHSMul) (:fv _uniq.2428) ((:c Prod) (:fv _uniq.2440) (:fv _uniq.2876)) ((:c Prod.smul) (:fv _uniq.2428) (:fv _uniq.2440) (:fv _uni...
[{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"N","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"E","sexp":"(:sort (+ u_4 1))"},{"name":"α","sexp":"(:sort (+ u_5 1))"},{"name":"β✝","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁶","sexp":"((:c SMul) (:fv _uniq.2428) (:fv _uniq.2440))"},{"nam...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV4)) (:arg :explicit 1 (:fv FV13)))) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Prod) (:arg :explicit 0 (:fv FV4)) (:arg :explicit 1 (:fv FV13)))) (:arg :implicit-type 2 (:app (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2428","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2431","is_instance":false,"is_let":false,"name":"N","sexp":"(:sort Type)"},{"binder_role":":implicit","conte...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":2699,"sourceStart":2697,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2701,"sourceStart":2700,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag...
[]
[{"source":"Prod.smul_mk","source_end":2713,"source_start":2701,"syntax_kind":"ident"},{"source":"smul_zero","source_end":2724,"source_start":2715,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2428","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2431","is_instance":false,"is_let":false,"user_name":"N"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq...
25
2
exact
true
1
18
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c76122475f4d5fd09698de2f26d64dcadfe320d3ab8bcd54561a06e35d0ecb86
a8323fda4b224b405080349c57692fc5b08bcf608e65cfd36e22b8d3381255be
9fea5671134920974caa2336e339cc5f04d56382449e5469ab662cbbb85ed4a0
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,462
Set.Ioc_union_Ioc_left
Mathlib/Order/Interval/Set/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Set.Ioc_union_Ioc</a>, <a>max_self</a>] <;> exact (<a>min_le_right</a> _ _).<a>LE.le.trans</a> (<a>le_max_right</a> _ _)
α : Type u_1 β : Type u_2 inst✝¹ : LinearOrder α inst✝ : LinearOrder β f : α → β a a₁ a₂ b b₁ b₂ c d : α ⊢ Ioc a c ∪ Ioc b c = Ioc (min a b) c
((:c Eq) ((:c Set) (:fv _uniq.191746)) ((:c Union.union) ((:c Set) (:fv _uniq.191746)) ((:c Set.instUnion) (:fv _uniq.191746)) ((:c Set.Ioc) (:fv _uniq.191746) ((:c PartialOrder.toPreorder) (:fv _uniq.191746) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.191746) ((:c Lattice.toSemilatticeInf) (:fv _uniq.191746) ((:c D...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrder) (:fv _uniq.191746))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.191749))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.191746) (:fv _uniq.191749))"},{"name":"a","sexp":"(:fv _uniq.191746)...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Union.union) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c Union) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :expl...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.191746","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.191749","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":73811,"sourceStart":73809,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":73813,"sourceStart":73812,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null"...
[]
[{"source":"Ioc_union_Ioc","source_end":73826,"source_start":73813,"syntax_kind":"ident"},{"source":"max_self","source_end":73836,"source_start":73828,"syntax_kind":"ident"},{"source":"(min_le_right _ _).trans (le_max_right _ _)","source_end":73891,"source_start":73848,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.191746","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.191749","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal...
742
2
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0b86db4481baa4217861cffa58299378db9d79470d13aa16846bba66dbb20717
19722385df65733f08cd36186b0688ab66dfbc452d41aad2bdb4a09920f01cfd
ddb7f5b17277dbb335f13c25c5102fcfe924dd3c458b09bfa50cdcafaf18e686
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,463
Finset.sup_product_right
Mathlib/Data/Finset/Lattice.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Finset.sup_product_left</a>, <a>Finset.sup_comm</a>]
F : Type u_1 α : Type u_2 β : Type u_3 γ : Type u_4 ι : Type u_5 κ : Type u_6 inst✝¹ : SemilatticeSup α inst✝ : OrderBot α s✝ s₁ s₂ : Finset β f✝ g : β → α a : α s : Finset β t : Finset γ f : β × γ → α ⊢ (s ×ˢ t).sup f = t.sup fun i' => s.sup fun i => f (i, i')
((:c Eq) (:fv _uniq.60542) ((:c Finset.sup) (:fv _uniq.60542) ((:c Prod) (:fv _uniq.60545) (:fv _uniq.60548)) (:fv _uniq.60557) (:fv _uniq.60817) ((:c SProd.sprod) ((:c Finset) (:fv _uniq.60545)) ((:c Finset) (:fv _uniq.60548)) ((:c Finset) ((:c Prod) (:fv _uniq.60545) (:fv _uniq.60548))) ((:c Finset.instSProd) (:fv _u...
[{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"κ","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝¹","sexp":"((:c SemilatticeSup) (:fv _uniq.60542))"},{"name":"ins...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Finset.sup) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV3)))) (:arg :instance 2 (:instance-of (:app (:c SemilatticeSup) (:arg :explicit 0 (:fv FV1))))) (:arg :in...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60539","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60542","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":6382,"sourceStart":6380,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6384,"sourceStart":6383,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag...
[]
[{"source":"sup_product_left","source_end":6400,"source_start":6384,"syntax_kind":"ident"},{"source":"Finset.sup_comm","source_end":6417,"source_start":6402,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60539","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60542","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
62
2
exact
true
1
17
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e2a17d62609592cbef16df9a6e965c8d8aaaf81a8c1df96b958ebdf99a7aeb33
a1c40da7fffc78e1c96a2faf2b51a1bddbf33732e3ca67e0531289dafa45e9c6
80f4847347d12d1a890317f127edd21c7ed14a3fb5d334c3940f3176f01d9870
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,464
isSolvable_of_comm
Mathlib/GroupTheory/Solvable.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
letI hG' : <a>CommGroup</a> G := { hG with mul_comm := h }
G✝ : Type u_1 G' : Type u_2 inst✝¹ : Group G✝ inst✝ : Group G' f : G✝ →* G' G : Type u_3 hG : Group G h : ∀ (a b : G), a * b = b * a ⊢ IsSolvable G
G✝ : Type u_1 G' : Type u_2 inst✝¹ : Group G✝ inst✝ : Group G' f : G✝ →* G' G : Type u_3 hG : Group G h : ∀ (a b : G), a * b = b * a hG' : CommGroup G := CommGroup.mk h ⊢ IsSolvable G
((:c IsSolvable) (:fv _uniq.15943) (:fv _uniq.15944))
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(:app (:c IsSolvable) (:arg :explicit 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV6))))))
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.14080","is_instance":false,"is_let":false,"name":"G✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14083","is_instance":false,"is_let":false,"name":"G'","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"letI","sourceEnd":4122,"sourceStart":4118,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"hG'","sourceEnd":4126,"sourceStart":4123,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hG'","sourceEnd":4126,"sourceStart":4123,"tag":"node"},{"children":[],"kind":"null","...
[]
[{"source":"CommGroup G","source_end":4140,"source_start":4129,"syntax_kind":"Lean.Parser.Term.app"},{"source":"{ hG with mul_comm := h }","source_end":4169,"source_start":4144,"syntax_kind":"Lean.Parser.Term.structInst"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.14080","is_instance":false,"is_let":false,"user_name":"G✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14083","is_instance":false,"is_let":false,"user_name":"G'"},{"binder_role":":instance-implicit","context_index":2,"internal...
36
4
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a5110db0636208885197491ec787459e818e8457962a8b2d461cdf5aa70947c1
b86a218e5fda92d3cba34cfeffac83ae8613192ec9544514825591d8a98b1b65
cb134d4c2218d736441d421477bc07ed8dbed1a27ebe8c750b268bd3d496bb2f
0b808bca3b13b5cec221752651abfe235360c5a5de513e9ffa260ba4a82a1ca5
cat-searcher/leandojo-benchmark-4-random
test
4,465
isSolvable_of_comm
Mathlib/GroupTheory/Solvable.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
cases hG
G✝ : Type u_1 G' : Type u_2 inst✝¹ : Group G✝ inst✝ : Group G' f : G✝ →* G' G : Type u_3 hG : Group G h : ∀ (a b : G), a * b = b * a hG' : CommGroup G := CommGroup.mk h ⊢ IsSolvable G
case mk G✝ : Type u_1 G' : Type u_2 inst✝¹ : Group G✝ inst✝ : Group G' f : G✝ →* G' G : Type u_3 toDivInvMonoid✝ : DivInvMonoid G mul_left_inv✝ : ∀ (a : G), a⁻¹ * a = 1 h : ∀ (a b : G), a * b = b * a hG' : CommGroup G := CommGroup.mk h ⊢ IsSolvable G
((:c IsSolvable) (:fv _uniq.15943) (:fv _uniq.15944))
[{"name":"G✝","sexp":"(:sort (+ u_1 1))"},{"name":"G'","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.14080))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.14083))"},{"name":"f","sexp":"((:c MonoidHom) (:fv _uniq.14080) (:fv _uniq.14083) ((:c Monoid.toMulOneClass) (:fv _uniq.14080) ((:c ...
(:app (:c IsSolvable) (:arg :explicit 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV6))))))
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.14080","is_instance":false,"is_let":false,"name":"G✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14083","is_instance":false,"is_let":false,"name":"G'","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"cases","sourceEnd":4177,"sourceStart":4172,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":7,"semanticRole":"local","source":"hG","sourceEnd":4180,"sourceStart":4178,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","sourc...
[]
[{"source":"hG","source_end":4180,"source_start":4178,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.14080","is_instance":false,"is_let":false,"user_name":"G✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14083","is_instance":false,"is_let":false,"user_name":"G'"},{"binder_role":":instance-implicit","context_index":2,"internal...
36
5
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
326ed05080936f8a2e973252771e1375f2ac12bd34b1cd9f60d179d3c78b6b2b
0b808bca3b13b5cec221752651abfe235360c5a5de513e9ffa260ba4a82a1ca5
c00cddd5000454d03be22df4c714f30a32ed95d1c6344a4e36e45088aceaeff0
f0b8929a475d2401e31c710887aa124ad0e75acfb0a1d0ea127199ddf417423b
cat-searcher/leandojo-benchmark-4-random
test
4,466
isSolvable_of_comm
Mathlib/GroupTheory/Solvable.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>CommGroup.isSolvable</a>
case mk G✝ : Type u_1 G' : Type u_2 inst✝¹ : Group G✝ inst✝ : Group G' f : G✝ →* G' G : Type u_3 toDivInvMonoid✝ : DivInvMonoid G mul_left_inv✝ : ∀ (a : G), a⁻¹ * a = 1 h : ∀ (a b : G), a * b = b * a hG' : CommGroup G := CommGroup.mk h ⊢ IsSolvable G
((:c IsSolvable) (:fv _uniq.15943) ((:c Group.mk) (:fv _uniq.15943) (:fv _uniq.15991) (:fv _uniq.15992)))
[{"name":"G✝","sexp":"(:sort (+ u_1 1))"},{"name":"G'","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.14080))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.14083))"},{"name":"f","sexp":"((:c MonoidHom) (:fv _uniq.14080) (:fv _uniq.14083) ((:c Monoid.toMulOneClass) (:fv _uniq.14080) ((:c ...
(:app (:c IsSolvable) (:arg :explicit 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV6))))))
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.14080","is_instance":false,"is_let":false,"name":"G✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14083","is_instance":false,"is_let":false,"name":"G'","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"exact","sourceEnd":4188,"sourceStart":4183,"tag":"atom"},{"name":"CommGroup.isSolvable","semanticRole":"global","source":"CommGroup.isSolvable","sourceEnd":4209,"sourceStart":4189,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact CommGroup.isSolvable","sourceEnd":4209,"sourc...
[]
[{"source":"CommGroup.isSolvable","source_end":4209,"source_start":4189,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.14080","is_instance":false,"is_let":false,"user_name":"G✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14083","is_instance":false,"is_let":false,"user_name":"G'"},{"binder_role":":instance-implicit","context_index":2,"internal...
36
6
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ebefa1f86391ce4b6664ba8dc8f53cf6faebcc2d20d597cfafe4463f56386f62
f0b8929a475d2401e31c710887aa124ad0e75acfb0a1d0ea127199ddf417423b
e2fa6c3fb80b46bdd764ad4991dc070f24888bc28bd950edbe820ef729385922
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,467
hasDerivAt_mul_const
Mathlib/Analysis/Calculus/Deriv/Mul.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simpa only [<a>one_mul</a>] using (<a>hasDerivAt_id'</a> x).<a>HasDerivAt.mul_const</a> c
𝕜 : Type u inst✝¹⁰ : NontriviallyNormedField 𝕜 F : Type v inst✝⁹ : NormedAddCommGroup F inst✝⁸ : NormedSpace 𝕜 F E : Type w inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E G : Type u_1 inst✝⁵ : NormedAddCommGroup G inst✝⁴ : NormedSpace 𝕜 G f f₀ f₁ g : 𝕜 → F f' f₀' f₁' g' : F x : 𝕜 s t : Set 𝕜 L L₁ L₂ : F...
((:c HasDerivAt) (:fv _uniq.377447) (:fv _uniq.377450) (:fv _uniq.377447) ((:c NonUnitalNormedRing.toNormedAddCommGroup) (:fv _uniq.377447) ((:c NonUnitalNormedCommRing.toNonUnitalNormedRing) (:fv _uniq.377447) ((:c NormedCommRing.toNonUnitalNormedCommRing) (:fv _uniq.377447) ((:c NormedField.toNormedCommRing) (:fv _un...
[{"name":"𝕜","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.377447))"},{"name":"F","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.377452))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.377447) (:fv _uniq.377452) ((:c Nontri...
(:app (:c HasDerivAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.377447","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.377450","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...
{"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":11183,"sourceStart":11178,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind...
[]
[{"source":"one_mul","source_end":11197,"source_start":11190,"syntax_kind":"ident"},{"source":"(hasDerivAt_id' x).mul_const c","source_end":11235,"source_start":11205,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.377447","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.377450","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...
82
2
exact
true
1
38
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9946aed80fcf051cf9ffcd71c3ff1955c1b8935a7c65780b52b1472eaa33feac
298fc2c0c25be434c38d39a094978a0bcfa3613be212b45a30b500cde0d2778b
6671cbfe195d3ab6fa587d849e4238bb12213db230d9aa1778c52671e6b1384d
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,468
Complex.arg_eq_nhds_of_re_neg_of_im_neg
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
suffices h_forall_nhds : ∀ᶠ y : ℂ in 𝓝 x, y.re < 0 ∧ y.im < 0 from h_forall_nhds.mono fun y hy => <a>Complex.arg_of_re_neg_of_im_neg</a> hy.1 hy.2
a x z : ℂ hx_re : x.re < 0 hx_im : x.im < 0 ⊢ arg =ᶠ[𝓝 x] fun x => Real.arcsin ((-x).im / abs x) - π
a x z : ℂ hx_re : x.re < 0 hx_im : x.im < 0 ⊢ ∀ᶠ (y : ℂ) in 𝓝 x, y.re < 0 ∧ y.im < 0
((:c Filter.EventuallyEq) (:c Complex) (:c Real) ((:c nhds) (:c Complex) ((:c UniformSpace.toTopologicalSpace) (:c Complex) ((:c PseudoMetricSpace.toUniformSpace) (:c Complex) ((:c SeminormedRing.toPseudoMetricSpace) (:c Complex) ((:c SeminormedCommRing.toSeminormedRing) (:c Complex) ((:c NormedCommRing.toSeminormedCom...
[{"name":"a","sexp":"(:c Complex)"},{"name":"x","sexp":"(:c Complex)"},{"name":"z","sexp":"(:c Complex)"},{"name":"hx_re","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c Complex.re) (:fv _uniq.218776)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"},{"name":"hx_im","sexp":...
(:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:c Complex)) (:arg :implicit-type 1 (:c Real)) (:arg :explicit 2 (:app (:c nhds) (:arg :implicit-type 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Complex))))) (:arg :explicit 2 (:fv FV1)))) (:arg :explicit 3 (:c...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.218774","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Complex)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.218776","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Complex)"},{"binder_role":":implicit","c...
{"children":[{"source":"suffices","sourceEnd":28641,"sourceStart":28633,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"h_forall_nhds","sourceEnd":28655,"sourceStart":28642,"tag":"identifier"},{"source":":","sourceEnd":28657,"sourceStart":28656,"tag":"atom"}],"kind":"group","source":"h_...
[]
[{"source":"∀ᶠ y : ℂ in 𝓝 x, y.re < 0 ∧ y.im < 0","source_end":28705,"source_start":28658,"syntax_kind":"Filter.«term∀ᶠ_In_,_»"},{"source":"h_forall_nhds.mono fun y hy => arg_of_re_neg_of_im_neg hy.1 hy.2","source_end":28779,"source_start":28715,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.218774","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.218776","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
155
4
exact
true
1
5
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
09d1566390c86ce775ff4b9b5e9ce295814e3a1d1a882ba1ea05ccc19f36a094
c64325396859e1e56077aac220fd1f928a44491ffae78ae826265c974a70a661
b7690e5acf98a8996f1c02206d4c3dfe2d51d0d14b9c76201c34c94f2288bea3
c896d6885469e90426504cc4926809df4eda4f73ea221fa52c14666422290ea4
cat-searcher/leandojo-benchmark-4-random
test
4,469
Complex.arg_eq_nhds_of_re_neg_of_im_neg
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine <a>IsOpen.eventually_mem</a> ?_ (⟨hx_re, hx_im⟩ : x.re < 0 ∧ x.im < 0)
a x z : ℂ hx_re : x.re < 0 hx_im : x.im < 0 ⊢ ∀ᶠ (y : ℂ) in 𝓝 x, y.re < 0 ∧ y.im < 0
a x z : ℂ hx_re : x.re < 0 hx_im : x.im < 0 ⊢ IsOpen fun y => y.re < 0 ∧ y.im < 0
((:c Filter.Eventually) (:c Complex) (:lambda y (:c Complex) ((:c And) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c Complex.re) 0) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c Complex.im) 0) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c ...
[{"name":"a","sexp":"(:c Complex)"},{"name":"x","sexp":"(:c Complex)"},{"name":"z","sexp":"(:c Complex)"},{"name":"hx_re","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c Complex.re) (:fv _uniq.218776)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"},{"name":"hx_im","sexp":...
(:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:lambda y :explicit (:c Complex) (:app (:c And) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Complex.re) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.218774","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Complex)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.218776","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Complex)"},{"binder_role":":implicit","c...
{"children":[{"source":"refine","sourceEnd":28788,"sourceStart":28782,"tag":"atom"},{"children":[{"name":"IsOpen.eventually_mem","semanticRole":"global","source":"IsOpen.eventually_mem","sourceEnd":28810,"sourceStart":28789,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":28812,"sourceStart":2881...
[]
[{"source":"IsOpen.eventually_mem ?_ (⟨hx_re, hx_im⟩ : x.re < 0 ∧ x.im < 0)","source_end":28858,"source_start":28789,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.218774","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.218776","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
155
5
exact
true
1
5
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c2f328bff1074c917ec0eb566f5900ad6ef8b8404d5fbbb3f717a71026fd2fee
c896d6885469e90426504cc4926809df4eda4f73ea221fa52c14666422290ea4
1cf6b9a9aaa1815997e4e6b3292dd38d3a3186915bf2c7f91beb20077c3f63a3
33e4b6527f5bfb5990a21c1edbe05616656dafae9df40339c50190fbc8ece7b6
cat-searcher/leandojo-benchmark-4-random
test
4,470
Complex.arg_eq_nhds_of_re_neg_of_im_neg
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>IsOpen.and</a> (<a>isOpen_lt</a> <a>Complex.continuous_re</a> <a>continuous_zero</a>) (<a>isOpen_lt</a> <a>Complex.continuous_im</a> <a>continuous_zero</a>)
a x z : ℂ hx_re : x.re < 0 hx_im : x.im < 0 ⊢ IsOpen fun y => y.re < 0 ∧ y.im < 0
((:c IsOpen) (:c Complex) ((:c UniformSpace.toTopologicalSpace) (:c Complex) ((:c PseudoMetricSpace.toUniformSpace) (:c Complex) ((:c SeminormedRing.toPseudoMetricSpace) (:c Complex) ((:c SeminormedCommRing.toSeminormedRing) (:c Complex) ((:c NormedCommRing.toSeminormedCommRing) (:c Complex) ((:c NormedField.toNormedCo...
[{"name":"a","sexp":"(:c Complex)"},{"name":"x","sexp":"(:c Complex)"},{"name":"z","sexp":"(:c Complex)"},{"name":"hx_re","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c Complex.re) (:fv _uniq.218776)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"},{"name":"hx_im","sexp":...
(:app (:c IsOpen) (:arg :implicit-type 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Complex))))) (:arg :explicit 2 (:lambda y :explicit (:c Complex) (:app (:c And) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.218774","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Complex)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.218776","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Complex)"},{"binder_role":":implicit","c...
{"children":[{"source":"exact","sourceEnd":28866,"sourceStart":28861,"tag":"atom"},{"children":[{"name":"IsOpen.and","semanticRole":"global","source":"IsOpen.and","sourceEnd":28881,"sourceStart":28871,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":28883,"sourceStart":28882,"tag":"atom"},{"child...
[]
[{"source":"IsOpen.and (isOpen_lt continuous_re continuous_zero) (isOpen_lt continuous_im continuous_zero)","source_end":28965,"source_start":28871,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.218774","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.218776","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
155
6
exact
true
1
5
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f141a72a1fc33287f6001da03e2eff014cb2e8ebbfacae03dd3f64805f7eb756
33e4b6527f5bfb5990a21c1edbe05616656dafae9df40339c50190fbc8ece7b6
ef1e70ac40c2078678f640fa8ac6fffad7afb5f27cca48d19a4e80cb74579922
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,471
CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ι
Mathlib/CategoryTheory/Abelian/InjectiveResolution.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>CategoryTheory.InjectiveResolution.homotopyEquiv</a>]
C : Type u inst✝¹ : Category.{v, u} C inst✝ : Abelian C X : C I J : InjectiveResolution X ⊢ I.ι ≫ (I.homotopyEquiv J).hom = J.ι
((:c Eq) ((:c Quiver.Hom) ((:c CochainComplex) (:fv _uniq.49091) (:fv _uniq.49094) ((:c CategoryTheory.Preadditive.preadditiveHasZeroMorphisms) (:fv _uniq.49091) (:fv _uniq.49094) ((:c CategoryTheory.Abelian.toPreadditive) (:fv _uniq.49091) (:fv _uniq.49094) (:fv _uniq.49109))) (:c Nat) ((:c AddRightCancelMonoid.toAddR...
[{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.49091))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Abelian) (:fv _uniq.49091) (:fv _uniq.49094))"},{"name":"X","sexp":"(:fv _uniq.49091)"},{"name":"I","sexp":"((:c CategoryTheory.InjectiveResolution) (:fv _uniq.4...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:app (:c CochainComplex) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c CategoryTheory.Limits.HasZeroMorphisms) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.49091","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.49094","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":11122,"sourceStart":11118,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...
[]
[{"source":"homotopyEquiv","source_end":11137,"source_start":11124,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.49091","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.49094","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":...
48
2
exact
true
1
6
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2d3ac979970fea517f9b3215d968239e7389c73ca987390da5a49592448a461c
ef1400d5c7c0174b9902f629bf7ae477c2e09247b08be4b1a6baeb153c673e32
dcd8737b561a19cfb620938690dfd97be8bb195d241a2320d73e525934499c6a
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,472
Polynomial.mul_coeff_zero
Mathlib/Algebra/Polynomial/Coeff.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>Polynomial.coeff_mul</a>]
R : Type u S : Type v a b : R n m : ℕ inst✝ : Semiring R p✝ q✝ r p q : R[X] ⊢ (p * q).coeff 0 = p.coeff 0 * q.coeff 0
((:c Eq) (:fv _uniq.20463) ((:c Polynomial.coeff) (:fv _uniq.20463) (:fv _uniq.20476) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.20463) (:fv _uniq.20476)) ((:c Polynomial) (:fv _uniq.20463) (:fv _uniq.20476)) ((:c Polynomial) (:fv _uniq.20463) (:fv _uniq.20476)) ((:c instHMul) ((:c Polynomial) (:fv _uniq.20463) (:fv _...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.20463)"},{"name":"b","sexp":"(:fv _uniq.20463)"},{"name":"n","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.20463))"},{"name":"p✝","sexp":"((:c Polynomial) (:f...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Polynomial.coeff) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv F...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20463","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20465","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":4879,"sourceStart":4875,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn...
[]
[{"source":"coeff_mul","source_end":4890,"source_start":4881,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20463","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20465","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
36
2
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b6737afc222f8ba553c4ab1085798d56b3a17caf8d5a01829e5da8eb60edcd09
9c4547536d8c9bbefce648c2a5a7479e692148e37ddeb63181b7e90240d91216
ac0be1462f5a9c3e97745e26329a61eff486acdac2a69ba3cf1da80bd771ed05
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,473
Monotone.cauchySeq_alternating_series_of_tendsto_zero
Mathlib/Analysis/SpecificLimits/Normed.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp_rw [<a>mul_comm</a>]
α : Type u_1 β : Type u_2 ι : Type u_3 E : Type u_4 inst✝¹ : NormedAddCommGroup E inst✝ : NormedSpace ℝ E b : ℝ f : ℕ → ℝ z : ℕ → E hfa : Monotone f hf0 : Tendsto f atTop (𝓝 0) ⊢ CauchySeq fun n => ∑ i ∈ Finset.range n, (-1) ^ i * f i
α : Type u_1 β : Type u_2 ι : Type u_3 E : Type u_4 inst✝¹ : NormedAddCommGroup E inst✝ : NormedSpace ℝ E b : ℝ f : ℕ → ℝ z : ℕ → E hfa : Monotone f hf0 : Tendsto f atTop (𝓝 0) ⊢ CauchySeq fun n => ∑ x ∈ Finset.range n, f x * (-1) ^ x
((:c CauchySeq) (:c Real) (:c Nat) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.pseudoMetricSpace)) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))) (:lambda n (:c Nat) ((:c Finset.sum) (:c Nat) (:c Real) (:c Real.instAddCommMon...
[{"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":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.236369))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.236369) (:c Real.normedF...
(:app (:c CauchySeq) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c UniformSpace) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 4 (:lambda n :explicit (:c Nat) (:app (:c Fin...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.236360","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.236363","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"simp_rw","sourceEnd":37292,"sourceStart":37285,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":37294,"sourceStart":37293,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"mul_comm","...
[]
[{"source":"mul_comm","source_end":37302,"source_start":37294,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.236360","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.236363","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
159
4
exact
true
1
11
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a12f223913b6217e96ef0ecea8eb04a68d90956b054af631b3d1aeec193e06a1
2cb2f7ba1936b11edde18861dc35a345691d48a15172c6650efa1e37a3038662
69161f1c5340fef7ecf9f3fff0d242d6aa305b20da19208fc248667b15c265f2
64ec54daa38c13e1bb362a59d03c36ebf98c8bb15ec63c31a3adf7894ad5eb3f
cat-searcher/leandojo-benchmark-4-random
test
4,474
Monotone.cauchySeq_alternating_series_of_tendsto_zero
Mathlib/Analysis/SpecificLimits/Normed.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact hfa.cauchySeq_series_mul_of_tendsto_zero_of_bounded hf0 <a>norm_sum_neg_one_pow_le</a>
α : Type u_1 β : Type u_2 ι : Type u_3 E : Type u_4 inst✝¹ : NormedAddCommGroup E inst✝ : NormedSpace ℝ E b : ℝ f : ℕ → ℝ z : ℕ → E hfa : Monotone f hf0 : Tendsto f atTop (𝓝 0) ⊢ CauchySeq fun n => ∑ x ∈ Finset.range n, f x * (-1) ^ x
((:c CauchySeq) (:c Real) (:c Nat) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.pseudoMetricSpace)) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))) (:lambda n (:c Nat) ((:c Finset.sum) (:c Nat) (:c Real) (:c Real.instAddCommMon...
[{"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":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.236369))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.236369) (:c Real.normedF...
(:app (:c CauchySeq) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c UniformSpace) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 4 (:lambda n :explicit (:c Nat) (:app (:c Fin...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.236360","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.236363","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"exact","sourceEnd":37311,"sourceStart":37306,"tag":"atom"},{"children":[{"source":"hfa.cauchySeq_series_mul_of_tendsto_zero_of_bounded","sourceEnd":37363,"sourceStart":37312,"tag":"identifier"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"hf0","sourceEnd":37367,"sourceStart":...
[]
[{"source":"hfa.cauchySeq_series_mul_of_tendsto_zero_of_bounded hf0 norm_sum_neg_one_pow_le","source_end":37391,"source_start":37312,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.236360","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.236363","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
159
7
exact
true
1
11
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
92666b938de6d515163cb3adf9a1b5d3feda5eeb4fda9123597115207cf95024
64ec54daa38c13e1bb362a59d03c36ebf98c8bb15ec63c31a3adf7894ad5eb3f
5b26a6c4fb016573a13661fba33b2253a9c29793927a4494bb6231c2fc37c2a9
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,475
MeasureTheory.restrict_trim
Mathlib/MeasureTheory/Measure/Trim.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine @<a>MeasureTheory.Measure.ext</a> _ m _ _ (fun t ht => ?_)
α : Type u_1 m m0 : MeasurableSpace α μ✝ : Measure α s : Set α hm : m ≤ m0 μ : Measure α hs : MeasurableSet s ⊢ (μ.trim hm).restrict s = (μ.restrict s).trim hm
α : Type u_1 m m0 : MeasurableSpace α μ✝ : Measure α s : Set α hm : m ≤ m0 μ : Measure α hs : MeasurableSet s t : Set α ht : MeasurableSet t ⊢ ((μ.trim hm).restrict s) t = ((μ.restrict s).trim hm) t
((:c Eq) ((:c MeasureTheory.Measure) (:fv _uniq.7633) (:fv _uniq.7636)) ((:c MeasureTheory.Measure.restrict) (:fv _uniq.7633) (:fv _uniq.7636) ((:c MeasureTheory.Measure.trim) (:fv _uniq.7633) (:fv _uniq.7636) (:fv _uniq.7639) (:fv _uniq.7718) (:fv _uniq.7717)) (:fv _uniq.7650)) ((:c MeasureTheory.Measure.trim) (:fv _u...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.7633))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.7633))"},{"name":"μ✝","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.7633) (:fv _uniq.7639))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.7633))"},{"name":"hm","sexp...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c MeasureTheory.Measure.restrict) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7633","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7636","is_instance":false,"is_let":false,"name":"m","sexp":"(:app (:c MeasurableSpace) (:arg :explicit 0 (:f...
{"children":[{"source":"refine","sourceEnd":4488,"sourceStart":4482,"tag":"atom"},{"children":[{"children":[{"source":"@","sourceEnd":4490,"sourceStart":4489,"tag":"atom"},{"name":"MeasureTheory.Measure.ext","semanticRole":"global","source":"Measure.ext","sourceEnd":4501,"sourceStart":4490,"tag":"identifier"}],"kind":"...
[]
[{"source":"@Measure.ext _ m _ _ (fun t ht => ?_)","source_end":4526,"source_start":4489,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7633","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7636","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq...
30
4
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5f9a0a3562d92ee4d556569183ecec9795f1708f1d71fc619809a5d440c13c7a
8350422de18a80974cbe5fca64a04edcddc74b28f66e335a81937552ca7ae1f9
4478b8c174cc3619515972533cad0a2fe0931110975f7df69eb05922ce637e9b
b4c6ad82ffe4e8bf244d719ce26e302612cd552d9f6e7a8a9a353d250ffa4d7d
cat-searcher/leandojo-benchmark-4-random
test
4,476
MeasureTheory.restrict_trim
Mathlib/MeasureTheory/Measure/Trim.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [@<a>MeasureTheory.Measure.restrict_apply</a> α m _ _ _ ht, <a>MeasureTheory.trim_measurableSet_eq</a> hm ht, <a>MeasureTheory.Measure.restrict_apply</a> (hm t ht), <a>MeasureTheory.trim_measurableSet_eq</a> hm (@<a>MeasurableSet.inter</a> α m t s ht hs)]
α : Type u_1 m m0 : MeasurableSpace α μ✝ : Measure α s : Set α hm : m ≤ m0 μ : Measure α hs : MeasurableSet s t : Set α ht : MeasurableSet t ⊢ ((μ.trim hm).restrict s) t = ((μ.restrict s).trim hm) t
((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.7633) (:fv _uniq.7636)) ((:c Set) (:fv _uniq.7633)) (:lambda _ ((:c Set) (:fv _uniq.7633)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.7633) (:fv _uniq.7636)) ((:c MeasureTheory.Measure.restrict) (:fv _uniq.7633) (:fv _...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.7633))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.7633))"},{"name":"μ✝","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.7633) (:fv _uniq.7639))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.7633))"},{"name":"hm","sexp...
(:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7633","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7636","is_instance":false,"is_let":false,"name":"m","sexp":"(:app (:c MeasurableSpace) (:arg :explicit 0 (:f...
{"children":[{"source":"rw","sourceEnd":4531,"sourceStart":4529,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4533,"sourceStart":4532,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"s...
[]
[{"source":"@Measure.restrict_apply α m _ _ _ ht","source_end":4570,"source_start":4533,"syntax_kind":"Lean.Parser.Term.app"},{"source":"trim_measurableSet_eq hm ht","source_end":4599,"source_start":4572,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Measure.restrict_apply (hm t ht)","source_end":4637,"source_start":...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7633","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7636","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq...
30
5
exact
true
1
10
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
73c3a1d5015e27b58e49c99a703630ce82b827fc26a9cc7c694e62c92e36743e
b4c6ad82ffe4e8bf244d719ce26e302612cd552d9f6e7a8a9a353d250ffa4d7d
5c4e77fea8cda26a47afcee8d6a017b04a296d7cf484855b0bfcbde4c1b074d8
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,477
SecondCountableTopology.of_separableSpace_orderTopology
Mathlib/Topology/Order/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rcases <a>TopologicalSpace.exists_countable_dense</a> α with ⟨s, hc, hd⟩
α : Type u β : Type v γ : Type w inst✝⁴ : TopologicalSpace α inst✝³ : LinearOrder α inst✝² : OrderTopology α inst✝¹ : DenselyOrdered α inst✝ : SeparableSpace α ⊢ SecondCountableTopology α
case intro.intro α : Type u β : Type v γ : Type w inst✝⁴ : TopologicalSpace α inst✝³ : LinearOrder α inst✝² : OrderTopology α inst✝¹ : DenselyOrdered α inst✝ : SeparableSpace α s : Set α hc : s.Countable hd : Dense s ⊢ SecondCountableTopology α
((:c SecondCountableTopology) (:fv _uniq.147457) (:fv _uniq.147464))
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"inst✝⁴","sexp":"((:c TopologicalSpace) (:fv _uniq.147457))"},{"name":"inst✝³","sexp":"((:c LinearOrder) (:fv _uniq.147457))"},{"name":"inst✝²","sexp":"((:c OrderTopology) (:fv _uniq.147457) (:fv _...
(:app (:c SecondCountableTopology) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))))
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.147457","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.147459","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"rcases","sourceEnd":29916,"sourceStart":29910,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"TopologicalSpace.exists_countable_dense","semanticRole":"global","source":"exists_countable_dense","sourceEnd":29939,"sourceStart":29...
[]
[{"source":"exists_countable_dense α","source_end":29942,"source_start":29917,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨s, hc, hd⟩","source_end":29963,"source_start":29948,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.147457","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.147459","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
143
4
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f467db2590f99abd52b1770951d37580c928cf7fb18216bf548da84aee6647f4
14c966347915a840b257d0be7063c4f1f784eb73fa35a4af50d15aea6a9e1d71
33fec0828371253e07e5f8adc8057d50ce9d4b015b76b7511394eef6302dc446
c13c7f7c219a1e053aff10b778c2c802523789631af423b50762a5d09c629625
cat-searcher/leandojo-benchmark-4-random
test
4,478
SecondCountableTopology.of_separableSpace_orderTopology
Mathlib/Topology/Order/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨⟨_, ?_, hd.topology_eq_generateFrom⟩⟩
case intro.intro α : Type u β : Type v γ : Type w inst✝⁴ : TopologicalSpace α inst✝³ : LinearOrder α inst✝² : OrderTopology α inst✝¹ : DenselyOrdered α inst✝ : SeparableSpace α s : Set α hc : s.Countable hd : Dense s ⊢ SecondCountableTopology α
case intro.intro α : Type u β : Type v γ : Type w inst✝⁴ : TopologicalSpace α inst✝³ : LinearOrder α inst✝² : OrderTopology α inst✝¹ : DenselyOrdered α inst✝ : SeparableSpace α s : Set α hc : s.Countable hd : Dense s ⊢ (Ioi '' s ∪ Iio '' s).Countable
((:c SecondCountableTopology) (:fv _uniq.147457) (:fv _uniq.147464))
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"inst✝⁴","sexp":"((:c TopologicalSpace) (:fv _uniq.147457))"},{"name":"inst✝³","sexp":"((:c LinearOrder) (:fv _uniq.147457))"},{"name":"inst✝²","sexp":"((:c OrderTopology) (:fv _uniq.147457) (:fv _...
(:app (:c SecondCountableTopology) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))))
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.147457","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.147459","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"refine","sourceEnd":29972,"sourceStart":29966,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":29976,"sourceStart":29973,"tag":"atom"},{"children":[{"children":[{"source":"⟨","sourceEnd":29979,"sourceStart":29976,"tag":"atom"},{"children":[{"children":[{"source":"_","sourceEnd":29980,"source...
[]
[{"source":"⟨⟨_, ?_, hd.topology_eq_generateFrom⟩⟩","source_end":30019,"source_start":29973,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.147457","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.147459","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
143
5
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
eb0acb04e2f0f893ee3ab8efa2fc2b6428ee1b01d57774ba6cb661b2b5feb532
c13c7f7c219a1e053aff10b778c2c802523789631af423b50762a5d09c629625
cffb981943352af518fba5c96c6b072926d8bd2873b912ccd6466c80e7d70797
c77bdd4ef360a2fb1d699abe7f847047c9044b8e868f8ca33bef1fa91d13fa4d
cat-searcher/leandojo-benchmark-4-random
test
4,479
SecondCountableTopology.of_separableSpace_orderTopology
Mathlib/Topology/Order/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact (hc.image _).<a>Set.Countable.union</a> (hc.image _)
case intro.intro α : Type u β : Type v γ : Type w inst✝⁴ : TopologicalSpace α inst✝³ : LinearOrder α inst✝² : OrderTopology α inst✝¹ : DenselyOrdered α inst✝ : SeparableSpace α s : Set α hc : s.Countable hd : Dense s ⊢ (Ioi '' s ∪ Iio '' s).Countable
((:c Set.Countable) ((:c Set) (:fv _uniq.147457)) ((:c Union.union) ((:c Set) ((:c Set) (:fv _uniq.147457))) ((:c Set.instUnion) ((:c Set) (:fv _uniq.147457))) ((:c Set.image) (:fv _uniq.147457) ((:c Set) (:fv _uniq.147457)) ((:c Set.Ioi) (:fv _uniq.147457) ((:c PartialOrder.toPreorder) (:fv _uniq.147457) ((:c Semilatt...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"inst✝⁴","sexp":"((:c TopologicalSpace) (:fv _uniq.147457))"},{"name":"inst✝³","sexp":"((:c LinearOrder) (:fv _uniq.147457))"},{"name":"inst✝²","sexp":"((:c OrderTopology) (:fv _uniq.147457) (:fv _...
(:app (:c Set.Countable) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Union.union) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))))) (:arg :instance 1 (:instance-of (:app (:c Union) (:arg :explicit 0 (:app (:c Set)...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.147457","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.147459","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"exact","sourceEnd":30027,"sourceStart":30022,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":30029,"sourceStart":30028,"tag":"atom"},{"children":[{"source":"hc.image","sourceEnd":30037,"sourceStart":30029,"tag":"identifier"},{"children":[{"children":[{"source":"_",...
[]
[{"source":"(hc.image _).union (hc.image _)","source_end":30059,"source_start":30028,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.147457","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.147459","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
143
6
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
51ff51f1f42df63ac7cdae98522ceea2c7d04820518649a7d6732bdeef43a52b
c77bdd4ef360a2fb1d699abe7f847047c9044b8e868f8ca33bef1fa91d13fa4d
487e676ad114b9799d29ec1acc25c4a6c4470f49958ab88a54a7fa3535711f64
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,480
Rat.add_def
.lake/packages/batteries/Batteries/Data/Rat/Lemmas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
show <a>Rat.add</a> .. = _
a b : Rat ⊢ a + b = normalize (a.num * ↑b.den + b.num * ↑a.den) (a.den * b.den) ⋯
a b : Rat ⊢ a.add b = normalize (a.num * ↑b.den + b.num * ↑a.den) (a.den * b.den) ⋯
((:c Eq) (:c Rat) ((:c HAdd.hAdd) (:c Rat) (:c Rat) (:c Rat) ((:c instHAdd) (:c Rat) (:c Rat.instAdd)) (:fv _uniq.16732) (:fv _uniq.16733)) ((:c Rat.normalize) ((:c HAdd.hAdd) (:c Int) (:c Int) (:c Int) ((:c instHAdd) (:c Int) (:c Int.instAdd)) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (:c Int....
[{"name":"a","sexp":"(:c Rat)"},{"name":"b","sexp":"(:c Rat)"}]
(:app (:c Eq) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Rat)) (:arg :implicit-type 1 (:c Rat)) (:arg :implicit-type 2 (:c Rat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Rat)) (:arg :explicit 1 (:c Rat)) (:arg :explicit 2 (:c Rat))))) ...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Rat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Rat)"}]
{"children":[{"source":"show","sourceEnd":8931,"sourceStart":8927,"tag":"atom"},{"children":[{"children":[{"name":"Rat.add","semanticRole":"global","source":"Rat.add","sourceEnd":8939,"sourceStart":8932,"tag":"identifier"},{"children":[{"children":[{"source":"..","sourceEnd":8942,"sourceStart":8940,"tag":"atom"}],"kind...
[]
[{"source":"Rat.add .. = _","source_end":8946,"source_start":8932,"syntax_kind":"«term_=_»"}]
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"user_name":"b"}]
49
4
exact
true
1
2
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2951c69452e66a53342e3ae219badd2c18502dcd2a5f5903acbd35cd86e7e702
013e215dafa0be0d0b8d51004d3a7ad067715cd7ae8669ebec8e419cba721a7c
b683af2051fd62e7cc007cca6d2ad756bf038731d0e64b892b73e6ed4143c3ab
26c73f1f5eb09fd89ca27e648916f1d5a04dc450355ef5e0a020b36e09677e5a
cat-searcher/leandojo-benchmark-4-random
test
4,481
Rat.add_def
.lake/packages/batteries/Batteries/Data/Rat/Lemmas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
delta <a>Rat.add</a>
a b : Rat ⊢ a.add b = normalize (a.num * ↑b.den + b.num * ↑a.den) (a.den * b.den) ⋯
a b : Rat ⊢ (let g := a.den.gcd b.den; if hg : g = 1 then let_fun den_nz := ⋯; let_fun reduced := ⋯; { num := a.num * ↑b.den + b.num * ↑a.den, den := a.den * b.den, den_nz := den_nz, reduced := reduced } else let den := a.den / g * b.den; let num := a.num * ↑(b.den / g) + b.num * ↑...
((:c Eq) (:c Rat) ((:c Rat.add) (:fv _uniq.16732) (:fv _uniq.16733)) ((:c Rat.normalize) ((:c HAdd.hAdd) (:c Int) (:c Int) (:c Int) ((:c instHAdd) (:c Int) (:c Int.instAdd)) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (:c Int.instMul)) ((:c Rat.num) (:fv _uniq.16732)) ((:c Nat.cast) (:c Int) (:c ...
[{"name":"a","sexp":"(:c Rat)"},{"name":"b","sexp":"(:c Rat)"}]
(:app (:c Eq) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c Rat.add) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))) (:arg :explicit 2 (:app (:c Rat.normalize) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:c Int)) (:arg :implicit-type 2 (:c I...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Rat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Rat)"}]
{"children":[{"source":"delta","sourceEnd":8953,"sourceStart":8948,"tag":"atom"},{"children":[{"name":"Rat.add","semanticRole":"global","source":"Rat.add","sourceEnd":8961,"sourceStart":8954,"tag":"identifier"}],"kind":"null","source":"Rat.add","sourceEnd":8961,"sourceStart":8954,"tag":"node"},{"children":[],"kind":"nu...
[]
[{"source":"Rat.add","source_end":8961,"source_start":8954,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"user_name":"b"}]
49
6
exact
true
1
2
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b10fedebd0b6a18bc538762b26fd54f82f4ffdc440f4fce1035ef16813822b5f
26c73f1f5eb09fd89ca27e648916f1d5a04dc450355ef5e0a020b36e09677e5a
173e2614efafd9fafc1fce18db2d7adb474398526df14dc5b0ba933885ed4213
f18ca58f7508cf7e943301def2ca051c0fb10d1fadbf943ad16ff02a3e953e92
cat-searcher/leandojo-benchmark-4-random
test
4,482
Rat.add_def
.lake/packages/batteries/Batteries/Data/Rat/Lemmas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
dsimp only
a b : Rat ⊢ (let g := a.den.gcd b.den; if hg : g = 1 then let_fun den_nz := ⋯; let_fun reduced := ⋯; { num := a.num * ↑b.den + b.num * ↑a.den, den := a.den * b.den, den_nz := den_nz, reduced := reduced } else let den := a.den / g * b.den; let num := a.num * ↑(b.den / g) + b.num * ↑...
a b : Rat ⊢ (if hg : a.den.gcd b.den = 1 then { num := a.num * ↑b.den + b.num * ↑a.den, den := a.den * b.den, den_nz := ⋯, reduced := ⋯ } else maybeNormalize (a.num * ↑(b.den / a.den.gcd b.den) + b.num * ↑(a.den / a.den.gcd b.den)) (a.den / a.den.gcd b.den * b.den) ((a.num * ↑(b.den / a....
((:c Eq) (:c Rat) (:let g (:c Nat) ((:c Nat.gcd) ((:c Rat.den) (:fv _uniq.16732)) ((:c Rat.den) (:fv _uniq.16733))) ((:c dite) (:c Rat) ((:c Eq) (:c Nat) 0 ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) ((:c Nat.instDecidableCoprime) ((:c Rat.den) (:fv _uniq.16732)) ((:c Rat.den) (:fv _uniq.16733)))...
[{"name":"a","sexp":"(:c Rat)"},{"name":"b","sexp":"(:c Rat)"}]
(:app (:c Eq) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:let g (:c Nat) (:app (:c Nat.gcd) (:arg :explicit 0 (:app (:c Rat.den) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Rat.den) (:arg :explicit 0 (:fv FV2))))) (:app (:c dite) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c Eq) (...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Rat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Rat)"}]
{"children":[{"source":"dsimp","sourceEnd":8968,"sourceStart":8963,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":8973,"sourceStart":8969,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":8973,"...
[]
[]
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"user_name":"b"}]
49
8
exact
true
1
2
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d612b4650d86d59a6bc0dba6b5e72bcc4e280cfc9e5ae7b351b0f30672157d57
f18ca58f7508cf7e943301def2ca051c0fb10d1fadbf943ad16ff02a3e953e92
a4e0c85d6bda4413b7728099944a8f316bd66db76d368a5fb7af15b2a8905273
996a3180c6ac6f4381368eb6afc50241d42b111cc186fa59427fbc9057ea3206
cat-searcher/leandojo-benchmark-4-random
test
4,483
Rat.add_def
.lake/packages/batteries/Batteries/Data/Rat/Lemmas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
split
a b : Rat ⊢ (if hg : a.den.gcd b.den = 1 then { num := a.num * ↑b.den + b.num * ↑a.den, den := a.den * b.den, den_nz := ⋯, reduced := ⋯ } else maybeNormalize (a.num * ↑(b.den / a.den.gcd b.den) + b.num * ↑(a.den / a.den.gcd b.den)) (a.den / a.den.gcd b.den * b.den) ((a.num * ↑(b.den / a....
case isTrue a b : Rat h✝ : a.den.gcd b.den = 1 ⊢ { num := a.num * ↑b.den + b.num * ↑a.den, den := a.den * b.den, den_nz := ⋯, reduced := ⋯ } = normalize (a.num * ↑b.den + b.num * ↑a.den) (a.den * b.den) ⋯ case isFalse a b : Rat h✝ : ¬a.den.gcd b.den = 1 ⊢ maybeNormalize (a.num * ↑(b.den / a.den.gcd b.den) + b.num *...
((:c Eq) (:c Rat) ((:c dite) (:c Rat) ((:c Eq) (:c Nat) ((:c Nat.gcd) ((:c Rat.den) (:fv _uniq.16732)) ((:c Rat.den) (:fv _uniq.16733))) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) ((:c Nat.instDecidableCoprime) ((:c Rat.den) (:fv _uniq.16732)) ((:c Rat.den) (:fv _uniq.16733))) (:lambda hg ((:c E...
[{"name":"a","sexp":"(:c Rat)"},{"name":"b","sexp":"(:c Rat)"}]
(:app (:c Eq) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c dite) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.gcd) (:arg :explicit 0 (:app (:c Rat.den) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Rat.den)...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Rat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Rat)"}]
{"children":[{"source":"split","sourceEnd":8980,"sourceStart":8975,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.split","source":"split","sourceEnd":8980,"sourceStart":8975,"tag":"node"}
[]
[]
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"user_name":"b"}]
49
10
exact
true
1
2
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4f73f5b63703a4cde8c950ec29751e8b38520601fd25068c147b5169d5d8ea36
996a3180c6ac6f4381368eb6afc50241d42b111cc186fa59427fbc9057ea3206
ad1a64057f9ab34fecfe3f4ee78660bb0316dbda9370581ffbeb1e8bddf3d598
024b6e4150c9ec8fe1bde0e403b7f74c77471136194404ca4e6b185de02344a1
cat-searcher/leandojo-benchmark-4-random
test
4,484
Rat.add_def
.lake/packages/batteries/Batteries/Data/Rat/Lemmas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact (<a>Rat.normalize_self</a> _).<a>Eq.symm</a>
case isTrue a b : Rat h✝ : a.den.gcd b.den = 1 ⊢ { num := a.num * ↑b.den + b.num * ↑a.den, den := a.den * b.den, den_nz := ⋯, reduced := ⋯ } = normalize (a.num * ↑b.den + b.num * ↑a.den) (a.den * b.den) ⋯
((:c Eq) (:c Rat) ((:c Rat.mk') ((:c HAdd.hAdd) (:c Int) (:c Int) (:c Int) ((:c instHAdd) (:c Int) (:c Int.instAdd)) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (:c Int.instMul)) ((:c Rat.num) (:fv _uniq.16732)) ((:c Nat.cast) (:c Int) (:c instNatCastInt) ((:c Rat.den) (:fv _uniq.16733)))) ((:c H...
[{"name":"a","sexp":"(:c Rat)"},{"name":"b","sexp":"(:c Rat)"},{"name":"h✝","sexp":"((:c Eq) (:c Nat) ((:c Nat.gcd) ((:c Rat.den) (:fv _uniq.16732)) ((:c Rat.den) (:fv _uniq.16733))) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))"}]
(:app (:c Eq) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c Rat.mk') (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:c Int)) (:arg :implicit-type 2 (:c Int)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Int)) (:arg :explicit 1 (:c ...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Rat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Rat)"},{"binder_role":":explicit","context_ind...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":8991,"sourceStart":8986,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":8993,"sourceStart":8992,"tag":"atom"},{"children":[{"name":"Rat.normalize_self","semanticRole":"global","source":"normalize_self","sourceEnd":9007,"...
[]
[{"source":"(normalize_self _).symm","source_end":9015,"source_start":8992,"syntax_kind":"Lean.Parser.Term.proj"}]
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":3,"internal_name":"_un...
49
13
exact
true
1
3
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
83a7c1840a9a73d12890e40b2457e4618823b374cf95742f4ed75e11df610e3f
0cc3d998a61fd5e5d2000fdd5db519eeb337f6aba642847d6032a215e9f5a380
e9afd1fdc71ba0648a5741416f9606f02e1240270c61a360bd577b9a3b022f87
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,485
Rat.add_def
.lake/packages/batteries/Batteries/Data/Rat/Lemmas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have : a.den.gcd b.den ≠ 0 := <a>Nat.gcd_ne_zero_left</a> a.den_nz
case isFalse a b : Rat h✝ : ¬a.den.gcd b.den = 1 ⊢ maybeNormalize (a.num * ↑(b.den / a.den.gcd b.den) + b.num * ↑(a.den / a.den.gcd b.den)) (a.den / a.den.gcd b.den * b.den) ((a.num * ↑(b.den / a.den.gcd b.den) + b.num * ↑(a.den / a.den.gcd b.den)).natAbs.gcd (a.den.gcd b.den)) ⋯ ⋯ = normalize (a.num * ...
case isFalse a b : Rat h✝ : ¬a.den.gcd b.den = 1 this : a.den.gcd b.den ≠ 0 ⊢ maybeNormalize (a.num * ↑(b.den / a.den.gcd b.den) + b.num * ↑(a.den / a.den.gcd b.den)) (a.den / a.den.gcd b.den * b.den) ((a.num * ↑(b.den / a.den.gcd b.den) + b.num * ↑(a.den / a.den.gcd b.den)).natAbs.gcd (a.den.gcd b.den)) ⋯ ...
((:c Eq) (:c Rat) ((:c Rat.maybeNormalize) ((:c HAdd.hAdd) (:c Int) (:c Int) (:c Int) ((:c instHAdd) (:c Int) (:c Int.instAdd)) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (:c Int.instMul)) ((:c Rat.num) (:fv _uniq.16732)) ((:c Nat.cast) (:c Int) (:c instNatCastInt) ((:c HDiv.hDiv) (:c Nat) (:c N...
[{"name":"a","sexp":"(:c Rat)"},{"name":"b","sexp":"(:c Rat)"},{"name":"h✝","sexp":"((:c Not) ((:c Eq) (:c Nat) ((:c Nat.gcd) ((:c Rat.den) (:fv _uniq.16732)) ((:c Rat.den) (:fv _uniq.16733))) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"}]
(:app (:c Eq) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c Rat.maybeNormalize) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:c Int)) (:arg :implicit-type 2 (:c Int)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Int)) (:arg :expl...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Rat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Rat)"},{"binder_role":":explicit","context_ind...
{"children":[{"source":"have","sourceEnd":9025,"sourceStart":9021,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":9026,"sourceStart":9026,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":9026,"sourceStart":9026,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","...
[]
[{"source":"a.den.gcd b.den ≠ 0","source_end":9049,"source_start":9028,"syntax_kind":"«term_≠_»"},{"source":"Nat.gcd_ne_zero_left a.den_nz","source_end":9082,"source_start":9053,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":3,"internal_name":"_un...
49
20
exact
true
1
3
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3819394447f3d6a3dd449362e133053c8a574199268538c9bcc218b2a1d99e06
41b1f256ad6a2b5b04e5ff62e00166b8bf70b4b4ad9a7e5ceab37877207cb18c
3b95e6714642a95c33d880c9a8178e5cfa5fa0017ccb985a7d7ce81cc4433188
e2c0aade66e96a3b04131fe40bf7db31780640451f675829e0ba0145bcd76133
cat-searcher/leandojo-benchmark-4-random
test
4,486
Rat.add_def
.lake/packages/batteries/Batteries/Data/Rat/Lemmas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Rat.maybeNormalize_eq_normalize</a> _ _ (<a>Int.ofNat_dvd_left</a>.2 <| <a>Nat.gcd_dvd_left</a> ..) (<a>Nat.dvd_trans</a> (<a>Nat.gcd_dvd_right</a> ..) <| <a>Nat.dvd_trans</a> (<a>Nat.gcd_dvd_right</a> ..) (<a>Nat.dvd_mul_left</a> ..)), ← <a>Rat.normalize_mul_right</a> _ this]
case isFalse a b : Rat h✝ : ¬a.den.gcd b.den = 1 this : a.den.gcd b.den ≠ 0 ⊢ maybeNormalize (a.num * ↑(b.den / a.den.gcd b.den) + b.num * ↑(a.den / a.den.gcd b.den)) (a.den / a.den.gcd b.den * b.den) ((a.num * ↑(b.den / a.den.gcd b.den) + b.num * ↑(a.den / a.den.gcd b.den)).natAbs.gcd (a.den.gcd b.den)) ⋯ ...
case isFalse a b : Rat h✝ : ¬a.den.gcd b.den = 1 this : a.den.gcd b.den ≠ 0 ⊢ normalize ((a.num * ↑(b.den / a.den.gcd b.den) + b.num * ↑(a.den / a.den.gcd b.den)) * ↑(a.den.gcd b.den)) (a.den / a.den.gcd b.den * b.den * a.den.gcd b.den) ⋯ = normalize (a.num * ↑b.den + b.num * ↑a.den) (a.den * b.den) ⋯
((:c Eq) (:c Rat) ((:c Rat.maybeNormalize) ((:c HAdd.hAdd) (:c Int) (:c Int) (:c Int) ((:c instHAdd) (:c Int) (:c Int.instAdd)) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (:c Int.instMul)) ((:c Rat.num) (:fv _uniq.16732)) ((:c Nat.cast) (:c Int) (:c instNatCastInt) ((:c HDiv.hDiv) (:c Nat) (:c N...
[{"name":"a","sexp":"(:c Rat)"},{"name":"b","sexp":"(:c Rat)"},{"name":"h✝","sexp":"((:c Not) ((:c Eq) (:c Nat) ((:c Nat.gcd) ((:c Rat.den) (:fv _uniq.16732)) ((:c Rat.den) (:fv _uniq.16733))) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"this","sexp":"((:c Ne) (:c Nat) ((:c Nat.gcd) ((...
(:app (:c Eq) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c Rat.maybeNormalize) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:c Int)) (:arg :implicit-type 2 (:c Int)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Int)) (:arg :expl...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Rat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Rat)"},{"binder_role":":explicit","context_ind...
{"children":[{"source":"rw","sourceEnd":9089,"sourceStart":9087,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9091,"sourceStart":9090,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Rat.may...
[]
[{"source":"maybeNormalize_eq_normalize _ _\n (Int.ofNat_dvd_left.2 <| Nat.gcd_dvd_left ..)\n (Nat.dvd_trans (Nat.gcd_dvd_right ..) <|\n Nat.dvd_trans (Nat.gcd_dvd_right ..) (Nat.dvd_mul_left ..))","source_end":9294,"source_start":9091,"syntax_kind":"Lean.Parser.Term.app"},{"source":"normalize_mul...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":3,"internal_name":"_un...
49
21
exact
true
1
4
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
26a0f89fd3bb3c3fbd1b0e312bac02348d2ab7cfd997580b1925736eb8819c4f
e2c0aade66e96a3b04131fe40bf7db31780640451f675829e0ba0145bcd76133
1e4774efb9a8315e7bd5b395e2d920a99e9407b085b726f22075e85fadc8d649
3cea4338e1a1f2778b25c9f8f0d333d2f608754513c6eaad41db34e569393e34
cat-searcher/leandojo-benchmark-4-random
test
4,487
Rat.add_def
.lake/packages/batteries/Batteries/Data/Rat/Lemmas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
congr 1
case isFalse a b : Rat h✝ : ¬a.den.gcd b.den = 1 this : a.den.gcd b.den ≠ 0 ⊢ normalize ((a.num * ↑(b.den / a.den.gcd b.den) + b.num * ↑(a.den / a.den.gcd b.den)) * ↑(a.den.gcd b.den)) (a.den / a.den.gcd b.den * b.den * a.den.gcd b.den) ⋯ = normalize (a.num * ↑b.den + b.num * ↑a.den) (a.den * b.den) ⋯
case isFalse.e_num a b : Rat h✝ : ¬a.den.gcd b.den = 1 this : a.den.gcd b.den ≠ 0 ⊢ (a.num * ↑(b.den / a.den.gcd b.den) + b.num * ↑(a.den / a.den.gcd b.den)) * ↑(a.den.gcd b.den) = a.num * ↑b.den + b.num * ↑a.den case isFalse.e_den a b : Rat h✝ : ¬a.den.gcd b.den = 1 this : a.den.gcd b.den ≠ 0 ⊢ a.den / a.den.gcd b...
((:c Eq) (:c Rat) ((:c Rat.normalize) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (:c Int.instMul)) ((:c HAdd.hAdd) (:c Int) (:c Int) (:c Int) ((:c instHAdd) (:c Int) (:c Int.instAdd)) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (:c Int.instMul)) ((:c Rat.num) (:fv _uniq.16...
[{"name":"a","sexp":"(:c Rat)"},{"name":"b","sexp":"(:c Rat)"},{"name":"h✝","sexp":"((:c Not) ((:c Eq) (:c Nat) ((:c Nat.gcd) ((:c Rat.den) (:fv _uniq.16732)) ((:c Rat.den) (:fv _uniq.16733))) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"this","sexp":"((:c Ne) (:c Nat) ((:c Nat.gcd) ((...
(:app (:c Eq) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c Rat.normalize) (:arg :explicit 0 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:c Int)) (:arg :implicit-type 2 (:c Int)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Int)) (:arg :explicit ...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Rat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Rat)"},{"binder_role":":explicit","context_ind...
{"children":[{"source":"congr","sourceEnd":9340,"sourceStart":9335,"tag":"atom"},{"children":[{"children":[{"source":"1","sourceEnd":9342,"sourceStart":9341,"tag":"atom"}],"kind":"num","source":"1","sourceEnd":9342,"sourceStart":9341,"tag":"node"}],"kind":"null","source":"1","sourceEnd":9342,"sourceStart":9341,"tag":"n...
[]
[]
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":3,"internal_name":"_un...
49
26
exact
true
1
4
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0a26e1f2ef4de050fffabce2cf38c0085dd40e18d2382f966d5a07e535c2bf31
3cea4338e1a1f2778b25c9f8f0d333d2f608754513c6eaad41db34e569393e34
8f6f3e102b5370312cdd673cdfe3acc12b0ae98d6a7b45eb025d5bd0bb778a5b
819768da8a2107e37987644df43ea63bc852e72e272cf7ec061cce795c0b04f4
cat-searcher/leandojo-benchmark-4-random
test
4,488
Rat.add_def
.lake/packages/batteries/Batteries/Data/Rat/Lemmas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>Int.add_mul</a>, <a>Int.mul_assoc</a>, <a>Int.ofNat_mul_ofNat</a>, <a>Nat.div_mul_cancel</a> (<a>Nat.gcd_dvd_left</a> ..), <a>Nat.div_mul_cancel</a> (<a>Nat.gcd_dvd_right</a> ..)]
case isFalse.e_num a b : Rat h✝ : ¬a.den.gcd b.den = 1 this : a.den.gcd b.den ≠ 0 ⊢ (a.num * ↑(b.den / a.den.gcd b.den) + b.num * ↑(a.den / a.den.gcd b.den)) * ↑(a.den.gcd b.den) = a.num * ↑b.den + b.num * ↑a.den
((:c Eq) (:c Int) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (:c Int.instMul)) ((:c HAdd.hAdd) (:c Int) (:c Int) (:c Int) ((:c instHAdd) (:c Int) (:c Int.instAdd)) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (:c Int.instMul)) ((:c Rat.num) (:fv _uniq.16732)) ((:c Nat.cast)...
[{"name":"a","sexp":"(:c Rat)"},{"name":"b","sexp":"(:c Rat)"},{"name":"h✝","sexp":"((:c Not) ((:c Eq) (:c Nat) ((:c Nat.gcd) ((:c Rat.den) (:fv _uniq.16732)) ((:c Rat.den) (:fv _uniq.16733))) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"this","sexp":"((:c Ne) (:c Nat) ((:c Nat.gcd) ((...
(:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:c Int)) (:arg :implicit-type 2 (:c Int)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Int)) (:arg :explicit 1 (:c Int)) (:arg :explicit 2 (:c Int))))) ...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Rat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Rat)"},{"binder_role":":explicit","context_ind...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":9354,"sourceStart":9350,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":9359,"sourceStart":9355,"tag":"atom"}],"kind":"nu...
[]
[{"source":"Int.add_mul","source_end":9372,"source_start":9361,"syntax_kind":"ident"},{"source":"Int.mul_assoc","source_end":9387,"source_start":9374,"syntax_kind":"ident"},{"source":"Int.ofNat_mul_ofNat","source_end":9408,"source_start":9389,"syntax_kind":"ident"},{"source":"Nat.div_mul_cancel (Nat.gcd_dvd_left ..)","...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":3,"internal_name":"_un...
49
29
exact
true
1
4
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
170fbbc0e972156d62d4d3577c1b6d622eb13f97679f029eb6f5b0a7ce4d8875
43f98eb12e31cb12c3ec97a3052f9778d477bd30819947410615955a35190b60
21b6560b9bfb0866fea8f13b1e02a6b17c4f4c34dfc3534f0ec7c273535fd97c
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,489
Rat.add_def
.lake/packages/batteries/Batteries/Data/Rat/Lemmas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Nat.mul_right_comm</a>, <a>Nat.div_mul_cancel</a> (<a>Nat.gcd_dvd_left</a> ..)]
case isFalse.e_den a b : Rat h✝ : ¬a.den.gcd b.den = 1 this : a.den.gcd b.den ≠ 0 ⊢ a.den / a.den.gcd b.den * b.den * a.den.gcd b.den = a.den * b.den
((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) ((:c HDiv.hDiv) (:c Nat) (:c Nat) (:c Nat) ((:c instHDiv) (:c Nat) (:c Nat.instDiv)) ((:c Rat.den) (:fv _uniq.16732)) ((:c Nat.gcd) ((...
[{"name":"a","sexp":"(:c Rat)"},{"name":"b","sexp":"(:c Rat)"},{"name":"h✝","sexp":"((:c Not) ((:c Eq) (:c Nat) ((:c Nat.gcd) ((:c Rat.den) (:fv _uniq.16732)) ((:c Rat.den) (:fv _uniq.16733))) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"this","sexp":"((:c Ne) (:c Nat) ((:c Nat.gcd) ((...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Rat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Rat)"},{"binder_role":":explicit","context_ind...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":9512,"sourceStart":9510,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9514,"sourceStart":9513,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag...
[]
[{"source":"Nat.mul_right_comm","source_end":9532,"source_start":9514,"syntax_kind":"ident"},{"source":"Nat.div_mul_cancel (Nat.gcd_dvd_left ..)","source_end":9574,"source_start":9534,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16732","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.16733","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":3,"internal_name":"_un...
49
34
exact
true
1
4
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
85d2f04eca208887e3495aa5fc05e28774c25a052379e393b8f9fa26b1f09b9d
33a7d7bada3f84b42666008ce0f2401ae3aa6fec8efc069383646c2a7ddd3bb6
06435c6bc86cdf397915bc3f6070ff25adb3d4c55870202263a08e5cf93ba6af
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,490
of_quotient_center_nilpotent
Mathlib/GroupTheory/Nilpotent.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨n, hn⟩ := h.nilpotent
G : Type u_1 inst✝¹ : Group G H : Subgroup G inst✝ : H.Normal h : Group.IsNilpotent (G ⧸ center G) ⊢ Group.IsNilpotent G
case intro G : Type u_1 inst✝¹ : Group G H : Subgroup G inst✝ : H.Normal h : Group.IsNilpotent (G ⧸ center G) n : ℕ hn : upperCentralSeries (G ⧸ center G) n = ⊤ ⊢ Group.IsNilpotent G
((:c Group.IsNilpotent) (:fv _uniq.168291) (:fv _uniq.168294))
[{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.168291))"},{"name":"H","sexp":"((:c Subgroup) (:fv _uniq.168291) (:fv _uniq.168294))"},{"name":"inst✝","sexp":"((:c Subgroup.Normal) (:fv _uniq.168291) (:fv _uniq.168294) (:fv _uniq.168302))"},{"name":"h","sexp":"((:c Group.IsNilpo...
(:app (:c Group.IsNilpotent) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV0))))))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.168291","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.168294","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explici...
{"children":[{"source":"obtain","sourceEnd":31619,"sourceStart":31613,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":31623,"sourceStart":31620,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"n","sourceEn...
[]
[{"source":"h.nilpotent","source_end":31646,"source_start":31635,"syntax_kind":"ident"},{"source":"⟨n, hn⟩","source_end":31631,"source_start":31620,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.168291","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.168294","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"inte...
128
4
exact
true
1
5
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3375fc3a62de4f3baea650c76035757bb2f2cc2381d8be43c834aba088fbaa46
ebd4b1a9b4c927c4f329bcb4dca5b408eb5e5e47adf7bcf034b065b60fcef6dd
8610fbc6c6c590bc58d907deeea44ddb6db22ae136b383fa4bb854dcb35a1f7f
7222082470b78e10f63d4667fde1a0894cbe7a17f0fd82332a3c0615864bb8ac
cat-searcher/leandojo-benchmark-4-random
test
4,491
of_quotient_center_nilpotent
Mathlib/GroupTheory/Nilpotent.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
use n.succ
case intro G : Type u_1 inst✝¹ : Group G H : Subgroup G inst✝ : H.Normal h : Group.IsNilpotent (G ⧸ center G) n : ℕ hn : upperCentralSeries (G ⧸ center G) n = ⊤ ⊢ Group.IsNilpotent G
case h G : Type u_1 inst✝¹ : Group G H : Subgroup G inst✝ : H.Normal h : Group.IsNilpotent (G ⧸ center G) n : ℕ hn : upperCentralSeries (G ⧸ center G) n = ⊤ ⊢ upperCentralSeries G n.succ = ⊤
((:c Group.IsNilpotent) (:fv _uniq.168291) (:fv _uniq.168294))
[{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.168291))"},{"name":"H","sexp":"((:c Subgroup) (:fv _uniq.168291) (:fv _uniq.168294))"},{"name":"inst✝","sexp":"((:c Subgroup.Normal) (:fv _uniq.168291) (:fv _uniq.168294) (:fv _uniq.168302))"},{"name":"h","sexp":"((:c Group.IsNilpo...
(:app (:c Group.IsNilpotent) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV0))))))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.168291","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.168294","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explici...
{"children":[{"source":"use","sourceEnd":31652,"sourceStart":31649,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"name":"Nat.succ","semanticRole":"constructor","source":"n.succ","sourceEnd":31659,"sourceStart":31653,"tag":"iden...
[]
[{"source":"n.succ","source_end":31659,"source_start":31653,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.168291","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.168294","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"inte...
128
5
exact
true
1
7
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
cf353b85d6fb23c92a2fd315372bf00f9d196c41f4ecad38bdb09028046cb938
7222082470b78e10f63d4667fde1a0894cbe7a17f0fd82332a3c0615864bb8ac
f97db829e3166375bddf24129bb69485de34bed1efc21a8d40bfa44f68928f5d
886bbdda5c76e62cf5f194d4809936545b2b59e5e340ee32c540e907967525e7
cat-searcher/leandojo-benchmark-4-random
test
4,492
of_quotient_center_nilpotent
Mathlib/GroupTheory/Nilpotent.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [← <a>comap_upperCentralSeries_quotient_center</a>, hn]
case h G : Type u_1 inst✝¹ : Group G H : Subgroup G inst✝ : H.Normal h : Group.IsNilpotent (G ⧸ center G) n : ℕ hn : upperCentralSeries (G ⧸ center G) n = ⊤ ⊢ upperCentralSeries G n.succ = ⊤
((:c Eq) ((:c Subgroup) (:fv _uniq.168291) (:fv _uniq.168294)) ((:c upperCentralSeries) (:fv _uniq.168291) (:fv _uniq.168294) ((:c Nat.succ) (:fv _uniq.170830))) ((:c Top.top) ((:c Subgroup) (:fv _uniq.168291) (:fv _uniq.168294)) ((:c Subgroup.instTop) (:fv _uniq.168291) (:fv _uniq.168294))))
[{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.168291))"},{"name":"H","sexp":"((:c Subgroup) (:fv _uniq.168291) (:fv _uniq.168294))"},{"name":"inst✝","sexp":"((:c Subgroup.Normal) (:fv _uniq.168291) (:fv _uniq.168294) (:fv _uniq.168302))"},{"name":"h","sexp":"((:c Group.IsNilpo...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subgroup) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c upperCentralSeries) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.168291","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.168294","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explici...
{"children":[{"source":"simp","sourceEnd":31666,"sourceStart":31662,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":31668,"sourceStart":31667,"tag":"a...
[]
[{"source":"comap_upperCentralSeries_quotient_center","source_end":31712,"source_start":31672,"syntax_kind":"ident"},{"source":"hn","source_end":31716,"source_start":31714,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.168291","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.168294","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"inte...
128
6
exact
true
1
7
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3ffe9c3a44758d07c0f21853630483a811e0da6117d58a6c66720a9be612809b
886bbdda5c76e62cf5f194d4809936545b2b59e5e340ee32c540e907967525e7
c7230a31804c7185b7f00accf27fdb45b8a8abf9894f711e29d9fdd3e1cec412
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,493
Metric.cthickening_closure
Mathlib/Topology/MetricSpace/Thickening.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp_rw [<a>Metric.cthickening</a>, <a>EMetric.infEdist_closure</a>]
ι : Sort u_1 α : Type u β : Type v inst✝ : PseudoEMetricSpace α δ ε : ℝ s t : Set α x : α ⊢ cthickening δ (closure s) = cthickening δ s
((:c Eq) ((:c Set) (:fv _uniq.61550)) ((:c Metric.cthickening) (:fv _uniq.61550) (:fv _uniq.61555) (:fv _uniq.61557) ((:c closure) (:fv _uniq.61550) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.61550) ((:c PseudoEMetricSpace.toUniformSpace) (:fv _uniq.61550) (:fv _uniq.61555))) (:fv _uniq.61562))) ((:c Metric.cthic...
[{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"inst✝","sexp":"((:c PseudoEMetricSpace) (:fv _uniq.61550))"},{"name":"δ","sexp":"(:c Real)"},{"name":"ε","sexp":"(:c Real)"},{"name":"s","sexp":"((:c Set) (:fv _uniq.61550))"},{"name":"t","sexp":"((:c...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Metric.cthickening) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c PseudoEMetricSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV4)) (:arg :explicit 3 (:app (:c clos...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61548","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61550","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":21897,"sourceStart":21890,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":21899,"sourceStart":21898,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source...
[]
[{"source":"cthickening","source_end":21910,"source_start":21899,"syntax_kind":"ident"},{"source":"infEdist_closure","source_end":21928,"source_start":21912,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61548","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61550","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
124
2
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
79c4950ddf00a8f91fdd76d877587821823a1dd87535d513fb662b3f312f349f
065261e3ba67f5a2483e156de67618fe78d03f14f1bda818bf7cf32a4a903721
13ed90e68dd350ae1fe20a88283ddbfd2561c0b83d750b89f8a10fb8e617ed43
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,494
Real.Angle.cos_pi_div_two_sub
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
induction θ using <a>Real.Angle.induction_on</a>
θ : Angle ⊢ (↑(π / 2) - θ).cos = θ.sin
case h x✝ : ℝ ⊢ (↑(π / 2) - ↑x✝).cos = (↑x✝).sin
((:c Eq) (:c Real) ((:c Real.Angle.cos) ((:c HSub.hSub) (:c Real.Angle) (:c Real.Angle) (:c Real.Angle) ((:c instHSub) (:c Real.Angle) ((:c SubNegMonoid.toSub) (:c Real.Angle) ((:c AddGroup.toSubNegMonoid) (:c Real.Angle) ((:c NormedAddGroup.toAddGroup) (:c Real.Angle) ((:c NormedAddCommGroup.toNormedAddGroup) (:c Real...
[{"name":"θ","sexp":"(:c Real.Angle)"}]
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Real.Angle.cos) (:arg :explicit 0 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :implicit-type 1 (:c Real.Angle)) (:arg :implicit-type 2 (:c Real.Angle)) (:arg :instance 3 (:instance-of (:app (:c HSub) (:arg :explicit 0 (:c...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.92793","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"}]
{"children":[{"source":"induction","sourceEnd":20508,"sourceStart":20499,"tag":"atom"},{"children":[{"contextIndex":1,"semanticRole":"local","source":"θ","sourceEnd":20511,"sourceStart":20509,"tag":"identifier"}],"kind":"null","source":"θ","sourceEnd":20511,"sourceStart":20509,"tag":"node"},{"children":[{"source":"usin...
[]
[{"source":"θ","source_end":20511,"source_start":20509,"syntax_kind":"ident"},{"source":"Real.Angle.induction_on","source_end":20541,"source_start":20518,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.92793","is_instance":false,"is_let":false,"user_name":"θ"}]
161
4
exact
true
1
1
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b5150e6a929ca57cb31331edbb70616ea8d7d5736d269fd4443d42a77b2b65f0
0c6aa77db81019ec2feec06997a5ad8b1f4d6ff10a33752bd61876f5c0b446db
15c3e600ed684e9286865c611ec4ee40a9bfde41d1c3a01ac033e2ccfbbcb770
6e227d5734989d332cb35a9ee1de7e8935fc63568bdc002dd5b85c3c55f82171
cat-searcher/leandojo-benchmark-4-random
test
4,495
Real.Angle.cos_pi_div_two_sub
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>Real.cos_pi_div_two_sub</a> _
case h x✝ : ℝ ⊢ (↑(π / 2) - ↑x✝).cos = (↑x✝).sin
((:c Eq) (:c Real) ((:c Real.Angle.cos) ((:c HSub.hSub) (:c Real.Angle) (:c Real.Angle) (:c Real.Angle) ((:c instHSub) (:c Real.Angle) ((:c SubNegMonoid.toSub) (:c Real.Angle) ((:c AddGroup.toSubNegMonoid) (:c Real.Angle) ((:c NormedAddGroup.toAddGroup) (:c Real.Angle) ((:c NormedAddCommGroup.toNormedAddGroup) (:c Real...
[{"name":"x✝","sexp":"(:c Real)"}]
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Real.Angle.cos) (:arg :explicit 0 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :implicit-type 1 (:c Real.Angle)) (:arg :implicit-type 2 (:c Real.Angle)) (:arg :instance 3 (:instance-of (:app (:c HSub) (:arg :explicit 0 (:c...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.92804","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"}]
{"children":[{"source":"exact","sourceEnd":20549,"sourceStart":20544,"tag":"atom"},{"children":[{"name":"Real.cos_pi_div_two_sub","semanticRole":"global","source":"Real.cos_pi_div_two_sub","sourceEnd":20573,"sourceStart":20550,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":20575,"sourceStart":2...
[]
[{"source":"Real.cos_pi_div_two_sub _","source_end":20575,"source_start":20550,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.92804","is_instance":false,"is_let":false,"user_name":"x✝"}]
161
5
exact
true
1
1
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
de94cf29605db8f702e16bb9dff7e4f0803060ccf2aa2299dcfaf832d50eaf62
6e227d5734989d332cb35a9ee1de7e8935fc63568bdc002dd5b85c3c55f82171
40bb89d1561a6a8de93af54bbf8c962a89c78a6779e942695c9ba74738fd0613
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,496
Ideal.isMaximal_iff
Mathlib/RingTheory/Ideal/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>lt_iff_le_not_le</a>]
α : Type u β : Type v inst✝ : Semiring α I✝ : Ideal α a b : α I J : Ideal α ⊢ I < J → J = ⊤ ↔ ∀ (x : α), I ≤ J → x ∉ I → x ∈ J → 1 ∈ J
α : Type u β : Type v inst✝ : Semiring α I✝ : Ideal α a b : α I J : Ideal α ⊢ I ≤ J ∧ ¬J ≤ I → J = ⊤ ↔ ∀ (x : α), I ≤ J → x ∉ I → x ∈ J → 1 ∈ J
((:c Iff) (:forall _ ((:c LT.lt) ((:c Ideal) (:fv _uniq.35768) (:fv _uniq.35773)) ((:c Preorder.toLT) ((:c Ideal) (:fv _uniq.35768) (:fv _uniq.35773)) ((:c PartialOrder.toPreorder) ((:c Ideal) (:fv _uniq.35768) (:fv _uniq.35773)) ((:c OmegaCompletePartialOrder.toPartialOrder) ((:c Ideal) (:fv _uniq.35768) (:fv _uniq.35...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.35768))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.35768) (:fv _uniq.35773))"},{"name":"a","sexp":"(:fv _uniq.35768)"},{"name":"b","sexp":"(:fv _uniq.35768)"},{"name":"I","sexp":"((:c Ideal)...
(:app (:c Iff) (:arg :explicit 0 (:forall _ :explicit (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c Ideal) (:arg :explic...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35768","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35770","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"rw","sourceEnd":11674,"sourceStart":11672,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11676,"sourceStart":11675,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"lt_iff_le_not_le...
[]
[{"source":"lt_iff_le_not_le","source_end":11692,"source_start":11676,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35768","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35770","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
111
4
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e8cb30df96c389f907dc053fe57fdb501e009d42a8481c9a90d4ac8106662f8e
a32d0ccf3a42aa5a203b47c3e62ff6af7cdf9de68299e2cd18f726b1f6cc3d0f
9def7c1e5e7936ab22fed4e9647f3997fbb531e37fb76440f3ea069abadbbcf1
7d35d83e01740346e87bca25aff6296374d5155e8b2c12c345805a20797f711b
cat-searcher/leandojo-benchmark-4-random
test
4,497
Ideal.isMaximal_iff
Mathlib/RingTheory/Ideal/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact ⟨fun H x h hx₁ hx₂ => J.eq_top_iff_one.1 <| H ⟨h, <a>Set.not_subset</a>.2 ⟨_, hx₂, hx₁⟩⟩, fun H ⟨h₁, h₂⟩ => let ⟨x, xJ, xI⟩ := <a>Set.not_subset</a>.1 h₂ J.eq_top_iff_one.2 <| H x h₁ xI xJ⟩
α : Type u β : Type v inst✝ : Semiring α I✝ : Ideal α a b : α I J : Ideal α ⊢ I ≤ J ∧ ¬J ≤ I → J = ⊤ ↔ ∀ (x : α), I ≤ J → x ∉ I → x ∈ J → 1 ∈ J
((:c Iff) (:forall _ ((:c And) ((:c LE.le) ((:c Ideal) (:fv _uniq.35768) (:fv _uniq.35773)) ((:c Preorder.toLE) ((:c Ideal) (:fv _uniq.35768) (:fv _uniq.35773)) ((:c PartialOrder.toPreorder) ((:c Ideal) (:fv _uniq.35768) (:fv _uniq.35773)) ((:c OmegaCompletePartialOrder.toPartialOrder) ((:c Ideal) (:fv _uniq.35768) (:f...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.35768))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.35768) (:fv _uniq.35773))"},{"name":"a","sexp":"(:fv _uniq.35768)"},{"name":"b","sexp":"(:fv _uniq.35768)"},{"name":"I","sexp":"((:c Ideal)...
(:app (:c Iff) (:arg :explicit 0 (:forall _ :explicit (:app (:c And) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35768","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35770","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"exact","sourceEnd":11710,"sourceStart":11705,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":11726,"sourceStart":11723,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":11729,"sourceStart":11726,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source...
[]
[{"source":"⟨fun H x h hx₁ hx₂ => J.eq_top_iff_one.1 <| H ⟨h, not_subset.2 ⟨_, hx₂, hx₁⟩⟩,\n fun H ⟨h₁, h₂⟩ =>\n let ⟨x, xJ, xI⟩ := not_subset.1 h₂\n J.eq_top_iff_one.2 <| H x h₁ xI xJ⟩","source_end":11968,"source_start":11723,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35768","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35770","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
111
8
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0cb9efe44bc59a9acdb7c3268931d3c86b39289eb81d3663187eba5e008abb13
7d35d83e01740346e87bca25aff6296374d5155e8b2c12c345805a20797f711b
a0831dd9dd120073536faa880ffc318f19f4b6af25e947de2df6850412cc9d4a
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,498
RelIso.preimage_eq_image_symm
Mathlib/Order/RelIso/Set.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [e.symm.image_eq_preimage_symm]
α✝ : Type u_1 β✝ : Type u_2 γ : Type u_3 δ : Type u_4 r✝ : α✝ → α✝ → Prop s✝ : β✝ → β✝ → Prop t✝ : γ → γ → Prop u : δ → δ → Prop α : Type u_5 β : Type u_6 r : α → α → Prop s : β → β → Prop e : r ≃r s t : Set β ⊢ ⇑e ⁻¹' t = ⇑e.symm '' t
α✝ : Type u_1 β✝ : Type u_2 γ : Type u_3 δ : Type u_4 r✝ : α✝ → α✝ → Prop s✝ : β✝ → β✝ → Prop t✝ : γ → γ → Prop u : δ → δ → Prop α : Type u_5 β : Type u_6 r : α → α → Prop s : β → β → Prop e : r ≃r s t : Set β ⊢ ⇑e ⁻¹' t = ⇑e.symm.symm ⁻¹' t
((:c Eq) ((:c Set) (:fv _uniq.5451)) ((:c Set.preimage) (:fv _uniq.5451) (:fv _uniq.5454) ((:c DFunLike.coe) ((:c RelIso) (:fv _uniq.5451) (:fv _uniq.5454) (:fv _uniq.5460) (:fv _uniq.5466)) (:fv _uniq.5451) (:lambda _ (:fv _uniq.5451) (:fv _uniq.5454)) ((:c RelIso.instFunLike) (:fv _uniq.5451) (:fv _uniq.5454) (:fv _u...
[{"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":"r✝","sexp":"(:forall _ (:fv _uniq.5415) (:forall _ (:fv _uniq.5415) (:sort 0)))"},{"name":"s✝","sexp":"(:forall _ (:fv _uniq.5418) (:forall _ (:fv _...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV8)))) (:arg :explicit 1 (:app (:c Set.preimage) (:arg :implicit-type 0 (:fv FV8)) (:arg :implicit-type 1 (:fv FV9)) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c RelIso) (:arg :implicit-type 0 (:fv FV8)) (:arg :imp...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5415","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5418","is_instance":false,"is_let":false,"name":"β✝","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"rw","sourceEnd":3739,"sourceStart":3737,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3741,"sourceStart":3740,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"RelIso.image_eq_prei...
[]
[{"source":"e.symm.image_eq_preimage_symm","source_end":3770,"source_start":3741,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5415","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5418","is_instance":false,"is_let":false,"user_name":"β✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
38
4
exact
true
1
14
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1468cd0cfdca452c01c58205aa2a2028b7cc5bcbfaceaacede4a25ea9c2fa703
c6ef3923af082c4ebd73f93fd62f0042887b35ad650e37aaa66d78e4d1ea9366
8a4e4caf91140982ca015623bb9d337400bd6dd1ced9dd223cd7831494a7bd93
b453926843fae00bf0ab4ee7f82b726bff9f2e842d252a46bc4a9eb4ae50880d
cat-searcher/leandojo-benchmark-4-random
test
4,499
RelIso.preimage_eq_image_symm
Mathlib/Order/RelIso/Set.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rfl
α✝ : Type u_1 β✝ : Type u_2 γ : Type u_3 δ : Type u_4 r✝ : α✝ → α✝ → Prop s✝ : β✝ → β✝ → Prop t✝ : γ → γ → Prop u : δ → δ → Prop α : Type u_5 β : Type u_6 r : α → α → Prop s : β → β → Prop e : r ≃r s t : Set β ⊢ ⇑e ⁻¹' t = ⇑e.symm.symm ⁻¹' t
((:c Eq) ((:c Set) (:fv _uniq.5451)) ((:c Set.preimage) (:fv _uniq.5451) (:fv _uniq.5454) ((:c DFunLike.coe) ((:c RelIso) (:fv _uniq.5451) (:fv _uniq.5454) (:fv _uniq.5460) (:fv _uniq.5466)) (:fv _uniq.5451) (:lambda _ (:fv _uniq.5451) (:fv _uniq.5454)) ((:c RelIso.instFunLike) (:fv _uniq.5451) (:fv _uniq.5454) (:fv _u...
[{"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":"r✝","sexp":"(:forall _ (:fv _uniq.5415) (:forall _ (:fv _uniq.5415) (:sort 0)))"},{"name":"s✝","sexp":"(:forall _ (:fv _uniq.5418) (:forall _ (:fv _...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV8)))) (:arg :explicit 1 (:app (:c Set.preimage) (:arg :implicit-type 0 (:fv FV8)) (:arg :implicit-type 1 (:fv FV9)) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c RelIso) (:arg :implicit-type 0 (:fv FV8)) (:arg :imp...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5415","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5418","is_instance":false,"is_let":false,"name":"β✝","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"rfl","sourceEnd":3776,"sourceStart":3773,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":3776,"sourceStart":3773,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5415","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5418","is_instance":false,"is_let":false,"user_name":"β✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
38
8
exact
true
1
14
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d4eba8647c36a7aad1c31f0d09b8d4905cc35483e6fa46e0dddb3f36b9a5b6a4
b453926843fae00bf0ab4ee7f82b726bff9f2e842d252a46bc4a9eb4ae50880d
5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,500
MeasureTheory.Measure.singularPart_of_not_haveLebesgueDecomposition
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>MeasureTheory.Measure.singularPart</a>, <a>dif_neg</a> h]
α : Type u_1 β : Type u_2 m : MeasurableSpace α μ ν : Measure α h : ¬μ.HaveLebesgueDecomposition ν ⊢ μ.singularPart ν = 0
((:c Eq) ((:c MeasureTheory.Measure) (:fv _uniq.1704) (:fv _uniq.1710)) ((:c MeasureTheory.Measure.singularPart) (:fv _uniq.1704) (:fv _uniq.1710) (:fv _uniq.1719) (:fv _uniq.1723)) ((:c OfNat.ofNat) ((:c MeasureTheory.Measure) (:fv _uniq.1704) (:fv _uniq.1710)) (:lit 0) ((:c Zero.toOfNat0) ((:c MeasureTheory.Measure) ...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.1704))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.1704) (:fv _uniq.1710))"},{"name":"ν","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.1704) (:fv _uniq.1710))"},{"name"...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c MeasureTheory.Measure.singularPart) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :expl...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1704","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1707","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":4828,"sourceStart":4826,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4830,"sourceStart":4829,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag...
[]
[{"source":"singularPart","source_end":4842,"source_start":4830,"syntax_kind":"ident"},{"source":"dif_neg h","source_end":4853,"source_start":4844,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1704","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1707","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq...
18
2
exact
true
1
6
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d9a3786d04be34358dfe5595c0b77147bf452d19574b9088caae7a3b73ede76f
55cfca973ba58b5096e38b5e1015881b3cabf4cce4e51139ba09b01e22ddfcd3
33bd85ee9c5ac71dbf94b66ae80e23ffb29f78bb20d14a73faf30e0e56d952aa
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,501
ProbabilityTheory.cond_univ
Mathlib/Probability/ConditionalProbability.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>ProbabilityTheory.cond</a>, <a>MeasureTheory.IsProbabilityMeasure.measure_univ</a>, <a>MeasureTheory.Measure.restrict_univ</a>]
Ω : Type u_1 Ω' : Type u_2 α : Type u_3 m : MeasurableSpace Ω m' : MeasurableSpace Ω' μ : Measure Ω s t : Set Ω inst✝ : IsProbabilityMeasure μ ⊢ μ[|univ] = μ
((:c Eq) ((:c MeasureTheory.Measure) (:fv _uniq.12157) (:fv _uniq.12166)) ((:c ProbabilityTheory.cond) (:fv _uniq.12157) (:fv _uniq.12166) (:fv _uniq.12177) ((:c Set.univ) (:fv _uniq.12157))) (:fv _uniq.12177))
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"Ω'","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.12157))"},{"name":"m'","sexp":"((:c MeasurableSpace) (:fv _uniq.12160))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.12157) (:fv ...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c ProbabilityTheory.cond) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12157","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12160","is_instance":false,"is_let":false,"name":"Ω'","sexp":"(:sort Type)"},{"binder_role":":implicit","co...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":5442,"sourceStart":5438,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn...
[]
[{"source":"cond","source_end":5448,"source_start":5444,"syntax_kind":"ident"},{"source":"measure_univ","source_end":5462,"source_start":5450,"syntax_kind":"ident"},{"source":"Measure.restrict_univ","source_end":5485,"source_start":5464,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12157","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12160","is_instance":false,"is_let":false,"user_name":"Ω'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
23
2
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
dff3614b29518307c99802062b112a17eec302f7e0862414a078d2dd9cc3ec40
bc7ac8e928af3629caf81edeeb514bc27d01847146fea6da6c5ded7697f0aa5b
84d83ce0d0c22ba040076d68db5335e85835d99e8c3623d32aecf6af9a4cb55b
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,502
AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'_fst_snd
Mathlib/AlgebraicGeometry/Gluing.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
delta <a>AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'</a>
X : Scheme 𝒰 : X.OpenCover x y z : 𝒰.J ⊢ 𝒰.gluedCoverT' x y z ≫ pullback.fst ≫ pullback.snd = pullback.snd ≫ pullback.snd
X : Scheme 𝒰 : X.OpenCover x y z : 𝒰.J ⊢ ((pullbackRightPullbackFstIso (𝒰.map x) (𝒰.map z) pullback.fst).hom ≫ (pullback.map (pullback.fst ≫ 𝒰.map x) (𝒰.map z) (pullback.fst ≫ 𝒰.map y) (𝒰.map z) (pullbackSymmetry (𝒰.map x) (𝒰.map y)).hom (𝟙 (𝒰.obj z)) (𝟙 X) ⋯ ⋯ ≫ (pullback...
((:c Eq) ((:c Quiver.Hom) (:c AlgebraicGeometry.Scheme) ((:c CategoryTheory.CategoryStruct.toQuiver) (:c AlgebraicGeometry.Scheme) ((:c CategoryTheory.Category.toCategoryStruct) (:c AlgebraicGeometry.Scheme) (:c AlgebraicGeometry.Scheme.instCategory))) ((:c CategoryTheory.Limits.pullback) (:c AlgebraicGeometry.Scheme) ...
[{"name":"X","sexp":"(:c AlgebraicGeometry.Scheme)"},{"name":"𝒰","sexp":"((:c AlgebraicGeometry.Scheme.OpenCover) (:fv _uniq.61496))"},{"name":"x","sexp":"((:c AlgebraicGeometry.Scheme.OpenCover.J) (:fv _uniq.61496) (:fv _uniq.61499))"},{"name":"y","sexp":"((:c AlgebraicGeometry.Scheme.OpenCover.J) (:fv _uniq.61496) (...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:c AlgebraicGeometry.Scheme)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:c AlgebraicGeometry.Scheme))))) (:arg :explicit 2 (:app (:c CategoryTheory.Limits.pullback) (:arg :implicit-type 0 (:c AlgebraicGeometry....
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61496","is_instance":false,"is_let":false,"name":"X","sexp":"(:c AlgebraicGeometry.Scheme)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.61499","is_instance":false,"is_let":false,"name":"𝒰","sexp":"(:app (:c AlgebraicGeometry....
{"children":[{"source":"delta","sourceEnd":13823,"sourceStart":13818,"tag":"atom"},{"children":[{"name":"AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'","semanticRole":"global","source":"gluedCoverT'","sourceEnd":13836,"sourceStart":13824,"tag":"identifier"}],"kind":"null","source":"gluedCoverT'","sourceEnd":13836,"so...
[]
[{"source":"gluedCoverT'","source_end":13836,"source_start":13824,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61496","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.61499","is_instance":false,"is_let":false,"user_name":"𝒰"},{"binder_role":":explicit","context_index":3,"internal_name":"_u...
65
4
exact
true
1
5
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
df97629cd6fcce0672dc0d36a48689d25cdc534ed81dde706cba9606ad30f78a
7c5e3d968889ce0bc40fbf34c20f9e9f81721d3338adaeb5f50a1bc11dd0e2fd
ed802b714176400f12bbcd28c24809d64e144a2d2a66022dce2e625eaff4798a
4ee93559b4af2e10b0716235e61bd0b8d1e57a4063097f10a5007828ab85f106
cat-searcher/leandojo-benchmark-4-random
test
4,503
AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'_fst_snd
Mathlib/AlgebraicGeometry/Gluing.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
X : Scheme 𝒰 : X.OpenCover x y z : 𝒰.J ⊢ ((pullbackRightPullbackFstIso (𝒰.map x) (𝒰.map z) pullback.fst).hom ≫ (pullback.map (pullback.fst ≫ 𝒰.map x) (𝒰.map z) (pullback.fst ≫ 𝒰.map y) (𝒰.map z) (pullbackSymmetry (𝒰.map x) (𝒰.map y)).hom (𝟙 (𝒰.obj z)) (𝟙 X) ⋯ ⋯ ≫ (pullback...
((:c Eq) ((:c Quiver.Hom) (:c AlgebraicGeometry.Scheme) ((:c CategoryTheory.CategoryStruct.toQuiver) (:c AlgebraicGeometry.Scheme) ((:c CategoryTheory.Category.toCategoryStruct) (:c AlgebraicGeometry.Scheme) (:c AlgebraicGeometry.Scheme.instCategory))) ((:c CategoryTheory.Limits.pullback) (:c AlgebraicGeometry.Scheme) ...
[{"name":"X","sexp":"(:c AlgebraicGeometry.Scheme)"},{"name":"𝒰","sexp":"((:c AlgebraicGeometry.Scheme.OpenCover) (:fv _uniq.61496))"},{"name":"x","sexp":"((:c AlgebraicGeometry.Scheme.OpenCover.J) (:fv _uniq.61496) (:fv _uniq.61499))"},{"name":"y","sexp":"((:c AlgebraicGeometry.Scheme.OpenCover.J) (:fv _uniq.61496) (...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:c AlgebraicGeometry.Scheme)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:c AlgebraicGeometry.Scheme))))) (:arg :explicit 2 (:app (:c CategoryTheory.Limits.pullback) (:arg :implicit-type 0 (:c AlgebraicGeometry....
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61496","is_instance":false,"is_let":false,"name":"X","sexp":"(:c AlgebraicGeometry.Scheme)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.61499","is_instance":false,"is_let":false,"name":"𝒰","sexp":"(:app (:c AlgebraicGeometry....
{"children":[{"source":"simp","sourceEnd":13842,"sourceStart":13838,"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.61496","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.61499","is_instance":false,"is_let":false,"user_name":"𝒰"},{"binder_role":":explicit","context_index":3,"internal_name":"_u...
65
6
exact
true
1
5
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a39dd1ee8836943c6db39787de5d28a32b411bc6459b95e3f65e5e4689e7a53e
4ee93559b4af2e10b0716235e61bd0b8d1e57a4063097f10a5007828ab85f106
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
4,504
MeasurableSet.cond
Mathlib/MeasureTheory/MeasurableSpace/Defs.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
cases i
α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 δ' : Type u_5 ι : Sort u_6 s t u : Set α m : MeasurableSpace α s₁ s₂ : Set α h₁ : MeasurableSet s₁ h₂ : MeasurableSet s₂ i : Bool ⊢ MeasurableSet (bif i then s₁ else s₂)
case false α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 δ' : Type u_5 ι : Sort u_6 s t u : Set α m : MeasurableSpace α s₁ s₂ : Set α h₁ : MeasurableSet s₁ h₂ : MeasurableSet s₂ ⊢ MeasurableSet (bif false then s₁ else s₂) case true α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 δ' : Type u_5 ι : Sort u_6 s t...
((:c MeasurableSet) (:fv _uniq.11732) (:fv _uniq.11759) ((:c cond) ((:c Set) (:fv _uniq.11732)) (:fv _uniq.11815) (:fv _uniq.11811) (:fv _uniq.11812)))
[{"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":"δ'","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort u_6)"},{"name":"s","sexp":"((:c Set) (:fv _uniq.11732))"},{"name":"t","sexp":"((:c Set) (:f...
(:app (:c MeasurableSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c cond) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:fv FV15)) (:arg :explicit 2 (:fv FV11)) (:arg :...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11732","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.11735","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"cases","sourceEnd":10052,"sourceStart":10047,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":15,"semanticRole":"local","source":"i","sourceEnd":10054,"sourceStart":10053,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","s...
[]
[{"source":"i","source_end":10054,"source_start":10053,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11732","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.11735","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
70
4
exact
true
1
15
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
16ba80208afc64c0dc867f3650006fb66998d89e51876251af3786a96246e85d
ec9a38c08b8331456ea5abb3972ab3a98ec7bc70d6c07c3598fa8907621de33e
8dcd98d9e143d2ca0867dad6699c3e83da487267a7c4c8ac76855f8b92ac2b4a
8e571f62db7259c451057cfea81691b83f8f4e34564da54da5da2463828b349f