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value | tactic stringlengths 3 2.13k | text_state stringlengths 7 2.31k | text_target_state stringlengths 0 4.07k | raw_goal_sexp stringlengths 10 11.8M | raw_hyp_sexps stringlengths 2 15.6M | model_goal_sexp stringlengths 10 2.68M | model_hyp_sexps stringlengths 2 3.62M | source_syntax stringlengths 179 164k | syntax_args stringclasses 256
values | term_ranges stringlengths 2 6.01k | local_context stringlengths 2 10.3k | unit_index int64 3 1.26k | invocation_index int64 0 357 | alignment_kind stringclasses 2
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classes | raw_schema_version int64 4 4 | raw_extractor_version stringclasses 1
value | model_schema_version int64 2 2 | model_normalization stringclasses 1
value | trace_schema_version int64 3 3 | trace_extractor_version stringclasses 1
value | pantograph_commit stringclasses 1
value | model_pantograph_commit stringclasses 1
value | raw_record_sha256 stringlengths 64 64 | state_sha256 stringlengths 64 64 | tactic_sha256 stringlengths 64 64 | target_state_sha256 stringlengths 64 64 |
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cat-searcher/leandojo-benchmark-4-random | test | 102 | FractionalIdeal.count_mul | Mathlib/RingTheory/DedekindDomain/Factorization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply v.associates_irreducible | R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
⊢ Irreducible (Associates.mk v.asIdeal) | ((:c Irreducible) ((:c Associates) ((:c Ideal) (:fv _uniq.73763) ((:c CommSemiring.toSemiring) (:fv _uniq.73763) ((:c CommRing.toCommSemiring) (:fv _uniq.73763) (:fv _uniq.73766)))) ((:c MonoidWithZero.toMonoid) ((:c Ideal) (:fv _uniq.73763) ((:c CommSemiring.toSemiring) (:fv _uniq.73763) ((:c CommRing.toCommSemiring) ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.73763))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.73769))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.73763) (:fv _uniq.73769) ((:c CommRing.toCommSemiring) (:fv _uniq.7376... | (:app (:c Irreducible) (:arg :implicit-type 0 (:app (:c Associates) (:arg :explicit 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 Monoid) (:arg :explicit 0 (:app (:c Ideal) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"apply","sourceEnd":18030,"sourceStart":18025,"tag":"atom"},{"name":"IsDedekindDomain.HeightOneSpectrum.associates_irreducible","semanticRole":"global","source":"v.associates_irreducible","sourceEnd":18055,"sourceStart":18031,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply ... | [] | [{"source":"v.associates_irreducible","source_end":18055,"source_start":18031,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 46 | 6 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fda90380cdf61bb47a2dfdfe21db9bc5968588fb94db0e2035c07c8694bf237b | d09df2375826850072ae5154ceec70d0ced34ecc23a9261ccf787704f81cae1b | 0c1344dee40f1674eb35941f9992afd63eb5fe02ffa3a28ebb27deedec92e96c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 103 | FractionalIdeal.count_mul | Mathlib/RingTheory/DedekindDomain/Factorization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>ne_eq</a>, <a>Associates.mk_eq_zero</a>, <a>Ideal.zero_eq_bot</a>, <a>Ideal.span_singleton_eq_bot</a>] | R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha : a ≠ 0
haJ : I = spanSingleton R⁰ ((alge... | R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha : a ≠ 0
haJ : I = spanSingleton R⁰ ((alge... | ((:c Ne) ((:c Associates) ((:c Ideal) (:fv _uniq.73763) ((:c CommSemiring.toSemiring) (:fv _uniq.73763) ((:c CommRing.toCommSemiring) (:fv _uniq.73763) (:fv _uniq.73766)))) ((:c MonoidWithZero.toMonoid) ((:c Ideal) (:fv _uniq.73763) ((:c CommSemiring.toSemiring) (:fv _uniq.73763) ((:c CommRing.toCommSemiring) (:fv _uni... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.73763))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.73769))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.73763) (:fv _uniq.73769) ((:c CommRing.toCommSemiring) (:fv _uniq.7376... | (:app (:c Ne) (:arg :implicit-type 0 (:app (:c Associates) (:arg :explicit 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 Monoid) (:arg :explicit 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"rw","sourceEnd":18197,"sourceStart":18195,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":18199,"sourceStart":18198,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"ne_eq","semantic... | [] | [{"source":"ne_eq","source_end":18204,"source_start":18199,"syntax_kind":"ident"},{"source":"Associates.mk_eq_zero","source_end":18227,"source_start":18206,"syntax_kind":"ident"},{"source":"Ideal.zero_eq_bot","source_end":18246,"source_start":18229,"syntax_kind":"ident"},{"source":"Ideal.span_singleton_eq_bot","source_... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 46 | 10 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 01c17d524de53438db81eb28ae55b525fd9117d9d0a7546172b2aa796b6aea90 | e030779410de922192281c0ad607e4422b740ef7427f1985d53b38fc375354ad | d73ae08592824c5479859b82544a86a3e36cac4cf4c6946ccd04e18b6cc3fce2 | 6998338456f71915f5fb142955453dbab0da78880c792e2126f3ce740fe5a2a8 |
cat-searcher/leandojo-benchmark-4-random | test | 104 | FractionalIdeal.count_mul | Mathlib/RingTheory/DedekindDomain/Factorization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ha | R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha : a ≠ 0
haJ : I = spanSingleton R⁰ ((alge... | ((:c Not) ((:c Eq) (:fv _uniq.73763) (:fv _uniq.75632) ((:c OfNat.ofNat) (:fv _uniq.73763) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.73763) ((:c MonoidWithZero.toZero) (:fv _uniq.73763) ((:c Semiring.toMonoidWithZero) (:fv _uniq.73763) ((:c CommSemiring.toSemiring) (:fv _uniq.73763) ((:c CommRing.toCommSemiring) (:fv _un... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.73763))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.73769))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.73763) (:fv _uniq.73769) ((:c CommRing.toCommSemiring) (:fv _uniq.7376... | (:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV14)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:lit 0)))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"exact","sourceEnd":18283,"sourceStart":18278,"tag":"atom"},{"contextIndex":16,"semanticRole":"local","source":"ha","sourceEnd":18286,"sourceStart":18284,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact ha","sourceEnd":18286,"sourceStart":18278,"tag":"node"} | [] | [{"source":"ha","source_end":18286,"source_start":18284,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 46 | 17 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ff821a202f5427fc1fdac85141025dc830e9982d86ec541443918d50917d047d | 6998338456f71915f5fb142955453dbab0da78880c792e2126f3ce740fe5a2a8 | ed7b20bfa58750585795fc60c8364f3d8cfaa54d8e6d316fdcf777f9aa77d07b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 105 | FractionalIdeal.count_mul | Mathlib/RingTheory/DedekindDomain/Factorization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>ne_eq</a>, <a>Associates.mk_eq_zero</a>, <a>Ideal.zero_eq_bot</a>, <a>Ideal.span_singleton_eq_bot</a>] | R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha : a ≠ 0
haJ : I = spanSingleton R⁰ ((alge... | R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha : a ≠ 0
haJ : I = spanSingleton R⁰ ((alge... | ((:c Ne) ((:c Associates) ((:c Ideal) (:fv _uniq.73763) ((:c CommSemiring.toSemiring) (:fv _uniq.73763) ((:c CommRing.toCommSemiring) (:fv _uniq.73763) (:fv _uniq.73766)))) ((:c MonoidWithZero.toMonoid) ((:c Ideal) (:fv _uniq.73763) ((:c CommSemiring.toSemiring) (:fv _uniq.73763) ((:c CommRing.toCommSemiring) (:fv _uni... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.73763))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.73769))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.73763) (:fv _uniq.73769) ((:c CommRing.toCommSemiring) (:fv _uniq.7376... | (:app (:c Ne) (:arg :implicit-type 0 (:app (:c Associates) (:arg :explicit 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 Monoid) (:arg :explicit 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"rw","sourceEnd":18536,"sourceStart":18534,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":18538,"sourceStart":18537,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"ne_eq","semantic... | [] | [{"source":"ne_eq","source_end":18543,"source_start":18538,"syntax_kind":"ident"},{"source":"Associates.mk_eq_zero","source_end":18566,"source_start":18545,"syntax_kind":"ident"},{"source":"Ideal.zero_eq_bot","source_end":18585,"source_start":18568,"syntax_kind":"ident"},{"source":"Ideal.span_singleton_eq_bot","source_... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 46 | 22 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 39906cb4192e6d1baf2d6b7ec8e21c17b95948c087be6d94cb0a95a0733a12e9 | 9cbdfafc1454b7d6d67ac124aa63d4231ac6a23233de08d46706bf7853d98613 | d73ae08592824c5479859b82544a86a3e36cac4cf4c6946ccd04e18b6cc3fce2 | 44ea85eb8b21646c266f5faa75217943417d795772549c080a4f33e08f4f921f |
cat-searcher/leandojo-benchmark-4-random | test | 106 | FractionalIdeal.count_mul | Mathlib/RingTheory/DedekindDomain/Factorization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ha' | R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha : a ≠ 0
haJ : I = spanSingleton R⁰ ((alge... | ((:c Not) ((:c Eq) (:fv _uniq.73763) (:fv _uniq.76671) ((:c OfNat.ofNat) (:fv _uniq.73763) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.73763) ((:c MonoidWithZero.toZero) (:fv _uniq.73763) ((:c Semiring.toMonoidWithZero) (:fv _uniq.73763) ((:c CommSemiring.toSemiring) (:fv _uniq.73763) ((:c CommRing.toCommSemiring) (:fv _un... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.73763))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.73769))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.73763) (:fv _uniq.73769) ((:c CommRing.toCommSemiring) (:fv _uniq.7376... | (:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV20)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:lit 0)))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"exact","sourceEnd":18622,"sourceStart":18617,"tag":"atom"},{"contextIndex":22,"semanticRole":"local","source":"ha'","sourceEnd":18626,"sourceStart":18623,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact ha'","sourceEnd":18626,"sourceStart":18617,"tag":"node"} | [] | [{"source":"ha'","source_end":18626,"source_start":18623,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 46 | 29 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f72c5129e95a95677b57ab73e993f3b30ea1347179afcbb6d66e669095216836 | 44ea85eb8b21646c266f5faa75217943417d795772549c080a4f33e08f4f921f | d52a67359d6a8fb6ef9811269119881d9b52cfbf0ba45e92204267902ddf8b39 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 107 | FractionalIdeal.count_mul | Mathlib/RingTheory/DedekindDomain/Factorization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [haJ, haJ', <a>mul_assoc</a>, <a>mul_comm</a> (J : <a>FractionalIdeal</a> R⁰ K), <a>mul_assoc</a>, ← <a>mul_assoc</a>, <a>FractionalIdeal.spanSingleton_mul_spanSingleton</a>, <a>FractionalIdeal.coeIdeal_mul</a>, <a>RingHom.map_mul</a>, <a>mul_inv</a>, <a>mul_comm</a> (J : <a>FractionalIdeal</a> R⁰ K)] | R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
I I' : FractionalIdeal R⁰ K
hI : I ≠ 0
hI' : I' ≠ 0
hv : Irreducible (Associates.mk v.asIdeal)
a : R
J : Ideal R
ha : a ≠ 0
haJ : I = spanSingleton R⁰ ((alge... | ((:c Eq) ((:c FractionalIdeal) (:fv _uniq.73763) (:fv _uniq.73766) ((:c nonZeroDivisors) (:fv _uniq.73763) ((:c Semiring.toMonoidWithZero) (:fv _uniq.73763) ((:c CommSemiring.toSemiring) (:fv _uniq.73763) ((:c CommRing.toCommSemiring) (:fv _uniq.73763) (:fv _uniq.73766))))) (:fv _uniq.73769) ((:c EuclideanDomain.toComm... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.73763))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.73769))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.73763) (:fv _uniq.73769) ((:c CommRing.toCommSemiring) (:fv _uniq.7376... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c FractionalIdeal) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c nonZeroDivisors) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MonoidWithZero) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"rw","sourceEnd":18839,"sourceStart":18837,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":18841,"sourceStart":18840,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":17,"seman... | [] | [{"source":"haJ","source_end":18844,"source_start":18841,"syntax_kind":"ident"},{"source":"haJ'","source_end":18850,"source_start":18846,"syntax_kind":"ident"},{"source":"mul_assoc","source_end":18861,"source_start":18852,"syntax_kind":"ident"},{"source":"mul_comm (J : FractionalIdeal R⁰ K)","source_end":18900,"source_... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73763","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.73766","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 46 | 33 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1f86e093e3a68edf8db2d31a6e8e0c489d8cac6ec9f60c7172833edc0aa3dbc9 | 86a2367608e2699e4ad1d23fe6efc41f3d2c051c959b67a0d3b67dc2a00b231b | 2269549eb8c1f737b4e26fcfecf80fcdbc878ea7a74c0e838633bf7cb3000709 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 108 | Booleanisation.lift_le_lift | Mathlib/Order/Booleanisation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨_⟩ | α : Type u_1
inst✝ : GeneralizedBooleanAlgebra α
x y : Booleanisation α
a b : α
⊢ lift a ≤ lift b → a ≤ b | case lift
α : Type u_1
inst✝ : GeneralizedBooleanAlgebra α
x y : Booleanisation α
a b : α
a✝ : a ≤ b
⊢ a ≤ b | (:forall _ ((:c LE.le) ((:c Booleanisation) (:fv _uniq.3393)) ((:c Booleanisation.instLE) (:fv _uniq.3393) (:fv _uniq.3396)) ((:c Booleanisation.lift) (:fv _uniq.3393) (:fv _uniq.3404)) ((:c Booleanisation.lift) (:fv _uniq.3393) (:fv _uniq.3406))) ((:c LE.le) (:fv _uniq.3393) ((:c Preorder.toLE) (:fv _uniq.3393) ((:c P... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c GeneralizedBooleanAlgebra) (:fv _uniq.3393))"},{"name":"x","sexp":"((:c Booleanisation) (:fv _uniq.3393))"},{"name":"y","sexp":"((:c Booleanisation) (:fv _uniq.3393))"},{"name":"a","sexp":"(:fv _uniq.3393)"},{"name":"b","sexp":"(:fv _uniq.3393)"}] | (:forall _ :explicit (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Booleanisation) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Booleanisation) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:c Booleanisation.lift) (:arg :implicit-type 0 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3393","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.3396","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c GeneralizedBooleanAlgebra)... | {"children":[{"source":"rintro","sourceEnd":5103,"sourceStart":5097,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":5107,"sourceStart":5104,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"_","sourceEnd":5108,"sourceStart":5107,"tag":"atom"}],"kind... | [] | [{"source":"⟨_⟩","source_end":5111,"source_start":5104,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3393","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.3396","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"internal_... | 19 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cbf9c25fdcc1ed76f1bf37703d74590a42ca9c1756a489d9daf0f04e92e92e25 | 56d7513079e5160de652ec5595b2f4d349bb9de7c3ff78c000db329b0f142027 | 99f51d1a38258230b735c65ac6bfc427eec7a581468f272d72aa938d48d77b16 | 5d894f00914d8c99e47df1b8f3cbde69b28e1148fea819eb40f8a3656800ccae |
cat-searcher/leandojo-benchmark-4-random | test | 109 | Booleanisation.lift_le_lift | Mathlib/Order/Booleanisation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | assumption | case lift
α : Type u_1
inst✝ : GeneralizedBooleanAlgebra α
x y : Booleanisation α
a b : α
a✝ : a ≤ b
⊢ a ≤ b | ((:c LE.le) (:fv _uniq.3393) ((:c Preorder.toLE) (:fv _uniq.3393) ((:c PartialOrder.toPreorder) (:fv _uniq.3393) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.3393) ((:c Lattice.toSemilatticeInf) (:fv _uniq.3393) ((:c GeneralizedCoheytingAlgebra.toLattice) (:fv _uniq.3393) ((:c GeneralizedBooleanAlgebra.toGeneralizedC... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c GeneralizedBooleanAlgebra) (:fv _uniq.3393))"},{"name":"x","sexp":"((:c Booleanisation) (:fv _uniq.3393))"},{"name":"y","sexp":"((:c Booleanisation) (:fv _uniq.3393))"},{"name":"a","sexp":"(:fv _uniq.3393)"},{"name":"b","sexp":"(:fv _uniq.3393)"},{"n... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV4)) (:arg :explicit 3 (:fv FV5))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3393","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.3396","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c GeneralizedBooleanAlgebra)... | {"children":[{"source":"assumption","sourceEnd":5123,"sourceStart":5113,"tag":"atom"}],"kind":"Lean.Parser.Tactic.assumption","source":"assumption","sourceEnd":5123,"sourceStart":5113,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3393","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.3396","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"internal_... | 19 | 6 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e27804cb66e975a08eeed015844e740721e293bc3c36f74d40bdcbbcf7cee89c | 5d894f00914d8c99e47df1b8f3cbde69b28e1148fea819eb40f8a3656800ccae | c081dd376ba93a530dd044cffc81e70953e86d86f7d0796dc26bc1597302573d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 110 | PowerBasis.equivAdjoinSimple_symm_aeval | Mathlib/FieldTheory/Adjoin.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>PowerBasis.equivAdjoinSimple</a>, <a>PowerBasis.equivOfMinpoly_symm</a>, <a>PowerBasis.equivOfMinpoly_aeval</a>, <a>IntermediateField.adjoin.powerBasis_gen</a>] | K : Type u_1
L : Type u_2
inst✝² : Field K
inst✝¹ : Field L
inst✝ : Algebra K L
pb : PowerBasis K L
f : K[X]
⊢ pb.equivAdjoinSimple.symm ((aeval pb.gen) f) = (aeval (AdjoinSimple.gen K pb.gen)) f | ((:c Eq) ((:c Subtype) (:fv _uniq.632664) (:lambda x (:fv _uniq.632664) ((:c Membership.mem) (:fv _uniq.632664) ((:c IntermediateField) (:fv _uniq.632661) (:fv _uniq.632664) (:fv _uniq.632667) (:fv _uniq.632670) (:fv _uniq.632912)) ((:c SetLike.instMembership) ((:c IntermediateField) (:fv _uniq.632661) (:fv _uniq.63266... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.632661))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.632664))"},{"name":"inst✝","sexp":"((:c Algebra) (:fv _uniq.632661) (:fv _uniq.632664) ((:c Semifield.toCommSemiring) (:fv _uniq.632... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c IntermediateField) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.632661","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.632664","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":72773,"sourceStart":72771,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":72775,"sourceStart":72774,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"equivAdjoinSimple","source_end":72792,"source_start":72775,"syntax_kind":"ident"},{"source":"equivOfMinpoly_symm","source_end":72813,"source_start":72794,"syntax_kind":"ident"},{"source":"equivOfMinpoly_aeval","source_end":72835,"source_start":72815,"syntax_kind":"ident"},{"source":"adjoin.powerBasis_gen","... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.632661","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.632664","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal... | 398 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9e0be249904ed9f28f53db8bd4563db5340c0d2be54ad40ad770c82f9a182885 | 19166004da3895e361d09d2e4693a24885f42ab1d06495d38dd79afae4c438e7 | 422448ad1385c876180605d86a6e67bf11f2f89189e9104b35743fcab619df48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 111 | Fin.zero_add | Mathlib/Data/Fin/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Fin.ext_iff</a>, <a>Fin.add_def</a>, <a>Nat.mod_eq_of_lt</a> (<a>Fin.is_lt</a> k)] | n m : ℕ
inst✝ : NeZero n
k : Fin n
⊢ 0 + k = k | ((:c Eq) ((:c Fin) (:fv _uniq.12288)) ((:c HAdd.hAdd) ((:c Fin) (:fv _uniq.12288)) ((:c Fin) (:fv _uniq.12288)) ((:c Fin) (:fv _uniq.12288)) ((:c instHAdd) ((:c Fin) (:fv _uniq.12288)) ((:c Fin.instAdd) (:fv _uniq.12288))) ((:c OfNat.ofNat) ((:c Fin) (:fv _uniq.12288)) (:lit 0) ((:c Zero.toOfNat0) ((:c Fin) (:fv _uniq.... | [{"name":"n","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c NeZero) (:c Nat) ((:c Zero.ofOfNat0) (:c Nat) ((:c instOfNatNat) (:lit 0))) (:fv _uniq.12288))"},{"name":"k","sexp":"((:c Fin) (:fv _uniq.12288))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Fin) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:app (:c Fin) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Fin) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 2 (:app (:c Fin) (:arg :explicit 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12288","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12290","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":instance-implicit","co... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":16059,"sourceStart":16055,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"ext_iff","source_end":16068,"source_start":16061,"syntax_kind":"ident"},{"source":"add_def","source_end":16077,"source_start":16070,"syntax_kind":"ident"},{"source":"mod_eq_of_lt (is_lt k)","source_end":16101,"source_start":16079,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12288","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12290","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":instance-implicit","context_index":3,"internal_n... | 164 | 2 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d33ef556e8711f9c2b529851915e473680f1b47e19bd1b6ccbe26b600bcd3306 | a1ad3a9c1f2dbe8a827c57323002063eec569ccb811e79f88313a0d3e4bc47a0 | 3590dc4254f698058f94dab1231f17c23305dc947e782b8f72fea1c2b4343697 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 112 | List.get_attach | Mathlib/Data/List/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | ι : Type u_1
α : Type u
β : Type v
γ : Type w
l₁ l₂ L : List α
i : Fin L.attach.length
⊢ ↑(L.attach.get i) = L.get ⟨↑i, ⋯⟩ | ((:c Eq) (:fv _uniq.249406) ((:c Subtype.val) (:fv _uniq.249406) (:lambda x (:fv _uniq.249406) ((:c Membership.mem) (:fv _uniq.249406) ((:c List) (:fv _uniq.249406)) ((:c List.instMembership) (:fv _uniq.249406)) 0 (:fv _uniq.249595))) ((:c List.get) ((:c Subtype) (:fv _uniq.249406) (:lambda x (:fv _uniq.249406) ((:c Me... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.249406))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.249406))"},{"name":"L","sexp":"((:c List) (:fv _uniq.249406))"},{"na... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Subtype.val) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c List.get) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membe... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249404","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249406","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":135577,"sourceStart":135573,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","so... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249404","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249406","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 1,255 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 12a6f814826c216d412ec8607d2d15411f348455689229194758bcbe2b7156a1 | 252617b4ff7309a265032e88529430e4c9ed48615e9c3f24cff7faef96f0d367 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 113 | Polynomial.associated_of_dvd_of_natDegree_le | Mathlib/Algebra/Polynomial/RingDivision.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [← <a>Polynomial.leadingCoeff_ne_zero</a>, ← <a>isUnit_iff_ne_zero</a>] at hq | R : Type u
S : Type v
T : Type w
a b : R
n : ℕ
inst✝² : CommRing R
inst✝¹ : IsDomain R
p✝ q✝ : R[X]
K : Type u_1
inst✝ : Field K
p q : K[X]
hpq : p ∣ q
hq : q ≠ 0
h₁ : q.natDegree ≤ p.natDegree
⊢ IsUnit q.leadingCoeff | ((:c IsUnit) (:fv _uniq.218803) ((:c MonoidWithZero.toMonoid) (:fv _uniq.218803) ((:c Semiring.toMonoidWithZero) (:fv _uniq.218803) ((:c DivisionSemiring.toSemiring) (:fv _uniq.218803) ((:c Semifield.toDivisionSemiring) (:fv _uniq.218803) ((:c Field.toSemifield) (:fv _uniq.218803) (:fv _uniq.218804)))))) ((:c Polynomia... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"a","sexp":"(:fv _uniq.218063)"},{"name":"b","sexp":"(:fv _uniq.218063)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝²","sexp":"((:c CommRing) (:fv _uniq.218063))"},{"name":"inst✝¹","sexp":"((:c ... | (:app (:c IsUnit) (:arg :implicit-type 0 (:fv FV11)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV11))))) (:arg :explicit 2 (:app (:c Polynomial.leadingCoeff) (:arg :implicit-type 0 (:fv FV11)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV11))))) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.218063","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.218065","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":29808,"sourceStart":29805,"tag":"atom"},{"children":[{"source":"[","sourceEnd":29810,"sourceStart":29809,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":29813,"sourceStart":29810,"tag... | [] | [{"source":"leadingCoeff_ne_zero","source_end":29834,"source_start":29814,"syntax_kind":"ident"},{"source":"hq","source_end":29865,"source_start":29863,"syntax_kind":"ident"},{"source":"isUnit_iff_ne_zero","source_end":29858,"source_start":29840,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.218063","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.218065","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 152 | 2 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 55acbaa1573d73e67b02610cc177e5635e3436567f2bb2ec7204d210d9e99e34 | 32de757d4249b8c0cdcee3c785bee8e7fd3490a66251906f9b674d76d99a58d4 | 18e5b79c8da1186ec850bc6fabff83136ea37e155a451cf05eafcda58cb9b776 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 118 | CategoryTheory.Idempotents.split_iff_of_iso | Mathlib/CategoryTheory/Idempotents/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | C : Type u_1
inst✝ : Category.{u_2, u_1} C
X X' : C
φ : X ≅ X'
p : X ⟶ X
p' : X' ⟶ X'
hpp' : p ≫ φ.hom = φ.hom ≫ p'
⊢ (∃ Y i e, i ≫ e = 𝟙 Y ∧ e ≫ i = p) ↔ ∃ Y' i' e', i' ≫ e' = 𝟙 Y' ∧ e' ≫ i' = p' | case mp
C : Type u_1
inst✝ : Category.{u_2, u_1} C
X X' : C
φ : X ≅ X'
p : X ⟶ X
p' : X' ⟶ X'
hpp' : p ≫ φ.hom = φ.hom ≫ p'
⊢ (∃ Y i e, i ≫ e = 𝟙 Y ∧ e ≫ i = p) → ∃ Y' i' e', i' ≫ e' = 𝟙 Y' ∧ e' ≫ i' = p'
case mpr
C : Type u_1
inst✝ : Category.{u_2, u_1} C
X X' : C
φ : X ≅ X'
p : X ⟶ X
p' : X' ⟶ X'
hpp' : p ≫ φ.hom =... | ((:c Iff) ((:c Exists) (:fv _uniq.18504) (:lambda Y (:fv _uniq.18504) ((:c Exists) ((:c Quiver.Hom) (:fv _uniq.18504) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.18504) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.18504) (:fv _uniq.18508))) 0 (:fv _uniq.19295)) (:lambda i ((:c Quiver.Hom) (:fv ... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.18504))"},{"name":"X","sexp":"(:fv _uniq.18504)"},{"name":"X'","sexp":"(:fv _uniq.18504)"},{"name":"φ","sexp":"((:c CategoryTheory.Iso) (:fv _uniq.18504) (:fv _uniq.18508) (:fv _uniq.19295) (:fv _uniq.19296))"},{"n... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda Y :explicit (:fv FV0) (:app (:c Exists) (: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 :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18504","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18508","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Category)... | {"children":[{"source":"constructor","sourceEnd":6335,"sourceStart":6324,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":6335,"sourceStart":6324,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18504","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18508","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna... | 25 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | df940121560551089faabe6312185bc1b0b03246516940a022b13772de279d9d | 84ea3190d7c5f7c89647223cd5b3299d580bf793b27ad04c29a765a04e9befd2 | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | b27044950a3bd5b962560ac9e09b87ac33d06cc41d8e242d29f229c7e4210967 |
cat-searcher/leandojo-benchmark-4-random | test | 119 | CategoryTheory.Idempotents.split_iff_of_iso | Mathlib/CategoryTheory/Idempotents/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>CategoryTheory.Idempotents.split_imp_of_iso</a> φ p p' hpp' | case mp
C : Type u_1
inst✝ : Category.{u_2, u_1} C
X X' : C
φ : X ≅ X'
p : X ⟶ X
p' : X' ⟶ X'
hpp' : p ≫ φ.hom = φ.hom ≫ p'
⊢ (∃ Y i e, i ≫ e = 𝟙 Y ∧ e ≫ i = p) → ∃ Y' i' e', i' ≫ e' = 𝟙 Y' ∧ e' ≫ i' = p' | (:forall _ ((:c Exists) (:fv _uniq.18504) (:lambda Y (:fv _uniq.18504) ((:c Exists) ((:c Quiver.Hom) (:fv _uniq.18504) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.18504) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.18504) (:fv _uniq.18508))) 0 (:fv _uniq.19295)) (:lambda i ((:c Quiver.Hom) (:fv... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.18504))"},{"name":"X","sexp":"(:fv _uniq.18504)"},{"name":"X'","sexp":"(:fv _uniq.18504)"},{"name":"φ","sexp":"((:c CategoryTheory.Iso) (:fv _uniq.18504) (:fv _uniq.18508) (:fv _uniq.19295) (:fv _uniq.19296))"},{"n... | (:forall _ :explicit (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda Y :explicit (:fv FV0) (:app (:c Exists) (: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 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18504","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18508","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Category)... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":6346,"sourceStart":6341,"tag":"atom"},{"children":[{"name":"CategoryTheory.Idempotents.split_imp_of_iso","semanticRole":"global","source":"split_imp_of_iso","sourceEnd":6363,"sourceStart":6347,"tag":"identifier"},{"children":[{"contextInd... | [] | [{"source":"split_imp_of_iso φ p p' hpp'","source_end":6376,"source_start":6347,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18504","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18508","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna... | 25 | 7 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b15dbc70b499bcca6a3b6a8b350ed592112e72fe9bd69e935c2cc02abed44753 | 38cd1ffb94aaf6e250a68719814888357b7be7f2482cdcf35212660e1e9c9341 | e961c8c222dd2540e9ede6d3349e9e7252256677143c7fe4839c238e5385a8a2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 120 | CategoryTheory.Idempotents.split_iff_of_iso | Mathlib/CategoryTheory/Idempotents/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>CategoryTheory.Idempotents.split_imp_of_iso</a> φ.symm p' p | case mpr
C : Type u_1
inst✝ : Category.{u_2, u_1} C
X X' : C
φ : X ≅ X'
p : X ⟶ X
p' : X' ⟶ X'
hpp' : p ≫ φ.hom = φ.hom ≫ p'
⊢ (∃ Y' i' e', i' ≫ e' = 𝟙 Y' ∧ e' ≫ i' = p') → ∃ Y i e, i ≫ e = 𝟙 Y ∧ e ≫ i = p | case mpr
C : Type u_1
inst✝ : Category.{u_2, u_1} C
X X' : C
φ : X ≅ X'
p : X ⟶ X
p' : X' ⟶ X'
hpp' : p ≫ φ.hom = φ.hom ≫ p'
⊢ p' ≫ φ.symm.hom = φ.symm.hom ≫ p | (:forall _ ((:c Exists) (:fv _uniq.18504) (:lambda Y' (:fv _uniq.18504) ((:c Exists) ((:c Quiver.Hom) (:fv _uniq.18504) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.18504) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.18504) (:fv _uniq.18508))) 0 (:fv _uniq.19296)) (:lambda i' ((:c Quiver.Hom) (:... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.18504))"},{"name":"X","sexp":"(:fv _uniq.18504)"},{"name":"X'","sexp":"(:fv _uniq.18504)"},{"name":"φ","sexp":"((:c CategoryTheory.Iso) (:fv _uniq.18504) (:fv _uniq.18508) (:fv _uniq.19295) (:fv _uniq.19296))"},{"n... | (:forall _ :explicit (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda Y' :explicit (:fv FV0) (:app (:c Exists) (: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 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18504","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18508","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Category)... | {"children":[{"source":"apply","sourceEnd":6387,"sourceStart":6382,"tag":"atom"},{"children":[{"name":"CategoryTheory.Idempotents.split_imp_of_iso","semanticRole":"global","source":"split_imp_of_iso","sourceEnd":6404,"sourceStart":6388,"tag":"identifier"},{"children":[{"name":"CategoryTheory.Iso.symm","semanticRole":"g... | [] | [{"source":"split_imp_of_iso φ.symm p' p","source_end":6417,"source_start":6388,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18504","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18508","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna... | 25 | 14 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 44bd5502591d8c40b32e44fab75671e9101de04adffaacf3a72d7b6f583de2f8 | 57d7b5d7944344a7fc9c2cabaf9c6491d736e03e8385cad69c02e14cc959a7c7 | 2d6d4dd28cd49d3fce13e4f9e12d13036e7dbbf772d8637190b915ba65c81615 | f9b65c3cfede994d4ef1907c879ca6c8b529dfc844173bccab822fd0237d2c63 |
cat-searcher/leandojo-benchmark-4-random | test | 121 | CategoryTheory.Idempotents.split_iff_of_iso | Mathlib/CategoryTheory/Idempotents/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>CategoryTheory.Category.comp_id</a> p, ← φ.hom_inv_id] | case mpr
C : Type u_1
inst✝ : Category.{u_2, u_1} C
X X' : C
φ : X ≅ X'
p : X ⟶ X
p' : X' ⟶ X'
hpp' : p ≫ φ.hom = φ.hom ≫ p'
⊢ p' ≫ φ.symm.hom = φ.symm.hom ≫ p | case mpr
C : Type u_1
inst✝ : Category.{u_2, u_1} C
X X' : C
φ : X ≅ X'
p : X ⟶ X
p' : X' ⟶ X'
hpp' : p ≫ φ.hom = φ.hom ≫ p'
⊢ p' ≫ φ.symm.hom = φ.symm.hom ≫ p ≫ φ.hom ≫ φ.inv | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.18504) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.18504) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.18504) (:fv _uniq.18508))) (:fv _uniq.19296) (:fv _uniq.19295)) ((:c CategoryTheory.CategoryStruct.comp) (:fv _uniq.18504) ((:c CategoryTheory.Category.toC... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.18504))"},{"name":"X","sexp":"(:fv _uniq.18504)"},{"name":"X'","sexp":"(:fv _uniq.18504)"},{"name":"φ","sexp":"((:c CategoryTheory.Iso) (:fv _uniq.18504) (:fv _uniq.18508) (:fv _uniq.19295) (:fv _uniq.19296))"},{"n... | (: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 (:fv FV4)) (:arg :explicit 3 (:fv FV3)))) (:arg :explicit 1 (:app (:c CategoryTheory.CategoryStruct.comp) (:arg :implicit-type ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18504","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18508","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Category)... | {"children":[{"source":"rw","sourceEnd":6424,"sourceStart":6422,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6426,"sourceStart":6425,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":6429,"sourceStart":... | [] | [{"source":"comp_id p","source_end":6439,"source_start":6430,"syntax_kind":"Lean.Parser.Term.app"},{"source":"φ.hom_inv_id","source_end":6458,"source_start":6445,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18504","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18508","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna... | 25 | 15 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a9eb75efc4510bb21246f301d5892c40575427812be83ef103ee571f83563735 | f9b65c3cfede994d4ef1907c879ca6c8b529dfc844173bccab822fd0237d2c63 | 30a69ab66d54128bcde2e223ba3e1a35c34f5e9a1e29bf3a65d58d0e3c7f6d26 | de2b68d29193e846e96a8def64d5bdb33700faff482618e6dc476b4a8bbbc0e0 |
cat-searcher/leandojo-benchmark-4-random | test | 122 | CategoryTheory.Idempotents.split_iff_of_iso | Mathlib/CategoryTheory/Idempotents/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | slice_rhs 2 3 => rw [hpp'] | case mpr
C : Type u_1
inst✝ : Category.{u_2, u_1} C
X X' : C
φ : X ≅ X'
p : X ⟶ X
p' : X' ⟶ X'
hpp' : p ≫ φ.hom = φ.hom ≫ p'
⊢ p' ≫ φ.symm.hom = φ.symm.hom ≫ p ≫ φ.hom ≫ φ.inv | case mpr
C : Type u_1
inst✝ : Category.{u_2, u_1} C
X X' : C
φ : X ≅ X'
p : X ⟶ X
p' : X' ⟶ X'
hpp' : p ≫ φ.hom = φ.hom ≫ p'
⊢ p' ≫ φ.symm.hom = φ.symm.hom ≫ (φ.hom ≫ p') ≫ φ.inv | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.18504) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.18504) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.18504) (:fv _uniq.18508))) (:fv _uniq.19296) (:fv _uniq.19295)) ((:c CategoryTheory.CategoryStruct.comp) (:fv _uniq.18504) ((:c CategoryTheory.Category.toC... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.18504))"},{"name":"X","sexp":"(:fv _uniq.18504)"},{"name":"X'","sexp":"(:fv _uniq.18504)"},{"name":"φ","sexp":"((:c CategoryTheory.Iso) (:fv _uniq.18504) (:fv _uniq.18508) (:fv _uniq.19295) (:fv _uniq.19296))"},{"n... | (: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 (:fv FV4)) (:arg :explicit 3 (:fv FV3)))) (:arg :explicit 1 (:app (:c CategoryTheory.CategoryStruct.comp) (:arg :implicit-type ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18504","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18508","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Category)... | {"children":[{"source":"slice_rhs","sourceEnd":6473,"sourceStart":6464,"tag":"atom"},{"children":[{"source":"2","sourceEnd":6475,"sourceStart":6474,"tag":"atom"}],"kind":"num","source":"2","sourceEnd":6475,"sourceStart":6474,"tag":"node"},{"children":[{"source":"3","sourceEnd":6477,"sourceStart":6476,"tag":"atom"}],"ki... | [] | [{"source":"hpp'","source_end":6489,"source_start":6485,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18504","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18508","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna... | 25 | 19 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1f01844975118fb63c020ef8f16bb8f2162e333ab552ea82f67e7595db0953ab | de2b68d29193e846e96a8def64d5bdb33700faff482618e6dc476b4a8bbbc0e0 | 13b1c877a0c23571c263625a083a4c9ba20c9386da5af4581c0074ebb130a478 | b8d60abaca2f6d935c170bddf1eca2deedc928ad05eb70f1fb5d23203e0dd29f |
cat-searcher/leandojo-benchmark-4-random | test | 123 | CategoryTheory.Idempotents.split_iff_of_iso | Mathlib/CategoryTheory/Idempotents/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | slice_rhs 1 2 => erw [φ.inv_hom_id] | case mpr
C : Type u_1
inst✝ : Category.{u_2, u_1} C
X X' : C
φ : X ≅ X'
p : X ⟶ X
p' : X' ⟶ X'
hpp' : p ≫ φ.hom = φ.hom ≫ p'
⊢ p' ≫ φ.symm.hom = φ.symm.hom ≫ (φ.hom ≫ p') ≫ φ.inv | case mpr
C : Type u_1
inst✝ : Category.{u_2, u_1} C
X X' : C
φ : X ≅ X'
p : X ⟶ X
p' : X' ⟶ X'
hpp' : p ≫ φ.hom = φ.hom ≫ p'
⊢ p' ≫ φ.symm.hom = (𝟙 X' ≫ p') ≫ φ.inv | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.18504) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.18504) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.18504) (:fv _uniq.18508))) (:fv _uniq.19296) (:fv _uniq.19295)) ((:c CategoryTheory.CategoryStruct.comp) (:fv _uniq.18504) ((:c CategoryTheory.Category.toC... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.18504))"},{"name":"X","sexp":"(:fv _uniq.18504)"},{"name":"X'","sexp":"(:fv _uniq.18504)"},{"name":"φ","sexp":"((:c CategoryTheory.Iso) (:fv _uniq.18504) (:fv _uniq.18508) (:fv _uniq.19295) (:fv _uniq.19296))"},{"n... | (: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 (:fv FV4)) (:arg :explicit 3 (:fv FV3)))) (:arg :explicit 1 (:app (:c CategoryTheory.CategoryStruct.comp) (:arg :implicit-type ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18504","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18508","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Category)... | {"children":[{"source":"slice_rhs","sourceEnd":6504,"sourceStart":6495,"tag":"atom"},{"children":[{"source":"1","sourceEnd":6506,"sourceStart":6505,"tag":"atom"}],"kind":"num","source":"1","sourceEnd":6506,"sourceStart":6505,"tag":"node"},{"children":[{"source":"2","sourceEnd":6508,"sourceStart":6507,"tag":"atom"}],"ki... | [] | [{"source":"φ.inv_hom_id","source_end":6530,"source_start":6517,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18504","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18508","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna... | 25 | 24 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f53d9a0ddf633ff72edeaa4711946596ddbbd30039df4bc824884f85b81cbd44 | b8d60abaca2f6d935c170bddf1eca2deedc928ad05eb70f1fb5d23203e0dd29f | bb0f6eec8cc2d2500d284cf5f81b8e7339f8994f0fb684bb1d69ea30f611e0d9 | e1eb1e94a8b8a8e90190a8588529877e9eaa48a77c88af0d0dd8bd8bca03ff90 |
cat-searcher/leandojo-benchmark-4-random | test | 124 | CategoryTheory.Idempotents.split_iff_of_iso | Mathlib/CategoryTheory/Idempotents/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>CategoryTheory.Category.id_comp</a>] | case mpr
C : Type u_1
inst✝ : Category.{u_2, u_1} C
X X' : C
φ : X ≅ X'
p : X ⟶ X
p' : X' ⟶ X'
hpp' : p ≫ φ.hom = φ.hom ≫ p'
⊢ p' ≫ φ.symm.hom = (𝟙 X' ≫ p') ≫ φ.inv | case mpr
C : Type u_1
inst✝ : Category.{u_2, u_1} C
X X' : C
φ : X ≅ X'
p : X ⟶ X
p' : X' ⟶ X'
hpp' : p ≫ φ.hom = φ.hom ≫ p'
⊢ p' ≫ φ.symm.hom = p' ≫ φ.inv | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.18504) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.18504) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.18504) (:fv _uniq.18508))) (:fv _uniq.19296) (:fv _uniq.19295)) ((:c CategoryTheory.CategoryStruct.comp) (:fv _uniq.18504) ((:c CategoryTheory.Category.toC... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.18504))"},{"name":"X","sexp":"(:fv _uniq.18504)"},{"name":"X'","sexp":"(:fv _uniq.18504)"},{"name":"φ","sexp":"((:c CategoryTheory.Iso) (:fv _uniq.18504) (:fv _uniq.18508) (:fv _uniq.19295) (:fv _uniq.19296))"},{"n... | (: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 (:fv FV4)) (:arg :explicit 3 (:fv FV3)))) (:arg :explicit 1 (:app (:c CategoryTheory.CategoryStruct.comp) (:arg :implicit-type ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18504","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18508","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Category)... | {"children":[{"source":"simp","sourceEnd":6540,"sourceStart":6536,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":6545,"sourceStart":6541,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":6545,"s... | [] | [{"source":"id_comp","source_end":6554,"source_start":6547,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18504","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18508","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna... | 25 | 29 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b0308a506161cc3ce779f8b7f85fd4361004209b30361b8701fcd9257ab31473 | e1eb1e94a8b8a8e90190a8588529877e9eaa48a77c88af0d0dd8bd8bca03ff90 | 58770c25603be0540af651c9343cfd273986b2f481d2077c51e7083d674fb090 | f95a803e6d5e9bc36f2142c1fbcd292029d68c1fee445bd708fd18cdccbd1e98 |
cat-searcher/leandojo-benchmark-4-random | test | 125 | CategoryTheory.Idempotents.split_iff_of_iso | Mathlib/CategoryTheory/Idempotents/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case mpr
C : Type u_1
inst✝ : Category.{u_2, u_1} C
X X' : C
φ : X ≅ X'
p : X ⟶ X
p' : X' ⟶ X'
hpp' : p ≫ φ.hom = φ.hom ≫ p'
⊢ p' ≫ φ.symm.hom = p' ≫ φ.inv | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.18504) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.18504) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.18504) (:fv _uniq.18508))) (:fv _uniq.19296) (:fv _uniq.19295)) ((:c CategoryTheory.CategoryStruct.comp) (:fv _uniq.18504) ((:c CategoryTheory.Category.toC... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.18504))"},{"name":"X","sexp":"(:fv _uniq.18504)"},{"name":"X'","sexp":"(:fv _uniq.18504)"},{"name":"φ","sexp":"((:c CategoryTheory.Iso) (:fv _uniq.18504) (:fv _uniq.18508) (:fv _uniq.19295) (:fv _uniq.19296))"},{"n... | (: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 (:fv FV4)) (:arg :explicit 3 (:fv FV3)))) (:arg :explicit 1 (:app (:c CategoryTheory.CategoryStruct.comp) (:arg :implicit-type ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18504","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18508","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Category)... | {"children":[{"source":"rfl","sourceEnd":6563,"sourceStart":6560,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":6563,"sourceStart":6560,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18504","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18508","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna... | 25 | 30 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9a975ab29e39f0207cce52ec15fa387f9cf9af38cde979a51935b40064ad6c5a | f95a803e6d5e9bc36f2142c1fbcd292029d68c1fee445bd708fd18cdccbd1e98 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 126 | Cardinal.mk_bounded_subset_le | Mathlib/SetTheory/Cardinal/Ordinal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>le_trans</a> ?_ (<a>Cardinal.mk_bounded_set_le</a> s c) | α : Type u
s : Set α
c : Cardinal.{u}
⊢ #{ t // t ⊆ s ∧ #↑t ≤ c } ≤ max #↑s ℵ₀ ^ c | α : Type u
s : Set α
c : Cardinal.{u}
⊢ #{ t // t ⊆ s ∧ #↑t ≤ c } ≤ #{ t // #↑t ≤ c } | ((:c LE.le) (:c Cardinal) (:c Cardinal.instLE) ((:c Cardinal.mk) ((:c Subtype) ((:c Set) (:fv _uniq.129627)) (:lambda t ((:c Set) (:fv _uniq.129627)) ((:c And) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.129627)) ((:c Set.instHasSubset) (:fv _uniq.129627)) 0 (:fv _uniq.129628)) ((:c LE.le) (:c Cardinal) (:c Cardinal.in... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.129627))"},{"name":"c","sexp":"(:c Cardinal)"}] | (:app (:c LE.le) (:arg :implicit-type 0 (:c Cardinal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Cardinal))))) (:arg :explicit 2 (:app (:c Cardinal.mk) (:arg :explicit 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:lambda t :explic... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129627","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.129628","is_instance":false,"is_let":false,"name":"s","sexp":"(:app (:c Set) (:arg :explicit 0 (:fv FV1)))... | {"children":[{"source":"refine","sourceEnd":55787,"sourceStart":55781,"tag":"atom"},{"children":[{"name":"le_trans","semanticRole":"global","source":"le_trans","sourceEnd":55796,"sourceStart":55788,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":55798,"sourceStart":55797,"tag":"atom"},{"children... | [] | [{"source":"le_trans ?_ (mk_bounded_set_le s c)","source_end":55823,"source_start":55788,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129627","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.129628","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 355 | 4 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8d7dc2543d4de61d1f1697c2a51335fc5704c0f07c1bba691f319a1abcc7d3ac | a6e3faf5152caea45d78de3e8d9682cc2d8c45e8228278f77982b8926223b16b | 5d81542408257ec9638537fd0533ea0211936008bc69ff09ba929fcc364262a9 | 99ee964fd4ce5f7d5fa4c5456d8ddf9373d3f2b6aaa80955bff1b9ff0d1c3c0a |
cat-searcher/leandojo-benchmark-4-random | test | 127 | Cardinal.mk_bounded_subset_le | Mathlib/SetTheory/Cardinal/Ordinal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨<a>Function.Embedding.codRestrict</a> _ ?_ ?_⟩ | α : Type u
s : Set α
c : Cardinal.{u}
⊢ #{ t // t ⊆ s ∧ #↑t ≤ c } ≤ #{ t // #↑t ≤ c } | case refine_1
α : Type u
s : Set α
c : Cardinal.{u}
⊢ { t // t ⊆ s ∧ #↑t ≤ c } ↪ Set ↑s
case refine_2
α : Type u
s : Set α
c : Cardinal.{u}
⊢ ∀ (a : { t // t ⊆ s ∧ #↑t ≤ c }), ?refine_1 a ∈ fun t => Quot.lift ((fun α β => Nonempty (α ↪ β)) ↑t) ⋯ c | ((:c LE.le) (:c Cardinal) ((:c Preorder.toLE) (:c Cardinal) ((:c PartialOrder.toPreorder) (:c Cardinal) (:c Cardinal.partialOrder))) ((:c Cardinal.mk) ((:c Subtype) ((:c Set) (:fv _uniq.129627)) (:lambda t ((:c Set) (:fv _uniq.129627)) ((:c And) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.129627)) ((:c Set.instHasSubse... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.129627))"},{"name":"c","sexp":"(:c Cardinal)"}] | (:app (:c LE.le) (:arg :implicit-type 0 (:c Cardinal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Cardinal))))) (:arg :explicit 2 (:app (:c Cardinal.mk) (:arg :explicit 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:lambda t :explic... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129627","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.129628","is_instance":false,"is_let":false,"name":"s","sexp":"(:app (:c Set) (:arg :explicit 0 (:fv FV1)))... | {"children":[{"source":"refine","sourceEnd":55832,"sourceStart":55826,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":55836,"sourceStart":55833,"tag":"atom"},{"children":[{"children":[{"name":"Function.Embedding.codRestrict","semanticRole":"global","source":"Embedding.codRestrict","sourceEnd":55857,"sourceStart":5... | [] | [{"source":"⟨Embedding.codRestrict _ ?_ ?_⟩","source_end":55868,"source_start":55833,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129627","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.129628","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 355 | 5 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dbadcf0d9f45ed693af7d3730877db6fbccbf456ab67a44663ce59e0fec67403 | 99ee964fd4ce5f7d5fa4c5456d8ddf9373d3f2b6aaa80955bff1b9ff0d1c3c0a | 59324525c9736f1cef083ed8d2e7487e1367c77d86989d4612aeeb784255d803 | 5e420a520df8f6e395acb2f4bcfccea89363f8ac4af5703c2cb36ff21e18232d |
cat-searcher/leandojo-benchmark-4-random | test | 128 | Cardinal.mk_bounded_subset_le | Mathlib/SetTheory/Cardinal/Ordinal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨t, _, h2t⟩ | case refine_2
α : Type u
s : Set α
c : Cardinal.{u}
⊢ ∀ (a : { t // t ⊆ s ∧ #↑t ≤ c }),
{ toFun := fun t => Subtype.val ⁻¹' ↑t, inj' := ⋯ } a ∈ fun t => Quot.lift ((fun α β => Nonempty (α ↪ β)) ↑t) ⋯ c | case refine_2.mk.intro
α : Type u
s : Set α
c : Cardinal.{u}
t : Set α
left✝ : t ⊆ s
h2t : #↑t ≤ c
⊢ { toFun := fun t => Subtype.val ⁻¹' ↑t, inj' := ⋯ } ⟨t, ⋯⟩ ∈ fun t => Quot.lift ((fun α β => Nonempty (α ↪ β)) ↑t) ⋯ c | (:forall a ((:c Subtype) ((:c Set) (:fv _uniq.129627)) (:lambda t ((:c Set) (:fv _uniq.129627)) ((:c And) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.129627)) ((:c Set.instHasSubset) (:fv _uniq.129627)) 0 (:fv _uniq.129628)) ((:c LE.le) (:c Cardinal) (:c Cardinal.instLE) ((:c Cardinal.mk) ((:c Set.Elem) (:fv _uniq.1296... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.129627))"},{"name":"c","sexp":"(:c Cardinal)"}] | (:forall a :explicit (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV1))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1))... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129627","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.129628","is_instance":false,"is_let":false,"name":"s","sexp":"(:app (:c Set) (:arg :explicit 0 (:fv FV1)))... | {"children":[{"source":"rintro","sourceEnd":56096,"sourceStart":56090,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":56100,"sourceStart":56097,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"t","sourceEnd":56101,"sou... | [{"role":"fresh_name","source":"t","source_end":56101,"source_start":56100,"syntax_kind":"ident"},{"role":"fresh_name","source":"h2t","source_end":56109,"source_start":56106,"syntax_kind":"ident"}] | [{"source":"⟨t, _, h2t⟩","source_end":56112,"source_start":56097,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129627","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.129628","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 355 | 27 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 780d0c8715b1b4dd36c401088fd3bb387c9fa8c3e3b8dd375204b60645c9d369 | 8a99d155dbd59d9103cef18e6cbdd537575ee6e1a85fa9d36ff1b6db74d7c22a | 62fde25587a3fbe177ed10d4f30d86f8ed532cfbaf1021e8623b167a372ca0e1 | 2cca48384db3ac288341aab31894f5d8ae108c8d8dd483ea99eb83f5d8e58d00 |
cat-searcher/leandojo-benchmark-4-random | test | 129 | Cardinal.mk_bounded_subset_le | Mathlib/SetTheory/Cardinal/Ordinal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>Cardinal.mk_preimage_of_injective</a> _ _ <a>Subtype.val_injective</a>).<a>LE.le.trans</a> h2t | case refine_2.mk.intro
α : Type u
s : Set α
c : Cardinal.{u}
t : Set α
left✝ : t ⊆ s
h2t : #↑t ≤ c
⊢ { toFun := fun t => Subtype.val ⁻¹' ↑t, inj' := ⋯ } ⟨t, ⋯⟩ ∈ fun t => Quot.lift ((fun α β => Nonempty (α ↪ β)) ↑t) ⋯ c | ((:c Membership.mem) ((:c Set) ((:c Set.Elem) (:fv _uniq.129627) (:fv _uniq.129628))) ((:c Set) ((:c Set) ((:c Set.Elem) (:fv _uniq.129627) (:fv _uniq.129628)))) ((:c Set.instMembership) ((:c Set) ((:c Set.Elem) (:fv _uniq.129627) (:fv _uniq.129628)))) ((:c DFunLike.coe) ((:c Function.Embedding) ((:c Subtype) ((:c Set)... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.129627))"},{"name":"c","sexp":"(:c Cardinal)"},{"name":"t","sexp":"((:c Set) (:fv _uniq.129627))"},{"name":"left✝","sexp":"((:c HasSubset.Subset) ((:c Set) (:fv _uniq.129627)) ((:c Set.instHasSubset) (:fv _uniq.129627)) (:fv _uniq.130383) (... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV1)) (:arg :e... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129627","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.129628","is_instance":false,"is_let":false,"name":"s","sexp":"(:app (:c Set) (:arg :explicit 0 (:fv FV1)))... | {"children":[{"source":"exact","sourceEnd":56119,"sourceStart":56114,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":56121,"sourceStart":56120,"tag":"atom"},{"children":[{"name":"Cardinal.mk_preimage_of_injective","semanticRole":"global","source":"mk_preimage_of_injective","sourceEnd":561... | [] | [{"source":"(mk_preimage_of_injective _ _ Subtype.val_injective).trans h2t","source_end":56182,"source_start":56120,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129627","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.129628","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 355 | 29 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7191f0217c2e8b6297f241ee8acd083c07d1d6561662eafc3a9cc56a3de92417 | 2cca48384db3ac288341aab31894f5d8ae108c8d8dd483ea99eb83f5d8e58d00 | 9a727e0bf2543b66694c2e461aa80e4201ea30f2b326a71539f599434c263371 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 130 | Cardinal.mk_bounded_subset_le | Mathlib/SetTheory/Cardinal/Ordinal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | use fun t => (↑) ⁻¹' t.1 | case refine_1
α : Type u
s : Set α
c : Cardinal.{u}
⊢ { t // t ⊆ s ∧ #↑t ≤ c } ↪ Set ↑s | case inj'
α : Type u
s : Set α
c : Cardinal.{u}
⊢ Injective fun t => Subtype.val ⁻¹' ↑t | ((:c Function.Embedding) ((:c Subtype) ((:c Set) (:fv _uniq.129627)) (:lambda t ((:c Set) (:fv _uniq.129627)) ((:c And) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.129627)) ((:c Set.instHasSubset) (:fv _uniq.129627)) 0 (:fv _uniq.129628)) ((:c LE.le) (:c Cardinal) (:c Cardinal.instLE) ((:c Cardinal.mk) ((:c Set.Elem) (... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.129627))"},{"name":"c","sexp":"(:c Cardinal)"}] | (:app (:c Function.Embedding) (:arg :explicit 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV1))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129627","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.129628","is_instance":false,"is_let":false,"name":"s","sexp":"(:app (:c Set) (:arg :explicit 0 (:fv FV1)))... | {"children":[{"source":"use","sourceEnd":55877,"sourceStart":55874,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"children":[{"source":"fun","sourceEnd":55881,"sourceStart":55878,"tag":"atom"},{"children":[{"children":[{"semant... | [] | [{"source":"fun t => (↑) ⁻¹' t.1","source_end":55903,"source_start":55878,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129627","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.129628","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 355 | 10 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4c76af7d2d0e5ccd64c378bcf92076c4bf2dc73f5917f37779cd495afab45ff6 | 5c77cfb511376233d8b93d88858cec2656363027f44c906653540ba97193cae4 | 1a28e9da75f60d4b9a9eb9cc30943ff4f4cd79b8c4be2af7bc879cf9ba6bd089 | eaab93e1da67b4e1be1920f0793d2aced0c4611ff0772f2712fc56cece8d6888 |
cat-searcher/leandojo-benchmark-4-random | test | 131 | Cardinal.mk_bounded_subset_le | Mathlib/SetTheory/Cardinal/Ordinal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨t, ht1, ht2⟩ ⟨t', h1t', h2t'⟩ h | case inj'
α : Type u
s : Set α
c : Cardinal.{u}
⊢ Injective fun t => Subtype.val ⁻¹' ↑t | case inj'.mk.intro.mk.intro
α : Type u
s : Set α
c : Cardinal.{u}
t : Set α
ht1 : t ⊆ s
ht2 : #↑t ≤ c
t' : Set α
h1t' : t' ⊆ s
h2t' : #↑t' ≤ c
h : (fun t => Subtype.val ⁻¹' ↑t) ⟨t, ⋯⟩ = (fun t => Subtype.val ⁻¹' ↑t) ⟨t', ⋯⟩
⊢ ⟨t, ⋯⟩ = ⟨t', ⋯⟩ | ((:c Function.Injective) ((:c Subtype) ((:c Set) (:fv _uniq.129627)) (:lambda t ((:c Set) (:fv _uniq.129627)) ((:c And) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.129627)) ((:c Set.instHasSubset) (:fv _uniq.129627)) 0 (:fv _uniq.129628)) ((:c LE.le) (:c Cardinal) (:c Cardinal.instLE) ((:c Cardinal.mk) ((:c Set.Elem) (... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.129627))"},{"name":"c","sexp":"(:c Cardinal)"}] | (:app (:c Function.Injective) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV1))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c S... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129627","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.129628","is_instance":false,"is_let":false,"name":"s","sexp":"(:app (:c Set) (:arg :explicit 0 (:fv FV1)))... | {"children":[{"source":"rintro","sourceEnd":55914,"sourceStart":55908,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":55918,"sourceStart":55915,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"t","sourceEnd":55919,"sou... | [{"role":"fresh_name","source":"t","source_end":55919,"source_start":55918,"syntax_kind":"ident"},{"role":"fresh_name","source":"ht1","source_end":55924,"source_start":55921,"syntax_kind":"ident"},{"role":"fresh_name","source":"ht2","source_end":55929,"source_start":55926,"syntax_kind":"ident"},{"role":"fresh_name","so... | [{"source":"⟨t, ht1, ht2⟩","source_end":55932,"source_start":55915,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"},{"source":"⟨t', h1t', h2t'⟩","source_end":55953,"source_start":55933,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129627","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.129628","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 355 | 11 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a5e2a69c1446665741cc6f724cb3bfaf11527b75f5a00ee0e2e27fa2628461d8 | eaab93e1da67b4e1be1920f0793d2aced0c4611ff0772f2712fc56cece8d6888 | b3fed7280b5ac63f099901a2e5f3b40f38967221bcb9f9378029816c693d1897 | d5b81bd6351a7d8fedb74ac6106604bb5962fc82c9ee33e2458dd17266ca682a |
cat-searcher/leandojo-benchmark-4-random | test | 132 | Cardinal.mk_bounded_subset_le | Mathlib/SetTheory/Cardinal/Ordinal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Subtype.eq</a> | case inj'.mk.intro.mk.intro
α : Type u
s : Set α
c : Cardinal.{u}
t : Set α
ht1 : t ⊆ s
ht2 : #↑t ≤ c
t' : Set α
h1t' : t' ⊆ s
h2t' : #↑t' ≤ c
h : (fun t => Subtype.val ⁻¹' ↑t) ⟨t, ⋯⟩ = (fun t => Subtype.val ⁻¹' ↑t) ⟨t', ⋯⟩
⊢ ⟨t, ⋯⟩ = ⟨t', ⋯⟩ | case inj'.mk.intro.mk.intro.a
α : Type u
s : Set α
c : Cardinal.{u}
t : Set α
ht1 : t ⊆ s
ht2 : #↑t ≤ c
t' : Set α
h1t' : t' ⊆ s
h2t' : #↑t' ≤ c
h : (fun t => Subtype.val ⁻¹' ↑t) ⟨t, ⋯⟩ = (fun t => Subtype.val ⁻¹' ↑t) ⟨t', ⋯⟩
⊢ ↑⟨t, ⋯⟩ = ↑⟨t', ⋯⟩ | ((:c Eq) ((:c Subtype) ((:c Set) (:fv _uniq.129627)) (:lambda t ((:c Set) (:fv _uniq.129627)) ((:c And) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.129627)) ((:c Set.instHasSubset) (:fv _uniq.129627)) 0 (:fv _uniq.129628)) ((:c LE.le) (:c Cardinal) (:c Cardinal.instLE) ((:c Cardinal.mk) ((:c Set.Elem) (:fv _uniq.129627... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.129627))"},{"name":"c","sexp":"(:c Cardinal)"},{"name":"t","sexp":"((:c Set) (:fv _uniq.129627))"},{"name":"ht1","sexp":"((:c HasSubset.Subset) ((:c Set) (:fv _uniq.129627)) ((:c Set.instHasSubset) (:fv _uniq.129627)) (:fv _uniq.130051) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV1))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :expli... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129627","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.129628","is_instance":false,"is_let":false,"name":"s","sexp":"(:app (:c Set) (:arg :explicit 0 (:fv FV1)))... | {"children":[{"source":"apply","sourceEnd":55965,"sourceStart":55960,"tag":"atom"},{"name":"Subtype.eq","semanticRole":"global","source":"Subtype.eq","sourceEnd":55976,"sourceStart":55966,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Subtype.eq","sourceEnd":55976,"sourceStart":55960,"tag":"node... | [] | [{"source":"Subtype.eq","source_end":55976,"source_start":55966,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129627","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.129628","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 355 | 12 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6d84929bea9d69ff0d83d6fa60cfb7666e96ef0d772c2ec8aff4ced64314b06a | d5b81bd6351a7d8fedb74ac6106604bb5962fc82c9ee33e2458dd17266ca682a | 74af7981e183cc68e027f6421df00b1319594dc053b419aaffd9c6b29111fcc9 | bc774217137d286df4540124e39e1019bea528a543d76bbdbeb0a8df969b3bee |
cat-searcher/leandojo-benchmark-4-random | test | 133 | Cardinal.mk_bounded_subset_le | Mathlib/SetTheory/Cardinal/Ordinal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp only at h ⊢ | case inj'.mk.intro.mk.intro.a
α : Type u
s : Set α
c : Cardinal.{u}
t : Set α
ht1 : t ⊆ s
ht2 : #↑t ≤ c
t' : Set α
h1t' : t' ⊆ s
h2t' : #↑t' ≤ c
h : (fun t => Subtype.val ⁻¹' ↑t) ⟨t, ⋯⟩ = (fun t => Subtype.val ⁻¹' ↑t) ⟨t', ⋯⟩
⊢ ↑⟨t, ⋯⟩ = ↑⟨t', ⋯⟩ | case inj'.mk.intro.mk.intro.a
α : Type u
s : Set α
c : Cardinal.{u}
t : Set α
ht1 : t ⊆ s
ht2 : #↑t ≤ c
t' : Set α
h1t' : t' ⊆ s
h2t' : #↑t' ≤ c
h : Subtype.val ⁻¹' t = Subtype.val ⁻¹' t'
⊢ t = t' | ((:c Eq) ((:c Set) (:fv _uniq.129627)) ((:c Subtype.val) ((:c Set) (:fv _uniq.129627)) (:lambda x ((:c Set) (:fv _uniq.129627)) ((:c And) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.129627)) ((:c Set.instHasSubset) (:fv _uniq.129627)) 0 (:fv _uniq.129628)) ((:c LE.le) (:c Cardinal) (:c Cardinal.instLE) ((:c Cardinal.mk... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.129627))"},{"name":"c","sexp":"(:c Cardinal)"},{"name":"t","sexp":"((:c Set) (:fv _uniq.129627))"},{"name":"ht1","sexp":"((:c HasSubset.Subset) ((:c Set) (:fv _uniq.129627)) ((:c Set.instHasSubset) (:fv _uniq.129627)) (:fv _uniq.130051) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Subtype.val) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit 1) (:arg :explicit 2 (:app (:c Subtype.mk) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129627","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.129628","is_instance":false,"is_let":false,"name":"s","sexp":"(:app (:c Set) (:arg :explicit 0 (:fv FV1)))... | {"children":[{"source":"dsimp","sourceEnd":55986,"sourceStart":55981,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":55991,"sourceStart":55987,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":55... | [] | [{"source":"h","source_end":55996,"source_start":55995,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129627","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.129628","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 355 | 13 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0a6014d2a5398dff77f528ba21e977bf8dd0fd67c32171ffaeb6d1718780ca1c | bc774217137d286df4540124e39e1019bea528a543d76bbdbeb0a8df969b3bee | 92a0fd71910f4242d076474b97cc116652e4383bdcac395f1479a8330901e981 | 38951c8ca59cc13578a07dc5aaa6b503b9c65e41f3a46a93f7a80c948db6efec |
cat-searcher/leandojo-benchmark-4-random | test | 134 | Cardinal.mk_bounded_subset_le | Mathlib/SetTheory/Cardinal/Ordinal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (<a>Set.preimage_eq_preimage'</a> ?_ ?_).1 h <;> rw [<a>Subtype.range_coe</a>] <;> assumption | case inj'.mk.intro.mk.intro.a
α : Type u
s : Set α
c : Cardinal.{u}
t : Set α
ht1 : t ⊆ s
ht2 : #↑t ≤ c
t' : Set α
h1t' : t' ⊆ s
h2t' : #↑t' ≤ c
h : Subtype.val ⁻¹' t = Subtype.val ⁻¹' t'
⊢ t = t' | ((:c Eq) ((:c Set) (:fv _uniq.129627)) (:fv _uniq.130051) (:fv _uniq.130097)) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.129627))"},{"name":"c","sexp":"(:c Cardinal)"},{"name":"t","sexp":"((:c Set) (:fv _uniq.129627))"},{"name":"ht1","sexp":"((:c HasSubset.Subset) ((:c Set) (:fv _uniq.129627)) ((:c Set.instHasSubset) (:fv _uniq.129627)) (:fv _uniq.130051) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:fv FV4)) (:arg :explicit 2 (:fv FV7))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129627","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.129628","is_instance":false,"is_let":false,"name":"s","sexp":"(:app (:c Set) (:arg :explicit 0 (:fv FV1)))... | {"children":[{"children":[{"children":[{"source":"refine","sourceEnd":56011,"sourceStart":56005,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":56013,"sourceStart":56012,"tag":"atom"},{"children":[{"name":"Set.preimage_eq_preimage'","semanticRole":"global","source":"preimage_eq_preimage'"... | [] | [{"source":"(preimage_eq_preimage' ?_ ?_).1 h","source_end":56045,"source_start":56012,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Subtype.range_coe","source_end":56071,"source_start":56054,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129627","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.129628","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 355 | 14 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f44e5d4a2c40c96538b161fbcd7eb27613337d6190abf465badd665def87b457 | 38951c8ca59cc13578a07dc5aaa6b503b9c65e41f3a46a93f7a80c948db6efec | 1ebe068729f890b12eab1abbe42686b0bba0c7180c783fbd641f051d3e9aaf58 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 135 | Matrix.transpose_nonsing_inv | Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Matrix.inv_def</a>, <a>Matrix.inv_def</a>, <a>Matrix.transpose_smul</a>, <a>Matrix.det_transpose</a>, <a>Matrix.adjugate_transpose</a>] | l : Type u_1
m : Type u
n : Type u'
α : Type v
inst✝² : Fintype n
inst✝¹ : DecidableEq n
inst✝ : CommRing α
A B : Matrix n n α
⊢ A⁻¹ᵀ = Aᵀ⁻¹ | ((:c Eq) ((:c Matrix) (:fv _uniq.66381) (:fv _uniq.66381) (:fv _uniq.66383)) ((:c Matrix.transpose) (:fv _uniq.66381) (:fv _uniq.66381) (:fv _uniq.66383) ((:c Inv.inv) ((:c Matrix) (:fv _uniq.66381) (:fv _uniq.66381) (:fv _uniq.66383)) ((:c Matrix.inv) (:fv _uniq.66381) (:fv _uniq.66383) (:fv _uniq.66386) (:fv _uniq.66... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u 1))"},{"name":"n","sexp":"(:sort (+ u' 1))"},{"name":"α","sexp":"(:sort (+ v 1))"},{"name":"inst✝²","sexp":"((:c Fintype) (:fv _uniq.66381))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.66381))"},{"name":"inst✝","sexp":"((:c CommRing) (... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)))) (:arg :explicit 1 (:app (:c Matrix.transpose) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:fv FV3)) (:arg :explicit 3 (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66377","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.66379","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":10550,"sourceStart":10548,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10552,"sourceStart":10551,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"inv_def","source_end":10559,"source_start":10552,"syntax_kind":"ident"},{"source":"inv_def","source_end":10568,"source_start":10561,"syntax_kind":"ident"},{"source":"transpose_smul","source_end":10584,"source_start":10570,"syntax_kind":"ident"},{"source":"det_transpose","source_end":10599,"source_start":105... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66377","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.66379","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 75 | 2 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 27d922a0a4f80757c3f5e195abaa5ea249342776be570c0ac8a500b76f729a1e | 8e41952f9554ba89a8a3d024bce11833c8e0228083dc9c0e3e071033ffb0229a | cfba554bd8db1bf8d9284b929582470c83e47300fd910acab53a23a10f99839b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 136 | Fin.cons_rev | Mathlib/Data/Fin/Tuple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using <a>Fin.insertNth_rev</a> 0 a f i | m n✝ : ℕ
α✝ : Fin (n✝ + 1) → Type u
β : Type v
α : Type u_1
n : ℕ
a : α
f : Fin n → α
i : Fin (n + 1)
⊢ cons a f i.rev = snoc (f ∘ rev) a i | ((:c Eq) (:fv _uniq.91323) ((:c Fin.cons) (:fv _uniq.91324) (:lambda _ ((:c Fin) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.91324) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) (:fv _uniq.91323)) (:fv _uniq.91325) (:fv _uniq.91326) ((:c Fin.rev) ... | [{"name":"m","sexp":"(:c Nat)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"α✝","sexp":"(:forall _ ((:c Fin) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.91124) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) (:sort (+ u 1)))"},{"name":"β","sexp":"(:sor... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:app (:c Fin.cons) (:arg :implicit 0) (:arg :implicit 1) (:arg :explicit 2 (:fv FV7)) (:arg :explicit 3 (:fv FV8)) (:arg :explicit 4 (:app (:c Fin.rev) (:arg :implicit 0) (:arg :explicit 1 (:fv FV9)))))) (:arg :explicit 2 (:app (:c Fin.snoc) (:arg :impl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91122","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91124","is_instance":false,"is_let":false,"name":"n✝","sexp":"(:c Nat)"},{"binder_role":":implicit","context_in... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":38556,"sourceStart":38551,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"insertNth_rev 0 a f i","source_end":38584,"source_start":38563,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91122","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91124","is_instance":false,"is_let":false,"user_name":"n✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 207 | 2 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b57a1bc8e40219407c1c3876d4ea5cfc86353ff2e1733cdc24b3bc2de6143030 | d4fdf290a637e6358d27ff0409585da1e2c4e918493ebebf1a766dd56fdc354e | f7864e946076bf751bff537702db5cd3892591e4d1d36cf39576d26f70eea361 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 137 | Nat.fib_dvd | Mathlib/Data/Nat/Fib/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>Nat.gcd_eq_left_iff_dvd</a>, ← <a>Nat.fib_gcd</a>, gcd_eq_left_iff_dvd.mp] | m n : ℕ
h : m ∣ n
⊢ fib m ∣ fib n | ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) ((:c Nat.fib) (:fv _uniq.34686)) ((:c Nat.fib) (:fv _uniq.34687))) | [{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.34686) (:fv _uniq.34687))"}] | (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Nat.fib) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 3 (:app (:c Nat.fib) (:arg :explicit 0 (:fv FV2))))) | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.34686","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34687","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_ind... | {"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":10504,"sourceStart":10501,"tag":"atom"},{"children":[{"source":"[","sourceEnd":10506,"sourceStart":10505,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Nat.gcd_eq_left_iff_dvd","seman... | [] | [{"source":"gcd_eq_left_iff_dvd","source_end":10525,"source_start":10506,"syntax_kind":"ident"},{"source":"fib_gcd","source_end":10538,"source_start":10531,"syntax_kind":"ident"},{"source":"gcd_eq_left_iff_dvd.mp","source_end":10562,"source_start":10540,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.34686","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34687","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 71 | 2 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f9e45eb11a74b592ed406a6bb97948520ea0898a8e9289b5a6a1cfb63adb1e33 | 5235e58762d37b540f5b11cf40e49926720abe498d7ca5cc0da0e1cc3f7b2fbe | f6c2f8b47f93849d25c65cded2eb6bc73d5ac2d6c0153fa209d7e805190fecf0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 139 | FiniteField.isSquare_iff | Mathlib/FieldTheory/Finite/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply (<a>iff_congr</a> _ (by simp [<a>Units.ext_iff</a>])).<a>Iff.mp</a> (<a>FiniteField.unit_isSquare_iff</a> hF (<a>Units.mk0</a> a ha)) | K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
a : F
ha : a ≠ 0
⊢ IsSquare a ↔ a ^ (Fintype.card F / 2) = 1 | K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
a : F
ha : a ≠ 0
⊢ IsSquare (Units.mk0 a ha) ↔ IsSquare a | ((:c Iff) ((:c IsSquare) (:fv _uniq.196464) ((:c NonUnitalNonAssocRing.toMul) (:fv _uniq.196464) ((:c NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing) (:fv _uniq.196464) ((:c NonUnitalCommRing.toNonUnitalNonAssocCommRing) (:fv _uniq.196464) ((:c CommRing.toNonUnitalCommRing) (:fv _uniq.196464) ((:c EuclideanDomain.to... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.196464))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.196464))"},{"name":"hF","sexp":"((:c Ne) (:c Nat) ((:c ringChar) (:fv _uniq.196464) ((:c Se... | (:app (:c Iff) (:arg :explicit 0 (:app (:c IsSquare) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Mul) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 (:fv FV7)))) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-ty... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"apply","sourceEnd":28088,"sourceStart":28083,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":28094,"sourceStart":28093,"tag":"atom"},{"children":[{"name":"iff_congr","semanticRole":"global","source":"iff_congr","sourceEnd":28103,"sourceStart":28094,"tag":"identifie... | [] | [{"source":"(iff_congr _ (by simp [Units.ext_iff])).mp (FiniteField.unit_isSquare_iff hF (Units.mk0 a ha))","source_end":28187,"source_start":28093,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 134 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1f35d051ab581d14eaa2ae56255f71fabd2b53e1856a429811f9750ed2238f52 | 683b6422df82b18777dabf39aef6fb5270a4e26713cec270c31f474cf0343839 | 36f76570935fb6e6608de58ed2dbaec18fd4031d5bbc601ffc3c6b078ef2e1bd | d338f209c07668226d4dfcae453ac311250af9db3af0f3dbf32785787115b529 |
cat-searcher/leandojo-benchmark-4-random | test | 140 | FiniteField.isSquare_iff | Mathlib/FieldTheory/Finite/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>IsSquare</a>, <a>Units.ext_iff</a>, <a>Units.val_mk0</a>, <a>Units.val_mul</a>] | K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
a : F
ha : a ≠ 0
⊢ IsSquare (Units.mk0 a ha) ↔ IsSquare a | K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
a : F
ha : a ≠ 0
⊢ (∃ r, a = ↑r * ↑r) ↔ ∃ r, a = r * r | ((:c Iff) ((:c IsSquare) ((:c Units) (:fv _uniq.196464) ((:c MonoidWithZero.toMonoid) (:fv _uniq.196464) ((:c Semiring.toMonoidWithZero) (:fv _uniq.196464) ((:c DivisionSemiring.toSemiring) (:fv _uniq.196464) ((:c Semifield.toDivisionSemiring) (:fv _uniq.196464) ((:c Field.toSemifield) (:fv _uniq.196464) (:fv _uniq.196... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.196464))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.196464))"},{"name":"hF","sexp":"((:c Ne) (:c Nat) ((:c ringChar) (:fv _uniq.196464) ((:c Se... | (:app (:c Iff) (:arg :explicit 0 (:app (:c IsSquare) (:arg :implicit-type 0 (:app (:c Units) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV2))))))) (:arg :instance 1 (:instance-of (:app (:c Mul) (:arg :explicit 0 (:app (:c Units) (:arg :explicit 0 (:fv FV2)) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":28194,"sourceStart":28190,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":28199,"sourceStart":28195,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":281... | [] | [{"source":"IsSquare","source_end":28209,"source_start":28201,"syntax_kind":"ident"},{"source":"Units.ext_iff","source_end":28224,"source_start":28211,"syntax_kind":"ident"},{"source":"Units.val_mk0","source_end":28239,"source_start":28226,"syntax_kind":"ident"},{"source":"Units.val_mul","source_end":28254,"source_star... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 134 | 10 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7b035f02395f00aa877f31097c10a94f9d4a79e9c06870d785acc2b2acec6d07 | d338f209c07668226d4dfcae453ac311250af9db3af0f3dbf32785787115b529 | 0b5a52b8fa8739fec2a8cfa080c36725e23942fa8e7ac1150fa7acb30b666aea | 7727008486765c8fef692db3da448fa8a49e3c1aa09883c4c3e3b2a46eed8bd7 |
cat-searcher/leandojo-benchmark-4-random | test | 141 | FiniteField.isSquare_iff | Mathlib/FieldTheory/Finite/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
a : F
ha : a ≠ 0
⊢ (∃ r, a = ↑r * ↑r) ↔ ∃ r, a = r * r | case mp
K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
a : F
ha : a ≠ 0
⊢ (∃ r, a = ↑r * ↑r) → ∃ r, a = r * r
case mpr
K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
a : F
ha : a ≠ 0
⊢ (∃ r, a = r * r) → ∃ r, a = ↑r * ↑r | ((:c Iff) ((:c Exists) ((:c Units) (:fv _uniq.196464) ((:c MonoidWithZero.toMonoid) (:fv _uniq.196464) ((:c Semiring.toMonoidWithZero) (:fv _uniq.196464) ((:c DivisionSemiring.toSemiring) (:fv _uniq.196464) ((:c Semifield.toDivisionSemiring) (:fv _uniq.196464) ((:c Field.toSemifield) (:fv _uniq.196464) (:fv _uniq.19646... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.196464))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.196464))"},{"name":"hF","sexp":"((:c Ne) (:c Nat) ((:c ringChar) (:fv _uniq.196464) ((:c Se... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Units) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 1 (:lambda r :explicit (:app (:c Units) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"constructor","sourceEnd":28269,"sourceStart":28258,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":28269,"sourceStart":28258,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 134 | 11 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 86c156c1b74ac0f5cd394688216b63f828f625bd0e5b086b34acf0e52294264f | 7727008486765c8fef692db3da448fa8a49e3c1aa09883c4c3e3b2a46eed8bd7 | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | 82026b5e19fb95a594e783c1b2e5590900406fcb6a0cb4177e9067911eaf0151 |
cat-searcher/leandojo-benchmark-4-random | test | 142 | FiniteField.isSquare_iff | Mathlib/FieldTheory/Finite/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Units.ext_iff</a>] | K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
a : F
ha : a ≠ 0
⊢ Units.mk0 a ha ^ (Fintype.card F / 2) = 1 ↔ a ^ (Fintype.card F / 2) = 1 | ((:c Iff) ((:c Eq) ((:c Units) (:fv _uniq.196464) ((:c MonoidWithZero.toMonoid) (:fv _uniq.196464) ((:c Semiring.toMonoidWithZero) (:fv _uniq.196464) ((:c DivisionSemiring.toSemiring) (:fv _uniq.196464) ((:c Semifield.toDivisionSemiring) (:fv _uniq.196464) ((:c Field.toSemifield) (:fv _uniq.196464) (:fv _uniq.196467)))... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.196464))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.196464))"},{"name":"hF","sexp":"((:c Ne) (:c Nat) ((:c ringChar) (:fv _uniq.196464) ((:c Se... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Units) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:app (:c Units) (:arg :explicit 0 (:fv FV2)) (:arg :insta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":28114,"sourceStart":28110,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"Units.ext_iff","source_end":28129,"source_start":28116,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 134 | 7 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2eb7b9b33003605ad1c2c6f9a43efcc9841d1f131576f94a0c1f01f6eb74218a | 275a1f15485e9b3414fda9b4030d3765d7dec388272f4160e560d8849daa29bb | 2f87893fcbdd9f682198374845170719afe55d03d0b9825bfd18c174effffe19 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 143 | FiniteField.isSquare_iff | Mathlib/FieldTheory/Finite/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨y, hy⟩ | case mp
K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
a : F
ha : a ≠ 0
⊢ (∃ r, a = ↑r * ↑r) → ∃ r, a = r * r | case mp.intro
K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
a : F
ha : a ≠ 0
y : Fˣ
hy : a = ↑y * ↑y
⊢ ∃ r, a = r * r | (:forall _ ((:c Exists) ((:c Units) (:fv _uniq.196464) ((:c MonoidWithZero.toMonoid) (:fv _uniq.196464) ((:c Semiring.toMonoidWithZero) (:fv _uniq.196464) ((:c DivisionSemiring.toSemiring) (:fv _uniq.196464) ((:c Semifield.toDivisionSemiring) (:fv _uniq.196464) ((:c Field.toSemifield) (:fv _uniq.196464) (:fv _uniq.1964... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.196464))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.196464))"},{"name":"hF","sexp":"((:c Ne) (:c Nat) ((:c ringChar) (:fv _uniq.196464) ((:c Se... | (:forall _ :explicit (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Units) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 1 (:lambda r :explicit (:app (:c Units) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c M... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rintro","sourceEnd":28281,"sourceStart":28275,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":28285,"sourceStart":28282,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":28286,"sou... | [{"role":"fresh_name","source":"y","source_end":28286,"source_start":28285,"syntax_kind":"ident"},{"role":"fresh_name","source":"hy","source_end":28290,"source_start":28288,"syntax_kind":"ident"}] | [{"source":"⟨y, hy⟩","source_end":28293,"source_start":28282,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 134 | 16 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8c19d311c02b4de5bc9368cbbfc6f636a20634c108af6085053dc41e3016684a | e6c92e27686c820608c0e651fd8af0111124867651ef0bcd61fa6e97df0f6216 | 813cc811905d2e7e9af04e80bc2c0ad03d98df053fe26eaaf7bb20ae162aefaf | 9c7966302b1da6174bcd19cf4028c6427c9a88bdd1e880dd45ef726462cc778a |
cat-searcher/leandojo-benchmark-4-random | test | 144 | FiniteField.isSquare_iff | Mathlib/FieldTheory/Finite/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨y, hy⟩ | case mp.intro
K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
a : F
ha : a ≠ 0
y : Fˣ
hy : a = ↑y * ↑y
⊢ ∃ r, a = r * r | ((:c Exists) (:fv _uniq.196464) (:lambda r (:fv _uniq.196464) ((:c Eq) (:fv _uniq.196464) (:fv _uniq.197167) ((:c HMul.hMul) (:fv _uniq.196464) (:fv _uniq.196464) (:fv _uniq.196464) ((:c instHMul) (:fv _uniq.196464) ((:c NonUnitalNonAssocRing.toMul) (:fv _uniq.196464) ((:c NonUnitalNonAssocCommRing.toNonUnitalNonAssocR... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.196464))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.196464))"},{"name":"hF","sexp":"((:c Ne) (:c Nat) ((:c ringChar) (:fv _uniq.196464) ((:c Se... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda r :explicit (:fv FV2) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:fv FV2)) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":28300,"sourceStart":28295,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":28304,"sourceStart":28301,"tag":"atom"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"y","sourceEnd":28305,"sourceStart":28304,"tag":"identifier"},{"source":",","sourceEnd":28306,"... | [] | [{"source":"⟨y, hy⟩","source_end":28312,"source_start":28301,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 134 | 18 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8e7c92346d265a314968c977b1514121065b184771acadbc6824c40d6ce98b13 | 9c7966302b1da6174bcd19cf4028c6427c9a88bdd1e880dd45ef726462cc778a | 25f07430166c7de106cfab78ede3d0737c69bea053939ebbe7efbd4dd43e1d4a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 145 | FiniteField.isSquare_iff | Mathlib/FieldTheory/Finite/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨y, rfl⟩ | case mpr
K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
a : F
ha : a ≠ 0
⊢ (∃ r, a = r * r) → ∃ r, a = ↑r * ↑r | case mpr.intro
K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
y : F
ha : y * y ≠ 0
⊢ ∃ r, y * y = ↑r * ↑r | (:forall _ ((:c Exists) (:fv _uniq.196464) (:lambda r (:fv _uniq.196464) ((:c Eq) (:fv _uniq.196464) (:fv _uniq.197167) ((:c HMul.hMul) (:fv _uniq.196464) (:fv _uniq.196464) (:fv _uniq.196464) ((:c instHMul) (:fv _uniq.196464) ((:c NonUnitalNonAssocRing.toMul) (:fv _uniq.196464) ((:c NonUnitalNonAssocCommRing.toNonUnit... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.196464))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.196464))"},{"name":"hF","sexp":"((:c Ne) (:c Nat) ((:c ringChar) (:fv _uniq.196464) ((:c Se... | (:forall _ :explicit (:app (:c Exists) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda r :explicit (:fv FV2) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rintro","sourceEnd":28324,"sourceStart":28318,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":28328,"sourceStart":28325,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":28329,"sou... | [{"role":"fresh_name","source":"y","source_end":28329,"source_start":28328,"syntax_kind":"ident"}] | [{"source":"⟨y, rfl⟩","source_end":28337,"source_start":28325,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 134 | 23 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 65c4d8b4a9e09dc0bcc68f6f11b0ee449c3a33b037e4d9cbb0c1b2c70dc7720c | 06a791d198e39b7e89b83bc6eaf6ca400d86588183b637ce585f5b7d4d730233 | f8e70510d1e10f6e294735ec5506753ca0c17491b8ace5591037eec2acc7844b | 600696a164a83b1f6aa308830450a5ea288746f90e2a9a644c3bbe1d4d751bd8 |
cat-searcher/leandojo-benchmark-4-random | test | 146 | FiniteField.isSquare_iff | Mathlib/FieldTheory/Finite/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hy : y ≠ 0 := by rintro rfl; simp at ha | case mpr.intro
K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
y : F
ha : y * y ≠ 0
⊢ ∃ r, y * y = ↑r * ↑r | case mpr.intro
K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
y : F
ha : y * y ≠ 0
hy : y ≠ 0
⊢ ∃ r, y * y = ↑r * ↑r | ((:c Exists) ((:c Units) (:fv _uniq.196464) ((:c MonoidWithZero.toMonoid) (:fv _uniq.196464) ((:c Semiring.toMonoidWithZero) (:fv _uniq.196464) ((:c DivisionSemiring.toSemiring) (:fv _uniq.196464) ((:c Semifield.toDivisionSemiring) (:fv _uniq.196464) ((:c Field.toSemifield) (:fv _uniq.196464) (:fv _uniq.196467))))))) (... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.196464))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.196464))"},{"name":"hF","sexp":"((:c Ne) (:c Nat) ((:c ringChar) (:fv _uniq.196464) ((:c Se... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Units) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 1 (:lambda r :explicit (:app (:c Units) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":28346,"sourceStart":28342,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hy","sourceEnd":28349,"sourceStart":28347,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hy","sourceEnd":28349,"sourceStart":28347,"tag":"nod... | [] | [{"source":"y ≠ 0","source_end":28359,"source_start":28352,"syntax_kind":"«term_≠_»"},{"source":"rfl","source_end":28376,"source_start":28373,"syntax_kind":"ident"},{"source":"ha","source_end":28388,"source_start":28386,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 134 | 24 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8900c33b57489b4579a5d5b3a1560461c0d37c95a6f7238ee89395cba0fc2b4b | 600696a164a83b1f6aa308830450a5ea288746f90e2a9a644c3bbe1d4d751bd8 | 50a74db74fe7a2e1b64a4f70c6dd58ec5a53eb4d6e224e9ac72119f0a2721ed6 | 4446dcc8322ec63f8ab76a033d0dac6b7c4efe3acd81b4fa32c1c82f5cb4433d |
cat-searcher/leandojo-benchmark-4-random | test | 147 | FiniteField.isSquare_iff | Mathlib/FieldTheory/Finite/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨<a>Units.mk0</a> y hy, ?_⟩ | case mpr.intro
K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
y : F
ha : y * y ≠ 0
hy : y ≠ 0
⊢ ∃ r, y * y = ↑r * ↑r | case mpr.intro
K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
y : F
ha : y * y ≠ 0
hy : y ≠ 0
⊢ y * y = ↑(Units.mk0 y hy) * ↑(Units.mk0 y hy) | ((:c Exists) ((:c Units) (:fv _uniq.196464) ((:c MonoidWithZero.toMonoid) (:fv _uniq.196464) ((:c Semiring.toMonoidWithZero) (:fv _uniq.196464) ((:c DivisionSemiring.toSemiring) (:fv _uniq.196464) ((:c Semifield.toDivisionSemiring) (:fv _uniq.196464) ((:c Field.toSemifield) (:fv _uniq.196464) (:fv _uniq.196467))))))) (... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.196464))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.196464))"},{"name":"hF","sexp":"((:c Ne) (:c Nat) ((:c ringChar) (:fv _uniq.196464) ((:c Se... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Units) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 1 (:lambda r :explicit (:app (:c Units) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":28399,"sourceStart":28393,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":28403,"sourceStart":28400,"tag":"atom"},{"children":[{"children":[{"name":"Units.mk0","semanticRole":"global","source":"Units.mk0","sourceEnd":28412,"sourceStart":28403,"tag":"identifier"},{"childr... | [] | [{"source":"⟨Units.mk0 y hy, ?_⟩","source_end":28424,"source_start":28400,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 134 | 29 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4c88fec2b85dc37c78ef038ce84cfa82fb1d85b597d563352e9bb0270d7e7251 | 4446dcc8322ec63f8ab76a033d0dac6b7c4efe3acd81b4fa32c1c82f5cb4433d | 37eb477b994e7883bafe3a9d6f10e5e2378c547c45a9255b05f54bdc6640fa7e | de5f00bbffccc19138e7cafa99b18201db6b248835099de5bbc124e9a8490e65 |
cat-searcher/leandojo-benchmark-4-random | test | 148 | FiniteField.isSquare_iff | Mathlib/FieldTheory/Finite/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case mpr.intro
K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
y : F
ha : y * y ≠ 0
hy : y ≠ 0
⊢ y * y = ↑(Units.mk0 y hy) * ↑(Units.mk0 y hy) | ((:c Eq) (:fv _uniq.196464) ((:c HMul.hMul) (:fv _uniq.196464) (:fv _uniq.196464) (:fv _uniq.196464) ((:c instHMul) (:fv _uniq.196464) ((:c NonUnitalNonAssocRing.toMul) (:fv _uniq.196464) ((:c NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing) (:fv _uniq.196464) ((:c NonUnitalCommRing.toNonUnitalNonAssocCommRing) (:fv ... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.196464))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.196464))"},{"name":"hF","sexp":"((:c Ne) (:c Nat) ((:c ringChar) (:fv _uniq.196464) ((:c Se... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":28430,"sourceStart":28426,"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.196458","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 134 | 31 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b8cbf2d66b98f45fb86bcc4099d942b3508a1781a7ad9b49ce3ae630fc003db9 | de5f00bbffccc19138e7cafa99b18201db6b248835099de5bbc124e9a8490e65 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 149 | FiniteField.isSquare_iff | Mathlib/FieldTheory/Finite/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro rfl | K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
y : F
ha : y * y ≠ 0
⊢ y ≠ 0 | K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
ha : 0 * 0 ≠ 0
⊢ False | ((:c Ne) (:fv _uniq.196464) (:fv _uniq.198454) ((:c OfNat.ofNat) (:fv _uniq.196464) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.196464) ((:c CommMonoidWithZero.toZero) (:fv _uniq.196464) ((:c CommGroupWithZero.toCommMonoidWithZero) (:fv _uniq.196464) ((:c Semifield.toCommGroupWithZero) (:fv _uniq.196464) ((:c Field.toSemif... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.196464))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.196464))"},{"name":"hF","sexp":"((:c Ne) (:c Nat) ((:c ringChar) (:fv _uniq.196464) ((:c Se... | (:app (:c Ne) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:lit 0)))))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rintro","sourceEnd":28372,"sourceStart":28366,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":28376,"sourceStart":28373,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl","sourceEnd":28376,"sourceStart":283... | [] | [{"source":"rfl","source_end":28376,"source_start":28373,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 134 | 26 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7634ad115cfde295084512f998820f4f5401e974cf13532b86463dabac546d7c | d8826552b023766b2c1af0ca971ede160099ddef3d2511bdd0824270524874c2 | 09e128cd6787f35d3c063b643315aff1382388dafa4e55b6546fbf9dcecb02da | d64060b808371292f3c7fd4e17c486b9ededf382a1a1cdfd82483879eaf83d2c |
cat-searcher/leandojo-benchmark-4-random | test | 150 | FiniteField.isSquare_iff | Mathlib/FieldTheory/Finite/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp at ha | K : Type u_1
R : Type u_2
F : Type u_3
inst✝¹ : Field F
inst✝ : Fintype F
hF : ringChar F ≠ 2
ha : 0 * 0 ≠ 0
⊢ False | (:c False) | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.196464))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.196464))"},{"name":"hF","sexp":"((:c Ne) (:c Nat) ((:c ringChar) (:fv _uniq.196464) ((:c Se... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":28382,"sourceStart":28378,"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":[{"chi... | [] | [{"source":"ha","source_end":28388,"source_start":28386,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.196458","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.196461","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 134 | 28 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1e31c38695a2c06d0450fc170744052a1505f600eba5a42c0b96fa2ec8edbf87 | d64060b808371292f3c7fd4e17c486b9ededf382a1a1cdfd82483879eaf83d2c | 9acce4dedbeef7bf8b85995817175934b425f6872bc1662647d1244241e750ad | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 151 | Seminorm.ball_finset_sup_eq_iInter | Mathlib/Analysis/Seminorm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | lift r to <a>NNReal</a> using hr.le | R : Type u_1
R' : Type u_2
𝕜 : Type u_3
𝕜₂ : Type u_4
𝕜₃ : Type u_5
𝕝 : Type u_6
E : Type u_7
E₂ : Type u_8
E₃ : Type u_9
F : Type u_10
G : Type u_11
ι : Type u_12
inst✝⁶ : SeminormedRing 𝕜
inst✝⁵ : AddCommGroup E
inst✝⁴ : Module 𝕜 E
inst✝³ : SeminormedRing 𝕜₂
inst✝² : AddCommGroup E₂
inst✝¹ : Module 𝕜₂ E₂
σ₁₂ ... | case intro
R : Type u_1
R' : Type u_2
𝕜 : Type u_3
𝕜₂ : Type u_4
𝕜₃ : Type u_5
𝕝 : Type u_6
E : Type u_7
E₂ : Type u_8
E₃ : Type u_9
F : Type u_10
G : Type u_11
ι : Type u_12
inst✝⁶ : SeminormedRing 𝕜
inst✝⁵ : AddCommGroup E
inst✝⁴ : Module 𝕜 E
inst✝³ : SeminormedRing 𝕜₂
inst✝² : AddCommGroup E₂
inst✝¹ : Module ... | ((:c Eq) ((:c Set) (:fv _uniq.695958)) ((:c Seminorm.ball) (:fv _uniq.695946) (:fv _uniq.695958) (:fv _uniq.695976) (:fv _uniq.695979) ((:c SMulZeroClass.toSMul) (:fv _uniq.695946) (:fv _uniq.695958) ((:c NegZeroClass.toZero) (:fv _uniq.695958) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.695958) ((:c SubtractionMo... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R'","sexp":"(:sort (+ u_2 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜₂","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜₃","sexp":"(:sort (+ u_5 1))"},{"name":"𝕝","sexp":"(:sort (+ u_6 1))"},{"name":"E","sexp":"(:sort (+ u_7 1))"},{"name":"E₂","sexp":"(:sort (+ u... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :explicit 1 (:app (:c Seminorm.ball) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV6)) (:arg :instance 2 (:instance-of (:app (:c SeminormedRing) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 3 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.695940","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.695943","is_instance":false,"is_let":false,"name":"R'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"lift","sourceEnd":37207,"sourceStart":37203,"tag":"atom"},{"contextIndex":25,"semanticRole":"local","source":"r","sourceEnd":37209,"sourceStart":37208,"tag":"identifier"},{"source":"to","sourceEnd":37212,"sourceStart":37210,"tag":"atom"},{"name":"NNReal","semanticRole":"global","source":"NNReal"... | [] | [{"source":"r","source_end":37209,"source_start":37208,"syntax_kind":"ident"},{"source":"NNReal","source_end":37219,"source_start":37213,"syntax_kind":"ident"},{"source":"hr.le","source_end":37231,"source_start":37226,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.695940","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.695943","is_instance":false,"is_let":false,"user_name":"R'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 264 | 4 | exact | true | 1 | 26 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 05e5774d128f9ec757f48f746a26f4231f935defdc33951f7e8de474e6511564 | 2508ee90e136fe5185ce620d197c9b51bd5feabcb73594d73e391591654bb144 | deca8fdfc754b98d0b798e7d78c9ffa1768ccd1c61764d1b5c9a334dff12c1ee | 9fe1948da816fdc20055453907f706b4b033c48d0c3b3b6d8569d136f9f89cb8 |
cat-searcher/leandojo-benchmark-4-random | test | 152 | Seminorm.ball_finset_sup_eq_iInter | Mathlib/Analysis/Seminorm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>Seminorm.ball</a>, <a>Set.iInter_setOf</a>, <a>Seminorm.finset_sup_apply</a>, <a>NNReal.coe_lt_coe</a>, <a>Finset.sup_lt_iff</a> (show ⊥ < r from hr), ← <a>NNReal.coe_lt_coe</a>, <a>NNReal.coe_mk</a>] | case intro
R : Type u_1
R' : Type u_2
𝕜 : Type u_3
𝕜₂ : Type u_4
𝕜₃ : Type u_5
𝕝 : Type u_6
E : Type u_7
E₂ : Type u_8
E₃ : Type u_9
F : Type u_10
G : Type u_11
ι : Type u_12
inst✝⁶ : SeminormedRing 𝕜
inst✝⁵ : AddCommGroup E
inst✝⁴ : Module 𝕜 E
inst✝³ : SeminormedRing 𝕜₂
inst✝² : AddCommGroup E₂
inst✝¹ : Module ... | ((:c Eq) ((:c Set) (:fv _uniq.695958)) ((:c Seminorm.ball) (:fv _uniq.695946) (:fv _uniq.695958) (:fv _uniq.695976) (:fv _uniq.695979) ((:c SMulZeroClass.toSMul) (:fv _uniq.695946) (:fv _uniq.695958) ((:c NegZeroClass.toZero) (:fv _uniq.695958) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.695958) ((:c SubtractionMo... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R'","sexp":"(:sort (+ u_2 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜₂","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜₃","sexp":"(:sort (+ u_5 1))"},{"name":"𝕝","sexp":"(:sort (+ u_6 1))"},{"name":"E","sexp":"(:sort (+ u_7 1))"},{"name":"E₂","sexp":"(:sort (+ u... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :explicit 1 (:app (:c Seminorm.ball) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV6)) (:arg :instance 2 (:instance-of (:app (:c SeminormedRing) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 3 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.695940","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.695943","is_instance":false,"is_let":false,"name":"R'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"simp_rw","sourceEnd":37241,"sourceStart":37234,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":37243,"sourceStart":37242,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Seminorm.ba... | [] | [{"source":"ball","source_end":37247,"source_start":37243,"syntax_kind":"ident"},{"source":"iInter_setOf","source_end":37261,"source_start":37249,"syntax_kind":"ident"},{"source":"finset_sup_apply","source_end":37279,"source_start":37263,"syntax_kind":"ident"},{"source":"NNReal.coe_lt_coe","source_end":37298,"source_st... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.695940","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.695943","is_instance":false,"is_let":false,"user_name":"R'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 264 | 5 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 40b7f69ca44690c8cd9f070ea12c073e8ada7bae6b95948d503d8b17c1df2efc | 9fe1948da816fdc20055453907f706b4b033c48d0c3b3b6d8569d136f9f89cb8 | d660a34a13e1b73edfb99d4939538bec87d787719f5b480df088b9d7dfc89eb9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 153 | Filter.EventuallyLE.mul_le_mul' | Mathlib/Order/Filter/Ring.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards [hf, hg] with x hfx hgx using <a>mul_le_mul'</a> hfx hgx | α : Type u
β : Type v
inst✝³ : Mul β
inst✝² : Preorder β
inst✝¹ : CovariantClass β β (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1
inst✝ : CovariantClass β β (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1
l : Filter α
f₁ f₂ g₁ g₂ : α → β
hf : f₁ ≤ᶠ[l] f₂
hg : g₁ ≤ᶠ[l] g₂
⊢ f₁ * g₁ ≤ᶠ[l] f₂ * g₂ | ((:c Filter.EventuallyLE) (:fv _uniq.2939) (:fv _uniq.2941) ((:c Preorder.toLE) (:fv _uniq.2941) (:fv _uniq.3471)) (:fv _uniq.3474) ((:c HMul.hMul) (:forall _ (:fv _uniq.2939) (:fv _uniq.2941)) (:forall _ (:fv _uniq.2939) (:fv _uniq.2941)) (:forall _ (:fv _uniq.2939) (:fv _uniq.2941)) ((:c instHMul) (:forall _ (:fv _un... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"inst✝³","sexp":"((:c Mul) (:fv _uniq.2941))"},{"name":"inst✝²","sexp":"((:c Preorder) (:fv _uniq.2941))"},{"name":"inst✝¹","sexp":"((:c CovariantClass) (:fv _uniq.2941) (:fv _uniq.2941) (:lambda _ (:fv _uniq.2941) (:lambda _ (:fv _uni... | (:app (:c Filter.EventuallyLE) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 3 (:fv FV7)) (:arg :explicit 4 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:fv FV1))) (:arg :im... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2939","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2941","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"children":[{"children":[{"children":[{"source":"filter_upwards","sourceEnd":1197,"sourceStart":1183,"tag":"atom"},{"children":[{"source":"[","sourceEnd":1199,"sourceStart":1198,"tag":"atom"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"hf","sourceEnd":1201,"sourceStart":1199,"tag":"id... | [] | [{"source":"hg","source_end":1205,"source_start":1203,"syntax_kind":"ident"},{"source":"hf","source_end":1201,"source_start":1199,"syntax_kind":"ident"},{"source":"_root_.mul_le_mul' hfx hgx","source_end":1254,"source_start":1228,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2939","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2941","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":3,"internal_nam... | 7 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5cea62d59123da8f9cefddeabfaf4ef71bb93ac7f843e2fb3045b7283f0496b1 | 8b293c1dae0e44b0054813e0f6a3e9cd49344ab7778c2ee617482f1ab5eef321 | 7b418cd2e026033d8e0ea6ac652fa21b7452b803998312585a8cc0092ca81cc4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 154 | CategoryTheory.GrothendieckTopology.Cover.preOneHypercover_sieve₁ | Mathlib/CategoryTheory/Sites/OneHypercover.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext Y f | C : Type u
inst✝¹ : Category.{v, u} C
A : Type u_1
inst✝ : Category.{?u.31721, u_1} A
J : GrothendieckTopology C
X : C
S : J.Cover X
f₁ f₂ : S.Arrow
W : C
p₁ : W ⟶ f₁.Y
p₂ : W ⟶ f₂.Y
w : p₁ ≫ f₁.f = p₂ ≫ f₂.f
⊢ S.preOneHypercover.sieve₁ p₁ p₂ = ⊤ | case h
C : Type u
inst✝¹ : Category.{v, u} C
A : Type u_1
inst✝ : Category.{?u.31721, u_1} A
J : GrothendieckTopology C
X : C
S : J.Cover X
f₁ f₂ : S.Arrow
W : C
p₁ : W ⟶ f₁.Y
p₂ : W ⟶ f₂.Y
w : p₁ ≫ f₁.f = p₂ ≫ f₂.f
Y : C
f : Y ⟶ W
⊢ (S.preOneHypercover.sieve₁ p₁ p₂).arrows f ↔ ⊤.arrows f | ((:c Eq) ((:c CategoryTheory.Sieve) (:fv _uniq.31712) (:fv _uniq.31715) (:fv _uniq.32142)) ((:c CategoryTheory.PreOneHypercover.sieve₁) (:fv _uniq.31712) (:fv _uniq.31715) (:fv _uniq.31739) ((:c CategoryTheory.GrothendieckTopology.Cover.preOneHypercover) (:fv _uniq.31712) (:fv _uniq.31715) (:fv _uniq.31737) (:fv _uniq.... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.31712))"},{"name":"A","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.31718))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.31712) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Sieve) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV10)))) (:arg :explicit 1 (:app (:c CategoryTheory.PreOneHypercover.sieve₁) (:arg :implicit-ty... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31712","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31715","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"ext","sourceEnd":9640,"sourceStart":9637,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"Y","sourceEnd":9642,"sourceStart":9641,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"Y","sourceEnd":9642,"sourceStart":9641,"tag":"nod... | [{"role":"fresh_name","source":"Y","source_end":9642,"source_start":9641,"syntax_kind":"ident"},{"role":"fresh_name","source":"f","source_end":9644,"source_start":9643,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31712","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31715","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 44 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e4c68210e550263d7ee36a39e5cac8a0b271fa50d87623d41479951342dc487b | 771093578976acec0bfaca7ef3c7ead00ddecf0599c81466cdc860621bc866d7 | b27477ea4f44fa5ffd9f42b471114c2cd56dbd85dd4a71b523dae729510a9cea | 0463ed3b1dc0823dc22ba4983d6f48c3aafd97f42e4be080120372420739a6ad |
cat-searcher/leandojo-benchmark-4-random | test | 155 | CategoryTheory.GrothendieckTopology.Cover.preOneHypercover_sieve₁ | Mathlib/CategoryTheory/Sites/OneHypercover.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>CategoryTheory.Sieve.top_apply</a>, <a>iff_true</a>] | case h
C : Type u
inst✝¹ : Category.{v, u} C
A : Type u_1
inst✝ : Category.{?u.31721, u_1} A
J : GrothendieckTopology C
X : C
S : J.Cover X
f₁ f₂ : S.Arrow
W : C
p₁ : W ⟶ f₁.Y
p₂ : W ⟶ f₂.Y
w : p₁ ≫ f₁.f = p₂ ≫ f₂.f
Y : C
f : Y ⟶ W
⊢ (S.preOneHypercover.sieve₁ p₁ p₂).arrows f ↔ ⊤.arrows f | case h
C : Type u
inst✝¹ : Category.{v, u} C
A : Type u_1
inst✝ : Category.{?u.31721, u_1} A
J : GrothendieckTopology C
X : C
S : J.Cover X
f₁ f₂ : S.Arrow
W : C
p₁ : W ⟶ f₁.Y
p₂ : W ⟶ f₂.Y
w : p₁ ≫ f₁.f = p₂ ≫ f₂.f
Y : C
f : Y ⟶ W
⊢ (S.preOneHypercover.sieve₁ p₁ p₂).arrows f | ((:c Iff) ((:c CategoryTheory.Sieve.arrows) (:fv _uniq.31712) (:fv _uniq.31715) (:fv _uniq.32142) ((:c CategoryTheory.PreOneHypercover.sieve₁) (:fv _uniq.31712) (:fv _uniq.31715) (:fv _uniq.31739) ((:c CategoryTheory.GrothendieckTopology.Cover.preOneHypercover) (:fv _uniq.31712) (:fv _uniq.31715) (:fv _uniq.31737) (:fv... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.31712))"},{"name":"A","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.31718))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.31712) (:fv _uniq... | (:app (:c Iff) (:arg :explicit 0 (:app (:c CategoryTheory.Sieve.arrows) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit 2) (:arg :explicit 3 (:app (:c CategoryTheory.PreOneHypercover.sieve₁) (:arg :implicit-type 0 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31712","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31715","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"simp","sourceEnd":9651,"sourceStart":9647,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":9656,"sourceStart":9652,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":9656,"s... | [] | [{"source":"Sieve.top_apply","source_end":9673,"source_start":9658,"syntax_kind":"ident"},{"source":"iff_true","source_end":9683,"source_start":9675,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31712","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31715","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 44 | 5 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 75415408ea26bf881dc3813f8463ba0cf22d26102dca5c9d8426fe0799ec6041 | 0463ed3b1dc0823dc22ba4983d6f48c3aafd97f42e4be080120372420739a6ad | 476ac145fb007e508ca1c43f7eaf5ca1db3462170ecea1de602407b45e6f4909 | 817195bfa569ea741a85f2bc1c229c4bc03d97249e7b5023451bb0be13d387d1 |
cat-searcher/leandojo-benchmark-4-random | test | 156 | CategoryTheory.GrothendieckTopology.Cover.preOneHypercover_sieve₁ | Mathlib/CategoryTheory/Sites/OneHypercover.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨{ w := w}, f, <a>rfl</a>, <a>rfl</a>⟩ | case h
C : Type u
inst✝¹ : Category.{v, u} C
A : Type u_1
inst✝ : Category.{?u.31721, u_1} A
J : GrothendieckTopology C
X : C
S : J.Cover X
f₁ f₂ : S.Arrow
W : C
p₁ : W ⟶ f₁.Y
p₂ : W ⟶ f₂.Y
w : p₁ ≫ f₁.f = p₂ ≫ f₂.f
Y : C
f : Y ⟶ W
⊢ (S.preOneHypercover.sieve₁ p₁ p₂).arrows f | ((:c CategoryTheory.Sieve.arrows) (:fv _uniq.31712) (:fv _uniq.31715) (:fv _uniq.32142) ((:c CategoryTheory.PreOneHypercover.sieve₁) (:fv _uniq.31712) (:fv _uniq.31715) (:fv _uniq.31739) ((:c CategoryTheory.GrothendieckTopology.Cover.preOneHypercover) (:fv _uniq.31712) (:fv _uniq.31715) (:fv _uniq.31737) (:fv _uniq.317... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.31712))"},{"name":"A","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.31718))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.31712) (:fv _uniq... | (:app (:c CategoryTheory.Sieve.arrows) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit 2) (:arg :explicit 3 (:app (:c CategoryTheory.PreOneHypercover.sieve₁) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31712","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31715","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"exact","sourceEnd":9692,"sourceStart":9687,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":9696,"sourceStart":9693,"tag":"atom"},{"children":[{"children":[{"source":"{","sourceEnd":9697,"sourceStart":9696,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"ch... | [] | [{"source":"⟨{ w := w}, f, rfl, rfl⟩","source_end":9721,"source_start":9693,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31712","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31715","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 44 | 6 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 41e5d9e4bfd07d49e34b9140f13f437a92d3ee0675e6c2c30997200f7488cf1e | 817195bfa569ea741a85f2bc1c229c4bc03d97249e7b5023451bb0be13d387d1 | d2e5dbbeb282f86db71b576f15c2f3172cfad5a3a812a2adaab2fce7d6c98ea7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 157 | Polynomial.nextCoeff_ne_zero | Mathlib/Algebra/Polynomial/Degree/Definitions.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Polynomial.nextCoeff</a>] | R : Type u
S : Type v
a b c d : R
n m : ℕ
inst✝ : Semiring R
p : R[X]
⊢ p.nextCoeff ≠ 0 ↔ p.natDegree ≠ 0 ∧ p.coeff (p.natDegree - 1) ≠ 0 | ((:c Iff) ((:c Ne) (:fv _uniq.94904) ((:c Polynomial.nextCoeff) (:fv _uniq.94904) (:fv _uniq.94921) (:fv _uniq.94934)) ((:c OfNat.ofNat) (:fv _uniq.94904) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.94904) ((:c MonoidWithZero.toZero) (:fv _uniq.94904) ((:c Semiring.toMonoidWithZero) (:fv _uniq.94904) (:fv _uniq.94921))))))... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.94904)"},{"name":"b","sexp":"(:fv _uniq.94904)"},{"name":"c","sexp":"(:fv _uniq.94904)"},{"name":"d","sexp":"(:fv _uniq.94904)"},{"name":"n","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"inst✝","sexp... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Ne) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Polynomial.nextCoeff) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV9)))) (:arg :explicit 2 (:app (:c OfNat.ofNat)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.94904","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.94906","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":24999,"sourceStart":24995,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"nextCoeff","source_end":25010,"source_start":25001,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.94904","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.94906","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 217 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b06a1979f7587c56b8a16467ee80a4dc59a3fa11412de80802212baf5de4dccf | fd297b0652ba07b79423c0268dc5820afccf6b414edc36c7dda4bff11007b483 | 0302270ce4a53ef0eeb999639543d30dedb8b53f5f4fbf9856fa1c571f9d201c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 158 | Mon_.mul_rightUnitor | Mathlib/CategoryTheory/Monoidal/Mon_.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>CategoryTheory.Category.id_comp</a> M.mul, ← <a>CategoryTheory.Category.comp_id</a> (λ_ (𝟙_ C)).<a>CategoryTheory.Iso.hom</a>, <a>CategoryTheory.MonoidalCategory.tensor_comp</a>] | C : Type u₁
inst✝² : Category.{v₁, u₁} C
inst✝¹ : MonoidalCategory C
inst✝ : BraidedCategory C
M : Mon_ C
⊢ (tensor_μ C (M.X, 𝟙_ C) (M.X, 𝟙_ C) ≫ (M.mul ⊗ (λ_ (𝟙_ C)).hom)) ≫ (ρ_ M.X).hom =
((ρ_ M.X).hom ⊗ (ρ_ M.X).hom) ≫ M.mul | C : Type u₁
inst✝² : Category.{v₁, u₁} C
inst✝¹ : MonoidalCategory C
inst✝ : BraidedCategory C
M : Mon_ C
⊢ (tensor_μ C (M.X, 𝟙_ C) (M.X, 𝟙_ C) ≫ (𝟙 (M.X ⊗ M.X) ⊗ (λ_ (𝟙_ C)).hom) ≫ (M.mul ⊗ 𝟙 (𝟙_ C))) ≫ (ρ_ M.X).hom =
((ρ_ M.X).hom ⊗ (ρ_ M.X).hom) ≫ 𝟙 (M.X ⊗ M.X) ≫ M.mul | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.252606) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.252606) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.252606) (:fv _uniq.252609))) ((:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:fv _uniq.252606) (:fv _uniq.252609) ((:c CategoryTheory.MonoidalCate... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.252606))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.MonoidalCategory) (:fv _uniq.252606) (:fv _uniq.252609))"},{"name":"inst✝","sexp":"((:c CategoryTheory.BraidedCategory) (:fv _uniq.252606) (:fv _uniq.252609) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252606","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252609","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Catego... | {"children":[{"source":"rw","sourceEnd":17085,"sourceStart":17083,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":17087,"sourceStart":17086,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":17090,"sourceSt... | [] | [{"source":"Category.id_comp M.mul","source_end":17113,"source_start":17091,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Category.comp_id (λ_ (𝟙_ C)).hom","source_end":17155,"source_start":17119,"syntax_kind":"Lean.Parser.Term.app"},{"source":"tensor_comp","source_end":17168,"source_start":17157,"syntax_kind":"ide... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252606","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252609","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 102 | 4 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5be57d8fdd1dbb1db3716a614fcd39017eac47780c08d340173eda9a71f0f79d | 54e83257873e11538df43030900ebf35a274a42f936e291b61fb8a8d77c91831 | cfe1e0a6c32d7c4b164b643f7bbe767dfa12eacc2a6a02997d231373187c41b6 | d3617d8658476b481b6b3bd7ac9d91c1f09279ec7fca388f09387d9db2a4ce44 |
cat-searcher/leandojo-benchmark-4-random | test | 159 | Mon_.mul_rightUnitor | Mathlib/CategoryTheory/Monoidal/Mon_.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>CategoryTheory.MonoidalCategory.tensorHom_id</a>, <a>CategoryTheory.MonoidalCategory.id_tensorHom</a>] | C : Type u₁
inst✝² : Category.{v₁, u₁} C
inst✝¹ : MonoidalCategory C
inst✝ : BraidedCategory C
M : Mon_ C
⊢ (tensor_μ C (M.X, 𝟙_ C) (M.X, 𝟙_ C) ≫ (𝟙 (M.X ⊗ M.X) ⊗ (λ_ (𝟙_ C)).hom) ≫ (M.mul ⊗ 𝟙 (𝟙_ C))) ≫ (ρ_ M.X).hom =
((ρ_ M.X).hom ⊗ (ρ_ M.X).hom) ≫ 𝟙 (M.X ⊗ M.X) ≫ M.mul | C : Type u₁
inst✝² : Category.{v₁, u₁} C
inst✝¹ : MonoidalCategory C
inst✝ : BraidedCategory C
M : Mon_ C
⊢ (tensor_μ C (M.X, 𝟙_ C) (M.X, 𝟙_ C) ≫ (M.X ⊗ M.X) ◁ (λ_ (𝟙_ C)).hom ≫ M.mul ▷ 𝟙_ C) ≫ (ρ_ M.X).hom =
((ρ_ M.X).hom ⊗ (ρ_ M.X).hom) ≫ 𝟙 (M.X ⊗ M.X) ≫ M.mul | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.252606) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.252606) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.252606) (:fv _uniq.252609))) ((:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:fv _uniq.252606) (:fv _uniq.252609) ((:c CategoryTheory.MonoidalCate... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.252606))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.MonoidalCategory) (:fv _uniq.252606) (:fv _uniq.252609))"},{"name":"inst✝","sexp":"((:c CategoryTheory.BraidedCategory) (:fv _uniq.252606) (:fv _uniq.252609) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252606","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252609","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Catego... | {"children":[{"source":"simp","sourceEnd":17176,"sourceStart":17172,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":17181,"sourceStart":17177,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":171... | [] | [{"source":"tensorHom_id","source_end":17195,"source_start":17183,"syntax_kind":"ident"},{"source":"id_tensorHom","source_end":17209,"source_start":17197,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252606","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252609","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 102 | 9 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dea9346259c1638d4212948b2572d3c4706c859c20a97d8a1048345749dc2d5a | d3617d8658476b481b6b3bd7ac9d91c1f09279ec7fca388f09387d9db2a4ce44 | 935edbc455af8cad19564368bda16bc6841f90cdfcf0bd1078f9b875fe2a5688 | ef0092f01900f3ecb2d4a92a9d5cfb4024dae3adb89b5ca3253f8fbacd5de776 |
cat-searcher/leandojo-benchmark-4-random | test | 160 | Mon_.mul_rightUnitor | Mathlib/CategoryTheory/Monoidal/Mon_.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | slice_lhs 3 4 => rw [<a>CategoryTheory.MonoidalCategory.rightUnitor_naturality</a>] | C : Type u₁
inst✝² : Category.{v₁, u₁} C
inst✝¹ : MonoidalCategory C
inst✝ : BraidedCategory C
M : Mon_ C
⊢ (tensor_μ C (M.X, 𝟙_ C) (M.X, 𝟙_ C) ≫ (M.X ⊗ M.X) ◁ (λ_ (𝟙_ C)).hom ≫ M.mul ▷ 𝟙_ C) ≫ (ρ_ M.X).hom =
((ρ_ M.X).hom ⊗ (ρ_ M.X).hom) ≫ 𝟙 (M.X ⊗ M.X) ≫ M.mul | C : Type u₁
inst✝² : Category.{v₁, u₁} C
inst✝¹ : MonoidalCategory C
inst✝ : BraidedCategory C
M : Mon_ C
⊢ tensor_μ C (M.X, 𝟙_ C) (M.X, 𝟙_ C) ≫ (M.X ⊗ M.X) ◁ (λ_ (𝟙_ C)).hom ≫ (ρ_ (M.X ⊗ M.X)).hom ≫ M.mul =
((ρ_ M.X).hom ⊗ (ρ_ M.X).hom) ≫ 𝟙 (M.X ⊗ M.X) ≫ M.mul | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.252606) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.252606) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.252606) (:fv _uniq.252609))) ((:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:fv _uniq.252606) (:fv _uniq.252609) ((:c CategoryTheory.MonoidalCate... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.252606))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.MonoidalCategory) (:fv _uniq.252606) (:fv _uniq.252609))"},{"name":"inst✝","sexp":"((:c CategoryTheory.BraidedCategory) (:fv _uniq.252606) (:fv _uniq.252609) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252606","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252609","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Catego... | {"children":[{"source":"slice_lhs","sourceEnd":17222,"sourceStart":17213,"tag":"atom"},{"children":[{"source":"3","sourceEnd":17224,"sourceStart":17223,"tag":"atom"}],"kind":"num","source":"3","sourceEnd":17224,"sourceStart":17223,"tag":"node"},{"children":[{"source":"4","sourceEnd":17226,"sourceStart":17225,"tag":"ato... | [] | [{"source":"rightUnitor_naturality","source_end":17256,"source_start":17234,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252606","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252609","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 102 | 10 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b5e2d26096d0cfcd01a95c7712d551f2b4a0a3922b94558be4f6eb1b35eac998 | ef0092f01900f3ecb2d4a92a9d5cfb4024dae3adb89b5ca3253f8fbacd5de776 | c5f8453b2cabb44b68d172bdfc15d64ca09f7c2aae4d9789ab9dd261f7bb1c99 | 78657b2537c8051a755cdb3a5e70d44af27118bdccc97fc9d4948a7e1ed39fc1 |
cat-searcher/leandojo-benchmark-4-random | test | 161 | Mon_.mul_rightUnitor | Mathlib/CategoryTheory/Monoidal/Mon_.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | slice_lhs 1 3 => rw [← <a>CategoryTheory.rightUnitor_monoidal</a>] | C : Type u₁
inst✝² : Category.{v₁, u₁} C
inst✝¹ : MonoidalCategory C
inst✝ : BraidedCategory C
M : Mon_ C
⊢ tensor_μ C (M.X, 𝟙_ C) (M.X, 𝟙_ C) ≫ (M.X ⊗ M.X) ◁ (λ_ (𝟙_ C)).hom ≫ (ρ_ (M.X ⊗ M.X)).hom ≫ M.mul =
((ρ_ M.X).hom ⊗ (ρ_ M.X).hom) ≫ 𝟙 (M.X ⊗ M.X) ≫ M.mul | C : Type u₁
inst✝² : Category.{v₁, u₁} C
inst✝¹ : MonoidalCategory C
inst✝ : BraidedCategory C
M : Mon_ C
⊢ ((ρ_ M.X).hom ⊗ (ρ_ M.X).hom) ≫ M.mul = ((ρ_ M.X).hom ⊗ (ρ_ M.X).hom) ≫ 𝟙 (M.X ⊗ M.X) ≫ M.mul | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.252606) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.252606) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.252606) (:fv _uniq.252609))) ((:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:fv _uniq.252606) (:fv _uniq.252609) ((:c CategoryTheory.MonoidalCate... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.252606))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.MonoidalCategory) (:fv _uniq.252606) (:fv _uniq.252609))"},{"name":"inst✝","sexp":"((:c CategoryTheory.BraidedCategory) (:fv _uniq.252606) (:fv _uniq.252609) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252606","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252609","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Catego... | {"children":[{"source":"slice_lhs","sourceEnd":17269,"sourceStart":17260,"tag":"atom"},{"children":[{"source":"1","sourceEnd":17271,"sourceStart":17270,"tag":"atom"}],"kind":"num","source":"1","sourceEnd":17271,"sourceStart":17270,"tag":"node"},{"children":[{"source":"3","sourceEnd":17273,"sourceStart":17272,"tag":"ato... | [] | [{"source":"rightUnitor_monoidal","source_end":17305,"source_start":17285,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252606","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252609","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 102 | 15 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7e361cf958f23f9a13af2e0bc4fe0e0c45626c16d4dbdfddedd21a41d6b1c4e1 | 78657b2537c8051a755cdb3a5e70d44af27118bdccc97fc9d4948a7e1ed39fc1 | fb575e013450138ab84c23c0d9b755fb709f92e01baf08664390142a2c6b31c8 | 7f4f601e2d1f44e6505b13b22004197dc8066c954a22f027159a0c22a2307934 |
cat-searcher/leandojo-benchmark-4-random | test | 162 | Mon_.mul_rightUnitor | Mathlib/CategoryTheory/Monoidal/Mon_.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>CategoryTheory.Category.assoc</a>, <a>CategoryTheory.Category.id_comp</a>] | C : Type u₁
inst✝² : Category.{v₁, u₁} C
inst✝¹ : MonoidalCategory C
inst✝ : BraidedCategory C
M : Mon_ C
⊢ ((ρ_ M.X).hom ⊗ (ρ_ M.X).hom) ≫ M.mul = ((ρ_ M.X).hom ⊗ (ρ_ M.X).hom) ≫ 𝟙 (M.X ⊗ M.X) ≫ M.mul | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.252606) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.252606) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.252606) (:fv _uniq.252609))) ((:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:fv _uniq.252606) (:fv _uniq.252609) ((:c CategoryTheory.MonoidalCate... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.252606))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.MonoidalCategory) (:fv _uniq.252606) (:fv _uniq.252609))"},{"name":"inst✝","sexp":"((:c CategoryTheory.BraidedCategory) (:fv _uniq.252606) (:fv _uniq.252609) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252606","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252609","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Catego... | {"children":[{"source":"simp","sourceEnd":17313,"sourceStart":17309,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":17318,"sourceStart":17314,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":173... | [] | [{"source":"Category.assoc","source_end":17334,"source_start":17320,"syntax_kind":"ident"},{"source":"Category.id_comp","source_end":17352,"source_start":17336,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252606","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252609","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 102 | 20 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a31dd8a82b051b305fd462794bc7e03071217195bc4bd3b7e21e7371665522ec | 7f4f601e2d1f44e6505b13b22004197dc8066c954a22f027159a0c22a2307934 | 0306510acf02b9f184724c6aeb74438f622fa6a695b540dc6d77b6614440842f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 163 | slope_vadd_const | Mathlib/LinearAlgebra/AffineSpace/Slope.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext a b | k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → E
c : PE
⊢ (slope fun x => f x +ᵥ c) = slope f | case h.h
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → E
c : PE
a b : k
⊢ slope (fun x => f x +ᵥ c) a b = slope f a b | ((:c Eq) (:forall a (:fv _uniq.18059) (:forall b (:fv _uniq.18059) (:fv _uniq.18062))) ((:c slope) (:fv _uniq.18059) (:fv _uniq.18062) (:fv _uniq.18065) (:fv _uniq.18068) (:fv _uniq.18071) (:fv _uniq.18509) (:fv _uniq.18595) (:lambda x (:fv _uniq.18059) ((:c HVAdd.hVAdd) (:fv _uniq.18062) (:fv _uniq.18065) (:fv _uniq.1... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"PE","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.18059))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.18062))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.18059) (:fv _uniq.18062) (... | (:app (:c Eq) (:arg :implicit-type 0 (:forall a :explicit (:fv FV0) (:forall b :explicit (:fv FV0) (:fv FV1)))) (:arg :explicit 1 (:app (:c slope) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18059","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18062","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"ext","sourceEnd":2479,"sourceStart":2476,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":2481,"sourceStart":2480,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"a","sourceEnd":2481,"sourceStart":2480,"tag":"nod... | [{"role":"fresh_name","source":"a","source_end":2481,"source_start":2480,"syntax_kind":"ident"},{"role":"fresh_name","source":"b","source_end":2483,"source_start":2482,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18059","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18062","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 20 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 204c73f892b0bf1cbf8cf827f20726fe13d153898ebd3c93b2549a437add541d | 911e9604247aff9524444ba1cbc97c75b171c2e2d4743f66cc7c94fb28a6378a | 9e460b8412bcd9fec0be30b72cc1b4e751cbf2fef52fe51c81ae9f5d8ec8aa29 | 315733ab77e0eedf04a650d0223e95a614f6cf172aaa803f359483b49fba7f8c |
cat-searcher/leandojo-benchmark-4-random | test | 164 | slope_vadd_const | Mathlib/LinearAlgebra/AffineSpace/Slope.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>slope</a>, <a>vadd_vsub_vadd_cancel_right</a>, <a>vsub_eq_sub</a>] | case h.h
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → E
c : PE
a b : k
⊢ slope (fun x => f x +ᵥ c) a b = slope f a b | ((:c Eq) (:fv _uniq.18062) ((:c slope) (:fv _uniq.18059) (:fv _uniq.18062) (:fv _uniq.18065) (:fv _uniq.18068) (:fv _uniq.18071) (:fv _uniq.18509) (:fv _uniq.18595) (:lambda x (:fv _uniq.18059) ((:c HVAdd.hVAdd) (:fv _uniq.18062) (:fv _uniq.18065) (:fv _uniq.18065) ((:c instHVAdd) (:fv _uniq.18062) (:fv _uniq.18065) ((... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"PE","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.18059))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.18062))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.18059) (:fv _uniq.18062) (... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c slope) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c AddCommGroup... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18059","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18062","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":2490,"sourceStart":2486,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":2495,"sourceStart":2491,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":2495,"s... | [] | [{"source":"slope","source_end":2502,"source_start":2497,"syntax_kind":"ident"},{"source":"vadd_vsub_vadd_cancel_right","source_end":2531,"source_start":2504,"syntax_kind":"ident"},{"source":"vsub_eq_sub","source_end":2544,"source_start":2533,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18059","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18062","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 20 | 5 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 48396abe843ef7b02f3f8c1b779e36e705d826933059c8068a3a4ef4592901a7 | 315733ab77e0eedf04a650d0223e95a614f6cf172aaa803f359483b49fba7f8c | fa92946f88bde0af0ea3486489c210efbfadbd760c4346174cff29e7aba95d01 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 165 | Set.le_chainHeight_add_nat_iff | Mathlib/Order/Height.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [← <a>tsub_le_iff_right</a>, ← <a>ENat.coe_sub</a>, (<a>Set.le_chainHeight_TFAE</a> s (n - m)).<a>List.TFAE.out</a> 0 2] | α : Type u_1
β : Type u_2
inst✝¹ : LT α
inst✝ : LT β
s t : Set α
l : List α
a : α
n m : ℕ
⊢ ↑n ≤ s.chainHeight + ↑m ↔ ∃ l ∈ s.subchain, n ≤ l.length + m | ((:c Iff) ((:c LE.le) (:c ENat) ((:c Preorder.toLE) (:c ENat) ((:c PartialOrder.toPreorder) (:c ENat) ((:c OrderedSemiring.toPartialOrder) (:c ENat) ((:c OrderedCommSemiring.toOrderedSemiring) (:c ENat) ((:c CanonicallyOrderedCommSemiring.toOrderedCommSemiring) (:c ENat) (:c instENatCanonicallyOrderedCommSemiring))))))... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c LT) (:fv _uniq.9803))"},{"name":"inst✝","sexp":"((:c LT) (:fv _uniq.9806))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.9803))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.9803))"},{"name":"l","sexp":"((:c List) (... | (:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c ENat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENat))))) (:arg :explicit 2 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c ENat)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c ENat))))) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9803","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9806","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":6571,"sourceStart":6564,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6573,"sourceStart":6572,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{... | [] | [{"source":"tsub_le_iff_right","source_end":6594,"source_start":6577,"syntax_kind":"ident"},{"source":"ENat.coe_sub","source_end":6612,"source_start":6600,"syntax_kind":"ident"},{"source":"(le_chainHeight_TFAE s (n - m)).out 0 2","source_end":6653,"source_start":6614,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9803","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9806","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 42 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 02c5e3f6c9d2c3a7a19bf61860710d8b2c164a4cfb291a5f0a9dcd2db0b31592 | 86913690ecd4acf35bd7154891aef09b108f1ae1a137009a137b456b2c44945a | b74419dff0a34ad107008e4d9e2e35f20b43d39de19bab5e9a17ad27499843ec | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 166 | antisymm_iff | Mathlib/Order/RelClasses.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro rfl | α : Type u
β : Type v
r : α → α → Prop
s : β → β → Prop
inst✝¹ : IsRefl α r
inst✝ : IsAntisymm α r
a b : α
⊢ a = b → r a b ∧ r b a | α : Type u
β : Type v
r : α → α → Prop
s : β → β → Prop
inst✝¹ : IsRefl α r
inst✝ : IsAntisymm α r
a : α
⊢ r a a ∧ r a a | (:forall _ ((:c Eq) (:fv _uniq.408) (:fv _uniq.443) (:fv _uniq.444)) ((:c And) ((:fv _uniq.416) (:fv _uniq.443) (:fv _uniq.444)) ((:fv _uniq.416) (:fv _uniq.444) (:fv _uniq.443)))) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.408) (:forall _ (:fv _uniq.408) (:sort 0)))"},{"name":"s","sexp":"(:forall _ (:fv _uniq.410) (:forall _ (:fv _uniq.410) (:sort 0)))"},{"name":"inst✝¹","sexp":"((:c IsRefl) (:fv _uniq.408) (:fv _uniq.41... | (:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:fv FV8))) (:app (:c And) (:arg :explicit 0 (:app (:fv FV2) (:arg :explicit 0 (:fv FV7)) (:arg :explicit 1 (:fv FV8)))) (:arg :explicit 1 (:app (:fv FV2) (:arg :explicit 0 (:fv FV8)) (:arg :explicit 1 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.408","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.410","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","context... | {"children":[{"source":"rintro","sourceEnd":1330,"sourceStart":1324,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":1334,"sourceStart":1331,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl","sourceEnd":1334,"sourceStart":1331,"ta... | [] | [{"source":"rfl","source_end":1334,"source_start":1331,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.408","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.410","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.4... | 11 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 63ecf2e4dab45c0b4c0f50e53c5584d440943e7ffee58889001b6226c6fb548b | 0e7cd385c9c8470ccf6f6bdfff0a14b7b07711b1b5b9844e55f3e1b9c2aff926 | 09e128cd6787f35d3c063b643315aff1382388dafa4e55b6546fbf9dcecb02da | 80eddc9c8923491c1138615d8e38f4a7aeec0569fbb562d8b8c9796ea8a15caa |
cat-searcher/leandojo-benchmark-4-random | test | 167 | antisymm_iff | Mathlib/Order/RelClasses.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨<a>refl</a> _, <a>refl</a> _⟩ | α : Type u
β : Type v
r : α → α → Prop
s : β → β → Prop
inst✝¹ : IsRefl α r
inst✝ : IsAntisymm α r
a : α
⊢ r a a ∧ r a a | ((:c And) ((:fv _uniq.416) (:fv _uniq.443) (:fv _uniq.443)) ((:fv _uniq.416) (:fv _uniq.443) (:fv _uniq.443))) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.408) (:forall _ (:fv _uniq.408) (:sort 0)))"},{"name":"s","sexp":"(:forall _ (:fv _uniq.410) (:forall _ (:fv _uniq.410) (:sort 0)))"},{"name":"inst✝¹","sexp":"((:c IsRefl) (:fv _uniq.408) (:fv _uniq.41... | (:app (:c And) (:arg :explicit 0 (:app (:fv FV2) (:arg :explicit 0 (:fv FV7)) (:arg :explicit 1 (:fv FV7)))) (:arg :explicit 1 (:app (:fv FV2) (:arg :explicit 0 (:fv FV7)) (:arg :explicit 1 (:fv FV7))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.408","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.410","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","context... | {"children":[{"source":"exact","sourceEnd":1344,"sourceStart":1339,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":1348,"sourceStart":1345,"tag":"atom"},{"children":[{"children":[{"name":"refl","semanticRole":"global","source":"refl","sourceEnd":1352,"sourceStart":1348,"tag":"identifier"},{"children":[{"children":... | [] | [{"source":"⟨refl _, refl _⟩","source_end":1365,"source_start":1345,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.408","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.410","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.4... | 11 | 5 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9756d474abd349ff9155b0288c611d64e0bb033cefcff54f47705b9309ebd4d1 | 80eddc9c8923491c1138615d8e38f4a7aeec0569fbb562d8b8c9796ea8a15caa | 4b235765a5c0024f758dbc38b2e1fccc73f2bc5bf0b1e83053ba398cfddf9b5d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 168 | Finpartition.parts_top_subset | Mathlib/Order/Partition/Finpartition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro b hb | α : Type u_1
inst✝² : Lattice α
inst✝¹ : OrderBot α
a✝ : α
P : Finpartition a✝
a : α
inst✝ : Decidable (a = ⊥)
⊢ ⊤.parts ⊆ {a} | α : Type u_1
inst✝² : Lattice α
inst✝¹ : OrderBot α
a✝ : α
P : Finpartition a✝
a : α
inst✝ : Decidable (a = ⊥)
b : α
hb : b ∈ ⊤.parts
⊢ b ∈ {a} | ((:c HasSubset.Subset) ((:c Finset) (:fv _uniq.31865)) ((:c Finset.instHasSubset) (:fv _uniq.31865)) ((:c Finpartition.parts) (:fv _uniq.31865) (:fv _uniq.31868) (:fv _uniq.32034) (:fv _uniq.32628) ((:c Top.top) ((:c Finpartition) (:fv _uniq.31865) (:fv _uniq.31868) (:fv _uniq.32034) (:fv _uniq.32628)) ((:c OrderTop.to... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c Lattice) (:fv _uniq.31865))"},{"name":"inst✝¹","sexp":"((:c OrderBot) (:fv _uniq.31865) ((:c Preorder.toLE) (:fv _uniq.31865) ((:c PartialOrder.toPreorder) (:fv _uniq.31865) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.31865) ((:c Lattice.toSemila... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:c Finpartition.parts) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31865","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31868","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Lattice) (:arg :explici... | {"children":[{"source":"intro","sourceEnd":10177,"sourceStart":10172,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"b","sourceEnd":10179,"sourceStart":10178,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hb","sourceEnd":10182,"sourceStart":10180,"tag":"identifier"}],"kind":"null","sou... | [{"role":"fresh_name","source":"b","source_end":10179,"source_start":10178,"syntax_kind":"ident"},{"role":"fresh_name","source":"hb","source_end":10182,"source_start":10180,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31865","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31868","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":... | 53 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ad2b2623ea3d776b774e8376f9e6cff0b2fd836e744da850628c33468a877d68 | e4342b619ec2047c13e493fb8da1cc9275fea90ed1693a4ca6f4abe409e20a6e | 2da7d8a2d234f34d6eefcdb206321e10a59f20aa70d4e73cedddb133aa95b27d | 80a63e21c5b8eb598287cdee11b552385451b3180671f7d0d6f3cbfec5ff44ee |
cat-searcher/leandojo-benchmark-4-random | test | 169 | Finpartition.parts_top_subset | Mathlib/Order/Partition/Finpartition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hb : b ∈ <a>Finpartition.parts</a> (<a>dite</a> _ _ _) := hb | α : Type u_1
inst✝² : Lattice α
inst✝¹ : OrderBot α
a✝ : α
P : Finpartition a✝
a : α
inst✝ : Decidable (a = ⊥)
b : α
hb : b ∈ ⊤.parts
⊢ b ∈ {a} | α : Type u_1
inst✝² : Lattice α
inst✝¹ : OrderBot α
a✝ : α
P : Finpartition a✝
a : α
inst✝ : Decidable (a = ⊥)
b : α
hb✝ : b ∈ ⊤.parts
hb : b ∈ (if ha : a = ⊥ then (Finpartition.empty α).copy ⋯ else indiscrete ha).parts
⊢ b ∈ {a} | ((:c Membership.mem) (:fv _uniq.31865) ((:c Finset) (:fv _uniq.31865)) ((:c Finset.instMembership) (:fv _uniq.31865)) (:fv _uniq.32631) ((:c Singleton.singleton) (:fv _uniq.31865) ((:c Finset) (:fv _uniq.31865)) ((:c Finset.instSingleton) (:fv _uniq.31865)) (:fv _uniq.32628))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c Lattice) (:fv _uniq.31865))"},{"name":"inst✝¹","sexp":"((:c OrderBot) (:fv _uniq.31865) ((:c Preorder.toLE) (:fv _uniq.31865) ((:c PartialOrder.toPreorder) (:fv _uniq.31865) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.31865) ((:c Lattice.toSemila... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV8)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31865","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31868","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Lattice) (:arg :explici... | {"children":[{"source":"have","sourceEnd":10189,"sourceStart":10185,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hb","sourceEnd":10192,"sourceStart":10190,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hb","sourceEnd":10192,"sourceStart":10190,"tag":"nod... | [] | [{"source":"b ∈ Finpartition.parts (dite _ _ _)","source_end":10232,"source_start":10195,"syntax_kind":"«term_∈_»"},{"source":"hb","source_end":10238,"source_start":10236,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31865","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31868","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":... | 53 | 5 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 170b7bb6ddbf14ea402fbb5e82c78d3cfa490891db3d56dfbc60ae8e3f4ef4cb | 80a63e21c5b8eb598287cdee11b552385451b3180671f7d0d6f3cbfec5ff44ee | eea9303f40aa7fd0cd4012f81cbd257d33e29710ae4ca96f291647dd0c462a26 | 50762909b10f9610ae6bff8ab15f23ea6df79f091925101cd279680e5e560a16 |
cat-searcher/leandojo-benchmark-4-random | test | 170 | Finpartition.parts_top_subset | Mathlib/Order/Partition/Finpartition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split_ifs at hb | α : Type u_1
inst✝² : Lattice α
inst✝¹ : OrderBot α
a✝ : α
P : Finpartition a✝
a : α
inst✝ : Decidable (a = ⊥)
b : α
hb✝ : b ∈ ⊤.parts
hb : b ∈ (if ha : a = ⊥ then (Finpartition.empty α).copy ⋯ else indiscrete ha).parts
⊢ b ∈ {a} | case pos
α : Type u_1
inst✝² : Lattice α
inst✝¹ : OrderBot α
a✝ : α
P : Finpartition a✝
a : α
inst✝ : Decidable (a = ⊥)
b : α
hb✝ : b ∈ ⊤.parts
h✝ : a = ⊥
hb : b ∈ ((Finpartition.empty α).copy ⋯).parts
⊢ b ∈ {a}
case neg
α : Type u_1
inst✝² : Lattice α
inst✝¹ : OrderBot α
a✝ : α
P : Finpartition a✝
a : α
inst✝ : Decida... | ((:c Membership.mem) (:fv _uniq.31865) ((:c Finset) (:fv _uniq.31865)) ((:c Finset.instMembership) (:fv _uniq.31865)) (:fv _uniq.32631) ((:c Singleton.singleton) (:fv _uniq.31865) ((:c Finset) (:fv _uniq.31865)) ((:c Finset.instSingleton) (:fv _uniq.31865)) (:fv _uniq.32628))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c Lattice) (:fv _uniq.31865))"},{"name":"inst✝¹","sexp":"((:c OrderBot) (:fv _uniq.31865) ((:c Preorder.toLE) (:fv _uniq.31865) ((:c PartialOrder.toPreorder) (:fv _uniq.31865) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.31865) ((:c Lattice.toSemila... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV8)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31865","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31868","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Lattice) (:arg :explici... | {"children":[{"source":"split_ifs","sourceEnd":10250,"sourceStart":10241,"tag":"atom"},{"children":[{"children":[{"source":"at","sourceEnd":10253,"sourceStart":10251,"tag":"atom"},{"children":[{"children":[{"contextIndex":10,"semanticRole":"local","source":"hb","sourceEnd":10256,"sourceStart":10254,"tag":"identifier"}]... | [] | [{"source":"hb","source_end":10256,"source_start":10254,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31865","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31868","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":... | 53 | 6 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d8769494d509b9d5cb928cb0b6f302793913ae1f995705418dc6e88c95dbeca7 | 50762909b10f9610ae6bff8ab15f23ea6df79f091925101cd279680e5e560a16 | 160aa470a4ee210da48a35ffd96ff2903c2dd7e7c2fad968636b22a68a81a093 | 7b66d6af4421b9f681d3e84545b485268d30c9fa7161def5fd84cc819adee519 |
cat-searcher/leandojo-benchmark-4-random | test | 171 | Finpartition.parts_top_subset | Mathlib/Order/Partition/Finpartition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Finpartition.copy_parts</a>, <a>Finpartition.empty_parts</a>, <a>Finset.not_mem_empty</a>] at hb | case pos
α : Type u_1
inst✝² : Lattice α
inst✝¹ : OrderBot α
a✝ : α
P : Finpartition a✝
a : α
inst✝ : Decidable (a = ⊥)
b : α
hb✝ : b ∈ ⊤.parts
h✝ : a = ⊥
hb : b ∈ ((Finpartition.empty α).copy ⋯).parts
⊢ b ∈ {a} | ((:c Membership.mem) (:fv _uniq.31865) ((:c Finset) (:fv _uniq.31865)) ((:c Finset.instMembership) (:fv _uniq.31865)) (:fv _uniq.32631) ((:c Singleton.singleton) (:fv _uniq.31865) ((:c Finset) (:fv _uniq.31865)) ((:c Finset.instSingleton) (:fv _uniq.31865)) (:fv _uniq.32628))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c Lattice) (:fv _uniq.31865))"},{"name":"inst✝¹","sexp":"((:c OrderBot) (:fv _uniq.31865) ((:c Preorder.toLE) (:fv _uniq.31865) ((:c PartialOrder.toPreorder) (:fv _uniq.31865) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.31865) ((:c Lattice.toSemila... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV8)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31865","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31868","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Lattice) (:arg :explici... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":10266,"sourceStart":10262,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":10271,"sourceStart":10267,"tag":"atom"}],"kind"... | [] | [{"source":"copy_parts","source_end":10283,"source_start":10273,"syntax_kind":"ident"},{"source":"empty_parts","source_end":10296,"source_start":10285,"syntax_kind":"ident"},{"source":"not_mem_empty","source_end":10311,"source_start":10298,"syntax_kind":"ident"},{"source":"hb","source_end":10318,"source_start":10316,"s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31865","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31868","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":... | 53 | 9 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3f671ac59439a95c9e682b95f2f87d3b0e64097317929d5273dcc0b2455ff07a | cd8093c6bfd425143be38a2b0dc7e85d2a86145b1121fcf94cc8b2959d35798e | b891e1c67a520cca981a38d73841637668a4b96c604846e3133a58d89a2b0eb4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 172 | Finpartition.parts_top_subset | Mathlib/Order/Partition/Finpartition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hb | case neg
α : Type u_1
inst✝² : Lattice α
inst✝¹ : OrderBot α
a✝ : α
P : Finpartition a✝
a : α
inst✝ : Decidable (a = ⊥)
b : α
hb✝ : b ∈ ⊤.parts
h✝ : ¬a = ⊥
hb : b ∈ (indiscrete h✝).parts
⊢ b ∈ {a} | ((:c Membership.mem) (:fv _uniq.31865) ((:c Finset) (:fv _uniq.31865)) ((:c Finset.instMembership) (:fv _uniq.31865)) (:fv _uniq.32631) ((:c Singleton.singleton) (:fv _uniq.31865) ((:c Finset) (:fv _uniq.31865)) ((:c Finset.instSingleton) (:fv _uniq.31865)) (:fv _uniq.32628))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c Lattice) (:fv _uniq.31865))"},{"name":"inst✝¹","sexp":"((:c OrderBot) (:fv _uniq.31865) ((:c Preorder.toLE) (:fv _uniq.31865) ((:c PartialOrder.toPreorder) (:fv _uniq.31865) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.31865) ((:c Lattice.toSemila... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV8)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31865","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31868","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Lattice) (:arg :explici... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":10329,"sourceStart":10324,"tag":"atom"},{"contextIndex":11,"semanticRole":"local","source":"hb","sourceEnd":10332,"sourceStart":10330,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact hb","sourceEnd":10332,"sourceStar... | [] | [{"source":"hb","source_end":10332,"source_start":10330,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31865","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.31868","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":... | 53 | 14 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ae3393c94d111e36fffddccd96ccd984ad2e68a2857ada7421f4bbb6f6c40ab2 | fda72cc8506d5f2159713a176e0d348db672c16d3b01a234833a994b134377b2 | 7a0f23d30a770b19acb7e119bb304f8b5fef2610a3d533e9674c1b18c455a21b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 173 | CategoryTheory.Functor.quasiIso'_of_map_quasiIso' | Mathlib/Algebra/Homology/QuasiIso.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>CategoryTheory.Functor.comp_map</a>, ← <a>CategoryTheory.NatIso.naturality_2</a> (F.homology'FunctorIso i) f, <a>CategoryTheory.Functor.comp_map</a>] | ι : Type u_1
V : Type u
inst✝¹⁴ : Category.{v, u} V
inst✝¹³ : HasZeroMorphisms V
inst✝¹² : HasZeroObject V
inst✝¹¹ : HasEqualizers V
inst✝¹⁰ : HasImages V
inst✝⁹ : HasImageMaps V
inst✝⁸ : HasCokernels V
c : ComplexShape ι
C✝ D✝ E : HomologicalComplex V c
A : Type u_2
inst✝⁷ : Category.{u_4, u_2} A
inst✝⁶ : Abelian A
B ... | ι : Type u_1
V : Type u
inst✝¹⁴ : Category.{v, u} V
inst✝¹³ : HasZeroMorphisms V
inst✝¹² : HasZeroObject V
inst✝¹¹ : HasEqualizers V
inst✝¹⁰ : HasImages V
inst✝⁹ : HasImageMaps V
inst✝⁸ : HasCokernels V
c : ComplexShape ι
C✝ D✝ E : HomologicalComplex V c
A : Type u_2
inst✝⁷ : Category.{u_4, u_2} A
inst✝⁶ : Abelian A
B ... | ((:c CategoryTheory.IsIso) (:fv _uniq.90759) (:fv _uniq.90763) ((:c Prefunctor.obj) (:fv _uniq.90737) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.90737) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.90737) (:fv _uniq.90741))) (:fv _uniq.90759) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _u... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.90565))"},{"name":"inst✝¹³","sexp":"((:c CategoryTheory.Limits.HasZeroMorphisms) (:fv _uniq.90565) (:fv _uniq.90568))"},{"name":"inst✝¹²","sexp":"((:c CategoryTheory.Limits.H... | (:app (:c CategoryTheory.IsIso) (:arg :implicit-type 0 (:fv FV16)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV16))))) (:arg :implicit 2) (:arg :implicit 3) (:arg :explicit 4 (:app (:c Prefunctor.map) (:arg :implicit-type 0 (:fv FV13)) (:arg :instance 1 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90563","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.90565","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":9393,"sourceStart":9391,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9395,"sourceStart":9394,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":9398,"sourceStart":... | [] | [{"source":"Functor.comp_map","source_end":9415,"source_start":9399,"syntax_kind":"ident"},{"source":"NatIso.naturality_2 (F.homology'FunctorIso i) f","source_end":9468,"source_start":9421,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Functor.comp_map","source_end":9486,"source_start":9470,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90563","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.90565","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 61 | 4 | exact | true | 1 | 29 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1d9593e1b4c271f976a33935a5b52fce39b6336164c66d2069bbb464e6f0c263 | da3bf773a2092e2d5300051185cd0d185d257b8165032d3d6726d337b14c5cf7 | d6a61456a5ef7001db60dab0dee5eb41f5d5b5a294f048923cde9bedc7af838e | 1ad1fa45a1a3f0918b76101e419736cd864cdf8e3ec2402458d6b85d0e20f54e |
cat-searcher/leandojo-benchmark-4-random | test | 174 | CategoryTheory.Functor.quasiIso'_of_map_quasiIso' | Mathlib/Algebra/Homology/QuasiIso.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | infer_instance | ι : Type u_1
V : Type u
inst✝¹⁴ : Category.{v, u} V
inst✝¹³ : HasZeroMorphisms V
inst✝¹² : HasZeroObject V
inst✝¹¹ : HasEqualizers V
inst✝¹⁰ : HasImages V
inst✝⁹ : HasImageMaps V
inst✝⁸ : HasCokernels V
c : ComplexShape ι
C✝ D✝ E : HomologicalComplex V c
A : Type u_2
inst✝⁷ : Category.{u_4, u_2} A
inst✝⁶ : Abelian A
B ... | ((:c CategoryTheory.IsIso) (:fv _uniq.90759) (:fv _uniq.90763) ((:c Prefunctor.obj) (:fv _uniq.90737) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.90737) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.90737) (:fv _uniq.90741))) (:fv _uniq.90759) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _u... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.90565))"},{"name":"inst✝¹³","sexp":"((:c CategoryTheory.Limits.HasZeroMorphisms) (:fv _uniq.90565) (:fv _uniq.90568))"},{"name":"inst✝¹²","sexp":"((:c CategoryTheory.Limits.H... | (:app (:c CategoryTheory.IsIso) (:arg :implicit-type 0 (:fv FV16)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV16))))) (:arg :implicit 2) (:arg :implicit 3) (:arg :explicit 4 (:app (:c CategoryTheory.CategoryStruct.comp) (:arg :implicit-type 0 (:fv FV16)) (:arg :instance ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90563","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.90565","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"infer_instance","sourceEnd":9508,"sourceStart":9494,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticInfer_instance","source":"infer_instance","sourceEnd":9508,"sourceStart":9494,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90563","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.90565","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 61 | 9 | exact | true | 1 | 29 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 65693a7b71f74789c8958f0399a66f68a5d490038d41710807e51e6d24d3e0a9 | 1ad1fa45a1a3f0918b76101e419736cd864cdf8e3ec2402458d6b85d0e20f54e | 1be023dbb859162463cfcba2e9fc80f1c85bab9d31edeb816d1518206e2b70fa | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 175 | MeasureTheory.IsFundamentalDomain.essSup_measure_restrict | Mathlib/MeasureTheory/Group/FundamentalDomain.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>le_antisymm</a> (<a>essSup_mono_measure'</a> <a>MeasureTheory.Measure.restrict_le_self</a>) ?_ | G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
E : Type u_5
inst✝¹² : Group G
inst✝¹¹ : Group H
inst✝¹⁰ : MulAction G α
inst✝⁹ : MeasurableSpace α
inst✝⁸ : MulAction H β
inst✝⁷ : MeasurableSpace β
inst✝⁶ : NormedAddCommGroup E
s t : Set α
μ : Measure α
inst✝⁵ : MeasurableSpace G
inst✝⁴ : MeasurableSMul G α
inst✝³ ... | G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
E : Type u_5
inst✝¹² : Group G
inst✝¹¹ : Group H
inst✝¹⁰ : MulAction G α
inst✝⁹ : MeasurableSpace α
inst✝⁸ : MulAction H β
inst✝⁷ : MeasurableSpace β
inst✝⁶ : NormedAddCommGroup E
s t : Set α
μ : Measure α
inst✝⁵ : MeasurableSpace G
inst✝⁴ : MeasurableSMul G α
inst✝³ ... | ((:c Eq) (:c ENNReal) ((:c essSup) (:fv _uniq.403745) (:c ENNReal) ((:c ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice) (:c ENNReal) ((:c ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder) (:c ENNReal) ((:c CompleteLinearOrder.toConditionallyCompleteLinearOrderBot) (:c ENNReal) (:c... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"E","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹²","sexp":"((:c Group) (:fv _uniq.403739))"},{"name":"inst✝¹¹","sexp":"((:c Group) (:fv _uniq.403742))"}... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c essSup) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :instance 2 (:instance-of (:app (:c ConditionallyCompleteLattice) (:arg :explicit 0 (:c ENNReal))))) (:arg :implicit 3) (:arg :explicit 4 (:fv FV24)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":35570,"sourceStart":35564,"tag":"atom"},{"children":[{"name":"le_antisymm","semanticRole":"global","source":"le_antisymm","sourceEnd":35582,"sourceStart":35571,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":35584,"sourceStart":35583,"tag":"atom"},{"ch... | [] | [{"source":"le_antisymm (essSup_mono_measure' Measure.restrict_le_self) ?_","source_end":35633,"source_start":35571,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 138 | 4 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 43a8447d1bbe514df5ab82bacdbc3a7b82f4f7ee6a57a37da0e1677c2baf1e38 | 6f8d01f9846ecf09b382ac3624d5320ec181a232e479042e1fd8635d21a78b89 | 9aaf4b36eb78d7046f8ded67dac00b20412c789409aca3650cf77ea518da79fb | e6edf5ecc4b12f3905047650c601921d65a5a147421b5501159b76f1a4d11f97 |
cat-searcher/leandojo-benchmark-4-random | test | 176 | MeasureTheory.IsFundamentalDomain.essSup_measure_restrict | Mathlib/MeasureTheory/Group/FundamentalDomain.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>essSup_eq_sInf</a> (μ.restrict s) f, <a>essSup_eq_sInf</a> μ f] | G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
E : Type u_5
inst✝¹² : Group G
inst✝¹¹ : Group H
inst✝¹⁰ : MulAction G α
inst✝⁹ : MeasurableSpace α
inst✝⁸ : MulAction H β
inst✝⁷ : MeasurableSpace β
inst✝⁶ : NormedAddCommGroup E
s t : Set α
μ : Measure α
inst✝⁵ : MeasurableSpace G
inst✝⁴ : MeasurableSMul G α
inst✝³ ... | G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
E : Type u_5
inst✝¹² : Group G
inst✝¹¹ : Group H
inst✝¹⁰ : MulAction G α
inst✝⁹ : MeasurableSpace α
inst✝⁸ : MulAction H β
inst✝⁷ : MeasurableSpace β
inst✝⁶ : NormedAddCommGroup E
s t : Set α
μ : Measure α
inst✝⁵ : MeasurableSpace G
inst✝⁴ : MeasurableSMul G α
inst✝³ ... | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"E","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹²","sexp":"((:c Group) (:fv _uniq.403739))"},{"name":"inst✝¹¹","sexp":"((:c Group) (:fv _uniq.403742))"}... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c essSup) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :instance 2 (:instance-of (:app (:c ConditionallyCompleteLattice) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":35638,"sourceStart":35636,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":35640,"sourceStart":35639,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"ess... | [] | [{"source":"essSup_eq_sInf (μ.restrict s) f","source_end":35672,"source_start":35640,"syntax_kind":"Lean.Parser.Term.app"},{"source":"essSup_eq_sInf μ f","source_end":35693,"source_start":35674,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 138 | 5 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ec6d7e04ae132a1ee84c8d9936cc5e03b50a5dc67caefaeb6184fc6704cd5898 | e6edf5ecc4b12f3905047650c601921d65a5a147421b5501159b76f1a4d11f97 | 4a43c62c5b78be6c2279c4d3e8c6927f5b46def0f2b2a26c0a0e4870a94e3be3 | b248bf3716faa9c024b7f6cb505d17bbe3edebf8c160dbc7e0463f03cafac68d |
cat-searcher/leandojo-benchmark-4-random | test | 177 | MeasureTheory.IsFundamentalDomain.essSup_measure_restrict | Mathlib/MeasureTheory/Group/FundamentalDomain.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>sInf_le_sInf</a> ?_ | G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
E : Type u_5
inst✝¹² : Group G
inst✝¹¹ : Group H
inst✝¹⁰ : MulAction G α
inst✝⁹ : MeasurableSpace α
inst✝⁸ : MulAction H β
inst✝⁷ : MeasurableSpace β
inst✝⁶ : NormedAddCommGroup E
s t : Set α
μ : Measure α
inst✝⁵ : MeasurableSpace G
inst✝⁴ : MeasurableSMul G α
inst✝³ ... | G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
E : Type u_5
inst✝¹² : Group G
inst✝¹¹ : Group H
inst✝¹⁰ : MulAction G α
inst✝⁹ : MeasurableSpace α
inst✝⁸ : MulAction H β
inst✝⁷ : MeasurableSpace β
inst✝⁶ : NormedAddCommGroup E
s t : Set α
μ : Measure α
inst✝⁵ : MeasurableSpace G
inst✝⁴ : MeasurableSMul G α
inst✝³ ... | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"E","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹²","sexp":"((:c Group) (:fv _uniq.403739))"},{"name":"inst✝¹¹","sexp":"((:c Group) (:fv _uniq.403742))"}... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c InfSet.sInf) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c InfSet) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":35703,"sourceStart":35697,"tag":"atom"},{"children":[{"name":"sInf_le_sInf","semanticRole":"global","source":"sInf_le_sInf","sourceEnd":35716,"sourceStart":35704,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":35718,"sourceStart":35717,"tag":"atom"},{"... | [] | [{"source":"sInf_le_sInf ?_","source_end":35719,"source_start":35704,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 138 | 9 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 50a242b9dc62a0cad9c163187c605b923fc8cdd6528bf781bb1c4e6c59f84c6d | b248bf3716faa9c024b7f6cb505d17bbe3edebf8c160dbc7e0463f03cafac68d | 434684b94cdd5c599bd03e7fc42e1f8de6ae9cb8de297d9d65c2853eee9b70c1 | 50b896e8d9d275be1e367f55c583081b57d8d3d60d3c40cc4c2a558a0bb8b12c |
cat-searcher/leandojo-benchmark-4-random | test | 178 | MeasureTheory.IsFundamentalDomain.essSup_measure_restrict | Mathlib/MeasureTheory/Group/FundamentalDomain.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro a (ha : (μ.restrict s) {x : α | a < f x} = 0) | G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
E : Type u_5
inst✝¹² : Group G
inst✝¹¹ : Group H
inst✝¹⁰ : MulAction G α
inst✝⁹ : MeasurableSpace α
inst✝⁸ : MulAction H β
inst✝⁷ : MeasurableSpace β
inst✝⁶ : NormedAddCommGroup E
s t : Set α
μ : Measure α
inst✝⁵ : MeasurableSpace G
inst✝⁴ : MeasurableSMul G α
inst✝³ ... | G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
E : Type u_5
inst✝¹² : Group G
inst✝¹¹ : Group H
inst✝¹⁰ : MulAction G α
inst✝⁹ : MeasurableSpace α
inst✝⁸ : MulAction H β
inst✝⁷ : MeasurableSpace β
inst✝⁶ : NormedAddCommGroup E
s t : Set α
μ : Measure α
inst✝⁵ : MeasurableSpace G
inst✝⁴ : MeasurableSMul G α
inst✝³ ... | ((:c HasSubset.Subset) ((:c Set) (:c ENNReal)) ((:c Set.instHasSubset) (:c ENNReal)) ((:c setOf) (:c ENNReal) (:lambda a (:c ENNReal) ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.403745) (:fv _uniq.404159)) ((:c Set) (:fv _uniq.403745)) (:lambda _ ((:c Set) (:fv _uniq.403745)) (:c ENN... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"E","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹²","sexp":"((:c Group) (:fv _uniq.403739))"},{"name":"inst✝¹¹","sexp":"((:c Group) (:fv _uniq.403742))"}... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:c ENNReal)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:c ENNReal))))))) (:arg :explicit 2 (:app (:c setOf) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:lambd... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rintro","sourceEnd":35728,"sourceStart":35722,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":35730,"sourceStart":35729,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"a","sourceEnd":35730,"sourceStart":35729,"... | [{"role":"fresh_name","source":"a","source_end":35730,"source_start":35729,"syntax_kind":"ident"},{"role":"fresh_name","source":"ha","source_end":35734,"source_start":35732,"syntax_kind":"ident"},{"role":"fresh_name","source":"a","source_end":35764,"source_start":35763,"syntax_kind":"ident"}] | [{"source":"(ha : (μ.restrict s) {x : α | a < f x} = 0)","source_end":35776,"source_start":35731,"syntax_kind":"Lean.Parser.Tactic.rintroPat.binder"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 138 | 10 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 54d0dfe6fea41cb098c0bc85293054eee9344b903bf39a1b6450c9f62fb0fc68 | 50b896e8d9d275be1e367f55c583081b57d8d3d60d3c40cc4c2a558a0bb8b12c | e97b129b5e6a995108345ca36ece89a85c939438a2e48c087b8f98603c0108c9 | bca0b0975a4dfbcaf260f5596ead9b29dfe694a8273d3355bb9ce0f168b198c6 |
cat-searcher/leandojo-benchmark-4-random | test | 179 | MeasureTheory.IsFundamentalDomain.essSup_measure_restrict | Mathlib/MeasureTheory/Group/FundamentalDomain.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.Measure.restrict_apply₀'</a> hs.nullMeasurableSet] at ha | G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
E : Type u_5
inst✝¹² : Group G
inst✝¹¹ : Group H
inst✝¹⁰ : MulAction G α
inst✝⁹ : MeasurableSpace α
inst✝⁸ : MulAction H β
inst✝⁷ : MeasurableSpace β
inst✝⁶ : NormedAddCommGroup E
s t : Set α
μ : Measure α
inst✝⁵ : MeasurableSpace G
inst✝⁴ : MeasurableSMul G α
inst✝³ ... | G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
E : Type u_5
inst✝¹² : Group G
inst✝¹¹ : Group H
inst✝¹⁰ : MulAction G α
inst✝⁹ : MeasurableSpace α
inst✝⁸ : MulAction H β
inst✝⁷ : MeasurableSpace β
inst✝⁶ : NormedAddCommGroup E
s t : Set α
μ : Measure α
inst✝⁵ : MeasurableSpace G
inst✝⁴ : MeasurableSMul G α
inst✝³ ... | ((:c Membership.mem) (:c ENNReal) ((:c Set) (:c ENNReal)) ((:c Set.instMembership) (:c ENNReal)) (:fv _uniq.410578) ((:c setOf) (:c ENNReal) (:lambda a (:c ENNReal) ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.403745) (:fv _uniq.404159)) ((:c Set) (:fv _uniq.403745)) (:lambda _ ((:c S... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"E","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹²","sexp":"((:c Group) (:fv _uniq.403739))"},{"name":"inst✝¹¹","sexp":"((:c Group) (:fv _uniq.403742))"}... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c ENNReal)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c ENNReal))))))) (:arg :explicit 3 (:fv FV26))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":35781,"sourceStart":35779,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":35783,"sourceStart":35782,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Mea... | [] | [{"source":"ha","source_end":35837,"source_start":35835,"syntax_kind":"ident"},{"source":"Measure.restrict_apply₀' hs.nullMeasurableSet","source_end":35830,"source_start":35783,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 138 | 11 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e633f87ed58c7ebb62d013542ac02be7d8e4a64d7cc7ab88acc6165001872a26 | bca0b0975a4dfbcaf260f5596ead9b29dfe694a8273d3355bb9ce0f168b198c6 | 680799c1468c84ccec9b7d27a33e435fc41a0c59b4f4c0de3635637678bde31c | 43d4268f7fa6e99d85fc62d1d5cd4eed286088093b27d2e662d0316b75a0854c |
cat-searcher/leandojo-benchmark-4-random | test | 180 | MeasureTheory.IsFundamentalDomain.essSup_measure_restrict | Mathlib/MeasureTheory/Group/FundamentalDomain.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>MeasureTheory.IsFundamentalDomain.measure_zero_of_invariant</a> hs _ ?_ ha | G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
E : Type u_5
inst✝¹² : Group G
inst✝¹¹ : Group H
inst✝¹⁰ : MulAction G α
inst✝⁹ : MeasurableSpace α
inst✝⁸ : MulAction H β
inst✝⁷ : MeasurableSpace β
inst✝⁶ : NormedAddCommGroup E
s t : Set α
μ : Measure α
inst✝⁵ : MeasurableSpace G
inst✝⁴ : MeasurableSMul G α
inst✝³ ... | G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
E : Type u_5
inst✝¹² : Group G
inst✝¹¹ : Group H
inst✝¹⁰ : MulAction G α
inst✝⁹ : MeasurableSpace α
inst✝⁸ : MulAction H β
inst✝⁷ : MeasurableSpace β
inst✝⁶ : NormedAddCommGroup E
s t : Set α
μ : Measure α
inst✝⁵ : MeasurableSpace G
inst✝⁴ : MeasurableSMul G α
inst✝³ ... | ((:c Membership.mem) (:c ENNReal) ((:c Set) (:c ENNReal)) ((:c Set.instMembership) (:c ENNReal)) (:fv _uniq.410578) ((:c setOf) (:c ENNReal) (:lambda a (:c ENNReal) ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.403745) (:fv _uniq.404159)) ((:c Set) (:fv _uniq.403745)) (:lambda _ ((:c S... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"E","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹²","sexp":"((:c Group) (:fv _uniq.403739))"},{"name":"inst✝¹¹","sexp":"((:c Group) (:fv _uniq.403742))"}... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c ENNReal)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c ENNReal))))))) (:arg :explicit 3 (:fv FV26))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":35846,"sourceStart":35840,"tag":"atom"},{"children":[{"name":"MeasureTheory.IsFundamentalDomain.measure_zero_of_invariant","semanticRole":"global","source":"measure_zero_of_invariant","sourceEnd":35872,"sourceStart":35847,"tag":"identifier"},{"children":[{"contextIndex":23,"s... | [] | [{"source":"measure_zero_of_invariant hs _ ?_ ha","source_end":35883,"source_start":35847,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 138 | 14 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 63d77eeb7f5b8b7f8fb3fdd9ab7a814064453c9cc7eb8949eb4beb10678641fc | 43d4268f7fa6e99d85fc62d1d5cd4eed286088093b27d2e662d0316b75a0854c | a2ce270f29f64baf6e22eb5950016595870b8077d969118697abc72cfd88609b | aff8755bca36f5fa811da0f904f720b5428cffb863cb54e21695d5982ce15e85 |
cat-searcher/leandojo-benchmark-4-random | test | 181 | MeasureTheory.IsFundamentalDomain.essSup_measure_restrict | Mathlib/MeasureTheory/Group/FundamentalDomain.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro γ | G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
E : Type u_5
inst✝¹² : Group G
inst✝¹¹ : Group H
inst✝¹⁰ : MulAction G α
inst✝⁹ : MeasurableSpace α
inst✝⁸ : MulAction H β
inst✝⁷ : MeasurableSpace β
inst✝⁶ : NormedAddCommGroup E
s t : Set α
μ : Measure α
inst✝⁵ : MeasurableSpace G
inst✝⁴ : MeasurableSMul G α
inst✝³ ... | G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
E : Type u_5
inst✝¹² : Group G
inst✝¹¹ : Group H
inst✝¹⁰ : MulAction G α
inst✝⁹ : MeasurableSpace α
inst✝⁸ : MulAction H β
inst✝⁷ : MeasurableSpace β
inst✝⁶ : NormedAddCommGroup E
s t : Set α
μ : Measure α
inst✝⁵ : MeasurableSpace G
inst✝⁴ : MeasurableSMul G α
inst✝³ ... | (:forall g (:fv _uniq.403739) ((:c Eq) ((:c Set) (:fv _uniq.403745)) ((:c HSMul.hSMul) (:fv _uniq.403739) ((:c Set) (:fv _uniq.403745)) ((:c Set) (:fv _uniq.403745)) ((:c instHSMul) (:fv _uniq.403739) ((:c Set) (:fv _uniq.403745)) ((:c Set.smulSet) (:fv _uniq.403739) (:fv _uniq.403745) ((:c MulAction.toSMul) (:fv _uniq... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"E","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹²","sexp":"((:c Group) (:fv _uniq.403739))"},{"name":"inst✝¹¹","sexp":"((:c Group) (:fv _uniq.403742))"}... | (:forall g :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :implicit-type 2 (:app (:c Set) (:arg :explicit 0 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"intro","sourceEnd":35891,"sourceStart":35886,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"γ","sourceEnd":35894,"sourceStart":35892,"tag":"identifier"}],"kind":"null","source":"γ","sourceEnd":35894,"sourceStart":35892,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"γ","source_end":35894,"source_start":35892,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 138 | 15 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 11514b655d0faaf7a980bf88abfbc46834b12d159440e94406a0bd2701896aaa | aff8755bca36f5fa811da0f904f720b5428cffb863cb54e21695d5982ce15e85 | e98a5612a54c4b82d8a6ccad4dc78bcbdf818f989bdac863d7c75a1687f545e9 | 8405aa32105164e8d5a93ef70ee9b39a0a46bd83d69c6cf3eb8f2f04ad38cef2 |
cat-searcher/leandojo-benchmark-4-random | test | 182 | MeasureTheory.IsFundamentalDomain.essSup_measure_restrict | Mathlib/MeasureTheory/Group/FundamentalDomain.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext x | G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
E : Type u_5
inst✝¹² : Group G
inst✝¹¹ : Group H
inst✝¹⁰ : MulAction G α
inst✝⁹ : MeasurableSpace α
inst✝⁸ : MulAction H β
inst✝⁷ : MeasurableSpace β
inst✝⁶ : NormedAddCommGroup E
s t : Set α
μ : Measure α
inst✝⁵ : MeasurableSpace G
inst✝⁴ : MeasurableSMul G α
inst✝³ ... | case h
G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
E : Type u_5
inst✝¹² : Group G
inst✝¹¹ : Group H
inst✝¹⁰ : MulAction G α
inst✝⁹ : MeasurableSpace α
inst✝⁸ : MulAction H β
inst✝⁷ : MeasurableSpace β
inst✝⁶ : NormedAddCommGroup E
s t : Set α
μ : Measure α
inst✝⁵ : MeasurableSpace G
inst✝⁴ : MeasurableSMul G α
... | ((:c Eq) ((:c Set) (:fv _uniq.403745)) ((:c HSMul.hSMul) (:fv _uniq.403739) ((:c Set) (:fv _uniq.403745)) ((:c Set) (:fv _uniq.403745)) ((:c instHSMul) (:fv _uniq.403739) ((:c Set) (:fv _uniq.403745)) ((:c Set.smulSet) (:fv _uniq.403739) (:fv _uniq.403745) ((:c MulAction.toSMul) (:fv _uniq.403739) (:fv _uniq.403745) ((... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"E","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹²","sexp":"((:c Group) (:fv _uniq.403739))"},{"name":"inst✝¹¹","sexp":"((:c Group) (:fv _uniq.403742))"}... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :implicit-type 2 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 3 (:inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"ext","sourceEnd":35900,"sourceStart":35897,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":35902,"sourceStart":35901,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":35902,"sourceStart":35901,"tag... | [{"role":"fresh_name","source":"x","source_end":35902,"source_start":35901,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 138 | 16 | exact | true | 1 | 28 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a86ed920da65c3974c16126b572cb88592aee3d7e72b653fd456d74c55876b70 | 8405aa32105164e8d5a93ef70ee9b39a0a46bd83d69c6cf3eb8f2f04ad38cef2 | ee522618587c4a8062e9541e92fad69d5c6e7dbdf5366e9d82c63ebe3c1e08c5 | 5c3ae58ed6382aa3cb3a6080a3f55322378c20d5eeff8b80a477b87cbc5fe35a |
cat-searcher/leandojo-benchmark-4-random | test | 183 | MeasureTheory.IsFundamentalDomain.essSup_measure_restrict | Mathlib/MeasureTheory/Group/FundamentalDomain.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.mem_smul_set_iff_inv_smul_mem</a>] | case h
G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
E : Type u_5
inst✝¹² : Group G
inst✝¹¹ : Group H
inst✝¹⁰ : MulAction G α
inst✝⁹ : MeasurableSpace α
inst✝⁸ : MulAction H β
inst✝⁷ : MeasurableSpace β
inst✝⁶ : NormedAddCommGroup E
s t : Set α
μ : Measure α
inst✝⁵ : MeasurableSpace G
inst✝⁴ : MeasurableSMul G α
... | case h
G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
E : Type u_5
inst✝¹² : Group G
inst✝¹¹ : Group H
inst✝¹⁰ : MulAction G α
inst✝⁹ : MeasurableSpace α
inst✝⁸ : MulAction H β
inst✝⁷ : MeasurableSpace β
inst✝⁶ : NormedAddCommGroup E
s t : Set α
μ : Measure α
inst✝⁵ : MeasurableSpace G
inst✝⁴ : MeasurableSMul G α
... | ((:c Iff) ((:c Membership.mem) (:fv _uniq.403745) ((:c Set) (:fv _uniq.403745)) ((:c Set.instMembership) (:fv _uniq.403745)) (:fv _uniq.410934) ((:c HSMul.hSMul) (:fv _uniq.403739) ((:c Set) (:fv _uniq.403745)) ((:c Set) (:fv _uniq.403745)) ((:c instHSMul) (:fv _uniq.403739) ((:c Set) (:fv _uniq.403745)) ((:c Set.smulS... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"E","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹²","sexp":"((:c Group) (:fv _uniq.403739))"},{"name":"inst✝¹¹","sexp":"((:c Group) (:fv _uniq.403742))"}... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":35907,"sourceStart":35905,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":35909,"sourceStart":35908,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.mem_smul_set... | [] | [{"source":"mem_smul_set_iff_inv_smul_mem","source_end":35938,"source_start":35909,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 138 | 17 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f09265cef50a14b18258adcafad8a93a0db83f13f5796504e94888238256c329 | 5c3ae58ed6382aa3cb3a6080a3f55322378c20d5eeff8b80a477b87cbc5fe35a | cfc7306e8e8413dd15eb9e859797d96cb8450d23a10aa5d50b911e538f8bd964 | 5656386343b0fb7e0b467cc2623007f756c4133c3c60898e561a48f078a7ca45 |
cat-searcher/leandojo-benchmark-4-random | test | 184 | MeasureTheory.IsFundamentalDomain.essSup_measure_restrict | Mathlib/MeasureTheory/Group/FundamentalDomain.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.mem_setOf_eq</a>, hf γ⁻¹ x] | case h
G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
E : Type u_5
inst✝¹² : Group G
inst✝¹¹ : Group H
inst✝¹⁰ : MulAction G α
inst✝⁹ : MeasurableSpace α
inst✝⁸ : MulAction H β
inst✝⁷ : MeasurableSpace β
inst✝⁶ : NormedAddCommGroup E
s t : Set α
μ : Measure α
inst✝⁵ : MeasurableSpace G
inst✝⁴ : MeasurableSMul G α
... | ((:c Iff) ((:c Membership.mem) (:fv _uniq.403745) ((:c Set) (:fv _uniq.403745)) ((:c Set.instMembership) (:fv _uniq.403745)) ((:c HSMul.hSMul) (:fv _uniq.403739) (:fv _uniq.403745) (:fv _uniq.403745) ((:c instHSMul) (:fv _uniq.403739) (:fv _uniq.403745) ((:c MulAction.toSMul) (:fv _uniq.403739) (:fv _uniq.403745) ((:c ... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"E","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹²","sexp":"((:c Group) (:fv _uniq.403739))"},{"name":"inst✝¹¹","sexp":"((:c Group) (:fv _uniq.403742))"}... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":35946,"sourceStart":35942,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":35951,"sourceStart":35947,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":359... | [] | [{"source":"mem_setOf_eq","source_end":35965,"source_start":35953,"syntax_kind":"ident"},{"source":"hf γ⁻¹ x","source_end":35979,"source_start":35967,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.403739","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.403742","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 138 | 20 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5e131463f6469d5a98279519331c2154660fd3f35c8572783bb2b5cdd03a89c2 | 5656386343b0fb7e0b467cc2623007f756c4133c3c60898e561a48f078a7ca45 | 32a9ef5fc78bb1cd680ef4c29681437aaf0e386d3146d1893735b94a365d7cf3 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 185 | Ideal.sup_mul_eq_of_coprime_right | Mathlib/RingTheory/Ideal/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>mul_comm</a>] | R : Type u
ι : Type u_1
inst✝ : CommSemiring R
I J K L : Ideal R
h : I ⊔ K = ⊤
⊢ I ⊔ J * K = I ⊔ J | R : Type u
ι : Type u_1
inst✝ : CommSemiring R
I J K L : Ideal R
h : I ⊔ K = ⊤
⊢ I ⊔ K * J = I ⊔ J | ((:c Eq) ((:c Ideal) (:fv _uniq.265126) ((:c CommSemiring.toSemiring) (:fv _uniq.265126) (:fv _uniq.265132))) ((:c Sup.sup) ((:c Ideal) (:fv _uniq.265126) ((:c CommSemiring.toSemiring) (:fv _uniq.265126) (:fv _uniq.265132))) ((:c SemilatticeSup.toSup) ((:c Ideal) (:fv _uniq.265126) ((:c CommSemiring.toSemiring) (:fv _u... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.265126))"},{"name":"I","sexp":"((:c Ideal) (:fv _uniq.265126) ((:c CommSemiring.toSemiring) (:fv _uniq.265126) (:fv _uniq.265132)))"},{"name":"J","sexp":"((:c Ideal) (:fv _uniq.265126) ((... | (: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 Sup.sup) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Sem... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.265126","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.265129","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rw","sourceEnd":29479,"sourceStart":29477,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":29481,"sourceStart":29480,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"mul_comm","seman... | [] | [{"source":"mul_comm","source_end":29489,"source_start":29481,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.265126","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.265129","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":instance-implicit","context_index":2,"internal... | 216 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 76927df8fdf74fd31fdf45b9471fc8055e2328b5da8e448276cb47883b140322 | 3c902ab687c654111a688e838cd8da6db4f84d0e3ae0e6896d78376151607b38 | b40139e2832d8f817070a6f57dda46abb72fcb05e2a85e2d0d7b1991ae7615d3 | 89554b80258752368fe1a34d7699239fffacb613771fb223632d8d09d4620c28 |
cat-searcher/leandojo-benchmark-4-random | test | 186 | Ideal.sup_mul_eq_of_coprime_right | Mathlib/RingTheory/Ideal/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Ideal.sup_mul_eq_of_coprime_left</a> h | R : Type u
ι : Type u_1
inst✝ : CommSemiring R
I J K L : Ideal R
h : I ⊔ K = ⊤
⊢ I ⊔ K * J = I ⊔ J | ((:c Eq) ((:c Ideal) (:fv _uniq.265126) ((:c CommSemiring.toSemiring) (:fv _uniq.265126) (:fv _uniq.265132))) ((:c Sup.sup) ((:c Ideal) (:fv _uniq.265126) ((:c CommSemiring.toSemiring) (:fv _uniq.265126) (:fv _uniq.265132))) ((:c SemilatticeSup.toSup) ((:c Ideal) (:fv _uniq.265126) ((:c CommSemiring.toSemiring) (:fv _u... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.265126))"},{"name":"I","sexp":"((:c Ideal) (:fv _uniq.265126) ((:c CommSemiring.toSemiring) (:fv _uniq.265126) (:fv _uniq.265132)))"},{"name":"J","sexp":"((:c Ideal) (:fv _uniq.265126) ((... | (: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 Sup.sup) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Sem... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.265126","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.265129","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"exact","sourceEnd":29498,"sourceStart":29493,"tag":"atom"},{"children":[{"name":"Ideal.sup_mul_eq_of_coprime_left","semanticRole":"global","source":"sup_mul_eq_of_coprime_left","sourceEnd":29525,"sourceStart":29499,"tag":"identifier"},{"children":[{"contextIndex":8,"semanticRole":"local","source... | [] | [{"source":"sup_mul_eq_of_coprime_left h","source_end":29527,"source_start":29499,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.265126","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.265129","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":instance-implicit","context_index":2,"internal... | 216 | 7 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7922de1fff492dfd4023451468947da259b5b255e0c431024e70e999b380a1bf | 89554b80258752368fe1a34d7699239fffacb613771fb223632d8d09d4620c28 | f2e7fe231a56e862cc9c2336cf93a204c1b810b4b844da9789e29a4dac1b0104 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 187 | LinearMap.continuous_of_nonzero_on_open | Mathlib/Topology/Algebra/Module/FiniteDimension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine l.continuous_of_isClosed_ker (l.isClosed_or_dense_ker.resolve_right fun hl => ?_) | 𝕜 : Type u
hnorm : NontriviallyNormedField 𝕜
E : Type v
inst✝¹⁴ : AddCommGroup E
inst✝¹³ : Module 𝕜 E
inst✝¹² : TopologicalSpace E
inst✝¹¹ : TopologicalAddGroup E
inst✝¹⁰ : ContinuousSMul 𝕜 E
F : Type w
inst✝⁹ : AddCommGroup F
inst✝⁸ : Module 𝕜 F
inst✝⁷ : TopologicalSpace F
inst✝⁶ : TopologicalAddGroup F
inst✝⁵ : ... | 𝕜 : Type u
hnorm : NontriviallyNormedField 𝕜
E : Type v
inst✝¹⁴ : AddCommGroup E
inst✝¹³ : Module 𝕜 E
inst✝¹² : TopologicalSpace E
inst✝¹¹ : TopologicalAddGroup E
inst✝¹⁰ : ContinuousSMul 𝕜 E
F : Type w
inst✝⁹ : AddCommGroup F
inst✝⁸ : Module 𝕜 F
inst✝⁷ : TopologicalSpace F
inst✝⁶ : TopologicalAddGroup F
inst✝⁵ : ... | ((:c Continuous) (:fv _uniq.90102) (:fv _uniq.90097) (:fv _uniq.90800) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.90097) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.90097) ((:c SeminormedRing.toPseudoMetricSpace) (:fv _uniq.90097) ((:c SeminormedCommRing.toSeminormedRing) (:fv _uniq.90097) ((:c NormedCommRi... | [{"name":"𝕜","sexp":"(:sort (+ u 1))"},{"name":"hnorm","sexp":"((:c NontriviallyNormedField) (:fv _uniq.90097))"},{"name":"E","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹⁴","sexp":"((:c AddCommGroup) (:fv _uniq.90102))"},{"name":"inst✝¹³","sexp":"((:c Module) (:fv _uniq.90097) (:fv _uniq.90102) ((:c DivisionSemiring.toSe... | (:app (:c Continuous) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 4 (:app (:c DFunLike.coe) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90097","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.90100","is_instance":true,"is_let":false,"name":"hnorm","sexp":"(:app (:c NontriviallyNormedField... | {"children":[{"source":"refine","sourceEnd":10344,"sourceStart":10338,"tag":"atom"},{"children":[{"source":"l.continuous_of_isClosed_ker","sourceEnd":10373,"sourceStart":10345,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":10375,"sourceStart":10374,"tag":"atom"},{"children":[{"source":"l.isClos... | [] | [{"source":"l.continuous_of_isClosed_ker (l.isClosed_or_dense_ker.resolve_right fun hl => ?_)","source_end":10426,"source_start":10345,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90097","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.90100","is_instance":true,"is_let":false,"user_name":"hnorm"},{"binder_role":":implicit","context_index":2,"intern... | 17 | 4 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fe704e5ef87091cc29bbef36341e8fcd479da32a96a1e1ccb93bbbad1f31a7e6 | b37f23ee2896cc3cdf06a20106ac3c6cb1ba0c9af209d6fb9ada3fc47eec6b7b | 99030bb73f653a94fd83dabdab4e04dbe8a355a01d264776588516cee1563b2d | 1d7b6b0c3235c0877a8b3a46b8a176bbbce139be5873067e4dde48093acb03ea |
cat-searcher/leandojo-benchmark-4-random | test | 188 | LinearMap.continuous_of_nonzero_on_open | Mathlib/Topology/Algebra/Module/FiniteDimension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases hs₂ with ⟨x, hx⟩ | 𝕜 : Type u
hnorm : NontriviallyNormedField 𝕜
E : Type v
inst✝¹⁴ : AddCommGroup E
inst✝¹³ : Module 𝕜 E
inst✝¹² : TopologicalSpace E
inst✝¹¹ : TopologicalAddGroup E
inst✝¹⁰ : ContinuousSMul 𝕜 E
F : Type w
inst✝⁹ : AddCommGroup F
inst✝⁸ : Module 𝕜 F
inst✝⁷ : TopologicalSpace F
inst✝⁶ : TopologicalAddGroup F
inst✝⁵ : ... | case intro
𝕜 : Type u
hnorm : NontriviallyNormedField 𝕜
E : Type v
inst✝¹⁴ : AddCommGroup E
inst✝¹³ : Module 𝕜 E
inst✝¹² : TopologicalSpace E
inst✝¹¹ : TopologicalAddGroup E
inst✝¹⁰ : ContinuousSMul 𝕜 E
F : Type w
inst✝⁹ : AddCommGroup F
inst✝⁸ : Module 𝕜 F
inst✝⁷ : TopologicalSpace F
inst✝⁶ : TopologicalAddGroup ... | (:c False) | [{"name":"𝕜","sexp":"(:sort (+ u 1))"},{"name":"hnorm","sexp":"((:c NontriviallyNormedField) (:fv _uniq.90097))"},{"name":"E","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹⁴","sexp":"((:c AddCommGroup) (:fv _uniq.90102))"},{"name":"inst✝¹³","sexp":"((:c Module) (:fv _uniq.90097) (:fv _uniq.90102) ((:c DivisionSemiring.toSe... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90097","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.90100","is_instance":true,"is_let":false,"name":"hnorm","sexp":"(:app (:c NontriviallyNormedField... | {"children":[{"source":"rcases","sourceEnd":10435,"sourceStart":10429,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":24,"semanticRole":"local","source":"hs₂","sourceEnd":10441,"sourceStart":10436,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget"... | [] | [{"source":"hs₂","source_end":10441,"source_start":10436,"syntax_kind":"ident"},{"source":"⟨x, hx⟩","source_end":10458,"source_start":10447,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90097","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.90100","is_instance":true,"is_let":false,"user_name":"hnorm"},{"binder_role":":implicit","context_index":2,"intern... | 17 | 5 | exact | true | 1 | 26 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 88f5cb6647bfc6a94544cba781009ce5b2660d502cec8fdf26532c4381552143 | 1d7b6b0c3235c0877a8b3a46b8a176bbbce139be5873067e4dde48093acb03ea | 14c6ff05dde851bfef15b84a5a8102d921464b1486b8e724555fe0ffb0e67d96 | e2c76646581f537505ee739a71e260a1566fc0c821857c881a09ed4603dda6a9 |
cat-searcher/leandojo-benchmark-4-random | test | 189 | LinearMap.continuous_of_nonzero_on_open | Mathlib/Topology/Algebra/Module/FiniteDimension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : x ∈ <a>interior</a> (<a>LinearMap.ker</a> l : <a>Set</a> E)ᶜ := by rw [<a>mem_interior_iff_mem_nhds</a>] exact <a>Filter.mem_of_superset</a> (hs₁.mem_nhds hx) hs₃ | case intro
𝕜 : Type u
hnorm : NontriviallyNormedField 𝕜
E : Type v
inst✝¹⁴ : AddCommGroup E
inst✝¹³ : Module 𝕜 E
inst✝¹² : TopologicalSpace E
inst✝¹¹ : TopologicalAddGroup E
inst✝¹⁰ : ContinuousSMul 𝕜 E
F : Type w
inst✝⁹ : AddCommGroup F
inst✝⁸ : Module 𝕜 F
inst✝⁷ : TopologicalSpace F
inst✝⁶ : TopologicalAddGroup ... | case intro
𝕜 : Type u
hnorm : NontriviallyNormedField 𝕜
E : Type v
inst✝¹⁴ : AddCommGroup E
inst✝¹³ : Module 𝕜 E
inst✝¹² : TopologicalSpace E
inst✝¹¹ : TopologicalAddGroup E
inst✝¹⁰ : ContinuousSMul 𝕜 E
F : Type w
inst✝⁹ : AddCommGroup F
inst✝⁸ : Module 𝕜 F
inst✝⁷ : TopologicalSpace F
inst✝⁶ : TopologicalAddGroup ... | (:c False) | [{"name":"𝕜","sexp":"(:sort (+ u 1))"},{"name":"hnorm","sexp":"((:c NontriviallyNormedField) (:fv _uniq.90097))"},{"name":"E","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹⁴","sexp":"((:c AddCommGroup) (:fv _uniq.90102))"},{"name":"inst✝¹³","sexp":"((:c Module) (:fv _uniq.90097) (:fv _uniq.90102) ((:c DivisionSemiring.toSe... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90097","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.90100","is_instance":true,"is_let":false,"name":"hnorm","sexp":"(:app (:c NontriviallyNormedField... | {"children":[{"source":"have","sourceEnd":10465,"sourceStart":10461,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":10466,"sourceStart":10466,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":10466,"sourceStart":10466,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"x ∈ interior (LinearMap.ker l : Set E)ᶜ","source_end":10511,"source_start":10468,"syntax_kind":"«term_∈_»"},{"source":"mem_interior_iff_mem_nhds","source_end":10551,"source_start":10526,"syntax_kind":"ident"},{"source":"mem_of_superset (hs₁.mem_nhds hx) hs₃","source_end":10604,"source_start":10563,"syntax_k... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90097","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.90100","is_instance":true,"is_let":false,"user_name":"hnorm"},{"binder_role":":implicit","context_index":2,"intern... | 17 | 6 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1cf5a6967cc74bba7bc602039bb26d5980cd1c7eccf58904d45be37f6db14f45 | e2c76646581f537505ee739a71e260a1566fc0c821857c881a09ed4603dda6a9 | 893cb46874a8a060944fbfc8ac535cfa9ea77db296107f08da235846aa95b699 | 4f17021c28b39db5e86f0fb3ef4c6cd4bb5321bc7c716fb73c2f7798dfa79410 |
cat-searcher/leandojo-benchmark-4-random | test | 190 | LinearMap.continuous_of_nonzero_on_open | Mathlib/Topology/Algebra/Module/FiniteDimension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [hl.interior_compl] at this | case intro
𝕜 : Type u
hnorm : NontriviallyNormedField 𝕜
E : Type v
inst✝¹⁴ : AddCommGroup E
inst✝¹³ : Module 𝕜 E
inst✝¹² : TopologicalSpace E
inst✝¹¹ : TopologicalAddGroup E
inst✝¹⁰ : ContinuousSMul 𝕜 E
F : Type w
inst✝⁹ : AddCommGroup F
inst✝⁸ : Module 𝕜 F
inst✝⁷ : TopologicalSpace F
inst✝⁶ : TopologicalAddGroup ... | (:c False) | [{"name":"𝕜","sexp":"(:sort (+ u 1))"},{"name":"hnorm","sexp":"((:c NontriviallyNormedField) (:fv _uniq.90097))"},{"name":"E","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹⁴","sexp":"((:c AddCommGroup) (:fv _uniq.90102))"},{"name":"inst✝¹³","sexp":"((:c Module) (:fv _uniq.90097) (:fv _uniq.90102) ((:c DivisionSemiring.toSe... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90097","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.90100","is_instance":true,"is_let":false,"name":"hnorm","sexp":"(:app (:c NontriviallyNormedField... | {"children":[{"source":"rwa","sourceEnd":10610,"sourceStart":10607,"tag":"atom"},{"children":[{"source":"[","sourceEnd":10612,"sourceStart":10611,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Dense.interior_compl","semanticRole":"global","source":"hl.interior_co... | [] | [{"source":"hl.interior_compl","source_end":10629,"source_start":10612,"syntax_kind":"ident"},{"source":"this","source_end":10638,"source_start":10634,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90097","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.90100","is_instance":true,"is_let":false,"user_name":"hnorm"},{"binder_role":":implicit","context_index":2,"intern... | 17 | 12 | exact | true | 1 | 28 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b9617196e7b7ba3bf52ac9e1e34476945e9ece870463ec5dd6b7a9c0e6af7ef5 | 4f17021c28b39db5e86f0fb3ef4c6cd4bb5321bc7c716fb73c2f7798dfa79410 | 5185e05f5d22b5b62bcf3ee46ae4bf60e603eaae6e9cd41cd3c7b4ba330fa045 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 191 | LinearMap.continuous_of_nonzero_on_open | Mathlib/Topology/Algebra/Module/FiniteDimension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>mem_interior_iff_mem_nhds</a>] | 𝕜 : Type u
hnorm : NontriviallyNormedField 𝕜
E : Type v
inst✝¹⁴ : AddCommGroup E
inst✝¹³ : Module 𝕜 E
inst✝¹² : TopologicalSpace E
inst✝¹¹ : TopologicalAddGroup E
inst✝¹⁰ : ContinuousSMul 𝕜 E
F : Type w
inst✝⁹ : AddCommGroup F
inst✝⁸ : Module 𝕜 F
inst✝⁷ : TopologicalSpace F
inst✝⁶ : TopologicalAddGroup F
inst✝⁵ : ... | 𝕜 : Type u
hnorm : NontriviallyNormedField 𝕜
E : Type v
inst✝¹⁴ : AddCommGroup E
inst✝¹³ : Module 𝕜 E
inst✝¹² : TopologicalSpace E
inst✝¹¹ : TopologicalAddGroup E
inst✝¹⁰ : ContinuousSMul 𝕜 E
F : Type w
inst✝⁹ : AddCommGroup F
inst✝⁸ : Module 𝕜 F
inst✝⁷ : TopologicalSpace F
inst✝⁶ : TopologicalAddGroup F
inst✝⁵ : ... | ((:c Membership.mem) (:fv _uniq.90102) ((:c Set) (:fv _uniq.90102)) ((:c Set.instMembership) (:fv _uniq.90102)) (:fv _uniq.99156) ((:c interior) (:fv _uniq.90102) (:fv _uniq.90800) ((:c HasCompl.compl) ((:c Set) (:fv _uniq.90102)) ((:c Set.instHasCompl) (:fv _uniq.90102)) ((:c SetLike.coe) ((:c Submodule) (:fv _uniq.90... | [{"name":"𝕜","sexp":"(:sort (+ u 1))"},{"name":"hnorm","sexp":"((:c NontriviallyNormedField) (:fv _uniq.90097))"},{"name":"E","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹⁴","sexp":"((:c AddCommGroup) (:fv _uniq.90102))"},{"name":"inst✝¹³","sexp":"((:c Module) (:fv _uniq.90097) (:fv _uniq.90102) ((:c DivisionSemiring.toSe... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 3 (:fv FV26)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90097","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.90100","is_instance":true,"is_let":false,"name":"hnorm","sexp":"(:app (:c NontriviallyNormedField... | {"children":[{"source":"rw","sourceEnd":10524,"sourceStart":10522,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10526,"sourceStart":10525,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"mem_interior_iff... | [] | [{"source":"mem_interior_iff_mem_nhds","source_end":10551,"source_start":10526,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90097","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.90100","is_instance":true,"is_let":false,"user_name":"hnorm"},{"binder_role":":implicit","context_index":2,"intern... | 17 | 8 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9255a5e91c42bbc0dcc4326458f0a320e933530e4953396e599ecfa8018d395a | 1f23b6aed2fc5b92b4db7246acf9fb0e55262d10394f0e2dcd7aa6b7487133bf | 1627b22fe88b998ef32b5ac36e9f4355a2eebabdb3d7517ef30feeae17e3aba1 | 544cc2d99e2736927d873b09a2df8faf20c34b798365973fb2571a80ead6d526 |
cat-searcher/leandojo-benchmark-4-random | test | 192 | LinearMap.continuous_of_nonzero_on_open | Mathlib/Topology/Algebra/Module/FiniteDimension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Filter.mem_of_superset</a> (hs₁.mem_nhds hx) hs₃ | 𝕜 : Type u
hnorm : NontriviallyNormedField 𝕜
E : Type v
inst✝¹⁴ : AddCommGroup E
inst✝¹³ : Module 𝕜 E
inst✝¹² : TopologicalSpace E
inst✝¹¹ : TopologicalAddGroup E
inst✝¹⁰ : ContinuousSMul 𝕜 E
F : Type w
inst✝⁹ : AddCommGroup F
inst✝⁸ : Module 𝕜 F
inst✝⁷ : TopologicalSpace F
inst✝⁶ : TopologicalAddGroup F
inst✝⁵ : ... | ((:c Membership.mem) ((:c Set) (:fv _uniq.90102)) ((:c Filter) (:fv _uniq.90102)) ((:c instMembershipSetFilter) (:fv _uniq.90102)) ((:c HasCompl.compl) ((:c Set) (:fv _uniq.90102)) ((:c Set.instHasCompl) (:fv _uniq.90102)) ((:c SetLike.coe) ((:c Submodule) (:fv _uniq.90097) (:fv _uniq.90102) ((:c DivisionSemiring.toSem... | [{"name":"𝕜","sexp":"(:sort (+ u 1))"},{"name":"hnorm","sexp":"((:c NontriviallyNormedField) (:fv _uniq.90097))"},{"name":"E","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹⁴","sexp":"((:c AddCommGroup) (:fv _uniq.90102))"},{"name":"inst✝¹³","sexp":"((:c Module) (:fv _uniq.90097) (:fv _uniq.90102) ((:c DivisionSemiring.toSe... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :implicit-type 1 (:app (:c Filter) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:app (:c Filter)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90097","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.90100","is_instance":true,"is_let":false,"name":"hnorm","sexp":"(:app (:c NontriviallyNormedField... | {"children":[{"source":"exact","sourceEnd":10562,"sourceStart":10557,"tag":"atom"},{"children":[{"name":"Filter.mem_of_superset","semanticRole":"global","source":"mem_of_superset","sourceEnd":10578,"sourceStart":10563,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":10580,"sourceStart":10579,"tag... | [] | [{"source":"mem_of_superset (hs₁.mem_nhds hx) hs₃","source_end":10604,"source_start":10563,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90097","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.90100","is_instance":true,"is_let":false,"user_name":"hnorm"},{"binder_role":":implicit","context_index":2,"intern... | 17 | 11 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 33f54bdde579a3dd31bdd0432099b161638a25cf4d8f1eafcb0dc5eb7c04e32d | 544cc2d99e2736927d873b09a2df8faf20c34b798365973fb2571a80ead6d526 | f1d89ce5c769fdc25a59e54cf5eac9f578ef6a73bf33650401f106f8ec650c39 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 193 | MeasureTheory.zero_convolution | Mathlib/Analysis/Convolution.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext | 𝕜 : Type u𝕜
G : Type uG
E : Type uE
E' : Type uE'
E'' : Type uE''
F : Type uF
F' : Type uF'
F'' : Type uF''
P : Type uP
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedAddCommGroup E'
inst✝⁹ : NormedAddCommGroup E''
inst✝⁸ : NormedAddCommGroup F
f f' : G → E
g g' : G → E'
x x' : G
y y' : E
inst✝⁷ : NontriviallyNormedF... | case h
𝕜 : Type u𝕜
G : Type uG
E : Type uE
E' : Type uE'
E'' : Type uE''
F : Type uF
F' : Type uF'
F'' : Type uF''
P : Type uP
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedAddCommGroup E'
inst✝⁹ : NormedAddCommGroup E''
inst✝⁸ : NormedAddCommGroup F
f f' : G → E
g g' : G → E'
x x' : G
y y' : E
inst✝⁷ : Nontrivially... | ((:c Eq) (:forall _ (:fv _uniq.577493) (:fv _uniq.577501)) ((:c MeasureTheory.convolution) (:fv _uniq.577491) (:fv _uniq.577493) (:fv _uniq.577495) (:fv _uniq.577497) (:fv _uniq.577501) (:fv _uniq.577510) (:fv _uniq.577513) (:fv _uniq.577519) (:fv _uniq.577546) (:fv _uniq.577670) (:fv _uniq.577787) (:fv _uniq.578021) (... | [{"name":"𝕜","sexp":"(:sort (+ u𝕜 1))"},{"name":"G","sexp":"(:sort (+ uG 1))"},{"name":"E","sexp":"(:sort (+ uE 1))"},{"name":"E'","sexp":"(:sort (+ uE' 1))"},{"name":"E''","sexp":"(:sort (+ uE'' 1))"},{"name":"F","sexp":"(:sort (+ uF 1))"},{"name":"F'","sexp":"(:sort (+ uF' 1))"},{"name":"F''","sexp":"(:sort (+ uF''... | (:app (:c Eq) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV1) (:fv FV5))) (:arg :explicit 1 (:app (:c MeasureTheory.convolution) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV2)) (:arg :implicit-type 3 (:fv FV3)) (:arg :implicit-type 4 (:fv FV5)) (:arg :instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.577491","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.577493","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"ext","sourceEnd":25551,"sourceStart":25548,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":25551,"sourceStart":25548,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.577491","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.577493","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 117 | 4 | exact | true | 1 | 32 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 79e37453f593ca548afa08e05f46c3728cc1f400e9c30689a3b89b175cbdb798 | 0899df7aa89127646dfa2643e5cc244d1e1fec5460f33956759a1283a278908c | a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de | df600d1d814e110fbbd54fb1feeeb9ca7b77aed726dcdcce9be768fd37fc26d0 |
cat-searcher/leandojo-benchmark-4-random | test | 194 | MeasureTheory.zero_convolution | Mathlib/Analysis/Convolution.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>MeasureTheory.convolution_def</a>, <a>Pi.zero_apply</a>, L.map_zero₂, <a>MeasureTheory.integral_zero</a>] | case h
𝕜 : Type u𝕜
G : Type uG
E : Type uE
E' : Type uE'
E'' : Type uE''
F : Type uF
F' : Type uF'
F'' : Type uF''
P : Type uP
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedAddCommGroup E'
inst✝⁹ : NormedAddCommGroup E''
inst✝⁸ : NormedAddCommGroup F
f f' : G → E
g g' : G → E'
x x' : G
y y' : E
inst✝⁷ : Nontrivially... | ((:c Eq) (:fv _uniq.577501) ((:c MeasureTheory.convolution) (:fv _uniq.577491) (:fv _uniq.577493) (:fv _uniq.577495) (:fv _uniq.577497) (:fv _uniq.577501) (:fv _uniq.577510) (:fv _uniq.577513) (:fv _uniq.577519) (:fv _uniq.577546) (:fv _uniq.577670) (:fv _uniq.577787) (:fv _uniq.578021) (:fv _uniq.582841) (:fv _uniq.58... | [{"name":"𝕜","sexp":"(:sort (+ u𝕜 1))"},{"name":"G","sexp":"(:sort (+ uG 1))"},{"name":"E","sexp":"(:sort (+ uE 1))"},{"name":"E'","sexp":"(:sort (+ uE' 1))"},{"name":"E''","sexp":"(:sort (+ uE'' 1))"},{"name":"F","sexp":"(:sort (+ uF 1))"},{"name":"F'","sexp":"(:sort (+ uF' 1))"},{"name":"F''","sexp":"(:sort (+ uF''... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:app (:c MeasureTheory.convolution) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV2)) (:arg :implicit-type 3 (:fv FV3)) (:arg :implicit-type 4 (:fv FV5)) (:arg :instance 5 (:instance-of (:app (:c Norme... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.577491","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.577493","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"simp_rw","sourceEnd":25561,"sourceStart":25554,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":25563,"sourceStart":25562,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MeasureTheo... | [] | [{"source":"convolution_def","source_end":25578,"source_start":25563,"syntax_kind":"ident"},{"source":"Pi.zero_apply","source_end":25593,"source_start":25580,"syntax_kind":"ident"},{"source":"L.map_zero₂","source_end":25608,"source_start":25595,"syntax_kind":"ident"},{"source":"integral_zero","source_end":25623,"source... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.577491","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.577493","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 117 | 5 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2bf0559600e819f07d40a4432ec95039875b3204008debce3ee2a393ca9842f0 | df600d1d814e110fbbd54fb1feeeb9ca7b77aed726dcdcce9be768fd37fc26d0 | 87997452fceb9f66a69997c806302a256e1fc855918cf316312007d3ccc04635 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 195 | Real.deriv_negMulLog | Mathlib/Analysis/SpecialFunctions/Log/NegMulLog.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Real.negMulLog_eq_neg</a>, <a>deriv.neg</a>, <a>Real.deriv_mul_log</a> hx] | x : ℝ
hx : x ≠ 0
⊢ deriv negMulLog x = -log x - 1 | x : ℝ
hx : x ≠ 0
⊢ -(log x + 1) = -log x - 1 | ((:c Eq) (:c Real) ((:c deriv) (:c Real) ((:c DenselyNormedField.toNontriviallyNormedField) (:c Real) (:c Real.denselyNormedField)) (:c Real) (:c Real.normedAddCommGroup) ((:c NormedField.toNormedSpace) (:c Real) ((:c NontriviallyNormedField.toNormedField) (:c Real) ((:c DenselyNormedField.toNontriviallyNormedField) (:... | [{"name":"x","sexp":"(:c Real)"},{"name":"hx","sexp":"((:c Ne) (:c Real) (:fv _uniq.22763) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c deriv) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:c Real))))) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :e... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22763","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.22764","is_instance":false,"is_let":false,"name":"hx","sexp":"(:app (:c Ne) (:arg :implicit-type 0 (:c Real)) ... | {"children":[{"source":"rw","sourceEnd":4358,"sourceStart":4356,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4360,"sourceStart":4359,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Real.negMulLog_eq_ne... | [] | [{"source":"negMulLog_eq_neg","source_end":4376,"source_start":4360,"syntax_kind":"ident"},{"source":"deriv.neg","source_end":4387,"source_start":4378,"syntax_kind":"ident"},{"source":"deriv_mul_log hx","source_end":4405,"source_start":4389,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22763","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.22764","is_instance":false,"is_let":false,"user_name":"hx"}] | 22 | 4 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0f3e81a97f4b57fe3df07d18f31bb4ca6a55ea3827e207e8d14cc120acbf59d5 | d9581871ec0a2480d3ee95e795e0fce49709c177c3e12246b0cb1f9722bf81a8 | 6f8fb424c1227676e932b7ad11f5a59be6c63eaa72b83ba14971d4ca15e0feb9 | 1be6f69ab3b9b97385dca1e7ca600eb3341b211d1074026ee280edb4ccc20607 |
cat-searcher/leandojo-benchmark-4-random | test | 196 | Real.deriv_negMulLog | Mathlib/Analysis/SpecialFunctions/Log/NegMulLog.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | x : ℝ
hx : x ≠ 0
⊢ -(log x + 1) = -log x - 1 | ((:c Eq) (:c Real) ((:c Neg.neg) (:c Real) ((:c NegZeroClass.toNeg) (:c Real) ((:c SubNegZeroMonoid.toNegZeroClass) (:c Real) ((:c SubtractionMonoid.toSubNegZeroMonoid) (:c Real) ((:c SubtractionCommMonoid.toSubtractionMonoid) (:c Real) ((:c AddCommGroup.toDivisionAddCommMonoid) (:c Real) ((:c NormedAddCommGroup.toAddC... | [{"name":"x","sexp":"(:c Real)"},{"name":"hx","sexp":"((:c Ne) (:c Real) (:fv _uniq.22763) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22763","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.22764","is_instance":false,"is_let":false,"name":"hx","sexp":"(:app (:c Ne) (:arg :implicit-type 0 (:c Real)) ... | {"children":[{"source":"ring","sourceEnd":4413,"sourceStart":4409,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":4413,"sourceStart":4409,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22763","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.22764","is_instance":false,"is_let":false,"user_name":"hx"}] | 22 | 9 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d7315515c94a2a664d5179bc564050614d76845a98151be0c9bcf765a9faffe6 | 1be6f69ab3b9b97385dca1e7ca600eb3341b211d1074026ee280edb4ccc20607 | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 197 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ⥤ D₂
H₂ ... | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | ((:c Iff) ((:c CategoryTheory.TwoSquare.GuitartExact) (:fv _uniq.68741) (:fv _uniq.68750) (:fv _uniq.68747) (:fv _uniq.68756) (:fv _uniq.68760) (:fv _uniq.68772) (:fv _uniq.68768) (:fv _uniq.68780) (:fv _uniq.68808) ((:c CategoryTheory.Functor.comp) (:fv _uniq.68741) (:fv _uniq.68760) (:fv _uniq.68744) (:fv _uniq.68764... | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:app (:c Iff) (:arg :explicit 0 (:app (:c CategoryTheory.TwoSquare.GuitartExact) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV2)) (:arg :implicit-type 3 (:fv FV5)) (:arg :instance 4 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"constructor","sourceEnd":4915,"sourceStart":4904,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":4915,"sourceStart":4904,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 4 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0b67f6f802e25643751c73265cb96736ab2ac45eb69c94e97cc16a07ff004d03 | 1e1c292f5d0d25a5ab573a3633195f8805c49754ce64afa553aee5d904541dbc | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | ed251ced0f88d53fbb8bf77451b74a5ba6117851fc5024a6eeae0430c9c544c4 |
cat-searcher/leandojo-benchmark-4-random | test | 198 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro hww' | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | (:forall _ ((:c CategoryTheory.TwoSquare.GuitartExact) (:fv _uniq.68741) (:fv _uniq.68750) (:fv _uniq.68747) (:fv _uniq.68756) (:fv _uniq.68760) (:fv _uniq.68772) (:fv _uniq.68768) (:fv _uniq.68780) (:fv _uniq.68808) ((:c CategoryTheory.Functor.comp) (:fv _uniq.68741) (:fv _uniq.68760) (:fv _uniq.68744) (:fv _uniq.6876... | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:forall _ :explicit (:app (:c CategoryTheory.TwoSquare.GuitartExact) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV2)) (:arg :implicit-type 3 (:fv FV5)) (:arg :instance 4 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"intro","sourceEnd":4926,"sourceStart":4921,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hww'","sourceEnd":4931,"sourceStart":4927,"tag":"identifier"}],"kind":"null","source":"hww'","sourceEnd":4931,"sourceStart":4927,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"hww'","source_end":4931,"source_start":4927,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 9 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1a00703e128c6f839570fc9d60a86ca19127270082904213738c80786c110219 | d4107d4d95caa630fbc71bd829cad77cb16a3e145556c1b96fc9af61b8786c5c | 8c07d2218ca2634d6a9ae381b59f662bab028b2b62dc57db3cb35a948e98add4 | fc8596e9cce949840f95331af41ec0422d1a685d525ed181d74014465a1af1a2 |
cat-searcher/leandojo-benchmark-4-random | test | 199 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | letI : <a>CategoryTheory.CatCommSq</a> H₂ eL.functor eR.functor H₃ := ⟨w'⟩ | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | ((:c CategoryTheory.TwoSquare.GuitartExact) (:fv _uniq.68741) (:fv _uniq.68750) (:fv _uniq.68744) (:fv _uniq.68753) (:fv _uniq.68760) (:fv _uniq.68772) (:fv _uniq.68764) (:fv _uniq.68776) (:fv _uniq.68808) (:fv _uniq.68835) (:fv _uniq.68862) (:fv _uniq.68888) (:fv _uniq.69398)) | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:app (:c CategoryTheory.TwoSquare.GuitartExact) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV1)) (:arg :implicit-type 3 (:fv FV4)) (:arg :instance 4 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 5 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"letI","sourceEnd":4940,"sourceStart":4936,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":4941,"sourceStart":4941,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":4941,"sourceStart":4941,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"CatCommSq H₂ eL.functor eR.functor H₃","source_end":4984,"source_start":4943,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨w'⟩","source_end":4996,"source_start":4988,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 10 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1511d7e692b4d048ef99ef4393f22a2a083728d8709c3bc92215124c76a69c0b | fc8596e9cce949840f95331af41ec0422d1a685d525ed181d74014465a1af1a2 | 51afd012ba4a86b764ab7f7543c2e1921f072a8fa5a2ef5897af9f62e79df159 | 86ab85eba560c837d1de563c2ac35efb97f05e81fdccc5ea109747a340c89dc5 |
cat-searcher/leandojo-benchmark-4-random | test | 200 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hw' : <a>CategoryTheory.CatCommSq.iso</a> H₂ eL.functor eR.functor H₃ = w' := <a>rfl</a> | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | ((:c CategoryTheory.TwoSquare.GuitartExact) (:fv _uniq.68741) (:fv _uniq.68750) (:fv _uniq.68744) (:fv _uniq.68753) (:fv _uniq.68760) (:fv _uniq.68772) (:fv _uniq.68764) (:fv _uniq.68776) (:fv _uniq.68808) (:fv _uniq.68835) (:fv _uniq.68862) (:fv _uniq.68888) (:fv _uniq.69398)) | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:app (:c CategoryTheory.TwoSquare.GuitartExact) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV1)) (:arg :implicit-type 3 (:fv FV4)) (:arg :instance 4 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 5 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":5005,"sourceStart":5001,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hw'","sourceEnd":5009,"sourceStart":5006,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hw'","sourceEnd":5009,"sourceStart":5006,"tag":"node"},... | [] | [{"source":"CatCommSq.iso H₂ eL.functor eR.functor H₃ = w'","source_end":5062,"source_start":5012,"syntax_kind":"«term_=_»"},{"source":"rfl","source_end":5069,"source_start":5066,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 11 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e1e558c1b01488bae3bec14fdb0deda10fc14b2593bf3e1cc580b346549610cc | 86ab85eba560c837d1de563c2ac35efb97f05e81fdccc5ea109747a340c89dc5 | 5b015c81249e3f204bb5b82a696ca4832eb43a5a75eab8bfd2007957e3471e6b | aa01fb0e5a66673f270272f3cecae5e1b6edfb7834e8a49e71b80fe0b1a021f1 |
cat-searcher/leandojo-benchmark-4-random | test | 201 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | letI : <a>CategoryTheory.CatCommSq</a> H₃ eL.inverse eR.inverse H₂ := <a>CategoryTheory.CatCommSq.vInvEquiv</a> _ _ _ _ <a>inferInstance</a> | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | ((:c CategoryTheory.TwoSquare.GuitartExact) (:fv _uniq.68741) (:fv _uniq.68750) (:fv _uniq.68744) (:fv _uniq.68753) (:fv _uniq.68760) (:fv _uniq.68772) (:fv _uniq.68764) (:fv _uniq.68776) (:fv _uniq.68808) (:fv _uniq.68835) (:fv _uniq.68862) (:fv _uniq.68888) (:fv _uniq.69398)) | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:app (:c CategoryTheory.TwoSquare.GuitartExact) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV1)) (:arg :implicit-type 3 (:fv FV4)) (:arg :instance 4 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 5 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"letI","sourceEnd":5078,"sourceStart":5074,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":5079,"sourceStart":5079,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":5079,"sourceStart":5079,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"CatCommSq H₃ eL.inverse eR.inverse H₂","source_end":5122,"source_start":5081,"syntax_kind":"Lean.Parser.Term.app"},{"source":"CatCommSq.vInvEquiv _ _ _ _ inferInstance","source_end":5167,"source_start":5126,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 12 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 165d9d5cf81f4e5fd8b6efcca91b12e69a7479b19fe81691cb5cb716162a3316 | aa01fb0e5a66673f270272f3cecae5e1b6edfb7834e8a49e71b80fe0b1a021f1 | 17ca2b04c4fdfc07beeea0308366eba29cd9330970f2b09c46168b35e9585532 | 29098720984b6a1572256b8e0e99e21ed50f3077cdc46b0b073611b6ab790bca |
cat-searcher/leandojo-benchmark-4-random | test | 202 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let w'' := <a>CategoryTheory.CatCommSq.iso</a> H₃ eL.inverse eR.inverse H₂ | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | ((:c CategoryTheory.TwoSquare.GuitartExact) (:fv _uniq.68741) (:fv _uniq.68750) (:fv _uniq.68744) (:fv _uniq.68753) (:fv _uniq.68760) (:fv _uniq.68772) (:fv _uniq.68764) (:fv _uniq.68776) (:fv _uniq.68808) (:fv _uniq.68835) (:fv _uniq.68862) (:fv _uniq.68888) (:fv _uniq.69398)) | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:app (:c CategoryTheory.TwoSquare.GuitartExact) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV1)) (:arg :implicit-type 3 (:fv FV4)) (:arg :instance 4 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 5 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"let","sourceEnd":5175,"sourceStart":5172,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"w''","sourceEnd":5179,"sourceStart":5176,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"s... | [] | [{"source":"CatCommSq.iso H₃ eL.inverse eR.inverse H₂","source_end":5228,"source_start":5183,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 13 | exact | true | 1 | 28 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0ecf730815911d9267646823a9df8d7e9a9bd24ef6fa906020886323e9ca90a5 | 29098720984b6a1572256b8e0e99e21ed50f3077cdc46b0b073611b6ab790bca | 99d905a7df3a4d269787d0118487262045a61b4993227ce6448afc310fabfe1d | 946c902d6d9a77eb79c83c1c7438fe3ea556c0d39a3f4794d5bef51a6f14a36a |
cat-searcher/leandojo-benchmark-4-random | test | 203 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let α : (L₁ ⋙ eL.functor) ⋙ eL.inverse ≅ L₁ := <a>CategoryTheory.Functor.associator</a> _ _ _ ≪≫ <a>CategoryTheory.isoWhiskerLeft</a> L₁ eL.unitIso.symm ≪≫ L₁.rightUnitor | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | ((:c CategoryTheory.TwoSquare.GuitartExact) (:fv _uniq.68741) (:fv _uniq.68750) (:fv _uniq.68744) (:fv _uniq.68753) (:fv _uniq.68760) (:fv _uniq.68772) (:fv _uniq.68764) (:fv _uniq.68776) (:fv _uniq.68808) (:fv _uniq.68835) (:fv _uniq.68862) (:fv _uniq.68888) (:fv _uniq.69398)) | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:app (:c CategoryTheory.TwoSquare.GuitartExact) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV1)) (:arg :implicit-type 3 (:fv FV4)) (:arg :instance 4 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 5 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"let","sourceEnd":5236,"sourceStart":5233,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"α","sourceEnd":5239,"sourceStart":5237,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":5241,"so... | [] | [{"source":"(L₁ ⋙ eL.functor) ⋙ eL.inverse ≅ L₁","source_end":5287,"source_start":5242,"syntax_kind":"CategoryTheory.«term_≅_»"},{"source":"Functor.associator _ _ _ ≪≫ isoWhiskerLeft L₁ eL.unitIso.symm ≪≫ L₁.rightUnitor","source_end":5388,"source_start":5297,"syntax_kind":"CategoryTheory.Iso.«term_≪≫_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 14 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ea73f98e35d5a2f56372724d9e8aeebb7ecd670f2a838a78fd8fe7259a335cf8 | 946c902d6d9a77eb79c83c1c7438fe3ea556c0d39a3f4794d5bef51a6f14a36a | 9039ea8fa0b8f9750557a130548d1718e871e078f985aec9e429037708cc0cfd | ef77cc974860926de05d6516fbd1bda5623c55af615bfc2870fb51e3b7967425 |
cat-searcher/leandojo-benchmark-4-random | test | 204 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let β : (R₁ ⋙ eR.functor) ⋙ eR.inverse ≅ R₁ := <a>CategoryTheory.Functor.associator</a> _ _ _ ≪≫ <a>CategoryTheory.isoWhiskerLeft</a> R₁ eR.unitIso.symm ≪≫ R₁.rightUnitor | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | ((:c CategoryTheory.TwoSquare.GuitartExact) (:fv _uniq.68741) (:fv _uniq.68750) (:fv _uniq.68744) (:fv _uniq.68753) (:fv _uniq.68760) (:fv _uniq.68772) (:fv _uniq.68764) (:fv _uniq.68776) (:fv _uniq.68808) (:fv _uniq.68835) (:fv _uniq.68862) (:fv _uniq.68888) (:fv _uniq.69398)) | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:app (:c CategoryTheory.TwoSquare.GuitartExact) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV1)) (:arg :implicit-type 3 (:fv FV4)) (:arg :instance 4 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 5 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"let","sourceEnd":5396,"sourceStart":5393,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"β","sourceEnd":5399,"sourceStart":5397,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":5401,"so... | [] | [{"source":"(R₁ ⋙ eR.functor) ⋙ eR.inverse ≅ R₁","source_end":5447,"source_start":5402,"syntax_kind":"CategoryTheory.«term_≅_»"},{"source":"Functor.associator _ _ _ ≪≫ isoWhiskerLeft R₁ eR.unitIso.symm ≪≫ R₁.rightUnitor","source_end":5548,"source_start":5457,"syntax_kind":"CategoryTheory.Iso.«term_≪≫_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 15 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ad9b869b15cf9392e5a82e7442089cba46c03d3c69d77e073cfdc73de9d0c64a | ef77cc974860926de05d6516fbd1bda5623c55af615bfc2870fb51e3b7967425 | 64573d4bea7b41fdee0413a6e01bb05ce2f6468037ea9fa5d6729187cdbcbc3d | 7bcf485f975cee043c9f39ba0e6203f59609336101504e913551cfba71076f54 |
cat-searcher/leandojo-benchmark-4-random | test | 205 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : w = (w.vComp w'.hom).<a>CategoryTheory.TwoSquare.vComp'</a> w''.hom α β := by ext X₁ dsimp simp? [w'', β, α] says simp only [<a>CategoryTheory.TwoSquare.vComp'_app</a>, <a>CategoryTheory.Functor.comp_obj</a>, <a>CategoryTheory.Iso.trans_inv</a>, <a>CategoryTheory.isoWhiskerLeft_inv</a>, <a>CategoryTheory.Iso.sym... | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | ((:c CategoryTheory.TwoSquare.GuitartExact) (:fv _uniq.68741) (:fv _uniq.68750) (:fv _uniq.68744) (:fv _uniq.68753) (:fv _uniq.68760) (:fv _uniq.68772) (:fv _uniq.68764) (:fv _uniq.68776) (:fv _uniq.68808) (:fv _uniq.68835) (:fv _uniq.68862) (:fv _uniq.68888) (:fv _uniq.69398)) | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:app (:c CategoryTheory.TwoSquare.GuitartExact) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV1)) (:arg :implicit-type 3 (:fv FV4)) (:arg :instance 4 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 5 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":5557,"sourceStart":5553,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":5558,"sourceStart":5558,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":5558,"sourceStart":5558,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"w = (w.vComp w'.hom).vComp' w''.hom α β","source_end":5601,"source_start":5560,"syntax_kind":"«term_=_»"},{"source":"vComp'_app","source_end":5695,"source_start":5685,"syntax_kind":"ident"},{"source":"Functor.comp_obj","source_end":5713,"source_start":5697,"syntax_kind":"ident"},{"source":"Iso.trans_inv","s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 16 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 70517d34200b54b4af0f3dcf6af7f202177cbc917eaac290dc299d561309ec11 | 7bcf485f975cee043c9f39ba0e6203f59609336101504e913551cfba71076f54 | d76c8545c9608a74e9e3070701821c11213d9986bff215318386c5717bc1274d | 2cded02e4f65272ad99a16ffe3f077e4686dd5973903abea179b6bf525732e81 |
cat-searcher/leandojo-benchmark-4-random | test | 206 | CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences | Mathlib/CategoryTheory/GuitartExact/VerticalComposition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [this] | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | case mp
C₁ : Type u_1
C₂ : Type u_2
C₃ : Type u_3
D₁ : Type u_4
D₂ : Type u_5
D₃ : Type u_6
inst✝⁵ : Category.{u_11, u_1} C₁
inst✝⁴ : Category.{u_7, u_2} C₂
inst✝³ : Category.{u_8, u_3} C₃
inst✝² : Category.{u_12, u_4} D₁
inst✝¹ : Category.{u_9, u_5} D₂
inst✝ : Category.{u_10, u_6} D₃
H₁ : C₁ ⥤ D₁
L₁ : C₁ ⥤ C₂
R₁ : D₁ ... | ((:c CategoryTheory.TwoSquare.GuitartExact) (:fv _uniq.68741) (:fv _uniq.68750) (:fv _uniq.68744) (:fv _uniq.68753) (:fv _uniq.68760) (:fv _uniq.68772) (:fv _uniq.68764) (:fv _uniq.68776) (:fv _uniq.68808) (:fv _uniq.68835) (:fv _uniq.68862) (:fv _uniq.68888) (:fv _uniq.69398)) | [{"name":"C₁","sexp":"(:sort (+ u_1 1))"},{"name":"C₂","sexp":"(:sort (+ u_2 1))"},{"name":"C₃","sexp":"(:sort (+ u_3 1))"},{"name":"D₁","sexp":"(:sort (+ u_4 1))"},{"name":"D₂","sexp":"(:sort (+ u_5 1))"},{"name":"D₃","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.68741))... | (:app (:c CategoryTheory.TwoSquare.GuitartExact) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV1)) (:arg :implicit-type 3 (:fv FV4)) (:arg :instance 4 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 5 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":6371,"sourceStart":6369,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6373,"sourceStart":6372,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":32,"semanticR... | [] | [{"source":"this","source_end":6377,"source_start":6373,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68741","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68744","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 22 | 35 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 76d2b00cd460d8b24fe9d9e0dcac1eedc2b2e2470f836b1ee457eff0de818ea7 | 2cded02e4f65272ad99a16ffe3f077e4686dd5973903abea179b6bf525732e81 | 65e47f2d4a9bfabc21e1664a0b073b87e8fee657aeade999395c39aa954c5bad | e361a50350ec8823fc1670482b8b5ba8a84926499e20320343e3748210427ebd |
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