dataset stringclasses 1
value | split stringclasses 1
value | row_index int64 0 4.5k | theorem stringlengths 7 81 | file_path stringclasses 723
values | repo_url stringclasses 1
value | repo_commit stringclasses 1
value | tactic stringlengths 3 2.13k | text_state stringlengths 7 2.31k | text_target_state stringlengths 0 4.07k | raw_goal_sexp stringlengths 10 11.8M | raw_hyp_sexps stringlengths 2 15.6M | model_goal_sexp stringlengths 10 2.68M | model_hyp_sexps stringlengths 2 3.62M | source_syntax stringlengths 179 164k | syntax_args stringclasses 256
values | term_ranges stringlengths 2 6.01k | local_context stringlengths 2 10.3k | unit_index int64 3 1.26k | invocation_index int64 0 357 | alignment_kind stringclasses 2
values | target_state_matches_invocation bool 2
classes | pending_goal_count int64 1 1 | hypothesis_count int64 0 77 | hypothesis_names_match bool 2
classes | raw_schema_version int64 4 4 | raw_extractor_version stringclasses 1
value | model_schema_version int64 2 2 | model_normalization stringclasses 1
value | trace_schema_version int64 3 3 | trace_extractor_version stringclasses 1
value | pantograph_commit stringclasses 1
value | model_pantograph_commit stringclasses 1
value | raw_record_sha256 stringlengths 64 64 | state_sha256 stringlengths 64 64 | tactic_sha256 stringlengths 64 64 | target_state_sha256 stringlengths 64 64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
cat-searcher/leandojo-benchmark-4-random | test | 1,143 | Ideal.map_includeRight_eq | Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Ideal.mem_map_of_mem</a> <a>Algebra.TensorProduct.includeRight</a> | case a
R : Type u_1
inst✝⁴ : CommSemiring R
A : Type u_2
B : Type u_3
inst✝³ : Semiring A
inst✝² : Semiring B
inst✝¹ : Algebra R A
inst✝ : Algebra R B
I : Ideal B
a : A
b : ↥(Submodule.restrictScalars R I)
this : a ⊗ₜ[R] ↑b = a ⊗ₜ[R] 1 * 1 ⊗ₜ[R] ↑b
⊢ 1 ⊗ₜ[R] ↑b ∈ map includeRight I | case a
R : Type u_1
inst✝⁴ : CommSemiring R
A : Type u_2
B : Type u_3
inst✝³ : Semiring A
inst✝² : Semiring B
inst✝¹ : Algebra R A
inst✝ : Algebra R B
I : Ideal B
a : A
b : ↥(Submodule.restrictScalars R I)
this : a ⊗ₜ[R] ↑b = a ⊗ₜ[R] 1 * 1 ⊗ₜ[R] ↑b
⊢ ↑b ∈ I | ((:c Membership.mem) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.75... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :... | {"children":[{"source":"apply","sourceEnd":26502,"sourceStart":26497,"tag":"atom"},{"children":[{"name":"Ideal.mem_map_of_mem","semanticRole":"global","source":"Ideal.mem_map_of_mem","sourceEnd":26523,"sourceStart":26503,"tag":"identifier"},{"children":[{"name":"Algebra.TensorProduct.includeRight","semanticRole":"globa... | [] | [{"source":"Ideal.mem_map_of_mem includeRight","source_end":26536,"source_start":26503,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte... | 64 | 110 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b296683bc4e41775c88a9dbf022e100928f573bf94305abb0ad1979452260162 | b3a14cf49864f30eb7982c19dc2e050ab59d62f783e0207b980afede37e0a710 | d4a341c32942e1e1c19d0a64d98b25d595a095d5e00ae08209a13052b0392211 | 8bb87796f3a96e44a12f549e594e4570df41bd0b8b91de34b272f5dc76d5212a |
cat-searcher/leandojo-benchmark-4-random | test | 1,144 | Ideal.map_includeRight_eq | Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Submodule.coe_mem</a> b | case a
R : Type u_1
inst✝⁴ : CommSemiring R
A : Type u_2
B : Type u_3
inst✝³ : Semiring A
inst✝² : Semiring B
inst✝¹ : Algebra R A
inst✝ : Algebra R B
I : Ideal B
a : A
b : ↥(Submodule.restrictScalars R I)
this : a ⊗ₜ[R] ↑b = a ⊗ₜ[R] 1 * 1 ⊗ₜ[R] ↑b
⊢ ↑b ∈ I | ((:c Membership.mem) (:fv _uniq.758431) ((:c Ideal) (:fv _uniq.758431) (:fv _uniq.758437)) ((:c SetLike.instMembership) ((:c Ideal) (:fv _uniq.758431) (:fv _uniq.758437)) (:fv _uniq.758431) ((:c Submodule.setLike) (:fv _uniq.758431) (:fv _uniq.758431) (:fv _uniq.758437) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c Ideal) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV3))))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :... | {"children":[{"source":"exact","sourceEnd":26552,"sourceStart":26547,"tag":"atom"},{"children":[{"name":"Submodule.coe_mem","semanticRole":"global","source":"Submodule.coe_mem","sourceEnd":26570,"sourceStart":26553,"tag":"identifier"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"b","sourceEnd":26572... | [] | [{"source":"Submodule.coe_mem b","source_end":26572,"source_start":26553,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte... | 64 | 111 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 843fc25d8f9d368c7c355dc37afceeb3719bc8e24b3a80d1416a987ec114ef54 | 8bb87796f3a96e44a12f549e594e4570df41bd0b8b91de34b272f5dc76d5212a | 2b4f4a4b6e6cb63f441bb0069efc20448ddda829b9b5ddb14d08ae1109a6a30d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,145 | Ideal.map_includeRight_eq | Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>map_add</a>] | case a.intro.add
R : Type u_1
inst✝⁴ : CommSemiring R
A : Type u_2
B : Type u_3
inst✝³ : Semiring A
inst✝² : Semiring B
inst✝¹ : Algebra R A
inst✝ : Algebra R B
I : Ideal B
x y : A ⊗[R] ↥(Submodule.restrictScalars R I)
hx :
(LinearMap.lTensor A (Submodule.restrictScalars R I).subtype) x ∈
(Submodule.restrictScala... | case a.intro.add
R : Type u_1
inst✝⁴ : CommSemiring R
A : Type u_2
B : Type u_3
inst✝³ : Semiring A
inst✝² : Semiring B
inst✝¹ : Algebra R A
inst✝ : Algebra R B
I : Ideal B
x y : A ⊗[R] ↥(Submodule.restrictScalars R I)
hx :
(LinearMap.lTensor A (Submodule.restrictScalars R I).subtype) x ∈
(Submodule.restrictScala... | ((:c Membership.mem) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.75... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :... | {"children":[{"source":"rw","sourceEnd":26721,"sourceStart":26719,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":26723,"sourceStart":26722,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"map_add","semant... | [] | [{"source":"map_add","source_end":26730,"source_start":26723,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte... | 64 | 116 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c8d21344255e819b479cd172c6e31b40465a0d24dc75bc44a0f86de96fa19f59 | fb79f75c0d2a9ef10eb2c3e7f92228427edaa3d6ee586b1ff1ec9c57ae74b613 | 703fd918770434727ed102301a80e78be6370811f42468bb3fa824a0e0999c1b | 5629408fc1f4dd3605c9ae96ee28028559eef39cc77bce9cfefb81694802bc00 |
cat-searcher/leandojo-benchmark-4-random | test | 1,146 | Ideal.map_includeRight_eq | Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Submodule.add_mem</a> _ hx hy | case a.intro.add
R : Type u_1
inst✝⁴ : CommSemiring R
A : Type u_2
B : Type u_3
inst✝³ : Semiring A
inst✝² : Semiring B
inst✝¹ : Algebra R A
inst✝ : Algebra R B
I : Ideal B
x y : A ⊗[R] ↥(Submodule.restrictScalars R I)
hx :
(LinearMap.lTensor A (Submodule.restrictScalars R I).subtype) x ∈
(Submodule.restrictScala... | ((:c Membership.mem) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.75... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :... | {"children":[{"source":"apply","sourceEnd":26745,"sourceStart":26740,"tag":"atom"},{"children":[{"name":"Submodule.add_mem","semanticRole":"global","source":"Submodule.add_mem","sourceEnd":26763,"sourceStart":26746,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":26765,"sourceStart":26764,"tag":"... | [] | [{"source":"Submodule.add_mem _ hx hy\n\n-- Now, we can prove the right exactness properties of the tensor product,\n-- in its versions for algebras","source_end":26771,"source_start":26746,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte... | 64 | 119 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 00ba5cf9f87a7c129fcf41d25c3f3a6f392ddec61c8bf071993a0cfa5923a755 | 5629408fc1f4dd3605c9ae96ee28028559eef39cc77bce9cfefb81694802bc00 | 3524bcaa2d7aa9b05e8252bb0cb7d60c47fcfd98565479396617c2df3d737cfd | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,147 | MvPFunctor.M.bisim' | Mathlib/Data/PFunctor/Multivariate/M.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have := <a>MvPFunctor.M.bisim₀</a> P (<a>EqvGen</a> R) ?_ ?_ | n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
R : P.M α → P.M α → Prop
h : ∀ (x y : P.M α), R x y → (TypeVec.id ::: Quot.mk R) <$$> dest P x = (TypeVec.id ::: Quot.mk R) <$$> dest P y
x y : P.M α
r : R x y
⊢ x = y | case refine_3
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
R : P.M α → P.M α → Prop
h : ∀ (x y : P.M α), R x y → (TypeVec.id ::: Quot.mk R) <$$> dest P x = (TypeVec.id ::: Quot.mk R) <$$> dest P y
x y : P.M α
r : R x y
this : ∀ (x y : P.M α), EqvGen R x y → x = y
⊢ x = y
case refine_1
n : ℕ
P : MvPFunctor.{u} (n ... | ((:c Eq) ((:c MvPFunctor.M) (:fv _uniq.35259) (:fv _uniq.35319) (:fv _uniq.36866)) (:fv _uniq.36869) (:fv _uniq.36870)) | [{"name":"n","sexp":"(:c Nat)"},{"name":"P","sexp":"((:c MvPFunctor) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.35259) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"α","sexp":"((:c TypeVec) (:fv _uniq.35259))"},{"name":"R","sexp":"(:fo... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MvPFunctor.M) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV3)))) (:arg :explicit 1 (:fv FV6)) (:arg :explicit 2 (:fv FV7))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"name":"P","sexp":"(:app (:c MvPFunctor) (:arg :explicit 0 (:app (:c ... | {"children":[{"source":"have","sourceEnd":12179,"sourceStart":12175,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":12180,"sourceStart":12180,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":12180,"sourceStart":12180,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"M.bisim₀ P (EqvGen R) ?_ ?_","source_end":12212,"source_start":12183,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 56 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f83061a9e459f1252294efb680cbe923150ba79ccbe25acff1881808cbb313aa | 3f1c2be2e116f84c7bee8f2a33776ade9540f0bff02d986313b7e54e315f011f | 7c48bd4ffc5e547d6b520040eb57369c4eab6bdc74b26b71afe3e6b62541d458 | 3886080866ead3302f72568354e8a6a46f312eb1e7a909da14e997f1b4226db0 |
cat-searcher/leandojo-benchmark-4-random | test | 1,148 | MvPFunctor.M.bisim' | Mathlib/Data/PFunctor/Multivariate/M.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | solve_by_elim [<a>EqvGen.rel</a>] | case refine_3
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
R : P.M α → P.M α → Prop
h : ∀ (x y : P.M α), R x y → (TypeVec.id ::: Quot.mk R) <$$> dest P x = (TypeVec.id ::: Quot.mk R) <$$> dest P y
x y : P.M α
r : R x y
this : ∀ (x y : P.M α), EqvGen R x y → x = y
⊢ x = y | ((:c Eq) ((:c MvPFunctor.M) (:fv _uniq.35259) (:fv _uniq.35319) (:fv _uniq.36866)) (:fv _uniq.36869) (:fv _uniq.36870)) | [{"name":"n","sexp":"(:c Nat)"},{"name":"P","sexp":"((:c MvPFunctor) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.35259) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"α","sexp":"((:c TypeVec) (:fv _uniq.35259))"},{"name":"R","sexp":"(:fo... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MvPFunctor.M) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV3)))) (:arg :explicit 1 (:fv FV6)) (:arg :explicit 2 (:fv FV7))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"name":"P","sexp":"(:app (:c MvPFunctor) (:arg :explicit 0 (:app (:c ... | {"children":[{"children":[{"children":[{"children":[{"source":"solve_by_elim","sourceEnd":12231,"sourceStart":12218,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":... | [] | [{"source":"EqvGen.rel","source_end":12243,"source_start":12233,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 56 | 7 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 57a6319312e69503c00d7a2a40bffba556c2420d106b93ef638d300fd20f73ed | ceb5d620ff4a30a78a0610a84bfc960a2354205c1faf5378f6f4e7cabece20da | fd7aa23b8077da704e81d77b2c9ba91b13286dba175dd01b76e30c8be61f69f3 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,149 | MvPFunctor.M.bisim' | Mathlib/Data/PFunctor/Multivariate/M.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>EqvGen.is_equivalence</a> | case refine_1
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
R : P.M α → P.M α → Prop
h : ∀ (x y : P.M α), R x y → (TypeVec.id ::: Quot.mk R) <$$> dest P x = (TypeVec.id ::: Quot.mk R) <$$> dest P y
x y : P.M α
r : R x y
⊢ Equivalence (EqvGen R) | ((:c Equivalence) ((:c MvPFunctor.M) (:fv _uniq.35259) (:fv _uniq.35319) (:fv _uniq.36866)) ((:c EqvGen) ((:c MvPFunctor.M) (:fv _uniq.35259) (:fv _uniq.35319) (:fv _uniq.36866)) (:fv _uniq.36867))) | [{"name":"n","sexp":"(:c Nat)"},{"name":"P","sexp":"((:c MvPFunctor) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.35259) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"α","sexp":"((:c TypeVec) (:fv _uniq.35259))"},{"name":"R","sexp":"(:fo... | (:app (:c Equivalence) (:arg :implicit-type 0 (:app (:c MvPFunctor.M) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV3)))) (:arg :explicit 1 (:app (:c EqvGen) (:arg :implicit-type 0 (:app (:c MvPFunctor.M) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV3)))) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"name":"P","sexp":"(:app (:c MvPFunctor) (:arg :explicit 0 (:app (:c ... | {"children":[{"children":[{"children":[{"children":[{"source":"apply","sourceEnd":12255,"sourceStart":12250,"tag":"atom"},{"name":"EqvGen.is_equivalence","semanticRole":"global","source":"EqvGen.is_equivalence","sourceEnd":12277,"sourceStart":12256,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply ... | [] | [{"source":"EqvGen.is_equivalence","source_end":12277,"source_start":12256,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 56 | 12 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b2949c36e3ce67d70c25821ce1f6486882c8dad43e1f8dbc73466932e9246686 | 5401a1e922f8e940989a57612a47f1e55b00521f27a2fad945e98e036f80a7c4 | 54536b1a7b46a99afef0e51a447017877ac89f3f5af7f9477fb5c7bf204ffe4e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,150 | MvPFunctor.M.bisim' | Mathlib/Data/PFunctor/Multivariate/M.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | clear r x y | case refine_2
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
R : P.M α → P.M α → Prop
h : ∀ (x y : P.M α), R x y → (TypeVec.id ::: Quot.mk R) <$$> dest P x = (TypeVec.id ::: Quot.mk R) <$$> dest P y
x y : P.M α
r : R x y
⊢ ∀ (x y : P.M α),
EqvGen R x y → (TypeVec.id ::: Quot.mk (EqvGen R)) <$$> dest P x = (Type... | case refine_2
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
R : P.M α → P.M α → Prop
h : ∀ (x y : P.M α), R x y → (TypeVec.id ::: Quot.mk R) <$$> dest P x = (TypeVec.id ::: Quot.mk R) <$$> dest P y
⊢ ∀ (x y : P.M α),
EqvGen R x y → (TypeVec.id ::: Quot.mk (EqvGen R)) <$$> dest P x = (TypeVec.id ::: Quot.mk (Eq... | (:forall x ((:c MvPFunctor.M) (:fv _uniq.35259) (:fv _uniq.35319) (:fv _uniq.36866)) (:forall y ((:c MvPFunctor.M) (:fv _uniq.35259) (:fv _uniq.35319) (:fv _uniq.36866)) (:forall _ ((:c EqvGen) ((:c MvPFunctor.M) (:fv _uniq.35259) (:fv _uniq.35319) (:fv _uniq.36866)) (:fv _uniq.36867) 1 0) ((:c Eq) ((:c MvPFunctor.Obj)... | [{"name":"n","sexp":"(:c Nat)"},{"name":"P","sexp":"((:c MvPFunctor) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.35259) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"α","sexp":"((:c TypeVec) (:fv _uniq.35259))"},{"name":"R","sexp":"(:fo... | (:forall x :explicit (:app (:c MvPFunctor.M) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV3))) (:forall y :explicit (:app (:c MvPFunctor.M) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV3))) (:forall _ :explicit (:app (:c EqvGen) (:arg :implicit-type 0 (:app (:c Mv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"name":"P","sexp":"(:app (:c MvPFunctor) (:arg :explicit 0 (:app (:c ... | {"children":[{"source":"clear","sourceEnd":12288,"sourceStart":12283,"tag":"atom"},{"children":[{"contextIndex":8,"semanticRole":"local","source":"r","sourceEnd":12290,"sourceStart":12289,"tag":"identifier"},{"contextIndex":6,"semanticRole":"local","source":"x","sourceEnd":12292,"sourceStart":12291,"tag":"identifier"},... | [] | [{"source":"r","source_end":12290,"source_start":12289,"syntax_kind":"ident"},{"source":"x","source_end":12292,"source_start":12291,"syntax_kind":"ident"},{"source":"y","source_end":12294,"source_start":12293,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 56 | 19 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 95803e4e83b94a0402305a4217398b722c19475a97a61dee32bc95acc73e86e7 | 5649c2a4a4854b9a00308cf8b6f44f3a494ee14035cd9a60ad668fff5d60327e | 6bff3282f2a4d16a249b6a4124c8ecbae0cc657d7e1fd387cd43f540bf18bb49 | 2f9cb0fe6089bc9783270a4cd3531fa4da72bca98f341a50c21f90c1e2ff1eb0 |
cat-searcher/leandojo-benchmark-4-random | test | 1,151 | MvPFunctor.M.bisim' | Mathlib/Data/PFunctor/Multivariate/M.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | introv Hr | case refine_2
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
R : P.M α → P.M α → Prop
h : ∀ (x y : P.M α), R x y → (TypeVec.id ::: Quot.mk R) <$$> dest P x = (TypeVec.id ::: Quot.mk R) <$$> dest P y
⊢ ∀ (x y : P.M α),
EqvGen R x y → (TypeVec.id ::: Quot.mk (EqvGen R)) <$$> dest P x = (TypeVec.id ::: Quot.mk (Eq... | case refine_2
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
R : P.M α → P.M α → Prop
h : ∀ (x y : P.M α), R x y → (TypeVec.id ::: Quot.mk R) <$$> dest P x = (TypeVec.id ::: Quot.mk R) <$$> dest P y
x y : P.M α
Hr : EqvGen R x y
⊢ (TypeVec.id ::: Quot.mk (EqvGen R)) <$$> dest P x = (TypeVec.id ::: Quot.mk (EqvGen R... | (:forall x ((:c MvPFunctor.M) (:fv _uniq.35259) (:fv _uniq.35319) (:fv _uniq.36866)) (:forall y ((:c MvPFunctor.M) (:fv _uniq.35259) (:fv _uniq.35319) (:fv _uniq.36866)) (:forall _ ((:c EqvGen) ((:c MvPFunctor.M) (:fv _uniq.35259) (:fv _uniq.35319) (:fv _uniq.36866)) (:fv _uniq.36867) 1 0) ((:c Eq) ((:c MvPFunctor.Obj)... | [{"name":"n","sexp":"(:c Nat)"},{"name":"P","sexp":"((:c MvPFunctor) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.35259) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"α","sexp":"((:c TypeVec) (:fv _uniq.35259))"},{"name":"R","sexp":"(:fo... | (:forall x :explicit (:app (:c MvPFunctor.M) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV3))) (:forall y :explicit (:app (:c MvPFunctor.M) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV3))) (:forall _ :explicit (:app (:c EqvGen) (:arg :implicit-type 0 (:app (:c Mv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"name":"P","sexp":"(:app (:c MvPFunctor) (:arg :explicit 0 (:app (:c ... | {"children":[{"source":"introv","sourceEnd":12305,"sourceStart":12299,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"Hr","sourceEnd":12308,"sourceStart":12306,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"Hr","sourceEnd":12308,"sourceStart":12306,"tag":"node"}],"kind":"null"... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 56 | 20 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1e511f1b0920bc195af986e3ae3f7cda2e5ec80610690eb088244bda703c35cf | 2f9cb0fe6089bc9783270a4cd3531fa4da72bca98f341a50c21f90c1e2ff1eb0 | b2b82669270ebc7fccc64ebb1dc8605d04e1c9eacc8d0859fff63dd402bbc8b6 | 3581329f49a692c52b0777c482d87bb5ddf44692d41e0e316677ea019eeaa13c |
cat-searcher/leandojo-benchmark-4-random | test | 1,152 | MvPFunctor.M.bisim' | Mathlib/Data/PFunctor/Multivariate/M.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : ∀ x y, R x y → <a>EqvGen</a> R x y := @<a>EqvGen.rel</a> _ R | case refine_2
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
R : P.M α → P.M α → Prop
h : ∀ (x y : P.M α), R x y → (TypeVec.id ::: Quot.mk R) <$$> dest P x = (TypeVec.id ::: Quot.mk R) <$$> dest P y
x y : P.M α
Hr : EqvGen R x y
⊢ (TypeVec.id ::: Quot.mk (EqvGen R)) <$$> dest P x = (TypeVec.id ::: Quot.mk (EqvGen R... | case refine_2
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
R : P.M α → P.M α → Prop
h : ∀ (x y : P.M α), R x y → (TypeVec.id ::: Quot.mk R) <$$> dest P x = (TypeVec.id ::: Quot.mk R) <$$> dest P y
x y : P.M α
Hr : EqvGen R x y
this : ∀ (x y : P.M α), R x y → EqvGen R x y
⊢ (TypeVec.id ::: Quot.mk (EqvGen R)) <$$>... | ((:c Eq) ((:c MvPFunctor.Obj) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.35259) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) (:fv _uniq.35319) ((:c TypeVec.append1) (:fv _uniq.35259) (:fv _uniq.36866) ((:c Quot) ((:c MvPFunctor.M) (:fv _uniq.3525... | [{"name":"n","sexp":"(:c Nat)"},{"name":"P","sexp":"((:c MvPFunctor) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.35259) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"α","sexp":"((:c TypeVec) (:fv _uniq.35259))"},{"name":"R","sexp":"(:fo... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MvPFunctor.Obj) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:app (:c TypeVec.append1) (:arg :implicit 0) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:app (:c Quot) (:arg :implicit-type 0 (:app (:c MvPFunctor.M) (:arg :implicit 0) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"name":"P","sexp":"(:app (:c MvPFunctor) (:arg :explicit 0 (:app (:c ... | {"children":[{"source":"have","sourceEnd":12317,"sourceStart":12313,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":12318,"sourceStart":12318,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":12318,"sourceStart":12318,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"∀ x y, R x y → EqvGen R x y","source_end":12351,"source_start":12320,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"@EqvGen.rel _ R","source_end":12370,"source_start":12355,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 56 | 21 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1a13a8e3a6bee175c110045e051f7ae4c01209203c81ddf56a8c7efce367cf3f | 3581329f49a692c52b0777c482d87bb5ddf44692d41e0e316677ea019eeaa13c | 088f60fe06cc26de4ac8c327cb84ba321de84059fd34456eb59a97a9b7660526 | 3636edc588ce11a64cc14ddf29e960a101fe9d5b774966a176d5992f8487e74a |
cat-searcher/leandojo-benchmark-4-random | test | 1,153 | MvPFunctor.M.bisim' | Mathlib/Data/PFunctor/Multivariate/M.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction Hr | case refine_2
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
R : P.M α → P.M α → Prop
h : ∀ (x y : P.M α), R x y → (TypeVec.id ::: Quot.mk R) <$$> dest P x = (TypeVec.id ::: Quot.mk R) <$$> dest P y
x y : P.M α
Hr : EqvGen R x y
this : ∀ (x y : P.M α), R x y → EqvGen R x y
⊢ (TypeVec.id ::: Quot.mk (EqvGen R)) <$$>... | case refine_2.rel
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
R : P.M α → P.M α → Prop
h : ∀ (x y : P.M α), R x y → (TypeVec.id ::: Quot.mk R) <$$> dest P x = (TypeVec.id ::: Quot.mk R) <$$> dest P y
x y : P.M α
this : ∀ (x y : P.M α), R x y → EqvGen R x y
x✝ y✝ : P.M α
a✝ : R x✝ y✝
⊢ (TypeVec.id ::: Quot.mk (Eq... | ((:c Eq) ((:c MvPFunctor.Obj) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.35259) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) (:fv _uniq.35319) ((:c TypeVec.append1) (:fv _uniq.35259) (:fv _uniq.36866) ((:c Quot) ((:c MvPFunctor.M) (:fv _uniq.3525... | [{"name":"n","sexp":"(:c Nat)"},{"name":"P","sexp":"((:c MvPFunctor) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.35259) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"α","sexp":"((:c TypeVec) (:fv _uniq.35259))"},{"name":"R","sexp":"(:fo... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MvPFunctor.Obj) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:app (:c TypeVec.append1) (:arg :implicit 0) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:app (:c Quot) (:arg :implicit-type 0 (:app (:c MvPFunctor.M) (:arg :implicit 0) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"name":"P","sexp":"(:app (:c MvPFunctor) (:arg :explicit 0 (:app (:c ... | {"children":[{"source":"induction","sourceEnd":12384,"sourceStart":12375,"tag":"atom"},{"children":[{"contextIndex":8,"semanticRole":"local","source":"Hr","sourceEnd":12387,"sourceStart":12385,"tag":"identifier"}],"kind":"null","source":"Hr","sourceEnd":12387,"sourceStart":12385,"tag":"node"},{"children":[],"kind":"nul... | [] | [{"source":"Hr","source_end":12387,"source_start":12385,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 56 | 22 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 25db6e2d948468e0efbc3c98d54f06afea11b09c25f6bac81826fa75b2476bc9 | 3636edc588ce11a64cc14ddf29e960a101fe9d5b774966a176d5992f8487e74a | 0a4dc709e166055de9cafdf8ed70733bba42063ff43d52f30ad78f0358feb16a | 0e53c33e5c27d687330b4bfdef726119a47fc4ff758fe06c240b8ab44d254181 |
cat-searcher/leandojo-benchmark-4-random | test | 1,155 | MvPFunctor.M.bisim' | Mathlib/Data/PFunctor/Multivariate/M.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Quot.factor_mk_eq</a> R (<a>EqvGen</a> R) this] | case refine_2.rel
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
R : P.M α → P.M α → Prop
h : ∀ (x y : P.M α), R x y → (TypeVec.id ::: Quot.mk R) <$$> dest P x = (TypeVec.id ::: Quot.mk R) <$$> dest P y
x y : P.M α
this : ∀ (x y : P.M α), R x y → EqvGen R x y
x✝ y✝ : P.M α
a✝ : R x✝ y✝
⊢ (TypeVec.id ::: Quot.mk (Eq... | case refine_2.rel
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
R : P.M α → P.M α → Prop
h : ∀ (x y : P.M α), R x y → (TypeVec.id ::: Quot.mk R) <$$> dest P x = (TypeVec.id ::: Quot.mk R) <$$> dest P y
x y : P.M α
this : ∀ (x y : P.M α), R x y → EqvGen R x y
x✝ y✝ : P.M α
a✝ : R x✝ y✝
⊢ (TypeVec.id ::: Quot.factor... | ((:c Eq) ((:c MvPFunctor.Obj) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.35259) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) (:fv _uniq.35319) ((:c TypeVec.append1) (:fv _uniq.35259) (:fv _uniq.36866) ((:c Quot) ((:c MvPFunctor.M) (:fv _uniq.3525... | [{"name":"n","sexp":"(:c Nat)"},{"name":"P","sexp":"((:c MvPFunctor) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.35259) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"α","sexp":"((:c TypeVec) (:fv _uniq.35259))"},{"name":"R","sexp":"(:fo... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MvPFunctor.Obj) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:app (:c TypeVec.append1) (:arg :implicit 0) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:app (:c Quot) (:arg :implicit-type 0 (:app (:c MvPFunctor.M) (:arg :implicit 0) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"name":"P","sexp":"(:app (:c MvPFunctor) (:arg :explicit 0 (:app (:c ... | {"children":[{"source":"rw","sourceEnd":12397,"sourceStart":12395,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12399,"sourceStart":12398,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":12402,"sourceSt... | [] | [{"source":"Quot.factor_mk_eq R (EqvGen R) this","source_end":12438,"source_start":12403,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 56 | 27 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b99c7226c46f54d622e4d1252829a931b1fcb29453e0f49132365a928a09f9f3 | a74111af900076c22a2037c7908fb3c59f3c2b5e0ecae0871e2dae7ef46aaf93 | cadf278eab1d0bdafd8a835ef991121c4232b3487c4e6760fb11c0e33f9fe274 | 29fd402c7f511520593bbc4b461a40131ed550f668ec9dac1c55dd75ca73e66b |
cat-searcher/leandojo-benchmark-4-random | test | 1,156 | MvPFunctor.M.bisim' | Mathlib/Data/PFunctor/Multivariate/M.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>TypeVec.appendFun_comp_id</a>, ← <a>MvFunctor.map_map</a>, ← <a>MvFunctor.map_map</a>, h] | case refine_2.rel
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
R : P.M α → P.M α → Prop
h : ∀ (x y : P.M α), R x y → (TypeVec.id ::: Quot.mk R) <$$> dest P x = (TypeVec.id ::: Quot.mk R) <$$> dest P y
x y : P.M α
this : ∀ (x y : P.M α), R x y → EqvGen R x y
x✝ y✝ : P.M α
a✝ : R x✝ y✝
⊢ (TypeVec.id ::: Quot.factor... | ((:c Eq) ((:c MvPFunctor.Obj) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.35259) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) (:fv _uniq.35319) ((:c TypeVec.append1) (:fv _uniq.35259) (:fv _uniq.36866) ((:c Quot) ((:c MvPFunctor.M) (:fv _uniq.3525... | [{"name":"n","sexp":"(:c Nat)"},{"name":"P","sexp":"((:c MvPFunctor) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.35259) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"α","sexp":"((:c TypeVec) (:fv _uniq.35259))"},{"name":"R","sexp":"(:fo... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MvPFunctor.Obj) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:app (:c TypeVec.append1) (:arg :implicit 0) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:app (:c Quot) (:arg :implicit-type 0 (:app (:c MvPFunctor.M) (:arg :implicit 0) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"name":"P","sexp":"(:app (:c MvPFunctor) (:arg :explicit 0 (:app (:c ... | {"children":[{"source":"rwa","sourceEnd":12449,"sourceStart":12446,"tag":"atom"},{"children":[{"source":"[","sourceEnd":12451,"sourceStart":12450,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"TypeVec.appendFun_comp_id","semanticRole":"global","source":"appendFun... | [] | [{"source":"appendFun_comp_id","source_end":12468,"source_start":12451,"syntax_kind":"ident"},{"source":"MvFunctor.map_map","source_end":12491,"source_start":12474,"syntax_kind":"ident"},{"source":"MvFunctor.map_map","source_end":12514,"source_start":12497,"syntax_kind":"ident"},{"source":"h","source_end":12517,"source... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 56 | 30 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c053b07beea29b816d663e75f8e99899adfa6ae40c53c1eab0ade6d38259b361 | 29fd402c7f511520593bbc4b461a40131ed550f668ec9dac1c55dd75ca73e66b | db3f8435606c62e60e75733e3cf78940cbd65e9d2c7f33d29ebf7c2c78c7dc63 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,157 | MvPFunctor.M.bisim' | Mathlib/Data/PFunctor/Multivariate/M.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | aesop | case refine_2.trans
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
R : P.M α → P.M α → Prop
h : ∀ (x y : P.M α), R x y → (TypeVec.id ::: Quot.mk R) <$$> dest P x = (TypeVec.id ::: Quot.mk R) <$$> dest P y
x y : P.M α
this : ∀ (x y : P.M α), R x y → EqvGen R x y
x✝ y✝ z✝ : P.M α
a✝¹ : EqvGen R x✝ y✝
a✝ : EqvGen R y✝... | ((:c Eq) ((:c MvPFunctor.Obj) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.35259) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) (:fv _uniq.35319) ((:c TypeVec.append1) (:fv _uniq.35259) (:fv _uniq.36866) ((:c Quot) ((:c MvPFunctor.M) (:fv _uniq.3525... | [{"name":"n","sexp":"(:c Nat)"},{"name":"P","sexp":"((:c MvPFunctor) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.35259) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"α","sexp":"((:c TypeVec) (:fv _uniq.35259))"},{"name":"R","sexp":"(:fo... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MvPFunctor.Obj) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:app (:c TypeVec.append1) (:arg :implicit 0) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:app (:c Quot) (:arg :implicit-type 0 (:app (:c MvPFunctor.M) (:arg :implicit 0) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"name":"P","sexp":"(:app (:c MvPFunctor) (:arg :explicit 0 (:app (:c ... | {"children":[{"children":[{"children":[{"children":[{"source":"aesop","sourceEnd":12538,"sourceStart":12533,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Aesop.Frontend.Parser.aesopTactic","source":"aesop","sourceEnd":12538,"sourceStart":12533,"tag":"node"}],"kind":"null","source":"aesop... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35259","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35319","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 56 | 43 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0ac800508cce22b2288ae1ed209df7cec10ae34f7ba305302a61e8f7b9cc3231 | 19abb2ace3b9ea6c3fc9eb9172041b2b7e9e949b62bd1cecc867d9cbf2a74942 | bf61abd9c8c94e02103733c96be27852844483acbf580158f224257e620356a8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,158 | Nat.even_or_odd' | Mathlib/Algebra/Ring/Parity.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [← <a>two_mul</a>, <a>exists_or</a>, <a>Odd</a>, <a>Even</a>] using <a>Nat.even_or_odd</a> n | F : Type u_1
α : Type u_2
β : Type u_3
R : Type u_4
m n✝ n : ℕ
⊢ ∃ k, n = 2 * k ∨ n = 2 * k + 1 | ((:c Exists) (:c Nat) (:lambda k (:c Nat) ((:c Or) ((:c Eq) (:c Nat) (:fv _uniq.43897) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2))) 0)) ((:c Eq) (:c Nat) (:fv _uniq.43897) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"(:c Nat)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda k :explicit (:c Nat) (:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43695","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.43698","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":9998,"sourceStart":9993,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"two_mul","source_end":10016,"source_start":10009,"syntax_kind":"ident"},{"source":"exists_or","source_end":10027,"source_start":10018,"syntax_kind":"ident"},{"source":"Odd","source_end":10032,"source_start":10029,"syntax_kind":"ident"},{"source":"Even","source_end":10038,"source_start":10034,"syntax_kind":"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43695","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.43698","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 124 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6917b83499b84beb024bfb9ed3ea87aeaac918932be408400815c26c1cecbc23 | c01ae2da4e4d4149f4455c67b3bbaaffa0d80c094cbb66363407c2bfc95a9070 | c68b325d5b87b2396866fd668b905fe3d4e776122c7cb6e49406966aab5e2011 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,159 | AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Asymptotics.IsTheta.norm_left</a> ?_ | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
p : ℝ
hp : p ≠ 0
⊢ (fun x => ‖deriv (fun z => z ^ p * (1 + ε z)) x‖) =Θ[atTop] fun z => z ^ (p - 1) | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
p : ℝ
hp : p ≠ 0
⊢ (deriv fun z => z ^ p * (1 + ε z)) =Θ[atTop] fun z => z ^ (p - 1) | ((:c Asymptotics.IsTheta) (:c Real) (:c Real) (:c Real) (:c Real.norm) (:c Real.norm) ((:c Filter.atTop) (:c Real) (:c Real.instPreorder)) (:lambda x (:c Real) ((:c Norm.norm) (:c Real) (:c Real.norm) ((:c deriv) (:c Real) ((:c DenselyNormedField.toNontriviallyNormedField) (:c Real) (:c Real.denselyNormedField)) (:c Re... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.1051103))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.1051103))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.105110... | (:app (:c Asymptotics.IsTheta) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:c Real))))) (:arg :instance 4 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:c Real))))) (:arg :explicit 5 (:app (:c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1051103","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1051106","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :exp... | {"children":[{"source":"refine","sourceEnd":47690,"sourceStart":47684,"tag":"atom"},{"children":[{"name":"Asymptotics.IsTheta.norm_left","semanticRole":"global","source":"IsTheta.norm_left","sourceEnd":47708,"sourceStart":47691,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":47710,"sourceStart":... | [] | [{"source":"IsTheta.norm_left ?_","source_end":47711,"source_start":47691,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1051103","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1051106","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_ind... | 94 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e2f78e4a13874aff99592a1e68e28828bf89101f00f9d85867e679476b2b9cb3 | e54a55aea01c332a7fa46fbe38b5da7f4e479c3e88f5c0ea1f1c829bbb6d4b69 | 46d18c1c55e035baf69953009bd539715bae39ccdc72f35fe1f4a66382b04d7c | 7854395521bd18595539dca210221d144187c4bd3d6d765961508911be186448 |
cat-searcher/leandojo-benchmark-4-random | test | 1,160 | AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | calc (fun x => <a>deriv</a> (fun z => z ^ p * (1 + ε z)) x) =Θ[<a>Filter.atTop</a>] fun z => p * z ^ (p-1) := (<a>AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn</a> hp).<a>Asymptotics.IsEquivalent.isTheta</a> _ =Θ[<a>Filter.atTop</a>] fun z => z ^ (p-1) := <a>Asymptotics.IsTheta.const_mul_left</a... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
p : ℝ
hp : p ≠ 0
⊢ (deriv fun z => z ^ p * (1 + ε z)) =Θ[atTop] fun z => z ^ (p - 1) | ((:c Asymptotics.IsTheta) (:c Real) (:c Real) (:c Real) ((:c SeminormedAddCommGroup.toNorm) (:c Real) ((:c NonUnitalSeminormedRing.toSeminormedAddCommGroup) (:c Real) ((:c NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing) (:c Real) ((:c SeminormedCommRing.toNonUnitalSeminormedCommRing) (:c Real) ((:c NormedCommRin... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.1051103))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.1051103))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.105110... | (:app (:c Asymptotics.IsTheta) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:c Real))))) (:arg :instance 4 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:c Real))))) (:arg :explicit 5 (:app (:c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1051103","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1051106","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :exp... | {"children":[{"source":"calc","sourceEnd":47718,"sourceStart":47714,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"(","sourceEnd":47720,"sourceStart":47719,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":47723,"sourceStart":47720,"tag":"atom"},{"children":[{"children":[{"semanticRol... | [] | [{"source":"(fun x => deriv (fun z => z ^ p * (1 + ε z)) x) =Θ[atTop] fun z => p * z ^ (p-1)","source_end":47801,"source_start":47719,"syntax_kind":"Asymptotics.«term_=Θ[_]_»"},{"source":"(isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn hp).isTheta","source_end":47879,"source_start":47817,"syntax_kind":"Lean.Parser.T... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1051103","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1051106","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_ind... | 94 | 5 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ef00268629c40dfbd2ececeb9330e40ac217475f25b91ea4802e643b850a57e3 | 7854395521bd18595539dca210221d144187c4bd3d6d765961508911be186448 | 6f401ffa7ddcea86954cce9ba8c5345bac1d6bd7c7f09780404430bec93620d2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,161 | InnerProductGeometry.angle_comm | Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | unfold <a>InnerProductGeometry.angle</a> | V : Type u_1
inst✝¹ : NormedAddCommGroup V
inst✝ : InnerProductSpace ℝ V
x✝ y✝ x y : V
⊢ angle x y = angle y x | V : Type u_1
inst✝¹ : NormedAddCommGroup V
inst✝ : InnerProductSpace ℝ V
x✝ y✝ x y : V
⊢ arccos (⟪x, y⟫_ℝ / (‖x‖ * ‖y‖)) = arccos (⟪y, x⟫_ℝ / (‖y‖ * ‖x‖)) | ((:c Eq) (:c Real) ((:c InnerProductGeometry.angle) (:fv _uniq.13615) (:fv _uniq.13618) (:fv _uniq.13631) (:fv _uniq.13667) (:fv _uniq.13668)) ((:c InnerProductGeometry.angle) (:fv _uniq.13615) (:fv _uniq.13618) (:fv _uniq.13631) (:fv _uniq.13668) (:fv _uniq.13667))) | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.13615))"},{"name":"inst✝","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.13615) (:c Real.RCLike) (:fv _uniq.13618))"},{"name":"x✝","sexp":"(:fv _uniq.13615)"},{"name":"y✝","sexp":"(:fv _uniq.13615)"},{"name":"x",... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c InnerProductGeometry.angle) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c InnerProductSpace) (:arg :explicit 0 (:c Real)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13615","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.13618","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (:a... | {"children":[{"source":"unfold","sourceEnd":3148,"sourceStart":3142,"tag":"atom"},{"children":[{"name":"InnerProductGeometry.angle","semanticRole":"global","source":"angle","sourceEnd":3154,"sourceStart":3149,"tag":"identifier"}],"kind":"null","source":"angle","sourceEnd":3154,"sourceStart":3149,"tag":"node"},{"childre... | [] | [{"source":"angle","source_end":3154,"source_start":3149,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13615","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.13618","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 22 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 94e3ef4272c8258971dea85196135d2b1738c04a9a8014610a8e66d102bdd17c | db7d7b38f9ccbdbda8b8ff7bb2457f2676b98903638c95bbacd5fc0f90265db5 | a4fb89c1365a7e07e5abcf64801292e9b45a2ede257798fedb7b758b1c4500d3 | 8b6ce7fe2ce2a28e55809fc0f049de2cd8eaf67c0f0d8de2d98a27d229050ff6 |
cat-searcher/leandojo-benchmark-4-random | test | 1,162 | InnerProductGeometry.angle_comm | Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>real_inner_comm</a>, <a>mul_comm</a>] | V : Type u_1
inst✝¹ : NormedAddCommGroup V
inst✝ : InnerProductSpace ℝ V
x✝ y✝ x y : V
⊢ arccos (⟪x, y⟫_ℝ / (‖x‖ * ‖y‖)) = arccos (⟪y, x⟫_ℝ / (‖y‖ * ‖x‖)) | ((:c Eq) (:c Real) ((:c Real.arccos) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Inner.inner) (:c Real) (:fv _uniq.13615) ((:c InnerProductSpace.toInner) (:c Real) (:fv _uniq.13615) (:c Real.RCLike) (:fv _uniq.13... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.13615))"},{"name":"inst✝","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.13615) (:c Real.RCLike) (:fv _uniq.13618))"},{"name":"x✝","sexp":"(:fv _uniq.13615)"},{"name":"y✝","sexp":"(:fv _uniq.13615)"},{"name":"x",... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Real.arccos) (:arg :explicit 0 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:c Real)) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13615","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.13618","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (:a... | {"children":[{"source":"rw","sourceEnd":3159,"sourceStart":3157,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3161,"sourceStart":3160,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"real_inner_comm","se... | [] | [{"source":"real_inner_comm","source_end":3176,"source_start":3161,"syntax_kind":"ident"},{"source":"mul_comm","source_end":3186,"source_start":3178,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13615","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.13618","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 22 | 5 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a22d1d839a59daab3410c4fa34d1252a501ca4fc29a7501ac6ea63b7211f0b3c | 8b6ce7fe2ce2a28e55809fc0f049de2cd8eaf67c0f0d8de2d98a27d229050ff6 | ba0c52807ff715a3f91a03860aa1c4452683cd4738f12018a50966bb7e3e009f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,163 | Subsemigroup.mem_sSup_of_directed_on | Mathlib/Algebra/Group/Subsemigroup/Membership.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>sSup_eq_iSup'</a>, <a>Subsemigroup.mem_iSup_of_directed</a> hS.directed_val, <a>SetCoe.exists</a>, <a>Subtype.coe_mk</a>, <a>exists_prop</a>] | ι : Sort u_1
M : Type u_2
A : Type u_3
B : Type u_4
inst✝ : Mul M
S : Set (Subsemigroup M)
hS : DirectedOn (fun x x_1 => x ≤ x_1) S
x : M
⊢ x ∈ sSup S ↔ ∃ s ∈ S, x ∈ s | ((:c Iff) ((:c Membership.mem) (:fv _uniq.3200) ((:c Subsemigroup) (:fv _uniq.3200) (:fv _uniq.3209)) ((:c SetLike.instMembership) ((:c Subsemigroup) (:fv _uniq.3200) (:fv _uniq.3209)) (:fv _uniq.3200) ((:c Subsemigroup.instSetLike) (:fv _uniq.3200) (:fv _uniq.3209))) (:fv _uniq.3439) ((:c SupSet.sSup) ((:c Subsemigrou... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"A","sexp":"(:sort (+ u_3 1))"},{"name":"B","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c Mul) (:fv _uniq.3200))"},{"name":"S","sexp":"((:c Set) ((:c Subsemigroup) (:fv _uniq.3200) (:fv _uniq.3209)))"},{"name":"hS","sexp":"((:... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Subsemigroup) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Mul) (:arg :explicit 0 (:fv FV1))))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3197","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3200","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":2786,"sourceStart":2782,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":2791,"sourceStart":2787,"tag":"atom"}],"kind":"nu... | [] | [{"source":"sSup_eq_iSup'","source_end":2806,"source_start":2793,"syntax_kind":"ident"},{"source":"mem_iSup_of_directed hS.directed_val","source_end":2844,"source_start":2808,"syntax_kind":"Lean.Parser.Term.app"},{"source":"SetCoe.exists","source_end":2859,"source_start":2846,"syntax_kind":"ident"},{"source":"Subtype.c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3197","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3200","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 14 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 43489d73a509f4221606e567268e22997f6288c3df738c120fca9fac0f41ea99 | cc8267981e2d4d6922083f8f8e189d23bcae7f529fbfd59f9cd74d95ae85ea21 | 702f5693c0b6790ce86079065f345c17f7aa9c7ff78cbdab0c204ba3dc9cf27b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,164 | Multiset.card_join | Mathlib/Data/Multiset/Bind.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | α : Type u_1
β : Type v
γ : Type u_2
δ : Type u_3
S : Multiset (Multiset α)
⊢ card (join 0) = (map (⇑card) 0).sum | ((:c Eq) (:c Nat) ((:c DFunLike.coe) ((:c AddMonoidHom) ((:c Multiset) (:fv _uniq.3287)) (:c Nat) ((:c AddMonoid.toAddZeroClass) ((:c Multiset) (:fv _uniq.3287)) ((:c AddCommMonoid.toAddMonoid) ((:c Multiset) (:fv _uniq.3287)) ((:c OrderedAddCommMonoid.toAddCommMonoid) ((:c Multiset) (:fv _uniq.3287)) ((:c CanonicallyO... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"S","sexp":"((:c Multiset) ((:c Multiset) (:fv _uniq.3287)))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AddMonoidHom) (:arg :explicit 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddZeroClass) (:arg :explicit 0 (:app (:c Mul... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3287","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3289","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":2326,"sourceStart":2322,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3287","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3289","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 22 | 2 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fc558b632f09548ad4915e79a8eeec310a96821595ebf9b823458f8d11be2b47 | b478e2b4d876f28a6bc51e8d8b82369225ef82b757957b04391755ee401e0f40 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,165 | Multiset.card_join | Mathlib/Data/Multiset/Bind.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | α : Type u_1
β : Type v
γ : Type u_2
δ : Type u_3
S : Multiset (Multiset α)
⊢ ∀ (a : Multiset α) (s : Multiset (Multiset α)),
card s.join = (map (⇑card) s).sum → card (a ::ₘ s).join = (map (⇑card) (a ::ₘ s)).sum | (:forall a ((:c Multiset) (:fv _uniq.3287)) (:forall s ((:c Multiset) ((:c Multiset) (:fv _uniq.3287))) (:forall _ ((:c Eq) (:c Nat) ((:c DFunLike.coe) ((:c AddMonoidHom) ((:c Multiset) (:fv _uniq.3287)) (:c Nat) ((:c AddMonoid.toAddZeroClass) ((:c Multiset) (:fv _uniq.3287)) ((:c AddCommMonoid.toAddMonoid) ((:c Multis... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"S","sexp":"((:c Multiset) ((:c Multiset) (:fv _uniq.3287)))"}] | (:forall a :explicit (:app (:c Multiset) (:arg :explicit 0 (:fv FV0))) (:forall s :explicit (:app (:c Multiset) (:arg :explicit 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0))))) (:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3287","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3289","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":2336,"sourceStart":2332,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3287","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3289","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 22 | 7 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7f975008fa5d700fd60242929ca9cbcd23b1ca52d5e5b4b8af9712c0439fae91 | a0427c5b076743ee5975d8720842e0c546a215e9b0740c985bd5f9acec312c09 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,166 | convexHull_union | Mathlib/Analysis/Convex/Join.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>convexHull_convexHull_union_left</a>, ← <a>convexHull_convexHull_union_right</a>] | ι : Sort u_1
𝕜 : Type u_2
E : Type u_3
inst✝² : LinearOrderedField 𝕜
inst✝¹ : AddCommGroup E
inst✝ : Module 𝕜 E
s t u : Set E
x y : E
hs : s.Nonempty
ht : t.Nonempty
⊢ (convexHull 𝕜) (s ∪ t) = convexJoin 𝕜 ((convexHull 𝕜) s) ((convexHull 𝕜) t) | ι : Sort u_1
𝕜 : Type u_2
E : Type u_3
inst✝² : LinearOrderedField 𝕜
inst✝¹ : AddCommGroup E
inst✝ : Module 𝕜 E
s t u : Set E
x y : E
hs : s.Nonempty
ht : t.Nonempty
⊢ (convexHull 𝕜) ((convexHull 𝕜) s ∪ (convexHull 𝕜) t) = convexJoin 𝕜 ((convexHull 𝕜) s) ((convexHull 𝕜) t) | ((:c Eq) ((:c Set) (:fv _uniq.125213)) ((:c DFunLike.coe) ((:c ClosureOperator) ((:c Set) (:fv _uniq.125213)) ((:c PartialOrder.toPreorder) ((:c Set) (:fv _uniq.125213)) ((:c OmegaCompletePartialOrder.toPartialOrder) ((:c Set) (:fv _uniq.125213)) ((:c CompleteLattice.instOmegaCompletePartialOrder) ((:c Set) (:fv _uniq.... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"𝕜","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c LinearOrderedField) (:fv _uniq.125210))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.125213))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.125210) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c ClosureOperator) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:app (:c S... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125207","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125210","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rw","sourceEnd":9297,"sourceStart":9295,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9299,"sourceStart":9298,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":9302,"sourceStart":... | [] | [{"source":"convexHull_convexHull_union_left","source_end":9335,"source_start":9303,"syntax_kind":"ident"},{"source":"convexHull_convexHull_union_right","source_end":9374,"source_start":9341,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125207","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125210","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 64 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3bba331b9af79e655fa881bcb2e1c2527b9a7a1d72ec925f1472c0d7140249e4 | dac8c3af2775fc28a9346d65e36f0654f34c819959735756e21cd843749c4f0b | 90b808200f117f121289d94b5ea4542e8f65ba2713cf82ff5f5318599b48072c | d61f3750b175ca6610de4d4a9435a56eddb82ca974aeca2dc1842a33a444fa64 |
cat-searcher/leandojo-benchmark-4-random | test | 1,167 | convexHull_union | Mathlib/Analysis/Convex/Join.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>convex_convexHull</a> 𝕜 s).<a>Convex.convexHull_union</a> (<a>convex_convexHull</a> 𝕜 t) hs.convexHull ht.convexHull | ι : Sort u_1
𝕜 : Type u_2
E : Type u_3
inst✝² : LinearOrderedField 𝕜
inst✝¹ : AddCommGroup E
inst✝ : Module 𝕜 E
s t u : Set E
x y : E
hs : s.Nonempty
ht : t.Nonempty
⊢ (convexHull 𝕜) ((convexHull 𝕜) s ∪ (convexHull 𝕜) t) = convexJoin 𝕜 ((convexHull 𝕜) s) ((convexHull 𝕜) t) | ((:c Eq) ((:c Set) (:fv _uniq.125213)) ((:c DFunLike.coe) ((:c ClosureOperator) ((:c Set) (:fv _uniq.125213)) ((:c PartialOrder.toPreorder) ((:c Set) (:fv _uniq.125213)) ((:c OmegaCompletePartialOrder.toPartialOrder) ((:c Set) (:fv _uniq.125213)) ((:c CompleteLattice.instOmegaCompletePartialOrder) ((:c Set) (:fv _uniq.... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"𝕜","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c LinearOrderedField) (:fv _uniq.125210))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.125213))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.125210) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c ClosureOperator) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:app (:c S... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125207","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125210","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"exact","sourceEnd":9383,"sourceStart":9378,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":9385,"sourceStart":9384,"tag":"atom"},{"children":[{"name":"convex_convexHull","semanticRole":"global","source":"convex_convexHull","sourceEnd":9402,"sourceStart":9385,"tag":... | [] | [{"source":"(convex_convexHull 𝕜 s).convexHull_union (convex_convexHull 𝕜 t) hs.convexHull ht.convexHull","source_end":9482,"source_start":9384,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125207","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125210","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 64 | 8 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 85d07282d55376c2aec63547e5717037654b9af4a72da187e760b3d884eccf4b | d61f3750b175ca6610de4d4a9435a56eddb82ca974aeca2dc1842a33a444fa64 | b13bd881e7d3a54c0887194625136b5d0d2d7c54cc30e4cc2a5df79b4a0a3f5b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,168 | t2_iff_ultrafilter | Mathlib/Topology/Separation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [← <a>Filter.exists_ultrafilter_iff</a>, <a>and_imp</a>, <a>le_inf_iff</a>, <a>exists_imp</a>] | X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : FirstCountableTopology X
⊢ (∀ {x y : X}, (𝓝 x ⊓ 𝓝 y).NeBot → x = y) ↔ ∀ {x y : X} (f : Ultrafilter X), ↑f ≤ 𝓝 x → ↑f ≤ 𝓝 y → x = y | ((:c Iff) (:forall x (:fv _uniq.129098) (:forall y (:fv _uniq.129098) (:forall _ ((:c Filter.NeBot) (:fv _uniq.129098) ((:c Inf.inf) ((:c Filter) (:fv _uniq.129098)) ((:c Filter.instInf) (:fv _uniq.129098)) ((:c nhds) (:fv _uniq.129098) (:fv _uniq.129104) 1) ((:c nhds) (:fv _uniq.129098) (:fv _uniq.129104) 0))) ((:c Eq... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.129098))"},{"name":"inst✝","sexp":"((:c FirstCountableTopology) (:fv _uniq.129098) (:fv _uniq.129104))"}] | (:app (:c Iff) (:arg :explicit 0 (:forall x :implicit (:fv FV0) (:forall y :implicit (:fv FV0) (:forall _ :explicit (:app (:c Filter.NeBot) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Inf.inf) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129098","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129101","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":74387,"sourceStart":74383,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":74392,"sourceStart":74388,"tag":"atom"}],"kind"... | [] | [{"source":"exists_ultrafilter_iff","source_end":74420,"source_start":74398,"syntax_kind":"ident"},{"source":"and_imp","source_end":74429,"source_start":74422,"syntax_kind":"ident"},{"source":"le_inf_iff","source_end":74441,"source_start":74431,"syntax_kind":"ident"},{"source":"exists_imp","source_end":74453,"source_st... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129098","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129101","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 388 | 2 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6dd9e10567534e176addc433052c6e0b8719a796a8eeb58c1fca3c1f8a57e1a6 | 5f63986f80ff7df709b218c44366ee6bc903c63c14d237e943e7339bee976940 | 5566e1124cabda0e1ae8e290d318308770ded44d89e8f31b5b3d74db97780195 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,169 | Part.inter_get_eq | Mathlib/Data/Part.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Part.inter_def</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
inst✝ : Inter α
a b : Part α
hab : (a ∩ b).Dom
⊢ (a ∩ b).get hab = a.get ⋯ ∩ b.get ⋯ | α : Type u_1
β : Type u_2
γ : Type u_3
inst✝ : Inter α
a b : Part α
hab : (a ∩ b).Dom
⊢ (a.bind fun y => map (fun x => y ∩ x) b).get ⋯ = a.get ⋯ ∩ b.get ⋯ | ((:c Eq) (:fv _uniq.59642) ((:c Part.get) (:fv _uniq.59642) ((:c Inter.inter) ((:c Part) (:fv _uniq.59642)) ((:c Part.instInter) (:fv _uniq.59642) (:fv _uniq.59725)) (:fv _uniq.59726) (:fv _uniq.59727)) (:fv _uniq.59728)) ((:c Inter.inter) (:fv _uniq.59642) (:fv _uniq.59725) ((:c Part.get) (:fv _uniq.59642) (:fv _uniq.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c Inter) (:fv _uniq.59642))"},{"name":"a","sexp":"((:c Part) (:fv _uniq.59642))"},{"name":"b","sexp":"((:c Part) (:fv _uniq.59642))"},{"name":"hab","sexp":"((:c Part.Dom) (... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Part.get) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Part) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c Inter) (:arg :explicit 0 (:app (:c Part) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.59642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.59645","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":31940,"sourceStart":31936,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":31942,"sourceStart":31941,"tag":"a... | [] | [{"source":"inter_def","source_end":31951,"source_start":31942,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.59642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.59645","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 305 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 15579b7c08b3052b642465d1c715970b9be659761d07df8fee5c44ea828e3902 | 9169dff9a255fd0e36efae7e320b9f58afb99c18ab910d6add93e837697e4df7 | de1e2aeae42103b4a201213f39e8db9d19775c1c7e14e48bba372121353f57b0 | ed058b5edc9008c328153fae30000425710676024d404f360327f5681be168ff |
cat-searcher/leandojo-benchmark-4-random | test | 1,170 | Part.inter_get_eq | Mathlib/Data/Part.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | aesop | α : Type u_1
β : Type u_2
γ : Type u_3
inst✝ : Inter α
a b : Part α
hab : (a ∩ b).Dom
⊢ (a.bind fun y => map (fun x => y ∩ x) b).get ⋯ = a.get ⋯ ∩ b.get ⋯ | ((:c Eq) (:fv _uniq.59642) ((:c Part.get) (:fv _uniq.59642) ((:c Part.bind) (:fv _uniq.59642) (:fv _uniq.59642) (:fv _uniq.59726) (:lambda y (:fv _uniq.59642) ((:c Part.map) (:fv _uniq.59642) (:fv _uniq.59642) (:lambda _ (:fv _uniq.59642) ((:c Inter.inter) (:fv _uniq.59642) (:fv _uniq.59725) 1 0)) (:fv _uniq.59727)))) ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c Inter) (:fv _uniq.59642))"},{"name":"a","sexp":"((:c Part) (:fv _uniq.59642))"},{"name":"b","sexp":"((:c Part) (:fv _uniq.59642))"},{"name":"hab","sexp":"((:c Part.Dom) (... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Part.get) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Part.bind) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:lambda y :explicit (:fv FV0) (:app (:c Part.... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.59642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.59645","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"aesop","sourceEnd":31959,"sourceStart":31954,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Aesop.Frontend.Parser.aesopTactic","source":"aesop","sourceEnd":31959,"sourceStart":31954,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.59642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.59645","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 305 | 6 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 97bfc8346b12303d8b92c1ea406d6a0a143c0f957c0a04c952265b65ea629939 | ed058b5edc9008c328153fae30000425710676024d404f360327f5681be168ff | bf61abd9c8c94e02103733c96be27852844483acbf580158f224257e620356a8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,171 | CategoryTheory.Limits.biprod.conePointUniqueUpToIso_inv | Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>CategoryTheory.Limits.biprod.hom_ext'</a> _ _ (hb.isLimit.hom_ext fun j => ?_) (hb.isLimit.hom_ext fun j => ?_) | J : Type w
C : Type u
inst✝⁴ : Category.{v, u} C
inst✝³ : HasZeroMorphisms C
D : Type uD
inst✝² : Category.{uD', uD} D
inst✝¹ : HasZeroMorphisms D
P Q X Y : C
inst✝ : HasBinaryBiproduct X Y
b : BinaryBicone X Y
hb : b.IsBilimit
⊢ (hb.isLimit.conePointUniqueUpToIso (BinaryBiproduct.isLimit X Y)).inv = desc b.inl b.inr | case refine_1
J : Type w
C : Type u
inst✝⁴ : Category.{v, u} C
inst✝³ : HasZeroMorphisms C
D : Type uD
inst✝² : Category.{uD', uD} D
inst✝¹ : HasZeroMorphisms D
P Q X Y : C
inst✝ : HasBinaryBiproduct X Y
b : BinaryBicone X Y
hb : b.IsBilimit
j : Discrete WalkingPair
⊢ (inl ≫ (hb.isLimit.conePointUniqueUpToIso (BinaryBi... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.559195) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.559195) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.559195) (:fv _uniq.559198))) ((:c CategoryTheory.Limits.Cone.pt) ((:c CategoryTheory.Discrete) (:c CategoryTheory.Limits.WalkingPair)) ((:c CategoryTheor... | [{"name":"J","sexp":"(:sort (+ w 1))"},{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.559195))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Limits.HasZeroMorphisms) (:fv _uniq.559195) (:fv _uniq.559198))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝²"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c CategoryTheory.Limits.Cone.pt) (:arg :implicit-type 0 (:app (:c CategoryTheory.Discrete) (:arg :explicit 0 (:c Catego... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.559193","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.559195","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":88857,"sourceStart":88851,"tag":"atom"},{"children":[{"name":"CategoryTheory.Limits.biprod.hom_ext'","semanticRole":"global","source":"biprod.hom_ext'","sourceEnd":88873,"sourceStart":88858,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":88875,"sourceS... | [] | [{"source":"biprod.hom_ext' _ _ (hb.isLimit.hom_ext fun j => ?_) (hb.isLimit.hom_ext fun j => ?_)","source_end":88943,"source_start":88858,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.559193","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.559195","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":2,"internal... | 505 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | be39c72f4b4bf0731d689d8443fc2a2e330776dfeb9ce1c5456e68dda7c3d533 | b42beb1b9da829884b70ae745d8c6e3c3d8ed4d39bc299e75a4a3eeca9b5fe18 | d416e332375a94f9f918477e68489ffdbd830ec67725ea62577301a5143dad04 | 30e7f9d05885606846f92d8cb0371c520ceb3714fbc56dd13aa1ebb882570ec3 |
cat-searcher/leandojo-benchmark-4-random | test | 1,174 | CategoryTheory.Limits.biprod.conePointUniqueUpToIso_inv | Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>CategoryTheory.Category.assoc</a>, <a>CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp</a>] | case refine_2
J : Type w
C : Type u
inst✝⁴ : Category.{v, u} C
inst✝³ : HasZeroMorphisms C
D : Type uD
inst✝² : Category.{uD', uD} D
inst✝¹ : HasZeroMorphisms D
P Q X Y : C
inst✝ : HasBinaryBiproduct X Y
b : BinaryBicone X Y
hb : b.IsBilimit
j : Discrete WalkingPair
⊢ (inr ≫ (hb.isLimit.conePointUniqueUpToIso (BinaryBi... | case refine_2
J : Type w
C : Type u
inst✝⁴ : Category.{v, u} C
inst✝³ : HasZeroMorphisms C
D : Type uD
inst✝² : Category.{uD', uD} D
inst✝¹ : HasZeroMorphisms D
P Q X Y : C
inst✝ : HasBinaryBiproduct X Y
b : BinaryBicone X Y
hb : b.IsBilimit
j : Discrete WalkingPair
⊢ inr ≫ (BinaryBiproduct.bicone X Y).toCone.π.app j =... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.559195) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.559195) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.559195) (:fv _uniq.559198))) (:fv _uniq.559836) ((:c Prefunctor.obj) ((:c CategoryTheory.Discrete) (:c CategoryTheory.Limits.WalkingPair)) ((:c CategoryT... | [{"name":"J","sexp":"(:sort (+ w 1))"},{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.559195))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Limits.HasZeroMorphisms) (:fv _uniq.559195) (:fv _uniq.559198))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝²"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV11)) (:arg :explicit 3 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c CategoryTheory.Discrete) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.559193","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.559195","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"simp","sourceEnd":88964,"sourceStart":88960,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":88969,"sourceStart":88965,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":889... | [] | [{"source":"Category.assoc","source_end":88985,"source_start":88971,"syntax_kind":"ident"},{"source":"IsLimit.conePointUniqueUpToIso_inv_comp","source_end":89026,"source_start":88987,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.559193","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.559195","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":2,"internal... | 505 | 12 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c9daa2e401f408a9689b47be3f9a6c4be0b9c01b525755618ddd5937d65d6cd9 | 6806b7468a1c623b45c39a9c976a0da0fe5c5d50092c9478eb22832d5e023233 | c17b362db313b3fa49282a2d7e65a1fa6f9aaf3bec5d33317f65abd989a1c53f | 5408bdd9f166339f134d65508ad22c42e7aa17af32d16794579419228287f262 |
cat-searcher/leandojo-benchmark-4-random | test | 1,175 | CategoryTheory.Limits.biprod.conePointUniqueUpToIso_inv | Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases j with ⟨⟨⟩⟩ | case refine_2
J : Type w
C : Type u
inst✝⁴ : Category.{v, u} C
inst✝³ : HasZeroMorphisms C
D : Type uD
inst✝² : Category.{uD', uD} D
inst✝¹ : HasZeroMorphisms D
P Q X Y : C
inst✝ : HasBinaryBiproduct X Y
b : BinaryBicone X Y
hb : b.IsBilimit
j : Discrete WalkingPair
⊢ inr ≫ (BinaryBiproduct.bicone X Y).toCone.π.app j =... | case refine_2.mk.left
J : Type w
C : Type u
inst✝⁴ : Category.{v, u} C
inst✝³ : HasZeroMorphisms C
D : Type uD
inst✝² : Category.{uD', uD} D
inst✝¹ : HasZeroMorphisms D
P Q X Y : C
inst✝ : HasBinaryBiproduct X Y
b : BinaryBicone X Y
hb : b.IsBilimit
⊢ inr ≫ (BinaryBiproduct.bicone X Y).toCone.π.app { as := WalkingPair.... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.559195) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.559195) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.559195) (:fv _uniq.559198))) (:fv _uniq.559836) ((:c Prefunctor.obj) ((:c CategoryTheory.Discrete) (:c CategoryTheory.Limits.WalkingPair)) ((:c CategoryT... | [{"name":"J","sexp":"(:sort (+ w 1))"},{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.559195))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Limits.HasZeroMorphisms) (:fv _uniq.559195) (:fv _uniq.559198))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝²"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV11)) (:arg :explicit 3 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c CategoryTheory.Discrete) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.559193","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.559195","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rcases","sourceEnd":89038,"sourceStart":89032,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":15,"semanticRole":"local","source":"j","sourceEnd":89040,"sourceStart":89039,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","... | [] | [{"source":"j","source_end":89040,"source_start":89039,"syntax_kind":"ident"},{"source":"⟨⟨⟩⟩","source_end":89058,"source_start":89046,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.559193","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.559195","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":2,"internal... | 505 | 13 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1ddbdecc044e9ca599037d3bc5195976cf1967af644f30a8da5a749d985453ab | 5408bdd9f166339f134d65508ad22c42e7aa17af32d16794579419228287f262 | 25da45a490babec4dd106858bd2dc9fdd5743e5c5dd913eda744020ab4aea674 | e728c5f2610f2161bc2688239357d1a4269ccea4e443cc10bc8fd97dac940c21 |
cat-searcher/leandojo-benchmark-4-random | test | 1,176 | CategoryTheory.Limits.biprod.conePointUniqueUpToIso_inv | Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case refine_2.mk.right
J : Type w
C : Type u
inst✝⁴ : Category.{v, u} C
inst✝³ : HasZeroMorphisms C
D : Type uD
inst✝² : Category.{uD', uD} D
inst✝¹ : HasZeroMorphisms D
P Q X Y : C
inst✝ : HasBinaryBiproduct X Y
b : BinaryBicone X Y
hb : b.IsBilimit
⊢ inr ≫ (BinaryBiproduct.bicone X Y).toCone.π.app { as := WalkingPair... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.559195) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.559195) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.559195) (:fv _uniq.559198))) (:fv _uniq.559836) ((:c Prefunctor.obj) ((:c CategoryTheory.Discrete) (:c CategoryTheory.Limits.WalkingPair)) ((:c CategoryT... | [{"name":"J","sexp":"(:sort (+ w 1))"},{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.559195))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Limits.HasZeroMorphisms) (:fv _uniq.559195) (:fv _uniq.559198))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝²"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV11)) (:arg :explicit 3 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c CategoryTheory.Discrete) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.559193","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.559195","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":89075,"sourceStart":89071,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","sour... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.559193","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.559195","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":2,"internal... | 505 | 24 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b7ea2300d0e25ef3532a04a138127e2071a8bdf5de2ee144e7a50259347367f7 | fd7d1d317fc67edc03ffe338f102c5a42625f6b0829a1d591f3d017de350cbd5 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,179 | iSup_const | Mathlib/Order/CompleteLattice.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>iSup</a>, <a>Set.range_const</a>, <a>sSup_singleton</a>] | α : Type u_1
β : Type u_2
β₂ : Type u_3
γ : Type u_4
ι : Sort u_5
ι' : Sort u_6
κ : ι → Sort u_7
κ' : ι' → Sort u_8
inst✝¹ : CompleteLattice α
f g s t : ι → α
a b : α
inst✝ : Nonempty ι
⊢ ⨆ x, a = a | ((:c Eq) (:fv _uniq.66473) ((:c iSup) (:fv _uniq.66473) (:fv _uniq.66485) ((:c CompleteLattice.toSupSet) (:fv _uniq.66473) (:fv _uniq.66501)) (:lambda _ (:fv _uniq.66485) (:fv _uniq.66519))) (:fv _uniq.66519)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"β₂","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort u_5)"},{"name":"ι'","sexp":"(:sort u_6)"},{"name":"κ","sexp":"(:forall _ (:fv _uniq.66485) (:sort u_7))"},{"name":"κ'","sexp":"(:fo... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c iSup) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV4)) (:arg :instance 2 (:instance-of (:app (:c SupSet) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 3 (:lambda _ :explicit (:fv FV4) (:fv FV13))))) (:arg :explicit 2 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66473","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.66476","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":37484,"sourceStart":37482,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":37486,"sourceStart":37485,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"iSup","source_end":37490,"source_start":37486,"syntax_kind":"ident"},{"source":"range_const","source_end":37503,"source_start":37492,"syntax_kind":"ident"},{"source":"sSup_singleton","source_end":37519,"source_start":37505,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66473","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.66476","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 348 | 2 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bba4edf8998b4071b664f3a379f1a17ee0d3ace48b3c83d3f4de5f86bf84ca5d | 7677fa51121632f4c35f9488355dd1fe53e134a5413a880c861f490706a89eb6 | 013e97d6355c806540da08836a71358727aa2840f7cf8d898b9bcddeb10d4265 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,180 | Pell.y_dvd_iff | Mathlib/NumberTheory/PellMatiyasevic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have co : <a>Nat.Coprime</a> (<a>Pell.yn</a> a1 m) (<a>Pell.xn</a> a1 (m * (n / m))) := <a>Nat.Coprime.symm</a> <| (<a>Pell.xy_coprime</a> a1 _).<a>Nat.Coprime.coprime_dvd_right</a> (<a>Pell.y_mul_dvd</a> a1 m (n / m)) | a : ℕ
a1 : 1 < a
m n : ℕ
h : yn a1 m ∣ yn a1 n
hp : n % m > 0
⊢ False | a : ℕ
a1 : 1 < a
m n : ℕ
h : yn a1 m ∣ yn a1 n
hp : n % m > 0
co : (yn a1 m).Coprime (xn a1 (m * (n / m)))
⊢ False | (:c False) | [{"name":"a","sexp":"(:c Nat)"},{"name":"a1","sexp":"((:c LT.lt) (:c Nat) (:c instLTNat) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))) (:fv _uniq.72978))"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) ((:c Pell.yn) (:fv _un... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72978","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.73018","is_instance":false,"is_let":false,"name":"a1","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat))... | {"children":[{"source":"have","sourceEnd":16128,"sourceStart":16124,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"co","sourceEnd":16131,"sourceStart":16129,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"co","sourceEnd":16131,"sourceStart":16129,"tag":"nod... | [] | [{"source":"Nat.Coprime (yn a1 m) (xn a1 (m * (n / m)))","source_end":16177,"source_start":16134,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Nat.Coprime.symm <| (xy_coprime a1 _).coprime_dvd_right (y_mul_dvd a1 m (n / m))","source_end":16271,"source_start":16191,"syntax_kind":"«term_<|_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72978","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.73018","is_instance":false,"is_let":false,"user_name":"a1"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 114 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e773b5dc53ae200138a7cddede8ee56e470ecfbc0ce565db4699fc7954ce00db | 594e9e68967fc2d9f41c3e1ddbf5ae8bead77cdcd2d8819cdb788d202bcb6d86 | 98becbead62317d0a4a613bcf2788bd9a694ad8c4f4c7d69e9b04b963d9691f5 | 9b2eff490dff2610489e14cc15a4c3d99e84a44eea443b1fa40b34a8b50da8e7 |
cat-searcher/leandojo-benchmark-4-random | test | 1,181 | Pell.y_dvd_iff | Mathlib/NumberTheory/PellMatiyasevic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have m0 : 0 < m := m.eq_zero_or_pos.resolve_left fun e => by rw [e, <a>Nat.mod_zero</a>] at hp;rw [e] at h exact <a>ne_of_lt</a> (<a>Pell.strictMono_y</a> a1 hp) (<a>eq_zero_of_zero_dvd</a> h).<a>Eq.symm</a> | a : ℕ
a1 : 1 < a
m n : ℕ
h : yn a1 m ∣ yn a1 n
hp : n % m > 0
co : (yn a1 m).Coprime (xn a1 (m * (n / m)))
⊢ False | a : ℕ
a1 : 1 < a
m n : ℕ
h : yn a1 m ∣ yn a1 n
hp : n % m > 0
co : (yn a1 m).Coprime (xn a1 (m * (n / m)))
m0 : 0 < m
⊢ False | (:c False) | [{"name":"a","sexp":"(:c Nat)"},{"name":"a1","sexp":"((:c LT.lt) (:c Nat) (:c instLTNat) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))) (:fv _uniq.72978))"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) ((:c Pell.yn) (:fv _un... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72978","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.73018","is_instance":false,"is_let":false,"name":"a1","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat))... | {"children":[{"source":"have","sourceEnd":16284,"sourceStart":16280,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"m0","sourceEnd":16287,"sourceStart":16285,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"m0","sourceEnd":16287,"sourceStart":16285,"tag":"nod... | [] | [{"source":"0 < m","source_end":16295,"source_start":16290,"syntax_kind":"«term_<_»"},{"source":"m.eq_zero_or_pos.resolve_left fun e => by\n rw [e, Nat.mod_zero] at hp;rw [e] at h\n exact _root_.ne_of_lt (strictMono_y a1 hp) (eq_zero_of_zero_dvd h).symm","source_end":16485,"source_start":16309,"sy... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72978","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.73018","is_instance":false,"is_let":false,"user_name":"a1"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 114 | 5 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0c0928c412cc7bb6175ae3ba4cc800f7031a20d8334dda9a261f3149ab4db6dd | 9b2eff490dff2610489e14cc15a4c3d99e84a44eea443b1fa40b34a8b50da8e7 | 99cf3b9f1df0c8a4e0ad49edfdc9ce79dca499f06dbf5d5d7c3bf4fe46c9eff1 | 7f66623789d5bca8538ffc0bd5ed47a5969342c3743d480f139fc99368401931 |
cat-searcher/leandojo-benchmark-4-random | test | 1,182 | Pell.y_dvd_iff | Mathlib/NumberTheory/PellMatiyasevic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Nat.mod_add_div</a> n m, <a>Pell.yn_add</a>] at h | a : ℕ
a1 : 1 < a
m n : ℕ
h : yn a1 m ∣ yn a1 n
hp : n % m > 0
co : (yn a1 m).Coprime (xn a1 (m * (n / m)))
m0 : 0 < m
⊢ False | a : ℕ
a1 : 1 < a
m n : ℕ
h : yn a1 m ∣ xn a1 (n % m) * yn a1 (m * (n / m)) + yn a1 (n % m) * xn a1 (m * (n / m))
hp : n % m > 0
co : (yn a1 m).Coprime (xn a1 (m * (n / m)))
m0 : 0 < m
⊢ False | (:c False) | [{"name":"a","sexp":"(:c Nat)"},{"name":"a1","sexp":"((:c LT.lt) (:c Nat) (:c instLTNat) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))) (:fv _uniq.72978))"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) ((:c Pell.yn) (:fv _un... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72978","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.73018","is_instance":false,"is_let":false,"name":"a1","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat))... | {"children":[{"source":"rw","sourceEnd":16496,"sourceStart":16494,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16498,"sourceStart":16497,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":16501,"sourceSt... | [] | [{"source":"h","source_end":16535,"source_start":16534,"syntax_kind":"ident"},{"source":"Nat.mod_add_div n m","source_end":16521,"source_start":16502,"syntax_kind":"Lean.Parser.Term.app"},{"source":"yn_add","source_end":16529,"source_start":16523,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72978","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.73018","is_instance":false,"is_let":false,"user_name":"a1"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 114 | 19 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 18c0a5bf3ebba42de72d19a54941ff739b34da5bf49332c9b0ac721af324471f | 7f66623789d5bca8538ffc0bd5ed47a5969342c3743d480f139fc99368401931 | e45258fc9044e66cccf736bdf5c6518f56f3e5a01d782ac2879c30f1b9bf1ab5 | 6bd45c894fc37a49389a46fa68a76e3bd4ae0789504a6c98f0646aaff77d6b56 |
cat-searcher/leandojo-benchmark-4-random | test | 1,183 | Pell.y_dvd_iff | Mathlib/NumberTheory/PellMatiyasevic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>not_le_of_gt</a> (<a>Pell.strictMono_y</a> _ <| <a>Nat.mod_lt</a> n m0) (<a>Nat.le_of_dvd</a> (<a>Pell.strictMono_y</a> _ hp) <| co.dvd_of_dvd_mul_right <| (<a>Nat.dvd_add_iff_right</a> <| (<a>Pell.y_mul_dvd</a> _ _ _).<a>Dvd.dvd.mul_left</a> _).2 h) | a : ℕ
a1 : 1 < a
m n : ℕ
h : yn a1 m ∣ xn a1 (n % m) * yn a1 (m * (n / m)) + yn a1 (n % m) * xn a1 (m * (n / m))
hp : n % m > 0
co : (yn a1 m).Coprime (xn a1 (m * (n / m)))
m0 : 0 < m
⊢ False | (:c False) | [{"name":"a","sexp":"(:c Nat)"},{"name":"a1","sexp":"((:c LT.lt) (:c Nat) (:c instLTNat) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))) (:fv _uniq.72978))"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) ((:c Pell.yn) (:fv _un... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72978","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.73018","is_instance":false,"is_let":false,"name":"a1","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat))... | {"children":[{"source":"exact","sourceEnd":16549,"sourceStart":16544,"tag":"atom"},{"children":[{"name":"not_le_of_gt","semanticRole":"global","source":"not_le_of_gt","sourceEnd":16572,"sourceStart":16560,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":16574,"sourceStart":16573,"tag":"atom"},{"c... | [] | [{"source":"not_le_of_gt (strictMono_y _ <| Nat.mod_lt n m0)\n (Nat.le_of_dvd (strictMono_y _ hp) <|\n co.dvd_of_dvd_mul_right <|\n (Nat.dvd_add_iff_right <| (y_mul_dvd _ _ _).mul_left _).2 h)","source_end":16776,"source_start":16560,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72978","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.73018","is_instance":false,"is_let":false,"user_name":"a1"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 114 | 23 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5ae8c7609870cfbf2d7cf9b6421ef883be8b1c0cf5af953cf19fd5d9d0430585 | 6bd45c894fc37a49389a46fa68a76e3bd4ae0789504a6c98f0646aaff77d6b56 | a8ce9416fbcddca3c685b7702a4778605f8196abc6f96fd5a8d426647d4a990d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,184 | Pell.y_dvd_iff | Mathlib/NumberTheory/PellMatiyasevic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [e, <a>Nat.mod_zero</a>] at hp | a : ℕ
a1 : 1 < a
m n : ℕ
h : yn a1 m ∣ yn a1 n
hp : n % m > 0
co : (yn a1 m).Coprime (xn a1 (m * (n / m)))
e : m = 0
⊢ False | a : ℕ
a1 : 1 < a
m n : ℕ
h : yn a1 m ∣ yn a1 n
hp : n > 0
co : (yn a1 m).Coprime (xn a1 (m * (n / m)))
e : m = 0
⊢ False | (:c False) | [{"name":"a","sexp":"(:c Nat)"},{"name":"a1","sexp":"((:c LT.lt) (:c Nat) (:c instLTNat) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))) (:fv _uniq.72978))"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) ((:c Pell.yn) (:fv _un... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72978","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.73018","is_instance":false,"is_let":false,"name":"a1","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat))... | {"children":[{"source":"rw","sourceEnd":16365,"sourceStart":16363,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16367,"sourceStart":16366,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":8,"semant... | [] | [{"source":"e","source_end":16368,"source_start":16367,"syntax_kind":"ident"},{"source":"hp","source_end":16389,"source_start":16387,"syntax_kind":"ident"},{"source":"Nat.mod_zero","source_end":16382,"source_start":16370,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72978","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.73018","is_instance":false,"is_let":false,"user_name":"a1"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 114 | 10 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e8f1a0dde54c30027eed02d9637f6e9fda0081a7e275db8d976715c47a9f369a | ef4897c226e41601191d80dee03f62e170a0a13f7a17d1068db232c6327beeb5 | 0a13e9c24e1c83cb4c80c0e950dae836da41c4e2db50fa6450a77a8830dfc626 | c7602c353a81228258de2af87a5ea58716203bbe5b145599cc9b31805a01eee5 |
cat-searcher/leandojo-benchmark-4-random | test | 1,185 | Pell.y_dvd_iff | Mathlib/NumberTheory/PellMatiyasevic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [e] at h | a : ℕ
a1 : 1 < a
m n : ℕ
h : yn a1 m ∣ yn a1 n
hp : n > 0
co : (yn a1 m).Coprime (xn a1 (m * (n / m)))
e : m = 0
⊢ False | a : ℕ
a1 : 1 < a
m n : ℕ
h : yn a1 0 ∣ yn a1 n
hp : n > 0
co : (yn a1 m).Coprime (xn a1 (m * (n / m)))
e : m = 0
⊢ False | (:c False) | [{"name":"a","sexp":"(:c Nat)"},{"name":"a1","sexp":"((:c LT.lt) (:c Nat) (:c instLTNat) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))) (:fv _uniq.72978))"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) ((:c Pell.yn) (:fv _un... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72978","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.73018","is_instance":false,"is_let":false,"name":"a1","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat))... | {"children":[{"source":"rw","sourceEnd":16392,"sourceStart":16390,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16394,"sourceStart":16393,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":8,"semant... | [] | [{"source":"e","source_end":16395,"source_start":16394,"syntax_kind":"ident"},{"source":"h","source_end":16401,"source_start":16400,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72978","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.73018","is_instance":false,"is_let":false,"user_name":"a1"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 114 | 15 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8a52dfbc1654666eef1e5e13e132a5072755848bb37887c22546b8c63ea872a7 | c7602c353a81228258de2af87a5ea58716203bbe5b145599cc9b31805a01eee5 | fb9c4ec294feed49d85b42907612c90682f8750017adeb9b612ca1555eaf4b32 | 5efccf38746e1459a2d3b6afe96752c9a2aa343aeae084eeec1516fcfc0ca8a5 |
cat-searcher/leandojo-benchmark-4-random | test | 1,186 | Pell.y_dvd_iff | Mathlib/NumberTheory/PellMatiyasevic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>ne_of_lt</a> (<a>Pell.strictMono_y</a> a1 hp) (<a>eq_zero_of_zero_dvd</a> h).<a>Eq.symm</a> | a : ℕ
a1 : 1 < a
m n : ℕ
h : yn a1 0 ∣ yn a1 n
hp : n > 0
co : (yn a1 m).Coprime (xn a1 (m * (n / m)))
e : m = 0
⊢ False | (:c False) | [{"name":"a","sexp":"(:c Nat)"},{"name":"a1","sexp":"((:c LT.lt) (:c Nat) (:c instLTNat) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))) (:fv _uniq.72978))"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) ((:c Pell.yn) (:fv _un... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72978","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.73018","is_instance":false,"is_let":false,"name":"a1","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat))... | {"children":[{"source":"exact","sourceEnd":16419,"sourceStart":16414,"tag":"atom"},{"children":[{"name":"ne_of_lt","semanticRole":"global","source":"_root_.ne_of_lt","sourceEnd":16435,"sourceStart":16420,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":16437,"sourceStart":16436,"tag":"atom"},{"ch... | [] | [{"source":"_root_.ne_of_lt (strictMono_y a1 hp) (eq_zero_of_zero_dvd h).symm","source_end":16485,"source_start":16420,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72978","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.73018","is_instance":false,"is_let":false,"user_name":"a1"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 114 | 18 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 52cfb69bfa83bb212f920847d29981e579e56cd64038cc0e3f016a388e30718b | 5efccf38746e1459a2d3b6afe96752c9a2aa343aeae084eeec1516fcfc0ca8a5 | 85e5ab87f9ff92fca5ec8236efc1ebba8b81edfa25d498042c256fdb8b112615 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,187 | Pell.y_dvd_iff | Mathlib/NumberTheory/PellMatiyasevic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [e] | a : ℕ
a1 : 1 < a
m n : ℕ
x✝ : m ∣ n
k : ℕ
e : n = m * k
⊢ yn a1 m ∣ yn a1 n | a : ℕ
a1 : 1 < a
m n : ℕ
x✝ : m ∣ n
k : ℕ
e : n = m * k
⊢ yn a1 m ∣ yn a1 (m * k) | ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) ((:c Pell.yn) (:fv _uniq.72978) (:fv _uniq.73018) (:fv _uniq.73042)) ((:c Pell.yn) (:fv _uniq.72978) (:fv _uniq.73018) (:fv _uniq.73043))) | [{"name":"a","sexp":"(:c Nat)"},{"name":"a1","sexp":"((:c LT.lt) (:c Nat) (:c instLTNat) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))) (:fv _uniq.72978))"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"x✝","sexp":"((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.73042) (:f... | (: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 Pell.yn) (:arg :implicit 0) (:arg :proof 1 (:proof-of (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72978","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.73018","is_instance":false,"is_let":false,"name":"a1","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat))... | {"children":[{"source":"rw","sourceEnd":16805,"sourceStart":16803,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16807,"sourceStart":16806,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":7,"semant... | [] | [{"source":"e","source_end":16808,"source_start":16807,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72978","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.73018","is_instance":false,"is_let":false,"user_name":"a1"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 114 | 28 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8e880221c88784d1536d2a8243649b389cd515b4c6fa8349e2cc3db1e684ff12 | 6b6c2981ad71787a163210cdac711f7355611a2bd3aac189e6c2228419fe93e2 | cbda8b3b810cd20ff3bb1e9bf5df7c7e8d6910e97009d1504aed3f92e865499d | abcce35b64d8bf0c361e86b4374b2b9a2e12e3cc4c5a4070a1b9e33890c581f6 |
cat-searcher/leandojo-benchmark-4-random | test | 1,188 | Pell.y_dvd_iff | Mathlib/NumberTheory/PellMatiyasevic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Pell.y_mul_dvd</a> | a : ℕ
a1 : 1 < a
m n : ℕ
x✝ : m ∣ n
k : ℕ
e : n = m * k
⊢ yn a1 m ∣ yn a1 (m * k) | ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) ((:c Pell.yn) (:fv _uniq.72978) (:fv _uniq.73018) (:fv _uniq.73042)) ((:c Pell.yn) (:fv _uniq.72978) (:fv _uniq.73018) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.73042) (:fv _uniq.73111)))) | [{"name":"a","sexp":"(:c Nat)"},{"name":"a1","sexp":"((:c LT.lt) (:c Nat) (:c instLTNat) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))) (:fv _uniq.72978))"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"x✝","sexp":"((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.73042) (:f... | (: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 Pell.yn) (:arg :implicit 0) (:arg :proof 1 (:proof-of (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72978","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.73018","is_instance":false,"is_let":false,"name":"a1","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat))... | {"children":[{"source":"apply","sourceEnd":16816,"sourceStart":16811,"tag":"atom"},{"name":"Pell.y_mul_dvd","semanticRole":"global","source":"y_mul_dvd","sourceEnd":16826,"sourceStart":16817,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply y_mul_dvd","sourceEnd":16826,"sourceStart":16811,"tag":"no... | [] | [{"source":"y_mul_dvd","source_end":16826,"source_start":16817,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72978","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.73018","is_instance":false,"is_let":false,"user_name":"a1"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 114 | 32 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 80a424825443e7baa4799583ba424b69175f6e6e4bc9cfbd532979e0d6827d41 | abcce35b64d8bf0c361e86b4374b2b9a2e12e3cc4c5a4070a1b9e33890c581f6 | 23db51d865107b1be12a06cf85416c16f95aa03b40664115492576d87072d8d6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,189 | Nat.floorRoot_def | Mathlib/Data/Nat/Factorization/Root.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | unfold <a>Nat.floorRoot</a> | a b n : ℕ
⊢ n.floorRoot a = if n = 0 ∨ a = 0 then 0 else (a.factorization ⌊/⌋ n).prod fun x x_1 => x ^ x_1 | a b n : ℕ
⊢ (if n = 0 ∨ a = 0 then 0 else a.factorization.prod fun p k => p ^ (k / n)) =
if n = 0 ∨ a = 0 then 0 else (a.factorization ⌊/⌋ n).prod fun x x_1 => x ^ x_1 | ((:c Eq) (:c Nat) ((:c Nat.floorRoot) (:fv _uniq.291) (:fv _uniq.287)) ((:c ite) (:c Nat) ((:c Or) ((:c Eq) (:c Nat) (:fv _uniq.291) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) ((:c Eq) (:c Nat) (:fv _uniq.287) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))) ((:c instDecidable... | [{"name":"a","sexp":"(:c Nat)"},{"name":"b","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.floorRoot) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV0)))) (:arg :explicit 2 (:app (:c ite) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.287","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.289","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":... | {"children":[{"source":"unfold","sourceEnd":2161,"sourceStart":2155,"tag":"atom"},{"children":[{"name":"Nat.floorRoot","semanticRole":"global","source":"floorRoot","sourceEnd":2171,"sourceStart":2162,"tag":"identifier"}],"kind":"null","source":"floorRoot","sourceEnd":2171,"sourceStart":2162,"tag":"node"},{"children":[]... | [] | [{"source":"floorRoot","source_end":2171,"source_start":2162,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.287","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.289","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.2... | 5 | 4 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 22175dadbba28d34690b6c74cd8600988c34de912c6c6a074d2d2b749dc427a5 | 117587cc0eaea841f76fac2e59bde784c6ea34af555c4179688e9c601415dff4 | 34a43670f870909b14345ad843314db9aedadb99853c21b1465cf7566e27b181 | c78eef9b9d0a8e6cda4d83eab994a2b63f9674dc2a05fc22bcd7d832303c58d2 |
cat-searcher/leandojo-benchmark-4-random | test | 1,190 | Nat.floorRoot_def | Mathlib/Data/Nat/Factorization/Root.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split_ifs with h <;> simp [<a>Finsupp.floorDiv_def</a>, <a>Finsupp.prod_mapRange_index</a> <a>pow_zero</a>] | a b n : ℕ
⊢ (if n = 0 ∨ a = 0 then 0 else a.factorization.prod fun p k => p ^ (k / n)) =
if n = 0 ∨ a = 0 then 0 else (a.factorization ⌊/⌋ n).prod fun x x_1 => x ^ x_1 | ((:c Eq) (:c Nat) ((:c ite) (:c Nat) ((:c Or) ((:c Eq) (:c Nat) (:fv _uniq.291) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) ((:c Eq) (:c Nat) (:fv _uniq.287) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))) ((:c instDecidableOr) ((:c Eq) (:c Nat) (:fv _uniq.291) ((:c OfNat.ofNa... | [{"name":"a","sexp":"(:c Nat)"},{"name":"b","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c ite) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.287","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.289","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":... | {"children":[{"children":[{"source":"split_ifs","sourceEnd":2182,"sourceStart":2173,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"with","sourceEnd":2187,"sourceStart":2183,"tag":"atom"},{"children":[{"children":[{"source":"h","sourceEnd":2189,"sourceStart":2188,"tag":"iden... | [] | [{"source":"Finsupp.floorDiv_def","source_end":2220,"source_start":2200,"syntax_kind":"ident"},{"source":"prod_mapRange_index pow_zero","source_end":2250,"source_start":2222,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.287","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.289","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.2... | 5 | 6 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | edc3311b9c8bc58de4d208bbe4247af2f433f7af41e341832962a8822e8e206e | c78eef9b9d0a8e6cda4d83eab994a2b63f9674dc2a05fc22bcd7d832303c58d2 | d166231bd5802f12f6273071266bf835887b3d1d576a38ffdf0564b9a5a62123 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,191 | HasDerivWithinAt.comp_hasFDerivWithinAt_of_eq | Mathlib/Analysis/Calculus/Deriv/Comp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hy] at hh | 𝕜 : Type u
inst✝⁸ : NontriviallyNormedField 𝕜
F : Type v
inst✝⁷ : NormedAddCommGroup F
inst✝⁶ : NormedSpace 𝕜 F
E : Type w
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
f✝ f₀ f₁ g : 𝕜 → F
f'✝ f₀' f₁' g' : F
x✝ : 𝕜
s✝ t✝ : Set 𝕜
L L₁ L₂ : Filter 𝕜
𝕜' : Type u_1
inst✝³ : NontriviallyNormedField 𝕜'
inst... | 𝕜 : Type u
inst✝⁸ : NontriviallyNormedField 𝕜
F : Type v
inst✝⁷ : NormedAddCommGroup F
inst✝⁶ : NormedSpace 𝕜 F
E : Type w
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
f✝ f₀ f₁ g : 𝕜 → F
f'✝ f₀' f₁' g' : F
x✝ : 𝕜
s✝ t✝ : Set 𝕜
L L₁ L₂ : Filter 𝕜
𝕜' : Type u_1
inst✝³ : NontriviallyNormedField 𝕜'
inst... | ((:c HasFDerivWithinAt) (:fv _uniq.189622) (:fv _uniq.189625) (:fv _uniq.189740) (:fv _uniq.189743) (:fv _uniq.189846) (:fv _uniq.189890) ((:c NonUnitalNormedRing.toNormedAddCommGroup) (:fv _uniq.189890) ((:c NonUnitalNormedCommRing.toNonUnitalNormedRing) (:fv _uniq.189890) ((:c NormedCommRing.toNonUnitalNormedCommRing... | [{"name":"𝕜","sexp":"(:sort (+ u 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.189622))"},{"name":"F","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCommGroup) (:fv _uniq.189627))"},{"name":"inst✝⁶","sexp":"((:c NormedSpace) (:fv _uniq.189622) (:fv _uniq.189627) ((:c Nontriv... | (:app (:c HasFDerivWithinAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.189622","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.189625","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"rw","sourceEnd":11072,"sourceStart":11070,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11074,"sourceStart":11073,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":48,"seman... | [] | [{"source":"hy","source_end":11076,"source_start":11074,"syntax_kind":"ident"},{"source":"hh","source_end":11083,"source_start":11081,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.189622","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.189625","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":implicit","context_index":2,"int... | 57 | 4 | exact | true | 1 | 48 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7b8c6b408ea5c5f19ea29d444bae3310d0f49f9a6022cd54477a38e95059fc28 | 1cb94f746cfaa1ad1273aac245c0dc1456cfdd4bee37b7bbfc7731951ab41a2c | b52f87fed04bd418a976f650516bcb63b618a96e2be2b17d47d1a3e646258184 | fd770fca7b7b2615e1393c03b0c13548393c04add7773e5a0b25ae2be70fef92 |
cat-searcher/leandojo-benchmark-4-random | test | 1,192 | HasDerivWithinAt.comp_hasFDerivWithinAt_of_eq | Mathlib/Analysis/Calculus/Deriv/Comp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hh.comp_hasFDerivWithinAt x hf hst | 𝕜 : Type u
inst✝⁸ : NontriviallyNormedField 𝕜
F : Type v
inst✝⁷ : NormedAddCommGroup F
inst✝⁶ : NormedSpace 𝕜 F
E : Type w
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
f✝ f₀ f₁ g : 𝕜 → F
f'✝ f₀' f₁' g' : F
x✝ : 𝕜
s✝ t✝ : Set 𝕜
L L₁ L₂ : Filter 𝕜
𝕜' : Type u_1
inst✝³ : NontriviallyNormedField 𝕜'
inst... | ((:c HasFDerivWithinAt) (:fv _uniq.189622) (:fv _uniq.189625) (:fv _uniq.189740) (:fv _uniq.189743) (:fv _uniq.189846) (:fv _uniq.189890) ((:c NonUnitalNormedRing.toNormedAddCommGroup) (:fv _uniq.189890) ((:c NonUnitalNormedCommRing.toNonUnitalNormedRing) (:fv _uniq.189890) ((:c NormedCommRing.toNonUnitalNormedCommRing... | [{"name":"𝕜","sexp":"(:sort (+ u 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.189622))"},{"name":"F","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCommGroup) (:fv _uniq.189627))"},{"name":"inst✝⁶","sexp":"((:c NormedSpace) (:fv _uniq.189622) (:fv _uniq.189627) ((:c Nontriv... | (:app (:c HasFDerivWithinAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.189622","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.189625","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"exact","sourceEnd":11090,"sourceStart":11085,"tag":"atom"},{"children":[{"source":"hh.comp_hasFDerivWithinAt","sourceEnd":11116,"sourceStart":11091,"tag":"identifier"},{"children":[{"contextIndex":44,"semanticRole":"local","source":"x","sourceEnd":11118,"sourceStart":11117,"tag":"identifier"},{"... | [] | [{"source":"hh.comp_hasFDerivWithinAt x hf hst","source_end":11125,"source_start":11091,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.189622","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.189625","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":implicit","context_index":2,"int... | 57 | 8 | exact | true | 1 | 48 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d97928da746b36c3e56e4dc65ae06c06960bac768c12b4f8d0f75283c020585a | fd770fca7b7b2615e1393c03b0c13548393c04add7773e5a0b25ae2be70fef92 | f58249ac7714956170d488d4b26f35b117e4705891ac9fe62852ffbe5719c612 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,193 | hasMellin_sub | Mathlib/Analysis/MellinTransform.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>MellinConvergent</a>, <a>smul_sub</a>] using hf.sub hg | E : Type u_1
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace ℂ E
f g : ℝ → E
s : ℂ
hf : MellinConvergent f s
hg : MellinConvergent g s
⊢ MellinConvergent (fun t => f t - g t) s | ((:c MellinConvergent) (:fv _uniq.89759) (:fv _uniq.89762) (:fv _uniq.89872) (:lambda t (:c Real) ((:c HSub.hSub) (:fv _uniq.89759) (:fv _uniq.89759) (:fv _uniq.89759) ((:c instHSub) (:fv _uniq.89759) ((:c SubNegMonoid.toSub) (:fv _uniq.89759) ((:c AddGroup.toSubNegMonoid) (:fv _uniq.89759) ((:c NormedAddGroup.toAddGro... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.89759))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Complex) (:fv _uniq.89759) (:c Complex.instNormedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.89759) (:fv _uniq.89762)))"},{"name":"f","sex... | (:app (:c MellinConvergent) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c NormedSpace) (:arg :explicit 0 (:c Complex)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Normed... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.89759","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.89762","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (:a... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":9348,"sourceStart":9343,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"MellinConvergent","source_end":9371,"source_start":9355,"syntax_kind":"ident"},{"source":"smul_sub","source_end":9381,"source_start":9373,"syntax_kind":"ident"},{"source":"hf.sub hg","source_end":9398,"source_start":9389,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.89759","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.89762","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 43 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | baf94919d63ea032e4135e5e7a0153afb9b30b01b27dee1a4995b7407df398fd | bec39a4ab8a27f549fb7c8494d3888c698e79a04e49feb84c619df83ed7eef9d | e1668b085ef901d38e75a0603dabf8b725c28995d7cbc8ae477a8dac6d751149 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,194 | hasMellin_sub | Mathlib/Analysis/MellinTransform.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>mellin</a>, <a>smul_sub</a>] using <a>MeasureTheory.integral_sub</a> hf hg | E : Type u_1
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace ℂ E
f g : ℝ → E
s : ℂ
hf : MellinConvergent f s
hg : MellinConvergent g s
⊢ mellin (fun t => f t - g t) s = mellin f s - mellin g s | ((:c Eq) (:fv _uniq.89759) ((:c mellin) (:fv _uniq.89759) (:fv _uniq.89762) (:fv _uniq.89872) (:lambda t (:c Real) ((:c HSub.hSub) (:fv _uniq.89759) (:fv _uniq.89759) (:fv _uniq.89759) ((:c instHSub) (:fv _uniq.89759) ((:c SubNegMonoid.toSub) (:fv _uniq.89759) ((:c AddGroup.toSubNegMonoid) (:fv _uniq.89759) ((:c Normed... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.89759))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Complex) (:fv _uniq.89759) (:c Complex.instNormedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.89759) (:fv _uniq.89762)))"},{"name":"f","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c mellin) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c NormedSpace) (:arg :explicit 0 (:c Complex)) (:arg :explicit 1 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.89759","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.89762","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (:a... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":9412,"sourceStart":9407,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"mellin","source_end":9425,"source_start":9419,"syntax_kind":"ident"},{"source":"smul_sub","source_end":9435,"source_start":9427,"syntax_kind":"ident"},{"source":"integral_sub hf hg","source_end":9461,"source_start":9443,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.89759","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.89762","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 43 | 7 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7c313579ab4028ce8a7c57de17139ea112dfdb55c0eba8213d819b777e7685da | c445e25afa05ac1a8a3ce66425eba76d837158a40b380cc5623644ed2088bd18 | 1b0ad391e45a43bd3139a8a8fc22917072bb4d0dbc67e313f66d4175efe1d2b1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,195 | Order.Ideal.PrimePair.I_isPrime | Mathlib/Order/PrimeIdeal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [IF.compl_I_eq_F] | P : Type u_1
inst✝ : Preorder P
IF : PrimePair P
⊢ IsPFilter (↑IF.I)ᶜ | P : Type u_1
inst✝ : Preorder P
IF : PrimePair P
⊢ IsPFilter ↑IF.F | ((:c Order.IsPFilter) (:fv _uniq.3262) (:fv _uniq.3265) ((:c HasCompl.compl) ((:c Set) (:fv _uniq.3262)) ((:c Set.instHasCompl) (:fv _uniq.3262)) ((:c SetLike.coe) ((:c Order.Ideal) (:fv _uniq.3262) ((:c Preorder.toLE) (:fv _uniq.3262) (:fv _uniq.3265))) (:fv _uniq.3262) ((:c Order.Ideal.instSetLike) (:fv _uniq.3262) (... | [{"name":"P","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Preorder) (:fv _uniq.3262))"},{"name":"IF","sexp":"((:c Order.Ideal.PrimePair) (:fv _uniq.3262) (:fv _uniq.3265))"}] | (:app (:c Order.IsPFilter) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HasCompl.compl) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasCompl) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3262","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.3265","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Preorder) (:arg :explicit ... | {"children":[{"source":"rw","sourceEnd":3495,"sourceStart":3493,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3497,"sourceStart":3496,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Order.Ideal.PrimePai... | [] | [{"source":"IF.compl_I_eq_F","source_end":3512,"source_start":3497,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3262","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.3265","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":3,"internal_... | 29 | 4 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7e9aaeb061a8060a37be08e2793607b2d9404afc2bc96ce02cccecad044fed8f | 21373f659f38a953a3e37ccec264a4cdc1948641eb296f6d65a067deb82113ac | a033170f487e8da5ea51dc306c2e09f85341fa8e0c4bf38c26d35c7e083ddffb | 83cbcded9a4ff589c85899b979c1bbec0aee36c8a9dd4086208e4f3931d0e81e |
cat-searcher/leandojo-benchmark-4-random | test | 1,196 | Order.Ideal.PrimePair.I_isPrime | Mathlib/Order/PrimeIdeal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact IF.F.isPFilter | P : Type u_1
inst✝ : Preorder P
IF : PrimePair P
⊢ IsPFilter ↑IF.F | ((:c Order.IsPFilter) (:fv _uniq.3262) (:fv _uniq.3265) ((:c SetLike.coe) ((:c Order.PFilter) (:fv _uniq.3262) (:fv _uniq.3265)) (:fv _uniq.3262) ((:c Order.PFilter.instSetLike) (:fv _uniq.3262) (:fv _uniq.3265)) ((:c Order.Ideal.PrimePair.F) (:fv _uniq.3262) (:fv _uniq.3265) (:fv _uniq.3305)))) | [{"name":"P","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Preorder) (:fv _uniq.3262))"},{"name":"IF","sexp":"((:c Order.Ideal.PrimePair) (:fv _uniq.3262) (:fv _uniq.3265))"}] | (:app (:c Order.IsPFilter) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c SetLike.coe) (:arg :implicit-type 0 (:app (:c Order.PFilter) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3262","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.3265","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Preorder) (:arg :explicit ... | {"children":[{"source":"exact","sourceEnd":3525,"sourceStart":3520,"tag":"atom"},{"name":"Order.PFilter.isPFilter","semanticRole":"global","source":"IF.F.isPFilter","sourceEnd":3540,"sourceStart":3526,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact IF.F.isPFilter","sourceEnd":3540,"sourceStart":3... | [] | [{"source":"IF.F.isPFilter","source_end":3540,"source_start":3526,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3262","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.3265","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":3,"internal_... | 29 | 7 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0dae1ea09dbb348d9e66d719075108c1eb0ef4f5372abf3bb3728b64ebac786e | 83cbcded9a4ff589c85899b979c1bbec0aee36c8a9dd4086208e4f3931d0e81e | 816f3d76ac380840767569b8264a0b7d4f4c58a824f68d13feb53c47b3b05f2f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,197 | Int.addRight_one_isCycle | Mathlib/GroupTheory/Perm/Cycle/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | ι : Type u_1
α : Type u_2
β : Type u_3
n : ℤ
x✝ : (Equiv.addRight 1) n ≠ n
⊢ (Equiv.addRight 1 ^ n) 0 = n | ((:c Eq) (:c Int) ((:c DFunLike.coe) ((:c Equiv.Perm) (:c Int)) (:c Int) (:lambda _ (:c Int) (:c Int)) ((:c Equiv.instFunLike) (:c Int) (:c Int)) ((:c HPow.hPow) ((:c Equiv.Perm) (:c Int)) (:c Int) ((:c Equiv.Perm) (:c Int)) ((:c instHPow) ((:c Equiv.Perm) (:c Int)) (:c Int) ((:c DivInvMonoid.Pow) ((:c Equiv.Perm) (:c ... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"n","sexp":"(:c Int)"},{"name":"x✝","sexp":"((:c Ne) (:c Int) ((:c DFunLike.coe) ((:c Equiv.Perm) (:c Int)) (:c Int) (:lambda _ (:c Int) (:c Int)) ((:c Equiv.instFunLike) (:c Int) (:c Int)) (... | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Equiv.Perm) (:arg :explicit 0 (:c Int)))) (:arg :implicit-type 1 (:c Int)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c FunLike) (:arg :explicit 0 (:app (:c Equiv) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141909","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":33025,"sourceStart":33021,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","sour... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141909","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 187 | 2 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e5e5590729280d612d1a60d4e166186c3fa301e777be337b37d893c134aebe28 | d9fc1bab23146fe928ad0d52cc191d7d910c5e11a02622b521071bbbf26226ba | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,198 | AffineIsometryEquiv.vadd_vsub | Mathlib/Analysis/NormedSpace/AffineIsometry.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert (<a>AffineIsometryEquiv.vaddConst</a> 𝕜 (f p)).symm.isometry.comp (hf.comp (<a>AffineIsometryEquiv.vaddConst</a> 𝕜 p).<a>AffineIsometryEquiv.isometry</a>) | 𝕜 : Type u_1
V : Type u_2
V₁ : Type u_3
V₁' : Type u_4
V₂ : Type u_5
V₃ : Type u_6
V₄ : Type u_7
P₁ : Type u_8
P₁' : Type u_9
P : Type u_10
P₂ : Type u_11
P₃ : Type u_12
P₄ : Type u_13
inst✝²⁵ : NormedField 𝕜
inst✝²⁴ : SeminormedAddCommGroup V
inst✝²³ : NormedSpace 𝕜 V
inst✝²² : PseudoMetricSpace P
inst✝²¹ : NormedA... | case h.e'_5
𝕜 : Type u_1
V : Type u_2
V₁ : Type u_3
V₁' : Type u_4
V₂ : Type u_5
V₃ : Type u_6
V₄ : Type u_7
P₁ : Type u_8
P₁' : Type u_9
P : Type u_10
P₂ : Type u_11
P₃ : Type u_12
P₄ : Type u_13
inst✝²⁵ : NormedField 𝕜
inst✝²⁴ : SeminormedAddCommGroup V
inst✝²³ : NormedSpace 𝕜 V
inst✝²² : PseudoMetricSpace P
inst✝... | ((:c Isometry) (:fv _uniq.231239) (:fv _uniq.231248) ((:c PseudoMetricSpace.toPseudoEMetricSpace) (:fv _uniq.231239) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:fv _uniq.231239) (:fv _uniq.231278))) ((:c PseudoMetricSpace.toPseudoEMetricSpace) (:fv _uniq.231248) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V₁","sexp":"(:sort (+ u_3 1))"},{"name":"V₁'","sexp":"(:sort (+ u_4 1))"},{"name":"V₂","sexp":"(:sort (+ u_5 1))"},{"name":"V₃","sexp":"(:sort (+ u_6 1))"},{"name":"V₄","sexp":"(:sort (+ u_7 1))"},{"name":"P₁","sexp":"(:sort (+ u... | (:app (:c Isometry) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV4)) (:arg :instance 2 (:instance-of (:app (:c PseudoEMetricSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoEMetricSpace) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 4 (:fv FV45))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.231236","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.231239","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"convert","sourceEnd":28563,"sourceStart":28556,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":28565,"sourceStart":28564,"tag":"atom"},{"children":[{"name"... | [] | [{"source":"(vaddConst 𝕜 (f p)).symm.isometry.comp (hf.comp (vaddConst 𝕜 p).isometry)","source_end":28643,"source_start":28564,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.231236","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.231239","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 283 | 4 | exact | true | 1 | 46 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4a5a7bcc08cd565675a75a0aec5981a8ac0fa73a6f1c18be232498d6a15a846d | dc769140cc8a641749ca450acefbac249163ef7a483970cf25debdabb2780d1d | 1741dfa4801076d8a0018a09a68e2ae86c97de97a0415dc6f408d65b7b00c7a2 | b98651b444566a281ff34673ad2fd045b7f59c6e8111c4e6e6f6277134289a44 |
cat-searcher/leandojo-benchmark-4-random | test | 1,199 | AffineIsometryEquiv.vadd_vsub | Mathlib/Analysis/NormedSpace/AffineIsometry.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>funext</a> hg | case h.e'_5
𝕜 : Type u_1
V : Type u_2
V₁ : Type u_3
V₁' : Type u_4
V₂ : Type u_5
V₃ : Type u_6
V₄ : Type u_7
P₁ : Type u_8
P₁' : Type u_9
P : Type u_10
P₂ : Type u_11
P₃ : Type u_12
P₄ : Type u_13
inst✝²⁵ : NormedField 𝕜
inst✝²⁴ : SeminormedAddCommGroup V
inst✝²³ : NormedSpace 𝕜 V
inst✝²² : PseudoMetricSpace P
inst✝... | ((:c Eq) (:forall _ (:fv _uniq.231239) (:fv _uniq.231248)) (:fv _uniq.233077) ((:c Function.comp) (:fv _uniq.231239) (:fv _uniq.231266) (:fv _uniq.231248) ((:c DFunLike.coe) ((:c AffineIsometryEquiv) (:fv _uniq.231236) (:fv _uniq.231248) (:fv _uniq.231248) (:fv _uniq.231266) (:fv _uniq.231248) (:fv _uniq.231275) (:fv _... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V₁","sexp":"(:sort (+ u_3 1))"},{"name":"V₁'","sexp":"(:sort (+ u_4 1))"},{"name":"V₂","sexp":"(:sort (+ u_5 1))"},{"name":"V₃","sexp":"(:sort (+ u_6 1))"},{"name":"V₄","sexp":"(:sort (+ u_7 1))"},{"name":"P₁","sexp":"(:sort (+ u... | (:app (:c Eq) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV1) (:fv FV4))) (:arg :explicit 1 (:fv FV45)) (:arg :explicit 2 (:app (:c Function.comp) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV10)) (:arg :implicit-type 2 (:fv FV4)) (:arg :explicit 3 (:app (:c DFunLike.coe) (:arg :implicit-type 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.231236","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.231239","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"exact","sourceEnd":28651,"sourceStart":28646,"tag":"atom"},{"children":[{"name":"funext","semanticRole":"global","source":"funext","sourceEnd":28658,"sourceStart":28652,"tag":"identifier"},{"children":[{"contextIndex":46,"semanticRole":"local","source":"hg","sourceEnd":28661,"sourceStart":28659,... | [] | [{"source":"funext hg","source_end":28661,"source_start":28652,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.231236","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.231239","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 283 | 5 | exact | true | 1 | 46 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4cd17a867cbfd619a1ed9adf7630e45da3aa741b51e8374946d861f3e2684476 | b98651b444566a281ff34673ad2fd045b7f59c6e8111c4e6e6f6277134289a44 | 18064cd1b7ca0c4e1a8a9356c63779914bffab376b74613a2ecee11c4f08722e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,200 | Polynomial.degree_modByMonic_lt | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have _wf := <a>Polynomial.div_wf_lemma</a> ⟨h.1, h.2⟩ hq | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this : DecidableEq R := Classical.decEq R
h : q.degree ≤ p.degree ∧ p ≠ 0
⊢ (p %ₘ q).degree < q.degree | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this : DecidableEq R := Classical.decEq R
h : q.degree ≤ p.degree ∧ p ≠ 0
_wf : (p - q * (C p.leadingCoeff * X ^ (p.natDegree - q.natDegree))).degree < p.degree
⊢ (p %ₘ q).degree < q.degre... | ((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.36866) ((:c Ring.toSemiring) (:fv _uniq.368... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.36866)"},{"name":"b","sexp":"(:fv _uniq.36866)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.36866))"}... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":5393,"sourceStart":5389,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"_wf","sourceEnd":5397,"sourceStart":5394,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"_wf","sourceEnd":5397,"sourceStart":5394,"tag":"node"},... | [] | [{"source":"div_wf_lemma ⟨h.1, h.2⟩ hq","source_end":5431,"source_start":5401,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 4 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e8941e7858c61da2f6b94fa04b3b5df4188d7fe06ce2f1c7fa99f9129432fecb | 0b746d64cc21da6a496c43b7e6e03b33ccb767e844bcc2f06b751b1fe32e7215 | 01479e2e17e5e5bb2f6cb5c0042ff14396918d81cf0f2321eb67e4155b34e99f | 8fe7d1ea82f4f33ea29947ea9d21b1461442c5166716ea4c82e0b6fde1132baf |
cat-searcher/leandojo-benchmark-4-random | test | 1,201 | Polynomial.degree_modByMonic_lt | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have := degree_modByMonic_lt (p - q * (<a>Polynomial.C</a> (<a>Polynomial.leadingCoeff</a> p) * <a>Polynomial.X</a> ^ (<a>Polynomial.natDegree</a> p - <a>Polynomial.natDegree</a> q))) hq | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this : DecidableEq R := Classical.decEq R
h : q.degree ≤ p.degree ∧ p ≠ 0
_wf : (p - q * (C p.leadingCoeff * X ^ (p.natDegree - q.natDegree))).degree < p.degree
⊢ (p %ₘ q).degree < q.degre... | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this✝ : DecidableEq R := Classical.decEq R
h : q.degree ≤ p.degree ∧ p ≠ 0
_wf : (p - q * (C p.leadingCoeff * X ^ (p.natDegree - q.natDegree))).degree < p.degree
this : ((p - q * (C p.lead... | ((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.36866) ((:c Ring.toSemiring) (:fv _uniq.368... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.36866)"},{"name":"b","sexp":"(:fv _uniq.36866)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.36866))"}... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":5442,"sourceStart":5438,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":5443,"sourceStart":5443,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":5443,"sourceStart":5443,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"degree_modByMonic_lt (p - q * (C (leadingCoeff p) * X ^ (natDegree p - natDegree q))) hq","source_end":5542,"source_start":5454,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 5 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 84021c2df01763be963ac5f60d8c447b9527226dcf8f65782f2441e1979569b5 | 8fe7d1ea82f4f33ea29947ea9d21b1461442c5166716ea4c82e0b6fde1132baf | c4d1e90c4432d092cd755ebb7a357a46f9ad7132f1cec12a98676218ab04340b | 425c6db15a56911a6866afc0250c87855342959936960788162b3ca6f2892426 |
cat-searcher/leandojo-benchmark-4-random | test | 1,202 | Polynomial.degree_modByMonic_lt | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | unfold <a>Polynomial.modByMonic</a> at this ⊢ | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this✝ : DecidableEq R := Classical.decEq R
h : q.degree ≤ p.degree ∧ p ≠ 0
_wf : (p - q * (C p.leadingCoeff * X ^ (p.natDegree - q.natDegree))).degree < p.degree
this : ((p - q * (C p.lead... | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this✝ : DecidableEq R := Classical.decEq R
h : q.degree ≤ p.degree ∧ p ≠ 0
_wf : (p - q * (C p.leadingCoeff * X ^ (p.natDegree - q.natDegree))).degree < p.degree
this :
(if hq : q.Monic ... | ((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.36866) ((:c Ring.toSemiring) (:fv _uniq.368... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.36866)"},{"name":"b","sexp":"(:fv _uniq.36866)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.36866))"}... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"unfold","sourceEnd":5555,"sourceStart":5549,"tag":"atom"},{"children":[{"name":"Polynomial.modByMonic","semanticRole":"global","source":"modByMonic","sourceEnd":5566,"sourceStart":5556,"tag":"identifier"}],"kind":"null","source":"modByMonic","sourceEnd":5566,"sourceStart":5556,"tag":"node"},{"ch... | [] | [{"source":"modByMonic","source_end":5566,"source_start":5556,"syntax_kind":"ident"},{"source":"this","source_end":5574,"source_start":5570,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 6 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7feb8c96d8f5767b76bc727685a9e1bbf3d37c71caa6c4655f30af60beebc832 | 425c6db15a56911a6866afc0250c87855342959936960788162b3ca6f2892426 | e8407b95ab7281de4e02c7c81d360441ffd010ef8a041bb64a52c8a066ea54ea | 470f73488f43722e17cf4ab769abf157743445be9c770258c8caf88bb22e07d2 |
cat-searcher/leandojo-benchmark-4-random | test | 1,203 | Polynomial.degree_modByMonic_lt | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | unfold <a>Polynomial.divModByMonicAux</a> | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this✝ : DecidableEq R := Classical.decEq R
h : q.degree ≤ p.degree ∧ p ≠ 0
_wf : (p - q * (C p.leadingCoeff * X ^ (p.natDegree - q.natDegree))).degree < p.degree
this :
(if hq : q.Monic ... | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this✝ : DecidableEq R := Classical.decEq R
h : q.degree ≤ p.degree ∧ p ≠ 0
_wf : (p - q * (C p.leadingCoeff * X ^ (p.natDegree - q.natDegree))).degree < p.degree
this :
(if hq : q.Monic ... | ((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.36866) ((:c Ring.toSemiring) (:fv _uniq.368... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.36866)"},{"name":"b","sexp":"(:fv _uniq.36866)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.36866))"}... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"unfold","sourceEnd":5591,"sourceStart":5585,"tag":"atom"},{"children":[{"name":"Polynomial.divModByMonicAux","semanticRole":"global","source":"divModByMonicAux","sourceEnd":5608,"sourceStart":5592,"tag":"identifier"}],"kind":"null","source":"divModByMonicAux","sourceEnd":5608,"sourceStart":5592,... | [] | [{"source":"divModByMonicAux","source_end":5608,"source_start":5592,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 7 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 96397889733d93c4ada6fb1a6105c6b5992ccc111e9777492dacb08446029e1e | 470f73488f43722e17cf4ab769abf157743445be9c770258c8caf88bb22e07d2 | 59b66dc56960a862c1a24f8b3013662f798040575dc4ee85ebd05022a321a6e4 | db6eeb04eea09ad5a78d991b81095c1dc9388e8cb2a324326035a84ae688fb9e |
cat-searcher/leandojo-benchmark-4-random | test | 1,204 | Polynomial.degree_modByMonic_lt | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this✝ : DecidableEq R := Classical.decEq R
h : q.degree ≤ p.degree ∧ p ≠ 0
_wf : (p - q * (C p.leadingCoeff * X ^ (p.natDegree - q.natDegree))).degree < p.degree
this :
(if hq : q.Monic ... | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this✝ : DecidableEq R := Classical.decEq R
h : q.degree ≤ p.degree ∧ p ≠ 0
_wf : (p - q * (C p.leadingCoeff * X ^ (p.natDegree - q.natDegree))).degree < p.degree
this :
(if hq : q.Monic ... | ((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.36866) ((:c Ring.toSemiring) (:fv _uniq.368... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.36866)"},{"name":"b","sexp":"(:fv _uniq.36866)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.36866))"}... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"dsimp","sourceEnd":5620,"sourceStart":5615,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kin... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 8 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6e1ddc5d76cd75367a5dfb86b41538a8b4a62e55f6c4186649a5dc2163ee53e4 | db6eeb04eea09ad5a78d991b81095c1dc9388e8cb2a324326035a84ae688fb9e | 7854eab90b5d1f0eed9d2f7f6b885100cc44bc732b41c876b3af083c01260845 | 92f1a79001ef0f00d7a22ec3ca65396e26c79396b17679fc25e98168b213bb23 |
cat-searcher/leandojo-benchmark-4-random | test | 1,205 | Polynomial.degree_modByMonic_lt | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>dif_pos</a> hq] at this ⊢ | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this✝ : DecidableEq R := Classical.decEq R
h : q.degree ≤ p.degree ∧ p ≠ 0
_wf : (p - q * (C p.leadingCoeff * X ^ (p.natDegree - q.natDegree))).degree < p.degree
this :
(if hq : q.Monic ... | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this✝ : DecidableEq R := Classical.decEq R
h : q.degree ≤ p.degree ∧ p ≠ 0
_wf : (p - q * (C p.leadingCoeff * X ^ (p.natDegree - q.natDegree))).degree < p.degree
this : ((p - q * (C p.lead... | ((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.36866) ((:c Ring.toSemiring) (:fv _uniq.368... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.36866)"},{"name":"b","sexp":"(:fv _uniq.36866)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.36866))"}... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":5629,"sourceStart":5627,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5631,"sourceStart":5630,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"dif_pos... | [] | [{"source":"this","source_end":5650,"source_start":5646,"syntax_kind":"ident"},{"source":"dif_pos hq","source_end":5641,"source_start":5631,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 9 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eacba771b39e33f33ce71e470e7223946ad79dec024a1e6e39175dbc49b6dcb2 | 92f1a79001ef0f00d7a22ec3ca65396e26c79396b17679fc25e98168b213bb23 | 6226166100742aba34b83703b52106279249d396bdec4160123a1da914177a1a | 407796d9b3195507b630686a7396115f9640551c3a3ab888f608bcee52551217 |
cat-searcher/leandojo-benchmark-4-random | test | 1,206 | Polynomial.degree_modByMonic_lt | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>if_pos</a> h] | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this✝ : DecidableEq R := Classical.decEq R
h : q.degree ≤ p.degree ∧ p ≠ 0
_wf : (p - q * (C p.leadingCoeff * X ^ (p.natDegree - q.natDegree))).degree < p.degree
this : ((p - q * (C p.lead... | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this✝ : DecidableEq R := Classical.decEq R
h : q.degree ≤ p.degree ∧ p ≠ 0
_wf : (p - q * (C p.leadingCoeff * X ^ (p.natDegree - q.natDegree))).degree < p.degree
this : ((p - q * (C p.lead... | ((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.36866) ((:c Ring.toSemiring) (:fv _uniq.368... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.36866)"},{"name":"b","sexp":"(:fv _uniq.36866)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.36866))"}... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":5663,"sourceStart":5661,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5665,"sourceStart":5664,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"if_pos"... | [] | [{"source":"if_pos h","source_end":5673,"source_start":5665,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 12 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3813defe179c8f8ebbaad4283b070a52bce0a85b32f9f1a12f4b14dd534d48f7 | 407796d9b3195507b630686a7396115f9640551c3a3ab888f608bcee52551217 | f8deb26c2bf7b66c57ae2500f3a32c03c8adb2c94dce531851949229489b63b8 | d7595d17ae1345a02683c2e38c9aecb6ca526648472bf8c8f635c712c1dee58c |
cat-searcher/leandojo-benchmark-4-random | test | 1,207 | Polynomial.degree_modByMonic_lt | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact this | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this✝ : DecidableEq R := Classical.decEq R
h : q.degree ≤ p.degree ∧ p ≠ 0
_wf : (p - q * (C p.leadingCoeff * X ^ (p.natDegree - q.natDegree))).degree < p.degree
this : ((p - q * (C p.lead... | ((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.36866) ((:c Ring.toSemiring) (:fv _uniq.368... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.36866)"},{"name":"b","sexp":"(:fv _uniq.36866)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.36866))"}... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":5686,"sourceStart":5681,"tag":"atom"},{"contextIndex":18,"semanticRole":"local","source":"this","sourceEnd":5691,"sourceStart":5687,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact this","sourceEnd":5691,"sourceStart":5681,"tag":"node"} | [] | [{"source":"this","source_end":5691,"source_start":5687,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 15 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f3b6af873ab250e02fc446cc31ff7e059ebb55798a9012aa890459f549665028 | d7595d17ae1345a02683c2e38c9aecb6ca526648472bf8c8f635c712c1dee58c | 4bf05ffe5319fff5c45a2736953c2c5d2fee7a5728be1458b77f126cd265f282 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,208 | Polynomial.degree_modByMonic_lt | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | unfold <a>Polynomial.modByMonic</a> <a>Polynomial.divModByMonicAux</a> | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this : DecidableEq R := Classical.decEq R
h : ¬(q.degree ≤ p.degree ∧ p ≠ 0)
⊢ ¬q.degree ≤ p.degree → (p %ₘ q).degree < q.degree | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this : DecidableEq R := Classical.decEq R
h : ¬(q.degree ≤ p.degree ∧ p ≠ 0)
⊢ ¬q.degree ≤ p.degree →
(if h : q.Monic then
(if h_1 : q.degree ≤ p.degree ∧ p ≠ 0 then
... | (:forall h ((:c Not) ((:c LE.le) ((:c WithBot) (:c Nat)) ((:c Preorder.toLE) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.36866) ((:c Ring.toSem... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.36866)"},{"name":"b","sexp":"(:fv _uniq.36866)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.36866))"}... | (:forall h :explicit (:app (:c Not) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"unfold","sourceEnd":5763,"sourceStart":5757,"tag":"atom"},{"children":[{"name":"Polynomial.modByMonic","semanticRole":"global","source":"modByMonic","sourceEnd":5774,"sourceStart":5764,"tag":"identifier"},{"name":"Polynomial.divModByMonicAux","semanticRole":"global","source":"divModByMonicAux","... | [] | [{"source":"modByMonic","source_end":5774,"source_start":5764,"syntax_kind":"ident"},{"source":"divModByMonicAux","source_end":5791,"source_start":5775,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 20 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3e06a52f8c794f99fe4ab4b770f4b7c126992a36dd7b955c16ed444348084156 | 881c662fac7824607574e6b2a0d6defdcbdb0e2ea1bca702f3554913f9d2721e | 153f2ae24278c3a6d90cd92bdf634819c79538aeb2a761af63916120d8f6fba0 | d3e1f9bd48faf359630720e49dce9229e2927f72d2aba71e9777cdb064494ca5 |
cat-searcher/leandojo-benchmark-4-random | test | 1,209 | Polynomial.degree_modByMonic_lt | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this : DecidableEq R := Classical.decEq R
h : ¬(q.degree ≤ p.degree ∧ p ≠ 0)
⊢ ¬q.degree ≤ p.degree →
(if h : q.Monic then
(if h_1 : q.degree ≤ p.degree ∧ p ≠ 0 then
... | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this : DecidableEq R := Classical.decEq R
h : ¬(q.degree ≤ p.degree ∧ p ≠ 0)
⊢ ¬q.degree ≤ p.degree →
(if h : q.Monic then
(if q.degree ≤ p.degree ∧ ¬p = 0 then
... | (:forall h ((:c Not) ((:c LE.le) ((:c WithBot) (:c Nat)) ((:c Preorder.toLE) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.36866) ((:c Ring.toSem... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.36866)"},{"name":"b","sexp":"(:fv _uniq.36866)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.36866))"}... | (:forall h :explicit (:app (:c Not) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"dsimp","sourceEnd":5807,"sourceStart":5802,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kin... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 21 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 65472d0344f374d0b54fe247d0fe8332c16b5e029367df784d7c72f714b2e9e4 | d3e1f9bd48faf359630720e49dce9229e2927f72d2aba71e9777cdb064494ca5 | 7854eab90b5d1f0eed9d2f7f6b885100cc44bc732b41c876b3af083c01260845 | e7587f8a03532be104cd12306a5b50714a158edc8c613274fa7a12ea67dbc3c3 |
cat-searcher/leandojo-benchmark-4-random | test | 1,210 | Polynomial.degree_modByMonic_lt | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>dif_pos</a> hq, <a>if_neg</a> h] | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this : DecidableEq R := Classical.decEq R
h : ¬(q.degree ≤ p.degree ∧ p ≠ 0)
⊢ ¬q.degree ≤ p.degree →
(if h : q.Monic then
(if q.degree ≤ p.degree ∧ ¬p = 0 then
... | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this : DecidableEq R := Classical.decEq R
h : ¬(q.degree ≤ p.degree ∧ p ≠ 0)
⊢ ¬q.degree ≤ p.degree → (0, p).2.degree < q.degree | (:forall h ((:c Not) ((:c LE.le) ((:c WithBot) (:c Nat)) ((:c Preorder.toLE) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.36866) ((:c Ring.toSem... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.36866)"},{"name":"b","sexp":"(:fv _uniq.36866)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.36866))"}... | (:forall h :explicit (:app (:c Not) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":5820,"sourceStart":5818,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5822,"sourceStart":5821,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"dif_pos... | [] | [{"source":"dif_pos hq","source_end":5832,"source_start":5822,"syntax_kind":"Lean.Parser.Term.app"},{"source":"if_neg h","source_end":5842,"source_start":5834,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 22 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7cf0a7b46448bd60af7b30e5a9b97f9d74b9015c4e12a99a5bd02e8ea2d70295 | e7587f8a03532be104cd12306a5b50714a158edc8c613274fa7a12ea67dbc3c3 | 17790d40d54370a9361933cbc7ce44b38545db31e5ab1c79100387324683f252 | f94d19230af0b989c36a513f85b38966c0bdaeb499cffd3ed85837ad1b6ce7d6 |
cat-searcher/leandojo-benchmark-4-random | test | 1,211 | Polynomial.degree_modByMonic_lt | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>lt_of_not_ge</a> | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this : DecidableEq R := Classical.decEq R
h : ¬(q.degree ≤ p.degree ∧ p ≠ 0)
⊢ ¬q.degree ≤ p.degree → (0, p).2.degree < q.degree | (:forall h ((:c Not) ((:c LE.le) ((:c WithBot) (:c Nat)) ((:c Preorder.toLE) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.36866) ((:c Ring.toSem... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.36866)"},{"name":"b","sexp":"(:fv _uniq.36866)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.36866))"}... | (:forall h :explicit (:app (:c Not) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":5859,"sourceStart":5854,"tag":"atom"},{"name":"lt_of_not_ge","semanticRole":"global","source":"lt_of_not_ge","sourceEnd":5872,"sourceStart":5860,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact lt_of_not_ge","sourceEnd":5872,"sourceStart":5854,"tag":"node... | [] | [{"source":"lt_of_not_ge","source_end":5872,"source_start":5860,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 26 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | afedd5184d0efcb34ebbee5d74654f79cafd547313337cbca6a52e74bed5a087 | f94d19230af0b989c36a513f85b38966c0bdaeb499cffd3ed85837ad1b6ce7d6 | 002c977871b4e7f508e20f5555f7689c6c4ef1fbb1e938ae047df0855ac954b9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,212 | Polynomial.degree_modByMonic_lt | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro hp | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this : DecidableEq R := Classical.decEq R
h : ¬(q.degree ≤ p.degree ∧ p ≠ 0)
⊢ ¬p ≠ 0 → (p %ₘ q).degree < q.degree | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this : DecidableEq R := Classical.decEq R
h : ¬(q.degree ≤ p.degree ∧ p ≠ 0)
hp : ¬p ≠ 0
⊢ (p %ₘ q).degree < q.degree | (:forall h ((:c Not) ((:c Ne) ((:c Polynomial) (:fv _uniq.36866) ((:c Ring.toSemiring) (:fv _uniq.36866) (:fv _uniq.36881))) (:fv _uniq.37560) ((:c OfNat.ofNat) ((:c Polynomial) (:fv _uniq.36866) ((:c Ring.toSemiring) (:fv _uniq.36866) (:fv _uniq.36881))) (:lit 0) ((:c Zero.toOfNat0) ((:c Polynomial) (:fv _uniq.36866) ... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.36866)"},{"name":"b","sexp":"(:fv _uniq.36866)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.36866))"}... | (:forall h :explicit (:app (:c Not) (:arg :explicit 0 (:app (:c Ne) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:fv FV12)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"intro","sourceEnd":5901,"sourceStart":5896,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hp","sourceEnd":5904,"sourceStart":5902,"tag":"identifier"}],"kind":"null","source":"hp","sourceEnd":5904,"sourceStart":5902,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source":"i... | [{"role":"fresh_name","source":"hp","source_end":5904,"source_start":5902,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 31 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 789f115b3ec435a24aa7a2aeb108df606f96d174db29b62357b66e491d35e16e | 436bead203d5ba9b58db42b7d8d5dac1ab8f26483eaec64f742debead82bd20a | 0cb4416f6d7aef7e54c2dde4bf0b653c3dcfc3726c7da28073bade9f641ef710 | f2b2fbaf41d37eccfe9179c11890eb7472cc1666610ecc4a1ce1a0830492dff5 |
cat-searcher/leandojo-benchmark-4-random | test | 1,213 | Polynomial.degree_modByMonic_lt | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | unfold <a>Polynomial.modByMonic</a> <a>Polynomial.divModByMonicAux</a> | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this : DecidableEq R := Classical.decEq R
h : ¬(q.degree ≤ p.degree ∧ p ≠ 0)
hp : ¬p ≠ 0
⊢ (p %ₘ q).degree < q.degree | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this : DecidableEq R := Classical.decEq R
h : ¬(q.degree ≤ p.degree ∧ p ≠ 0)
hp : ¬p ≠ 0
⊢ (if h : q.Monic then
(if h_1 : q.degree ≤ p.degree ∧ p ≠ 0 then
let z := C p.... | ((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.36866) ((:c Ring.toSemiring) (:fv _uniq.368... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.36866)"},{"name":"b","sexp":"(:fv _uniq.36866)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.36866))"}... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"unfold","sourceEnd":5921,"sourceStart":5915,"tag":"atom"},{"children":[{"name":"Polynomial.modByMonic","semanticRole":"global","source":"modByMonic","sourceEnd":5932,"sourceStart":5922,"tag":"identifier"},{"name":"Polynomial.divModByMonicAux","semanticRole":"global","source":"divModByMonicAux","... | [] | [{"source":"modByMonic","source_end":5932,"source_start":5922,"syntax_kind":"ident"},{"source":"divModByMonicAux","source_end":5949,"source_start":5933,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 32 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 06316da1a03291880bbb129ad4197afd0240e7cd9f56fb4d3e0560474e20753f | f2b2fbaf41d37eccfe9179c11890eb7472cc1666610ecc4a1ce1a0830492dff5 | 153f2ae24278c3a6d90cd92bdf634819c79538aeb2a761af63916120d8f6fba0 | 74193fd801f0802e08fcb4f10b726a9c49b2a9d4b558ea3b8ee4cc4cb01cc0c3 |
cat-searcher/leandojo-benchmark-4-random | test | 1,214 | Polynomial.degree_modByMonic_lt | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this : DecidableEq R := Classical.decEq R
h : ¬(q.degree ≤ p.degree ∧ p ≠ 0)
hp : ¬p ≠ 0
⊢ (if h : q.Monic then
(if h_1 : q.degree ≤ p.degree ∧ p ≠ 0 then
let z := C p.... | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this : DecidableEq R := Classical.decEq R
h : ¬(q.degree ≤ p.degree ∧ p ≠ 0)
hp : ¬p ≠ 0
⊢ (if h : q.Monic then
(if q.degree ≤ p.degree ∧ ¬p = 0 then
(C p.leadingCoeff ... | ((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.36866) ((:c Ring.toSemiring) (:fv _uniq.368... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.36866)"},{"name":"b","sexp":"(:fv _uniq.36866)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.36866))"}... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"dsimp","sourceEnd":5965,"sourceStart":5960,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kin... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 33 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5ac449237f89c253eac06c442268c7e9fab98fc92cb92f46b292bc6fae21640b | 74193fd801f0802e08fcb4f10b726a9c49b2a9d4b558ea3b8ee4cc4cb01cc0c3 | 7854eab90b5d1f0eed9d2f7f6b885100cc44bc732b41c876b3af083c01260845 | 2b93cbb65f28bcabc2377cc14b65fe3a92f25c982feda5ab83d26a333b55a7ec |
cat-searcher/leandojo-benchmark-4-random | test | 1,215 | Polynomial.degree_modByMonic_lt | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>dif_pos</a> hq, <a>if_neg</a> h, <a>Classical.not_not</a>.1 hp] | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this : DecidableEq R := Classical.decEq R
h : ¬(q.degree ≤ p.degree ∧ p ≠ 0)
hp : ¬p ≠ 0
⊢ (if h : q.Monic then
(if q.degree ≤ p.degree ∧ ¬p = 0 then
(C p.leadingCoeff ... | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this : DecidableEq R := Classical.decEq R
h : ¬(q.degree ≤ p.degree ∧ p ≠ 0)
hp : ¬p ≠ 0
⊢ (0, 0).2.degree < q.degree | ((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.36866) ((:c Ring.toSemiring) (:fv _uniq.368... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.36866)"},{"name":"b","sexp":"(:fv _uniq.36866)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.36866))"}... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":5978,"sourceStart":5976,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5980,"sourceStart":5979,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"dif_pos... | [] | [{"source":"dif_pos hq","source_end":5990,"source_start":5980,"syntax_kind":"Lean.Parser.Term.app"},{"source":"if_neg h","source_end":6000,"source_start":5992,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Classical.not_not.1 hp","source_end":6024,"source_start":6002,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 34 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dd72dc7a40f36d9a4aa72f153321dcbbfe5a43bff821a73dcb1c8e58ffd3ecb8 | 2b93cbb65f28bcabc2377cc14b65fe3a92f25c982feda5ab83d26a333b55a7ec | 2c259ec8dc94d523fc9e19b0e7376fc7d28597f102d419cb8dcf814234f91c2d | be811360b2bfd1cba53005015b019d02c65abd447f829b2da3056f8bf2d6a420 |
cat-searcher/leandojo-benchmark-4-random | test | 1,216 | Polynomial.degree_modByMonic_lt | Mathlib/Algebra/Polynomial/Div.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>lt_of_le_of_ne</a> <a>bot_le</a> (<a>Ne.symm</a> (<a>mt</a> <a>Polynomial.degree_eq_bot</a>.1 hq.ne_zero)) | R : Type u
S : Type v
T : Type w
A : Type z
a b : R
n : ℕ
inst✝¹ : Ring R
p✝ q✝ : R[X]
inst✝ : Nontrivial R
p q : R[X]
hq : q.Monic
this : DecidableEq R := Classical.decEq R
h : ¬(q.degree ≤ p.degree ∧ p ≠ 0)
hp : ¬p ≠ 0
⊢ (0, 0).2.degree < q.degree | ((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.36866) ((:c Ring.toSemiring) (:fv _uniq.368... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.36866)"},{"name":"b","sexp":"(:fv _uniq.36866)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.36866))"}... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":6041,"sourceStart":6036,"tag":"atom"},{"children":[{"name":"lt_of_le_of_ne","semanticRole":"global","source":"lt_of_le_of_ne","sourceEnd":6056,"sourceStart":6042,"tag":"identifier"},{"children":[{"name":"bot_le","semanticRole":"global","source":"bot_le","sourceEnd":6063,"sourc... | [] | [{"source":"lt_of_le_of_ne bot_le (Ne.symm (mt degree_eq_bot.1 hq.ne_zero))","source_end":6105,"source_start":6042,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36866","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36868","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 39 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d114a0f65c8ac0e9704ebb9db0ffdd5aa4337f6541ea787273d7d90170e0465e | be811360b2bfd1cba53005015b019d02c65abd447f829b2da3056f8bf2d6a420 | 0d61e698dc2388b1e3be9beeecd2ee2a055baf7d10049b55e5bec523a9427107 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,217 | Nat.Primes.coe_pnat_injective | Mathlib/Data/PNat/Prime.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | injection h | p q : Primes
h : ↑p = ↑q
⊢ ↑p = ↑q | ((:c Eq) (:c Nat) ((:c Subtype.val) (:c Nat) (:lambda x (:c Nat) ((:c Nat.Prime) 0)) (:fv _uniq.515)) ((:c Subtype.val) (:c Nat) (:lambda x (:c Nat) ((:c Nat.Prime) 0)) (:fv _uniq.518))) | [{"name":"p","sexp":"(:c Nat.Primes)"},{"name":"q","sexp":"(:c Nat.Primes)"},{"name":"h","sexp":"((:c Eq) (:c PNat) ((:c Nat.Primes.toPNat) (:fv _uniq.515)) ((:c Nat.Primes.toPNat) (:fv _uniq.518)))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Subtype.val) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV1)))) (:arg :explicit 2 (:app (:c Subtype.val) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV2))))) | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.515","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat.Primes)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.518","is_instance":false,"is_let":false,"name":"q","sexp":"(:c Nat.Primes)"},{"binder_role":":explicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"injection","sourceEnd":1066,"sourceStart":1057,"tag":"atom"},{"contextIndex":3,"semanticRole":"local","source":"h","sourceEnd":1068,"sourceStart":1067,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.inj... | [] | [{"source":"h","source_end":1068,"source_start":1067,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.515","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.518","is_instance":false,"is_let":false,"user_name":"q"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.5... | 8 | 2 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3a2a0b24a838224b09fd4099e62addbcd06d85f097bb203f52a2825e45ce5062 | 13369ebe0b76e8360ce33d2d993fab7569c8afd4143ecfe245bddde54015c962 | eab6615bd3c5163f9a2f2862a347619a247489ed991f499a15e2635a6ade44fa | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,218 | ProbabilityTheory.kernel.fst_map_id_prod | Mathlib/Probability/Kernel/Composition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>ProbabilityTheory.kernel.fst_map_prod</a> _ <a>measurable_id'</a> hf, <a>ProbabilityTheory.kernel.map_id'</a>] | α : Type u_1
β : Type u_2
ι : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
δ : Type u_4
mδ : MeasurableSpace δ
γ✝ : Type u_5
mγ✝ : MeasurableSpace γ✝
f✝ : β → γ✝
g : γ✝ → α
κ : ↥(kernel α β)
γ : Type u_6
mγ : MeasurableSpace γ
f : β → γ
hf : Measurable f
⊢ fst (map κ (fun a => (a, f a)) ⋯) = κ | ((:c Eq) ((:c Subtype) (:forall _ (:fv _uniq.219489) ((:c MeasureTheory.Measure) (:fv _uniq.219492) (:fv _uniq.219501))) (:lambda x (:forall _ (:fv _uniq.219489) ((:c MeasureTheory.Measure) (:fv _uniq.219492) (:fv _uniq.219501))) ((:c Membership.mem) (:forall _ (:fv _uniq.219489) ((:c MeasureTheory.Measure) (:fv _uniq.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.219489))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.219492))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"mδ","sexp":"((:c Mea... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit 1 (:lambda x :explicit (:forall _ :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.219489","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.219492","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":48381,"sourceStart":48379,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":48383,"sourceStart":48382,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"fst_map_prod _ measurable_id' hf","source_end":48415,"source_start":48383,"syntax_kind":"Lean.Parser.Term.app"},{"source":"kernel.map_id'","source_end":48431,"source_start":48417,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.219489","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.219492","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 223 | 2 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9eae887d1377f6aff6d505110911463917e1394f2fe00a9802027a5732afb238 | 5c9014478498d952d545cb1861232bb63346e1f402be05cfa5c87ebac7f266c4 | b4094ce28e6d0aae170639eed7f6b675cbfba1937bb0c43d56793b07a2c3fa0d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,219 | volume_regionBetween_eq_lintegral | Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h₁ : (fun y => <a>ENNReal.ofReal</a> ((g - f) y)) =ᵐ[μ.restrict s] fun y => <a>ENNReal.ofReal</a> ((<a>AEMeasurable.mk</a> g hg - <a>AEMeasurable.mk</a> f hf) y) := (hg.ae_eq_mk.sub hf.ae_eq_mk).<a>Filter.EventuallyEq.fun_comp</a> <a>ENNReal.ofReal</a> | α : Type u_1
inst✝¹ : MeasurableSpace α
μ : Measure α
f g : α → ℝ
s : Set α
inst✝ : SigmaFinite μ
hf : AEMeasurable f (μ.restrict s)
hg : AEMeasurable g (μ.restrict s)
hs : MeasurableSet s
⊢ (μ.prod volume) (regionBetween f g s) = ∫⁻ (y : α) in s, ofReal ((g - f) y) ∂μ | α : Type u_1
inst✝¹ : MeasurableSpace α
μ : Measure α
f g : α → ℝ
s : Set α
inst✝ : SigmaFinite μ
hf : AEMeasurable f (μ.restrict s)
hg : AEMeasurable g (μ.restrict s)
hs : MeasurableSet s
h₁ :
(fun y => ofReal ((g - f) y)) =ᶠ[ae (μ.restrict s)] fun y => ofReal ((AEMeasurable.mk g hg - AEMeasurable.mk f hf) y)
⊢ (μ.p... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) ((:c Prod) (:fv _uniq.228799) (:c Real)) ((:c Prod.instMeasurableSpace) (:fv _uniq.228799) (:c Real) (:fv _uniq.228802) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)))) ((:c Set) ((:c Prod) (:fv _uniq.228799) (:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.228799))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.228799) (:fv _uniq.228802))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.228799) (:c Real))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.228799) (:c Real... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c MeasurableSpace) (:ar... | {"children":[{"source":"have","sourceEnd":25785,"sourceStart":25781,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h₁","sourceEnd":25790,"sourceStart":25786,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h₁","sourceEnd":25790,"sourceStart":25786,"tag":"nod... | [] | [{"source":"(fun y => ENNReal.ofReal ((g - f) y)) =ᵐ[μ.restrict s] fun y =>\n ENNReal.ofReal ((AEMeasurable.mk g hg - AEMeasurable.mk f hf) y)","source_end":25934,"source_start":25797,"syntax_kind":"MeasureTheory.«term_=ᵐ[_]_»"},{"source":"(hg.ae_eq_mk.sub hf.ae_eq_mk).fun_comp ENNReal.ofReal","source_end":25995,"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"inte... | 129 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d6641db24bd2bcecaa54d116918b76a4fc24979e7bbd62832d631fbe1556d747 | 041c6c235e0fb79289c2f9264a10cefa5b599e72e89e24720f033ddea3d4255a | 641aebb6adfeac9b849a49eef528cfc63132f12a53eee519d1a165aab8427fa1 | 2b1d0e92f1d55e72184404ab8b68b67cb2ebe302783d09fe5785aa35d8b33ca7 |
cat-searcher/leandojo-benchmark-4-random | test | 1,220 | volume_regionBetween_eq_lintegral | Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h₂ : (μ.restrict s).<a>MeasureTheory.Measure.prod</a> <a>MeasureTheory.MeasureSpace.volume</a> (<a>regionBetween</a> f g s) = (μ.restrict s).<a>MeasureTheory.Measure.prod</a> <a>MeasureTheory.MeasureSpace.volume</a> (<a>regionBetween</a> (<a>AEMeasurable.mk</a> f hf) (<a>AEMeasurable.mk</a> g hg) s) := by apply <a... | α : Type u_1
inst✝¹ : MeasurableSpace α
μ : Measure α
f g : α → ℝ
s : Set α
inst✝ : SigmaFinite μ
hf : AEMeasurable f (μ.restrict s)
hg : AEMeasurable g (μ.restrict s)
hs : MeasurableSet s
h₁ :
(fun y => ofReal ((g - f) y)) =ᶠ[ae (μ.restrict s)] fun y => ofReal ((AEMeasurable.mk g hg - AEMeasurable.mk f hf) y)
⊢ (μ.p... | α : Type u_1
inst✝¹ : MeasurableSpace α
μ : Measure α
f g : α → ℝ
s : Set α
inst✝ : SigmaFinite μ
hf : AEMeasurable f (μ.restrict s)
hg : AEMeasurable g (μ.restrict s)
hs : MeasurableSet s
h₁ :
(fun y => ofReal ((g - f) y)) =ᶠ[ae (μ.restrict s)] fun y => ofReal ((AEMeasurable.mk g hg - AEMeasurable.mk f hf) y)
h₂ :
... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) ((:c Prod) (:fv _uniq.228799) (:c Real)) ((:c Prod.instMeasurableSpace) (:fv _uniq.228799) (:c Real) (:fv _uniq.228802) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)))) ((:c Set) ((:c Prod) (:fv _uniq.228799) (:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.228799))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.228799) (:fv _uniq.228802))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.228799) (:c Real))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.228799) (:c Real... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c MeasurableSpace) (:ar... | {"children":[{"source":"have","sourceEnd":26002,"sourceStart":25998,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h₂","sourceEnd":26007,"sourceStart":26003,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h₂","sourceEnd":26007,"sourceStart":26003,"tag":"nod... | [] | [{"source":"(μ.restrict s).prod volume (regionBetween f g s) =\n (μ.restrict s).prod volume\n (regionBetween (AEMeasurable.mk f hf) (AEMeasurable.mk g hg) s)","source_end":26171,"source_start":26014,"syntax_kind":"«term_=_»"},{"source":"measure_congr","source_end":26201,"source_start":26188,"syntax_kind":"i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"inte... | 129 | 5 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2c1eb9fe675bf89c4df91ba0f2b004e9efd86564ccd4fd09856981da4c9cfcab | 2b1d0e92f1d55e72184404ab8b68b67cb2ebe302783d09fe5785aa35d8b33ca7 | 704bebf64d6ad0231a6a24b091815a4ed0c60892329d445169166eeaeb4cefd3 | 599ccc8e39d67bbab00e20bb9e0bd09502fa2f061a7dc4c1d69fbaa7b5e6e3b4 |
cat-searcher/leandojo-benchmark-4-random | test | 1,221 | volume_regionBetween_eq_lintegral | Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.lintegral_congr_ae</a> h₁, ← <a>volume_regionBetween_eq_lintegral'</a> hf.measurable_mk hg.measurable_mk hs] | α : Type u_1
inst✝¹ : MeasurableSpace α
μ : Measure α
f g : α → ℝ
s : Set α
inst✝ : SigmaFinite μ
hf : AEMeasurable f (μ.restrict s)
hg : AEMeasurable g (μ.restrict s)
hs : MeasurableSet s
h₁ :
(fun y => ofReal ((g - f) y)) =ᶠ[ae (μ.restrict s)] fun y => ofReal ((AEMeasurable.mk g hg - AEMeasurable.mk f hf) y)
h₂ :
... | α : Type u_1
inst✝¹ : MeasurableSpace α
μ : Measure α
f g : α → ℝ
s : Set α
inst✝ : SigmaFinite μ
hf : AEMeasurable f (μ.restrict s)
hg : AEMeasurable g (μ.restrict s)
hs : MeasurableSet s
h₁ :
(fun y => ofReal ((g - f) y)) =ᶠ[ae (μ.restrict s)] fun y => ofReal ((AEMeasurable.mk g hg - AEMeasurable.mk f hf) y)
h₂ :
... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) ((:c Prod) (:fv _uniq.228799) (:c Real)) ((:c Prod.instMeasurableSpace) (:fv _uniq.228799) (:c Real) (:fv _uniq.228802) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)))) ((:c Set) ((:c Prod) (:fv _uniq.228799) (:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.228799))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.228799) (:fv _uniq.228802))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.228799) (:c Real))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.228799) (:c Real... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c MeasurableSpace) (:ar... | {"children":[{"source":"rw","sourceEnd":26432,"sourceStart":26430,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":26434,"sourceStart":26433,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Mea... | [] | [{"source":"lintegral_congr_ae h₁","source_end":26457,"source_start":26434,"syntax_kind":"Lean.Parser.Term.app"},{"source":"volume_regionBetween_eq_lintegral' hf.measurable_mk hg.measurable_mk hs","source_end":26538,"source_start":26467,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"inte... | 129 | 10 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 60437e4dc49a5663788f850765bd88c49fc1abc084034ad06206c2e9004f16c2 | 599ccc8e39d67bbab00e20bb9e0bd09502fa2f061a7dc4c1d69fbaa7b5e6e3b4 | bb643b13ff5b596394104aa997917b659bb0a13166c45f5249c7928f8b41eb18 | a93e12cb291cf988917ba043810febcffda348c22e8110506c522d99888bd2f1 |
cat-searcher/leandojo-benchmark-4-random | test | 1,222 | volume_regionBetween_eq_lintegral | Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert h₂ using 1 | α : Type u_1
inst✝¹ : MeasurableSpace α
μ : Measure α
f g : α → ℝ
s : Set α
inst✝ : SigmaFinite μ
hf : AEMeasurable f (μ.restrict s)
hg : AEMeasurable g (μ.restrict s)
hs : MeasurableSet s
h₁ :
(fun y => ofReal ((g - f) y)) =ᶠ[ae (μ.restrict s)] fun y => ofReal ((AEMeasurable.mk g hg - AEMeasurable.mk f hf) y)
h₂ :
... | case h.e'_2
α : Type u_1
inst✝¹ : MeasurableSpace α
μ : Measure α
f g : α → ℝ
s : Set α
inst✝ : SigmaFinite μ
hf : AEMeasurable f (μ.restrict s)
hg : AEMeasurable g (μ.restrict s)
hs : MeasurableSet s
h₁ :
(fun y => ofReal ((g - f) y)) =ᶠ[ae (μ.restrict s)] fun y => ofReal ((AEMeasurable.mk g hg - AEMeasurable.mk f h... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) ((:c Prod) (:fv _uniq.228799) (:c Real)) ((:c Prod.instMeasurableSpace) (:fv _uniq.228799) (:c Real) (:fv _uniq.228802) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)))) ((:c Set) ((:c Prod) (:fv _uniq.228799) (:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.228799))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.228799) (:fv _uniq.228802))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.228799) (:c Real))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.228799) (:c Real... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c MeasurableSpace) (:ar... | {"children":[{"source":"convert","sourceEnd":26549,"sourceStart":26542,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":12,"semanticRole":"local","source":"h₂","sourceEnd":26554,"sourceStart":26550,"tag":"identifier"},{"children"... | [] | [{"source":"h₂","source_end":26554,"source_start":26550,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"inte... | 129 | 14 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 631e184eb1a10ef566649e427f42b9f2f74c14d102e8b4b5ff1e3a2d9fe358ae | a93e12cb291cf988917ba043810febcffda348c22e8110506c522d99888bd2f1 | 1291eaacce0844170bd7816a48dee1fc1f4285225af26640ba7c9a12363c82b6 | 829430337369b152b7e4bd51141d7c5817f5ad3975948d058357effaf4c37a5e |
cat-searcher/leandojo-benchmark-4-random | test | 1,223 | volume_regionBetween_eq_lintegral | Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>MeasureTheory.measure_congr</a> | α : Type u_1
inst✝¹ : MeasurableSpace α
μ : Measure α
f g : α → ℝ
s : Set α
inst✝ : SigmaFinite μ
hf : AEMeasurable f (μ.restrict s)
hg : AEMeasurable g (μ.restrict s)
hs : MeasurableSet s
h₁ :
(fun y => ofReal ((g - f) y)) =ᶠ[ae (μ.restrict s)] fun y => ofReal ((AEMeasurable.mk g hg - AEMeasurable.mk f hf) y)
⊢ ((μ.... | case H
α : Type u_1
inst✝¹ : MeasurableSpace α
μ : Measure α
f g : α → ℝ
s : Set α
inst✝ : SigmaFinite μ
hf : AEMeasurable f (μ.restrict s)
hg : AEMeasurable g (μ.restrict s)
hs : MeasurableSet s
h₁ :
(fun y => ofReal ((g - f) y)) =ᶠ[ae (μ.restrict s)] fun y => ofReal ((AEMeasurable.mk g hg - AEMeasurable.mk f hf) y)... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) ((:c Prod) (:fv _uniq.228799) (:c Real)) ((:c Prod.instMeasurableSpace) (:fv _uniq.228799) (:c Real) (:fv _uniq.228802) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)))) ((:c Set) ((:c Prod) (:fv _uniq.228799) (:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.228799))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.228799) (:fv _uniq.228802))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.228799) (:c Real))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.228799) (:c Real... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c MeasurableSpace) (:ar... | {"children":[{"source":"apply","sourceEnd":26187,"sourceStart":26182,"tag":"atom"},{"name":"MeasureTheory.measure_congr","semanticRole":"global","source":"measure_congr","sourceEnd":26201,"sourceStart":26188,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply measure_congr","sourceEnd":26201,"sourceS... | [] | [{"source":"measure_congr","source_end":26201,"source_start":26188,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"inte... | 129 | 7 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3025c0b042f2568f6baecb72b179940237340d2765e4bcb1911769b96fb42666 | 43d479bd4488e42d6619eba7b5fc054ef945428c08569d2a0bea7d0900bb4e34 | d7ce8c6b4fd051e9d32369994749a30b43cd3afc8461d4b4834a4dabb9cb77ae | c9dbbf38ca59a9fc515a44d3b4429677647c8b976f2c6be4b571e5299df40e81 |
cat-searcher/leandojo-benchmark-4-random | test | 1,224 | volume_regionBetween_eq_lintegral | Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply EventuallyEq.rfl.inter | case H
α : Type u_1
inst✝¹ : MeasurableSpace α
μ : Measure α
f g : α → ℝ
s : Set α
inst✝ : SigmaFinite μ
hf : AEMeasurable f (μ.restrict s)
hg : AEMeasurable g (μ.restrict s)
hs : MeasurableSet s
h₁ :
(fun y => ofReal ((g - f) y)) =ᶠ[ae (μ.restrict s)] fun y => ofReal ((AEMeasurable.mk g hg - AEMeasurable.mk f hf) y)... | case H
α : Type u_1
inst✝¹ : MeasurableSpace α
μ : Measure α
f g : α → ℝ
s : Set α
inst✝ : SigmaFinite μ
hf : AEMeasurable f (μ.restrict s)
hg : AEMeasurable g (μ.restrict s)
hs : MeasurableSet s
h₁ :
(fun y => ofReal ((g - f) y)) =ᶠ[ae (μ.restrict s)] fun y => ofReal ((AEMeasurable.mk g hg - AEMeasurable.mk f hf) y)... | ((:c Filter.EventuallyEq) ((:c Prod) (:fv _uniq.228799) (:c Real)) (:sort 0) ((:c MeasureTheory.ae) ((:c Prod) (:fv _uniq.228799) (:c Real)) ((:c MeasureTheory.Measure) ((:c Prod) (:fv _uniq.228799) (:c Real)) ((:c Prod.instMeasurableSpace) (:fv _uniq.228799) (:c Real) (:fv _uniq.228802) ((:c MeasureTheory.MeasureSpace... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.228799))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.228799) (:fv _uniq.228802))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.228799) (:c Real))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.228799) (:c Real... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)))) (:arg :implicit-type 1 (:sort Prop)) (:arg :explicit 2 (:app (:c MeasureTheory.ae) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)))) (:arg :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c MeasurableSpace) (:ar... | {"children":[{"source":"apply","sourceEnd":26211,"sourceStart":26206,"tag":"atom"},{"name":"Filter.EventuallyEq.inter","semanticRole":"global","source":"EventuallyEq.rfl.inter","sourceEnd":26234,"sourceStart":26212,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply EventuallyEq.rfl.inter","sourceEnd... | [] | [{"source":"EventuallyEq.rfl.inter","source_end":26234,"source_start":26212,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"inte... | 129 | 8 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 460ee05319d1c8e02cb3648f49653527a7ed6b6c777ba879b357a6c07b432c52 | c9dbbf38ca59a9fc515a44d3b4429677647c8b976f2c6be4b571e5299df40e81 | 5a2b3159fc6d68d7d8caa6cb749ae13dba1dcf46795b953e4d5bc0785089353a | 129844afe3fd6dbe2ad878c1d102daeaadf299d182c0cb94486ed8393b5e7ac7 |
cat-searcher/leandojo-benchmark-4-random | test | 1,225 | volume_regionBetween_eq_lintegral | Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ((quasiMeasurePreserving_fst.ae_eq_comp hf.ae_eq_mk).<a>Filter.EventuallyEq.comp₂</a> _ <a>Filter.EventuallyEq.rfl</a>).<a>Filter.EventuallyEq.inter</a> (EventuallyEq.rfl.comp₂ _ <| quasiMeasurePreserving_fst.ae_eq_comp hg.ae_eq_mk) | case H
α : Type u_1
inst✝¹ : MeasurableSpace α
μ : Measure α
f g : α → ℝ
s : Set α
inst✝ : SigmaFinite μ
hf : AEMeasurable f (μ.restrict s)
hg : AEMeasurable g (μ.restrict s)
hs : MeasurableSet s
h₁ :
(fun y => ofReal ((g - f) y)) =ᶠ[ae (μ.restrict s)] fun y => ofReal ((AEMeasurable.mk g hg - AEMeasurable.mk f hf) y)... | ((:c Filter.EventuallyEq) ((:c Prod) (:fv _uniq.228799) (:c Real)) (:sort 0) ((:c MeasureTheory.ae) ((:c Prod) (:fv _uniq.228799) (:c Real)) ((:c MeasureTheory.Measure) ((:c Prod) (:fv _uniq.228799) (:c Real)) ((:c Prod.instMeasurableSpace) (:fv _uniq.228799) (:c Real) (:fv _uniq.228802) ((:c MeasureTheory.MeasureSpace... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.228799))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.228799) (:fv _uniq.228802))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.228799) (:c Real))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.228799) (:c Real... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)))) (:arg :implicit-type 1 (:sort Prop)) (:arg :explicit 2 (:app (:c MeasureTheory.ae) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)))) (:arg :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c MeasurableSpace) (:ar... | {"children":[{"source":"exact","sourceEnd":26244,"sourceStart":26239,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":26252,"sourceStart":26251,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":26253,"sourceStart":26252,"tag":"atom"},{"children":[{"source":"qua... | [] | [{"source":"((quasiMeasurePreserving_fst.ae_eq_comp hf.ae_eq_mk).comp₂ _ EventuallyEq.rfl).inter\n (EventuallyEq.rfl.comp₂ _ <| quasiMeasurePreserving_fst.ae_eq_comp hg.ae_eq_mk)","source_end":26427,"source_start":26251,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"inte... | 129 | 9 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bc2b9faee8a5fb0eff57c88ae6a2f63b33050b3d9156812736568047d06c76ba | 129844afe3fd6dbe2ad878c1d102daeaadf299d182c0cb94486ed8393b5e7ac7 | 3976298baab4757aea7b17f6b2c78faef1aef6d6cf16e61f48080881abc0807b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,226 | volume_regionBetween_eq_lintegral | Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.Measure.restrict_prod_eq_prod_univ</a>] | case h.e'_2
α : Type u_1
inst✝¹ : MeasurableSpace α
μ : Measure α
f g : α → ℝ
s : Set α
inst✝ : SigmaFinite μ
hf : AEMeasurable f (μ.restrict s)
hg : AEMeasurable g (μ.restrict s)
hs : MeasurableSet s
h₁ :
(fun y => ofReal ((g - f) y)) =ᶠ[ae (μ.restrict s)] fun y => ofReal ((AEMeasurable.mk g hg - AEMeasurable.mk f h... | case h.e'_2
α : Type u_1
inst✝¹ : MeasurableSpace α
μ : Measure α
f g : α → ℝ
s : Set α
inst✝ : SigmaFinite μ
hf : AEMeasurable f (μ.restrict s)
hg : AEMeasurable g (μ.restrict s)
hs : MeasurableSet s
h₁ :
(fun y => ofReal ((g - f) y)) =ᶠ[ae (μ.restrict s)] fun y => ofReal ((AEMeasurable.mk g hg - AEMeasurable.mk f h... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) ((:c Prod) (:fv _uniq.228799) (:c Real)) ((:c Prod.instMeasurableSpace) (:fv _uniq.228799) (:c Real) (:fv _uniq.228802) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)))) ((:c Set) ((:c Prod) (:fv _uniq.228799) (:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.228799))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.228799) (:fv _uniq.228802))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.228799) (:c Real))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.228799) (:c Real... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c MeasurableSpace) (:ar... | {"children":[{"source":"rw","sourceEnd":26570,"sourceStart":26568,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":26572,"sourceStart":26571,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MeasureTheory.Me... | [] | [{"source":"Measure.restrict_prod_eq_prod_univ","source_end":26606,"source_start":26572,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"inte... | 129 | 19 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 25e81df1cdb7160db3dca31fbd19fc846c4dc789659639630f3e121088f6f9da | fe2ab6812c0f87ebc9f385cc6013c9d0da15d5e2fd1f07f9a0ee06b19c775626 | 11cbb30d3af69a070cca9a304f246af3ce62084f20a905ebbbb0641add3eef2f | a70a3f201648d0e516cf3db431b4eedb17049d9b752be1fa62b361ef07b9b054 |
cat-searcher/leandojo-benchmark-4-random | test | 1,227 | volume_regionBetween_eq_lintegral | Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>MeasureTheory.Measure.restrict_eq_self</a> _ (<a>regionBetween_subset</a> f g s)).<a>Eq.symm</a> | case h.e'_2
α : Type u_1
inst✝¹ : MeasurableSpace α
μ : Measure α
f g : α → ℝ
s : Set α
inst✝ : SigmaFinite μ
hf : AEMeasurable f (μ.restrict s)
hg : AEMeasurable g (μ.restrict s)
hs : MeasurableSet s
h₁ :
(fun y => ofReal ((g - f) y)) =ᶠ[ae (μ.restrict s)] fun y => ofReal ((AEMeasurable.mk g hg - AEMeasurable.mk f h... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) ((:c Prod) (:fv _uniq.228799) (:c Real)) ((:c Prod.instMeasurableSpace) (:fv _uniq.228799) (:c Real) (:fv _uniq.228802) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)))) ((:c Set) ((:c Prod) (:fv _uniq.228799) (:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.228799))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.228799) (:fv _uniq.228802))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.228799) (:c Real))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.228799) (:c Real... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c MeasurableSpace) (:ar... | {"children":[{"source":"exact","sourceEnd":26617,"sourceStart":26612,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":26619,"sourceStart":26618,"tag":"atom"},{"children":[{"name":"MeasureTheory.Measure.restrict_eq_self","semanticRole":"global","source":"Measure.restrict_eq_self","sourceEnd":26643,"sour... | [] | [{"source":"(Measure.restrict_eq_self _ (regionBetween_subset f g s)).symm","source_end":26680,"source_start":26618,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"inte... | 129 | 22 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8237cd7fc82ce791a7f34939edbf870b9ac88bdc864e86d182a267eeebe76c2e | a70a3f201648d0e516cf3db431b4eedb17049d9b752be1fa62b361ef07b9b054 | 2410d8253ef1ec9773870dd3602c0d26a6103b77de49e137b5398048d8a63177 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,228 | volume_regionBetween_eq_lintegral | Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.Measure.restrict_prod_eq_prod_univ</a>] | case h.e'_3
α : Type u_1
inst✝¹ : MeasurableSpace α
μ : Measure α
f g : α → ℝ
s : Set α
inst✝ : SigmaFinite μ
hf : AEMeasurable f (μ.restrict s)
hg : AEMeasurable g (μ.restrict s)
hs : MeasurableSet s
h₁ :
(fun y => ofReal ((g - f) y)) =ᶠ[ae (μ.restrict s)] fun y => ofReal ((AEMeasurable.mk g hg - AEMeasurable.mk f h... | case h.e'_3
α : Type u_1
inst✝¹ : MeasurableSpace α
μ : Measure α
f g : α → ℝ
s : Set α
inst✝ : SigmaFinite μ
hf : AEMeasurable f (μ.restrict s)
hg : AEMeasurable g (μ.restrict s)
hs : MeasurableSet s
h₁ :
(fun y => ofReal ((g - f) y)) =ᶠ[ae (μ.restrict s)] fun y => ofReal ((AEMeasurable.mk g hg - AEMeasurable.mk f h... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) ((:c Prod) (:fv _uniq.228799) (:c Real)) ((:c Prod.instMeasurableSpace) (:fv _uniq.228799) (:c Real) (:fv _uniq.228802) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)))) ((:c Set) ((:c Prod) (:fv _uniq.228799) (:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.228799))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.228799) (:fv _uniq.228802))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.228799) (:c Real))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.228799) (:c Real... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c MeasurableSpace) (:ar... | {"children":[{"source":"rw","sourceEnd":26688,"sourceStart":26686,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":26690,"sourceStart":26689,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MeasureTheory.Me... | [] | [{"source":"Measure.restrict_prod_eq_prod_univ","source_end":26724,"source_start":26690,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"inte... | 129 | 27 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2ddca11a75c2dfa804f7168da4c79f2b2c81ec7a89b87f225cfa2ad09e41c4e0 | 00d41352eaf11ec56758bd5489736b8aff53858309126834528053d982cab6c5 | 11cbb30d3af69a070cca9a304f246af3ce62084f20a905ebbbb0641add3eef2f | 96ed87bcbf935bc0e992a13361545cfbbba9fb1f24a49efe76d368d23d76482d |
cat-searcher/leandojo-benchmark-4-random | test | 1,229 | volume_regionBetween_eq_lintegral | Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>MeasureTheory.Measure.restrict_eq_self</a> _ (<a>regionBetween_subset</a> (<a>AEMeasurable.mk</a> f hf) (<a>AEMeasurable.mk</a> g hg) s)).<a>Eq.symm</a> | case h.e'_3
α : Type u_1
inst✝¹ : MeasurableSpace α
μ : Measure α
f g : α → ℝ
s : Set α
inst✝ : SigmaFinite μ
hf : AEMeasurable f (μ.restrict s)
hg : AEMeasurable g (μ.restrict s)
hs : MeasurableSet s
h₁ :
(fun y => ofReal ((g - f) y)) =ᶠ[ae (μ.restrict s)] fun y => ofReal ((AEMeasurable.mk g hg - AEMeasurable.mk f h... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) ((:c Prod) (:fv _uniq.228799) (:c Real)) ((:c Prod.instMeasurableSpace) (:fv _uniq.228799) (:c Real) (:fv _uniq.228802) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)))) ((:c Set) ((:c Prod) (:fv _uniq.228799) (:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.228799))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.228799) (:fv _uniq.228802))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.228799) (:c Real))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.228799) (:c Real... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c MeasurableSpace) (:ar... | {"children":[{"source":"exact","sourceEnd":26735,"sourceStart":26730,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":26743,"sourceStart":26742,"tag":"atom"},{"children":[{"name":"MeasureTheory.Measure.restrict_eq_self","semanticRole":"global","source":"Measure.restrict_eq_self","sourceEnd":26767,"sour... | [] | [{"source":"(Measure.restrict_eq_self _\n (regionBetween_subset (AEMeasurable.mk f hf) (AEMeasurable.mk g hg) s)).symm","source_end":26856,"source_start":26742,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.228799","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.228802","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"inte... | 129 | 30 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7edd5b167f4f8818f5fe59786f6f27c2409f528a416d0ba76ab192f45a67bcc3 | 96ed87bcbf935bc0e992a13361545cfbbba9fb1f24a49efe76d368d23d76482d | 218d5d95a1697ccfb4a80bebfc01ace4bb42e1c790d3910ace4e89c427140811 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,230 | WittVector.ghostComponent_zero_verschiebungFun | Mathlib/RingTheory/WittVector/Verschiebung.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>WittVector.ghostComponent_apply</a>, <a>aeval_wittPolynomial</a>, <a>Finset.range_one</a>, <a>Finset.sum_singleton</a>, <a>WittVector.verschiebungFun_coeff_zero</a>, <a>pow_zero</a>, <a>pow_zero</a>, <a>pow_one</a>, <a>one_mul</a>] | p : ℕ
R : Type u_1
S : Type u_2
hp : Fact (Nat.Prime p)
inst✝¹ : CommRing R
inst✝ : CommRing S
x : 𝕎 R
⊢ (ghostComponent 0) x.verschiebungFun = 0 | ((:c Eq) (:fv _uniq.2871) ((:c DFunLike.coe) ((:c RingHom) ((:c WittVector) (:fv _uniq.2868) (:fv _uniq.2871)) (:fv _uniq.2871) ((:c Semiring.toNonAssocSemiring) ((:c WittVector) (:fv _uniq.2868) (:fv _uniq.2871)) ((:c CommSemiring.toSemiring) ((:c WittVector) (:fv _uniq.2868) (:fv _uniq.2871)) ((:c CommRing.toCommSemi... | [{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.2868)))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.2871))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.2874))"},{"name":"x","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c RingHom) (:arg :explicit 0 (:app (:c WittVector) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NonAssocSemiring)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2868","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2871","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_i... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":1977,"sourceStart":1975,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1979,"sourceStart":1978,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"ghostComponent_apply","source_end":1999,"source_start":1979,"syntax_kind":"ident"},{"source":"aeval_wittPolynomial","source_end":2021,"source_start":2001,"syntax_kind":"ident"},{"source":"Finset.range_one","source_end":2039,"source_start":2023,"syntax_kind":"ident"},{"source":"Finset.sum_singleton","source_... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2868","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2871","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 15 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 02a87b997d66e7e0870e35af9b7cfa189076d755d036ba20a1f18488703fc20c | 34f1bbce7dfae1bd288df9d55e69dce562f79b9d1ea821499e13d350a5ca5184 | 62fe8188c53156c5e3f70d25058e91272afb83201307a6d1ebd177a3cdfd8a5f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,231 | Real.sin_three_mul | Mathlib/Data/Complex/Exponential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Complex.ofReal_inj</a>] | x y : ℝ
⊢ sin (3 * x) = 3 * sin x - 4 * sin x ^ 3 | x y : ℝ
⊢ ↑(sin (3 * x)) = ↑(3 * sin x - 4 * sin x ^ 3) | ((:c Eq) (:c Real) ((:c Real.sin) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c OfNat.ofNat) (:c Real) (:lit 3) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 3) (:c Real.instNatCast) ((:c instNatAtLeastTwo) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))))... | [{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Real.sin) (:arg :explicit 0 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.181051","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.181053","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"}] | {"children":[{"source":"rw","sourceEnd":38899,"sourceStart":38897,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":38901,"sourceStart":38900,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":38904,"sourceSt... | [] | [{"source":"ofReal_inj","source_end":38915,"source_start":38905,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.181051","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.181053","is_instance":false,"is_let":false,"user_name":"y"}] | 402 | 4 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a053e14948c9e840035aa9b345562f70041bdd6a70822f6cd74c0c1fb7dc5f91 | 7caf672b1feb5bbe68bd24e53bdb3c1cc71b1753e7523b43dbc2d0d2a7c84752 | 3b705cbe8ff58ba4736b9cb2e22df35f4307a4254a2983126dcdfa2ce35e02b6 | 15a6515e2a091b4d6c0bd7a7e9d83570608d38ac72dc2ac63c8f4c2df4074319 |
cat-searcher/leandojo-benchmark-4-random | test | 1,232 | Real.sin_three_mul | Mathlib/Data/Complex/Exponential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Complex.sin_three_mul</a>] | x y : ℝ
⊢ ↑(sin (3 * x)) = ↑(3 * sin x - 4 * sin x ^ 3) | ((:c Eq) (:c Complex) ((:c Complex.ofReal') ((:c Real.sin) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c OfNat.ofNat) (:c Real) (:lit 3) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 3) (:c Real.instNatCast) ((:c instNatAtLeastTwo) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c in... | [{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c Complex.ofReal') (:arg :explicit 0 (:app (:c Real.sin) (:arg :explicit 0 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMu... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.181051","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.181053","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"}] | {"children":[{"source":"simp","sourceEnd":38922,"sourceStart":38918,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":38924,"sourceStart":38923,"tag":"a... | [] | [{"source":"sin_three_mul","source_end":38937,"source_start":38924,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.181051","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.181053","is_instance":false,"is_let":false,"user_name":"y"}] | 402 | 8 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 50451c7cd394e87d6e8b8b07043e1170c029017684a4c9d881f37b2dc4eb8015 | 15a6515e2a091b4d6c0bd7a7e9d83570608d38ac72dc2ac63c8f4c2df4074319 | 0eecab15cc3f16fbafc2e878cb6a1636f6ab9153be6e58ed66ae5355e417c995 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,233 | MeasureTheory.snormEssSup_zero | Mathlib/MeasureTheory/Function/LpSeminorm/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>MeasureTheory.snormEssSup</a>, <a>Pi.zero_apply</a>, <a>nnnorm_zero</a>, <a>ENNReal.coe_zero</a>, ← <a>ENNReal.bot_eq_zero</a>] | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedAddCommGroup G
⊢ snormEssSup 0 μ = 0 | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedAddCommGroup G
⊢ essSup (fun x => ⊥) μ = ⊥ | ((:c Eq) (:c ENNReal) ((:c MeasureTheory.snormEssSup) (:fv _uniq.32393) (:fv _uniq.32399) (:fv _uniq.32431) (:fv _uniq.32408) ((:c OfNat.ofNat) (:forall _ (:fv _uniq.32393) (:fv _uniq.32399)) (:lit 0) ((:c Zero.toOfNat0) (:forall _ (:fv _uniq.32393) (:fv _uniq.32399)) ((:c Pi.instZero) (:fv _uniq.32393) (:lambda _ (:fv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.32393))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.32393))"},{"name":"p","sexp":"(:c ENNReal)... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.snormEssSup) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :implicit 3) (:arg :explicit 4 (:app (:c OfNat... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32393","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32396","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp_rw","sourceEnd":9594,"sourceStart":9587,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9596,"sourceStart":9595,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MeasureTheory.s... | [] | [{"source":"snormEssSup","source_end":9607,"source_start":9596,"syntax_kind":"ident"},{"source":"Pi.zero_apply","source_end":9622,"source_start":9609,"syntax_kind":"ident"},{"source":"nnnorm_zero","source_end":9635,"source_start":9624,"syntax_kind":"ident"},{"source":"ENNReal.coe_zero","source_end":9653,"source_start":... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32393","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32396","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 58 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8f46f7341aed0a81b013d4959aa677fea3d3b3aae69a0e69f1337d671a706ddc | 949ad5a8579f16444411309704d43a8d5f58acf328edd564ce5e7a6020c47749 | b6cbae94892b811c9d56768913b79e1574a1497cb5223f7b7455e65c1a5aa510 | 01fcd1efe443f1db7315a51dcecff4fe123cefd2c54add742b5797d94e02f070 |
cat-searcher/leandojo-benchmark-4-random | test | 1,234 | MeasureTheory.snormEssSup_zero | Mathlib/MeasureTheory/Function/LpSeminorm/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>essSup_const_bot</a> | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedAddCommGroup G
⊢ essSup (fun x => ⊥) μ = ⊥ | ((:c Eq) (:c ENNReal) ((:c essSup) (:fv _uniq.32393) (:c ENNReal) ((:c ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice) (:c ENNReal) ((:c ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder) (:c ENNReal) ((:c CompleteLinearOrder.toConditionallyCompleteLinearOrderBot) (:c ENNReal) (:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.32393))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.32393))"},{"name":"p","sexp":"(:c ENNReal)... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c essSup) (:arg :implicit-type 0 (:fv FV0)) (: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 (:lambda x :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32393","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32396","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":9687,"sourceStart":9682,"tag":"atom"},{"name":"essSup_const_bot","semanticRole":"global","source":"essSup_const_bot","sourceEnd":9704,"sourceStart":9688,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact essSup_const_bot","sourceEnd":9704,"sourceStart":9682... | [] | [{"source":"essSup_const_bot","source_end":9704,"source_start":9688,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32393","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32396","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 58 | 11 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b925101b06eec5213e7852b7698f59310fce94c388bed07199558beaca9a643f | 01fcd1efe443f1db7315a51dcecff4fe123cefd2c54add742b5797d94e02f070 | f4471987e5e517ac587529cfccadf5c05c3f1837931e33fe0a08cb04fbe3d411 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,235 | contDiff_zero_fun | Mathlib/Analysis/Calculus/ContDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>iteratedFDeriv_zero_fun</a>] | 𝕜 : Type u_1
inst✝¹⁰ : NontriviallyNormedField 𝕜
D : Type uD
inst✝⁹ : NormedAddCommGroup D
inst✝⁸ : NormedSpace 𝕜 D
E : Type uE
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
F : Type uF
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
G : Type uG
inst✝³ : NormedAddCommGroup G
inst✝² : NormedSpace 𝕜... | 𝕜 : Type u_1
inst✝¹⁰ : NontriviallyNormedField 𝕜
D : Type uD
inst✝⁹ : NormedAddCommGroup D
inst✝⁸ : NormedSpace 𝕜 D
E : Type uE
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
F : Type uF
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
G : Type uG
inst✝³ : NormedAddCommGroup G
inst✝² : NormedSpace 𝕜... | ((:c Differentiable) (:fv _uniq.20092) (:fv _uniq.20095) (:fv _uniq.20215) (:fv _uniq.20218) (:fv _uniq.20326) ((:c ContinuousMultilinearMap) (:fv _uniq.20092) ((:c Fin) (:fv _uniq.24916)) (:lambda _ ((:c Fin) (:fv _uniq.24916)) (:fv _uniq.20215)) (:fv _uniq.20328) ((:c DivisionSemiring.toSemiring) (:fv _uniq.20092) ((... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.20092))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.20097))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.20092) (:fv _uniq.20097) ((:c Nontriv... | (:app (:c Differentiable) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-of (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20092","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20095","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedFie... | {"children":[{"source":"rw","sourceEnd":2896,"sourceStart":2894,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2898,"sourceStart":2897,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"iteratedFDeriv_zero_... | [] | [{"source":"iteratedFDeriv_zero_fun","source_end":2921,"source_start":2898,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20092","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20095","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"inte... | 14 | 4 | exact | true | 1 | 33 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1f492c974e69fcb607aa934c93f9edddfe78868c9988b983a7dc477ae31dfd64 | eec6134c0560d60c5820f1e1be6ec0fe05b643806924813cf30ae797670f8ee9 | 3ce8d3fb1aae1879d98fd475a46101e878ee58594898bca45b68f5df416207c6 | 0e0f1760fdeabddc213e9124c98d4a611e6f4a3ce6765097b2dcfb716e99a659 |
cat-searcher/leandojo-benchmark-4-random | test | 1,236 | contDiff_zero_fun | Mathlib/Analysis/Calculus/ContDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>differentiable_const</a> (0 : E[×m]→L[𝕜] F) | 𝕜 : Type u_1
inst✝¹⁰ : NontriviallyNormedField 𝕜
D : Type uD
inst✝⁹ : NormedAddCommGroup D
inst✝⁸ : NormedSpace 𝕜 D
E : Type uE
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
F : Type uF
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
G : Type uG
inst✝³ : NormedAddCommGroup G
inst✝² : NormedSpace 𝕜... | ((:c Differentiable) (:fv _uniq.20092) (:fv _uniq.20095) (:fv _uniq.20215) (:fv _uniq.20218) (:fv _uniq.20326) ((:c ContinuousMultilinearMap) (:fv _uniq.20092) ((:c Fin) (:fv _uniq.24916)) (:lambda _ ((:c Fin) (:fv _uniq.24916)) (:fv _uniq.20215)) (:fv _uniq.20328) ((:c DivisionSemiring.toSemiring) (:fv _uniq.20092) ((... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.20092))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.20097))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.20092) (:fv _uniq.20097) ((:c Nontriv... | (:app (:c Differentiable) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-of (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20092","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20095","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedFie... | {"children":[{"source":"exact","sourceEnd":2932,"sourceStart":2927,"tag":"atom"},{"children":[{"name":"differentiable_const","semanticRole":"global","source":"differentiable_const","sourceEnd":2953,"sourceStart":2933,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":2955,"sourceStart":2954,"tag":"... | [] | [{"source":"differentiable_const (0 : E[×m]→L[𝕜] F)","source_end":2978,"source_start":2933,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20092","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20095","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"inte... | 14 | 7 | exact | true | 1 | 33 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5c98d1b6f7aad0669730ea266c5f8b5a898fb440ca371397fca9b401ccacde06 | 0e0f1760fdeabddc213e9124c98d4a611e6f4a3ce6765097b2dcfb716e99a659 | 25487918fd720d19614b8d99dd17f60314edb7a2b7ca21a7a071010206136a5a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,237 | NonUnitalSemiring.toNonUnitalNonAssocSemiring_injective | Mathlib/Algebra/Ring/Ext.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨⟩ ⟨⟩ _ | R : Type u
⊢ Function.Injective (@toNonUnitalNonAssocSemiring R) | case mk.mk
R : Type u
toNonUnitalNonAssocSemiring✝¹ : NonUnitalNonAssocSemiring R
mul_assoc✝¹ : ∀ (a b c : R), a * b * c = a * (b * c)
toNonUnitalNonAssocSemiring✝ : NonUnitalNonAssocSemiring R
mul_assoc✝ : ∀ (a b c : R), a * b * c = a * (b * c)
a✝ : toNonUnitalNonAssocSemiring = toNonUnitalNonAssocSemiring
⊢ mk mul_as... | ((:c Function.Injective) ((:c NonUnitalSemiring) (:fv _uniq.4424)) ((:c NonUnitalNonAssocSemiring) (:fv _uniq.4424)) ((:c NonUnitalSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.4424))) | [{"name":"R","sexp":"(:sort (+ u 1))"}] | (:app (:c Function.Injective) (:arg :implicit-type 0 (:app (:c NonUnitalSemiring) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c NonUnitalNonAssocSemiring) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 2 (:app (:c NonUnitalSemiring.toNonUnitalNonAssocSemiring) (:arg :implicit-type 0 (:fv FV0))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4424","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"}] | {"children":[{"source":"rintro","sourceEnd":3393,"sourceStart":3387,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":3397,"sourceStart":3394,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":"⟩","sourceEnd":3400,"sourceStart":3397,"tag":"atom"}],"kind":"Lean.Pa... | [] | [{"source":"⟨⟩","source_end":3400,"source_start":3394,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"},{"source":"⟨⟩","source_end":3407,"source_start":3401,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4424","is_instance":false,"is_let":false,"user_name":"R"}] | 18 | 4 | exact | true | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ffc8d3e823514cc0e4f4ce096d3ef48b01f0a88037b53c561a9e8d75b0f4406e | 7c188a80d765d0398f42e3124eb19709429693a3c1a0fbc7af7e03e14247ecdd | c335baa0e647cb65dc043adbcaada8b0d40486410d554f3a1a3dc1342aaab05d | 7b945dddfba4e321a3077b36e2a10e5e6d1e082a7f042c18f7efe29916cc1c16 |
cat-searcher/leandojo-benchmark-4-random | test | 1,238 | NonUnitalSemiring.toNonUnitalNonAssocSemiring_injective | Mathlib/Algebra/Ring/Ext.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr | case mk.mk
R : Type u
toNonUnitalNonAssocSemiring✝¹ : NonUnitalNonAssocSemiring R
mul_assoc✝¹ : ∀ (a b c : R), a * b * c = a * (b * c)
toNonUnitalNonAssocSemiring✝ : NonUnitalNonAssocSemiring R
mul_assoc✝ : ∀ (a b c : R), a * b * c = a * (b * c)
a✝ : toNonUnitalNonAssocSemiring = toNonUnitalNonAssocSemiring
⊢ mk mul_as... | ((:c Eq) ((:c NonUnitalSemiring) (:fv _uniq.4424)) ((:c NonUnitalSemiring.mk) (:fv _uniq.4424) (:fv _uniq.4461) (:fv _uniq.4462)) ((:c NonUnitalSemiring.mk) (:fv _uniq.4424) (:fv _uniq.4482) (:fv _uniq.4483))) | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"toNonUnitalNonAssocSemiring✝¹","sexp":"((:c NonUnitalNonAssocSemiring) (:fv _uniq.4424))"},{"name":"mul_assoc✝¹","sexp":"(:forall a (:fv _uniq.4424) (:forall b (:fv _uniq.4424) (:forall c (:fv _uniq.4424) ((:c Eq) (:fv _uniq.4424) ((:c HMul.hMul) (:fv _uniq.4424) (:fv _un... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c NonUnitalSemiring) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c NonUnitalSemiring.mk) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NonUnitalNonAssocSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :proof 2 (:proof-of (:forall a :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4424","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.4461","is_instance":true,"is_let":false,"name":"toNonUnitalNonAssocSemiring✝¹","sexp":"(:app (:c No... | {"children":[{"source":"congr","sourceEnd":3416,"sourceStart":3411,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.congr","source":"congr","sourceEnd":3416,"sourceStart":3411,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4424","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.4461","is_instance":true,"is_let":false,"user_name":"toNonUnitalNonAssocSemiring✝¹"},{"binder_role":":explicit","con... | 18 | 6 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9216bfe7773725c471128385ef2ca78b4b3c429d7ea87908a98b986a44392b0d | 7b945dddfba4e321a3077b36e2a10e5e6d1e082a7f042c18f7efe29916cc1c16 | 092b163cac48997cb6cc327c63cda260e694055f56ff3698a70cdfda80ffbb2b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,239 | TopologicalSpace.IsTopologicalBasis.sigma | Mathlib/Topology/Bases.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine .of_hasBasis_nhds fun a ↦ ?_ | α : Type u
t : TopologicalSpace α
ι : Type u_1
E : ι → Type u_2
inst✝ : (i : ι) → TopologicalSpace (E i)
s : (i : ι) → Set (Set (E i))
hs : ∀ (i : ι), IsTopologicalBasis (s i)
⊢ IsTopologicalBasis (⋃ i, (fun u => Sigma.mk i '' u) '' s i) | α : Type u
t : TopologicalSpace α
ι : Type u_1
E : ι → Type u_2
inst✝ : (i : ι) → TopologicalSpace (E i)
s : (i : ι) → Set (Set (E i))
hs : ∀ (i : ι), IsTopologicalBasis (s i)
a : (i : ι) × E i
⊢ (𝓝 a).HasBasis (fun t => t ∈ ⋃ i, (fun u => Sigma.mk i '' u) '' s i ∧ a ∈ t) id | ((:c TopologicalSpace.IsTopologicalBasis) ((:c Sigma) (:fv _uniq.138251) (:lambda i (:fv _uniq.138251) ((:fv _uniq.138256) 0))) ((:c instTopologicalSpaceSigma) (:fv _uniq.138251) (:lambda i (:fv _uniq.138251) ((:fv _uniq.138256) 0)) (:fv _uniq.138264)) ((:c Set.iUnion) ((:c Set) ((:c Sigma) (:fv _uniq.138251) (:lambda ... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"t","sexp":"((:c TopologicalSpace) (:fv _uniq.138245))"},{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.138251) (:sort (+ u_2 1)))"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.138251) ((:c TopologicalSpace) ((:fv _uniq.138256) 0)))"},{... | (:app (:c TopologicalSpace.IsTopologicalBasis) (:arg :implicit-type 0 (:app (:c Sigma) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda i :explicit (:fv FV2) (:app (:fv FV3) (:arg :explicit 0 0)))))) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:app (:c Sigma) (:arg :implic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138245","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.138248","is_instance":true,"is_let":false,"name":"t","sexp":"(:app (:c TopologicalSpace) (:arg :e... | {"children":[{"source":"refine","sourceEnd":51821,"sourceStart":51815,"tag":"atom"},{"children":[{"children":[{"source":".","sourceEnd":51823,"sourceStart":51822,"tag":"atom"},{"source":"of_hasBasis_nhds","sourceEnd":51839,"sourceStart":51823,"tag":"identifier"}],"kind":"Lean.Parser.Term.dotIdent","source":".of_hasBasi... | [] | [{"source":".of_hasBasis_nhds fun a ↦ ?_","source_end":51852,"source_start":51822,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138245","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.138248","is_instance":true,"is_let":false,"user_name":"t"},{"binder_role":":implicit","context_index":2,"internal_... | 221 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 915e6c09ceeb5c866f325d6133158076eed87b5f1322ed0ed022e06fe5ffcee2 | fa238544369099cfc28f9c57802f4721a6492376698fdee77c190776d30789d2 | dfb4236490e478cb10927d0580908f2d0fd4d18724a27ccb11c2de90acc82c42 | 2b298d07f19b06d905a6fcfe5f12ccddf9dc732a140207c20d33529eb4b15418 |
cat-searcher/leandojo-benchmark-4-random | test | 1,240 | TopologicalSpace.IsTopologicalBasis.sigma | Mathlib/Topology/Bases.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Sigma.nhds_eq</a>] | α : Type u
t : TopologicalSpace α
ι : Type u_1
E : ι → Type u_2
inst✝ : (i : ι) → TopologicalSpace (E i)
s : (i : ι) → Set (Set (E i))
hs : ∀ (i : ι), IsTopologicalBasis (s i)
a : (i : ι) × E i
⊢ (𝓝 a).HasBasis (fun t => t ∈ ⋃ i, (fun u => Sigma.mk i '' u) '' s i ∧ a ∈ t) id | α : Type u
t : TopologicalSpace α
ι : Type u_1
E : ι → Type u_2
inst✝ : (i : ι) → TopologicalSpace (E i)
s : (i : ι) → Set (Set (E i))
hs : ∀ (i : ι), IsTopologicalBasis (s i)
a : (i : ι) × E i
⊢ (map (Sigma.mk a.fst) (𝓝 a.snd)).HasBasis (fun t => t ∈ ⋃ i, (fun u => Sigma.mk i '' u) '' s i ∧ a ∈ t) id | ((:c Filter.HasBasis) ((:c Sigma) (:fv _uniq.138251) (:lambda i (:fv _uniq.138251) ((:fv _uniq.138256) 0))) ((:c Set) ((:c Sigma) (:fv _uniq.138251) (:lambda i (:fv _uniq.138251) ((:fv _uniq.138256) 0)))) ((:c nhds) ((:c Sigma) (:fv _uniq.138251) (:lambda i (:fv _uniq.138251) ((:fv _uniq.138256) 0))) ((:c instTopologic... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"t","sexp":"((:c TopologicalSpace) (:fv _uniq.138245))"},{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.138251) (:sort (+ u_2 1)))"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.138251) ((:c TopologicalSpace) ((:fv _uniq.138256) 0)))"},{... | (:app (:c Filter.HasBasis) (:arg :implicit-type 0 (:app (:c Sigma) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda i :explicit (:fv FV2) (:app (:fv FV3) (:arg :explicit 0 0)))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Sigma) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:l... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138245","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.138248","is_instance":true,"is_let":false,"name":"t","sexp":"(:app (:c TopologicalSpace) (:arg :e... | {"children":[{"source":"rw","sourceEnd":51857,"sourceStart":51855,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":51859,"sourceStart":51858,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Sigma.nhds_eq","... | [] | [{"source":"Sigma.nhds_eq","source_end":51872,"source_start":51859,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138245","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.138248","is_instance":true,"is_let":false,"user_name":"t"},{"binder_role":":implicit","context_index":2,"internal_... | 221 | 5 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bc0bea210570ea8fff6459e6d0fb460cb19b23c518e227f0fc80b1913b2deb97 | 2b298d07f19b06d905a6fcfe5f12ccddf9dc732a140207c20d33529eb4b15418 | ed9a86f08d8817be0d8e9119991d5c3c6658ae0c1f5ce6675ba699af8743da99 | a91d2a4b9e4cfcf5804268c4ecb997140c06bb238b3a3586092a8e0b5d332fea |
cat-searcher/leandojo-benchmark-4-random | test | 1,241 | TopologicalSpace.IsTopologicalBasis.sigma | Mathlib/Topology/Bases.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert (((hs a.1).<a>TopologicalSpace.IsTopologicalBasis.nhds_hasBasis</a>).<a>Filter.HasBasis.map</a> _).<a>Filter.HasBasis.to_image_id</a> | α : Type u
t : TopologicalSpace α
ι : Type u_1
E : ι → Type u_2
inst✝ : (i : ι) → TopologicalSpace (E i)
s : (i : ι) → Set (Set (E i))
hs : ∀ (i : ι), IsTopologicalBasis (s i)
a : (i : ι) × E i
⊢ (map (Sigma.mk a.fst) (𝓝 a.snd)).HasBasis (fun t => t ∈ ⋃ i, (fun u => Sigma.mk i '' u) '' s i ∧ a ∈ t) id | case h.e'_4.h.a
α : Type u
t : TopologicalSpace α
ι : Type u_1
E : ι → Type u_2
inst✝ : (i : ι) → TopologicalSpace (E i)
s : (i : ι) → Set (Set (E i))
hs : ∀ (i : ι), IsTopologicalBasis (s i)
a : (i : ι) × E i
x✝ : Set ((i : ι) × E i)
⊢ x✝ ∈ ⋃ i, (fun u => Sigma.mk i '' u) '' s i ∧ a ∈ x✝ ↔
x✝ ∈ (fun i => Sigma.mk ... | ((:c Filter.HasBasis) ((:c Sigma) (:fv _uniq.138251) (:lambda i (:fv _uniq.138251) ((:fv _uniq.138256) 0))) ((:c Set) ((:c Sigma) (:fv _uniq.138251) (:lambda i (:fv _uniq.138251) ((:fv _uniq.138256) 0)))) ((:c Filter.map) ((:fv _uniq.138256) ((:c Sigma.fst) (:fv _uniq.138251) (:lambda i (:fv _uniq.138251) ((:fv _uniq.1... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"t","sexp":"((:c TopologicalSpace) (:fv _uniq.138245))"},{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.138251) (:sort (+ u_2 1)))"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.138251) ((:c TopologicalSpace) ((:fv _uniq.138256) 0)))"},{... | (:app (:c Filter.HasBasis) (:arg :implicit-type 0 (:app (:c Sigma) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda i :explicit (:fv FV2) (:app (:fv FV3) (:arg :explicit 0 0)))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Sigma) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:l... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138245","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.138248","is_instance":true,"is_let":false,"name":"t","sexp":"(:app (:c TopologicalSpace) (:arg :e... | {"children":[{"source":"convert","sourceEnd":51883,"sourceStart":51876,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":"(","sourceEnd":51885,"sourceStart":51884,"tag":"atom"},{"children":[{"children":[{"child... | [] | [{"source":"(((hs a.1).nhds_hasBasis).map _).to_image_id","source_end":51928,"source_start":51884,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138245","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.138248","is_instance":true,"is_let":false,"user_name":"t"},{"binder_role":":implicit","context_index":2,"internal_... | 221 | 8 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b0f2021c3b97e483ca195559bf800c024b6d666ad9797bad8cd8c38d5b87cd56 | a91d2a4b9e4cfcf5804268c4ecb997140c06bb238b3a3586092a8e0b5d332fea | e7400b35d547b254b77cbcdf949c75f9ee28ed60a07a459cebdab6af5eacdeed | d84c00404657f882678eac9d6145e50eb6f17a66316db27383c5b00806ea0dd5 |
cat-searcher/leandojo-benchmark-4-random | test | 1,242 | TopologicalSpace.IsTopologicalBasis.sigma | Mathlib/Topology/Bases.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | aesop | case h.e'_4.h.a
α : Type u
t : TopologicalSpace α
ι : Type u_1
E : ι → Type u_2
inst✝ : (i : ι) → TopologicalSpace (E i)
s : (i : ι) → Set (Set (E i))
hs : ∀ (i : ι), IsTopologicalBasis (s i)
a : (i : ι) × E i
x✝ : Set ((i : ι) × E i)
⊢ x✝ ∈ ⋃ i, (fun u => Sigma.mk i '' u) '' s i ∧ a ∈ x✝ ↔
x✝ ∈ (fun i => Sigma.mk ... | ((:c Iff) ((:c And) ((:c Membership.mem) ((:c Set) ((:c Sigma) (:fv _uniq.138251) (:lambda i (:fv _uniq.138251) ((:fv _uniq.138256) 0)))) ((:c Set) ((:c Set) ((:c Sigma) (:fv _uniq.138251) (:lambda i (:fv _uniq.138251) ((:fv _uniq.138256) 0))))) ((:c Set.instMembership) ((:c Set) ((:c Sigma) (:fv _uniq.138251) (:lambda... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"t","sexp":"((:c TopologicalSpace) (:fv _uniq.138245))"},{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.138251) (:sort (+ u_2 1)))"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.138251) ((:c TopologicalSpace) ((:fv _uniq.138256) 0)))"},{... | (:app (:c Iff) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c Sigma) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda i :explicit (:fv FV2) (:app (:fv FV3) (:arg :explicit 0 0)))))))) (:arg :implicit-type 1 (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138245","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.138248","is_instance":true,"is_let":false,"name":"t","sexp":"(:app (:c TopologicalSpace) (:arg :e... | {"children":[{"source":"aesop","sourceEnd":51936,"sourceStart":51931,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Aesop.Frontend.Parser.aesopTactic","source":"aesop","sourceEnd":51936,"sourceStart":51931,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138245","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.138248","is_instance":true,"is_let":false,"user_name":"t"},{"binder_role":":implicit","context_index":2,"internal_... | 221 | 9 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 583e224e6c47e9fe734013e7bb5d09ff96cdcd75cbff7da1c745c6f9af7f58c4 | d84c00404657f882678eac9d6145e50eb6f17a66316db27383c5b00806ea0dd5 | bf61abd9c8c94e02103733c96be27852844483acbf580158f224257e620356a8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,243 | MeasureTheory.Lp.ext_iff | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [h] | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedAddCommGroup G
f g : ↥(Lp E p μ)
h : f = g
⊢ ↑↑f =ᶠ[ae μ] ↑↑g | ((:c Filter.EventuallyEq) (:fv _uniq.20805) (:fv _uniq.20808) ((:c MeasureTheory.ae) (:fv _uniq.20805) ((:c MeasureTheory.Measure) (:fv _uniq.20805) (:fv _uniq.20820)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.20805) (:fv _uniq.20820)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.20805) (:fv _u... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.20805))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.20805))"},{"name":"p","sexp":"(:c ENNReal)... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:app (:c MeasureTheory.ae) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpac... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20805","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20808","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":7250,"sourceStart":7248,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7252,"sourceStart":7251,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"h","source_end":7253,"source_start":7252,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20805","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20808","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 40 | 2 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3e6e2b22bbb6269a54ede15406c060808885cd32a04092c4f4bd0225ffe0106c | 54ed2244e8da691b962015f394f12538187db7038f57cfae483730d569a6a54c | 8e1ff58c9c2ffe38f33c0acb9a280a2097eb986bf9afb4a3b7b955b60bd0b8f6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,244 | Complex.interior_setOf_le_im | Mathlib/Analysis/Complex/ReImTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>interior_Ici</a>] using <a>Complex.interior_preimage_im</a> (<a>Set.Ici</a> a) | a : ℝ
⊢ interior {z | a ≤ z.im} = {z | a < z.im} | ((:c Eq) ((:c Set) (:c Complex)) ((:c interior) (:c Complex) ((:c UniformSpace.toTopologicalSpace) (:c Complex) ((:c PseudoMetricSpace.toUniformSpace) (:c Complex) ((:c SeminormedRing.toPseudoMetricSpace) (:c Complex) ((:c SeminormedCommRing.toSeminormedRing) (:c Complex) ((:c NormedCommRing.toSeminormedCommRing) (:c C... | [{"name":"a","sexp":"(:c Real)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:c Complex)))) (:arg :explicit 1 (:app (:c interior) (:arg :implicit-type 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Complex))))) (:arg :explicit 2 (:app (:c setOf) (:arg :implicit-type 0 (:c Co... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.4935","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Real)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":5026,"sourceStart":5021,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"interior_Ici","source_end":5045,"source_start":5033,"syntax_kind":"ident"},{"source":"interior_preimage_im (Ici a)","source_end":5081,"source_start":5053,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.4935","is_instance":false,"is_let":false,"user_name":"a"}] | 35 | 2 | exact | true | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 83bf6391b47821dd4df815010cf4754988bf37f78ff48dc330ef83dd57098b69 | 824ee41cd02345915f4eea73364d1814c833620f09d9e51d7363829814d943b8 | 9efdea50621f5a9abfd590671536923e083d3c60ba33abc34d0c5e85878503cc | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,245 | Batteries.RBNode.Balanced.ins | .lake/packages/batteries/Batteries/Data/RBMap/WF.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact .balanced (.red .nil .nil) | case nil
α : Type u_1
c : RBColor
n : Nat
cmp : α → α → Ordering
v : α
t : RBNode α
⊢ RedRed (nil.isRed = red) (ins cmp v nil) 0 | ((:c Batteries.RBNode.RedRed) ((:c Eq) (:c Batteries.RBColor) ((:c Batteries.RBNode.isRed) (:fv _uniq.69971) ((:c Batteries.RBNode.nil) (:fv _uniq.69971))) (:c Batteries.RBColor.red)) (:fv _uniq.69971) ((:c Batteries.RBNode.ins) (:fv _uniq.69971) (:fv _uniq.69974) (:fv _uniq.69975) ((:c Batteries.RBNode.nil) (:fv _uniq... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"c","sexp":"(:c Batteries.RBColor)"},{"name":"n","sexp":"(:c Nat)"},{"name":"cmp","sexp":"(:forall _ (:fv _uniq.69971) (:forall _ (:fv _uniq.69971) (:c Ordering)))"},{"name":"v","sexp":"(:fv _uniq.69971)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.69971))"}] | (:app (:c Batteries.RBNode.RedRed) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Batteries.RBColor)) (:arg :explicit 1 (:app (:c Batteries.RBNode.isRed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.RBNode.nil) (:arg :implicit-type 0 (:fv FV1)))))) (:arg :explicit 2 (:c Batteries.... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Batteries.RBColor)"},{"binder_role":":impl... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":11634,"sourceStart":11629,"tag":"atom"},{"children":[{"children":[{"source":".","sourceEnd":11636,"sourceStart":11635,"tag":"atom"},{"source":"balanced","sourceEnd":11644,"sourceStart":11636,"tag":"identifier"}],"kind":"Lean.Parser.Term.d... | [] | [{"source":".balanced (.red .nil .nil)","source_end":11661,"source_start":11635,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 46 | 7 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d0510a92bab57e5c5eaddcd31721ce667ed1698d63e03728ba3830124a9552d9 | f000158bc4c60f5755a1a92f20f1ffa0fb58aa5b63bdbfccf4cdd0afe8057eef | 9cf76c7a5ae92621254a1d396d7a964f7e103605d5379f0c2920216687307314 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,246 | Batteries.RBNode.Balanced.ins | .lake/packages/batteries/Batteries/Data/RBMap/WF.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | unfold <a>Batteries.RBNode.ins</a> | case red
α : Type u_1
c : RBColor
n✝ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
n : Nat
b : RBNode α
x : α
hl : a.Balanced black n
hr : b.Balanced black n
ihl : RedRed (a.isRed = red) (ins cmp v a) n
ihr : RedRed (b.isRed = red) (ins cmp v b) n
⊢ RedRed ((node red a x b).isRed = red) (ins cmp v (node red a x b))... | case red
α : Type u_1
c : RBColor
n✝ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
n : Nat
b : RBNode α
x : α
hl : a.Balanced black n
hr : b.Balanced black n
ihl : RedRed (a.isRed = red) (ins cmp v a) n
ihr : RedRed (b.isRed = red) (ins cmp v b) n
⊢ RedRed ((node red a x b).isRed = red)
(match cmp v x with
... | ((:c Batteries.RBNode.RedRed) ((:c Eq) (:c Batteries.RBColor) ((:c Batteries.RBNode.isRed) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _uniq.69971) (:c Batteries.RBColor.red) (:fv _uniq.70065) (:fv _uniq.70068) (:fv _uniq.70067))) (:c Batteries.RBColor.red)) (:fv _uniq.69971) ((:c Batteries.RBNode.ins) (:fv _uni... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"c","sexp":"(:c Batteries.RBColor)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"cmp","sexp":"(:forall _ (:fv _uniq.69971) (:forall _ (:fv _uniq.69971) (:c Ordering)))"},{"name":"v","sexp":"(:fv _uniq.69971)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.69971))"},... | (:app (:c Batteries.RBNode.RedRed) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Batteries.RBColor)) (:arg :explicit 1 (:app (:c Batteries.RBNode.isRed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.RBNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:c Batteries.RBC... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Batteries.RBColor)"},{"binder_role":":impl... | {"children":[{"source":"unfold","sourceEnd":11706,"sourceStart":11700,"tag":"atom"},{"children":[{"name":"Batteries.RBNode.ins","semanticRole":"global","source":"ins","sourceEnd":11710,"sourceStart":11707,"tag":"identifier"}],"kind":"null","source":"ins","sourceEnd":11710,"sourceStart":11707,"tag":"node"},{"children":[... | [] | [{"source":"ins","source_end":11710,"source_start":11707,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 46 | 13 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d109059d4f449307da73c0bc2a5c3f14787dbadaf0c3905618dbf15a33822569 | ac1e218a589bb210e37734d62c243bcd0fd6bf57c70e7ae51903ab202bddcd98 | 1f65e6bfeed629bfe8364ce0534222ae5ddc0fa2bdbd994c1c5c731e84ae8ffc | 50deed65341c0f56fb4fa3c0f32b4600dcbf6a38c3d1cd00663b35b853198894 |
cat-searcher/leandojo-benchmark-4-random | test | 1,247 | Batteries.RBNode.Balanced.ins | .lake/packages/batteries/Batteries/Data/RBMap/WF.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split | case red
α : Type u_1
c : RBColor
n✝ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
n : Nat
b : RBNode α
x : α
hl : a.Balanced black n
hr : b.Balanced black n
ihl : RedRed (a.isRed = red) (ins cmp v a) n
ihr : RedRed (b.isRed = red) (ins cmp v b) n
⊢ RedRed ((node red a x b).isRed = red)
(match cmp v x with
... | case red.h_1
α : Type u_1
c : RBColor
n✝ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
n : Nat
b : RBNode α
x : α
hl : a.Balanced black n
hr : b.Balanced black n
ihl : RedRed (a.isRed = red) (ins cmp v a) n
ihr : RedRed (b.isRed = red) (ins cmp v b) n
x✝ : Ordering
heq✝ : cmp v x = Ordering.lt
⊢ RedRed ((node red a... | ((:c Batteries.RBNode.RedRed) ((:c Eq) (:c Batteries.RBColor) ((:c Batteries.RBNode.isRed) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _uniq.69971) (:c Batteries.RBColor.red) (:fv _uniq.70065) (:fv _uniq.70068) (:fv _uniq.70067))) (:c Batteries.RBColor.red)) (:fv _uniq.69971) ((:c Batteries.RBNode.ins.match_1) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"c","sexp":"(:c Batteries.RBColor)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"cmp","sexp":"(:forall _ (:fv _uniq.69971) (:forall _ (:fv _uniq.69971) (:c Ordering)))"},{"name":"v","sexp":"(:fv _uniq.69971)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.69971))"},... | (:app (:c Batteries.RBNode.RedRed) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Batteries.RBColor)) (:arg :explicit 1 (:app (:c Batteries.RBNode.isRed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.RBNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:c Batteries.RBC... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Batteries.RBColor)"},{"binder_role":":impl... | {"children":[{"source":"split","sourceEnd":11717,"sourceStart":11712,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.split","source":"split","sourceEnd":11717,"sourceStart":11712,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 46 | 15 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c032af65898f824c5f94f3fe39ee750fd0b73ce2d313f1b78d64b5d52593f44b | 50deed65341c0f56fb4fa3c0f32b4600dcbf6a38c3d1cd00663b35b853198894 | ad1a64057f9ab34fecfe3f4ee78660bb0316dbda9370581ffbeb1e8bddf3d598 | 1705de40e385a1a4c2f8a02dc47cf4588a84238fc4f8fb1534c6a7b757e7b8b6 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.