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 | 2,571 | CategoryTheory.PresheafHom.IsSheafFor.exists_app | Mathlib/CategoryTheory/Sites/SheafHom.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have H := hx f.left (𝟙 _) hZ₁ hZ₂ (by simp) | case op.mk.op.mk.op
C : Type u
inst✝¹ : Category.{v, u} C
J : GrothendieckTopology C
A : Type u'
inst✝ : Category.{v', u'} A
F G : Cᵒᵖ ⥤ A
X : C
S : Sieve X
hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op)
x : Presieve.FamilyOfElements (presheafHom F G) S.arrows
hx : x.Compatible
Y... | case op.mk.op.mk.op
C : Type u
inst✝¹ : Category.{v, u} C
J : GrothendieckTopology C
A : Type u'
inst✝ : Category.{v', u'} A
F G : Cᵒᵖ ⥤ A
X : C
S : Sieve X
hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op)
x : Presieve.FamilyOfElements (presheafHom F G) S.arrows
hx : x.Compatible
Y... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.24589) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.24589) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.24589) (:fv _uniq.24592))) ((:c Prefunctor.obj) ((:c Opposite) (:fv _uniq.24569)) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c Opposite) (:fv _uniq.24... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.24569))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.24569) (:fv _uniq.24572))"},{"name":"A","sexp":"(:sort (+ u' 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c Opposite) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"have","sourceEnd":5082,"sourceStart":5078,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"H","sourceEnd":5084,"sourceStart":5083,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"H","sourceEnd":5084,"sourceStart":5083,"tag":"node"},{"ch... | [] | [{"source":"hx f.left (𝟙 _) hZ₁ hZ₂ (by simp)","source_end":5128,"source_start":5088,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 18 | 15 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3f901abb85a5d478466c4247ae7f91146be27f58da47dbc66fd6f3b177532fcc | b8ace57e375173be4453efb58b017d832e97fd371c1cb4915181e4ddc46896de | 7377ccd7e1b019ab7be2b05d707a2c36f72afe77932ea84e36f190ce5bd17dd8 | c8b4387560edb5c18f4dace35e21d6525b462a43e51cedddaf7c22ceb6bdf100 |
cat-searcher/leandojo-benchmark-4-random | test | 2,572 | CategoryTheory.PresheafHom.IsSheafFor.exists_app | Mathlib/CategoryTheory/Sites/SheafHom.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>CategoryTheory.presheafHom_obj</a>, <a>Opposite.unop_op</a>, <a>CategoryTheory.Functor.id_obj</a>, <a>CategoryTheory.op_id</a>, <a>CategoryTheory.FunctorToTypes.map_id_apply</a>] at H | case op.mk.op.mk.op
C : Type u
inst✝¹ : Category.{v, u} C
J : GrothendieckTopology C
A : Type u'
inst✝ : Category.{v', u'} A
F G : Cᵒᵖ ⥤ A
X : C
S : Sieve X
hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op)
x : Presieve.FamilyOfElements (presheafHom F G) S.arrows
hx : x.Compatible
Y... | case op.mk.op.mk.op
C : Type u
inst✝¹ : Category.{v, u} C
J : GrothendieckTopology C
A : Type u'
inst✝ : Category.{v', u'} A
F G : Cᵒᵖ ⥤ A
X : C
S : Sieve X
hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op)
x : Presieve.FamilyOfElements (presheafHom F G) S.arrows
hx : x.Compatible
Y... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.24589) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.24589) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.24589) (:fv _uniq.24592))) ((:c Prefunctor.obj) ((:c Opposite) (:fv _uniq.24569)) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c Opposite) (:fv _uniq.24... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.24569))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.24569) (:fv _uniq.24572))"},{"name":"A","sexp":"(:sort (+ u' 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c Opposite) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"simp","sourceEnd":5145,"sourceStart":5141,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":5150,"sourceStart":5146,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":5150,"s... | [] | [{"source":"presheafHom_obj","source_end":5167,"source_start":5152,"syntax_kind":"ident"},{"source":"unop_op","source_end":5176,"source_start":5169,"syntax_kind":"ident"},{"source":"Functor.id_obj","source_end":5192,"source_start":5178,"syntax_kind":"ident"},{"source":"op_id","source_end":5199,"source_start":5194,"synt... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 18 | 21 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1dc1be17470c06069a9d23ebde9296238c828e3537ad61364a22b26571503602 | c8b4387560edb5c18f4dace35e21d6525b462a43e51cedddaf7c22ceb6bdf100 | 33dc50e0b290de8466aae47371da074ec63fa163ee0c7508e8efa499e346a3cb | 2e1090e87c2721023e80d66f654651f293efa96bc0a8d61ee084aebdac43c7ce |
cat-searcher/leandojo-benchmark-4-random | test | 2,573 | CategoryTheory.PresheafHom.IsSheafFor.exists_app | Mathlib/CategoryTheory/Sites/SheafHom.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let φ : <a>CategoryTheory.Over.mk</a> f.left ⟶ <a>CategoryTheory.Over.mk</a> (𝟙 Z₁.left) := <a>CategoryTheory.Over.homMk</a> f.left | case op.mk.op.mk.op
C : Type u
inst✝¹ : Category.{v, u} C
J : GrothendieckTopology C
A : Type u'
inst✝ : Category.{v', u'} A
F G : Cᵒᵖ ⥤ A
X : C
S : Sieve X
hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op)
x : Presieve.FamilyOfElements (presheafHom F G) S.arrows
hx : x.Compatible
Y... | case op.mk.op.mk.op
C : Type u
inst✝¹ : Category.{v, u} C
J : GrothendieckTopology C
A : Type u'
inst✝ : Category.{v', u'} A
F G : Cᵒᵖ ⥤ A
X : C
S : Sieve X
hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op)
x : Presieve.FamilyOfElements (presheafHom F G) S.arrows
hx : x.Compatible
Y... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.24589) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.24589) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.24589) (:fv _uniq.24592))) ((:c Prefunctor.obj) ((:c Opposite) (:fv _uniq.24569)) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c Opposite) (:fv _uniq.24... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.24569))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.24569) (:fv _uniq.24572))"},{"name":"A","sexp":"(:sort (+ u' 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c Opposite) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"let","sourceEnd":5264,"sourceStart":5261,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"φ","sourceEnd":5267,"sourceStart":5265,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":5269,"so... | [] | [{"source":"Over.mk f.left ⟶ Over.mk (𝟙 Z₁.left)","source_end":5313,"source_start":5270,"syntax_kind":"«term_⟶_»"},{"source":"Over.homMk f.left","source_end":5334,"source_start":5317,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 18 | 22 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 78b87b8662f39966804d010b2e1c13b20ec33543d53626ec6a7e76e2574278fa | 2e1090e87c2721023e80d66f654651f293efa96bc0a8d61ee084aebdac43c7ce | af800b9b6606b97d24eaf5af516b1a4d132ad0ae9a593143a7aa2add1de2f988 | 51d67fa79a07b93e2e94aef25ea3385886cdbba333a10e2609c869ea74ef9497 |
cat-searcher/leandojo-benchmark-4-random | test | 2,574 | CategoryTheory.PresheafHom.IsSheafFor.exists_app | Mathlib/CategoryTheory/Sites/SheafHom.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have H' := (x (Z₁.hom ≫ g) hZ₁).<a>CategoryTheory.NatTrans.naturality</a> φ.op | case op.mk.op.mk.op
C : Type u
inst✝¹ : Category.{v, u} C
J : GrothendieckTopology C
A : Type u'
inst✝ : Category.{v', u'} A
F G : Cᵒᵖ ⥤ A
X : C
S : Sieve X
hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op)
x : Presieve.FamilyOfElements (presheafHom F G) S.arrows
hx : x.Compatible
Y... | case op.mk.op.mk.op
C : Type u
inst✝¹ : Category.{v, u} C
J : GrothendieckTopology C
A : Type u'
inst✝ : Category.{v', u'} A
F G : Cᵒᵖ ⥤ A
X : C
S : Sieve X
hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op)
x : Presieve.FamilyOfElements (presheafHom F G) S.arrows
hx : x.Compatible
Y... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.24589) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.24589) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.24589) (:fv _uniq.24592))) ((:c Prefunctor.obj) ((:c Opposite) (:fv _uniq.24569)) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c Opposite) (:fv _uniq.24... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.24569))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.24569) (:fv _uniq.24572))"},{"name":"A","sexp":"(:sort (+ u' 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c Opposite) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"have","sourceEnd":5351,"sourceStart":5347,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"H'","sourceEnd":5354,"sourceStart":5352,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"H'","sourceEnd":5354,"sourceStart":5352,"tag":"node"},{"... | [] | [{"source":"(x (Z₁.hom ≫ g) hZ₁).naturality φ.op","source_end":5401,"source_start":5358,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 18 | 23 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ebbefe8efed560c50347a844709b27a15925199629df941ac5266c0d0e013e08 | 51d67fa79a07b93e2e94aef25ea3385886cdbba333a10e2609c869ea74ef9497 | e9aa2ad58ed7e1eb746eaf7b14c639e56113b7571fdcb14d97df06a67ae450e1 | da12ae728f5b3ee2fcaaa7ee44939eeca671d65ca294274aff58612208abd95d |
cat-searcher/leandojo-benchmark-4-random | test | 2,575 | CategoryTheory.PresheafHom.IsSheafFor.exists_app | Mathlib/CategoryTheory/Sites/SheafHom.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp at H H' ⊢ | case op.mk.op.mk.op
C : Type u
inst✝¹ : Category.{v, u} C
J : GrothendieckTopology C
A : Type u'
inst✝ : Category.{v', u'} A
F G : Cᵒᵖ ⥤ A
X : C
S : Sieve X
hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op)
x : Presieve.FamilyOfElements (presheafHom F G) S.arrows
hx : x.Compatible
Y... | case op.mk.op.mk.op
C : Type u
inst✝¹ : Category.{v, u} C
J : GrothendieckTopology C
A : Type u'
inst✝ : Category.{v', u'} A
F G : Cᵒᵖ ⥤ A
X : C
S : Sieve X
hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op)
x : Presieve.FamilyOfElements (presheafHom F G) S.arrows
hx : x.Compatible
Y... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.24589) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.24589) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.24589) (:fv _uniq.24592))) ((:c Prefunctor.obj) ((:c Opposite) (:fv _uniq.24569)) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c Opposite) (:fv _uniq.24... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.24569))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.24569) (:fv _uniq.24572))"},{"name":"A","sexp":"(:sort (+ u' 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c Opposite) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"dsimp","sourceEnd":5419,"sourceStart":5414,"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":[{"chil... | [] | [{"source":"H","source_end":5424,"source_start":5423,"syntax_kind":"ident"},{"source":"H'","source_end":5427,"source_start":5425,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 18 | 24 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6c4ddf8d06cfb7fc0325cab3a3d77fe267e85d75957811f7c3ac3c544e875be0 | da12ae728f5b3ee2fcaaa7ee44939eeca671d65ca294274aff58612208abd95d | 82ce5617dd275790dbd598f7bf904dc3b09158a0f801d23deb8239983a89763e | d3d8ad3f357ad2476117bb1a33108ce86a59c670fac16f62299f76ec8aa63179 |
cat-searcher/leandojo-benchmark-4-random | test | 2,576 | CategoryTheory.PresheafHom.IsSheafFor.exists_app | Mathlib/CategoryTheory/Sites/SheafHom.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | erw [← H, ← H', <a>CategoryTheory.presheafHom_map_app_op_mk_id</a>, ← F.map_comp_assoc, ← <a>CategoryTheory.op_comp</a>, <a>CategoryTheory.Over.w</a> f] | case op.mk.op.mk.op
C : Type u
inst✝¹ : Category.{v, u} C
J : GrothendieckTopology C
A : Type u'
inst✝ : Category.{v', u'} A
F G : Cᵒᵖ ⥤ A
X : C
S : Sieve X
hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op)
x : Presieve.FamilyOfElements (presheafHom F G) S.arrows
hx : x.Compatible
Y... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.24589) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.24589) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.24589) (:fv _uniq.24592))) ((:c Prefunctor.obj) ((:c Opposite) (:fv _uniq.24569)) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c Opposite) (:fv _uniq.24... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.24569))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.24569) (:fv _uniq.24572))"},{"name":"A","sexp":"(:sort (+ u' 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c Opposite) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"erw","sourceEnd":5447,"sourceStart":5444,"tag":"atom"},{"children":[{"source":"[","sourceEnd":5449,"sourceStart":5448,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":5452,"sourceStart":5449,"tag":"atom"}],"kind":"token.«← »","source":"←","... | [] | [{"source":"H","source_end":5454,"source_start":5453,"syntax_kind":"ident"},{"source":"H'","source_end":5462,"source_start":5460,"syntax_kind":"ident"},{"source":"presheafHom_map_app_op_mk_id","source_end":5492,"source_start":5464,"syntax_kind":"ident"},{"source":"F.map_comp_assoc","source_end":5514,"source_start":5498... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 18 | 25 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 265052fdd8d65c8b46f9433899e7bf2f2eaf6062a1d135333612208e64b2ba4e | d3d8ad3f357ad2476117bb1a33108ce86a59c670fac16f62299f76ec8aa63179 | e6bbb88a29e61b36dbe67aec8f1a084d8b74e2763cee6c655ccebc74c7e6dcf1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,577 | CategoryTheory.PresheafHom.IsSheafFor.exists_app | Mathlib/CategoryTheory/Sites/SheafHom.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | C : Type u
inst✝¹ : Category.{v, u} C
J : GrothendieckTopology C
A : Type u'
inst✝ : Category.{v', u'} A
F G : Cᵒᵖ ⥤ A
X : C
S : Sieve X
hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op)
x : Presieve.FamilyOfElements (presheafHom F G) S.arrows
hx : x.Compatible
Y : C
g : Y ⟶ X
Z₁ : ... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.24569) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.24569) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.24569) (:fv _uniq.24572))) ((:c CategoryTheory.Comma.left) (:fv _uniq.24569) (:fv _uniq.24572) ((:c CategoryTheory.Discrete) (:c PUnit)) ((:c CategoryTheor... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.24569))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.24569) (:fv _uniq.24572))"},{"name":"A","sexp":"(:sort (+ u' 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c CategoryTheory.Comma.left) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":5127,"sourceStart":5123,"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.24569","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 18 | 18 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 69f059a84e52408895f1cd723b169a4f9f91fc9d93fe29faef7e331ec3a4ac47 | 5b8cca084b21fbfb51f9191f11a86d77ecbbed29006361a7a578c252e6ca7f15 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,578 | AdjoinRoot.isRoot_root | Mathlib/RingTheory/AdjoinRoot.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Polynomial.IsRoot</a>, <a>Polynomial.eval_map</a>, <a>AdjoinRoot.eval₂_root</a>] | R : Type u
S : Type v
K : Type w
inst✝ : CommRing R
f✝ f : R[X]
⊢ (Polynomial.map (of f) f).IsRoot (root f) | ((:c Polynomial.IsRoot) ((:c AdjoinRoot) (:fv _uniq.70637) (:fv _uniq.70644) (:fv _uniq.71390)) ((:c CommSemiring.toSemiring) ((:c AdjoinRoot) (:fv _uniq.70637) (:fv _uniq.70644) (:fv _uniq.71390)) ((:c CommRing.toCommSemiring) ((:c AdjoinRoot) (:fv _uniq.70637) (:fv _uniq.70644) (:fv _uniq.71390)) ((:c AdjoinRoot.inst... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"K","sexp":"(:sort (+ w 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.70637))"},{"name":"f✝","sexp":"((:c Polynomial) (:fv _uniq.70637) ((:c CommSemiring.toSemiring) (:fv _uniq.70637) ((:c CommRing.toCommSemiring) (:fv _uniq.... | (:app (:c Polynomial.IsRoot) (:arg :implicit-type 0 (:app (:c AdjoinRoot) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV6)))) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:app (:c AdjoinRoot) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.70637","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.70639","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":9030,"sourceStart":9028,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9032,"sourceStart":9031,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"IsRoot","source_end":9038,"source_start":9032,"syntax_kind":"ident"},{"source":"eval_map","source_end":9048,"source_start":9040,"syntax_kind":"ident"},{"source":"eval₂_root","source_end":9062,"source_start":9050,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.70637","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.70639","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 74 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c5bd2cb1e813149a727ff74bac262839c4e13918da78d6b3514451cdf4e6320d | 9ddcf1432eca505ee552ee2a6716b7e54722fea59d59a6e5220c93a4968cc5f6 | 27e48c073c61b3fd26ea5fd6c99befc88e7d6abce289a83367e580dfa6f792b8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,579 | CauSeq.abv_pos_of_not_limZero | Mathlib/Algebra/Order/CauSeq/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | haveI := <a>Classical.propDecidable</a> | α : Type u_1
β : Type u_2
inst✝² : LinearOrderedField α
inst✝¹ : Ring β
abv : β → α
inst✝ : IsAbsoluteValue abv
f : CauSeq β abv
hf : ¬f.LimZero
⊢ ∃ K > 0, ∃ i, ∀ j ≥ i, K ≤ abv (↑f j) | α : Type u_1
β : Type u_2
inst✝² : LinearOrderedField α
inst✝¹ : Ring β
abv : β → α
inst✝ : IsAbsoluteValue abv
f : CauSeq β abv
hf : ¬f.LimZero
this : (a : Prop) → Decidable a
⊢ ∃ K > 0, ∃ i, ∀ j ≥ i, K ≤ abv (↑f j) | ((:c Exists) (:fv _uniq.138880) (:lambda K (:fv _uniq.138880) ((:c And) ((:c GT.gt) (:fv _uniq.138880) ((:c Preorder.toLT) (:fv _uniq.138880) ((:c PartialOrder.toPreorder) (:fv _uniq.138880) ((:c StrictOrderedRing.toPartialOrder) (:fv _uniq.138880) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.138880) ((:c Lin... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c LinearOrderedField) (:fv _uniq.138880))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.138883))"},{"name":"abv","sexp":"(:forall _ (:fv _uniq.138883) (:fv _uniq.138880))"},{"name":"inst✝","sexp":"((:c IsAbso... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda K :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c GT.gt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 0) (:arg :explicit 3 (:app (:c OfNat.of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"haveI","sourceEnd":19036,"sourceStart":19031,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":19037,"sourceStart":19037,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":19037,"sourceStart":19037,"tag":"node"}],"kind":"Lean.Parser.Term.ha... | [] | [{"source":"Classical.propDecidable","source_end":19063,"source_start":19040,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal... | 167 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5352c118ad230716c47e04d41d940d2f6bb518c4f747f18e4dae7adfae3083af | 5abaae65131dcf4ec58928acd11476e91b5a9a5482d0b947499aa8625b80d920 | 65ff87683f7d283ccba41045b0db19a6e4b84a07fc35a436f18d8b2b630797b8 | fdb5cba81a4f6da6577decb26397ddd8814889444e527ca7bc95a56112b1ddf3 |
cat-searcher/leandojo-benchmark-4-random | test | 2,580 | CauSeq.abv_pos_of_not_limZero | Mathlib/Algebra/Order/CauSeq/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_contra nk | α : Type u_1
β : Type u_2
inst✝² : LinearOrderedField α
inst✝¹ : Ring β
abv : β → α
inst✝ : IsAbsoluteValue abv
f : CauSeq β abv
hf : ¬f.LimZero
this : (a : Prop) → Decidable a
⊢ ∃ K > 0, ∃ i, ∀ j ≥ i, K ≤ abv (↑f j) | α : Type u_1
β : Type u_2
inst✝² : LinearOrderedField α
inst✝¹ : Ring β
abv : β → α
inst✝ : IsAbsoluteValue abv
f : CauSeq β abv
hf : ¬f.LimZero
this : (a : Prop) → Decidable a
nk : ¬∃ K > 0, ∃ i, ∀ j ≥ i, K ≤ abv (↑f j)
⊢ False | ((:c Exists) (:fv _uniq.138880) (:lambda K (:fv _uniq.138880) ((:c And) ((:c GT.gt) (:fv _uniq.138880) ((:c Preorder.toLT) (:fv _uniq.138880) ((:c PartialOrder.toPreorder) (:fv _uniq.138880) ((:c StrictOrderedRing.toPartialOrder) (:fv _uniq.138880) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.138880) ((:c Lin... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c LinearOrderedField) (:fv _uniq.138880))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.138883))"},{"name":"abv","sexp":"(:forall _ (:fv _uniq.138883) (:fv _uniq.138880))"},{"name":"inst✝","sexp":"((:c IsAbso... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda K :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c GT.gt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 0) (:arg :explicit 3 (:app (:c OfNat.of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"by_contra","sourceEnd":19075,"sourceStart":19066,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"nk","sourceEnd":19078,"sourceStart":19076,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"nk","sourceEnd":19078,"sourceStart":19076,"tag":"node"}],"kind":"nu... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal... | 167 | 5 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7ff38ef9fc4defae152edf586b727dc8cc07ea8acc3874ef8d64be809be7084b | fdb5cba81a4f6da6577decb26397ddd8814889444e527ca7bc95a56112b1ddf3 | 20512fcc84495a3ff1f775283cc80767e164ee79610f8d57ef6ea9e801857788 | 5ac7de7f96c7127fe6c7cb2b96d8d224c16c8ac8bc879d134099ac731910b539 |
cat-searcher/leandojo-benchmark-4-random | test | 2,581 | CauSeq.abv_pos_of_not_limZero | Mathlib/Algebra/Order/CauSeq/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine hf fun ε ε0 => ?_ | α : Type u_1
β : Type u_2
inst✝² : LinearOrderedField α
inst✝¹ : Ring β
abv : β → α
inst✝ : IsAbsoluteValue abv
f : CauSeq β abv
hf : ¬f.LimZero
this : (a : Prop) → Decidable a
nk : ¬∃ K > 0, ∃ i, ∀ j ≥ i, K ≤ abv (↑f j)
⊢ False | α : Type u_1
β : Type u_2
inst✝² : LinearOrderedField α
inst✝¹ : Ring β
abv : β → α
inst✝ : IsAbsoluteValue abv
f : CauSeq β abv
hf : ¬f.LimZero
this : (a : Prop) → Decidable a
nk : ¬∃ K > 0, ∃ i, ∀ j ≥ i, K ≤ abv (↑f j)
ε : α
ε0 : ε > 0
⊢ ∃ i, ∀ j ≥ i, abv (↑f j) < ε | (:c False) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c LinearOrderedField) (:fv _uniq.138880))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.138883))"},{"name":"abv","sexp":"(:forall _ (:fv _uniq.138883) (:fv _uniq.138880))"},{"name":"inst✝","sexp":"((:c IsAbso... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":19087,"sourceStart":19081,"tag":"atom"},{"children":[{"contextIndex":8,"semanticRole":"local","source":"hf","sourceEnd":19090,"sourceStart":19088,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":19094,"sourceStart":19091,"tag":"atom"},{"children":[{"c... | [] | [{"source":"hf fun ε ε0 => ?_","source_end":19107,"source_start":19088,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal... | 167 | 6 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a1dc011adca886eb89237b074c26b5ba3e3f8964a5a48882fce4debf2380d9d3 | 5ac7de7f96c7127fe6c7cb2b96d8d224c16c8ac8bc879d134099ac731910b539 | 2df78e1e3038f8341905633f5a6348634c77328550c226655651a4c887f5d4d0 | 29184518b5d61256b1d0dc62c14fdc170f3f83ad75cf476aace9b9cba466f797 |
cat-searcher/leandojo-benchmark-4-random | test | 2,582 | CauSeq.abv_pos_of_not_limZero | Mathlib/Algebra/Order/CauSeq/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp? [not_forall] at nk says simp only [<a>gt_iff_lt</a>, <a>ge_iff_le</a>, <a>not_exists</a>, <a>not_and</a>, <a>Classical.not_forall</a>, <a>Classical.not_imp</a>, <a>not_le</a>] at nk | α : Type u_1
β : Type u_2
inst✝² : LinearOrderedField α
inst✝¹ : Ring β
abv : β → α
inst✝ : IsAbsoluteValue abv
f : CauSeq β abv
hf : ¬f.LimZero
this : (a : Prop) → Decidable a
nk : ¬∃ K > 0, ∃ i, ∀ j ≥ i, K ≤ abv (↑f j)
ε : α
ε0 : ε > 0
⊢ ∃ i, ∀ j ≥ i, abv (↑f j) < ε | α : Type u_1
β : Type u_2
inst✝² : LinearOrderedField α
inst✝¹ : Ring β
abv : β → α
inst✝ : IsAbsoluteValue abv
f : CauSeq β abv
hf : ¬f.LimZero
this : (a : Prop) → Decidable a
ε : α
ε0 : ε > 0
nk : ∀ (x : α), 0 < x → ∀ (x_1 : ℕ), ∃ x_2, ∃ (_ : x_1 ≤ x_2), abv (↑f x_2) < x
⊢ ∃ i, ∀ j ≥ i, abv (↑f j) < ε | ((:c Exists) (:c Nat) (:lambda i (:c Nat) (:forall j (:c Nat) (:forall _ ((:c GE.ge) (:c Nat) (:c instLENat) 0 1) ((:c LT.lt) (:fv _uniq.138880) ((:c Preorder.toLT) (:fv _uniq.138880) ((:c PartialOrder.toPreorder) (:fv _uniq.138880) ((:c StrictOrderedRing.toPartialOrder) (:fv _uniq.138880) ((:c LinearOrderedRing.toStri... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c LinearOrderedField) (:fv _uniq.138880))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.138883))"},{"name":"abv","sexp":"(:forall _ (:fv _uniq.138883) (:fv _uniq.138880))"},{"name":"inst✝","sexp":"((:c IsAbso... | (:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda i :explicit (:c Nat) (:forall j :explicit (:c Nat) (:forall _ :explicit (:app (:c GE.ge) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 0) (:arg :explicit 3 1)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"source":"simp?","sourceEnd":19115,"sourceStart":19110,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag"... | [] | [{"source":"gt_iff_lt","source_end":19164,"source_start":19155,"syntax_kind":"ident"},{"source":"ge_iff_le","source_end":19175,"source_start":19166,"syntax_kind":"ident"},{"source":"not_exists","source_end":19187,"source_start":19177,"syntax_kind":"ident"},{"source":"not_and","source_end":19196,"source_start":19189,"sy... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal... | 167 | 7 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6eba7d49b606d636a732a6dcd2e5f67d483178c0d912ee5890612709dc2cc024 | 29184518b5d61256b1d0dc62c14fdc170f3f83ad75cf476aace9b9cba466f797 | b60538e87896000398c646d9c723d84eaae9f494c755de90eaaf432d8cdf346c | f53ecdffd7f5b87383a3fabbfed8ae9aad1f482d6a5e1947d6500857d1ae150f |
cat-searcher/leandojo-benchmark-4-random | test | 2,583 | CauSeq.abv_pos_of_not_limZero | Mathlib/Algebra/Order/CauSeq/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases' f.cauchy₃ (<a>half_pos</a> ε0) with i hi | α : Type u_1
β : Type u_2
inst✝² : LinearOrderedField α
inst✝¹ : Ring β
abv : β → α
inst✝ : IsAbsoluteValue abv
f : CauSeq β abv
hf : ¬f.LimZero
this : (a : Prop) → Decidable a
ε : α
ε0 : ε > 0
nk : ∀ (x : α), 0 < x → ∀ (x_1 : ℕ), ∃ x_2, ∃ (_ : x_1 ≤ x_2), abv (↑f x_2) < x
⊢ ∃ i, ∀ j ≥ i, abv (↑f j) < ε | case intro
α : Type u_1
β : Type u_2
inst✝² : LinearOrderedField α
inst✝¹ : Ring β
abv : β → α
inst✝ : IsAbsoluteValue abv
f : CauSeq β abv
hf : ¬f.LimZero
this : (a : Prop) → Decidable a
ε : α
ε0 : ε > 0
nk : ∀ (x : α), 0 < x → ∀ (x_1 : ℕ), ∃ x_2, ∃ (_ : x_1 ≤ x_2), abv (↑f x_2) < x
i : ℕ
hi : ∀ j ≥ i, ∀ k ≥ j, abv (↑... | ((:c Exists) (:c Nat) (:lambda i (:c Nat) (:forall j (:c Nat) (:forall _ ((:c GE.ge) (:c Nat) (:c instLENat) 0 1) ((:c LT.lt) (:fv _uniq.138880) ((:c Preorder.toLT) (:fv _uniq.138880) ((:c PartialOrder.toPreorder) (:fv _uniq.138880) ((:c StrictOrderedRing.toPartialOrder) (:fv _uniq.138880) ((:c LinearOrderedRing.toStri... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c LinearOrderedField) (:fv _uniq.138880))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.138883))"},{"name":"abv","sexp":"(:forall _ (:fv _uniq.138883) (:fv _uniq.138880))"},{"name":"inst✝","sexp":"((:c IsAbso... | (:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda i :explicit (:c Nat) (:forall j :explicit (:c Nat) (:forall _ :explicit (:app (:c GE.ge) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 0) (:arg :explicit 3 1)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"cases'","sourceEnd":19257,"sourceStart":19251,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"f.cauchy₃","sourceEnd":19269,"sourceStart":19258,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":19271,"sou... | [] | [{"source":"f.cauchy₃ (half_pos ε0)","source_end":19284,"source_start":19258,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal... | 167 | 11 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dcb23184a334a9e42b8bc0d8e76b11bf9584b6b7ab8a521dafe5d11781780c44 | f53ecdffd7f5b87383a3fabbfed8ae9aad1f482d6a5e1947d6500857d1ae150f | 199da3a3a10a29dc99461a17325979b4869efecf6cb47b10e12447640722b7f1 | fc2da13e38c4adb2d772f950cfe1ace77f2a426c0efcf486395c78e0f6fa48a0 |
cat-searcher/leandojo-benchmark-4-random | test | 2,584 | CauSeq.abv_pos_of_not_limZero | Mathlib/Algebra/Order/CauSeq/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases nk _ (<a>half_pos</a> ε0) i with ⟨j, ij, hj⟩ | case intro
α : Type u_1
β : Type u_2
inst✝² : LinearOrderedField α
inst✝¹ : Ring β
abv : β → α
inst✝ : IsAbsoluteValue abv
f : CauSeq β abv
hf : ¬f.LimZero
this : (a : Prop) → Decidable a
ε : α
ε0 : ε > 0
nk : ∀ (x : α), 0 < x → ∀ (x_1 : ℕ), ∃ x_2, ∃ (_ : x_1 ≤ x_2), abv (↑f x_2) < x
i : ℕ
hi : ∀ j ≥ i, ∀ k ≥ j, abv (↑... | case intro.intro.intro
α : Type u_1
β : Type u_2
inst✝² : LinearOrderedField α
inst✝¹ : Ring β
abv : β → α
inst✝ : IsAbsoluteValue abv
f : CauSeq β abv
hf : ¬f.LimZero
this : (a : Prop) → Decidable a
ε : α
ε0 : ε > 0
nk : ∀ (x : α), 0 < x → ∀ (x_1 : ℕ), ∃ x_2, ∃ (_ : x_1 ≤ x_2), abv (↑f x_2) < x
i : ℕ
hi : ∀ j ≥ i, ∀ k... | ((:c Exists) (:c Nat) (:lambda i (:c Nat) (:forall j (:c Nat) (:forall _ ((:c GE.ge) (:c Nat) (:c instLENat) 0 1) ((:c LT.lt) (:fv _uniq.138880) ((:c Preorder.toLT) (:fv _uniq.138880) ((:c PartialOrder.toPreorder) (:fv _uniq.138880) ((:c StrictOrderedRing.toPartialOrder) (:fv _uniq.138880) ((:c LinearOrderedRing.toStri... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c LinearOrderedField) (:fv _uniq.138880))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.138883))"},{"name":"abv","sexp":"(:forall _ (:fv _uniq.138883) (:fv _uniq.138880))"},{"name":"inst✝","sexp":"((:c IsAbso... | (:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda i :explicit (:c Nat) (:forall j :explicit (:c Nat) (:forall _ :explicit (:app (:c GE.ge) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 0) (:arg :explicit 3 1)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rcases","sourceEnd":19303,"sourceStart":19297,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"nk","sourceEnd":19306,"sourceStart":19304,"tag":"identifier"},{"children":[{"children":[{"... | [] | [{"source":"nk _ (half_pos ε0) i","source_end":19325,"source_start":19304,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨j, ij, hj⟩","source_end":19346,"source_start":19331,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal... | 167 | 12 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 18e0f16c16610b6370515b29edc8daf28a5e30fe49705b55bce614d6a76121c0 | fc2da13e38c4adb2d772f950cfe1ace77f2a426c0efcf486395c78e0f6fa48a0 | 798dc635e9df91db792166ac27f80440cc5d4d5ab542ec76989b01f50dd029f0 | 5ed89a14fb1be046dba8bf9f64c3063c8f04f17a63a0b7911f92cc3fc819d808 |
cat-searcher/leandojo-benchmark-4-random | test | 2,585 | CauSeq.abv_pos_of_not_limZero | Mathlib/Algebra/Order/CauSeq/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨j, fun k jk => ?_⟩ | case intro.intro.intro
α : Type u_1
β : Type u_2
inst✝² : LinearOrderedField α
inst✝¹ : Ring β
abv : β → α
inst✝ : IsAbsoluteValue abv
f : CauSeq β abv
hf : ¬f.LimZero
this : (a : Prop) → Decidable a
ε : α
ε0 : ε > 0
nk : ∀ (x : α), 0 < x → ∀ (x_1 : ℕ), ∃ x_2, ∃ (_ : x_1 ≤ x_2), abv (↑f x_2) < x
i : ℕ
hi : ∀ j ≥ i, ∀ k... | case intro.intro.intro
α : Type u_1
β : Type u_2
inst✝² : LinearOrderedField α
inst✝¹ : Ring β
abv : β → α
inst✝ : IsAbsoluteValue abv
f : CauSeq β abv
hf : ¬f.LimZero
this : (a : Prop) → Decidable a
ε : α
ε0 : ε > 0
nk : ∀ (x : α), 0 < x → ∀ (x_1 : ℕ), ∃ x_2, ∃ (_ : x_1 ≤ x_2), abv (↑f x_2) < x
i : ℕ
hi : ∀ j ≥ i, ∀ k... | ((:c Exists) (:c Nat) (:lambda i (:c Nat) (:forall j (:c Nat) (:forall _ ((:c GE.ge) (:c Nat) (:c instLENat) 0 1) ((:c LT.lt) (:fv _uniq.138880) ((:c Preorder.toLT) (:fv _uniq.138880) ((:c PartialOrder.toPreorder) (:fv _uniq.138880) ((:c StrictOrderedRing.toPartialOrder) (:fv _uniq.138880) ((:c LinearOrderedRing.toStri... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c LinearOrderedField) (:fv _uniq.138880))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.138883))"},{"name":"abv","sexp":"(:forall _ (:fv _uniq.138883) (:fv _uniq.138880))"},{"name":"inst✝","sexp":"((:c IsAbso... | (:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda i :explicit (:c Nat) (:forall j :explicit (:c Nat) (:forall _ :explicit (:app (:c GE.ge) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 0) (:arg :explicit 3 1)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":19355,"sourceStart":19349,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":19359,"sourceStart":19356,"tag":"atom"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"j","sourceEnd":19360,"sourceStart":19359,"tag":"identifier"},{"source":",","sourceEnd":19361... | [] | [{"source":"⟨j, fun k jk => ?_⟩","source_end":19379,"source_start":19356,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal... | 167 | 13 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bb5c101d503bf330f89d5311596ee1e9ce1bde08ef26dbbb954b632451ad691c | 5ed89a14fb1be046dba8bf9f64c3063c8f04f17a63a0b7911f92cc3fc819d808 | a94f3304d5c433301eaabc9d0ae3b87cf1cd8e3f5663a457eaa8acde945e7bf0 | 56ece2637f5226fca7f78c2ce31ac4b2ba24c0751288e0abb0d4e66e6a8da293 |
cat-searcher/leandojo-benchmark-4-random | test | 2,586 | CauSeq.abv_pos_of_not_limZero | Mathlib/Algebra/Order/CauSeq/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have := <a>lt_of_le_of_lt</a> (<a>IsAbsoluteValue.abv_add</a> abv _ _) (<a>add_lt_add</a> (hi j ij k jk) hj) | case intro.intro.intro
α : Type u_1
β : Type u_2
inst✝² : LinearOrderedField α
inst✝¹ : Ring β
abv : β → α
inst✝ : IsAbsoluteValue abv
f : CauSeq β abv
hf : ¬f.LimZero
this : (a : Prop) → Decidable a
ε : α
ε0 : ε > 0
nk : ∀ (x : α), 0 < x → ∀ (x_1 : ℕ), ∃ x_2, ∃ (_ : x_1 ≤ x_2), abv (↑f x_2) < x
i : ℕ
hi : ∀ j ≥ i, ∀ k... | case intro.intro.intro
α : Type u_1
β : Type u_2
inst✝² : LinearOrderedField α
inst✝¹ : Ring β
abv : β → α
inst✝ : IsAbsoluteValue abv
f : CauSeq β abv
hf : ¬f.LimZero
this✝ : (a : Prop) → Decidable a
ε : α
ε0 : ε > 0
nk : ∀ (x : α), 0 < x → ∀ (x_1 : ℕ), ∃ x_2, ∃ (_ : x_1 ≤ x_2), abv (↑f x_2) < x
i : ℕ
hi : ∀ j ≥ i, ∀ ... | ((:c LT.lt) (:fv _uniq.138880) ((:c Preorder.toLT) (:fv _uniq.138880) ((:c PartialOrder.toPreorder) (:fv _uniq.138880) ((:c StrictOrderedRing.toPartialOrder) (:fv _uniq.138880) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.138880) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.138880) ((:c LinearOr... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c LinearOrderedField) (:fv _uniq.138880))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.138883))"},{"name":"abv","sexp":"(:forall _ (:fv _uniq.138883) (:fv _uniq.138880))"},{"name":"inst✝","sexp":"((:c IsAbso... | (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:fv FV4) (:arg :explicit 0 (:app (:c Subtype.val) (:arg :implicit-type 0 (:forall _ :explicit (:c Nat) (:fv FV1))) (:arg :implicit 1) (:arg :explicit 2 (:fv FV7)) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"have","sourceEnd":19386,"sourceStart":19382,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":19387,"sourceStart":19387,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":19387,"sourceStart":19387,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"lt_of_le_of_lt (abv_add abv _ _) (add_lt_add (hi j ij k jk) hj)","source_end":19453,"source_start":19390,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal... | 167 | 14 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9edb3127834d7f55de2cf6b2a7f1020bf0c4b8498d21818230a01c02d6b90f1a | 56ece2637f5226fca7f78c2ce31ac4b2ba24c0751288e0abb0d4e66e6a8da293 | fba07b2ac72b377bd2f8c04cfdbecdc7fb88987747e83c5050ea9eb4465deda7 | bf17e3430a1ae516b691369fcfb3ab38e6ba06830190b88e0a887cac72f02c8e |
cat-searcher/leandojo-benchmark-4-random | test | 2,587 | CauSeq.abv_pos_of_not_limZero | Mathlib/Algebra/Order/CauSeq/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>sub_add_cancel</a>, <a>add_halves</a>] at this | case intro.intro.intro
α : Type u_1
β : Type u_2
inst✝² : LinearOrderedField α
inst✝¹ : Ring β
abv : β → α
inst✝ : IsAbsoluteValue abv
f : CauSeq β abv
hf : ¬f.LimZero
this✝ : (a : Prop) → Decidable a
ε : α
ε0 : ε > 0
nk : ∀ (x : α), 0 < x → ∀ (x_1 : ℕ), ∃ x_2, ∃ (_ : x_1 ≤ x_2), abv (↑f x_2) < x
i : ℕ
hi : ∀ j ≥ i, ∀ ... | ((:c LT.lt) (:fv _uniq.138880) ((:c Preorder.toLT) (:fv _uniq.138880) ((:c PartialOrder.toPreorder) (:fv _uniq.138880) ((:c StrictOrderedRing.toPartialOrder) (:fv _uniq.138880) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.138880) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.138880) ((:c LinearOr... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c LinearOrderedField) (:fv _uniq.138880))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.138883))"},{"name":"abv","sexp":"(:forall _ (:fv _uniq.138883) (:fv _uniq.138880))"},{"name":"inst✝","sexp":"((:c IsAbso... | (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:fv FV4) (:arg :explicit 0 (:app (:c Subtype.val) (:arg :implicit-type 0 (:forall _ :explicit (:c Nat) (:fv FV1))) (:arg :implicit 1) (:arg :explicit 2 (:fv FV7)) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rwa","sourceEnd":19459,"sourceStart":19456,"tag":"atom"},{"children":[{"source":"[","sourceEnd":19461,"sourceStart":19460,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"sub_add_cancel","semanticRole":"global","source":"sub_add_cancel","sou... | [] | [{"source":"sub_add_cancel","source_end":19475,"source_start":19461,"syntax_kind":"ident"},{"source":"this","source_end":19496,"source_start":19492,"syntax_kind":"ident"},{"source":"add_halves","source_end":19487,"source_start":19477,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal... | 167 | 15 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 55e2cf18f597f3917f40d8919b55f497beddf243efc0078b742ec1de4dbe7281 | bf17e3430a1ae516b691369fcfb3ab38e6ba06830190b88e0a887cac72f02c8e | 971dc4a1ba8dc66c5daca72696ab92c8e9265a750641d2c652687db03e3cbf66 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,588 | CauSeq.abv_pos_of_not_limZero | Mathlib/Algebra/Order/CauSeq/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>gt_iff_lt</a>, <a>ge_iff_le</a>, <a>not_exists</a>, <a>not_and</a>, <a>Classical.not_forall</a>, <a>Classical.not_imp</a>, <a>not_le</a>] at nk | α : Type u_1
β : Type u_2
inst✝² : LinearOrderedField α
inst✝¹ : Ring β
abv : β → α
inst✝ : IsAbsoluteValue abv
f : CauSeq β abv
hf : ¬f.LimZero
this : (a : Prop) → Decidable a
nk : ¬∃ K > 0, ∃ i, ∀ j ≥ i, K ≤ abv (↑f j)
ε : α
ε0 : ε > 0
⊢ ∃ i, ∀ j ≥ i, abv (↑f j) < ε | α : Type u_1
β : Type u_2
inst✝² : LinearOrderedField α
inst✝¹ : Ring β
abv : β → α
inst✝ : IsAbsoluteValue abv
f : CauSeq β abv
hf : ¬f.LimZero
this : (a : Prop) → Decidable a
ε : α
ε0 : ε > 0
nk : ∀ (x : α), 0 < x → ∀ (x_1 : ℕ), ∃ x_2, ∃ (_ : x_1 ≤ x_2), abv (↑f x_2) < x
⊢ ∃ i, ∀ j ≥ i, abv (↑f j) < ε | ((:c Exists) (:c Nat) (:lambda i (:c Nat) (:forall j (:c Nat) (:forall _ ((:c GE.ge) (:c Nat) (:c instLENat) 0 1) ((:c LT.lt) (:fv _uniq.138880) ((:c Preorder.toLT) (:fv _uniq.138880) ((:c PartialOrder.toPreorder) (:fv _uniq.138880) ((:c StrictOrderedRing.toPartialOrder) (:fv _uniq.138880) ((:c LinearOrderedRing.toStri... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c LinearOrderedField) (:fv _uniq.138880))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.138883))"},{"name":"abv","sexp":"(:forall _ (:fv _uniq.138883) (:fv _uniq.138880))"},{"name":"inst✝","sexp":"((:c IsAbso... | (:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda i :explicit (:c Nat) (:forall j :explicit (:c Nat) (:forall _ :explicit (:app (:c GE.ge) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 0) (:arg :explicit 3 1)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":19148,"sourceStart":19144,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":19153,"sourceStart":19149,"tag":"atom"}],"kind"... | [] | [{"source":"gt_iff_lt","source_end":19164,"source_start":19155,"syntax_kind":"ident"},{"source":"ge_iff_le","source_end":19175,"source_start":19166,"syntax_kind":"ident"},{"source":"not_exists","source_end":19187,"source_start":19177,"syntax_kind":"ident"},{"source":"not_and","source_end":19196,"source_start":19189,"sy... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138880","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138883","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal... | 167 | 8 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 38836f6734dc9c9b6c99e840231a62aa1a9639993529a64f4f344d11a6e7a52a | 29184518b5d61256b1d0dc62c14fdc170f3f83ad75cf476aace9b9cba466f797 | 22b89fa39986f71a6cf708a23221b4bec129be212ddf52a7f1bcf175cbb88531 | f53ecdffd7f5b87383a3fabbfed8ae9aad1f482d6a5e1947d6500857d1ae150f |
cat-searcher/leandojo-benchmark-4-random | test | 2,589 | MeasureTheory.norm_condexpIndL1_le | Mathlib/MeasureTheory/Function/ConditionalExpectation/CondexpL1.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases hs : <a>MeasurableSet</a> s | α : Type u_1
β : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
G' : Type u_6
𝕜 : Type u_7
p : ℝ≥0∞
inst✝¹² : RCLike 𝕜
inst✝¹¹ : NormedAddCommGroup F
inst✝¹⁰ : NormedSpace 𝕜 F
inst✝⁹ : NormedAddCommGroup F'
inst✝⁸ : NormedSpace 𝕜 F'
inst✝⁷ : NormedSpace ℝ F'
inst✝⁶ : CompleteSpace F'
inst✝⁵ : NormedAddCommGroup G... | case pos
α : Type u_1
β : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
G' : Type u_6
𝕜 : Type u_7
p : ℝ≥0∞
inst✝¹² : RCLike 𝕜
inst✝¹¹ : NormedAddCommGroup F
inst✝¹⁰ : NormedSpace 𝕜 F
inst✝⁹ : NormedAddCommGroup F'
inst✝⁸ : NormedSpace 𝕜 F'
inst✝⁷ : NormedSpace ℝ F'
inst✝⁶ : CompleteSpace F'
inst✝⁵ : NormedAddCo... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) ((:c Subtype) ((:c MeasureTheory.AEEqFun) (:fv _uniq.115055) (:fv _uniq.115067) (:fv _uniq.115748) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.115067) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.115067) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"G'","sexp":"(:sort (+ u_6 1))"},{"name":"𝕜","sexp":"(:sort (+ u_7 1))"},{"name":"p","sexp":"(:c ENNReal)"},{... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c MeasureTheory.AEEqFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.115055","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.115058","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"by_cases","sourceEnd":11103,"sourceStart":11095,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hs","sourceEnd":11106,"sourceStart":11104,"tag":"identifier"},{"source":":","sourceEnd":11108,"sourceStart":11107,"tag":"atom"}],"kind":"null","source":"hs :","sourceEnd":11108,"so... | [] | [{"source":"MeasurableSet s","source_end":11124,"source_start":11109,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.115055","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.115058","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 47 | 4 | exact | true | 1 | 28 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 676de5bc8066eb17d49c3fc486d96ca632cc7f7d6d0ee6acbc7733d9522c2b7f | 549044c75fb413157f6db4ea056d401d0198ac7a2dad19624849b11c8b004caa | ef7686bb926d6cc6dcdcf47a4c8ac0b459690869977139728fe51d31efb8773c | 8a5ed0f5742c6416fe89316350ebb48ae795b95d7f049e0526a1668db03f5893 |
cat-searcher/leandojo-benchmark-4-random | test | 2,591 | MeasureTheory.norm_condexpIndL1_le | Mathlib/MeasureTheory/Function/ConditionalExpectation/CondexpL1.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases hμs : μ s = ∞ | case pos
α : Type u_1
β : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
G' : Type u_6
𝕜 : Type u_7
p : ℝ≥0∞
inst✝¹² : RCLike 𝕜
inst✝¹¹ : NormedAddCommGroup F
inst✝¹⁰ : NormedSpace 𝕜 F
inst✝⁹ : NormedAddCommGroup F'
inst✝⁸ : NormedSpace 𝕜 F'
inst✝⁷ : NormedSpace ℝ F'
inst✝⁶ : CompleteSpace F'
inst✝⁵ : NormedAddCo... | case pos
α : Type u_1
β : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
G' : Type u_6
𝕜 : Type u_7
p : ℝ≥0∞
inst✝¹² : RCLike 𝕜
inst✝¹¹ : NormedAddCommGroup F
inst✝¹⁰ : NormedSpace 𝕜 F
inst✝⁹ : NormedAddCommGroup F'
inst✝⁸ : NormedSpace 𝕜 F'
inst✝⁷ : NormedSpace ℝ F'
inst✝⁶ : CompleteSpace F'
inst✝⁵ : NormedAddCo... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) ((:c Subtype) ((:c MeasureTheory.AEEqFun) (:fv _uniq.115055) (:fv _uniq.115067) (:fv _uniq.115748) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.115067) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.115067) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"G'","sexp":"(:sort (+ u_6 1))"},{"name":"𝕜","sexp":"(:sort (+ u_7 1))"},{"name":"p","sexp":"(:c ENNReal)"},{... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c MeasureTheory.AEEqFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.115055","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.115058","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"by_cases","sourceEnd":11272,"sourceStart":11264,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hμs","sourceEnd":11277,"sourceStart":11273,"tag":"identifier"},{"source":":","sourceEnd":11279,"sourceStart":11278,"tag":"atom"}],"kind":"null","source":"hμs :","sourceEnd":11279,"... | [] | [{"source":"μ s = ∞","source_end":11290,"source_start":11280,"syntax_kind":"«term_=_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.115055","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.115058","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 47 | 18 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | df5b051110a2bcb120a17a076cdd332061f9c2979514361a461324e4b642feed | 84037b382555e98d0c5e60575feb287eaa15866591f36d2de527900fec6b9c7f | 4a59662b3e3b734e0e6268bf70c3dcc43313ec4194e2a2649e67c7462494f626 | a7ee2bb289a2dccb16aaf238e1e3bcd4be89382778353954b1f09f15d159d803 |
cat-searcher/leandojo-benchmark-4-random | test | 2,592 | MeasureTheory.norm_condexpIndL1_le | Mathlib/MeasureTheory/Function/ConditionalExpectation/CondexpL1.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>MeasureTheory.condexpIndL1_of_not_measurableSet</a> hs] | case neg
α : Type u_1
β : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
G' : Type u_6
𝕜 : Type u_7
p : ℝ≥0∞
inst✝¹² : RCLike 𝕜
inst✝¹¹ : NormedAddCommGroup F
inst✝¹⁰ : NormedSpace 𝕜 F
inst✝⁹ : NormedAddCommGroup F'
inst✝⁸ : NormedSpace 𝕜 F'
inst✝⁷ : NormedSpace ℝ F'
inst✝⁶ : CompleteSpace F'
inst✝⁵ : NormedAddCo... | case neg
α : Type u_1
β : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
G' : Type u_6
𝕜 : Type u_7
p : ℝ≥0∞
inst✝¹² : RCLike 𝕜
inst✝¹¹ : NormedAddCommGroup F
inst✝¹⁰ : NormedSpace 𝕜 F
inst✝⁹ : NormedAddCommGroup F'
inst✝⁸ : NormedSpace 𝕜 F'
inst✝⁷ : NormedSpace ℝ F'
inst✝⁶ : CompleteSpace F'
inst✝⁵ : NormedAddCo... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) ((:c Subtype) ((:c MeasureTheory.AEEqFun) (:fv _uniq.115055) (:fv _uniq.115067) (:fv _uniq.115748) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.115067) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.115067) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"G'","sexp":"(:sort (+ u_6 1))"},{"name":"𝕜","sexp":"(:sort (+ u_7 1))"},{"name":"p","sexp":"(:c ENNReal)"},{... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c MeasureTheory.AEEqFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.115055","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.115058","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp_rw","sourceEnd":11144,"sourceStart":11137,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11146,"sourceStart":11145,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name"... | [] | [{"source":"condexpIndL1_of_not_measurableSet hs","source_end":11182,"source_start":11146,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.115055","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.115058","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 47 | 10 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d5522626b83ec8fb1fc85cecd2396d5cfba48eb84b6844b9bc65ed358e078c51 | 153217074de6c1bd038e216405600bd7663068a31d9030ee7db9b3e89d5e70a5 | 425059a92f5785dcb44c9e7bab7fa36f996bd8ddc708a6a8ff73ee196d27c96a | 8110f82e73b5f130f8f952024935a6c0ac825c05bbda379cb15650bb36b2da08 |
cat-searcher/leandojo-benchmark-4-random | test | 2,593 | MeasureTheory.norm_condexpIndL1_le | Mathlib/MeasureTheory/Function/ConditionalExpectation/CondexpL1.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.Lp.norm_zero</a>] | case neg
α : Type u_1
β : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
G' : Type u_6
𝕜 : Type u_7
p : ℝ≥0∞
inst✝¹² : RCLike 𝕜
inst✝¹¹ : NormedAddCommGroup F
inst✝¹⁰ : NormedSpace 𝕜 F
inst✝⁹ : NormedAddCommGroup F'
inst✝⁸ : NormedSpace 𝕜 F'
inst✝⁷ : NormedSpace ℝ F'
inst✝⁶ : CompleteSpace F'
inst✝⁵ : NormedAddCo... | case neg
α : Type u_1
β : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
G' : Type u_6
𝕜 : Type u_7
p : ℝ≥0∞
inst✝¹² : RCLike 𝕜
inst✝¹¹ : NormedAddCommGroup F
inst✝¹⁰ : NormedSpace 𝕜 F
inst✝⁹ : NormedAddCommGroup F'
inst✝⁸ : NormedSpace 𝕜 F'
inst✝⁷ : NormedSpace ℝ F'
inst✝⁶ : CompleteSpace F'
inst✝⁵ : NormedAddCo... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) ((:c Subtype) ((:c MeasureTheory.AEEqFun) (:fv _uniq.115055) (:fv _uniq.115067) (:fv _uniq.115748) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.115067) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.115067) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"G'","sexp":"(:sort (+ u_6 1))"},{"name":"𝕜","sexp":"(:sort (+ u_7 1))"},{"name":"p","sexp":"(:c ENNReal)"},{... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c MeasureTheory.AEEqFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.115055","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.115058","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":11187,"sourceStart":11185,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11189,"sourceStart":11188,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MeasureTheory.Lp... | [] | [{"source":"Lp.norm_zero","source_end":11201,"source_start":11189,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.115055","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.115058","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 47 | 14 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b968d962f41c7aff55ec2cb2e080606c50dc1454e42c08dd71d6d6f51a039d69 | 8110f82e73b5f130f8f952024935a6c0ac825c05bbda379cb15650bb36b2da08 | 1addb266eb2832c7e6f0916056bcf32508d786b8cbc1e889898ed6c03226f53f | 944d6cfd4c024f99b350f3b3fefb6f0c275c19f04216c95a9a82b9abbd497387 |
cat-searcher/leandojo-benchmark-4-random | test | 2,594 | MeasureTheory.norm_condexpIndL1_le | Mathlib/MeasureTheory/Function/ConditionalExpectation/CondexpL1.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>mul_nonneg</a> <a>ENNReal.toReal_nonneg</a> (<a>norm_nonneg</a> _) | case neg
α : Type u_1
β : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
G' : Type u_6
𝕜 : Type u_7
p : ℝ≥0∞
inst✝¹² : RCLike 𝕜
inst✝¹¹ : NormedAddCommGroup F
inst✝¹⁰ : NormedSpace 𝕜 F
inst✝⁹ : NormedAddCommGroup F'
inst✝⁸ : NormedSpace 𝕜 F'
inst✝⁷ : NormedSpace ℝ F'
inst✝⁶ : CompleteSpace F'
inst✝⁵ : NormedAddCo... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c ENNReal.toReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.115055) (:fv _uniq.11574... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"G'","sexp":"(:sort (+ u_6 1))"},{"name":"𝕜","sexp":"(:sort (+ u_7 1))"},{"name":"p","sexp":"(:c ENNReal)"},{... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.115055","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.115058","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":11212,"sourceStart":11207,"tag":"atom"},{"children":[{"name":"mul_nonneg","semanticRole":"global","source":"mul_nonneg","sourceEnd":11223,"sourceStart":11213,"tag":"identifier"},{"children":[{"name":"ENNReal.toReal_nonneg","semanticRole":"global","source":"ENNReal.toReal_nonne... | [] | [{"source":"mul_nonneg ENNReal.toReal_nonneg (norm_nonneg _)","source_end":11261,"source_start":11213,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.115055","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.115058","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 47 | 17 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 271d5b2419e5580b4ff46e8548eb64486597a3bea4f450a67c31244694510c3b | 944d6cfd4c024f99b350f3b3fefb6f0c275c19f04216c95a9a82b9abbd497387 | 7c23dd7d7a07581b25f8eed3807289780350451700153191bc498a37d63d5cf9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,595 | MeasureTheory.norm_condexpIndL1_le | Mathlib/MeasureTheory/Function/ConditionalExpectation/CondexpL1.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.condexpIndL1_of_measure_eq_top</a> hμs x, <a>MeasureTheory.Lp.norm_zero</a>] | case pos
α : Type u_1
β : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
G' : Type u_6
𝕜 : Type u_7
p : ℝ≥0∞
inst✝¹² : RCLike 𝕜
inst✝¹¹ : NormedAddCommGroup F
inst✝¹⁰ : NormedSpace 𝕜 F
inst✝⁹ : NormedAddCommGroup F'
inst✝⁸ : NormedSpace 𝕜 F'
inst✝⁷ : NormedSpace ℝ F'
inst✝⁶ : CompleteSpace F'
inst✝⁵ : NormedAddCo... | case pos
α : Type u_1
β : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
G' : Type u_6
𝕜 : Type u_7
p : ℝ≥0∞
inst✝¹² : RCLike 𝕜
inst✝¹¹ : NormedAddCommGroup F
inst✝¹⁰ : NormedSpace 𝕜 F
inst✝⁹ : NormedAddCommGroup F'
inst✝⁸ : NormedSpace 𝕜 F'
inst✝⁷ : NormedSpace ℝ F'
inst✝⁶ : CompleteSpace F'
inst✝⁵ : NormedAddCo... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) ((:c Subtype) ((:c MeasureTheory.AEEqFun) (:fv _uniq.115055) (:fv _uniq.115067) (:fv _uniq.115748) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.115067) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.115067) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"G'","sexp":"(:sort (+ u_6 1))"},{"name":"𝕜","sexp":"(:sort (+ u_7 1))"},{"name":"p","sexp":"(:c ENNReal)"},{... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c MeasureTheory.AEEqFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.115055","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.115058","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":11298,"sourceStart":11296,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11300,"sourceStart":11299,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Mea... | [] | [{"source":"condexpIndL1_of_measure_eq_top hμs x","source_end":11337,"source_start":11300,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Lp.norm_zero","source_end":11351,"source_start":11339,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.115055","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.115058","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 47 | 23 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 85ccec214b893b4a21a2ecd63c4ec7d92afe2e793705d55def09c32557937338 | 04b86df57bc762c1b3ff2c408fc585f6ae329de03d78bc43fa5b6bc384dffdbb | 4823367d4a6d9edeb5fd7dfa018c79ff793b7e260fac2168894bf90b6596032b | 5c811c1c6338e989a559aa5c8a3c5b3978ee962d6ae3c5a92f7de7b6d1f93788 |
cat-searcher/leandojo-benchmark-4-random | test | 2,596 | MeasureTheory.norm_condexpIndL1_le | Mathlib/MeasureTheory/Function/ConditionalExpectation/CondexpL1.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>mul_nonneg</a> <a>ENNReal.toReal_nonneg</a> (<a>norm_nonneg</a> _) | case pos
α : Type u_1
β : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
G' : Type u_6
𝕜 : Type u_7
p : ℝ≥0∞
inst✝¹² : RCLike 𝕜
inst✝¹¹ : NormedAddCommGroup F
inst✝¹⁰ : NormedSpace 𝕜 F
inst✝⁹ : NormedAddCommGroup F'
inst✝⁸ : NormedSpace 𝕜 F'
inst✝⁷ : NormedSpace ℝ F'
inst✝⁶ : CompleteSpace F'
inst✝⁵ : NormedAddCo... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c ENNReal.toReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.115055) (:fv _uniq.11574... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"G'","sexp":"(:sort (+ u_6 1))"},{"name":"𝕜","sexp":"(:sort (+ u_7 1))"},{"name":"p","sexp":"(:c ENNReal)"},{... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.115055","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.115058","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":11362,"sourceStart":11357,"tag":"atom"},{"children":[{"name":"mul_nonneg","semanticRole":"global","source":"mul_nonneg","sourceEnd":11373,"sourceStart":11363,"tag":"identifier"},{"children":[{"name":"ENNReal.toReal_nonneg","semanticRole":"global","source":"ENNReal.toReal_nonne... | [] | [{"source":"mul_nonneg ENNReal.toReal_nonneg (norm_nonneg _)","source_end":11411,"source_start":11363,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.115055","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.115058","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 47 | 27 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9daeb098df5b1d11f3176f2f1398487d9bec8eb76fa3d49cf4d132dfab4f6eb4 | 5c811c1c6338e989a559aa5c8a3c5b3978ee962d6ae3c5a92f7de7b6d1f93788 | 7c23dd7d7a07581b25f8eed3807289780350451700153191bc498a37d63d5cf9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,597 | MeasureTheory.norm_condexpIndL1_le | Mathlib/MeasureTheory/Function/ConditionalExpectation/CondexpL1.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.condexpIndL1_of_measurableSet_of_measure_ne_top</a> hs hμs x] | case neg
α : Type u_1
β : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
G' : Type u_6
𝕜 : Type u_7
p : ℝ≥0∞
inst✝¹² : RCLike 𝕜
inst✝¹¹ : NormedAddCommGroup F
inst✝¹⁰ : NormedSpace 𝕜 F
inst✝⁹ : NormedAddCommGroup F'
inst✝⁸ : NormedSpace 𝕜 F'
inst✝⁷ : NormedSpace ℝ F'
inst✝⁶ : CompleteSpace F'
inst✝⁵ : NormedAddCo... | case neg
α : Type u_1
β : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
G' : Type u_6
𝕜 : Type u_7
p : ℝ≥0∞
inst✝¹² : RCLike 𝕜
inst✝¹¹ : NormedAddCommGroup F
inst✝¹⁰ : NormedSpace 𝕜 F
inst✝⁹ : NormedAddCommGroup F'
inst✝⁸ : NormedSpace 𝕜 F'
inst✝⁷ : NormedSpace ℝ F'
inst✝⁶ : CompleteSpace F'
inst✝⁵ : NormedAddCo... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) ((:c Subtype) ((:c MeasureTheory.AEEqFun) (:fv _uniq.115055) (:fv _uniq.115067) (:fv _uniq.115748) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.115067) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.115067) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"G'","sexp":"(:sort (+ u_6 1))"},{"name":"𝕜","sexp":"(:sort (+ u_7 1))"},{"name":"p","sexp":"(:c ENNReal)"},{... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c MeasureTheory.AEEqFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.115055","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.115058","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":11419,"sourceStart":11417,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11421,"sourceStart":11420,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Mea... | [] | [{"source":"condexpIndL1_of_measurableSet_of_measure_ne_top hs hμs x","source_end":11478,"source_start":11421,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.115055","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.115058","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 47 | 32 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 58d59d2e34ea083d65db60c2564c9120bec241f6cb4264bf0d0fed4c0a872ce5 | a5cfd3377de84bb47bb5ce116c4979292dcb704a7d80da08499ee52434e9200b | 85582c488f345649684f53c6eb80ebc05e61f728bb2f4114533b5c1337f32d4f | 9db6c1a57a019f0227798359ec3ba671286a20a076f88d581601c7cda1312104 |
cat-searcher/leandojo-benchmark-4-random | test | 2,598 | MeasureTheory.norm_condexpIndL1_le | Mathlib/MeasureTheory/Function/ConditionalExpectation/CondexpL1.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>MeasureTheory.norm_condexpIndL1Fin_le</a> hs hμs x | case neg
α : Type u_1
β : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
G' : Type u_6
𝕜 : Type u_7
p : ℝ≥0∞
inst✝¹² : RCLike 𝕜
inst✝¹¹ : NormedAddCommGroup F
inst✝¹⁰ : NormedSpace 𝕜 F
inst✝⁹ : NormedAddCommGroup F'
inst✝⁸ : NormedSpace 𝕜 F'
inst✝⁷ : NormedSpace ℝ F'
inst✝⁶ : CompleteSpace F'
inst✝⁵ : NormedAddCo... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) ((:c Subtype) ((:c MeasureTheory.AEEqFun) (:fv _uniq.115055) (:fv _uniq.115067) (:fv _uniq.115748) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.115067) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.115067) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"G'","sexp":"(:sort (+ u_6 1))"},{"name":"𝕜","sexp":"(:sort (+ u_7 1))"},{"name":"p","sexp":"(:c ENNReal)"},{... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c MeasureTheory.AEEqFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.115055","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.115058","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":11489,"sourceStart":11484,"tag":"atom"},{"children":[{"name":"MeasureTheory.norm_condexpIndL1Fin_le","semanticRole":"global","source":"norm_condexpIndL1Fin_le","sourceEnd":11513,"sourceStart":11490,"tag":"identifier"},{"children":[{"contextIndex":29,"semanticRole":"local","sou... | [] | [{"source":"norm_condexpIndL1Fin_le hs hμs x","source_end":11523,"source_start":11490,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.115055","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.115058","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 47 | 35 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4dc3026bb5e847af3faa2f3e9608c5c1bd2bdd42b76a744450ea33198f0e1dd5 | 9db6c1a57a019f0227798359ec3ba671286a20a076f88d581601c7cda1312104 | 3cc3d91f86b885cb18e6d0e4687a0094227f989621b87367c67970d50f30daf9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,599 | Function.Antiperiodic.add | Mathlib/Algebra/Periodic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_all [← <a>add_assoc</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
f g : α → β
c c₁ c₂ x : α
inst✝¹ : AddGroup α
inst✝ : InvolutiveNeg β
h1 : Antiperiodic f c₁
h2 : Antiperiodic f c₂
⊢ Periodic f (c₁ + c₂) | ((:c Function.Periodic) (:fv _uniq.222183) (:fv _uniq.222186) ((:c AddSemigroup.toAdd) (:fv _uniq.222183) ((:c AddMonoid.toAddSemigroup) (:fv _uniq.222183) ((:c SubNegMonoid.toAddMonoid) (:fv _uniq.222183) ((:c AddGroup.toSubNegMonoid) (:fv _uniq.222183) (:fv _uniq.224227))))) (:fv _uniq.222193) ((:c HAdd.hAdd) (:fv _u... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.222183) (:fv _uniq.222186))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.222183) (:fv _uniq.222186))"},{"name":"c","sexp":"(:fv _uniq.222183)"},{"name":"c₁","... | (:app (:c Function.Periodic) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Add) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 3 (:fv FV3)) (:arg :explicit 4 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.222183","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222186","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp_all","sourceEnd":29718,"sourceStart":29710,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","so... | [] | [{"source":"add_assoc","source_end":29733,"source_start":29724,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.222183","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222186","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 209 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ec18e06aa2d22deefb613b3ceca5d5f65ce99665907e763436f149d3a020cbef | c8a8810c8fbce9de369dc87a35ddf745ca21de68b4b5af80633e9aa7ef1ffb07 | e3da0a95421f5a21ab540f1ef2107c0a0442da23d545e8bf571c2f0a4dcd2e6d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,600 | MulMemClass.mul_mem_add_closure | Mathlib/Algebra/Group/Submonoid/Membership.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | revert a | M : Type u_1
A : Type u_2
B : Type u_3
R : Type u_4
inst✝² : NonUnitalNonAssocSemiring R
inst✝¹ : SetLike M R
inst✝ : MulMemClass M R
S : M
a b : R
ha : a ∈ AddSubmonoid.closure ↑S
hb : b ∈ AddSubmonoid.closure ↑S
⊢ a * b ∈ AddSubmonoid.closure ↑S | M : Type u_1
A : Type u_2
B : Type u_3
R : Type u_4
inst✝² : NonUnitalNonAssocSemiring R
inst✝¹ : SetLike M R
inst✝ : MulMemClass M R
S : M
b : R
hb : b ∈ AddSubmonoid.closure ↑S
⊢ ∀ {a : R}, a ∈ AddSubmonoid.closure ↑S → a * b ∈ AddSubmonoid.closure ↑S | ((:c Membership.mem) (:fv _uniq.119715) ((:c AddSubmonoid) (:fv _uniq.119715) ((:c AddMonoid.toAddZeroClass) (:fv _uniq.119715) ((:c AddCommMonoid.toAddMonoid) (:fv _uniq.119715) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.119715) (:fv _uniq.119718))))) ((:c SetLike.instMembership) ((:c AddSubmonoid) (:f... | [{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝²","sexp":"((:c NonUnitalNonAssocSemiring) (:fv _uniq.119715))"},{"name":"inst✝¹","sexp":"((:c SetLike) (:fv _uniq.119706) (:fv _uniq.119715))"},... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c AddSubmonoid) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c AddZeroClass) (:arg :explicit 0 (:fv FV3))))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV3)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119706","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119709","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"revert","sourceEnd":33379,"sourceStart":33373,"tag":"atom"},{"children":[{"contextIndex":8,"semanticRole":"local","source":"a","sourceEnd":33381,"sourceStart":33380,"tag":"identifier"}],"kind":"null","source":"a","sourceEnd":33381,"sourceStart":33380,"tag":"node"}],"kind":"Lean.Parser.Tactic.rev... | [] | [{"source":"a","source_end":33381,"source_start":33380,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119706","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119709","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 242 | 4 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e53b81c3ff5cc36a7e88784d22721d8de1926fac65d59e0d79b6da401bf47dd1 | 1c0e0805e61ddefe207415749badd8c2bf4c0e1b0cb82b8da6e0560c005e3950 | a45796021adb705601308dbe4a0ee2ad0c154a34a7e73413baf54d570db73dc5 | 48e18af18c9d8c1ed44ec2d56801a1682733a22c75e26bd0fdee2f12352fe83e |
cat-searcher/leandojo-benchmark-4-random | test | 2,601 | MulMemClass.mul_mem_add_closure | Mathlib/Algebra/Group/Submonoid/Membership.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply @<a>AddSubmonoid.closure_induction</a> _ _ _ (fun z => ∀ {a : R}, a ∈ <a>AddSubmonoid.closure</a> ↑S → a * z ∈ <a>AddSubmonoid.closure</a> ↑S) _ hb <;> clear hb b | M : Type u_1
A : Type u_2
B : Type u_3
R : Type u_4
inst✝² : NonUnitalNonAssocSemiring R
inst✝¹ : SetLike M R
inst✝ : MulMemClass M R
S : M
b : R
hb : b ∈ AddSubmonoid.closure ↑S
⊢ ∀ {a : R}, a ∈ AddSubmonoid.closure ↑S → a * b ∈ AddSubmonoid.closure ↑S | case mem
M : Type u_1
A : Type u_2
B : Type u_3
R : Type u_4
inst✝² : NonUnitalNonAssocSemiring R
inst✝¹ : SetLike M R
inst✝ : MulMemClass M R
S : M
⊢ ∀ x ∈ ↑S, ∀ {a : R}, a ∈ AddSubmonoid.closure ↑S → a * x ∈ AddSubmonoid.closure ↑S
case one
M : Type u_1
A : Type u_2
B : Type u_3
R : Type u_4
inst✝² : NonUnitalNonAsso... | (:forall a (:fv _uniq.119715) (:forall ha ((:c Membership.mem) (:fv _uniq.119715) ((:c AddSubmonoid) (:fv _uniq.119715) ((:c AddMonoid.toAddZeroClass) (:fv _uniq.119715) ((:c AddCommMonoid.toAddMonoid) (:fv _uniq.119715) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.119715) (:fv _uniq.119718))))) ((:c SetL... | [{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝²","sexp":"((:c NonUnitalNonAssocSemiring) (:fv _uniq.119715))"},{"name":"inst✝¹","sexp":"((:c SetLike) (:fv _uniq.119706) (:fv _uniq.119715))"},... | (:forall a :implicit (:fv FV3) (:forall ha :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c AddSubmonoid) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c AddZeroClass) (:arg :explicit 0 (:fv FV3))))))) (:arg :instance 2 (:instance-of (:app (:c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119706","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119709","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"source":"apply","sourceEnd":33389,"sourceStart":33384,"tag":"atom"},{"children":[{"children":[{"source":"@","sourceEnd":33391,"sourceStart":33390,"tag":"atom"},{"name":"AddSubmonoid.closure_induction","semanticRole":"global","source":"AddSubmonoid.closure_induction","sourceEnd":33421,"source... | [] | [{"source":"@AddSubmonoid.closure_induction _ _ _\n (fun z => ∀ {a : R}, a ∈ AddSubmonoid.closure ↑S → a * z ∈ AddSubmonoid.closure ↑S)\n _ hb","source_end":33538,"source_start":33390,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hb","source_end":33551,"source_start":33549,"syntax_kind":"ident"},{"source":"b... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119706","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119709","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 242 | 5 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7615607298ddf15c892596af91279ee4dd493c4785568f68c075edf42786ee76 | 48e18af18c9d8c1ed44ec2d56801a1682733a22c75e26bd0fdee2f12352fe83e | c3815119d98b5a47007298d3c12faa58c8d4adcb0e91214856c5b2150dc95084 | 3622cbf94cae695e49d74d30e1b757b124ab453a3354daf5281c4fe8937b9951 |
cat-searcher/leandojo-benchmark-4-random | test | 2,602 | MulMemClass.mul_mem_add_closure | Mathlib/Algebra/Group/Submonoid/Membership.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun r hr b hb => <a>MulMemClass.mul_right_mem_add_closure</a> hb hr | case mem
M : Type u_1
A : Type u_2
B : Type u_3
R : Type u_4
inst✝² : NonUnitalNonAssocSemiring R
inst✝¹ : SetLike M R
inst✝ : MulMemClass M R
S : M
⊢ ∀ x ∈ ↑S, ∀ {a : R}, a ∈ AddSubmonoid.closure ↑S → a * x ∈ AddSubmonoid.closure ↑S | (:forall x (:fv _uniq.119715) (:forall _ ((:c Membership.mem) (:fv _uniq.119715) ((:c Set) (:fv _uniq.119715)) ((:c Set.instMembership) (:fv _uniq.119715)) 0 ((:c SetLike.coe) (:fv _uniq.119706) (:fv _uniq.119715) (:fv _uniq.119722) (:fv _uniq.119844))) (:forall a (:fv _uniq.119715) (:forall _ ((:c Membership.mem) (:fv... | [{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝²","sexp":"((:c NonUnitalNonAssocSemiring) (:fv _uniq.119715))"},{"name":"inst✝¹","sexp":"((:c SetLike) (:fv _uniq.119706) (:fv _uniq.119715))"},... | (:forall x :explicit (:fv FV3) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119706","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119709","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":33564,"sourceStart":33559,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":33568,"sourceStart":33565,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"r","sourceEnd":33570,"sourceStart":33569,"tag":"id... | [] | [{"source":"fun r hr b hb => MulMemClass.mul_right_mem_add_closure hb hr","source_end":33625,"source_start":33565,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119706","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119709","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 242 | 13 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cccb7f0f5840b9607760cf01598a498f71e6c4b02e2cf52c51839a3b9fa13a8d | 4515eda3abb5e7e0b94cabf07beff3683f07c376124e35a72af88aaa788ae8b3 | 32c90680475ce2f0ca00d3828fe5a4a0029660dda950b743d81d25bfb9b5d596 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,603 | MulMemClass.mul_mem_add_closure | Mathlib/Algebra/Group/Submonoid/Membership.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun _ => by simp only [<a>MulZeroClass.mul_zero</a>, (<a>AddSubmonoid.closure</a> (S : <a>Set</a> R)).<a>AddSubmonoid.zero_mem</a>] | case one
M : Type u_1
A : Type u_2
B : Type u_3
R : Type u_4
inst✝² : NonUnitalNonAssocSemiring R
inst✝¹ : SetLike M R
inst✝ : MulMemClass M R
S : M
⊢ ∀ {a : R}, a ∈ AddSubmonoid.closure ↑S → a * 0 ∈ AddSubmonoid.closure ↑S | (:forall a (:fv _uniq.119715) (:forall _ ((:c Membership.mem) (:fv _uniq.119715) ((:c AddSubmonoid) (:fv _uniq.119715) ((:c AddMonoid.toAddZeroClass) (:fv _uniq.119715) ((:c AddCommMonoid.toAddMonoid) (:fv _uniq.119715) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.119715) (:fv _uniq.119718))))) ((:c SetLi... | [{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝²","sexp":"((:c NonUnitalNonAssocSemiring) (:fv _uniq.119715))"},{"name":"inst✝¹","sexp":"((:c SetLike) (:fv _uniq.119706) (:fv _uniq.119715))"},... | (:forall a :implicit (:fv FV3) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c AddSubmonoid) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c AddZeroClass) (:arg :explicit 0 (:fv FV3))))))) (:arg :instance 2 (:instance-of (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119706","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119709","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":33636,"sourceStart":33631,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":33640,"sourceStart":33637,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"_","sourceEnd":33642,"sourceStart":33641,"tag":"atom"}],"kind":"Lea... | [] | [{"source":"fun _ => by simp only [mul_zero, (AddSubmonoid.closure (S : Set R)).zero_mem]","source_end":33714,"source_start":33637,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119706","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119709","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 242 | 18 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eec66d6f75b9bcb7fe7f41df68cd7c06f322b822b0fd09ea3fd7ea6ae34e46f3 | 6fcd9bb2e58249619e320427b64c69616fd7cc00a9e061c972d56dc5741b73dc | 3aa38512a077b5354d53068c41dfc6a806f8a03621f3be1e551784e618010180 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,604 | MulMemClass.mul_mem_add_closure | Mathlib/Algebra/Group/Submonoid/Membership.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>MulZeroClass.mul_zero</a>, (<a>AddSubmonoid.closure</a> (S : <a>Set</a> R)).<a>AddSubmonoid.zero_mem</a>] | M : Type u_1
A : Type u_2
B : Type u_3
R : Type u_4
inst✝² : NonUnitalNonAssocSemiring R
inst✝¹ : SetLike M R
inst✝ : MulMemClass M R
S : M
a✝ : R
x✝ : a✝ ∈ AddSubmonoid.closure ↑S
⊢ a✝ * 0 ∈ AddSubmonoid.closure ↑S | ((:c Membership.mem) (:fv _uniq.119715) ((:c AddSubmonoid) (:fv _uniq.119715) ((:c AddMonoid.toAddZeroClass) (:fv _uniq.119715) ((:c AddCommMonoid.toAddMonoid) (:fv _uniq.119715) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.119715) (:fv _uniq.119718))))) ((:c SetLike.instMembership) ((:c AddSubmonoid) (:f... | [{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝²","sexp":"((:c NonUnitalNonAssocSemiring) (:fv _uniq.119715))"},{"name":"inst✝¹","sexp":"((:c SetLike) (:fv _uniq.119706) (:fv _uniq.119715))"},... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c AddSubmonoid) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c AddZeroClass) (:arg :explicit 0 (:fv FV3))))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV3)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119706","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119709","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":33653,"sourceStart":33649,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":33658,"sourceStart":33654,"tag":"atom"}],"kind"... | [] | [{"source":"mul_zero","source_end":33668,"source_start":33660,"syntax_kind":"ident"},{"source":"(AddSubmonoid.closure (S : Set R)).zero_mem","source_end":33713,"source_start":33670,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119706","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119709","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 242 | 23 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 21b234ddb81fff255f026bc15cbfdf178dfa966f8e30ca3a2408396c146473af | 04a937c3eb5ea1308d4466b2ac425a40bdc8d131cc4ab5255a125a68744632c0 | 29aaa97bdb897ab264a51b76afab1b2055ea88e87177ac24df676061f114f16e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,605 | MulMemClass.mul_mem_add_closure | Mathlib/Algebra/Group/Submonoid/Membership.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>mul_add</a>] | case mul
M : Type u_1
A : Type u_2
B : Type u_3
R : Type u_4
inst✝² : NonUnitalNonAssocSemiring R
inst✝¹ : SetLike M R
inst✝ : MulMemClass M R
S : M
⊢ ∀ (x y : R),
(∀ {a : R}, a ∈ AddSubmonoid.closure ↑S → a * x ∈ AddSubmonoid.closure ↑S) →
(∀ {a : R}, a ∈ AddSubmonoid.closure ↑S → a * y ∈ AddSubmonoid.closur... | case mul
M : Type u_1
A : Type u_2
B : Type u_3
R : Type u_4
inst✝² : NonUnitalNonAssocSemiring R
inst✝¹ : SetLike M R
inst✝ : MulMemClass M R
S : M
⊢ ∀ (x y : R),
(∀ {a : R}, a ∈ AddSubmonoid.closure ↑S → a * x ∈ AddSubmonoid.closure ↑S) →
(∀ {a : R}, a ∈ AddSubmonoid.closure ↑S → a * y ∈ AddSubmonoid.closur... | (:forall x (:fv _uniq.119715) (:forall y (:fv _uniq.119715) (:forall _ (:forall a (:fv _uniq.119715) (:forall _ ((:c Membership.mem) (:fv _uniq.119715) ((:c AddSubmonoid) (:fv _uniq.119715) ((:c AddMonoid.toAddZeroClass) (:fv _uniq.119715) ((:c AddCommMonoid.toAddMonoid) (:fv _uniq.119715) ((:c NonUnitalNonAssocSemirin... | [{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝²","sexp":"((:c NonUnitalNonAssocSemiring) (:fv _uniq.119715))"},{"name":"inst✝¹","sexp":"((:c SetLike) (:fv _uniq.119706) (:fv _uniq.119715))"},... | (:forall x :explicit (:fv FV3) (:forall y :explicit (:fv FV3) (:forall _ :explicit (:forall a :implicit (:fv FV3) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c AddSubmonoid) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c AddZero... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119706","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119709","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp_rw","sourceEnd":33727,"sourceStart":33720,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":33729,"sourceStart":33728,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"mul_add","s... | [] | [{"source":"mul_add","source_end":33736,"source_start":33729,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119706","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119709","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 242 | 30 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2d53c877bcde78bb974641e92c06204998aa2c9375932d7f1d28271928d1e56d | a60a16919345363541d5be1a1c862295f3445f21fd5a5b43d0f2ac1b72c04ae0 | 23b82807147a7d5aa706b83488b9fb23d624cb9da143683854a9c627f3955bed | 23ee66445e8bc3db9d2b66832a04b3a48b41f938ccd12b9bffd7ddec335ddf1d |
cat-searcher/leandojo-benchmark-4-random | test | 2,606 | MulMemClass.mul_mem_add_closure | Mathlib/Algebra/Group/Submonoid/Membership.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun r s hr hs b hb => (<a>AddSubmonoid.closure</a> (S : <a>Set</a> R)).<a>AddSubmonoid.add_mem</a> (hr hb) (hs hb) | case mul
M : Type u_1
A : Type u_2
B : Type u_3
R : Type u_4
inst✝² : NonUnitalNonAssocSemiring R
inst✝¹ : SetLike M R
inst✝ : MulMemClass M R
S : M
⊢ ∀ (x y : R),
(∀ {a : R}, a ∈ AddSubmonoid.closure ↑S → a * x ∈ AddSubmonoid.closure ↑S) →
(∀ {a : R}, a ∈ AddSubmonoid.closure ↑S → a * y ∈ AddSubmonoid.closur... | (:forall x (:fv _uniq.119715) (:forall y (:fv _uniq.119715) (:forall _ (:forall a (:fv _uniq.119715) (:forall _ ((:c Membership.mem) (:fv _uniq.119715) ((:c AddSubmonoid) (:fv _uniq.119715) ((:c AddMonoid.toAddZeroClass) (:fv _uniq.119715) ((:c AddCommMonoid.toAddMonoid) (:fv _uniq.119715) ((:c NonUnitalNonAssocSemirin... | [{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝²","sexp":"((:c NonUnitalNonAssocSemiring) (:fv _uniq.119715))"},{"name":"inst✝¹","sexp":"((:c SetLike) (:fv _uniq.119706) (:fv _uniq.119715))"},... | (:forall x :explicit (:fv FV3) (:forall y :explicit (:fv FV3) (:forall _ :explicit (:forall a :implicit (:fv FV3) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c AddSubmonoid) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c AddZero... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119706","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119709","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":33747,"sourceStart":33742,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":33751,"sourceStart":33748,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"r","sourceEnd":33753,"sourceStart":33752,"tag":"identifier"},{"semanticRole":"scoped_loca... | [] | [{"source":"fun r s hr hs b hb => (AddSubmonoid.closure (S : Set R)).add_mem (hr hb) (hs hb)","source_end":33828,"source_start":33748,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119706","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119709","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 242 | 33 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c93846dd423378470e8a0be45ed76617f463507efb95653c326156cb29b7ae2d | 23ee66445e8bc3db9d2b66832a04b3a48b41f938ccd12b9bffd7ddec335ddf1d | fc01e10bcf0a716dd0cb7b2b52e57b8f5bbaeaf71e43b19901a799c6d8ad4a36 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,607 | Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map | Mathlib/RingTheory/Polynomial/GaussLemma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases h_dvd with ⟨r, hr⟩ | R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
h_dvd : map (algebraMap R K) p ∣ map (algebraMap R K) q
⊢ p ∣ q | case intro
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
⊢ p ∣ q | ((:c Dvd.dvd) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv _uniq.79792)))) ((:c semigroupDvd) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.79789))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.79795))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.79789) (:fv _uniq.79795) ((:c CommRing.toCommSemiring) (:fv _uniq.7978... | (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:insta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"rcases","sourceEnd":15059,"sourceStart":15053,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":13,"semanticRole":"local","source":"h_dvd","sourceEnd":15065,"sourceStart":15060,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarge... | [] | [{"source":"h_dvd","source_end":15065,"source_start":15060,"syntax_kind":"ident"},{"source":"⟨r, hr⟩","source_end":15082,"source_start":15071,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"intern... | 47 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 119c9458ced0b9ecbd5717f9700d75196c325592d8cccbe4f86c7d88b6a5848e | 5cbc8f7a16d63a94701dc9341b0df5a55dd53fbb196f687b337ea31394e32307 | 73b8b12fc42e49697d8a50f3a799c121e9f1eaf5d17e4323a405f94f8b69b003 | 70ee91c750b0e379b8962354d137450c76934b67024f373fb7279fea2d223255 |
cat-searcher/leandojo-benchmark-4-random | test | 2,608 | Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map | Mathlib/RingTheory/Polynomial/GaussLemma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨⟨s, s0⟩, hs⟩ := <a>IsLocalization.integerNormalization_map_to_map</a> R⁰ r | case intro
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
⊢ p ∣ q | case intro.intro.mk
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : ... | ((:c Dvd.dvd) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv _uniq.79792)))) ((:c semigroupDvd) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.79789))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.79795))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.79789) (:fv _uniq.79795) ((:c CommRing.toCommSemiring) (:fv _uniq.7978... | (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:insta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"obtain","sourceEnd":15091,"sourceStart":15085,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":15095,"sourceStart":15092,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":15098,"sourceStart":15095,"... | [] | [{"source":"integerNormalization_map_to_map R⁰ r","source_end":15155,"source_start":15117,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨⟨s, s0⟩, hs⟩","source_end":15113,"source_start":15092,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"intern... | 47 | 5 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 08a1f908c65fb7f8cb66a28df007b0d96f63efaec4f022a41ab2c274e95277cb | 70ee91c750b0e379b8962354d137450c76934b67024f373fb7279fea2d223255 | 304f487a498df73f7b8f3acfb2d6c0d625d08707ba40bdae5797f7b11ac5b94a | 6260b223e232799dbada783287169ed78d17f5e604c03dcb533e922152339916 |
cat-searcher/leandojo-benchmark-4-random | test | 2,609 | Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map | Mathlib/RingTheory/Polynomial/GaussLemma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Subtype.coe_mk</a>, <a>Algebra.smul_def</a>, <a>Polynomial.algebraMap_apply</a>] at hs | case intro.intro.mk
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : ... | case intro.intro.mk
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : ... | ((:c Dvd.dvd) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv _uniq.79792)))) ((:c semigroupDvd) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.79789))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.79795))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.79789) (:fv _uniq.79795) ((:c CommRing.toCommSemiring) (:fv _uniq.7978... | (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:insta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"rw","sourceEnd":15160,"sourceStart":15158,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15162,"sourceStart":15161,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Subtype.coe_mk",... | [] | [{"source":"Subtype.coe_mk","source_end":15176,"source_start":15162,"syntax_kind":"ident"},{"source":"hs","source_end":15219,"source_start":15217,"syntax_kind":"ident"},{"source":"Algebra.smul_def","source_end":15194,"source_start":15178,"syntax_kind":"ident"},{"source":"algebraMap_apply","source_end":15212,"source_sta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"intern... | 47 | 6 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c4b0ba6f145aa68177d49634a002a7d142eb5b63881e6ffaecf3eb366057bc24 | 6260b223e232799dbada783287169ed78d17f5e604c03dcb533e922152339916 | a3a9c2afaec1f5cd5a8bf2bc702b652e04474850746b953dcf32b96466607210 | dcaea8265a7fd609b92c5d38a78deca69f5da974436833a147d3ca2b69dc7994 |
cat-searcher/leandojo-benchmark-4-random | test | 2,610 | Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map | Mathlib/RingTheory/Polynomial/GaussLemma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h : p ∣ q * <a>Polynomial.C</a> s := by use <a>IsLocalization.integerNormalization</a> R⁰ r apply <a>Polynomial.map_injective</a> (<a>algebraMap</a> R K) (<a>IsFractionRing.injective</a> _ _) rw [<a>Polynomial.map_mul</a>, <a>Polynomial.map_mul</a>, hs, hr, <a>mul_assoc</a>, <a>mul_comm</a> r] simp | case intro.intro.mk
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : ... | case intro.intro.mk
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : ... | ((:c Dvd.dvd) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv _uniq.79792)))) ((:c semigroupDvd) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.79789))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.79795))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.79789) (:fv _uniq.79795) ((:c CommRing.toCommSemiring) (:fv _uniq.7978... | (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:insta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"have","sourceEnd":15226,"sourceStart":15222,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":15228,"sourceStart":15227,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":15228,"sourceStart":15227,"tag":"node"... | [] | [{"source":"p ∣ q * C s","source_end":15244,"source_start":15231,"syntax_kind":"«term_∣_»"},{"source":"integerNormalization R⁰ r","source_end":15286,"source_start":15259,"syntax_kind":"Lean.Parser.Term.app"},{"source":"map_injective (algebraMap R K) (IsFractionRing.injective _ _)","source_end":15358,"source_start":1529... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"intern... | 47 | 11 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 17fcddc5a2bb76b826e1f50fa5d1f6cf8e589dca879f4e084b60a978f746306d | dcaea8265a7fd609b92c5d38a78deca69f5da974436833a147d3ca2b69dc7994 | 203d189d57d010233db42cea465d0aae9120691af0169e1e2cf12ad46b1e4aec | 3654efee8108ee42b55db79858665f1b37060559c046d602c49542f2d0781457 |
cat-searcher/leandojo-benchmark-4-random | test | 2,611 | Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map | Mathlib/RingTheory/Polynomial/GaussLemma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hp.dvd_primPart_iff_dvd, <a>Polynomial.primPart_mul</a>, hq.primPart_eq, <a>Associated.dvd_iff_dvd_right</a>] at h | case intro.intro.mk
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : ... | case intro.intro.mk
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : ... | ((:c Dvd.dvd) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv _uniq.79792)))) ((:c semigroupDvd) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.79789))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.79795))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.79789) (:fv _uniq.79795) ((:c CommRing.toCommSemiring) (:fv _uniq.7978... | (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:insta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"rw","sourceEnd":15451,"sourceStart":15449,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15453,"sourceStart":15452,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":15456,"sourceSt... | [] | [{"source":"hp.dvd_primPart_iff_dvd","source_end":15480,"source_start":15457,"syntax_kind":"ident"},{"source":"h","source_end":15546,"source_start":15545,"syntax_kind":"ident"},{"source":"primPart_mul","source_end":15494,"source_start":15482,"syntax_kind":"ident"},{"source":"hq.primPart_eq","source_end":15510,"source_s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"intern... | 47 | 24 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8714f8bcfe530527a2a58c0ccaf1896f76cd6d3f7eba93b531d650f7a5d01ddc | 3654efee8108ee42b55db79858665f1b37060559c046d602c49542f2d0781457 | 19469851e749003beb3e18f0e5ace4c11a7bb9afe18a872117ecc1e041313cc1 | c16de4ad273ca0662208e2306e52eb20d9916eac893eab947950710672dda63b |
cat-searcher/leandojo-benchmark-4-random | test | 2,613 | Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map | Mathlib/RingTheory/Polynomial/GaussLemma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | use <a>IsLocalization.integerNormalization</a> R⁰ r | R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : map (algebraMap R K)... | case h
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : map (algebraM... | ((:c Dvd.dvd) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv _uniq.79792)))) ((:c semigroupDvd) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.79789))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.79795))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.79789) (:fv _uniq.79795) ((:c CommRing.toCommSemiring) (:fv _uniq.7978... | (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:insta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"use","sourceEnd":15258,"sourceStart":15255,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"children":[{"name":"IsLocalization.integerNormalization","semanticRole":"global","source":"integerNormalization",... | [] | [{"source":"integerNormalization R⁰ r","source_end":15286,"source_start":15259,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"intern... | 47 | 13 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f4be216790594a7ae86251bbd9045d7bb102a5115072789a39b6a21ddada6b84 | 982d59e58b5b29286921105595c94fd4cd38be702c218949529e03a9f479d2a1 | b8de91f509f582cc9336201eb46328a4a591d8b7162af5af90294f643b5d2763 | c55660fd28cf34f79858bce87823015d06a65c31fa8e34b870eca73a5dbb0fc8 |
cat-searcher/leandojo-benchmark-4-random | test | 2,614 | Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map | Mathlib/RingTheory/Polynomial/GaussLemma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Polynomial.map_injective</a> (<a>algebraMap</a> R K) (<a>IsFractionRing.injective</a> _ _) | case h
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : map (algebraM... | case h.a
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : map (algebr... | ((:c Eq) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv _uniq.79792)))) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv _uniq.7... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.79789))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.79795))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.79789) (:fv _uniq.79795) ((:c CommRing.toCommSemiring) (:fv _uniq.7978... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"apply","sourceEnd":15296,"sourceStart":15291,"tag":"atom"},{"children":[{"name":"Polynomial.map_injective","semanticRole":"global","source":"map_injective","sourceEnd":15310,"sourceStart":15297,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":15312,"sourceStart":15311,"tag... | [] | [{"source":"map_injective (algebraMap R K) (IsFractionRing.injective _ _)","source_end":15358,"source_start":15297,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"intern... | 47 | 14 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e6ec342b15350979d253884c5073dde14bba4aeb5ce704e183068b7c8cfe216f | c55660fd28cf34f79858bce87823015d06a65c31fa8e34b870eca73a5dbb0fc8 | c77cea1c0377dafbdab995084e216812b00b74c725bb54fc8934facbd39ce97b | 077f57a57f93c69dd939588e39db35d20ab44a81d41caddfe4a561f76355a67a |
cat-searcher/leandojo-benchmark-4-random | test | 2,615 | Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map | Mathlib/RingTheory/Polynomial/GaussLemma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Polynomial.map_mul</a>, <a>Polynomial.map_mul</a>, hs, hr, <a>mul_assoc</a>, <a>mul_comm</a> r] | case h.a
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : map (algebr... | case h.a
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : map (algebr... | ((:c Eq) ((:c Polynomial) (:fv _uniq.79795) ((:c DivisionSemiring.toSemiring) (:fv _uniq.79795) ((:c Semifield.toDivisionSemiring) (:fv _uniq.79795) ((:c Field.toSemifield) (:fv _uniq.79795) (:fv _uniq.79798))))) ((:c Polynomial.map) (:fv _uniq.79789) (:fv _uniq.79795) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.79789))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.79795))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.79789) (:fv _uniq.79795) ((:c CommRing.toCommSemiring) (:fv _uniq.7978... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 1 (:app (:c Polynomial.map) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"rw","sourceEnd":15365,"sourceStart":15363,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15367,"sourceStart":15366,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Polynomial.map_m... | [] | [{"source":"Polynomial.map_mul","source_end":15385,"source_start":15367,"syntax_kind":"ident"},{"source":"Polynomial.map_mul","source_end":15405,"source_start":15387,"syntax_kind":"ident"},{"source":"hs","source_end":15409,"source_start":15407,"syntax_kind":"ident"},{"source":"hr","source_end":15413,"source_start":1541... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"intern... | 47 | 15 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2b2103441b55c0fbefa4ca25bdcabb2d1b1367e2de07938be46efc0239edab59 | 077f57a57f93c69dd939588e39db35d20ab44a81d41caddfe4a561f76355a67a | cdd892502f62fa3b820705f56f0a057f6c5ae58a11ee33c0bd869686a3e4f52b | d2818e6fe3d772bf4b75b27c96f0555b1c5de27fa2d4514f4655ba36cefe0397 |
cat-searcher/leandojo-benchmark-4-random | test | 2,616 | Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map | Mathlib/RingTheory/Polynomial/GaussLemma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case h.a
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : map (algebr... | ((:c Eq) ((:c Polynomial) (:fv _uniq.79795) ((:c DivisionSemiring.toSemiring) (:fv _uniq.79795) ((:c Semifield.toDivisionSemiring) (:fv _uniq.79795) ((:c Field.toSemifield) (:fv _uniq.79795) (:fv _uniq.79798))))) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.79795) ((:c DivisionSemiring.toSemiring) (:fv _uniq.79795) ((:c... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.79789))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.79795))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.79789) (:fv _uniq.79795) ((:c CommRing.toCommSemiring) (:fv _uniq.7978... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"simp","sourceEnd":15446,"sourceStart":15442,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"ki... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"intern... | 47 | 23 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a0d10b0bf067f883e6e31bb1e038a7405d6188968a4d9ce89cbc386a9c686212 | d2818e6fe3d772bf4b75b27c96f0555b1c5de27fa2d4514f4655ba36cefe0397 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,617 | Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map | Mathlib/RingTheory/Polynomial/GaussLemma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact h | case intro.intro.mk
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : ... | ((:c Dvd.dvd) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv _uniq.79792)))) ((:c semigroupDvd) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.79789))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.79795))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.79789) (:fv _uniq.79795) ((:c CommRing.toCommSemiring) (:fv _uniq.7978... | (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:insta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":15557,"sourceStart":15552,"tag":"atom"},{"contextIndex":19,"semanticRole":"local","source":"h","sourceEnd":15559,"sourceStart":15558,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact h","sourceEnd":15559,"sourceStart"... | [] | [{"source":"h","source_end":15559,"source_start":15558,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"intern... | 47 | 32 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 714e16189bfb37ddb6fe9624fa02a6cecc4f6ffad7e8f17626d034615f76bab2 | b57014ec27b83e74efe2d43d75353ec2a45186ae4458bbb1179b61fa734ec28d | c2ce0e21ffddde69d6a80e187a5bf12b7761df4be076519945be8ed7a7a77294 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,618 | Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map | Mathlib/RingTheory/Polynomial/GaussLemma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | symm | case intro.intro.mk
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : ... | case intro.intro.mk
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : ... | ((:c Associated) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv _uniq.79792)))) ((:c MonoidWithZero.toMonoid) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _un... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.79789))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.79795))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.79789) (:fv _uniq.79795) ((:c CommRing.toCommSemiring) (:fv _uniq.7978... | (:app (:c Associated) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"symm","sourceEnd":15569,"sourceStart":15565,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.symm","source":"symm","sourceEnd":15569,"sourceStart":15565,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"intern... | 47 | 39 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2bc481809b985485c6479e0d31a742717211367c569bd74276677f2e58425e54 | 3010610278ad937ce9547d9a5ae86cf2b5b8c54d5afc9cc1103e0ea25baf0ff0 | f97373c83b943be1711d624ac8176e49b7c19e0f5ce55ad3a0ad56d8d1aae1fa | f479145aa3fff4d6bfa88be6f08d377c58ecbb6bbbba9fc1f23ad7ea6b478c9f |
cat-searcher/leandojo-benchmark-4-random | test | 2,619 | Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map | Mathlib/RingTheory/Polynomial/GaussLemma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>Polynomial.isUnit_primPart_C</a> s with ⟨u, hu⟩ | case intro.intro.mk
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : ... | case intro.intro.mk.intro
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰... | ((:c Associated) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv _uniq.79792)))) ((:c MonoidWithZero.toMonoid) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _un... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.79789))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.79795))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.79789) (:fv _uniq.79795) ((:c CommRing.toCommSemiring) (:fv _uniq.7978... | (:app (:c Associated) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"rcases","sourceEnd":15580,"sourceStart":15574,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Polynomial.isUnit_primPart_C","semanticRole":"global","source":"isUnit_primPart_C","sourceEnd":15598,"sourceStart":15581,"tag":"ident... | [] | [{"source":"isUnit_primPart_C s","source_end":15600,"source_start":15581,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨u, hu⟩","source_end":15617,"source_start":15606,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"intern... | 47 | 40 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c6291c962566b90276268dac08a2135d9e0b0afd483f5dd5708501a214ea8546 | f479145aa3fff4d6bfa88be6f08d377c58ecbb6bbbba9fc1f23ad7ea6b478c9f | c61fed4db92a99c3a25e95939b1795e768a59d54f37d1e98a13bcac0c4bbf67c | a0ee6fe16cc2f1e74b62d620f86015b6cc8ff0e6ca89518bf2d1c16de5ee040f |
cat-searcher/leandojo-benchmark-4-random | test | 2,620 | Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map | Mathlib/RingTheory/Polynomial/GaussLemma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | use u | case intro.intro.mk.intro
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰... | case h
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : map (algebraM... | ((:c Associated) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv _uniq.79792)))) ((:c MonoidWithZero.toMonoid) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _un... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.79789))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.79795))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.79789) (:fv _uniq.79795) ((:c CommRing.toCommSemiring) (:fv _uniq.7978... | (:app (:c Associated) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"use","sourceEnd":15625,"sourceStart":15622,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"contextIndex":19,"semanticRole":"local","source":"u","sourceEnd":15627,"sourceStart":15626,"tag":"identifier"}],"... | [] | [{"source":"u","source_end":15627,"source_start":15626,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"intern... | 47 | 41 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3ae7a88d08c34d970cbba2d2fb6d5ad32959f0827e161a279de5d225223bcb5c | a0ee6fe16cc2f1e74b62d620f86015b6cc8ff0e6ca89518bf2d1c16de5ee040f | 8a81a8e37d5c6b1be320977bfc1be30e50741dee48a19983cbe63ebd391a109b | 03be7aaf78e178e504644c8b192c913c71b32e6a0bd106dd603072dcbad5c298 |
cat-searcher/leandojo-benchmark-4-random | test | 2,621 | Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map | Mathlib/RingTheory/Polynomial/GaussLemma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hu] | case h
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : map (algebraM... | ((:c Eq) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv _uniq.79792)))) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv _uniq.7... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.79789))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.79795))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.79789) (:fv _uniq.79795) ((:c CommRing.toCommSemiring) (:fv _uniq.7978... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"rw","sourceEnd":15634,"sourceStart":15632,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15636,"sourceStart":15635,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":20,"seman... | [] | [{"source":"hu","source_end":15638,"source_start":15636,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"intern... | 47 | 42 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f0153a6103abf61e0a647e91c20ff43a5cd676e0ab042a2cf766b90083b82d22 | 03be7aaf78e178e504644c8b192c913c71b32e6a0bd106dd603072dcbad5c298 | 4dd797ecc61ac2a0f756a4cfd23f08cbf68fbb8a9670e9ff74bd781adb50cbf7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,622 | Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map | Mathlib/RingTheory/Polynomial/GaussLemma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>mul_ne_zero</a> hq.ne_zero | case intro.intro.mk
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : ... | case intro.intro.mk
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : ... | ((:c Ne) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv _uniq.79792)))) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv _uniq.7... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.79789))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.79795))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.79789) (:fv _uniq.79795) ((:c CommRing.toCommSemiring) (:fv _uniq.7978... | (: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 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"apply","sourceEnd":15661,"sourceStart":15656,"tag":"atom"},{"children":[{"name":"mul_ne_zero","semanticRole":"global","source":"mul_ne_zero","sourceEnd":15673,"sourceStart":15662,"tag":"identifier"},{"children":[{"name":"Polynomial.IsPrimitive.ne_zero","semanticRole":"global","source":"hq.ne_zer... | [] | [{"source":"mul_ne_zero hq.ne_zero","source_end":15684,"source_start":15662,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"intern... | 47 | 57 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 48c4b0d466620ba41c202c17b36622b1699430f2ee2e7deae28875f5f61e5048 | cb0936eb8115cbce66498d4e3ee5da2570945b52b6616495bea990d7494f3d64 | 48070cba09e448e1d18e0c056d06975e2924c706cf254d729cc7c6d9d11cb6fd | 77fac9a56e3e5d84a054cb20094d5ba664c01f362f6a4196b5a01aea6af37ac8 |
cat-searcher/leandojo-benchmark-4-random | test | 2,623 | Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map | Mathlib/RingTheory/Polynomial/GaussLemma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Ne</a>, <a>Polynomial.C_eq_zero</a>] | case intro.intro.mk
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : ... | case intro.intro.mk
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : ... | ((:c Ne) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _uniq.79789) (:fv _uniq.79792)))) ((:c DFunLike.coe) ((:c RingHom) (:fv _uniq.79789) ((:c Polynomial) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemir... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.79789))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.79795))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.79789) (:fv _uniq.79795) ((:c CommRing.toCommSemiring) (:fv _uniq.7978... | (: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 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c RingHom) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Polyn... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"rw","sourceEnd":15691,"sourceStart":15689,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15693,"sourceStart":15692,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Ne","semanticRol... | [] | [{"source":"Ne","source_end":15695,"source_start":15693,"syntax_kind":"ident"},{"source":"C_eq_zero","source_end":15706,"source_start":15697,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"intern... | 47 | 58 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bbcf533bb5108f6715d1909fc18ea8776eeb76bdef1fbea81936cd312b5473b6 | 77fac9a56e3e5d84a054cb20094d5ba664c01f362f6a4196b5a01aea6af37ac8 | 4c86fa90dcb68e1eb77547116b78db3c3e59a2a36b0cd44c71672821d8c3397f | 44f8dd6cdb707fb5fa38b01849cc0986319411ea362609d882530a72d2419c31 |
cat-searcher/leandojo-benchmark-4-random | test | 2,624 | Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map | Mathlib/RingTheory/Polynomial/GaussLemma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | contrapose! s0 | case intro.intro.mk
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
s0 : s ∈ R⁰
hs : ... | case intro.intro.mk
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
hs : map (algebra... | ((:c Not) ((:c Eq) (:fv _uniq.79789) (:fv _uniq.81381) ((:c OfNat.ofNat) (:fv _uniq.79789) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.79789) ((:c MonoidWithZero.toZero) (:fv _uniq.79789) ((:c Semiring.toMonoidWithZero) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemiring) (:fv _un... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.79789))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.79795))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.79789) (:fv _uniq.79795) ((:c CommRing.toCommSemiring) (:fv _uniq.7978... | (:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV15)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:lit 0)))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"contrapose!","sourceEnd":15723,"sourceStart":15712,"tag":"atom"},{"children":[{"contextIndex":16,"semanticRole":"local","source":"s0","sourceEnd":15726,"sourceStart":15724,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"null","source":"s0","sourceEnd":15726,"s... | [] | [{"source":"s0","source_end":15726,"source_start":15724,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"intern... | 47 | 62 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c7a5f5de9d4ab69a90d06454e0175558727e581f41f7766acb576572578baf67 | 44f8dd6cdb707fb5fa38b01849cc0986319411ea362609d882530a72d2419c31 | 32c9e8fcccbe4ee813bf5544e09fe2915352d209b3cd6e9ebbdc75d27ab3a2cb | b10e25c7e9a0351a65c3b588da1a62b91332d17ecee339dea36d7dea6505863d |
cat-searcher/leandojo-benchmark-4-random | test | 2,625 | Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map | Mathlib/RingTheory/Polynomial/GaussLemma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [s0, <a>mem_nonZeroDivisors_iff_ne_zero</a>] | case intro.intro.mk
R : Type u_1
inst✝⁵ : CommRing R
K : Type u_2
inst✝⁴ : Field K
inst✝³ : Algebra R K
inst✝² : IsFractionRing R K
inst✝¹ : IsDomain R
inst✝ : NormalizedGCDMonoid R
p q : R[X]
hp : p.IsPrimitive
hq : q.IsPrimitive
r : K[X]
hr : map (algebraMap R K) q = map (algebraMap R K) p * r
s : R
hs : map (algebra... | ((:c Not) ((:c Membership.mem) (:fv _uniq.79789) ((:c Submonoid) (:fv _uniq.79789) ((:c MulZeroOneClass.toMulOneClass) (:fv _uniq.79789) ((:c NonAssocSemiring.toMulZeroOneClass) (:fv _uniq.79789) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.79789) ((:c CommSemiring.toSemiring) (:fv _uniq.79789) ((:c CommRing.toCommSemi... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.79789))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.79795))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.79789) (:fv _uniq.79795) ((:c CommRing.toCommSemiring) (:fv _uniq.7978... | (:app (:c Not) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Submonoid) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MulOneClass) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"simp","sourceEnd":15735,"sourceStart":15731,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15737,"sourceStart":15736,"tag":"a... | [] | [{"source":"s0","source_end":15739,"source_start":15737,"syntax_kind":"ident"},{"source":"mem_nonZeroDivisors_iff_ne_zero","source_end":15772,"source_start":15741,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.79789","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.79792","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"intern... | 47 | 63 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 57e3158dffbe7ac0a20d001efaae0e778caf01f8b9cceba7d3fe27657484f83c | b10e25c7e9a0351a65c3b588da1a62b91332d17ecee339dea36d7dea6505863d | 312eddd78d5e2a1d9794c79230f5910a837010e35e041a5cace3a08d587b3852 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,626 | Nat.swap_mem_divisorsAntidiagonal | Mathlib/NumberTheory/Divisors.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Nat.mem_divisorsAntidiagonal</a>, <a>Nat.mem_divisorsAntidiagonal</a>, <a>mul_comm</a>, <a>Prod.swap</a>] | n : ℕ
x : ℕ × ℕ
⊢ x.swap ∈ n.divisorsAntidiagonal ↔ x ∈ n.divisorsAntidiagonal | ((:c Iff) ((:c Membership.mem) ((:c Prod) (:c Nat) (:c Nat)) ((:c Finset) ((:c Prod) (:c Nat) (:c Nat))) ((:c Finset.instMembership) ((:c Prod) (:c Nat) (:c Nat))) ((:c Prod.swap) (:c Nat) (:c Nat) (:fv _uniq.20126)) ((:c Nat.divisorsAntidiagonal) (:fv _uniq.20089))) ((:c Membership.mem) ((:c Prod) (:c Nat) (:c Nat)) (... | [{"name":"n","sexp":"(:c Nat)"},{"name":"x","sexp":"((:c Prod) (:c Nat) (:c Nat))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))))) (:arg :instance 2 (:instance-... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20089","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.20126","is_instance":false,"is_let":false,"name":"x","sexp":"(:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg ... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":11025,"sourceStart":11023,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11027,"sourceStart":11026,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"mem_divisorsAntidiagonal","source_end":11051,"source_start":11027,"syntax_kind":"ident"},{"source":"mem_divisorsAntidiagonal","source_end":11077,"source_start":11053,"syntax_kind":"ident"},{"source":"mul_comm","source_end":11087,"source_start":11079,"syntax_kind":"ident"},{"source":"Prod.swap","source_end":... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20089","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.20126","is_instance":false,"is_let":false,"user_name":"x"}] | 73 | 2 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2a20a210ed81e943e808e7596bc9406cd31d792d4217249f9ca3bc2d9f81c3d2 | 6855cd822b0468a21dbebb568b3f6ebaeec9daff795371d11d98c47241ff3e98 | 5138dfa513088a3d72e0d3c64c0339f50cadc84bdf25f3091de11cebf2aafaf6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,627 | Representation.asAlgebraHom_single | Mathlib/RepresentationTheory/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Representation.asAlgebraHom_def</a>, <a>MonoidAlgebra.lift_single</a>] | k : Type u_1
G : Type u_2
V : Type u_3
inst✝³ : CommSemiring k
inst✝² : Monoid G
inst✝¹ : AddCommMonoid V
inst✝ : Module k V
ρ : Representation k G V
g : G
r : k
⊢ ρ.asAlgebraHom (Finsupp.single g r) = r • ρ g | ((:c Eq) ((:c Module.End) (:fv _uniq.11200) (:fv _uniq.11206) ((:c CommSemiring.toSemiring) (:fv _uniq.11200) (:fv _uniq.11209)) (:fv _uniq.11215) (:fv _uniq.11399)) ((:c DFunLike.coe) ((:c AlgHom) (:fv _uniq.11200) ((:c MonoidAlgebra) (:fv _uniq.11200) (:fv _uniq.11203) ((:c CommSemiring.toSemiring) (:fv _uniq.11200) ... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"V","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c CommSemiring) (:fv _uniq.11200))"},{"name":"inst✝²","sexp":"((:c Monoid) (:fv _uniq.11203))"},{"name":"inst✝¹","sexp":"((:c AddCommMonoid) (:fv _uniq.11206))"},{"name":"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Module.End) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11200","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.11203","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":3282,"sourceStart":3278,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":3287,"sourceStart":3283,"tag":"atom"}],"kind":"nu... | [] | [{"source":"asAlgebraHom_def","source_end":3305,"source_start":3289,"syntax_kind":"ident"},{"source":"MonoidAlgebra.lift_single","source_end":3332,"source_start":3307,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11200","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.11203","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 28 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a9178c8cb98bce2c920a8d956deb9c2e396be64e1c4c565de0b48c20313ab547 | 1170f1b3c896aa2c08b10a8f0e6991a353c5d02bd26ddb3399ca01115bdde52a | 0aa4ece482fe54b6447093192b5e57561625c539304bd5d23ba2c241936a8c1f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,628 | Topology.IsLowerSet.monotone_iff_continuous | Mathlib/Topology/Order/UpperLowerSetTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>monotone_dual_iff</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
inst✝⁵ : Preorder α
inst✝⁴ : Preorder β
inst✝³ : TopologicalSpace α
inst✝² : TopologicalSpace β
inst✝¹ : Topology.IsLowerSet α
inst✝ : Topology.IsLowerSet β
f : α → β
⊢ Monotone f ↔ Continuous f | α : Type u_1
β : Type u_2
γ : Type u_3
inst✝⁵ : Preorder α
inst✝⁴ : Preorder β
inst✝³ : TopologicalSpace α
inst✝² : TopologicalSpace β
inst✝¹ : Topology.IsLowerSet α
inst✝ : Topology.IsLowerSet β
f : α → β
⊢ Monotone (⇑toDual ∘ f ∘ ⇑ofDual) ↔ Continuous f | ((:c Iff) ((:c Monotone) (:fv _uniq.11845) (:fv _uniq.11848) (:fv _uniq.11854) (:fv _uniq.11857) (:fv _uniq.11926)) ((:c Continuous) (:fv _uniq.11845) (:fv _uniq.11848) (:fv _uniq.11922) (:fv _uniq.11923) (:fv _uniq.11926))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁵","sexp":"((:c Preorder) (:fv _uniq.11845))"},{"name":"inst✝⁴","sexp":"((:c Preorder) (:fv _uniq.11848))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.11845))"},{"name":... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Monotone) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 4 (:fv FV10))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11845","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.11848","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":13196,"sourceStart":13194,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13198,"sourceStart":13197,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":13201,"sourceSt... | [] | [{"source":"monotone_dual_iff","source_end":13219,"source_start":13202,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11845","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.11848","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 97 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9b64cc07dd052a4f078a996fb8520a9d6b050ee9ee64a6344af9e228c2bdfae1 | 919d187f8376c5466368e1cdfd9829333cc8e2daef54adf5d9935c9fd2e4e213 | 9b8dedc3ade5e1984d5f19bdfa5f44b4d482f44395fcc2bbe2f357c9dde8ef0f | 4129e4a1c59f41b3009d1ed06cbbe960257eb2de3c90e1062e8845f9cc112638 |
cat-searcher/leandojo-benchmark-4-random | test | 2,629 | Topology.IsLowerSet.monotone_iff_continuous | Mathlib/Topology/Order/UpperLowerSetTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Topology.IsUpperSet.monotone_iff_continuous</a> (α := αᵒᵈ) (β := βᵒᵈ) (f := (<a>OrderDual.toDual</a> ∘ f ∘ <a>OrderDual.ofDual</a> : αᵒᵈ → βᵒᵈ)) | α : Type u_1
β : Type u_2
γ : Type u_3
inst✝⁵ : Preorder α
inst✝⁴ : Preorder β
inst✝³ : TopologicalSpace α
inst✝² : TopologicalSpace β
inst✝¹ : Topology.IsLowerSet α
inst✝ : Topology.IsLowerSet β
f : α → β
⊢ Monotone (⇑toDual ∘ f ∘ ⇑ofDual) ↔ Continuous f | ((:c Iff) ((:c Monotone) ((:c OrderDual) (:fv _uniq.11845)) ((:c OrderDual) (:fv _uniq.11848)) ((:c OrderDual.instPreorder) (:fv _uniq.11845) (:fv _uniq.11854)) ((:c OrderDual.instPreorder) (:fv _uniq.11848) (:fv _uniq.11857)) ((:c Function.comp) ((:c OrderDual) (:fv _uniq.11845)) (:fv _uniq.11848) ((:c OrderDual) (:fv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁵","sexp":"((:c Preorder) (:fv _uniq.11845))"},{"name":"inst✝⁴","sexp":"((:c Preorder) (:fv _uniq.11848))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.11845))"},{"name":... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Monotone) (:arg :implicit-type 0 (:app (:c OrderDual) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c OrderDual) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:app (:c OrderDual) (:arg :explicit 0 (:fv FV0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11845","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.11848","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":13228,"sourceStart":13223,"tag":"atom"},{"children":[{"name":"Topology.IsUpperSet.monotone_iff_continuous","semanticRole":"global","source":"IsUpperSet.monotone_iff_continuous","sourceEnd":13263,"sourceStart":13229,"tag":"identifier"},{"children":[{"children":[{"source":"(","s... | [] | [{"source":"IsUpperSet.monotone_iff_continuous (α := αᵒᵈ) (β := βᵒᵈ)\n (f := (toDual ∘ f ∘ ofDual : αᵒᵈ → βᵒᵈ))","source_end":13358,"source_start":13229,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11845","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.11848","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 97 | 7 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7fc28ac370238e74f6d58238b0153b27aadc51ac8f8adc4868f2d00eecb611fc | 4129e4a1c59f41b3009d1ed06cbbe960257eb2de3c90e1062e8845f9cc112638 | 4fd1141819f8a9cbe8b12a372380c8898acc9fbe44575822015c65ef25434382 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,630 | DifferentiableWithinAt.mono | Mathlib/Analysis/Calculus/FDeriv/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases h with ⟨f', hf'⟩ | 𝕜 : Type u_1
inst✝⁸ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
F : Type u_3
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
G : Type u_4
inst✝³ : NormedAddCommGroup G
inst✝² : NormedSpace 𝕜 G
G' : Type u_5
inst✝¹ : NormedAddCommGroup G'
inst✝ : NormedSpac... | case intro
𝕜 : Type u_1
inst✝⁸ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
F : Type u_3
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
G : Type u_4
inst✝³ : NormedAddCommGroup G
inst✝² : NormedSpace 𝕜 G
G' : Type u_5
inst✝¹ : NormedAddCommGroup G'
inst✝ :... | ((:c DifferentiableWithinAt) (:fv _uniq.337523) (:fv _uniq.337526) (:fv _uniq.337529) (:fv _uniq.337532) (:fv _uniq.337640) (:fv _uniq.337643) (:fv _uniq.337646) (:fv _uniq.337749) (:fv _uniq.337971) (:fv _uniq.340200) (:fv _uniq.340197)) | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.337523))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCommGroup) (:fv _uniq.337529))"},{"name":"inst✝⁶","sexp":"((:c NormedSpace) (:fv _uniq.337523) (:fv _uniq.337529) ((:c Non... | (:app (:c DifferentiableWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.337523","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.337526","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"rcases","sourceEnd":31356,"sourceStart":31350,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":30,"semanticRole":"local","source":"h","sourceEnd":31358,"sourceStart":31357,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","... | [] | [{"source":"h","source_end":31358,"source_start":31357,"syntax_kind":"ident"},{"source":"⟨f', hf'⟩","source_end":31377,"source_start":31364,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.337523","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.337526","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":implicit","context_index":2,"int... | 152 | 4 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b34e13e8fef8a84ee97c7145a45d6d7e540ac1008e9021bddb940b28074c1aba | 2383798dfad8b40622da8ac52fcab861a8bba91af5a20e1da54d0852452a5321 | 0af1dc8a14cd171048d64020cf242aff13c11ea108041a7cf6ac6d5e927ece5b | 19308238e1179321cb5b36eb248bcd2d75c5bd6ebb2a4c152aa0f1ec728dd347 |
cat-searcher/leandojo-benchmark-4-random | test | 2,631 | DifferentiableWithinAt.mono | Mathlib/Analysis/Calculus/FDeriv/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨f', hf'.mono st⟩ | case intro
𝕜 : Type u_1
inst✝⁸ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
F : Type u_3
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
G : Type u_4
inst✝³ : NormedAddCommGroup G
inst✝² : NormedSpace 𝕜 G
G' : Type u_5
inst✝¹ : NormedAddCommGroup G'
inst✝ :... | ((:c DifferentiableWithinAt) (:fv _uniq.337523) (:fv _uniq.337526) (:fv _uniq.337529) (:fv _uniq.337532) (:fv _uniq.337640) (:fv _uniq.337643) (:fv _uniq.337646) (:fv _uniq.337749) (:fv _uniq.337971) (:fv _uniq.340200) (:fv _uniq.340197)) | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.337523))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCommGroup) (:fv _uniq.337529))"},{"name":"inst✝⁶","sexp":"((:c NormedSpace) (:fv _uniq.337523) (:fv _uniq.337529) ((:c Non... | (:app (:c DifferentiableWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.337523","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.337526","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"exact","sourceEnd":31385,"sourceStart":31380,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":31389,"sourceStart":31386,"tag":"atom"},{"children":[{"contextIndex":31,"semanticRole":"local","source":"f'","sourceEnd":31391,"sourceStart":31389,"tag":"identifier"},{"source":",","sourceEnd":31392... | [] | [{"source":"⟨f', hf'.mono st⟩","source_end":31407,"source_start":31386,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.337523","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.337526","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":implicit","context_index":2,"int... | 152 | 5 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a52d973776539e9b8b1ae56d73ee91938608d99c997cc9674fcf7f8422063787 | 19308238e1179321cb5b36eb248bcd2d75c5bd6ebb2a4c152aa0f1ec728dd347 | 1e00eff06194639d275d8bad5c3e38b886c58f57206e36e630b3a54357178385 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,632 | Equiv.toFun_inducedStructureEquiv_Symm | Mathlib/ModelTheory/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | letI : L.Structure N := <a>Equiv.inducedStructure</a> e | L : Language
M : Type u_1
N : Type u_2
inst✝ : L.Structure M
e : M ≃ N
⊢ N → M | L : Language
M : Type u_1
N : Type u_2
inst✝ : L.Structure M
e : M ≃ N
this : L.Structure N := e.inducedStructure
⊢ N → M | (:forall a (:fv _uniq.130454) (:fv _uniq.130451)) | [{"name":"L","sexp":"(:c FirstOrder.Language)"},{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"N","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c FirstOrder.Language.Structure) (:fv _uniq.130448) (:fv _uniq.130451))"},{"name":"e","sexp":"((:c Equiv) (:fv _uniq.130451) (:fv _uniq.130454))"}] | (:forall a :explicit (:fv FV2) (:fv FV1)) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.130448","is_instance":false,"is_let":false,"name":"L","sexp":"(:c FirstOrder.Language)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.130451","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":... | {"children":[{"source":"letI","sourceEnd":47862,"sourceStart":47858,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":47863,"sourceStart":47863,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":47863,"sourceStart":47863,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"L.Structure N","source_end":47878,"source_start":47865,"syntax_kind":"Lean.Parser.Term.app"},{"source":"inducedStructure e","source_end":47900,"source_start":47882,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.130448","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.130451","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 362 | 4 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ae4f09957006a4927616e93a4d72b7f3261b72c0b4010f03f3d505a98a89675b | 0bf444df1b7f661234e746293a86fca283deb7ef45aee55f69d67456bacf53ab | 40955c4e350b57b84c4d9a6d3d5d090f6b6dccb05e30d16b794975d922a3f4a6 | fe240f0aea5766f3108341a7b5fb6a1e3ee285c5fa21e281fe2cf94b4ec6c708 |
cat-searcher/leandojo-benchmark-4-random | test | 2,633 | Equiv.toFun_inducedStructureEquiv_Symm | Mathlib/ModelTheory/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>DFunLike.coe</a> (@<a>Equiv.inducedStructureEquiv</a> L M N _ e).<a>FirstOrder.Language.Equiv.symm</a> | L : Language
M : Type u_1
N : Type u_2
inst✝ : L.Structure M
e : M ≃ N
this : L.Structure N := e.inducedStructure
⊢ N → M | (:forall a (:fv _uniq.130454) (:fv _uniq.130451)) | [{"name":"L","sexp":"(:c FirstOrder.Language)"},{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"N","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c FirstOrder.Language.Structure) (:fv _uniq.130448) (:fv _uniq.130451))"},{"name":"e","sexp":"((:c Equiv) (:fv _uniq.130451) (:fv _uniq.130454))"},{"name":"this","se... | (:forall a :explicit (:fv FV2) (:fv FV1)) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.130448","is_instance":false,"is_let":false,"name":"L","sexp":"(:c FirstOrder.Language)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.130451","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":... | {"children":[{"source":"exact","sourceEnd":47910,"sourceStart":47905,"tag":"atom"},{"children":[{"name":"DFunLike.coe","semanticRole":"global","source":"DFunLike.coe","sourceEnd":47923,"sourceStart":47911,"tag":"identifier"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":47925,"sourceStart":47924,"tag... | [] | [{"source":"DFunLike.coe (@inducedStructureEquiv L M N _ e).symm","source_end":47963,"source_start":47911,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.130448","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.130451","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 362 | 5 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fc121a3f9c03f4db567a37505af48e7872bc68e2593c2861281a3689fb7ba524 | fe240f0aea5766f3108341a7b5fb6a1e3ee285c5fa21e281fe2cf94b4ec6c708 | d9262a892bc100d551fc0774939382b079fa3156bd359455def4feb615e7ae59 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,634 | UpperHalfPlane.dist_coe_le | Mathlib/Analysis/Complex/UpperHalfPlane/Metric.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>UpperHalfPlane.dist_center_dist</a>, <a>UpperHalfPlane.dist_self_center</a>, ← <a>mul_add</a>, ← <a>add_sub_assoc</a>, <a>Real.sinh_add_cosh</a>] | z✝ w✝ : ℍ
r R : ℝ
z w : ℍ
⊢ dist ↑z ↑(w.center (dist z w)) + dist ↑w ↑(w.center (dist z w)) = w.im * (rexp (dist z w) - 1) | ((:c Eq) (:c Real) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) ((:c Dist.dist) (:c Complex) ((:c PseudoMetricSpace.toDist) (:c Complex) ((:c SeminormedRing.toPseudoMetricSpace) (:c Complex) ((:c SeminormedCommRing.toSeminormedRing) (:c Complex) ((:c NormedCommRing.toSeminor... | [{"name":"z✝","sexp":"(:c UpperHalfPlane)"},{"name":"w✝","sexp":"(:c UpperHalfPlane)"},{"name":"r","sexp":"(:c Real)"},{"name":"R","sexp":"(:c Real)"},{"name":"z","sexp":"(:c UpperHalfPlane)"},{"name":"w","sexp":"(:c UpperHalfPlane)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (: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 HAdd) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.95433","is_instance":false,"is_let":false,"name":"z✝","sexp":"(:c UpperHalfPlane)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.95435","is_instance":false,"is_let":false,"name":"w✝","sexp":"(:c UpperHalfPlane)"},{"binder_role":... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":13394,"sourceStart":13392,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13396,"sourceStart":13395,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"dist_center_dist","source_end":13412,"source_start":13396,"syntax_kind":"ident"},{"source":"dist_self_center","source_end":13430,"source_start":13414,"syntax_kind":"ident"},{"source":"mul_add","source_end":13443,"source_start":13436,"syntax_kind":"ident"},{"source":"add_sub_assoc","source_end":13462,"source... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.95433","is_instance":false,"is_let":false,"user_name":"z✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.95435","is_instance":false,"is_let":false,"user_name":"w✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 75 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a059c8ea35dc39ab07d2b05c46d8e7c91a1a5e47e9b3b113942bb45dc576adc2 | 2895cb206ae094a2105c800d1cb561a4145537b20a6d6688753d461c84c9b9e1 | d91249cca86f69f86fe0211d31f043dd48e61c171b2e7ed8843cff68fc6a4d8e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,635 | CategoryTheory.Functor.flip_injective | Mathlib/CategoryTheory/Functor/Currying.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>CategoryTheory.Functor.flip_flip</a> F₁, ← <a>CategoryTheory.Functor.flip_flip</a> F₂, h] | B : Type u₁
inst✝⁴ : Category.{v₁, u₁} B
C : Type u₂
inst✝³ : Category.{v₂, u₂} C
D : Type u₃
inst✝² : Category.{v₃, u₃} D
E : Type u₄
inst✝¹ : Category.{v₄, u₄} E
H : Type u₅
inst✝ : Category.{v₅, u₅} H
F₁ F₂ : B ⥤ C ⥤ D
h : F₁.flip = F₂.flip
⊢ F₁ = F₂ | ((:c Eq) ((:c CategoryTheory.Functor) (:fv _uniq.77352) (:fv _uniq.77355) ((:c CategoryTheory.Functor) (:fv _uniq.77357) (:fv _uniq.77360) (:fv _uniq.77362) (:fv _uniq.77365)) ((:c CategoryTheory.Functor.category) (:fv _uniq.77357) (:fv _uniq.77360) (:fv _uniq.77362) (:fv _uniq.77365))) (:fv _uniq.77532) (:fv _uniq.775... | [{"name":"B","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.77352))"},{"name":"C","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.77357))"},{"name":"D","sexp":"(:sort (+ u₃ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Categ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Functor) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c CategoryTheory.Functor) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77352","is_instance":false,"is_let":false,"name":"B","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.77355","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":5842,"sourceStart":5840,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5844,"sourceStart":5843,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"sour... | [] | [{"source":"flip_flip F₁","source_end":5862,"source_start":5848,"syntax_kind":"Lean.Parser.Term.app"},{"source":"flip_flip F₂","source_end":5882,"source_start":5868,"syntax_kind":"Lean.Parser.Term.app"},{"source":"h","source_end":5885,"source_start":5884,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77352","is_instance":false,"is_let":false,"user_name":"B"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.77355","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"intern... | 27 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 02070cae2e9854f2825b5c798cd5b39acafa112c79421e019e30ae8e2312e752 | 1f604725657eb01b9a9434537b39a4e7a28650b44654093a34018e9dc5fd34aa | 5c76ed65bde7c3412273738e9efd5af797dbb7e35961fff59982e567b5de2755 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,636 | ProbabilityTheory.monotone_defaultRatCDF | Mathlib/Probability/Kernel/Disintegration/MeasurableStieltjes.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | unfold <a>ProbabilityTheory.defaultRatCDF</a> | α : Type u_1
β : Type u_2
ι : Type u_3
inst✝ : MeasurableSpace α
⊢ Monotone defaultRatCDF | α : Type u_1
β : Type u_2
ι : Type u_3
inst✝ : MeasurableSpace α
⊢ Monotone fun q => if q < 0 then 0 else 1 | ((:c Monotone) (:c Rat) (:c Real) (:c Rat.instPreorder) (:c Real.instPreorder) (:c ProbabilityTheory.defaultRatCDF)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c MeasurableSpace) (:fv _uniq.9800))"}] | (:app (:c Monotone) (:arg :implicit-type 0 (:c Rat)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c Rat))))) (:arg :instance 3 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c Real))))) (:arg :explicit 4 (:c ProbabilityTheory.defaultRatCDF))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9800","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9803","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"unfold","sourceEnd":7336,"sourceStart":7330,"tag":"atom"},{"children":[{"name":"ProbabilityTheory.defaultRatCDF","semanticRole":"global","source":"defaultRatCDF","sourceEnd":7350,"sourceStart":7337,"tag":"identifier"}],"kind":"null","source":"defaultRatCDF","sourceEnd":7350,"sourceStart":7337,"t... | [] | [{"source":"defaultRatCDF","source_end":7350,"source_start":7337,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9800","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9803","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 20 | 4 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0f641fc2900052ceb77942e32eaea425c2f272b0c0baf4ce9c445e26cdd40604 | 164d5aa90edd0ec791be35cefbcc739ee9be5d2aecd98d6115a750e302890ec3 | 2898eebeae482b4b770728311b759b6a74fab52f91fa4a8dbf307eb9f256e904 | cca42db6e7303e1c02cdff5ad96e41efca81e8bf7b5a922e63378c75d62fbf1c |
cat-searcher/leandojo-benchmark-4-random | test | 2,637 | ProbabilityTheory.monotone_defaultRatCDF | Mathlib/Probability/Kernel/Disintegration/MeasurableStieltjes.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro x y hxy | α : Type u_1
β : Type u_2
ι : Type u_3
inst✝ : MeasurableSpace α
⊢ Monotone fun q => if q < 0 then 0 else 1 | α : Type u_1
β : Type u_2
ι : Type u_3
inst✝ : MeasurableSpace α
x y : ℚ
hxy : x ≤ y
⊢ (fun q => if q < 0 then 0 else 1) x ≤ (fun q => if q < 0 then 0 else 1) y | ((:c Monotone) (:c Rat) (:c Real) (:c Rat.instPreorder) (:c Real.instPreorder) (:lambda q (:c Rat) ((:c ite) (:c Real) ((:c LT.lt) (:c Rat) (:c Rat.instLT) 0 ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0)))) ((:c Rat.instDecidableLt) 0 ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0)))... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c MeasurableSpace) (:fv _uniq.9800))"}] | (:app (:c Monotone) (:arg :implicit-type 0 (:c Rat)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c Rat))))) (:arg :instance 3 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c Real))))) (:arg :explicit 4 (:lambda q :explicit (:c Rat) (:app (:c ite) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9800","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9803","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"intro","sourceEnd":7358,"sourceStart":7353,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":7360,"sourceStart":7359,"tag":"identifier"},{"semanticRole":"scoped_local","source":"y","sourceEnd":7362,"sourceStart":7361,"tag":"identifier"},{"semanticRole":"scoped_lo... | [{"role":"fresh_name","source":"x","source_end":7360,"source_start":7359,"syntax_kind":"ident"},{"role":"fresh_name","source":"y","source_end":7362,"source_start":7361,"syntax_kind":"ident"},{"role":"fresh_name","source":"hxy","source_end":7366,"source_start":7363,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9800","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9803","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 20 | 5 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ad117130ba2147a50452b483f9bab2d486162fa41df4b20d1976fc09f46c8b3a | cca42db6e7303e1c02cdff5ad96e41efca81e8bf7b5a922e63378c75d62fbf1c | 9d18871bcc40256d494e3c2910f4536b5629b313423890104c3b65cedfcfdac0 | a64efa1b8e292a357df63be063c525ffa359da18fd5193f1b0b2464a9348de5e |
cat-searcher/leandojo-benchmark-4-random | test | 2,638 | ProbabilityTheory.monotone_defaultRatCDF | Mathlib/Probability/Kernel/Disintegration/MeasurableStieltjes.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp only | α : Type u_1
β : Type u_2
ι : Type u_3
inst✝ : MeasurableSpace α
x y : ℚ
hxy : x ≤ y
⊢ (fun q => if q < 0 then 0 else 1) x ≤ (fun q => if q < 0 then 0 else 1) y | α : Type u_1
β : Type u_2
ι : Type u_3
inst✝ : MeasurableSpace α
x y : ℚ
hxy : x ≤ y
⊢ (if x < 0 then 0 else 1) ≤ if y < 0 then 0 else 1 | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:lambda q (:c Rat) ((:c ite) (:c Real) ((:c LT.lt) (:c Rat) (:c Rat.instLT) 0 ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0)))) ((:c Rat.instDecidableLt) 0 ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0)))) ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c MeasurableSpace) (:fv _uniq.9800))"},{"name":"x","sexp":"(:c Rat)"},{"name":"y","sexp":"(:c Rat)"},{"name":"hxy","sexp":"((:c LE.le) (:c Rat) ((:c Preorder.toLE) (:c Rat)... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:lambda q :explicit (:c Rat) (:app (:c ite) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c LT.lt) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9800","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9803","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"dsimp","sourceEnd":7374,"sourceStart":7369,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":7379,"sourceStart":7375,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":7379,"... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9800","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9803","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 20 | 6 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e51ee2e3b820fb0e0ca5f22b2a4226ac65eafd7943754f5737b91f28a02be53a | a64efa1b8e292a357df63be063c525ffa359da18fd5193f1b0b2464a9348de5e | a4e0c85d6bda4413b7728099944a8f316bd66db76d368a5fb7af15b2a8905273 | d7cc55dd534838f9c78c8b2134d6dc8b478d6aca7af7d9598bb9d8c1d2ebacff |
cat-searcher/leandojo-benchmark-4-random | test | 2,639 | ProbabilityTheory.monotone_defaultRatCDF | Mathlib/Probability/Kernel/Disintegration/MeasurableStieltjes.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split_ifs with h_1 h_2 h_2 | α : Type u_1
β : Type u_2
ι : Type u_3
inst✝ : MeasurableSpace α
x y : ℚ
hxy : x ≤ y
⊢ (if x < 0 then 0 else 1) ≤ if y < 0 then 0 else 1 | case pos
α : Type u_1
β : Type u_2
ι : Type u_3
inst✝ : MeasurableSpace α
x y : ℚ
hxy : x ≤ y
h_1 : x < 0
h_2 : y < 0
⊢ 0 ≤ 0
case neg
α : Type u_1
β : Type u_2
ι : Type u_3
inst✝ : MeasurableSpace α
x y : ℚ
hxy : x ≤ y
h_1 : x < 0
h_2 : ¬y < 0
⊢ 0 ≤ 1
case pos
α : Type u_1
β : Type u_2
ι : Type u_3
inst✝ : MeasurableS... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c ite) (:c Real) ((:c LT.lt) (:c Rat) (:c Rat.instLT) (:fv _uniq.9910) ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0)))) ((:c Rat.instDecidableLt) (:fv _uniq.9910) ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:l... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c MeasurableSpace) (:fv _uniq.9800))"},{"name":"x","sexp":"(:c Rat)"},{"name":"y","sexp":"(:c Rat)"},{"name":"hxy","sexp":"((:c LE.le) (:c Rat) ((:c Preorder.toLE) (:c Rat)... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c ite) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c LT.lt) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9800","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9803","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"split_ifs","sourceEnd":7391,"sourceStart":7382,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"with","sourceEnd":7396,"sourceStart":7392,"tag":"atom"},{"children":[{"children":[{"source":"h_1","sourceEnd":7400,"sourceStart":7397,"tag":"identifier"}],"... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9800","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9803","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 20 | 7 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fe1abaac144737102423243b6a17cf4a8eac42966827e395a45a37e8cc87338e | d7cc55dd534838f9c78c8b2134d6dc8b478d6aca7af7d9598bb9d8c1d2ebacff | 6f4ae7fb1f51f48fc1abd18c9842434641eedd6ca70fe0bf04be23f4b56b5b72 | 742c2aa59e5c5e5e3c563b21072f476805214f5a4c9c689407508b58454fdf62 |
cat-searcher/leandojo-benchmark-4-random | test | 2,641 | Filter.map₂_mk_eq_prod | Mathlib/Order/Filter/NAry.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [← <a>Filter.map_prod_eq_map₂</a>, <a>Filter.map_id'</a>] | α : Type u_1
α' : Type u_2
β : Type u_3
β' : Type u_4
γ : Type u_5
γ' : Type u_6
δ : Type u_7
δ' : Type u_8
ε : Type u_9
ε' : Type u_10
m : α → β → γ
f✝ f₁ f₂ : Filter α
g✝ g₁ g₂ : Filter β
h h₁ h₂ : Filter γ
s s₁ s₂ : Set α
t t₁ t₂ : Set β
u : Set γ
v : Set δ
a : α
b : β
c : γ
f : Filter α
g : Filter β
⊢ map₂ Prod.mk ... | ((:c Eq) ((:c Filter) ((:c Prod) (:fv _uniq.2185) (:fv _uniq.2191))) ((:c Filter.map₂) (:fv _uniq.2185) (:fv _uniq.2191) ((:c Prod) (:fv _uniq.2185) (:fv _uniq.2191)) ((:c Prod.mk) (:fv _uniq.2185) (:fv _uniq.2191)) (:fv _uniq.2333) (:fv _uniq.2334)) ((:c SProd.sprod) ((:c Filter) (:fv _uniq.2185)) ((:c Filter) (:fv _u... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"α'","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"β'","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"γ'","sexp":"(:sort (+ u_6 1))"},{"name":"δ","sexp":"(:sort (+ u_7 1))"},{"name":"δ'","sexp":"(:sort (+ u_8 1... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)))))) (:arg :explicit 1 (:app (:c Filter.map₂) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:app (:c Prod) (:arg :explicit 0 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2185","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2188","is_instance":false,"is_let":false,"name":"α'","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":2440,"sourceStart":2436,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":2445,"sourceStart":2441,"tag":"atom"}],"kind":"nu... | [] | [{"source":"map_prod_eq_map₂","source_end":2469,"source_start":2451,"syntax_kind":"ident"},{"source":"map_id'","source_end":2478,"source_start":2471,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2185","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2188","is_instance":false,"is_let":false,"user_name":"α'"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 16 | 2 | exact | true | 1 | 33 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 76c27e4dd9f4937aa3baf7295df1e3628e8a67975c9987da1c9d71cc1aefc15e | d987ab3a5d529a30fcdc798f38d1ad192d0e6edb991b28dd23bfdff725636803 | 974e193492d303d8aefcdc9161f901ad014f22bd00de70a5edb1f85e5e01cf24 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,642 | ULower.up_down | Mathlib/Logic/Encodable/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>ULower.up</a>, <a>ULower.down</a>,<a>Equiv.left_inv</a> _ _, <a>Equiv.symm_apply_apply</a>] | α : Type u_1
inst✝ : Encodable α
a : α
⊢ (down a).up = a | ((:c Eq) (:fv _uniq.19915) ((:c ULower.up) (:fv _uniq.19915) (:fv _uniq.19918) ((:c ULower.down) (:fv _uniq.19915) (:fv _uniq.19918) (:fv _uniq.19940))) (:fv _uniq.19940)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Encodable) (:fv _uniq.19915))"},{"name":"a","sexp":"(:fv _uniq.19915)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c ULower.up) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Encodable) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c ULower.down) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.19915","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.19918","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Encodable) (:arg :explic... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":19767,"sourceStart":19763,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"up","source_end":19771,"source_start":19769,"syntax_kind":"ident"},{"source":"down","source_end":19777,"source_start":19773,"syntax_kind":"ident"},{"source":"Equiv.left_inv _ _","source_end":19796,"source_start":19778,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Equiv.symm_apply_apply","source_end":1982... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.19915","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.19918","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna... | 179 | 2 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fd81bdb320e87afd380a8a9b5cfdf9aca77e7649c13aae5a4a5b4571ecc5838e | d8f7f5c6de1c78d6a4be2dd1533cbe877a61b50baaf56515f0c3f7102e23a220 | 025516540e5b9a1473f2e691f52691db2c7107b8e26e5dedb40d08e515f04309 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,643 | MultilinearMap.bound_of_shell_of_norm_map_coord_zero | Mathlib/Analysis/NormedSpace/Multilinear/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>em</a> (∃ i, ‖m i‖ = 0) with (⟨i, hi⟩ | hm) | 𝕜 : Type u
ι : Type v
ι' : Type v'
E : ι → Type wE
E₁ : ι → Type wE₁
E' : ι' → Type wE'
G : Type wG
G' : Type wG'
inst✝¹² : Fintype ι
inst✝¹¹ : Fintype ι'
inst✝¹⁰ : NontriviallyNormedField 𝕜
inst✝⁹ : (i : ι) → SeminormedAddCommGroup (E i)
inst✝⁸ : (i : ι) → NormedSpace 𝕜 (E i)
inst✝⁷ : (i : ι) → SeminormedAddCommGro... | case inl.intro
𝕜 : Type u
ι : Type v
ι' : Type v'
E : ι → Type wE
E₁ : ι → Type wE₁
E' : ι' → Type wE'
G : Type wG
G' : Type wG'
inst✝¹² : Fintype ι
inst✝¹¹ : Fintype ι'
inst✝¹⁰ : NontriviallyNormedField 𝕜
inst✝⁹ : (i : ι) → SeminormedAddCommGroup (E i)
inst✝⁸ : (i : ι) → NormedSpace 𝕜 (E i)
inst✝⁷ : (i : ι) → Semin... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.8195) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.8195) (:fv _uniq.8322)) ((:c DFunLike.coe) ((:c MultilinearMap) (:fv _uniq.8177) (:fv _uniq.8179) (:fv _uniq.8185) (:fv _uniq.8195) ((:c DivisionSemiring.toSemiring) (:fv _uniq.8177) ((:c Semifield.toD... | [{"name":"𝕜","sexp":"(:sort (+ u 1))"},{"name":"ι","sexp":"(:sort (+ v 1))"},{"name":"ι'","sexp":"(:sort (+ v' 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.8179) (:sort (+ wE 1)))"},{"name":"E₁","sexp":"(:forall _ (:fv _uniq.8179) (:sort (+ wE₁ 1)))"},{"name":"E'","sexp":"(:forall _ (:fv _uniq.8181) (:sort (+ wE' 1... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV6))))) (:arg :explicit 2 (:app (:c DFunLike.c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8177","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.8179","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"source":"rcases","sourceEnd":5245,"sourceStart":5239,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"em","semanticRole":"global","source":"em","sourceEnd":5248,"sourceStart":5246,"tag":"identifier"},{"children":[{"children":[{"source":"... | [] | [{"source":"em (∃ i, ‖m i‖ = 0)","source_end":5271,"source_start":5246,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(⟨i, hi⟩ | hm)","source_end":5295,"source_start":5277,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8177","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.8179","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 14 | 4 | exact | true | 1 | 30 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b8698c1a20533ed92482eabcbe16ef8d9321efa707f92c7288c9d56d43d131d3 | 6c8fb17a2ac283b27d1e9f0327f6d00679fd48429c74187bc5836563271d66f6 | 7a6ef4ffd3703153bbfc5aba79f1b2a320dc896c477fc1d7def7a69717c52cca | a64e37adc8215471db241d22aa70a09f46c49f2527203d8e016f13bf722e69c9 |
cat-searcher/leandojo-benchmark-4-random | test | 2,644 | MultilinearMap.bound_of_shell_of_norm_map_coord_zero | Mathlib/Analysis/NormedSpace/Multilinear/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | push_neg at hm | case inr
𝕜 : Type u
ι : Type v
ι' : Type v'
E : ι → Type wE
E₁ : ι → Type wE₁
E' : ι' → Type wE'
G : Type wG
G' : Type wG'
inst✝¹² : Fintype ι
inst✝¹¹ : Fintype ι'
inst✝¹⁰ : NontriviallyNormedField 𝕜
inst✝⁹ : (i : ι) → SeminormedAddCommGroup (E i)
inst✝⁸ : (i : ι) → NormedSpace 𝕜 (E i)
inst✝⁷ : (i : ι) → SeminormedA... | case inr
𝕜 : Type u
ι : Type v
ι' : Type v'
E : ι → Type wE
E₁ : ι → Type wE₁
E' : ι' → Type wE'
G : Type wG
G' : Type wG'
inst✝¹² : Fintype ι
inst✝¹¹ : Fintype ι'
inst✝¹⁰ : NontriviallyNormedField 𝕜
inst✝⁹ : (i : ι) → SeminormedAddCommGroup (E i)
inst✝⁸ : (i : ι) → NormedSpace 𝕜 (E i)
inst✝⁷ : (i : ι) → SeminormedA... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.8195) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.8195) (:fv _uniq.8322)) ((:c DFunLike.coe) ((:c MultilinearMap) (:fv _uniq.8177) (:fv _uniq.8179) (:fv _uniq.8185) (:fv _uniq.8195) ((:c DivisionSemiring.toSemiring) (:fv _uniq.8177) ((:c Semifield.toD... | [{"name":"𝕜","sexp":"(:sort (+ u 1))"},{"name":"ι","sexp":"(:sort (+ v 1))"},{"name":"ι'","sexp":"(:sort (+ v' 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.8179) (:sort (+ wE 1)))"},{"name":"E₁","sexp":"(:forall _ (:fv _uniq.8179) (:sort (+ wE₁ 1)))"},{"name":"E'","sexp":"(:forall _ (:fv _uniq.8181) (:sort (+ wE' 1... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV6))))) (:arg :explicit 2 (:app (:c DFunLike.c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8177","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.8179","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"source":"push_neg","sourceEnd":5365,"sourceStart":5357,"tag":"atom"},{"children":[{"children":[{"source":"at","sourceEnd":5368,"sourceStart":5366,"tag":"atom"},{"children":[{"children":[{"contextIndex":31,"semanticRole":"local","source":"hm","sourceEnd":5371,"sourceStart":5369,"tag":"identifier"}],"kind"... | [] | [{"source":"hm","source_end":5371,"source_start":5369,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8177","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.8179","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 14 | 14 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5159043cdbca2e2c5b8e9ad2061eb429664e9426545981f2ffd563c0eaeb4a40 | 87a343f638ff6b3dacf817f7aa027456c171638ca15b6425b8c71cbb2fd96c9a | 8cca2df5f2048f2c1febb514b8d7a39d810778199ddcd98ab9b9e282a24610df | 73aa8920a2a2609eb8f040c03d1c91f02cb1fc4c55d1acfeeed5be74f32dae2a |
cat-searcher/leandojo-benchmark-4-random | test | 2,645 | MultilinearMap.bound_of_shell_of_norm_map_coord_zero | Mathlib/Analysis/NormedSpace/Multilinear/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | choose δ hδ0 hδm_lt hle_δm _ using fun i => <a>rescale_to_shell_semi_normed</a> (hc i) (hε i) (hm i) | case inr
𝕜 : Type u
ι : Type v
ι' : Type v'
E : ι → Type wE
E₁ : ι → Type wE₁
E' : ι' → Type wE'
G : Type wG
G' : Type wG'
inst✝¹² : Fintype ι
inst✝¹¹ : Fintype ι'
inst✝¹⁰ : NontriviallyNormedField 𝕜
inst✝⁹ : (i : ι) → SeminormedAddCommGroup (E i)
inst✝⁸ : (i : ι) → NormedSpace 𝕜 (E i)
inst✝⁷ : (i : ι) → SeminormedA... | case inr
𝕜 : Type u
ι : Type v
ι' : Type v'
E : ι → Type wE
E₁ : ι → Type wE₁
E' : ι' → Type wE'
G : Type wG
G' : Type wG'
inst✝¹² : Fintype ι
inst✝¹¹ : Fintype ι'
inst✝¹⁰ : NontriviallyNormedField 𝕜
inst✝⁹ : (i : ι) → SeminormedAddCommGroup (E i)
inst✝⁸ : (i : ι) → NormedSpace 𝕜 (E i)
inst✝⁷ : (i : ι) → SeminormedA... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.8195) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.8195) (:fv _uniq.8322)) ((:c DFunLike.coe) ((:c MultilinearMap) (:fv _uniq.8177) (:fv _uniq.8179) (:fv _uniq.8185) (:fv _uniq.8195) ((:c DivisionSemiring.toSemiring) (:fv _uniq.8177) ((:c Semifield.toD... | [{"name":"𝕜","sexp":"(:sort (+ u 1))"},{"name":"ι","sexp":"(:sort (+ v 1))"},{"name":"ι'","sexp":"(:sort (+ v' 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.8179) (:sort (+ wE 1)))"},{"name":"E₁","sexp":"(:forall _ (:fv _uniq.8179) (:sort (+ wE₁ 1)))"},{"name":"E'","sexp":"(:forall _ (:fv _uniq.8181) (:sort (+ wE' 1... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV6))))) (:arg :explicit 2 (:app (:c DFunLike.c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8177","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.8179","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"source":"choose","sourceEnd":5380,"sourceStart":5374,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"δ","sourceEnd":5383,"sourceStart":5381,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"δ","sourceEnd":5383,... | [] | [{"source":"fun i => rescale_to_shell_semi_normed (hc i) (hε i) (hm i)","source_end":5472,"source_start":5413,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8177","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.8179","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 14 | 15 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4061487de9388be9f4a9d237421a393c89bb8afad263b640cd0fb4e6d561e1d6 | 73aa8920a2a2609eb8f040c03d1c91f02cb1fc4c55d1acfeeed5be74f32dae2a | be39da61a4e3d187447ea9b6ebb1a9cc01d1582e2f16c6fecbb1fd303376af01 | 0f0acb8c57b2a97d01f1506c02a324b576110b05a79bd73f5c6d1ccb4299b351 |
cat-searcher/leandojo-benchmark-4-random | test | 2,647 | MultilinearMap.bound_of_shell_of_norm_map_coord_zero | Mathlib/Analysis/NormedSpace/Multilinear/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [<a>MultilinearMap.map_smul_univ</a>, <a>norm_smul</a>, <a>Finset.prod_mul_distrib</a>, <a>mul_left_comm</a> C, <a>mul_le_mul_left</a> hδ0] using hf (fun i => δ i • m i) hle_δm hδm_lt | case inr
𝕜 : Type u
ι : Type v
ι' : Type v'
E : ι → Type wE
E₁ : ι → Type wE₁
E' : ι' → Type wE'
G : Type wG
G' : Type wG'
inst✝¹² : Fintype ι
inst✝¹¹ : Fintype ι'
inst✝¹⁰ : NontriviallyNormedField 𝕜
inst✝⁹ : (i : ι) → SeminormedAddCommGroup (E i)
inst✝⁸ : (i : ι) → NormedSpace 𝕜 (E i)
inst✝⁷ : (i : ι) → SeminormedA... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.8195) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.8195) (:fv _uniq.8322)) ((:c DFunLike.coe) ((:c MultilinearMap) (:fv _uniq.8177) (:fv _uniq.8179) (:fv _uniq.8185) (:fv _uniq.8195) ((:c DivisionSemiring.toSemiring) (:fv _uniq.8177) ((:c Semifield.toD... | [{"name":"𝕜","sexp":"(:sort (+ u 1))"},{"name":"ι","sexp":"(:sort (+ v 1))"},{"name":"ι'","sexp":"(:sort (+ v' 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.8179) (:sort (+ wE 1)))"},{"name":"E₁","sexp":"(:forall _ (:fv _uniq.8179) (:sort (+ wE₁ 1)))"},{"name":"E'","sexp":"(:forall _ (:fv _uniq.8181) (:sort (+ wE' 1... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV6))))) (:arg :explicit 2 (:app (:c DFunLike.c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8177","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.8179","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"source":"simpa","sourceEnd":5563,"sourceStart":5558,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"chil... | [] | [{"source":"map_smul_univ","source_end":5578,"source_start":5565,"syntax_kind":"ident"},{"source":"norm_smul","source_end":5589,"source_start":5580,"syntax_kind":"ident"},{"source":"prod_mul_distrib","source_end":5607,"source_start":5591,"syntax_kind":"ident"},{"source":"mul_left_comm C","source_end":5624,"source_start... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8177","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.8179","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 14 | 17 | exact | true | 1 | 37 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5f7f10b090773c42a2c27d9f1312cdc86167f457327e75c858fc953ae2ece23a | 94393f9597d93f598c3a9958d8a8265f6663eb38ce2f9942db0052cdb9043c8c | 9ba02e2c4a0ddb4a20307007bbcdede6187687bcc43ddfebb72ccd3c1077f03e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,648 | MultilinearMap.bound_of_shell_of_norm_map_coord_zero | Mathlib/Analysis/NormedSpace/Multilinear/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hf₀ hi, <a>Finset.prod_eq_zero</a> (<a>Finset.mem_univ</a> i) hi, <a>MulZeroClass.mul_zero</a>] | case inl.intro
𝕜 : Type u
ι : Type v
ι' : Type v'
E : ι → Type wE
E₁ : ι → Type wE₁
E' : ι' → Type wE'
G : Type wG
G' : Type wG'
inst✝¹² : Fintype ι
inst✝¹¹ : Fintype ι'
inst✝¹⁰ : NontriviallyNormedField 𝕜
inst✝⁹ : (i : ι) → SeminormedAddCommGroup (E i)
inst✝⁸ : (i : ι) → NormedSpace 𝕜 (E i)
inst✝⁷ : (i : ι) → Semin... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.8195) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.8195) (:fv _uniq.8322)) ((:c DFunLike.coe) ((:c MultilinearMap) (:fv _uniq.8177) (:fv _uniq.8179) (:fv _uniq.8185) (:fv _uniq.8195) ((:c DivisionSemiring.toSemiring) (:fv _uniq.8177) ((:c Semifield.toD... | [{"name":"𝕜","sexp":"(:sort (+ u 1))"},{"name":"ι","sexp":"(:sort (+ v 1))"},{"name":"ι'","sexp":"(:sort (+ v' 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.8179) (:sort (+ wE 1)))"},{"name":"E₁","sexp":"(:forall _ (:fv _uniq.8179) (:sort (+ wE₁ 1)))"},{"name":"E'","sexp":"(:forall _ (:fv _uniq.8181) (:sort (+ wE' 1... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV6))))) (:arg :explicit 2 (:app (:c DFunLike.c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8177","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.8179","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":5303,"sourceStart":5301,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5305,"sourceStart":5304,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"hf₀ hi","source_end":5313,"source_start":5305,"syntax_kind":"Lean.Parser.Term.app"},{"source":"prod_eq_zero (mem_univ i) hi","source_end":5343,"source_start":5315,"syntax_kind":"Lean.Parser.Term.app"},{"source":"mul_zero","source_end":5353,"source_start":5345,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8177","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.8179","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 14 | 7 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 299da9ed8d4144ad4e737076d7521a6b2da5434554ecedb70b9022ac737e1f0e | ddaba214d0172d26b3e17970ab18841195ee724f522c40f6609c9394bdad455e | dd8087de5494b6c753bbb27a68eadd86c940366adad9a639c1d1b1043a239458 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,649 | contMDiff_inclusion | Mathlib/Geometry/Manifold/ContMDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨x, hx : x ∈ U⟩ | 𝕜 : Type u_1
inst✝¹⁷ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁶ : NormedAddCommGroup E
inst✝¹⁵ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁴ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹³ : TopologicalSpace M
inst✝¹² : ChartedSpace H M
inst✝¹¹ : SmoothManifoldWithCorners I M
E' : Type u_5
inst✝... | case mk
𝕜 : Type u_1
inst✝¹⁷ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁶ : NormedAddCommGroup E
inst✝¹⁵ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁴ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹³ : TopologicalSpace M
inst✝¹² : ChartedSpace H M
inst✝¹¹ : SmoothManifoldWithCorners I M
E' : Type u... | ((:c ContMDiff) (:fv _uniq.119205) (:fv _uniq.119208) (:fv _uniq.119211) (:fv _uniq.119214) (:fv _uniq.119327) (:fv _uniq.119330) (:fv _uniq.119333) (:fv _uniq.119365) ((:c Set.Elem) (:fv _uniq.119368) ((:c SetLike.coe) ((:c TopologicalSpace.Opens) (:fv _uniq.119368) (:fv _uniq.119371)) (:fv _uniq.119368) ((:c Topologi... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁷","sexp":"((:c NontriviallyNormedField) (:fv _uniq.119205))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁶","sexp":"((:c NormedAddCommGroup) (:fv _uniq.119211))"},{"name":"inst✝¹⁵","sexp":"((:c NormedSpace) (:fv _uniq.119205) (:fv _uniq.119211) ((:c ... | (:app (:c ContMDiff) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119205","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.119208","is_instance":true,"is_let":false,"name":"inst✝¹⁷","sexp":"(:app (:c NontriviallyNormedF... | {"children":[{"source":"rintro","sourceEnd":16442,"sourceStart":16436,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":16446,"sourceStart":16443,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":16447,"sou... | [{"role":"fresh_name","source":"x","source_end":16447,"source_start":16446,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":16451,"source_start":16449,"syntax_kind":"ident"},{"role":"fresh_name","source":"x","source_end":16455,"source_start":16454,"syntax_kind":"ident"}] | [{"source":"⟨x, hx : x ∈ U⟩","source_end":16464,"source_start":16443,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119205","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.119208","is_instance":true,"is_let":false,"user_name":"inst✝¹⁷"},{"binder_role":":implicit","context_index":2,"in... | 122 | 4 | exact | true | 1 | 45 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 00d11b37deba6990fe5b33033fae586c8d1f193d22a1cfee831e72c8b4a5ee32 | 747ea17ec76657f0d906c4b9105f31e53f1c7d8efe7c2a54606d104276c5e037 | 3363cc200c3761d6d9d31a2f9bae7edf62648d58e5d46c17c3a3c8e6acb3ca97 | 51623f025089728ec1e09a36cc02001f687bda3359ea0312f37cac220d50e4e5 |
cat-searcher/leandojo-benchmark-4-random | test | 2,650 | contMDiff_inclusion | Mathlib/Geometry/Manifold/ContMDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply (<a>contDiffWithinAt_localInvariantProp</a> I I n).<a>StructureGroupoid.LocalInvariantProp.liftProp_inclusion</a> | case mk
𝕜 : Type u_1
inst✝¹⁷ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁶ : NormedAddCommGroup E
inst✝¹⁵ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁴ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹³ : TopologicalSpace M
inst✝¹² : ChartedSpace H M
inst✝¹¹ : SmoothManifoldWithCorners I M
E' : Type u... | case mk.hQ
𝕜 : Type u_1
inst✝¹⁷ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁶ : NormedAddCommGroup E
inst✝¹⁵ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁴ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹³ : TopologicalSpace M
inst✝¹² : ChartedSpace H M
inst✝¹¹ : SmoothManifoldWithCorners I M
E' : Typ... | ((:c ContMDiffAt) (:fv _uniq.119205) (:fv _uniq.119208) (:fv _uniq.119211) (:fv _uniq.119214) (:fv _uniq.119327) (:fv _uniq.119330) (:fv _uniq.119333) (:fv _uniq.119365) ((:c Set.Elem) (:fv _uniq.119368) ((:c SetLike.coe) ((:c TopologicalSpace.Opens) (:fv _uniq.119368) (:fv _uniq.119371)) (:fv _uniq.119368) ((:c Topolo... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁷","sexp":"((:c NontriviallyNormedField) (:fv _uniq.119205))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁶","sexp":"((:c NormedAddCommGroup) (:fv _uniq.119211))"},{"name":"inst✝¹⁵","sexp":"((:c NormedSpace) (:fv _uniq.119205) (:fv _uniq.119211) ((:c ... | (:app (:c ContMDiffAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119205","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.119208","is_instance":true,"is_let":false,"name":"inst✝¹⁷","sexp":"(:app (:c NontriviallyNormedF... | {"children":[{"source":"apply","sourceEnd":16472,"sourceStart":16467,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":16474,"sourceStart":16473,"tag":"atom"},{"children":[{"name":"contDiffWithinAt_localInvariantProp","semanticRole":"global","source":"contDiffWithinAt_localInvariantProp","sourceEnd":165... | [] | [{"source":"(contDiffWithinAt_localInvariantProp I I n).liftProp_inclusion","source_end":16535,"source_start":16473,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119205","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.119208","is_instance":true,"is_let":false,"user_name":"inst✝¹⁷"},{"binder_role":":implicit","context_index":2,"in... | 122 | 5 | exact | true | 1 | 47 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3828fa24f668b2cb20213d6be81792ef201d1c38f24d69ad14f6343f580acdfe | 51623f025089728ec1e09a36cc02001f687bda3359ea0312f37cac220d50e4e5 | 977ab88bd390c868a321cb9202b0ffbc584d0f518f19fb6f3702e5be1fb694b7 | 2ae2ef1aa285a493ce88223b30c62514b94e8da76d157ec7034252f0913de0aa |
cat-searcher/leandojo-benchmark-4-random | test | 2,651 | contMDiff_inclusion | Mathlib/Geometry/Manifold/ContMDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro y | case mk.hQ
𝕜 : Type u_1
inst✝¹⁷ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁶ : NormedAddCommGroup E
inst✝¹⁵ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁴ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹³ : TopologicalSpace M
inst✝¹² : ChartedSpace H M
inst✝¹¹ : SmoothManifoldWithCorners I M
E' : Typ... | case mk.hQ
𝕜 : Type u_1
inst✝¹⁷ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁶ : NormedAddCommGroup E
inst✝¹⁵ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁴ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹³ : TopologicalSpace M
inst✝¹² : ChartedSpace H M
inst✝¹¹ : SmoothManifoldWithCorners I M
E' : Typ... | (:forall y (:fv _uniq.119330) ((:c ContDiffWithinAtProp) (:fv _uniq.119205) (:fv _uniq.119208) (:fv _uniq.119211) (:fv _uniq.119214) (:fv _uniq.119327) (:fv _uniq.119330) (:fv _uniq.119333) (:fv _uniq.119365) (:fv _uniq.119211) (:fv _uniq.119214) (:fv _uniq.119327) (:fv _uniq.119330) (:fv _uniq.119333) (:fv _uniq.11936... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁷","sexp":"((:c NontriviallyNormedField) (:fv _uniq.119205))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁶","sexp":"((:c NormedAddCommGroup) (:fv _uniq.119211))"},{"name":"inst✝¹⁵","sexp":"((:c NormedSpace) (:fv _uniq.119205) (:fv _uniq.119211) ((:c ... | (:forall y :explicit (:fv FV5) (:app (:c ContDiffWithinAtProp) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119205","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.119208","is_instance":true,"is_let":false,"name":"inst✝¹⁷","sexp":"(:app (:c NontriviallyNormedF... | {"children":[{"source":"intro","sourceEnd":16543,"sourceStart":16538,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":16545,"sourceStart":16544,"tag":"identifier"}],"kind":"null","source":"y","sourceEnd":16545,"sourceStart":16544,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"y","source_end":16545,"source_start":16544,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119205","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.119208","is_instance":true,"is_let":false,"user_name":"inst✝¹⁷"},{"binder_role":":implicit","context_index":2,"in... | 122 | 6 | exact | true | 1 | 47 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3d8a0249cc14430f6b20c200114b9228697a304871f37527b8560d16caf4078c | 2ae2ef1aa285a493ce88223b30c62514b94e8da76d157ec7034252f0913de0aa | 85390ac44bda3124c08903df1f981e2eead2a91d5d3d503fc936003a462be0d3 | 2fcdac467b0ffd57e52f3fe1b511b9c5758636787492d4126e17f13e7776a102 |
cat-searcher/leandojo-benchmark-4-random | test | 2,652 | contMDiff_inclusion | Mathlib/Geometry/Manifold/ContMDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp only [<a>ContDiffWithinAtProp</a>, <a>Function.id_comp</a>, <a>Set.preimage_univ</a>] | case mk.hQ
𝕜 : Type u_1
inst✝¹⁷ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁶ : NormedAddCommGroup E
inst✝¹⁵ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁴ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹³ : TopologicalSpace M
inst✝¹² : ChartedSpace H M
inst✝¹¹ : SmoothManifoldWithCorners I M
E' : Typ... | case mk.hQ
𝕜 : Type u_1
inst✝¹⁷ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁶ : NormedAddCommGroup E
inst✝¹⁵ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁴ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹³ : TopologicalSpace M
inst✝¹² : ChartedSpace H M
inst✝¹¹ : SmoothManifoldWithCorners I M
E' : Typ... | ((:c ContDiffWithinAtProp) (:fv _uniq.119205) (:fv _uniq.119208) (:fv _uniq.119211) (:fv _uniq.119214) (:fv _uniq.119327) (:fv _uniq.119330) (:fv _uniq.119333) (:fv _uniq.119365) (:fv _uniq.119211) (:fv _uniq.119214) (:fv _uniq.119327) (:fv _uniq.119330) (:fv _uniq.119333) (:fv _uniq.119365) (:fv _uniq.120622) ((:c id)... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁷","sexp":"((:c NontriviallyNormedField) (:fv _uniq.119205))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁶","sexp":"((:c NormedAddCommGroup) (:fv _uniq.119211))"},{"name":"inst✝¹⁵","sexp":"((:c NormedSpace) (:fv _uniq.119205) (:fv _uniq.119211) ((:c ... | (:app (:c ContDiffWithinAtProp) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119205","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.119208","is_instance":true,"is_let":false,"name":"inst✝¹⁷","sexp":"(:app (:c NontriviallyNormedF... | {"children":[{"source":"dsimp","sourceEnd":16553,"sourceStart":16548,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":16558,"sourceStart":16554,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":16... | [] | [{"source":"ContDiffWithinAtProp","source_end":16580,"source_start":16560,"syntax_kind":"ident"},{"source":"id_comp","source_end":16589,"source_start":16582,"syntax_kind":"ident"},{"source":"preimage_univ","source_end":16604,"source_start":16591,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119205","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.119208","is_instance":true,"is_let":false,"user_name":"inst✝¹⁷"},{"binder_role":":implicit","context_index":2,"in... | 122 | 7 | exact | true | 1 | 48 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bc63cbcabdcb040c6b467529824039173736890b2b98c98afa13c8e4a17cc046 | 2fcdac467b0ffd57e52f3fe1b511b9c5758636787492d4126e17f13e7776a102 | 4b4ed16af3b43a11e7282cef4278682696ffe8c5a441bc2c47ecbd5363bb5219 | bf4a81e1c1ad1564adfbb36c7dcf510a06a2d86eb41c5f0e2cd0036b9edd04be |
cat-searcher/leandojo-benchmark-4-random | test | 2,653 | contMDiff_inclusion | Mathlib/Geometry/Manifold/ContMDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.univ_inter</a>] | case mk.hQ
𝕜 : Type u_1
inst✝¹⁷ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁶ : NormedAddCommGroup E
inst✝¹⁵ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁴ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹³ : TopologicalSpace M
inst✝¹² : ChartedSpace H M
inst✝¹¹ : SmoothManifoldWithCorners I M
E' : Typ... | case mk.hQ
𝕜 : Type u_1
inst✝¹⁷ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁶ : NormedAddCommGroup E
inst✝¹⁵ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁴ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹³ : TopologicalSpace M
inst✝¹² : ChartedSpace H M
inst✝¹¹ : SmoothManifoldWithCorners I M
E' : Typ... | ((:c ContDiffWithinAt) (:fv _uniq.119205) (:fv _uniq.119208) (:fv _uniq.119211) (:fv _uniq.119214) (:fv _uniq.119327) (:fv _uniq.119211) (:fv _uniq.119214) (:fv _uniq.119327) (:fv _uniq.120622) ((:c Function.comp) (:fv _uniq.119211) (:fv _uniq.119330) (:fv _uniq.119211) ((:c ModelWithCorners.toFun') (:fv _uniq.119205) ... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁷","sexp":"((:c NontriviallyNormedField) (:fv _uniq.119205))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁶","sexp":"((:c NormedAddCommGroup) (:fv _uniq.119211))"},{"name":"inst✝¹⁵","sexp":"((:c NormedSpace) (:fv _uniq.119205) (:fv _uniq.119211) ((:c ... | (:app (:c ContDiffWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119205","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.119208","is_instance":true,"is_let":false,"name":"inst✝¹⁷","sexp":"(:app (:c NontriviallyNormedF... | {"children":[{"source":"rw","sourceEnd":16610,"sourceStart":16608,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16612,"sourceStart":16611,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.univ_inter",... | [] | [{"source":"Set.univ_inter","source_end":16626,"source_start":16612,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119205","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.119208","is_instance":true,"is_let":false,"user_name":"inst✝¹⁷"},{"binder_role":":implicit","context_index":2,"in... | 122 | 8 | exact | true | 1 | 48 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e0caaf19ceb356935700c813ebc9416c4f84e553e15da102801f14f4458154ec | bf4a81e1c1ad1564adfbb36c7dcf510a06a2d86eb41c5f0e2cd0036b9edd04be | 0dc0f6c94f5308879d5a243a48cd59234f2fb8ceb81bb627880100f74d463a2f | 0c3ff1e28bb1679c04a56ebaa9fdf61a13a8285c56d1bfe2561edcc80e3b63e3 |
cat-searcher/leandojo-benchmark-4-random | test | 2,654 | contMDiff_inclusion | Mathlib/Geometry/Manifold/ContMDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact contDiffWithinAt_id.congr I.rightInvOn (<a>congr_arg</a> I (I.left_inv y)) | case mk.hQ
𝕜 : Type u_1
inst✝¹⁷ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁶ : NormedAddCommGroup E
inst✝¹⁵ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁴ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹³ : TopologicalSpace M
inst✝¹² : ChartedSpace H M
inst✝¹¹ : SmoothManifoldWithCorners I M
E' : Typ... | ((:c ContDiffWithinAt) (:fv _uniq.119205) (:fv _uniq.119208) (:fv _uniq.119211) (:fv _uniq.119214) (:fv _uniq.119327) (:fv _uniq.119211) (:fv _uniq.119214) (:fv _uniq.119327) (:fv _uniq.120622) ((:c Function.comp) (:fv _uniq.119211) (:fv _uniq.119330) (:fv _uniq.119211) ((:c ModelWithCorners.toFun') (:fv _uniq.119205) ... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁷","sexp":"((:c NontriviallyNormedField) (:fv _uniq.119205))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁶","sexp":"((:c NormedAddCommGroup) (:fv _uniq.119211))"},{"name":"inst✝¹⁵","sexp":"((:c NormedSpace) (:fv _uniq.119205) (:fv _uniq.119211) ((:c ... | (:app (:c ContDiffWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119205","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.119208","is_instance":true,"is_let":false,"name":"inst✝¹⁷","sexp":"(:app (:c NontriviallyNormedF... | {"children":[{"source":"exact","sourceEnd":16635,"sourceStart":16630,"tag":"atom"},{"children":[{"source":"contDiffWithinAt_id.congr","sourceEnd":16661,"sourceStart":16636,"tag":"identifier"},{"children":[{"name":"ModelWithCorners.rightInvOn","semanticRole":"global","source":"I.rightInvOn","sourceEnd":16674,"sourceStar... | [] | [{"source":"contDiffWithinAt_id.congr I.rightInvOn (congr_arg I (I.left_inv y))","source_end":16703,"source_start":16636,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119205","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.119208","is_instance":true,"is_let":false,"user_name":"inst✝¹⁷"},{"binder_role":":implicit","context_index":2,"in... | 122 | 11 | exact | true | 1 | 48 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a8e46762775eced05179b9ad30504f34fe9d401fff179ceb35c464aac781dca7 | 0c3ff1e28bb1679c04a56ebaa9fdf61a13a8285c56d1bfe2561edcc80e3b63e3 | a12b4e67adac8d6b1119eae37e5d44042b8a59b23141d620a4a8b5ae16a1fab6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,655 | Nat.prime_three | Mathlib/Data/Nat/Prime.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | decide | n : ℕ
⊢ Prime 3 | ((:c Nat.Prime) ((:c OfNat.ofNat) (:c Nat) (:lit 3) ((:c instOfNatNat) (:lit 3)))) | [{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Nat.Prime) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 3)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:lit 3)))))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5601","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"decide","sourceEnd":6330,"sourceStart":6324,"tag":"atom"}],"kind":"Lean.Parser.Tactic.decide","source":"decide","sourceEnd":6330,"sourceStart":6324,"tag":"node"}],"kind":"null","source":"decide","sourceEnd":6330,"sourceStart":6324,"tag":"node"}],"kind":"Lea... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5601","is_instance":false,"is_let":false,"user_name":"n"}] | 44 | 2 | exact | true | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 423cca8c69705553a3f29739a044fb216b38a0f7f2d415aeba8776cce6fdc08a | 506599d2bed751f171b4cc09cd82a7e02bb23c93fd19fb7c888af81d4798328f | 5589aa5863c2d85622d06d651add002416e5513afdbb455666cdde01bb3e257d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,656 | LinearMap.trace_tensorProduct' | Mathlib/LinearAlgebra/Trace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h := <a>LinearMap.ext_iff</a>.1 (<a>LinearMap.ext_iff</a>.1 (<a>LinearMap.trace_tensorProduct</a> R M N) f) g | R : Type u_1
inst✝¹² : CommRing R
M : Type u_2
inst✝¹¹ : AddCommGroup M
inst✝¹⁰ : Module R M
N : Type u_3
P : Type u_4
inst✝⁹ : AddCommGroup N
inst✝⁸ : Module R N
inst✝⁷ : AddCommGroup P
inst✝⁶ : Module R P
ι : Type u_5
inst✝⁵ : Module.Free R M
inst✝⁴ : Module.Finite R M
inst✝³ : Module.Free R N
inst✝² : Module.Finite ... | R : Type u_1
inst✝¹² : CommRing R
M : Type u_2
inst✝¹¹ : AddCommGroup M
inst✝¹⁰ : Module R M
N : Type u_3
P : Type u_4
inst✝⁹ : AddCommGroup N
inst✝⁸ : Module R N
inst✝⁷ : AddCommGroup P
inst✝⁶ : Module R P
ι : Type u_5
inst✝⁵ : Module.Free R M
inst✝⁴ : Module.Finite R M
inst✝³ : Module.Free R N
inst✝² : Module.Finite ... | ((:c Eq) (:fv _uniq.273517) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.273517) (:fv _uniq.273517) ((:c CommSemiring.toSemiring) (:fv _uniq.273517) ((:c CommRing.toCommSemiring) (:fv _uniq.273517) (:fv _uniq.273520))) ((:c CommSemiring.toSemiring) (:fv _uniq.273517) ((:c CommRing.toCommSemiring) (:fv _uniq.273517) (:... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹²","sexp":"((:c CommRing) (:fv _uniq.273517))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c AddCommGroup) (:fv _uniq.273523))"},{"name":"inst✝¹⁰","sexp":"((:c Module) (:fv _uniq.273517) (:fv _uniq.273523) ((:c CommSemiring.toSemiring) (:... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.273517","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.273520","is_instance":true,"is_let":false,"name":"inst✝¹²","sexp":"(:app (:c CommRing) (:arg :exp... | {"children":[{"source":"have","sourceEnd":11685,"sourceStart":11681,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":11687,"sourceStart":11686,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":11687,"sourceStart":11686,"tag":"node"... | [] | [{"source":"ext_iff.1 (ext_iff.1 (trace_tensorProduct R M N) f) g","source_end":11744,"source_start":11691,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.273517","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.273520","is_instance":true,"is_let":false,"user_name":"inst✝¹²"},{"binder_role":":implicit","context_index":2,"int... | 72 | 4 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d1dbf7a7c1bdc3e56b9889fff3a5edaf351ad39e3b1a469d016152c0343d0cea | 22fe3fd4f9785d08e3d29b12cef0f7691935c1b48d5db8012bc58661419e50d2 | 3dcc572de62f06222d9fcedfb05d59273b9b66f9768963951890f8e4887ba8ff | 8f84344d6329c9e3fc78cb5941cc034750ea0e5c453d201ec5ec791d083a6d8f |
cat-searcher/leandojo-benchmark-4-random | test | 2,657 | LinearMap.trace_tensorProduct' | Mathlib/LinearAlgebra/Trace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>LinearMap.compr₂_apply</a>, <a>TensorProduct.mapBilinear_apply</a>, <a>LinearMap.compl₁₂_apply</a>, <a>LinearMap.lsmul_apply</a>, <a>Algebra.id.smul_eq_mul</a>] at h | R : Type u_1
inst✝¹² : CommRing R
M : Type u_2
inst✝¹¹ : AddCommGroup M
inst✝¹⁰ : Module R M
N : Type u_3
P : Type u_4
inst✝⁹ : AddCommGroup N
inst✝⁸ : Module R N
inst✝⁷ : AddCommGroup P
inst✝⁶ : Module R P
ι : Type u_5
inst✝⁵ : Module.Free R M
inst✝⁴ : Module.Finite R M
inst✝³ : Module.Free R N
inst✝² : Module.Finite ... | R : Type u_1
inst✝¹² : CommRing R
M : Type u_2
inst✝¹¹ : AddCommGroup M
inst✝¹⁰ : Module R M
N : Type u_3
P : Type u_4
inst✝⁹ : AddCommGroup N
inst✝⁸ : Module R N
inst✝⁷ : AddCommGroup P
inst✝⁶ : Module R P
ι : Type u_5
inst✝⁵ : Module.Free R M
inst✝⁴ : Module.Finite R M
inst✝³ : Module.Free R N
inst✝² : Module.Finite ... | ((:c Eq) (:fv _uniq.273517) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.273517) (:fv _uniq.273517) ((:c CommSemiring.toSemiring) (:fv _uniq.273517) ((:c CommRing.toCommSemiring) (:fv _uniq.273517) (:fv _uniq.273520))) ((:c CommSemiring.toSemiring) (:fv _uniq.273517) ((:c CommRing.toCommSemiring) (:fv _uniq.273517) (:... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹²","sexp":"((:c CommRing) (:fv _uniq.273517))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c AddCommGroup) (:fv _uniq.273523))"},{"name":"inst✝¹⁰","sexp":"((:c Module) (:fv _uniq.273517) (:fv _uniq.273523) ((:c CommSemiring.toSemiring) (:... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.273517","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.273520","is_instance":true,"is_let":false,"name":"inst✝¹²","sexp":"(:app (:c CommRing) (:arg :exp... | {"children":[{"source":"simp","sourceEnd":11751,"sourceStart":11747,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":11756,"sourceStart":11752,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":117... | [] | [{"source":"compr₂_apply","source_end":11772,"source_start":11758,"syntax_kind":"ident"},{"source":"mapBilinear_apply","source_end":11791,"source_start":11774,"syntax_kind":"ident"},{"source":"compl₁₂_apply","source_end":11810,"source_start":11793,"syntax_kind":"ident"},{"source":"lsmul_apply","source_end":11823,"sourc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.273517","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.273520","is_instance":true,"is_let":false,"user_name":"inst✝¹²"},{"binder_role":":implicit","context_index":2,"int... | 72 | 5 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eca1837e3d4dd314afc07d087f65917cb9218ebf3ca4685a989e716a70d451cf | 8f84344d6329c9e3fc78cb5941cc034750ea0e5c453d201ec5ec791d083a6d8f | aeebcc065933540fdf15f3bf8c22bac5afa11679ea7d88e14b964614229da2da | 3cde853e20da65ab57dcb7f39d3b45a2c8a2a51af299efcf1b4537fe97152e6f |
cat-searcher/leandojo-benchmark-4-random | test | 2,658 | LinearMap.trace_tensorProduct' | Mathlib/LinearAlgebra/Trace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact h | R : Type u_1
inst✝¹² : CommRing R
M : Type u_2
inst✝¹¹ : AddCommGroup M
inst✝¹⁰ : Module R M
N : Type u_3
P : Type u_4
inst✝⁹ : AddCommGroup N
inst✝⁸ : Module R N
inst✝⁷ : AddCommGroup P
inst✝⁶ : Module R P
ι : Type u_5
inst✝⁵ : Module.Free R M
inst✝⁴ : Module.Finite R M
inst✝³ : Module.Free R N
inst✝² : Module.Finite ... | ((:c Eq) (:fv _uniq.273517) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.273517) (:fv _uniq.273517) ((:c CommSemiring.toSemiring) (:fv _uniq.273517) ((:c CommRing.toCommSemiring) (:fv _uniq.273517) (:fv _uniq.273520))) ((:c CommSemiring.toSemiring) (:fv _uniq.273517) ((:c CommRing.toCommSemiring) (:fv _uniq.273517) (:... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹²","sexp":"((:c CommRing) (:fv _uniq.273517))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c AddCommGroup) (:fv _uniq.273523))"},{"name":"inst✝¹⁰","sexp":"((:c Module) (:fv _uniq.273517) (:fv _uniq.273523) ((:c CommSemiring.toSemiring) (:... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.273517","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.273520","is_instance":true,"is_let":false,"name":"inst✝¹²","sexp":"(:app (:c CommRing) (:arg :exp... | {"children":[{"source":"exact","sourceEnd":11865,"sourceStart":11860,"tag":"atom"},{"contextIndex":21,"semanticRole":"local","source":"h","sourceEnd":11867,"sourceStart":11866,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact h","sourceEnd":11867,"sourceStart":11860,"tag":"node"} | [] | [{"source":"h","source_end":11867,"source_start":11866,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.273517","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.273520","is_instance":true,"is_let":false,"user_name":"inst✝¹²"},{"binder_role":":implicit","context_index":2,"int... | 72 | 6 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5e5fdcbe33c2cf660f46cf0db0482e118d8ed183b5e7fcb93ce43b2b927022d7 | 3cde853e20da65ab57dcb7f39d3b45a2c8a2a51af299efcf1b4537fe97152e6f | c2ce0e21ffddde69d6a80e187a5bf12b7761df4be076519945be8ed7a7a77294 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,659 | Set.Ioo_add_bij | Mathlib/Algebra/Order/Interval/Set/Monoid.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Set.Ioi_inter_Iio</a>, ← <a>Set.Ioi_inter_Iio</a>] | M : Type u_1
inst✝¹ : OrderedCancelAddCommMonoid M
inst✝ : ExistsAddOfLE M
a b c d : M
⊢ BijOn (fun x => x + d) (Ioo a b) (Ioo (a + d) (b + d)) | M : Type u_1
inst✝¹ : OrderedCancelAddCommMonoid M
inst✝ : ExistsAddOfLE M
a b c d : M
⊢ BijOn (fun x => x + d) (Ioi a ∩ Iio b) (Ioi (a + d) ∩ Iio (b + d)) | ((:c Set.BijOn) (:fv _uniq.4793) (:fv _uniq.4793) (:lambda _ (:fv _uniq.4793) ((:c HAdd.hAdd) (:fv _uniq.4793) (:fv _uniq.4793) (:fv _uniq.4793) ((:c instHAdd) (:fv _uniq.4793) ((:c AddCommMagma.toAdd) (:fv _uniq.4793) ((:c AddCommSemigroup.toAddCommMagma) (:fv _uniq.4793) ((:c AddCommMonoid.toAddCommSemigroup) (:fv _u... | [{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c OrderedCancelAddCommMonoid) (:fv _uniq.4793))"},{"name":"inst✝","sexp":"((:c ExistsAddOfLE) (:fv _uniq.4793) ((:c AddCommMagma.toAdd) (:fv _uniq.4793) ((:c AddCommSemigroup.toAddCommMagma) (:fv _uniq.4793) ((:c AddCommMonoid.toAddCommSemigroup) (:fv... | (:app (:c Set.BijOn) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:lambda _ :explicit (:fv FV0) (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4793","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4796","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c OrderedCancelAddCommMonoi... | {"children":[{"source":"rw","sourceEnd":2046,"sourceStart":2044,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2048,"sourceStart":2047,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":2051,"sourceStart":... | [] | [{"source":"Ioi_inter_Iio","source_end":2065,"source_start":2052,"syntax_kind":"ident"},{"source":"Ioi_inter_Iio","source_end":2084,"source_start":2071,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4793","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4796","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":2,... | 10 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5312c94420888097403e0c85ecdbf537ffaf5e41f691deda423f47d754caa954 | 235650df8406f6cdd6725ae53eb938119adfbd006d41ba3b0170485b1d3a2d5d | 47ee15b55828799cf40eb871c87006303067861939d29a16ca84c978c62fa35b | 5acc71a55d64dd43b5aa1f884d0d7a9b5df709b6efaf1d2d89baf2655b9ce877 |
cat-searcher/leandojo-benchmark-4-random | test | 2,660 | Set.Ioo_add_bij | Mathlib/Algebra/Order/Interval/Set/Monoid.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>Set.Ioi_add_bij</a> a d).<a>Set.BijOn.inter_mapsTo</a> (fun x hx => <a>add_lt_add_right</a> hx _) fun x hx => <a>lt_of_add_lt_add_right</a> hx.2 | M : Type u_1
inst✝¹ : OrderedCancelAddCommMonoid M
inst✝ : ExistsAddOfLE M
a b c d : M
⊢ BijOn (fun x => x + d) (Ioi a ∩ Iio b) (Ioi (a + d) ∩ Iio (b + d)) | ((:c Set.BijOn) (:fv _uniq.4793) (:fv _uniq.4793) (:lambda _ (:fv _uniq.4793) ((:c HAdd.hAdd) (:fv _uniq.4793) (:fv _uniq.4793) (:fv _uniq.4793) ((:c instHAdd) (:fv _uniq.4793) ((:c AddCommMagma.toAdd) (:fv _uniq.4793) ((:c AddCommSemigroup.toAddCommMagma) (:fv _uniq.4793) ((:c AddCommMonoid.toAddCommSemigroup) (:fv _u... | [{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c OrderedCancelAddCommMonoid) (:fv _uniq.4793))"},{"name":"inst✝","sexp":"((:c ExistsAddOfLE) (:fv _uniq.4793) ((:c AddCommMagma.toAdd) (:fv _uniq.4793) ((:c AddCommSemigroup.toAddCommMagma) (:fv _uniq.4793) ((:c AddCommMonoid.toAddCommSemigroup) (:fv... | (:app (:c Set.BijOn) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:lambda _ :explicit (:fv FV0) (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4793","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4796","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c OrderedCancelAddCommMonoi... | {"children":[{"source":"exact","sourceEnd":2093,"sourceStart":2088,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":2099,"sourceStart":2098,"tag":"atom"},{"children":[{"name":"Set.Ioi_add_bij","semanticRole":"global","source":"Ioi_add_bij","sourceEnd":2110,"sourceStart":2099,"tag":"identif... | [] | [{"source":"(Ioi_add_bij a d).inter_mapsTo (fun x hx => add_lt_add_right hx _) fun x hx =>\n lt_of_add_lt_add_right hx.2","source_end":2210,"source_start":2098,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4793","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4796","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":2,... | 10 | 8 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9f4e15315bbdcffe8bed27ada48ebbfc3bff70c92b70d07b6a7b87e5435e473d | 5acc71a55d64dd43b5aa1f884d0d7a9b5df709b6efaf1d2d89baf2655b9ce877 | 2181eb8fe72318f61a27bcc7275570a8fbda4bc692ffa5023bd016d20ebe4f80 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,661 | Set.Ioc_union_Ioi' | Mathlib/Order/Interval/Set/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext1 x | α : Type u_1
β : Type u_2
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
h₁ : c ≤ b
⊢ Ioc a b ∪ Ioi c = Ioi (min a c) | case h
α : Type u_1
β : Type u_2
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
h₁ : c ≤ b
x : α
⊢ x ∈ Ioc a b ∪ Ioi c ↔ x ∈ Ioi (min a c) | ((:c Eq) ((:c Set) (:fv _uniq.81671)) ((:c Union.union) ((:c Set) (:fv _uniq.81671)) ((:c Set.instUnion) (:fv _uniq.81671)) ((:c Set.Ioc) (:fv _uniq.81671) ((:c PartialOrder.toPreorder) (:fv _uniq.81671) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.81671) ((:c Lattice.toSemilatticeInf) (:fv _uniq.81671) ((:c DistribL... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.81671))"},{"name":"a","sexp":"(:fv _uniq.81671)"},{"name":"a₁","sexp":"(:fv _uniq.81671)"},{"name":"a₂","sexp":"(:fv _uniq.81671)"},{"name":"b","sexp":"(:fv _uniq.81671)"},{"name":"b₁","... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Union.union) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c Union) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81671","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81674","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"ext1","sourceEnd":48847,"sourceStart":48843,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":48849,"sourceStart":48848,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":48849,"sourceStart":48848,"ta... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81671","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81674","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 554 | 4 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7c37fe6771a821fae1124304ff6683cbcf4ada0b7f8e86b87977809fefbb16c6 | c2e01d86071a217cf143060c4b28a10cc9dd1ce734f3e9d103acc94cb5518540 | 2304e737f6f625b8e592a74a9d350f049144a7ca562205d460f4a0d776587aa9 | f2865eb61e628e6b3696be33bf1aea19be60d2bd0426ae03c3f675c45a38643a |
cat-searcher/leandojo-benchmark-4-random | test | 2,662 | Set.Ioc_union_Ioi' | Mathlib/Order/Interval/Set/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>Set.mem_union</a>, <a>Set.mem_Ioc</a>, <a>Set.mem_Ioi</a>, <a>min_lt_iff</a>] | case h
α : Type u_1
β : Type u_2
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
h₁ : c ≤ b
x : α
⊢ x ∈ Ioc a b ∪ Ioi c ↔ x ∈ Ioi (min a c) | case h
α : Type u_1
β : Type u_2
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
h₁ : c ≤ b
x : α
⊢ a < x ∧ x ≤ b ∨ c < x ↔ a < x ∨ c < x | ((:c Iff) ((:c Membership.mem) (:fv _uniq.81671) ((:c Set) (:fv _uniq.81671)) ((:c Set.instMembership) (:fv _uniq.81671)) (:fv _uniq.81947) ((:c Union.union) ((:c Set) (:fv _uniq.81671)) ((:c Set.instUnion) (:fv _uniq.81671)) ((:c Set.Ioc) (:fv _uniq.81671) ((:c PartialOrder.toPreorder) (:fv _uniq.81671) ((:c Semilatti... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.81671))"},{"name":"a","sexp":"(:fv _uniq.81671)"},{"name":"a₁","sexp":"(:fv _uniq.81671)"},{"name":"a₂","sexp":"(:fv _uniq.81671)"},{"name":"b","sexp":"(:fv _uniq.81671)"},{"name":"b₁","... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81671","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81674","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"simp_rw","sourceEnd":48859,"sourceStart":48852,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":48861,"sourceStart":48860,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.mem_uni... | [] | [{"source":"mem_union","source_end":48870,"source_start":48861,"syntax_kind":"ident"},{"source":"mem_Ioc","source_end":48879,"source_start":48872,"syntax_kind":"ident"},{"source":"mem_Ioi","source_end":48888,"source_start":48881,"syntax_kind":"ident"},{"source":"min_lt_iff","source_end":48900,"source_start":48890,"synt... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81671","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81674","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 554 | 5 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1e336e40c0b08e200488883712f95af39037851d9887b651916cf5e9cb9446b1 | f2865eb61e628e6b3696be33bf1aea19be60d2bd0426ae03c3f675c45a38643a | d08c52a6e0cd87dd51a40e9e55aee6567c3af84854dedf40f21971264abe7d20 | 0ee358d7550647fc25aae9ee38064594349828cfdb34ff339291010a0c78ac61 |
cat-searcher/leandojo-benchmark-4-random | test | 2,663 | Set.Ioc_union_Ioi' | Mathlib/Order/Interval/Set/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases hc : c < x | case h
α : Type u_1
β : Type u_2
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
h₁ : c ≤ b
x : α
⊢ a < x ∧ x ≤ b ∨ c < x ↔ a < x ∨ c < x | case pos
α : Type u_1
β : Type u_2
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
h₁ : c ≤ b
x : α
hc : c < x
⊢ a < x ∧ x ≤ b ∨ c < x ↔ a < x ∨ c < x
case neg
α : Type u_1
β : Type u_2
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
h₁ : c ≤ b
x : α
hc : ¬c < x
⊢ a < x ∧ x ≤ b ∨ c < x ↔ a < x ∨ c < x | ((:c Iff) ((:c Or) ((:c And) ((:c LT.lt) (:fv _uniq.81671) ((:c Preorder.toLT) (:fv _uniq.81671) ((:c PartialOrder.toPreorder) (:fv _uniq.81671) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.81671) ((:c Lattice.toSemilatticeInf) (:fv _uniq.81671) ((:c DistribLattice.toLattice) (:fv _uniq.81671) ((:c instDistribLattice... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.81671))"},{"name":"a","sexp":"(:fv _uniq.81671)"},{"name":"a₁","sexp":"(:fv _uniq.81671)"},{"name":"a₂","sexp":"(:fv _uniq.81671)"},{"name":"b","sexp":"(:fv _uniq.81671)"},{"name":"b₁","... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Or) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:fv FV13)))) (:arg :explicit 1 (:app (:c LE.l... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81671","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81674","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"by_cases","sourceEnd":48912,"sourceStart":48904,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hc","sourceEnd":48915,"sourceStart":48913,"tag":"identifier"},{"source":":","sourceEnd":48917,"sourceStart":48916,"tag":"atom"}],"kind":"null","source":"hc :","sourceEnd":48917,"so... | [] | [{"source":"c < x","source_end":48923,"source_start":48918,"syntax_kind":"«term_<_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81671","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81674","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 554 | 11 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | edcf233d44763111c40b50be8c663dd1e0d5b76908202c53c6cb0ba6b9bb71e6 | 0ee358d7550647fc25aae9ee38064594349828cfdb34ff339291010a0c78ac61 | 6f5ecd6030696532559e18b4cf3322c0934fe3c9901d818a04b2af9509ec1c87 | 4f2f92a3b51f011484266b2cb7cdb69752b6577c8a75ae4242060127386e67a7 |
cat-searcher/leandojo-benchmark-4-random | test | 2,664 | Set.Ioc_union_Ioi' | Mathlib/Order/Interval/Set/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [hc, <a>or_true</a>] | case pos
α : Type u_1
β : Type u_2
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
h₁ : c ≤ b
x : α
hc : c < x
⊢ a < x ∧ x ≤ b ∨ c < x ↔ a < x ∨ c < x | ((:c Iff) ((:c Or) ((:c And) ((:c LT.lt) (:fv _uniq.81671) ((:c Preorder.toLT) (:fv _uniq.81671) ((:c PartialOrder.toPreorder) (:fv _uniq.81671) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.81671) ((:c Lattice.toSemilatticeInf) (:fv _uniq.81671) ((:c DistribLattice.toLattice) (:fv _uniq.81671) ((:c instDistribLattice... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.81671))"},{"name":"a","sexp":"(:fv _uniq.81671)"},{"name":"a₁","sexp":"(:fv _uniq.81671)"},{"name":"a₂","sexp":"(:fv _uniq.81671)"},{"name":"b","sexp":"(:fv _uniq.81671)"},{"name":"b₁","... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Or) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:fv FV13)))) (:arg :explicit 1 (:app (:c LE.l... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81671","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81674","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":48933,"sourceStart":48929,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":48938,"sourceStart":48934,"tag":"atom"}],"kind"... | [] | [{"source":"hc","source_end":48942,"source_start":48940,"syntax_kind":"ident"},{"source":"or_true","source_end":48951,"source_start":48944,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81671","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81674","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 554 | 14 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5727081f83015dabafd2039f1fc70b7b29e530b943d341691b83aad89d55e64f | 117e99a50c80084315114f6ab47438f83a191dd023ed273d376dd439b5017010 | ed5ecc5b40affbbbe78e3ab7972e7027a16e192ef72b5ec4c9a43819c19ca5a0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,665 | Set.Ioc_union_Ioi' | Mathlib/Order/Interval/Set/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hxb : x ≤ b := (<a>le_of_not_gt</a> hc).<a>LE.le.trans</a> h₁ | case neg
α : Type u_1
β : Type u_2
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
h₁ : c ≤ b
x : α
hc : ¬c < x
⊢ a < x ∧ x ≤ b ∨ c < x ↔ a < x ∨ c < x | case neg
α : Type u_1
β : Type u_2
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
h₁ : c ≤ b
x : α
hc : ¬c < x
hxb : x ≤ b
⊢ a < x ∧ x ≤ b ∨ c < x ↔ a < x ∨ c < x | ((:c Iff) ((:c Or) ((:c And) ((:c LT.lt) (:fv _uniq.81671) ((:c Preorder.toLT) (:fv _uniq.81671) ((:c PartialOrder.toPreorder) (:fv _uniq.81671) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.81671) ((:c Lattice.toSemilatticeInf) (:fv _uniq.81671) ((:c DistribLattice.toLattice) (:fv _uniq.81671) ((:c instDistribLattice... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.81671))"},{"name":"a","sexp":"(:fv _uniq.81671)"},{"name":"a₁","sexp":"(:fv _uniq.81671)"},{"name":"a₂","sexp":"(:fv _uniq.81671)"},{"name":"b","sexp":"(:fv _uniq.81671)"},{"name":"b₁","... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Or) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:fv FV13)))) (:arg :explicit 1 (:app (:c LE.l... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81671","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81674","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"have","sourceEnd":48995,"sourceStart":48991,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hxb","sourceEnd":48999,"sourceStart":48996,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hxb","sourceEnd":48999,"sourceStart":48996,"tag":"n... | [] | [{"source":"x ≤ b","source_end":49009,"source_start":49002,"syntax_kind":"«term_≤_»"},{"source":"(le_of_not_gt hc).trans h₁","source_end":49041,"source_start":49013,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81671","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81674","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 554 | 21 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5474e6ba4b72c9b8eed5364e819beb6bc548c3fe010f8f43d17e7278308aa093 | c48a98a4c7f28fcd91318b2ad9e4da2b79a4993def3c2211474be9b9ce3fe51a | 8e3496eed426b3f6fdd098ef5b4a5a5280d6e3521f7ddc94702a939caa49fbb5 | 93765d4edc82ca47ccc5f53e0c2bd2a8fbd6e86ca231af0fce99e0bac0b7ab6d |
cat-searcher/leandojo-benchmark-4-random | test | 2,666 | Set.Ioc_union_Ioi' | Mathlib/Order/Interval/Set/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [hxb, <a>and_true</a>] | case neg
α : Type u_1
β : Type u_2
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
h₁ : c ≤ b
x : α
hc : ¬c < x
hxb : x ≤ b
⊢ a < x ∧ x ≤ b ∨ c < x ↔ a < x ∨ c < x | ((:c Iff) ((:c Or) ((:c And) ((:c LT.lt) (:fv _uniq.81671) ((:c Preorder.toLT) (:fv _uniq.81671) ((:c PartialOrder.toPreorder) (:fv _uniq.81671) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.81671) ((:c Lattice.toSemilatticeInf) (:fv _uniq.81671) ((:c DistribLattice.toLattice) (:fv _uniq.81671) ((:c instDistribLattice... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.81671))"},{"name":"a","sexp":"(:fv _uniq.81671)"},{"name":"a₁","sexp":"(:fv _uniq.81671)"},{"name":"a₂","sexp":"(:fv _uniq.81671)"},{"name":"b","sexp":"(:fv _uniq.81671)"},{"name":"b₁","... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Or) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:fv FV13)))) (:arg :explicit 1 (:app (:c LE.l... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81671","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81674","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"simp","sourceEnd":49050,"sourceStart":49046,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":49055,"sourceStart":49051,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":490... | [] | [{"source":"hxb","source_end":49060,"source_start":49057,"syntax_kind":"ident"},{"source":"and_true","source_end":49070,"source_start":49062,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81671","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81674","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 554 | 22 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eea6c205d2cafdb2aa592c833e1a785a4bde9794b4dabfc136b865bf0845b6f4 | 93765d4edc82ca47ccc5f53e0c2bd2a8fbd6e86ca231af0fce99e0bac0b7ab6d | db6ed077a472f2ff29190dbfb65ca16f6800cf6b11357f0f5ef8bb7a8f8317b9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,667 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp [<a>LucasLehmer.lucasLehmerResidue</a>] at h | p' : ℕ
h : lucasLehmerResidue (p' + 2) = 0
⊢ ∃ k, ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | p' : ℕ
h : sZMod (p' + 2) (p' + 2 - 2) = 0
⊢ ∃ k, ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | ((:c Exists) (:c Int) (:lambda k (:c Int) ((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HPow.hPow) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((... | [{"name":"p'","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c Eq) ((:c ZMod) ((:c HSub.hSub) (:c Nat) (:c Nat) (:c Nat) ((:c instHSub) (:c Nat) (:c instSubNat)) ((:c HPow.hPow) (:c Nat) (:c Nat) (:c Nat) ((:c instHPow) (:c Nat) (:c Nat) ((:c Monoid.toNatPow) (:c Nat) (:c Nat.instMonoid))) ((:c OfNat.ofNat) (:c Nat) (:lit 2... | (:app (:c Exists) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:lambda k :explicit (:c Int) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:app (:c LucasLehmer.q) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :impl... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.87781","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c Eq) (:arg :implicit-type 0 (:app (:c ZM... | {"children":[{"source":"dsimp","sourceEnd":16855,"sourceStart":16850,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16857,"sourceStart":16856,"tag":"... | [] | [{"source":"lucasLehmerResidue","source_end":16875,"source_start":16857,"syntax_kind":"ident"},{"source":"h","source_end":16881,"source_start":16880,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.87781","is_instance":false,"is_let":false,"user_name":"h"}] | 137 | 4 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b7a43334210bb3b744f8e9d798988cfebecbc85e7a2f6de362efb213bed9e3c0 | bc527e9fc6a06547ee155508bfcad8ecfe38435791f30f482b086797b0f8983c | 4985bb77bb5d72a2fcccae33e8d8eedfabb4710fc6f29b1447453922eee670f4 | 7e0191b01526bb4de278acdf5139bdd77ce2a0cd13764089be0aaf0dd8f6c6db |
cat-searcher/leandojo-benchmark-4-random | test | 2,668 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>LucasLehmer.sZMod_eq_s</a> p'] at h | p' : ℕ
h : sZMod (p' + 2) (p' + 2 - 2) = 0
⊢ ∃ k, ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | p' : ℕ
h : ↑(s (p' + 2 - 2)) = 0
⊢ ∃ k, ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | ((:c Exists) (:c Int) (:lambda k (:c Int) ((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HPow.hPow) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((... | [{"name":"p'","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c Eq) ((:c ZMod) ((:c HSub.hSub) (:c Nat) (:c Nat) (:c Nat) ((:c instHSub) (:c Nat) (:c instSubNat)) ((:c HPow.hPow) (:c Nat) (:c Nat) (:c Nat) ((:c instHPow) (:c Nat) (:c Nat) ((:c Monoid.toNatPow) (:c Nat) (:c Nat.instMonoid))) ((:c OfNat.ofNat) (:c Nat) (:lit 2... | (:app (:c Exists) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:lambda k :explicit (:c Int) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:app (:c LucasLehmer.q) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :impl... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.87781","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c Eq) (:arg :implicit-type 0 (:app (:c ZM... | {"children":[{"source":"rw","sourceEnd":16886,"sourceStart":16884,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16888,"sourceStart":16887,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Luc... | [] | [{"source":"h","source_end":16907,"source_start":16906,"syntax_kind":"ident"},{"source":"sZMod_eq_s p'","source_end":16901,"source_start":16888,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.87781","is_instance":false,"is_let":false,"user_name":"h"}] | 137 | 5 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6965cada632cb8f6d21e42fdf4809d3bbb8045dc1f8eb9687287fa76c9b0f503 | 7e0191b01526bb4de278acdf5139bdd77ce2a0cd13764089be0aaf0dd8f6c6db | be80f267f4c966a017ff6202b5219519198f33a3da9ace1655f6e4f9df81a0fd | 4569f781b3a8488e94594705c7020ff10ffe0e6751378ba718f2ef9cbbfcffb6 |
cat-searcher/leandojo-benchmark-4-random | test | 2,669 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp? [ZMod.intCast_zmod_eq_zero_iff_dvd] at h says simp only [<a>add_tsub_cancel_right</a>, <a>ZMod.intCast_zmod_eq_zero_iff_dvd</a>, <a>Nat.ofNat_pos</a>, <a>pow_pos</a>, <a>Nat.cast_pred</a>, <a>Nat.cast_pow</a>, <a>Nat.cast_ofNat</a>] at h | p' : ℕ
h : ↑(s (p' + 2 - 2)) = 0
⊢ ∃ k, ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | p' : ℕ
h : 2 ^ (p' + 2) - 1 ∣ s p'
⊢ ∃ k, ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | ((:c Exists) (:c Int) (:lambda k (:c Int) ((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HPow.hPow) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((... | [{"name":"p'","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c Eq) ((:c ZMod) ((:c HSub.hSub) (:c Nat) (:c Nat) (:c Nat) ((:c instHSub) (:c Nat) (:c instSubNat)) ((:c HPow.hPow) (:c Nat) (:c Nat) (:c Nat) ((:c instHPow) (:c Nat) (:c Nat) ((:c Monoid.toNatPow) (:c Nat) (:c Nat.instMonoid))) ((:c OfNat.ofNat) (:c Nat) (:lit 2... | (:app (:c Exists) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:lambda k :explicit (:c Int) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:app (:c LucasLehmer.q) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :impl... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.87798","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c Eq) (:arg :implicit-type 0 (:app (:c ZM... | {"children":[{"children":[{"source":"simp?","sourceEnd":16915,"sourceStart":16910,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag"... | [] | [{"source":"add_tsub_cancel_right","source_end":16998,"source_start":16977,"syntax_kind":"ident"},{"source":"ZMod.intCast_zmod_eq_zero_iff_dvd","source_end":17033,"source_start":17000,"syntax_kind":"ident"},{"source":"ofNat_pos","source_end":17044,"source_start":17035,"syntax_kind":"ident"},{"source":"pow_pos","source_... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.87798","is_instance":false,"is_let":false,"user_name":"h"}] | 137 | 8 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 06ff2a1f8809b20a3e0a82e43442eed6e2c45253b2aa76043ab656f7331385aa | 4569f781b3a8488e94594705c7020ff10ffe0e6751378ba718f2ef9cbbfcffb6 | 0fbee9ee9a4cdd20466ebf50dfd18a0b8c9f62c77b6ab33ed7cc401d7dac67ec | eddf0396018619cd8ec4c75845fb81bf15d5826a71873942c297fe155dfff68c |
cat-searcher/leandojo-benchmark-4-random | test | 2,670 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases' h with k h | p' : ℕ
h : 2 ^ (p' + 2) - 1 ∣ s p'
⊢ ∃ k, ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | case intro
p' : ℕ
k : ℤ
h : s p' = (2 ^ (p' + 2) - 1) * k
⊢ ∃ k, ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | ((:c Exists) (:c Int) (:lambda k (:c Int) ((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HPow.hPow) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((... | [{"name":"p'","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c Dvd.dvd) (:c Int) (:c Int.instDvd) ((:c HSub.hSub) (:c Int) (:c Int) (:c Int) ((:c instHSub) (:c Int) ((:c AddGroupWithOne.toSub) (:c Int) ((:c Ring.toAddGroupWithOne) (:c Int) (:c Int.instRing)))) ((:c HPow.hPow) (:c Int) (:c Nat) (:c Int) ((:c instHPow) (:c In... | (:app (:c Exists) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:lambda k :explicit (:c Int) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:app (:c LucasLehmer.q) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :impl... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88950","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c Dvd.dvd) (:arg :implicit-type 0 (:c Int... | {"children":[{"source":"cases'","sourceEnd":17107,"sourceStart":17101,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":2,"semanticRole":"local","source":"h","sourceEnd":17109,"sourceStart":17108,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","s... | [] | [{"source":"h","source_end":17109,"source_start":17108,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88950","is_instance":false,"is_let":false,"user_name":"h"}] | 137 | 12 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7d82d288685be0961767950c2e5683a70b761a03c0098bf1921736b2c0821d70 | eddf0396018619cd8ec4c75845fb81bf15d5826a71873942c297fe155dfff68c | a6e1cb22edff459046cf10029d888790e0ec1edd7a9b15f4e1cc9e2e641899ab | 2cd953faa0c483cb7e236567184c8dbb6ef0764bc6d367676a73289bdaff5610 |
cat-searcher/leandojo-benchmark-4-random | test | 2,671 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | use k | case intro
p' : ℕ
k : ℤ
h : s p' = (2 ^ (p' + 2) - 1) * k
⊢ ∃ k, ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | case h
p' : ℕ
k : ℤ
h : s p' = (2 ^ (p' + 2) - 1) * k
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | ((:c Exists) (:c Int) (:lambda k (:c Int) ((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HPow.hPow) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((... | [{"name":"p'","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Int)"},{"name":"h","sexp":"((:c Eq) (:c Int) ((:c LucasLehmer.s) (:fv _uniq.87780)) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (:c Int.instMul)) ((:c HSub.hSub) (:c Int) (:c Int) (:c Int) ((:c instHSub) (:c Int) ((:c AddGroupWithOne.toSub)... | (:app (:c Exists) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:lambda k :explicit (:c Int) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:app (:c LucasLehmer.q) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :impl... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"name":"k","sexp":"(:c Int)"},{"binder_role":":explicit","context_in... | {"children":[{"source":"use","sourceEnd":17124,"sourceStart":17121,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"contextIndex":2,"semanticRole":"local","source":"k","sourceEnd":17126,"sourceStart":17125,"tag":"identifier"}],"k... | [] | [{"source":"k","source_end":17126,"source_start":17125,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 137 | 13 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b5f05ffe39ac235d89354dbcfbb545f3b275b77c2aa393dd67291e7d68704596 | 2cd953faa0c483cb7e236567184c8dbb6ef0764bc6d367676a73289bdaff5610 | e7d806fe3bd4b41b9d6770fa5342e53a575412f52582bfaddcefb723bc43aa5c | 67a9a1f16f257c6342c003b6c1f98b8cef46079d8716f775304ec0c35a56c192 |
cat-searcher/leandojo-benchmark-4-random | test | 2,672 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | replace h := <a>congr_arg</a> (fun n : ℤ => (n : <a>LucasLehmer.X</a> (<a>LucasLehmer.q</a> (p' + 2)))) h | case h
p' : ℕ
k : ℤ
h : s p' = (2 ^ (p' + 2) - 1) * k
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | case h
p' : ℕ
k : ℤ
h : (fun n => ↑n) (s p') = (fun n => ↑n) ((2 ^ (p' + 2) - 1) * k)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | ((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HPow.hPow) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) (... | [{"name":"p'","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Int)"},{"name":"h","sexp":"((:c Eq) (:c Int) ((:c LucasLehmer.s) (:fv _uniq.87780)) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (:c Int.instMul)) ((:c HSub.hSub) (:c Int) (:c Int) (:c Int) ((:c instHSub) (:c Int) ((:c AddGroupWithOne.toSub)... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:app (:c LucasLehmer.q) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"name":"k","sexp":"(:c Int)"},{"binder_role":":explicit","context_in... | {"children":[{"source":"replace","sourceEnd":17136,"sourceStart":17129,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":17138,"sourceStart":17137,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":17138,"sourceStart":17137,"tag":"no... | [] | [{"source":"congr_arg (fun n : ℤ => (n : X (q (p' + 2)))) h\n -- coercion from ℤ to X q","source_end":17191,"source_start":17142,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 137 | 14 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bb31e6ff3830daf26c59a86867e3be0cad94c6ea7067d8e03bae2ff95dacd059 | 67a9a1f16f257c6342c003b6c1f98b8cef46079d8716f775304ec0c35a56c192 | 33b17399dc6020de1e3a324e12414026ac14f1c7b60dd1bb8d9ac5704ecd85be | b7890042e10b2f7fda58c503a67b5856add83a32a4f6f365a5a187458cc47fe9 |
cat-searcher/leandojo-benchmark-4-random | test | 2,673 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp at h | case h
p' : ℕ
k : ℤ
h : (fun n => ↑n) (s p') = (fun n => ↑n) ((2 ^ (p' + 2) - 1) * k)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | case h
p' : ℕ
k : ℤ
h : ↑(s p') = ↑((2 ^ (p' + 2) - 1) * k)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | ((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HPow.hPow) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) (... | [{"name":"p'","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Int)"},{"name":"h","sexp":"((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:lambda n (:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:app (:c LucasLehmer.q) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"name":"k","sexp":"(:c Int)"},{"binder_role":":explicit","context_in... | {"children":[{"source":"dsimp","sourceEnd":17229,"sourceStart":17224,"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":[{"ch... | [] | [{"source":"h","source_end":17234,"source_start":17233,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 137 | 15 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cf29ebacf4d80154bdccea8d0a97a7db92166d5893dced46de97b68e022cae5a | b7890042e10b2f7fda58c503a67b5856add83a32a4f6f365a5a187458cc47fe9 | 77a3f35897bdf6b787da21ef08ddf8dafef80050e286f9c04243531c1e998d85 | 1cba5bff1eafa8e0372f8a1d7afa7ceff19c79e84bff1fa185348fc6dd6936a7 |
cat-searcher/leandojo-benchmark-4-random | test | 2,674 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>LucasLehmer.X.closed_form</a>] at h | case h
p' : ℕ
k : ℤ
h : ↑(s p') = ↑((2 ^ (p' + 2) - 1) * k)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | case h
p' : ℕ
k : ℤ
h : ω ^ 2 ^ p' + ωb ^ 2 ^ p' = ↑((2 ^ (p' + 2) - 1) * k)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | ((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HPow.hPow) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) (... | [{"name":"p'","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Int)"},{"name":"h","sexp":"((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c Int.cast) (... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:app (:c LucasLehmer.q) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"name":"k","sexp":"(:c Int)"},{"binder_role":":explicit","context_in... | {"children":[{"source":"rw","sourceEnd":17239,"sourceStart":17237,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":17241,"sourceStart":17240,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"LucasLehmer.X.cl... | [] | [{"source":"closed_form","source_end":17252,"source_start":17241,"syntax_kind":"ident"},{"source":"h","source_end":17258,"source_start":17257,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 137 | 16 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c3f30ac4c897d0da4c6a076f2f8e4acf2fcb3328f71c68cd0a5033dc3fb0f5ea | 1cba5bff1eafa8e0372f8a1d7afa7ceff19c79e84bff1fa185348fc6dd6936a7 | d35ff62f8f349b35f1912236efee849fd17ddefdc207dcaf7e4b5c39bc53445c | 12f8021e3e22cb5cfb346035a51112d630e7536f7a54630c6763a69d33e4e199 |
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