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iCogLabs-Dev
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Mathlib-Normalized-Sexpr

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cat-searcher/leandojo-benchmark-4-random
test
2,165
TopCat.GlueData.isOpen_iff
Mathlib/Topology/Gluing.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← (<a>TopCat.homeoOfIso</a> (<a>CategoryTheory.Limits.Multicoequalizer.isoCoequalizer</a> 𝖣.<a>CategoryTheory.GlueData.diagram</a>).<a>CategoryTheory.Iso.symm</a>).<a>Homeomorph.isOpen_preimage</a>]
D : GlueData U : Set ↑D.glued ⊢ IsOpen U ↔ ∀ (i : D.J), IsOpen (⇑(Sigma.ι D.diagram.right i ≫ Multicoequalizer.sigmaπ D.diagram) ⁻¹' U)
D : GlueData U : Set ↑D.glued ⊢ IsOpen (⇑(homeoOfIso (Multicoequalizer.isoCoequalizer D.diagram).symm) ⁻¹' U) ↔ ∀ (i : D.J), IsOpen (⇑(Sigma.ι D.diagram.right i ≫ Multicoequalizer.sigmaπ D.diagram) ⁻¹' U)
((:c Iff) ((:c IsOpen) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c CategoryTheory.GlueData.glued) (:c TopCat) (:c instTopCatLargeCategory) ((:c TopCat.GlueData.toGlueData) (:fv _uniq.1514)) ((:c CategoryTheory.Limits.hasColimitOfHasColimitsOfShape) (:c TopCat) (:c instTopCatLargeCategory) ((:c CategoryThe...
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(:app (:c Iff) (:arg :explicit 0 (:app (:c IsOpen) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c CategoryTheory.GlueData.glued) (:arg :implicit-type 0 (:c TopCat)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.LargeCategory) (:arg :explicit 0 (:c To...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1514","is_instance":false,"is_let":false,"name":"D","sexp":"(:c TopCat.GlueData)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2012","is_instance":false,"is_let":false,"name":"U","sexp":"(:app (:c Set) (:arg :explicit 0 (:app (...
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[]
[{"source":"(homeoOfIso (Multicoequalizer.isoCoequalizer 𝖣.diagram).symm).isOpen_preimage","source_end":4548,"source_start":4468,"syntax_kind":"Lean.Parser.Term.proj"}]
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14
8
exact
true
1
2
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
de2ab4d20509ba5038eb2034c36af7322ec5839ae3c322a7a35b920989b6c978
518e977c2bc96a42bf3bbc8712f8383cdb758836aa09852533549c9829961808
7fea801b4153ebea92ef1b0f674d07405ee0518bbe994ca89994949a5ac773fe
038f1ce20986b50254dcd3c1c6ab1469f65f480b449aa8a24a317707735268e6
cat-searcher/leandojo-benchmark-4-random
test
2,166
TopCat.GlueData.isOpen_iff
Mathlib/Topology/Gluing.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>TopCat.coequalizer_isOpen_iff</a>]
D : GlueData U : Set ↑D.glued ⊢ IsOpen (⇑(homeoOfIso (Multicoequalizer.isoCoequalizer D.diagram).symm) ⁻¹' U) ↔ ∀ (i : D.J), IsOpen (⇑(Sigma.ι D.diagram.right i ≫ Multicoequalizer.sigmaπ D.diagram) ⁻¹' U)
D : GlueData U : Set ↑D.glued ⊢ IsOpen (⇑(colimit.ι (parallelPair D.diagram.fstSigmaMap D.diagram.sndSigmaMap) WalkingParallelPair.one) ⁻¹' (⇑(homeoOfIso (Multicoequalizer.isoCoequalizer D.diagram).symm) ⁻¹' U)) ↔ ∀ (i : D.J), IsOpen (⇑(Sigma.ι D.diagram.right i ≫ Multicoequalizer.sigmaπ D.diagram) ⁻¹...
((:c Iff) ((:c IsOpen) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c CategoryTheory.Limits.coequalizer) (:c TopCat) (:c instTopCatLargeCategory) ((:c CategoryTheory.Limits.sigmaObj) ((:c CategoryTheory.Limits.MultispanIndex.L) (:c TopCat) (:c instTopCatLargeCategory) ((:c CategoryTheory.GlueData.diagram) (:...
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(:app (:c Iff) (:arg :explicit 0 (:app (:c IsOpen) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c CategoryTheory.Limits.coequalizer) (:arg :implicit-type 0 (:c TopCat)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.LargeCategory) (:arg :explicit 0 (:...
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[]
[{"source":"coequalizer_isOpen_iff","source_end":4578,"source_start":4556,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1514","is_instance":false,"is_let":false,"user_name":"D"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2012","is_instance":false,"is_let":false,"user_name":"U"}]
14
11
exact
true
1
2
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
32ab503d92e665d73b284a412e01a32140d716eaea614c2112ab7fda5bae6974
038f1ce20986b50254dcd3c1c6ab1469f65f480b449aa8a24a317707735268e6
8f7c6cf764d746863c6cb7f68e22d327eecc775c1145b5716b4e25e2d5a6812a
9a7428448df8402c2d901fae77dab11a3ce65d37a9983128809bc2ba96d2c278
cat-searcher/leandojo-benchmark-4-random
test
2,167
TopCat.GlueData.isOpen_iff
Mathlib/Topology/Gluing.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
dsimp only [<a>CategoryTheory.GlueData.diagram_l</a>, <a>CategoryTheory.GlueData.diagram_left</a>, <a>CategoryTheory.GlueData.diagram_r</a>, <a>CategoryTheory.GlueData.diagram_right</a>, <a>CategoryTheory.Limits.parallelPair_obj_one</a>]
D : GlueData U : Set ↑D.glued ⊢ IsOpen (⇑(colimit.ι (parallelPair D.diagram.fstSigmaMap D.diagram.sndSigmaMap) WalkingParallelPair.one) ⁻¹' (⇑(homeoOfIso (Multicoequalizer.isoCoequalizer D.diagram).symm) ⁻¹' U)) ↔ ∀ (i : D.J), IsOpen (⇑(Sigma.ι D.diagram.right i ≫ Multicoequalizer.sigmaπ D.diagram) ⁻¹...
D : GlueData U : Set ↑D.glued ⊢ IsOpen (⇑(colimit.ι (parallelPair D.diagram.fstSigmaMap D.diagram.sndSigmaMap) WalkingParallelPair.one) ⁻¹' (⇑(homeoOfIso (Multicoequalizer.isoCoequalizer D.diagram).symm) ⁻¹' U)) ↔ ∀ (i : D.J), IsOpen (⇑(Sigma.ι D.U i ≫ Multicoequalizer.sigmaπ D.diagram) ⁻¹' U)
((:c Iff) ((:c IsOpen) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c Prefunctor.obj) (:c CategoryTheory.Limits.WalkingParallelPair) ((:c CategoryTheory.CategoryStruct.toQuiver) (:c CategoryTheory.Limits.WalkingParallelPair) ((:c CategoryTheory.Category.toCategoryStruct) (:c CategoryTheory.Limits.WalkingPara...
[{"name":"D","sexp":"(:c TopCat.GlueData)"},{"name":"U","sexp":"((:c Set) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c CategoryTheory.GlueData.glued) (:c TopCat) (:c instTopCatLargeCategory) ((:c TopCat.GlueData.toGlueData) (:fv _uniq.1514)) ((:c CategoryTheory.Limits.hasColimitOfHasColimitsOfShape) (:c To...
(:app (:c Iff) (:arg :explicit 0 (:app (:c IsOpen) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:c CategoryTheory.Limits.WalkingParallelPair)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:c Cate...
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{"children":[{"source":"dsimp","sourceEnd":4587,"sourceStart":4582,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":4592,"sourceStart":4588,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":4592,"...
[]
[{"source":"GlueData.diagram_l","source_end":4612,"source_start":4594,"syntax_kind":"ident"},{"source":"GlueData.diagram_left","source_end":4635,"source_start":4614,"syntax_kind":"ident"},{"source":"GlueData.diagram_r","source_end":4655,"source_start":4637,"syntax_kind":"ident"},{"source":"GlueData.diagram_right","sour...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1514","is_instance":false,"is_let":false,"user_name":"D"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2012","is_instance":false,"is_let":false,"user_name":"U"}]
14
14
exact
true
1
2
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e28f98f31dd312558a25342eb9e74c8740ee464b4396ed1b8521d335c917b8f6
9a7428448df8402c2d901fae77dab11a3ce65d37a9983128809bc2ba96d2c278
b0b118960ab1c5481b8b465e84828f6db62fde66975d9c93d4742bb4d1950a04
73f5fea727599c0b8b35bd7b1b939712103f2cb33068a5103010cfb16472c116
cat-searcher/leandojo-benchmark-4-random
test
2,168
TopCat.GlueData.isOpen_iff
Mathlib/Topology/Gluing.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>TopCat.colimit_isOpen_iff</a>.{_,u}]
D : GlueData U : Set ↑D.glued ⊢ IsOpen (⇑(colimit.ι (parallelPair D.diagram.fstSigmaMap D.diagram.sndSigmaMap) WalkingParallelPair.one) ⁻¹' (⇑(homeoOfIso (Multicoequalizer.isoCoequalizer D.diagram).symm) ⁻¹' U)) ↔ ∀ (i : D.J), IsOpen (⇑(Sigma.ι D.U i ≫ Multicoequalizer.sigmaπ D.diagram) ⁻¹' U)
D : GlueData U : Set ↑D.glued ⊢ (∀ (j : Discrete D.J), IsOpen (⇑(colimit.ι (Discrete.functor D.U) j) ⁻¹' (⇑(colimit.ι (parallelPair D.diagram.fstSigmaMap D.diagram.sndSigmaMap) WalkingParallelPair.one) ⁻¹' (⇑(homeoOfIso (Multicoequalizer.isoCoequalizer D.diagram).symm) ⁻¹' U)))) ↔ ...
((:c Iff) ((:c IsOpen) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c CategoryTheory.Limits.sigmaObj) ((:c CategoryTheory.GlueData.J) (:c TopCat) (:c instTopCatLargeCategory) ((:c TopCat.GlueData.toGlueData) (:fv _uniq.1514))) (:c TopCat) (:c instTopCatLargeCategory) ((:c CategoryTheory.GlueData.U) (:c TopCa...
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(:app (:c Iff) (:arg :explicit 0 (:app (:c IsOpen) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c CategoryTheory.Limits.sigmaObj) (:arg :implicit-type 0 (:app (:c CategoryTheory.GlueData.J) (:arg :implicit-type 0 (:c TopCat)) (:arg :instance 1 (:instance-of (:a...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1514","is_instance":false,"is_let":false,"name":"D","sexp":"(:c TopCat.GlueData)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2012","is_instance":false,"is_let":false,"name":"U","sexp":"(:app (:c Set) (:arg :explicit 0 (:app (...
{"children":[{"source":"rw","sourceEnd":4711,"sourceStart":4709,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4713,"sourceStart":4712,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"TopCat....
[]
[{"source":"colimit_isOpen_iff.{_,u}","source_end":4737,"source_start":4713,"syntax_kind":"Lean.Parser.Term.explicitUniv"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1514","is_instance":false,"is_let":false,"user_name":"D"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2012","is_instance":false,"is_let":false,"user_name":"U"}]
14
15
exact
true
1
2
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2a7397810fff261c878ef3d13ee21b3400d3807e13cee984b8da3d9d8329f137
73f5fea727599c0b8b35bd7b1b939712103f2cb33068a5103010cfb16472c116
479d183575042f3db711ac9cf850dbe612f1dc09b9b885cf3dfa909a55261e74
a11a4e10dc1f29f4309abd77912088010c2e9ee26fe6d48300ed5d2fef2818f2
cat-searcher/leandojo-benchmark-4-random
test
2,169
TopCat.GlueData.isOpen_iff
Mathlib/Topology/Gluing.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
constructor
D : GlueData U : Set ↑D.glued ⊢ (∀ (j : Discrete D.J), IsOpen (⇑(colimit.ι (Discrete.functor D.U) j) ⁻¹' (⇑(colimit.ι (parallelPair D.diagram.fstSigmaMap D.diagram.sndSigmaMap) WalkingParallelPair.one) ⁻¹' (⇑(homeoOfIso (Multicoequalizer.isoCoequalizer D.diagram).symm) ⁻¹' U)))) ↔ ...
case mp D : GlueData U : Set ↑D.glued ⊢ (∀ (j : Discrete D.J), IsOpen (⇑(colimit.ι (Discrete.functor D.U) j) ⁻¹' (⇑(colimit.ι (parallelPair D.diagram.fstSigmaMap D.diagram.sndSigmaMap) WalkingParallelPair.one) ⁻¹' (⇑(homeoOfIso (Multicoequalizer.isoCoequalizer D.diagram).symm) ⁻¹' U)...
((:c Iff) (:forall j ((:c CategoryTheory.Discrete) ((:c CategoryTheory.GlueData.J) (:c TopCat) (:c instTopCatLargeCategory) ((:c TopCat.GlueData.toGlueData) (:fv _uniq.1514)))) ((:c IsOpen) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c Prefunctor.obj) ((:c CategoryTheory.Discrete) ((:c CategoryTheory.GlueDa...
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(:app (:c Iff) (:arg :explicit 0 (:forall j :explicit (:app (:c CategoryTheory.Discrete) (:arg :explicit 0 (:app (:c CategoryTheory.GlueData.J) (:arg :implicit-type 0 (:c TopCat)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.LargeCategory) (:arg :explicit 0 (:c TopCat))))) (:arg :explicit 2 (:app (:c TopCat...
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{"children":[{"source":"constructor","sourceEnd":4911,"sourceStart":4900,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":4911,"sourceStart":4900,"tag":"node"}
[]
[]
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14
18
exact
true
1
2
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9d9573b1d9dcf0b00a7f061498d2de8e300ed60fbe2419a6c74e08af09e41e2f
a11a4e10dc1f29f4309abd77912088010c2e9ee26fe6d48300ed5d2fef2818f2
e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068
67ab8d947db0311ba225879b08f73fd7f1a3c9b370cc45a9fc0a12cfdf9f5cf9
cat-searcher/leandojo-benchmark-4-random
test
2,170
TopCat.GlueData.isOpen_iff
Mathlib/Topology/Gluing.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro h j
case mp D : GlueData U : Set ↑D.glued ⊢ (∀ (j : Discrete D.J), IsOpen (⇑(colimit.ι (Discrete.functor D.U) j) ⁻¹' (⇑(colimit.ι (parallelPair D.diagram.fstSigmaMap D.diagram.sndSigmaMap) WalkingParallelPair.one) ⁻¹' (⇑(homeoOfIso (Multicoequalizer.isoCoequalizer D.diagram).symm) ⁻¹' U)...
case mp D : GlueData U : Set ↑D.glued h : ∀ (j : Discrete D.J), IsOpen (⇑(colimit.ι (Discrete.functor D.U) j) ⁻¹' (⇑(colimit.ι (parallelPair D.diagram.fstSigmaMap D.diagram.sndSigmaMap) WalkingParallelPair.one) ⁻¹' (⇑(homeoOfIso (Multicoequalizer.isoCoequalizer D.diagram).symm) ⁻¹' U))) j ...
(:forall _ (:forall j ((:c CategoryTheory.Discrete) ((:c CategoryTheory.GlueData.J) (:c TopCat) (:c instTopCatLargeCategory) ((:c TopCat.GlueData.toGlueData) (:fv _uniq.1514)))) ((:c IsOpen) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c Prefunctor.obj) ((:c CategoryTheory.Discrete) ((:c CategoryTheory.GlueD...
[{"name":"D","sexp":"(:c TopCat.GlueData)"},{"name":"U","sexp":"((:c Set) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c CategoryTheory.GlueData.glued) (:c TopCat) (:c instTopCatLargeCategory) ((:c TopCat.GlueData.toGlueData) (:fv _uniq.1514)) ((:c CategoryTheory.Limits.hasColimitOfHasColimitsOfShape) (:c To...
(:forall _ :explicit (:forall j :explicit (:app (:c CategoryTheory.Discrete) (:arg :explicit 0 (:app (:c CategoryTheory.GlueData.J) (:arg :implicit-type 0 (:c TopCat)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.LargeCategory) (:arg :explicit 0 (:c TopCat))))) (:arg :explicit 2 (:app (:c TopCat.GlueData.to...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1514","is_instance":false,"is_let":false,"name":"D","sexp":"(:c TopCat.GlueData)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2012","is_instance":false,"is_let":false,"name":"U","sexp":"(:app (:c Set) (:arg :explicit 0 (:app (...
{"children":[{"source":"intro","sourceEnd":4922,"sourceStart":4917,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":4924,"sourceStart":4923,"tag":"identifier"},{"semanticRole":"scoped_local","source":"j","sourceEnd":4926,"sourceStart":4925,"tag":"identifier"}],"kind":"null","source":"h...
[{"role":"fresh_name","source":"h","source_end":4924,"source_start":4923,"syntax_kind":"ident"},{"role":"fresh_name","source":"j","source_end":4926,"source_start":4925,"syntax_kind":"ident"}]
[]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1514","is_instance":false,"is_let":false,"user_name":"D"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2012","is_instance":false,"is_let":false,"user_name":"U"}]
14
23
exact
true
1
2
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a164156d4141e163adad01a9873b87f177287cdc506d6e09f4b1be1fb0a05eaf
cc6cd3387288420455e54922827fca55762cdda03d77c0ac14c4c02af825ff8d
3428e3b0afed431838d8552c2a6b9a641d192a07efc81c714f16fc7942d432ed
35056612467224d3f26717020e8c8846b184bb34a6511f9ccae30f752c09a924
cat-searcher/leandojo-benchmark-4-random
test
2,171
TopCat.GlueData.isOpen_iff
Mathlib/Topology/Gluing.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact h ⟨j⟩
case mp D : GlueData U : Set ↑D.glued h : ∀ (j : Discrete D.J), IsOpen (⇑(colimit.ι (Discrete.functor D.U) j) ⁻¹' (⇑(colimit.ι (parallelPair D.diagram.fstSigmaMap D.diagram.sndSigmaMap) WalkingParallelPair.one) ⁻¹' (⇑(homeoOfIso (Multicoequalizer.isoCoequalizer D.diagram).symm) ⁻¹' U))) j ...
((:c IsOpen) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c CategoryTheory.GlueData.U) (:c TopCat) (:c instTopCatLargeCategory) ((:c TopCat.GlueData.toGlueData) (:fv _uniq.1514)) (:fv _uniq.5822))) ((:c TopCat.topologicalSpace_coe) ((:c CategoryTheory.GlueData.U) (:c TopCat) (:c instTopCatLargeCategory) ((:c...
[{"name":"D","sexp":"(:c TopCat.GlueData)"},{"name":"U","sexp":"((:c Set) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c CategoryTheory.GlueData.glued) (:c TopCat) (:c instTopCatLargeCategory) ((:c TopCat.GlueData.toGlueData) (:fv _uniq.1514)) ((:c CategoryTheory.Limits.hasColimitOfHasColimitsOfShape) (:c To...
(:app (:c IsOpen) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c CategoryTheory.GlueData.U) (:arg :implicit-type 0 (:c TopCat)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.LargeCategory) (:arg :explicit 0 (:c TopCat))))) (:arg :explicit 2 (:app (:c...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1514","is_instance":false,"is_let":false,"name":"D","sexp":"(:c TopCat.GlueData)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2012","is_instance":false,"is_let":false,"name":"U","sexp":"(:app (:c Set) (:arg :explicit 0 (:app (...
{"children":[{"source":"exact","sourceEnd":4933,"sourceStart":4928,"tag":"atom"},{"children":[{"contextIndex":3,"semanticRole":"local","source":"h","sourceEnd":4935,"sourceStart":4934,"tag":"identifier"},{"children":[{"children":[{"source":"⟨","sourceEnd":4939,"sourceStart":4936,"tag":"atom"},{"children":[{"contextInde...
[]
[{"source":"h ⟨j⟩","source_end":4943,"source_start":4934,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1514","is_instance":false,"is_let":false,"user_name":"D"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2012","is_instance":false,"is_let":false,"user_name":"U"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq...
14
25
exact
true
1
4
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c5ef0e65d5f4fb88c6eaaf1be6fdf5c1185e13523584ef67dfe264b0466d3ac5
35056612467224d3f26717020e8c8846b184bb34a6511f9ccae30f752c09a924
716080e9b7105940b1e3246e4188ba687e33c6930484a2c779efa9524306a407
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,172
TopCat.GlueData.isOpen_iff
Mathlib/Topology/Gluing.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro h j
case mpr D : GlueData U : Set ↑D.glued ⊢ (∀ (i : D.J), IsOpen (⇑(Sigma.ι D.U i ≫ Multicoequalizer.sigmaπ D.diagram) ⁻¹' U)) → ∀ (j : Discrete D.J), IsOpen (⇑(colimit.ι (Discrete.functor D.U) j) ⁻¹' (⇑(colimit.ι (parallelPair D.diagram.fstSigmaMap D.diagram.sndSigmaMap) WalkingParallelPair.on...
case mpr D : GlueData U : Set ↑D.glued h : ∀ (i : D.J), IsOpen (⇑(Sigma.ι D.U i ≫ Multicoequalizer.sigmaπ D.diagram) ⁻¹' U) j : Discrete D.J ⊢ IsOpen (⇑(colimit.ι (Discrete.functor D.U) j) ⁻¹' (⇑(colimit.ι (parallelPair D.diagram.fstSigmaMap D.diagram.sndSigmaMap) WalkingParallelPair.one) ⁻¹' (⇑(homeo...
(:forall _ (:forall i ((:c CategoryTheory.GlueData.J) (:c TopCat) (:c instTopCatLargeCategory) ((:c TopCat.GlueData.toGlueData) (:fv _uniq.1514))) ((:c IsOpen) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c CategoryTheory.GlueData.U) (:c TopCat) (:c instTopCatLargeCategory) ((:c TopCat.GlueData.toGlueData) (...
[{"name":"D","sexp":"(:c TopCat.GlueData)"},{"name":"U","sexp":"((:c Set) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c CategoryTheory.GlueData.glued) (:c TopCat) (:c instTopCatLargeCategory) ((:c TopCat.GlueData.toGlueData) (:fv _uniq.1514)) ((:c CategoryTheory.Limits.hasColimitOfHasColimitsOfShape) (:c To...
(:forall _ :explicit (:forall i :explicit (:app (:c CategoryTheory.GlueData.J) (:arg :implicit-type 0 (:c TopCat)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.LargeCategory) (:arg :explicit 0 (:c TopCat))))) (:arg :explicit 2 (:app (:c TopCat.GlueData.toGlueData) (:arg :explicit 0 (:fv FV0))))) (:app (:c I...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1514","is_instance":false,"is_let":false,"name":"D","sexp":"(:c TopCat.GlueData)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2012","is_instance":false,"is_let":false,"name":"U","sexp":"(:app (:c Set) (:arg :explicit 0 (:app (...
{"children":[{"source":"intro","sourceEnd":4954,"sourceStart":4949,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":4956,"sourceStart":4955,"tag":"identifier"},{"semanticRole":"scoped_local","source":"j","sourceEnd":4958,"sourceStart":4957,"tag":"identifier"}],"kind":"null","source":"h...
[{"role":"fresh_name","source":"h","source_end":4956,"source_start":4955,"syntax_kind":"ident"},{"role":"fresh_name","source":"j","source_end":4958,"source_start":4957,"syntax_kind":"ident"}]
[]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1514","is_instance":false,"is_let":false,"user_name":"D"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2012","is_instance":false,"is_let":false,"user_name":"U"}]
14
30
exact
true
1
2
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4569cc731817bce413fa4ccf03b2ddb5a78c38af953c8fa72aeef19149b34521
1c765371eadc0b0ea7ca0a531e104ebaa55e2683a032c2afe6745cbaf97b34cf
3428e3b0afed431838d8552c2a6b9a641d192a07efc81c714f16fc7942d432ed
827115e5593e50b2e646bbed902e42bd7ea8b5729b6863a12ebbd3334c034c65
cat-searcher/leandojo-benchmark-4-random
test
2,173
TopCat.GlueData.isOpen_iff
Mathlib/Topology/Gluing.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
cases j
case mpr D : GlueData U : Set ↑D.glued h : ∀ (i : D.J), IsOpen (⇑(Sigma.ι D.U i ≫ Multicoequalizer.sigmaπ D.diagram) ⁻¹' U) j : Discrete D.J ⊢ IsOpen (⇑(colimit.ι (Discrete.functor D.U) j) ⁻¹' (⇑(colimit.ι (parallelPair D.diagram.fstSigmaMap D.diagram.sndSigmaMap) WalkingParallelPair.one) ⁻¹' (⇑(homeo...
case mpr.mk D : GlueData U : Set ↑D.glued h : ∀ (i : D.J), IsOpen (⇑(Sigma.ι D.U i ≫ Multicoequalizer.sigmaπ D.diagram) ⁻¹' U) as✝ : D.J ⊢ IsOpen (⇑(colimit.ι (Discrete.functor D.U) { as := as✝ }) ⁻¹' (⇑(colimit.ι (parallelPair D.diagram.fstSigmaMap D.diagram.sndSigmaMap) WalkingParallelPair.one) ⁻¹' ...
((:c IsOpen) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c Prefunctor.obj) ((:c CategoryTheory.Discrete) ((:c CategoryTheory.GlueData.J) (:c TopCat) (:c instTopCatLargeCategory) ((:c TopCat.GlueData.toGlueData) (:fv _uniq.1514)))) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c CategoryTheory.Discrete) ((...
[{"name":"D","sexp":"(:c TopCat.GlueData)"},{"name":"U","sexp":"((:c Set) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c CategoryTheory.GlueData.glued) (:c TopCat) (:c instTopCatLargeCategory) ((:c TopCat.GlueData.toGlueData) (:fv _uniq.1514)) ((:c CategoryTheory.Limits.hasColimitOfHasColimitsOfShape) (:c To...
(:app (:c IsOpen) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c CategoryTheory.Discrete) (:arg :explicit 0 (:app (:c CategoryTheory.GlueData.J) (:arg :implicit-type 0 (:c TopCat)) (:arg :instance 1 (:instance-of...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1514","is_instance":false,"is_let":false,"name":"D","sexp":"(:c TopCat.GlueData)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2012","is_instance":false,"is_let":false,"name":"U","sexp":"(:app (:c Set) (:arg :explicit 0 (:app (...
{"children":[{"source":"cases","sourceEnd":4965,"sourceStart":4960,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":4,"semanticRole":"local","source":"j","sourceEnd":4967,"sourceStart":4966,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","source...
[]
[{"source":"j","source_end":4967,"source_start":4966,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1514","is_instance":false,"is_let":false,"user_name":"D"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2012","is_instance":false,"is_let":false,"user_name":"U"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq...
14
32
exact
true
1
4
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8a6ca3e2105a50d2cd8712cc5793600950f810e0a53d72cf560225d5797ec2f6
827115e5593e50b2e646bbed902e42bd7ea8b5729b6863a12ebbd3334c034c65
31293912eb1d3025799c4ad7b0b981fa8f3f506b8d1a1b8f3e4dbb35fc03d26f
7a28caf3971d7bad41724c7bad5be064d1195d9533b37999fff82c5b3e686271
cat-searcher/leandojo-benchmark-4-random
test
2,174
TopCat.GlueData.isOpen_iff
Mathlib/Topology/Gluing.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply h
case mpr.mk D : GlueData U : Set ↑D.glued h : ∀ (i : D.J), IsOpen (⇑(Sigma.ι D.U i ≫ Multicoequalizer.sigmaπ D.diagram) ⁻¹' U) as✝ : D.J ⊢ IsOpen (⇑(colimit.ι (Discrete.functor D.U) { as := as✝ }) ⁻¹' (⇑(colimit.ι (parallelPair D.diagram.fstSigmaMap D.diagram.sndSigmaMap) WalkingParallelPair.one) ⁻¹' ...
((:c IsOpen) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c Prefunctor.obj) ((:c CategoryTheory.Discrete) ((:c CategoryTheory.GlueData.J) (:c TopCat) (:c instTopCatLargeCategory) ((:c TopCat.GlueData.toGlueData) (:fv _uniq.1514)))) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c CategoryTheory.Discrete) ((...
[{"name":"D","sexp":"(:c TopCat.GlueData)"},{"name":"U","sexp":"((:c Set) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c CategoryTheory.GlueData.glued) (:c TopCat) (:c instTopCatLargeCategory) ((:c TopCat.GlueData.toGlueData) (:fv _uniq.1514)) ((:c CategoryTheory.Limits.hasColimitOfHasColimitsOfShape) (:c To...
(:app (:c IsOpen) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c CategoryTheory.Discrete) (:arg :explicit 0 (:app (:c CategoryTheory.GlueData.J) (:arg :implicit-type 0 (:c TopCat)) (:arg :instance 1 (:instance-of...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1514","is_instance":false,"is_let":false,"name":"D","sexp":"(:c TopCat.GlueData)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2012","is_instance":false,"is_let":false,"name":"U","sexp":"(:app (:c Set) (:arg :explicit 0 (:app (...
{"children":[{"source":"apply","sourceEnd":4974,"sourceStart":4969,"tag":"atom"},{"contextIndex":3,"semanticRole":"local","source":"h","sourceEnd":4976,"sourceStart":4975,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply h","sourceEnd":4976,"sourceStart":4969,"tag":"node"}
[]
[{"source":"h","source_end":4976,"source_start":4975,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1514","is_instance":false,"is_let":false,"user_name":"D"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2012","is_instance":false,"is_let":false,"user_name":"U"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq...
14
34
exact
true
1
4
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1d800e943b41d94ef8495d04dca29f09ce53ac491062ea1ad65d281fb1ea1dff
7a28caf3971d7bad41724c7bad5be064d1195d9533b37999fff82c5b3e686271
91aa7fe7b28f9560108b087187578d0ab5c29f07c9b0e3291f4fe6454dc284a4
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,175
Erased.out_mk
Mathlib/Data/Erased.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
let h := (<a>Erased.mk</a> a).2
α : Sort u_1 a : α ⊢ (mk a).out = a
α : Sort u_1 a : α h : ∃ a_1, (fun b => a_1 = b) = (mk a).fst := (mk a).snd ⊢ (mk a).out = a
((:c Eq) (:fv _uniq.374) ((:c Erased.out) (:fv _uniq.374) ((:c Erased.mk) (:fv _uniq.374) (:fv _uniq.375))) (:fv _uniq.375))
[{"name":"α","sexp":"(:sort u_1)"},{"name":"a","sexp":"(:fv _uniq.374)"}]
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Erased.out) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Erased.mk) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))))) (:arg :explicit 2 (:fv FV2)))
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.374","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.375","is_instance":false,"is_let":false,"name":"a","sexp":"(:fv FV1)"}]
{"children":[{"source":"let","sourceEnd":1593,"sourceStart":1590,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":1595,"sourceStart":1594,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"sou...
[]
[{"source":"(mk a).2","source_end":1607,"source_start":1599,"syntax_kind":"Lean.Parser.Term.proj"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.374","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.375","is_instance":false,"is_let":false,"user_name":"a"}]
14
4
exact
true
1
2
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c0bc833448e00ab7c2b5ae6dacae0c4a2d2355ae3a4ed305acb887525b6b7321
ec746424f260ed2a892c8f9a597a44795aeeaecfd4eb394207609ddcf6c956ae
5fa56bde72198f50347f91852ad70d0a0bab83bcea16cfc9b6a64099317767b9
57e22d579da4a352d06d964502acb92443c1e93075b96f2156892c82a33990c9
cat-searcher/leandojo-benchmark-4-random
test
2,176
Erased.out_mk
Mathlib/Data/Erased.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
show <a>Classical.choose</a> h = a
α : Sort u_1 a : α h : ∃ a_1, (fun b => a_1 = b) = (mk a).fst := (mk a).snd ⊢ (mk a).out = a
α : Sort u_1 a : α h : ∃ a_1, (fun b => a_1 = b) = (mk a).fst := (mk a).snd ⊢ Classical.choose h = a
((:c Eq) (:fv _uniq.374) ((:c Erased.out) (:fv _uniq.374) ((:c Erased.mk) (:fv _uniq.374) (:fv _uniq.375))) (:fv _uniq.375))
[{"name":"α","sexp":"(:sort u_1)"},{"name":"a","sexp":"(:fv _uniq.374)"},{"name":"h","sexp":"((:c Exists) (:fv _uniq.374) (:lambda a (:fv _uniq.374) ((:c Eq) (:forall b (:fv _uniq.374) (:sort 0)) (:lambda b (:fv _uniq.374) ((:c Eq) (:fv _uniq.374) 1 0)) ((:c PSigma.fst) (:forall _ (:fv _uniq.374) (:sort 0)) (:lambda s ...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Erased.out) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Erased.mk) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))))) (:arg :explicit 2 (:fv FV2)))
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.374","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.375","is_instance":false,"is_let":false,"name":"a","sexp":"(:fv FV1)"},{"binder_role":":let","context_index":...
{"children":[{"source":"show","sourceEnd":1613,"sourceStart":1609,"tag":"atom"},{"children":[{"children":[{"name":"Classical.choose","semanticRole":"global","source":"Classical.choose","sourceEnd":1630,"sourceStart":1614,"tag":"identifier"},{"children":[{"contextIndex":3,"semanticRole":"local","source":"h","sourceEnd":...
[]
[{"source":"Classical.choose h = a","source_end":1636,"source_start":1614,"syntax_kind":"«term_=_»"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.374","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.375","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":let","context_index":3,"internal_name":"_uniq.391","...
14
6
exact
true
1
3
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a0a137eb3c88c6732c990426ae186e2d99a9ef6213851f7c15f050518997df3c
57e22d579da4a352d06d964502acb92443c1e93075b96f2156892c82a33990c9
d845acd41ae21909b2a91bc5bfac0b61b8ca01d39aad05f15f8d693097f3fa82
c31162881e390fcc1d1d58739b39b0be38075955336223e33b1e0d71c3c0eb3d
cat-searcher/leandojo-benchmark-4-random
test
2,177
Erased.out_mk
Mathlib/Data/Erased.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have := <a>Classical.choose_spec</a> h
α : Sort u_1 a : α h : ∃ a_1, (fun b => a_1 = b) = (mk a).fst := (mk a).snd ⊢ Classical.choose h = a
α : Sort u_1 a : α h : ∃ a_1, (fun b => a_1 = b) = (mk a).fst := (mk a).snd this : (fun b => Classical.choose h = b) = (mk a).fst ⊢ Classical.choose h = a
((:c Eq) (:fv _uniq.374) ((:c Classical.choose) (:fv _uniq.374) (:lambda x (:fv _uniq.374) ((:c Eq) (:forall b (:fv _uniq.374) (:sort 0)) (:lambda b (:fv _uniq.374) ((:c Eq) (:fv _uniq.374) 1 0)) ((:c PSigma.fst) (:forall _ (:fv _uniq.374) (:sort 0)) (:lambda s (:forall _ (:fv _uniq.374) (:sort 0)) ((:c Exists) (:fv _u...
[{"name":"α","sexp":"(:sort u_1)"},{"name":"a","sexp":"(:fv _uniq.374)"},{"name":"h","sexp":"((:c Exists) (:fv _uniq.374) (:lambda a (:fv _uniq.374) ((:c Eq) (:forall b (:fv _uniq.374) (:sort 0)) (:lambda b (:fv _uniq.374) ((:c Eq) (:fv _uniq.374) 1 0)) ((:c PSigma.fst) (:forall _ (:fv _uniq.374) (:sort 0)) (:lambda s ...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Classical.choose) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit 1) (:arg :proof 2 (:proof-of (:metavar))))) (:arg :explicit 2 (:fv FV2)))
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.374","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.375","is_instance":false,"is_let":false,"name":"a","sexp":"(:fv FV1)"},{"binder_role":":let","context_index":...
{"children":[{"source":"have","sourceEnd":1643,"sourceStart":1639,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":1644,"sourceStart":1644,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":1644,"sourceStart":1644,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","...
[]
[{"source":"Classical.choose_spec h","source_end":1670,"source_start":1647,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.374","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.375","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":let","context_index":3,"internal_name":"_uniq.391","...
14
7
exact
true
1
3
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5847b0d5ab675eb1bf69ec5f1e472bf4e325ed60166f37fa6fb914594366f57e
c31162881e390fcc1d1d58739b39b0be38075955336223e33b1e0d71c3c0eb3d
d51e4e9a374296dbe084547a63699e5797cc6c7fe44b56c9553892e41e9abdb3
f88e1f3d64da8de924a4794c7c13d1e43cde3f3dd6fc2eed969384d0bc552a80
cat-searcher/leandojo-benchmark-4-random
test
2,178
Erased.out_mk
Mathlib/Data/Erased.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>cast</a> (<a>congr_fun</a> this a).<a>Eq.symm</a> <a>rfl</a>
α : Sort u_1 a : α h : ∃ a_1, (fun b => a_1 = b) = (mk a).fst := (mk a).snd this : (fun b => Classical.choose h = b) = (mk a).fst ⊢ Classical.choose h = a
((:c Eq) (:fv _uniq.374) ((:c Classical.choose) (:fv _uniq.374) (:lambda x (:fv _uniq.374) ((:c Eq) (:forall b (:fv _uniq.374) (:sort 0)) (:lambda b (:fv _uniq.374) ((:c Eq) (:fv _uniq.374) 1 0)) ((:c PSigma.fst) (:forall _ (:fv _uniq.374) (:sort 0)) (:lambda s (:forall _ (:fv _uniq.374) (:sort 0)) ((:c Exists) (:fv _u...
[{"name":"α","sexp":"(:sort u_1)"},{"name":"a","sexp":"(:fv _uniq.374)"},{"name":"h","sexp":"((:c Exists) (:fv _uniq.374) (:lambda a (:fv _uniq.374) ((:c Eq) (:forall b (:fv _uniq.374) (:sort 0)) (:lambda b (:fv _uniq.374) ((:c Eq) (:fv _uniq.374) 1 0)) ((:c PSigma.fst) (:forall _ (:fv _uniq.374) (:sort 0)) (:lambda s ...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Classical.choose) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit 1) (:arg :proof 2 (:proof-of (:metavar))))) (:arg :explicit 2 (:fv FV2)))
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.374","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.375","is_instance":false,"is_let":false,"name":"a","sexp":"(:fv FV1)"},{"binder_role":":let","context_index":...
{"children":[{"source":"exact","sourceEnd":1678,"sourceStart":1673,"tag":"atom"},{"children":[{"name":"cast","semanticRole":"global","source":"cast","sourceEnd":1683,"sourceStart":1679,"tag":"identifier"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":1685,"sourceStart":1684,"tag":"atom"},{"children":...
[]
[{"source":"cast (congr_fun this a).symm rfl","source_end":1711,"source_start":1679,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.374","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.375","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":let","context_index":3,"internal_name":"_uniq.391","...
14
8
exact
true
1
4
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e215b129a24978bf08ee0f3120f1ec1b4b94f5243fd3fa8438586402bdfdb26e
f88e1f3d64da8de924a4794c7c13d1e43cde3f3dd6fc2eed969384d0bc552a80
3c244fa8f42b37b36014eda024c6de8f948439002d34136d4ee6cb38503b105f
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,179
exists_vector_zero
Mathlib/Data/Vector3.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>Vector3.eq_nil</a> v]
α : Type u_1 m n : ℕ f : Vector3 α 0 → Prop x✝ : Exists f v : Vector3 α 0 fv : f v ⊢ f []
α : Type u_1 m n : ℕ f : Vector3 α 0 → Prop x✝ : Exists f v : Vector3 α 0 fv : f v ⊢ f v
((:fv _uniq.22885) ((:c Vector3.nil) (:fv _uniq.22852)))
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"f","sexp":"(:forall _ ((:c Vector3) (:fv _uniq.22852) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) (:sort 0))"},{"name":"x✝","sexp":"((:c Exists) ((:c Vector3) (:fv _uniq.22852) ((:c OfN...
(:app (:fv FV4) (:arg :explicit 0 (:app (:c Vector3.nil) (:arg :implicit-type 0 (:fv FV0)))))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22852","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22854","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":implicit","context...
{"children":[{"source":"rw","sourceEnd":7743,"sourceStart":7741,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7745,"sourceStart":7744,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":7748,"sourceStart":...
[]
[{"source":"eq_nil v","source_end":7757,"source_start":7749,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22852","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22854","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
74
4
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5214d63d797cb09c4d6b1150e9563f571ed12430e09b5d4f2069300a684094ee
abedf96ce1a285a6fc5e175baf820e062f3947b7544670fa9da1a098b7da4e03
08c032b67601c7394943e465d3616dbaf35e99c8fa71d416d6c081a777f32a73
d55c26da1f2570ecd8312b4d672dfb3aee0bc72b6fe7b6899c866995943a3e0f
cat-searcher/leandojo-benchmark-4-random
test
2,180
exists_vector_zero
Mathlib/Data/Vector3.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact fv
α : Type u_1 m n : ℕ f : Vector3 α 0 → Prop x✝ : Exists f v : Vector3 α 0 fv : f v ⊢ f v
((:fv _uniq.22885) (:fv _uniq.22920))
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"f","sexp":"(:forall _ ((:c Vector3) (:fv _uniq.22852) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) (:sort 0))"},{"name":"x✝","sexp":"((:c Exists) ((:c Vector3) (:fv _uniq.22852) ((:c OfN...
(:app (:fv FV4) (:arg :explicit 0 (:fv FV6)))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22852","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22854","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":implicit","context...
{"children":[{"source":"exact","sourceEnd":7765,"sourceStart":7760,"tag":"atom"},{"contextIndex":7,"semanticRole":"local","source":"fv","sourceEnd":7768,"sourceStart":7766,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact fv","sourceEnd":7768,"sourceStart":7760,"tag":"node"}
[]
[{"source":"fv","source_end":7768,"source_start":7766,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22852","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22854","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
74
8
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
deaedee52b867ddaace39d2c5ff5cae2887fe69635204ca5ad92eaed75fd6698
d55c26da1f2570ecd8312b4d672dfb3aee0bc72b6fe7b6899c866995943a3e0f
c3b480dcb33c6a9e8d19a97ff6ae18709ab66faf45fa53f5a9ac6fd571e746be
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,181
negSucc_zsmul
Mathlib/Algebra/Group/Defs.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>natCast_zsmul</a>]
G✝ : Type u_1 inst✝¹ : DivInvMonoid G✝ a✝ b : G✝ G : Type u_2 inst✝ : SubNegMonoid G a : G n : ℕ ⊢ Int.negSucc n • a = -((n + 1) • a)
G✝ : Type u_1 inst✝¹ : DivInvMonoid G✝ a✝ b : G✝ G : Type u_2 inst✝ : SubNegMonoid G a : G n : ℕ ⊢ Int.negSucc n • a = -(↑(n + 1) • a)
((:c Eq) (:fv _uniq.25046) ((:c HSMul.hSMul) (:c Int) (:fv _uniq.25046) (:fv _uniq.25046) ((:c instHSMul) (:c Int) (:fv _uniq.25046) ((:c SubNegMonoid.SMulInt) (:fv _uniq.25046) (:fv _uniq.25047))) ((:c Int.negSucc) (:fv _uniq.25049)) (:fv _uniq.25048)) ((:c Neg.neg) (:fv _uniq.25046) ((:c SubNegMonoid.toNeg) (:fv _uni...
[{"name":"G✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c DivInvMonoid) (:fv _uniq.24890))"},{"name":"a✝","sexp":"(:fv _uniq.24890)"},{"name":"b","sexp":"(:fv _uniq.24890)"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c SubNegMonoid) (:fv _uniq.25046))"},{"name":"a","sexp":"(:fv _un...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:fv FV5)) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c HSMul) (:arg :explicit 0 (:c Int)) (:arg :explicit 1 (:fv FV5)) (:arg :explicit 2 (:fv F...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24890","is_instance":false,"is_let":false,"name":"G✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24893","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c DivInvMonoid) (:arg :e...
{"children":[{"source":"rw","sourceEnd":46015,"sourceStart":46013,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":46017,"sourceStart":46016,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":46020,"sourceSt...
[]
[{"source":"natCast_zsmul","source_end":46034,"source_start":46021,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24890","is_instance":false,"is_let":false,"user_name":"G✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24893","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"inter...
334
4
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3d2f85dab701ce0813a7fedf3294873c7fc2397fc040a63af952f7520d3fea42
ef70a2a3169b58fe00e1fc78be879b95ffcaf6467e43712a4e5ed8e849fb6ee1
89f53f88bdcde9d2040ef581e59cf4be80eae2e7d681fc95b2deaddcb97bb7d0
b2b9f765bbd54248e541faebd6405a207ad81907aac5f3937081fe77763364ab
cat-searcher/leandojo-benchmark-4-random
test
2,182
negSucc_zsmul
Mathlib/Algebra/Group/Defs.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>SubNegMonoid.zsmul_neg'</a> n a
G✝ : Type u_1 inst✝¹ : DivInvMonoid G✝ a✝ b : G✝ G : Type u_2 inst✝ : SubNegMonoid G a : G n : ℕ ⊢ Int.negSucc n • a = -(↑(n + 1) • a)
((:c Eq) (:fv _uniq.25046) ((:c HSMul.hSMul) (:c Int) (:fv _uniq.25046) (:fv _uniq.25046) ((:c instHSMul) (:c Int) (:fv _uniq.25046) ((:c SubNegMonoid.SMulInt) (:fv _uniq.25046) (:fv _uniq.25047))) ((:c Int.negSucc) (:fv _uniq.25049)) (:fv _uniq.25048)) ((:c Neg.neg) (:fv _uniq.25046) ((:c SubNegMonoid.toNeg) (:fv _uni...
[{"name":"G✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c DivInvMonoid) (:fv _uniq.24890))"},{"name":"a✝","sexp":"(:fv _uniq.24890)"},{"name":"b","sexp":"(:fv _uniq.24890)"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c SubNegMonoid) (:fv _uniq.25046))"},{"name":"a","sexp":"(:fv _un...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:fv FV5)) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c HSMul) (:arg :explicit 0 (:c Int)) (:arg :explicit 1 (:fv FV5)) (:arg :explicit 2 (:fv F...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24890","is_instance":false,"is_let":false,"name":"G✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24893","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c DivInvMonoid) (:arg :e...
{"children":[{"source":"exact","sourceEnd":46043,"sourceStart":46038,"tag":"atom"},{"children":[{"name":"SubNegMonoid.zsmul_neg'","semanticRole":"global","source":"SubNegMonoid.zsmul_neg'","sourceEnd":46067,"sourceStart":46044,"tag":"identifier"},{"children":[{"contextIndex":8,"semanticRole":"local","source":"n","sourc...
[]
[{"source":"SubNegMonoid.zsmul_neg' n a","source_end":46071,"source_start":46044,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24890","is_instance":false,"is_let":false,"user_name":"G✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24893","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"inter...
334
7
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c15599d7b948041b4befe0b4ce2b535e237dc33f19e8ce623bf956e076010831
b2b9f765bbd54248e541faebd6405a207ad81907aac5f3937081fe77763364ab
c6852c431c6d94639ff5fe2f5aeb57f356751432057e0e2ff9572da73f948000
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,183
CategoryTheory.Functor.Monoidal.tensorHom_app_snd
Mathlib/CategoryTheory/ChosenFiniteProducts/FunctorCategory.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
change (f ⊗ g).<a>CategoryTheory.NatTrans.app</a> j ≫ (<a>CategoryTheory.ChosenFiniteProducts.snd</a> F₁' F₂').<a>CategoryTheory.NatTrans.app</a> j = _
J : Type u_1 C : Type u_2 inst✝² : Category.{u_3, u_1} J inst✝¹ : Category.{u_4, u_2} C inst✝ : ChosenFiniteProducts C F₁ F₁' F₂ F₂' : J ⥤ C f : F₁ ⟶ F₁' g : F₂ ⟶ F₂' j : J ⊢ (f ⊗ g).app j ≫ snd (F₁'.obj j) (F₂'.obj j) = snd (F₁.obj j) (F₂.obj j) ≫ g.app j
J : Type u_1 C : Type u_2 inst✝² : Category.{u_3, u_1} J inst✝¹ : Category.{u_4, u_2} C inst✝ : ChosenFiniteProducts C F₁ F₁' F₂ F₂' : J ⥤ C f : F₁ ⟶ F₁' g : F₂ ⟶ F₂' j : J ⊢ (f ⊗ g).app j ≫ (snd F₁' F₂').app j = snd (F₁.obj j) (F₂.obj j) ≫ g.app j
((:c Eq) ((:c Quiver.Hom) (:fv _uniq.31389) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.31389) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.31389) (:fv _uniq.31397))) ((:c Prefunctor.obj) (:fv _uniq.31386) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.31386) ((:c CategoryTheory.Catego...
[{"name":"J","sexp":"(:sort (+ u_1 1))"},{"name":"C","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.31386))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.31389))"},{"name":"inst✝","sexp":"((:c CategoryTheory.ChosenFiniteProducts) (:fv _uniq.31389) (:f...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31386","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31389","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"change","sourceEnd":3413,"sourceStart":3407,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"(","sourceEnd":3415,"sourceStart":3414,"tag":"atom"},{"children":[{"children":[{"contextIndex":10,"semanticRole":"local","source":"f","sourceEnd":3416,"sourceStar...
[]
[{"source":"(f ⊗ g).app j ≫ (snd F₁' F₂').app j = _","source_end":3461,"source_start":3414,"syntax_kind":"«term_=_»"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31386","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31389","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
26
4
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7c91f1a7d464d7f9853e52d8c9354d3706029554665d97a51701b4e6f3b2c41d
70b6ac8c2f8717ebfb5b2161b7146158bbab063f3ba22e4ede31bb990219519b
827774212d6ba6675992647e171c8fc9807d2ed0e1b97e77dcf5bd62da51b47e
b87965be5e2b3562515b2ef25de8a309bfbd61625c1f7483413e18d4e60ad017
cat-searcher/leandojo-benchmark-4-random
test
2,184
CategoryTheory.Functor.Monoidal.tensorHom_app_snd
Mathlib/CategoryTheory/ChosenFiniteProducts/FunctorCategory.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>CategoryTheory.NatTrans.comp_app</a>, <a>CategoryTheory.ChosenFiniteProducts.tensorHom_snd</a>, <a>CategoryTheory.NatTrans.comp_app</a>]
J : Type u_1 C : Type u_2 inst✝² : Category.{u_3, u_1} J inst✝¹ : Category.{u_4, u_2} C inst✝ : ChosenFiniteProducts C F₁ F₁' F₂ F₂' : J ⥤ C f : F₁ ⟶ F₁' g : F₂ ⟶ F₂' j : J ⊢ (f ⊗ g).app j ≫ (snd F₁' F₂').app j = snd (F₁.obj j) (F₂.obj j) ≫ g.app j
J : Type u_1 C : Type u_2 inst✝² : Category.{u_3, u_1} J inst✝¹ : Category.{u_4, u_2} C inst✝ : ChosenFiniteProducts C F₁ F₁' F₂ F₂' : J ⥤ C f : F₁ ⟶ F₁' g : F₂ ⟶ F₂' j : J ⊢ (snd F₁ F₂).app j ≫ g.app j = snd (F₁.obj j) (F₂.obj j) ≫ g.app j
((:c Eq) ((:c Quiver.Hom) (:fv _uniq.31389) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.31389) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.31389) (:fv _uniq.31397))) ((:c Prefunctor.obj) (:fv _uniq.31386) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.31386) ((:c CategoryTheory.Catego...
[{"name":"J","sexp":"(:sort (+ u_1 1))"},{"name":"C","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.31386))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.31389))"},{"name":"inst✝","sexp":"((:c CategoryTheory.ChosenFiniteProducts) (:fv _uniq.31389) (:f...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31386","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31389","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"rw","sourceEnd":3466,"sourceStart":3464,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3468,"sourceStart":3467,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":3471,"sourceStart":...
[]
[{"source":"NatTrans.comp_app","source_end":3489,"source_start":3472,"syntax_kind":"ident"},{"source":"tensorHom_snd","source_end":3504,"source_start":3491,"syntax_kind":"ident"},{"source":"NatTrans.comp_app","source_end":3523,"source_start":3506,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31386","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31389","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
26
5
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
af72263995ca0f51c7a2233ee0ea0f431b02012402c81866c179edb4efc31ebe
b87965be5e2b3562515b2ef25de8a309bfbd61625c1f7483413e18d4e60ad017
5a3076883c5e1c3dacc10af86492d364a610ca44a12588aceb2deac3600581a5
32633042812aca095c784591e0a67fd56711e81eb81ffa3ca78923e904d93c36
cat-searcher/leandojo-benchmark-4-random
test
2,185
CategoryTheory.Functor.Monoidal.tensorHom_app_snd
Mathlib/CategoryTheory/ChosenFiniteProducts/FunctorCategory.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rfl
J : Type u_1 C : Type u_2 inst✝² : Category.{u_3, u_1} J inst✝¹ : Category.{u_4, u_2} C inst✝ : ChosenFiniteProducts C F₁ F₁' F₂ F₂' : J ⥤ C f : F₁ ⟶ F₁' g : F₂ ⟶ F₂' j : J ⊢ (snd F₁ F₂).app j ≫ g.app j = snd (F₁.obj j) (F₂.obj j) ≫ g.app j
((:c Eq) ((:c Quiver.Hom) (:fv _uniq.31389) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.31389) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.31389) (:fv _uniq.31397))) ((:c Prefunctor.obj) (:fv _uniq.31386) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.31386) ((:c CategoryTheory.Catego...
[{"name":"J","sexp":"(:sort (+ u_1 1))"},{"name":"C","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.31386))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.31389))"},{"name":"inst✝","sexp":"((:c CategoryTheory.ChosenFiniteProducts) (:fv _uniq.31389) (:f...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31386","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31389","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"rfl","sourceEnd":3530,"sourceStart":3527,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":3530,"sourceStart":3527,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31386","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31389","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
26
10
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4b7dd914a65f26701287c2ebb2b4f591fc1ab4fdbab63883366153d54f9c8ec0
32633042812aca095c784591e0a67fd56711e81eb81ffa3ca78923e904d93c36
5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,186
CategoryTheory.Limits.prod.lift_fst_snd
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
ext <;> simp
C : Type u inst✝¹ : Category.{v, u} C X✝ Y✝ X Y : C inst✝ : HasBinaryProduct X Y ⊢ lift fst snd = 𝟙 (X ⨯ Y)
((:c Eq) ((:c Quiver.Hom) (:fv _uniq.106532) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.106532) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.106532) (:fv _uniq.106535))) ((:c CategoryTheory.Limits.prod) (:fv _uniq.106532) (:fv _uniq.106535) (:fv _uniq.109844) (:fv _uniq.109845) (:fv _uniq.1098...
[{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.106532))"},{"name":"X✝","sexp":"(:fv _uniq.106532)"},{"name":"Y✝","sexp":"(:fv _uniq.106532)"},{"name":"X","sexp":"(:fv _uniq.106532)"},{"name":"Y","sexp":"(:fv _uniq.106532)"},{"name":"inst✝","sexp":"((:c CategoryT...
(: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.Limits.prod) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheor...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.106532","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.106535","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Catego...
{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"ext","sourceEnd":35731,"sourceStart":35728,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":35731,"sourceSt...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.106532","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.106535","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"inte...
215
2
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
fd15c7af0c5ea097aa2f5d319cd03cb34812408ff7b763df4c0fbf83c9a94424
a11b8ccb8ff98655886effb6c710210d651207d2f53c88197ea1e83d1f352443
713034734afd1314a043e8a1a1465e1d87063abb19f50189203b0e64690a9a31
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,187
DFinsupp.toFinsupp_single
Mathlib/Data/Finsupp/ToDFinsupp.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
ext
ι : Type u_1 R : Type u_2 M : Type u_3 inst✝² : DecidableEq ι inst✝¹ : Zero M inst✝ : (m : M) → Decidable (m ≠ 0) i : ι m : M ⊢ (single i m).toFinsupp = Finsupp.single i m
case h ι : Type u_1 R : Type u_2 M : Type u_3 inst✝² : DecidableEq ι inst✝¹ : Zero M inst✝ : (m : M) → Decidable (m ≠ 0) i : ι m : M a✝ : ι ⊢ (single i m).toFinsupp a✝ = (Finsupp.single i m) a✝
((:c Eq) ((:c Finsupp) (:fv _uniq.6979) (:fv _uniq.6985) (:fv _uniq.6997)) ((:c DFinsupp.toFinsupp) (:fv _uniq.6979) (:fv _uniq.6985) (:fv _uniq.6992) (:fv _uniq.6997) (:fv _uniq.7032) ((:c DFinsupp.single) (:fv _uniq.6979) (:lambda _ (:fv _uniq.6979) (:fv _uniq.6985)) (:fv _uniq.6992) (:lambda i (:fv _uniq.6979) (:fv ...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.6979))"},{"name":"inst✝¹","sexp":"((:c Zero) (:fv _uniq.6985))"},{"name":"inst✝","sexp":"(:forall m (:fv _uniq.6985) ((:c Decidable) ((:c Ne) (:f...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Finsupp) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 1 (:app (:c DFinsupp.toFinsupp) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :i...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6979","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6982","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","conte...
{"children":[{"source":"ext","sourceEnd":4341,"sourceStart":4338,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":4341,"sourceStart":4338,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6979","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6982","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq...
22
4
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
88073c071e9f90629410c293f37721878fbce0df6d8945a2d5ceb60e5a0a3146
9c31cc77e5bf2ee8c0a951f6d940f6391ac4f833a2095a8d81f2d56d22217b93
a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de
baeefce7f2d354099f400eba0d1b1432050bd9d467702813b1b9ca25b3bc6208
cat-searcher/leandojo-benchmark-4-random
test
2,188
DFinsupp.toFinsupp_single
Mathlib/Data/Finsupp/ToDFinsupp.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>Finsupp.single_apply</a>, <a>DFinsupp.single_apply</a>]
case h ι : Type u_1 R : Type u_2 M : Type u_3 inst✝² : DecidableEq ι inst✝¹ : Zero M inst✝ : (m : M) → Decidable (m ≠ 0) i : ι m : M a✝ : ι ⊢ (single i m).toFinsupp a✝ = (Finsupp.single i m) a✝
((:c Eq) (:fv _uniq.6985) ((:c DFunLike.coe) ((:c Finsupp) (:fv _uniq.6979) (:fv _uniq.6985) (:fv _uniq.6997)) (:fv _uniq.6979) (:lambda _ (:fv _uniq.6979) (:fv _uniq.6985)) ((:c Finsupp.instFunLike) (:fv _uniq.6979) (:fv _uniq.6985) (:fv _uniq.6997)) ((:c DFinsupp.toFinsupp) (:fv _uniq.6979) (:fv _uniq.6985) (:fv _uni...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.6979))"},{"name":"inst✝¹","sexp":"((:c Zero) (:fv _uniq.6985))"},{"name":"inst✝","sexp":"(:forall m (:fv _uniq.6985) ((:c Decidable) ((:c Ne) (:f...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Finsupp) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:fv FV2))))))) (:arg :implicit-type 1 (:fv FV0)) (:arg :implici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6979","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6982","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","conte...
{"children":[{"source":"simp","sourceEnd":4348,"sourceStart":4344,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4350,"sourceStart":4349,"tag":"atom"...
[]
[{"source":"Finsupp.single_apply","source_end":4370,"source_start":4350,"syntax_kind":"ident"},{"source":"DFinsupp.single_apply","source_end":4393,"source_start":4372,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6979","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6982","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq...
22
5
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
aed591dedbb2a9ef7cea760ce87fcc0890e3c9a684a40f71131e4bcfd1e9c7c5
baeefce7f2d354099f400eba0d1b1432050bd9d467702813b1b9ca25b3bc6208
476364c82d22b0a0de8d624c5743a6ad7ca14c81b218a35cd58827886ea5a49e
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,189
StrictConcaveOn.lt_slope_of_hasDerivWithinAt_Iio
Mathlib/Analysis/Convex/Deriv.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simpa only [<a>Pi.neg_def</a>, <a>slope_neg</a>, <a>neg_neg</a>] using <a>neg_lt_neg</a> (hfc.neg.slope_lt_of_hasDerivWithinAt_Iio hx hy hxy hf'.neg)
S : Set ℝ f : ℝ → ℝ x y f' : ℝ hfc : StrictConcaveOn ℝ S f hx : x ∈ S hy : y ∈ S hxy : x < y hf' : HasDerivWithinAt f f' (Iio y) y ⊢ f' < slope f x y
((:c LT.lt) (:c Real) (:c Real.instLT) (:fv _uniq.124989) ((:c slope) (:c Real) (:c Real) (:c Real) (:c Real.field) (:c Real.instAddCommGroup) ((:c NormedSpace.toModule) (:c Real) (:c Real) (:c Real.normedField) ((:c NonUnitalSeminormedRing.toSeminormedAddCommGroup) (:c Real) ((:c NonUnitalSeminormedCommRing.toNonUnita...
[{"name":"S","sexp":"((:c Set) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"f'","sexp":"(:c Real)"},{"name":"hfc","sexp":"((:c StrictConcaveOn) (:c Real) (:c Real) (:c Real) (:c Real.orderedSemiring) (:c Real.instAddCommMonoi...
(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV4)) (:arg :explicit 3 (:app (:c slope) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:insta...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.124979","is_instance":false,"is_let":false,"name":"S","sexp":"(:app (:c Set) (:arg :explicit 0 (:c Real)))"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.124983","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :...
{"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":43327,"sourceStart":43322,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind...
[]
[{"source":"Pi.neg_def","source_end":43344,"source_start":43334,"syntax_kind":"ident"},{"source":"slope_neg","source_end":43355,"source_start":43346,"syntax_kind":"ident"},{"source":"neg_neg","source_end":43364,"source_start":43357,"syntax_kind":"ident"},{"source":"neg_lt_neg (hfc.neg.slope_lt_of_hasDerivWithinAt_Iio h...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.124979","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.124983","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
145
2
exact
true
1
10
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
55fd0cd9905481422b50617788b8614970e88bd79eff7d96188670b8ddbdd69e
72fc1aa0fdf54affdce8af62891e1b671064fb66d221ede05d64177d0529c849
f2d2917e9c1a7b8e4d380f5d898aa0cd723e96b4a49f17f0cc78904ad2c214ef
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,190
lt_compl_self
Mathlib/Order/Heyting/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>lt_iff_le_and_ne</a>]
ι : Type u_1 α : Type u_2 β : Type u_3 inst✝¹ : HeytingAlgebra α a b c : α inst✝ : Nontrivial α ⊢ a < aᶜ ↔ a = ⊥
ι : Type u_1 α : Type u_2 β : Type u_3 inst✝¹ : HeytingAlgebra α a b c : α inst✝ : Nontrivial α ⊢ a ≤ aᶜ ∧ a ≠ aᶜ ↔ a = ⊥
((:c Iff) ((:c LT.lt) (:fv _uniq.127966) ((:c Preorder.toLT) (:fv _uniq.127966) ((:c PartialOrder.toPreorder) (:fv _uniq.127966) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.127966) ((:c Lattice.toSemilatticeInf) (:fv _uniq.127966) ((:c GeneralizedHeytingAlgebra.toLattice) (:fv _uniq.127966) ((:c HeytingAlgebra.toGen...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c HeytingAlgebra) (:fv _uniq.127966))"},{"name":"a","sexp":"(:fv _uniq.127966)"},{"name":"b","sexp":"(:fv _uniq.127966)"},{"name":"c","sexp":"(:fv _uniq.127966)"},{"name":...
(:app (:c Iff) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV4)) (:arg :explicit 3 (:app (:c HasCompl.compl) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c HasCompl)...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.127963","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.127966","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"rw","sourceEnd":32105,"sourceStart":32103,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32107,"sourceStart":32106,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"lt_iff_le_and_ne...
[]
[{"source":"lt_iff_le_and_ne","source_end":32123,"source_start":32107,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.127963","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.127966","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
337
4
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c1cd30e163c4a8dc0f7a8a19896be2f8baaaf707de53f441375b7bf38c2b2ebe
84b4df5be208649034315a2e48096901d3193af9b720d86d5003ba0dbcca01c3
e1c86cb74a389fe36b2d1a1772d4b988a61460be86bca11c6aa9ec6c34b72556
9365a079d8d7842055ada71496f4115e561b74568d16d356a0ad7bcba2dff3bd
cat-searcher/leandojo-benchmark-4-random
test
2,191
lt_compl_self
Mathlib/Order/Heyting/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
ι : Type u_1 α : Type u_2 β : Type u_3 inst✝¹ : HeytingAlgebra α a b c : α inst✝ : Nontrivial α ⊢ a ≤ aᶜ ∧ a ≠ aᶜ ↔ a = ⊥
((:c Iff) ((:c And) ((:c LE.le) (:fv _uniq.127966) ((:c Preorder.toLE) (:fv _uniq.127966) ((:c PartialOrder.toPreorder) (:fv _uniq.127966) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.127966) ((:c Lattice.toSemilatticeInf) (:fv _uniq.127966) ((:c GeneralizedHeytingAlgebra.toLattice) (:fv _uniq.127966) ((:c HeytingAlg...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c HeytingAlgebra) (:fv _uniq.127966))"},{"name":"a","sexp":"(:fv _uniq.127966)"},{"name":"b","sexp":"(:fv _uniq.127966)"},{"name":"c","sexp":"(:fv _uniq.127966)"},{"name":...
(:app (:c Iff) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV4)) (:arg :explicit 3 (:app (:c HasCompl.compl) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.127963","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.127966","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"simp","sourceEnd":32130,"sourceStart":32126,"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.127963","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.127966","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
337
8
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
feee6c84637aa8f20c85beba6336fc213a72a90ee3ae87fc87e1ee92cae83fde
9365a079d8d7842055ada71496f4115e561b74568d16d356a0ad7bcba2dff3bd
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,192
Ring.image_closure
Mathlib/Deprecated/Subring.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine <a>le_antisymm</a> ?_ (<a>Ring.closure_subset</a> (<a>RingHom.isSubring_image</a> _ <a>Ring.closure.isSubring</a>) <| <a>Set.image_subset</a> _ <a>Ring.subset_closure</a>)
R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R ⊢ ⇑f '' closure s = closure (⇑f '' s)
R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R ⊢ ⇑f '' closure s ≤ closure (⇑f '' s)
((:c Eq) ((:c Set) (:fv _uniq.20887)) ((:c Set.image) (:fv _uniq.20356) (:fv _uniq.20887) ((:c DFunLike.coe) ((:c RingHom) (:fv _uniq.20356) (:fv _uniq.20887) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.20356) ((:c Ring.toSemiring) (:fv _uniq.20356) (:fv _uniq.20359))) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.2088...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.20356))"},{"name":"cR","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20361))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.20356))"},{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Rin...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :explicit 1 (:app (:c Set.image) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV6)) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c RingHom) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Ring) (:arg :explicit 0...
{"children":[{"source":"refine","sourceEnd":9176,"sourceStart":9170,"tag":"atom"},{"children":[{"name":"le_antisymm","semanticRole":"global","source":"le_antisymm","sourceEnd":9188,"sourceStart":9177,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":9190,"sourceStart":9189,"tag":"atom"},{"children...
[]
[{"source":"le_antisymm ?_ (closure_subset (RingHom.isSubring_image _ closure.isSubring) <|\n Set.image_subset _ subset_closure)","source_end":9295,"source_start":9177,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern...
44
4
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
12ec0716656818d3ae19a0732085d71c997adbed3b4fbe8d32ae682afed2c933
3df59222ebc721f9f40a96893735a88675a0d93be90187b7756b536392430a58
8a5fe54c9d86e4f5ddaf62a8a5c12fdf21cd97638ab4727bd078e95af491f304
2f6d087d3abfcb380f002e8f2c2c431496629d536a5d350d12cae8232d28b702
cat-searcher/leandojo-benchmark-4-random
test
2,193
Ring.image_closure
Mathlib/Deprecated/Subring.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro _ ⟨x, hx, rfl⟩
R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R ⊢ ⇑f '' closure s ≤ closure (⇑f '' s)
case intro.intro R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s ⊢ f x ∈ closure (⇑f '' s)
((:c LE.le) ((:c Set) (:fv _uniq.20887)) ((:c Preorder.toLE) ((:c Set) (:fv _uniq.20887)) ((:c PartialOrder.toPreorder) ((:c Set) (:fv _uniq.20887)) ((:c CompleteSemilatticeInf.toPartialOrder) ((:c Set) (:fv _uniq.20887)) ((:c CompleteLattice.toCompleteSemilatticeInf) ((:c Set) (:fv _uniq.20887)) ((:c CompletelyDistrib...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.20356))"},{"name":"cR","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20361))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.20356))"},{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Rin...
(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV6))))))) (:arg :explicit 2 (:app (:c Set.image) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV6)) (:arg :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Ring) (:arg :explicit 0...
{"children":[{"source":"rintro","sourceEnd":9304,"sourceStart":9298,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"_","sourceEnd":9306,"sourceStart":9305,"tag":"atom"}],"kind":"Lean.Parser.Tactic.rcasesPat.ignore","source":"_","sourceEnd":9306,"sourceStart":9305,"tag":"node"}],"kind":"Lean.Parser.Tacti...
[{"role":"fresh_name","source":"x","source_end":9311,"source_start":9310,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":9315,"source_start":9313,"syntax_kind":"ident"}]
[{"source":"⟨x, hx, rfl⟩","source_end":9323,"source_start":9307,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern...
44
5
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e4b825a2c844df2b79b10ef4f6d25843a532cbe765be79f1c1c59eab66356145
2f6d087d3abfcb380f002e8f2c2c431496629d536a5d350d12cae8232d28b702
b2945dc9b8e145073627cb1f744258cfb6b7d041a55952d1b4b95051bf263c28
b943c731b5b49be2669606de6502d6d990e9e1d17250229d92aa791336189dfe
cat-searcher/leandojo-benchmark-4-random
test
2,194
Ring.image_closure
Mathlib/Deprecated/Subring.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>AddGroup.InClosure.recOn</a> (motive := fun {x} _ ↦ f x ∈ <a>Ring.closure</a> (f '' s)) hx _ <;> intros
case intro.intro R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s ⊢ f x ∈ closure (⇑f '' s)
case intro.intro.zero R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s ⊢ f 0 ∈ closure (⇑f '' s) case intro.intro.neg R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R ...
((:c Membership.mem) (:fv _uniq.20887) ((:c Set) (:fv _uniq.20887)) ((:c Set.instMembership) (:fv _uniq.20887)) ((:c DFunLike.coe) ((:c RingHom) (:fv _uniq.20356) (:fv _uniq.20887) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.20356) ((:c Ring.toSemiring) (:fv _uniq.20356) (:fv _uniq.20359))) ((:c Semiring.toNonAssocSem...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.20356))"},{"name":"cR","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20361))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.20356))"},{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Rin...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6))))))) (:arg :explicit 3 (:app (:c DFunLike.coe)...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Ring) (:arg :explicit 0...
{"children":[{"children":[{"source":"apply","sourceEnd":9331,"sourceStart":9326,"tag":"atom"},{"children":[{"name":"AddGroup.InClosure.recOn","semanticRole":"global","source":"AddGroup.InClosure.recOn","sourceEnd":9356,"sourceStart":9332,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":9358,"sour...
[]
[{"source":"AddGroup.InClosure.recOn (motive := fun {x} _ ↦ f x ∈ closure (f '' s)) hx _","source_end":9412,"source_start":9332,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern...
44
6
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
37d04c6e12a1bd99842e748df85769149bac5b0b8f56922e3484d74fb54309af
b943c731b5b49be2669606de6502d6d990e9e1d17250229d92aa791336189dfe
d8c5251d2cc1eed435f899a4388ad81b9ae72ee7297237dd27b9b6a35980e49e
72d3643032cc28f5cb33ad7951ab0f3bed1f5c51b58fc6d8bedebf589cb6479d
cat-searcher/leandojo-benchmark-4-random
test
2,195
Ring.image_closure
Mathlib/Deprecated/Subring.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [f.map_zero]
case intro.intro.zero R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s ⊢ f 0 ∈ closure (⇑f '' s)
case intro.intro.zero R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s ⊢ 0 ∈ closure (⇑f '' s)
((:c Membership.mem) (:fv _uniq.20887) ((:c Set) (:fv _uniq.20887)) ((:c Set.instMembership) (:fv _uniq.20887)) ((:c DFunLike.coe) ((:c RingHom) (:fv _uniq.20356) (:fv _uniq.20887) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.20356) ((:c Ring.toSemiring) (:fv _uniq.20356) (:fv _uniq.20359))) ((:c Semiring.toNonAssocSem...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.20356))"},{"name":"cR","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20361))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.20356))"},{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Rin...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6))))))) (:arg :explicit 3 (:app (:c DFunLike.coe)...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Ring) (:arg :explicit 0...
{"children":[{"source":"rw","sourceEnd":9431,"sourceStart":9429,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9433,"sourceStart":9432,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"RingHom.map_zero","s...
[]
[{"source":"f.map_zero","source_end":9443,"source_start":9433,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern...
44
17
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d18ddd37b2eb0a6c874dad52e58a477682730ba0bb7f6b564ea7cf256c537f5a
6787ec41e68067b363f4a0398ac0d23ada25572730ecd15d231dd95dfc715339
656a0e3777b435a6227cdb44470fe61d7966231ef2cf3ca1271272b534153761
558ec64f0e1fcbec44a43048860a38d363c1d54b7e49067ba96189f96d54211d
cat-searcher/leandojo-benchmark-4-random
test
2,196
Ring.image_closure
Mathlib/Deprecated/Subring.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply closure.isSubring.zero_mem
case intro.intro.zero R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s ⊢ 0 ∈ closure (⇑f '' s)
((:c Membership.mem) (:fv _uniq.20887) ((:c Set) (:fv _uniq.20887)) ((:c Set.instMembership) (:fv _uniq.20887)) ((:c OfNat.ofNat) (:fv _uniq.20887) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.20887) ((:c MulZeroOneClass.toZero) (:fv _uniq.20887) ((:c NonAssocSemiring.toMulZeroOneClass) (:fv _uniq.20887) ((:c Semiring.toNon...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.20356))"},{"name":"cR","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20361))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.20356))"},{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Rin...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6))))))) (:arg :explicit 3 (:app (:c OfNat.ofNat) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Ring) (:arg :explicit 0...
{"children":[{"source":"apply","sourceEnd":9454,"sourceStart":9449,"tag":"atom"},{"name":"IsAddSubmonoid.zero_mem","semanticRole":"global","source":"closure.isSubring.zero_mem","sourceEnd":9481,"sourceStart":9455,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply closure.isSubring.zero_mem","sourceE...
[]
[{"source":"closure.isSubring.zero_mem","source_end":9481,"source_start":9455,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern...
44
20
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b2a72ebde7dc48193fbeb992004d8206064afae274cd54729d35738f62124a3e
558ec64f0e1fcbec44a43048860a38d363c1d54b7e49067ba96189f96d54211d
9779140b461424c427a8340af5ce1d4601c33c9c179e02b73328769940e6be52
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,197
Ring.image_closure
Mathlib/Deprecated/Subring.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [f.map_neg]
case intro.intro.neg R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s a✝¹ : R a✝ : AddGroup.InClosure (Monoid.Closure s) a✝¹ a_ih✝ : f a✝¹ ∈ closure (⇑f '' s) ⊢ f (-a✝¹) ∈ closure (⇑f '' s)
case intro.intro.neg R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s a✝¹ : R a✝ : AddGroup.InClosure (Monoid.Closure s) a✝¹ a_ih✝ : f a✝¹ ∈ closure (⇑f '' s) ⊢ -f a✝¹ ∈ closure (⇑f '' s)
((:c Membership.mem) (:fv _uniq.20887) ((:c Set) (:fv _uniq.20887)) ((:c Set.instMembership) (:fv _uniq.20887)) ((:c DFunLike.coe) ((:c RingHom) (:fv _uniq.20356) (:fv _uniq.20887) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.20356) ((:c Ring.toSemiring) (:fv _uniq.20356) (:fv _uniq.20359))) ((:c Semiring.toNonAssocSem...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.20356))"},{"name":"cR","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20361))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.20356))"},{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Rin...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6))))))) (:arg :explicit 3 (:app (:c DFunLike.coe)...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Ring) (:arg :explicit 0...
{"children":[{"source":"rw","sourceEnd":9489,"sourceStart":9487,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9491,"sourceStart":9490,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"RingHom.map_neg","se...
[]
[{"source":"f.map_neg","source_end":9500,"source_start":9491,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern...
44
25
exact
true
1
14
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
cdb93255ae32864875c301e753453f186be4717138e5f2ab4a96609d67de242d
cc68074e8f196f20772d82d890f7a407e8eb31c135fe51d1157115245e29e733
32f5427ca226d7704b042f1431c7bbd26381008ec000778caf155a8ab1288b41
1d664fdd3c50ca6696a2cd47825090d6405ec8c46041c1bca0cbb09663923aa8
cat-searcher/leandojo-benchmark-4-random
test
2,198
Ring.image_closure
Mathlib/Deprecated/Subring.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply closure.isSubring.neg_mem
case intro.intro.neg R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s a✝¹ : R a✝ : AddGroup.InClosure (Monoid.Closure s) a✝¹ a_ih✝ : f a✝¹ ∈ closure (⇑f '' s) ⊢ -f a✝¹ ∈ closure (⇑f '' s)
case intro.intro.neg R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s a✝¹ : R a✝ : AddGroup.InClosure (Monoid.Closure s) a✝¹ a_ih✝ : f a✝¹ ∈ closure (⇑f '' s) ⊢ f a✝¹ ∈ closure (⇑f '' s)
((:c Membership.mem) (:fv _uniq.20887) ((:c Set) (:fv _uniq.20887)) ((:c Set.instMembership) (:fv _uniq.20887)) ((:c Neg.neg) (:fv _uniq.20887) ((:c AddGroupWithOne.toNeg) (:fv _uniq.20887) ((:c AddCommGroupWithOne.toAddGroupWithOne) (:fv _uniq.20887) ((:c NonAssocRing.toAddCommGroupWithOne) (:fv _uniq.20887) ((:c Ring...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.20356))"},{"name":"cR","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20361))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.20356))"},{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Rin...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6))))))) (:arg :explicit 3 (:app (:c Neg.neg) (:ar...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Ring) (:arg :explicit 0...
{"children":[{"source":"apply","sourceEnd":9511,"sourceStart":9506,"tag":"atom"},{"name":"IsAddSubgroup.neg_mem","semanticRole":"global","source":"closure.isSubring.neg_mem","sourceEnd":9537,"sourceStart":9512,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply closure.isSubring.neg_mem","sourceEnd":...
[]
[{"source":"closure.isSubring.neg_mem","source_end":9537,"source_start":9512,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern...
44
28
exact
true
1
14
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3acfe8de2a730c0f8058a28b5200766479e3ed10d2b4e201bc74ecbcbba8d4ec
1d664fdd3c50ca6696a2cd47825090d6405ec8c46041c1bca0cbb09663923aa8
5168ad2acf943b7b72fa817d7906b6c504b314b225bb5b5bca5f80d80921acea
e4005801a3c8822e615ee038b287bee1f7c533eb8a63ec7f5ed48e292ba2a15f
cat-searcher/leandojo-benchmark-4-random
test
2,199
Ring.image_closure
Mathlib/Deprecated/Subring.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
assumption
case intro.intro.neg R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s a✝¹ : R a✝ : AddGroup.InClosure (Monoid.Closure s) a✝¹ a_ih✝ : f a✝¹ ∈ closure (⇑f '' s) ⊢ f a✝¹ ∈ closure (⇑f '' s)
((:c Membership.mem) (:fv _uniq.20887) ((:c Set) (:fv _uniq.20887)) ((:c Set.instMembership) (:fv _uniq.20887)) ((:c DFunLike.coe) ((:c RingHom) (:fv _uniq.20356) (:fv _uniq.20887) ((:c NonAssocRing.toNonAssocSemiring) (:fv _uniq.20356) ((:c Ring.toNonAssocRing) (:fv _uniq.20356) (:fv _uniq.20359))) ((:c NonAssocRing.t...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.20356))"},{"name":"cR","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20361))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.20356))"},{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Rin...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6))))))) (:arg :explicit 3 (:app (:c DFunLike.coe)...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Ring) (:arg :explicit 0...
{"children":[{"source":"assumption","sourceEnd":9552,"sourceStart":9542,"tag":"atom"}],"kind":"Lean.Parser.Tactic.assumption","source":"assumption","sourceEnd":9552,"sourceStart":9542,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern...
44
29
exact
true
1
14
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1ebaaa9e9e9d78a84b777d971203c820d2896fc3e52ad1cf5e75b56ba968a4ce
e4005801a3c8822e615ee038b287bee1f7c533eb8a63ec7f5ed48e292ba2a15f
c081dd376ba93a530dd044cffc81e70953e86d86f7d0796dc26bc1597302573d
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,200
Ring.image_closure
Mathlib/Deprecated/Subring.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [f.map_add]
case intro.intro.add R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s a✝² b✝ : R a✝¹ : AddGroup.InClosure (Monoid.Closure s) a✝² a✝ : AddGroup.InClosure (Monoid.Closure s) b✝ a_ih✝¹ : f a✝² ∈ closure (⇑f '' s) a_ih✝ : f b✝ ...
case intro.intro.add R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s a✝² b✝ : R a✝¹ : AddGroup.InClosure (Monoid.Closure s) a✝² a✝ : AddGroup.InClosure (Monoid.Closure s) b✝ a_ih✝¹ : f a✝² ∈ closure (⇑f '' s) a_ih✝ : f b✝ ...
((:c Membership.mem) (:fv _uniq.20887) ((:c Set) (:fv _uniq.20887)) ((:c Set.instMembership) (:fv _uniq.20887)) ((:c DFunLike.coe) ((:c RingHom) (:fv _uniq.20356) (:fv _uniq.20887) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.20356) ((:c Ring.toSemiring) (:fv _uniq.20356) (:fv _uniq.20359))) ((:c Semiring.toNonAssocSem...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.20356))"},{"name":"cR","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20361))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.20356))"},{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Rin...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6))))))) (:arg :explicit 3 (:app (:c DFunLike.coe)...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Ring) (:arg :explicit 0...
{"children":[{"source":"rw","sourceEnd":9560,"sourceStart":9558,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9562,"sourceStart":9561,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"RingHom.map_add","se...
[]
[{"source":"f.map_add","source_end":9571,"source_start":9562,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern...
44
34
exact
true
1
17
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
680273bcd46e33e2e36aef271d8ae1f0ff1082f5601649bf1007a253e62df0ca
5370f4a7eb50c3f34bce59ef13b986ef84172b23937c19a729e5ed461d653277
a4f86c10b5fe96c2908e2b3de5c8644636e8248748e89085c6dff0f1713c0390
b2a8ccb45b636f0fbe4ccf039c20f7ae8738d9bd39fe9c07e59556982865a546
cat-searcher/leandojo-benchmark-4-random
test
2,201
Ring.image_closure
Mathlib/Deprecated/Subring.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply closure.isSubring.add_mem
case intro.intro.add R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s a✝² b✝ : R a✝¹ : AddGroup.InClosure (Monoid.Closure s) a✝² a✝ : AddGroup.InClosure (Monoid.Closure s) b✝ a_ih✝¹ : f a✝² ∈ closure (⇑f '' s) a_ih✝ : f b✝ ...
case intro.intro.add.a R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s a✝² b✝ : R a✝¹ : AddGroup.InClosure (Monoid.Closure s) a✝² a✝ : AddGroup.InClosure (Monoid.Closure s) b✝ a_ih✝¹ : f a✝² ∈ closure (⇑f '' s) a_ih✝ : f b...
((:c Membership.mem) (:fv _uniq.20887) ((:c Set) (:fv _uniq.20887)) ((:c Set.instMembership) (:fv _uniq.20887)) ((:c HAdd.hAdd) (:fv _uniq.20887) (:fv _uniq.20887) (:fv _uniq.20887) ((:c instHAdd) (:fv _uniq.20887) ((:c Distrib.toAdd) (:fv _uniq.20887) ((:c NonUnitalNonAssocSemiring.toDistrib) (:fv _uniq.20887) ((:c No...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.20356))"},{"name":"cR","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20361))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.20356))"},{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Rin...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6))))))) (:arg :explicit 3 (:app (:c HAdd.hAdd) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Ring) (:arg :explicit 0...
{"children":[{"source":"apply","sourceEnd":9582,"sourceStart":9577,"tag":"atom"},{"name":"IsAddSubmonoid.add_mem","semanticRole":"global","source":"closure.isSubring.add_mem","sourceEnd":9608,"sourceStart":9583,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply closure.isSubring.add_mem","sourceEnd"...
[]
[{"source":"closure.isSubring.add_mem","source_end":9608,"source_start":9583,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern...
44
37
exact
true
1
17
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
6d31185828082e4992eee775a38f01cc7311ccf45a8fdf9d961d0725b074d5eb
b2a8ccb45b636f0fbe4ccf039c20f7ae8738d9bd39fe9c07e59556982865a546
cf6d021d02b9c3658a63e532568f1c9f4800024bc535aebac0af6b38ca14a2ad
ee3becb1561cb3883a252225efe2863e13dd68a65fbc07233c7596723d7a85f5
cat-searcher/leandojo-benchmark-4-random
test
2,203
Ring.image_closure
Mathlib/Deprecated/Subring.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>AddGroup.mem_closure</a>
R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s a✝¹ : R a✝ : a✝¹ ∈ Monoid.Closure s ⊢ f a✝¹ ∈ closure (⇑f '' s)
case a R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s a✝¹ : R a✝ : a✝¹ ∈ Monoid.Closure s ⊢ f a✝¹ ∈ Monoid.Closure (⇑f '' s)
((:c Membership.mem) (:fv _uniq.20887) ((:c Set) (:fv _uniq.20887)) ((:c Set.instMembership) (:fv _uniq.20887)) ((:c DFunLike.coe) ((:c RingHom) (:fv _uniq.20356) (:fv _uniq.20887) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.20356) ((:c Ring.toSemiring) (:fv _uniq.20356) (:fv _uniq.20359))) ((:c Semiring.toNonAssocSem...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.20356))"},{"name":"cR","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20361))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.20356))"},{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Rin...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6))))))) (:arg :explicit 3 (:app (:c DFunLike.coe)...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Ring) (:arg :explicit 0...
{"children":[{"source":"apply","sourceEnd":9635,"sourceStart":9630,"tag":"atom"},{"name":"AddGroup.mem_closure","semanticRole":"global","source":"AddGroup.mem_closure","sourceEnd":9656,"sourceStart":9636,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply AddGroup.mem_closure","sourceEnd":9656,"sourc...
[]
[{"source":"AddGroup.mem_closure","source_end":9656,"source_start":9636,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern...
44
43
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b8f41d479d946429736e3714d1cdf78174a9a7659872263ca8bc2b0b8d2274a3
8f1bfec16f4feb0f658772326b4248e9c2059aa1193d4a2a444fe7d9d096781f
0ef068a7cc1ab7de3c451d1b8f08be0607cedc57eb2347902bf754ef151db541
9e47d2fbcdc70c73f87b01da9aa724099ec1f7f296eb16d381aeb9848e62d3f6
cat-searcher/leandojo-benchmark-4-random
test
2,204
Ring.image_closure
Mathlib/Deprecated/Subring.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>Monoid.image_closure</a> f.to_isMonoidHom]
case a R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s a✝¹ : R a✝ : a✝¹ ∈ Monoid.Closure s ⊢ f a✝¹ ∈ Monoid.Closure (⇑f '' s)
case a R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s a✝¹ : R a✝ : a✝¹ ∈ Monoid.Closure s ⊢ f a✝¹ ∈ ⇑f '' Monoid.Closure s
((:c Membership.mem) (:fv _uniq.20887) ((:c Set) (:fv _uniq.20887)) ((:c Set.instMembership) (:fv _uniq.20887)) ((:c DFunLike.coe) ((:c RingHom) (:fv _uniq.20356) (:fv _uniq.20887) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.20356) ((:c Ring.toSemiring) (:fv _uniq.20356) (:fv _uniq.20359))) ((:c Semiring.toNonAssocSem...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.20356))"},{"name":"cR","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20361))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.20356))"},{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Rin...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6))))))) (:arg :explicit 3 (:app (:c DFunLike.coe)...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Ring) (:arg :explicit 0...
{"children":[{"source":"rw","sourceEnd":9663,"sourceStart":9661,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9665,"sourceStart":9664,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":9668,"sourceStart":...
[]
[{"source":"Monoid.image_closure f.to_isMonoidHom","source_end":9706,"source_start":9669,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern...
44
44
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
98c8b0c6037c3f7e69ae5371de020838c48ee667511ee126e065fccf12ef3ffc
9e47d2fbcdc70c73f87b01da9aa724099ec1f7f296eb16d381aeb9848e62d3f6
72545d9c76525ca9aaa4587d89aa44e81fd1a08d4d412515774acf7ad078be8b
7ccaa477eb52f9c82d563bcf9e1ba89b843208e43d2865d45831cb119ba9e1b7
cat-searcher/leandojo-benchmark-4-random
test
2,205
Ring.image_closure
Mathlib/Deprecated/Subring.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>Set.mem_image_of_mem</a>
case a R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s a✝¹ : R a✝ : a✝¹ ∈ Monoid.Closure s ⊢ f a✝¹ ∈ ⇑f '' Monoid.Closure s
case a.h R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s a✝¹ : R a✝ : a✝¹ ∈ Monoid.Closure s ⊢ a✝¹ ∈ Monoid.Closure s
((:c Membership.mem) (:fv _uniq.20887) ((:c Set) (:fv _uniq.20887)) ((:c Set.instMembership) (:fv _uniq.20887)) ((:c DFunLike.coe) ((:c RingHom) (:fv _uniq.20356) (:fv _uniq.20887) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.20356) ((:c Ring.toSemiring) (:fv _uniq.20356) (:fv _uniq.20359))) ((:c Semiring.toNonAssocSem...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.20356))"},{"name":"cR","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20361))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.20356))"},{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Rin...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6))))))) (:arg :explicit 3 (:app (:c DFunLike.coe)...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Ring) (:arg :explicit 0...
{"children":[{"source":"apply","sourceEnd":9717,"sourceStart":9712,"tag":"atom"},{"name":"Set.mem_image_of_mem","semanticRole":"global","source":"Set.mem_image_of_mem","sourceEnd":9738,"sourceStart":9718,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Set.mem_image_of_mem","sourceEnd":9738,"sourc...
[]
[{"source":"Set.mem_image_of_mem","source_end":9738,"source_start":9718,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern...
44
47
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d44671513109766504067464efe5edbd38a071fd1c7235cbb213f1d4edc7d8e7
7ccaa477eb52f9c82d563bcf9e1ba89b843208e43d2865d45831cb119ba9e1b7
ec126f338d336c482dc75fd4e147c8d612baaab96c37d34990b84886d46fc6fa
a4757c8f0ed49839446e882d7fb850a410de0ad90bf8f722cecae8fe974225f3
cat-searcher/leandojo-benchmark-4-random
test
2,206
Ring.image_closure
Mathlib/Deprecated/Subring.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
assumption
case a.h R : Type u inst✝² : Ring R cR : Type u inst✝¹ : CommRing cR s✝ : Set R S : Type u_1 inst✝ : Ring S f : R →+* S s : Set R x : R hx : x ∈ closure s a✝¹ : R a✝ : a✝¹ ∈ Monoid.Closure s ⊢ a✝¹ ∈ Monoid.Closure s
((:c Membership.mem) (:fv _uniq.20356) ((:c Set) (:fv _uniq.20356)) ((:c Set.instMembership) (:fv _uniq.20356)) (:fv _uniq.21894) ((:c Monoid.Closure) (:fv _uniq.20356) ((:c MonoidWithZero.toMonoid) (:fv _uniq.20356) ((:c Semiring.toMonoidWithZero) (:fv _uniq.20356) ((:c Ring.toSemiring) (:fv _uniq.20356) (:fv _uniq.20...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.20356))"},{"name":"cR","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20361))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.20356))"},{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Rin...
(: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 :explicit 3 (:fv FV12)) (:arg :expl...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Ring) (:arg :explicit 0...
{"children":[{"source":"assumption","sourceEnd":9753,"sourceStart":9743,"tag":"atom"}],"kind":"Lean.Parser.Tactic.assumption","source":"assumption","sourceEnd":9753,"sourceStart":9743,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20356","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20359","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern...
44
48
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
fc56a751d67e88a0269e3ac9f52c8c688b2dcba0701cd19992aa81e9dee5af64
a4757c8f0ed49839446e882d7fb850a410de0ad90bf8f722cecae8fe974225f3
c081dd376ba93a530dd044cffc81e70953e86d86f7d0796dc26bc1597302573d
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,207
CategoryTheory.Subobject.inf_factors
Mathlib/CategoryTheory/Subobject/Lattice.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
revert X Y
C : Type u₁ inst✝² : Category.{v₁, u₁} C X✝ Y✝ Z : C D : Type u₂ inst✝¹ : Category.{v₂, u₂} D inst✝ : HasPullbacks C A B : C X Y : Subobject B f : A ⟶ B ⊢ X.Factors f ∧ Y.Factors f → (X ⊓ Y).Factors f
C : Type u₁ inst✝² : Category.{v₁, u₁} C X Y Z : C D : Type u₂ inst✝¹ : Category.{v₂, u₂} D inst✝ : HasPullbacks C A B : C f : A ⟶ B ⊢ ∀ {X Y : Subobject B}, X.Factors f ∧ Y.Factors f → (X ⊓ Y).Factors f
(:forall _ ((:c And) ((:c CategoryTheory.Subobject.Factors) (:fv _uniq.116930) (:fv _uniq.116933) (:fv _uniq.117511) (:fv _uniq.117512) (:fv _uniq.117513) (:fv _uniq.117515)) ((:c CategoryTheory.Subobject.Factors) (:fv _uniq.116930) (:fv _uniq.116933) (:fv _uniq.117511) (:fv _uniq.117512) (:fv _uniq.117514) (:fv _uniq....
[{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.116930))"},{"name":"X✝","sexp":"(:fv _uniq.116930)"},{"name":"Y✝","sexp":"(:fv _uniq.116930)"},{"name":"Z","sexp":"(:fv _uniq.116930)"},{"name":"D","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝¹","sexp":"((:c CategoryT...
(:forall _ :explicit (:app (:c And) (:arg :explicit 0 (:app (:c CategoryTheory.Subobject.Factors) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit 2) (:arg :implicit 3) (:arg :explicit 4 (:fv FV11)) (:arg :explicit 5 (:f...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.116930","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.116933","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Catego...
{"children":[{"source":"revert","sourceEnd":16283,"sourceStart":16277,"tag":"atom"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"X","sourceEnd":16285,"sourceStart":16284,"tag":"identifier"},{"contextIndex":12,"semanticRole":"local","source":"Y","sourceEnd":16287,"sourceStart":16286,"tag":"identifier...
[]
[{"source":"X","source_end":16285,"source_start":16284,"syntax_kind":"ident"},{"source":"Y","source_end":16287,"source_start":16286,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.116930","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.116933","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inte...
154
4
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8af0bc3a0ab074d5311ce59192ac706cf675bfcd454fa3fa2f38a3186398e51d
c124ec06ee7b4f0c6a61d1d41c0f1614c019affe3b8ad98c5a7f430304c0b653
1abb9a63041d462c0735a88417a93f6a566686803601b6be43a371fb2876fe1e
73e63b64e3a3b040f33d50c5d19d9786b6d455c8dfa1bc919427444233039fc7
cat-searcher/leandojo-benchmark-4-random
test
2,208
CategoryTheory.Subobject.inf_factors
Mathlib/CategoryTheory/Subobject/Lattice.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>Quotient.ind₂'</a>
C : Type u₁ inst✝² : Category.{v₁, u₁} C X Y Z : C D : Type u₂ inst✝¹ : Category.{v₂, u₂} D inst✝ : HasPullbacks C A B : C f : A ⟶ B ⊢ ∀ {X Y : Subobject B}, X.Factors f ∧ Y.Factors f → (X ⊓ Y).Factors f
case h C : Type u₁ inst✝² : Category.{v₁, u₁} C X Y Z : C D : Type u₂ inst✝¹ : Category.{v₂, u₂} D inst✝ : HasPullbacks C A B : C f : A ⟶ B ⊢ ∀ (a₁ a₂ : MonoOver B), Factors (Quotient.mk'' a₁) f ∧ Factors (Quotient.mk'' a₂) f → (Quotient.mk'' a₁ ⊓ Quotient.mk'' a₂).Factors f
(:forall X ((:c CategoryTheory.Subobject) (:fv _uniq.116930) (:fv _uniq.116933) (:fv _uniq.117512)) (:forall Y ((:c CategoryTheory.Subobject) (:fv _uniq.116930) (:fv _uniq.116933) (:fv _uniq.117512)) (:forall _ ((:c And) ((:c CategoryTheory.Subobject.Factors) (:fv _uniq.116930) (:fv _uniq.116933) (:fv _uniq.117511) (:f...
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(:forall X :implicit (:app (:c CategoryTheory.Subobject) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV10))) (:forall Y :implicit (:app (:c CategoryTheory.Subobject) (:arg :implicit-type 0 (:fv FV0)) (:arg :i...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.116930","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.116933","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Catego...
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[]
[{"source":"Quotient.ind₂'","source_end":16314,"source_start":16298,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.116930","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.116933","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inte...
154
5
exact
true
1
11
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
759f7d4296e3ac2db0b4b63dc4aa853c896bfcf769d38cb746f2b5a8fc6ef2c8
73e63b64e3a3b040f33d50c5d19d9786b6d455c8dfa1bc919427444233039fc7
bd4cb2ed485732796d8c8a736f739c3f29ff0bea4a04a7fb0b1103a03b20d636
4dabbb104f63a6e044cf9b4363f947a38841c0ead6436036a0509b7a0d01cb94
cat-searcher/leandojo-benchmark-4-random
test
2,209
CategoryTheory.Subobject.inf_factors
Mathlib/CategoryTheory/Subobject/Lattice.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro X Y ⟨⟨g₁, rfl⟩, ⟨g₂, hg₂⟩⟩
case h C : Type u₁ inst✝² : Category.{v₁, u₁} C X Y Z : C D : Type u₂ inst✝¹ : Category.{v₂, u₂} D inst✝ : HasPullbacks C A B : C f : A ⟶ B ⊢ ∀ (a₁ a₂ : MonoOver B), Factors (Quotient.mk'' a₁) f ∧ Factors (Quotient.mk'' a₂) f → (Quotient.mk'' a₁ ⊓ Quotient.mk'' a₂).Factors f
case h.intro.intro.intro C : Type u₁ inst✝² : Category.{v₁, u₁} C X✝ Y✝ Z : C D : Type u₂ inst✝¹ : Category.{v₂, u₂} D inst✝ : HasPullbacks C A B : C X Y : MonoOver B g₁ : A ⟶ X.obj.left g₂ : A ⟶ Y.obj.left hg₂ : g₂ ≫ Y.arrow = g₁ ≫ X.arrow ⊢ (Quotient.mk'' X ⊓ Quotient.mk'' Y).Factors (g₁ ≫ X.arrow)
(:forall a₁ ((:c CategoryTheory.MonoOver) (:fv _uniq.116930) (:fv _uniq.116933) (:fv _uniq.117512)) (:forall a₂ ((:c CategoryTheory.MonoOver) (:fv _uniq.116930) (:fv _uniq.116933) (:fv _uniq.117512)) (:forall _ ((:c And) ((:c CategoryTheory.Subobject.Factors) (:fv _uniq.116930) (:fv _uniq.116933) (:fv _uniq.117511) (:f...
[{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.116930))"},{"name":"X","sexp":"(:fv _uniq.116930)"},{"name":"Y","sexp":"(:fv _uniq.116930)"},{"name":"Z","sexp":"(:fv _uniq.116930)"},{"name":"D","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝¹","sexp":"((:c CategoryThe...
(:forall a₁ :explicit (:app (:c CategoryTheory.MonoOver) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV10))) (:forall a₂ :explicit (:app (:c CategoryTheory.MonoOver) (:arg :implicit-type 0 (:fv FV0)) (:arg :i...
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{"children":[{"source":"rintro","sourceEnd":16325,"sourceStart":16319,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"X","sourceEnd":16327,"sourceStart":16326,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"X","sourceEnd":16327,"sourceStart":16326,"...
[{"role":"fresh_name","source":"X","source_end":16327,"source_start":16326,"syntax_kind":"ident"},{"role":"fresh_name","source":"Y","source_end":16329,"source_start":16328,"syntax_kind":"ident"},{"role":"fresh_name","source":"g₁","source_end":16340,"source_start":16336,"syntax_kind":"ident"},{"role":"fresh_name","sourc...
[{"source":"⟨⟨g₁, rfl⟩, ⟨g₂, hg₂⟩⟩","source_end":16370,"source_start":16330,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.116930","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.116933","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inte...
154
6
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d95e42cc9a7d6fce979cf94f018838c0b4f22f30abdda4621c6ab0c4da241458
4dabbb104f63a6e044cf9b4363f947a38841c0ead6436036a0509b7a0d01cb94
cd6cd0757dab28dac5f0ff8094a21414f5dbe2bd17c5abc0e11b2cbd050dbb18
76a9acbb487574133dfc86efc3f4a67451696a8decdb3cc1323e730108ee493b
cat-searcher/leandojo-benchmark-4-random
test
2,210
CategoryTheory.Subobject.inf_factors
Mathlib/CategoryTheory/Subobject/Lattice.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact ⟨_, <a>CategoryTheory.Limits.pullback.lift_snd_assoc</a> _ _ hg₂ _⟩
case h.intro.intro.intro C : Type u₁ inst✝² : Category.{v₁, u₁} C X✝ Y✝ Z : C D : Type u₂ inst✝¹ : Category.{v₂, u₂} D inst✝ : HasPullbacks C A B : C X Y : MonoOver B g₁ : A ⟶ X.obj.left g₂ : A ⟶ Y.obj.left hg₂ : g₂ ≫ Y.arrow = g₁ ≫ X.arrow ⊢ (Quotient.mk'' X ⊓ Quotient.mk'' Y).Factors (g₁ ≫ X.arrow)
((:c CategoryTheory.Subobject.Factors) (:fv _uniq.116930) (:fv _uniq.116933) (:fv _uniq.117511) (:fv _uniq.117512) ((:c Inf.inf) ((:c CategoryTheory.Subobject) (:fv _uniq.116930) (:fv _uniq.116933) (:fv _uniq.117512)) ((:c SemilatticeInf.toInf) ((:c CategoryTheory.Subobject) (:fv _uniq.116930) (:fv _uniq.116933) (:fv _...
[{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.116930))"},{"name":"X✝","sexp":"(:fv _uniq.116930)"},{"name":"Y✝","sexp":"(:fv _uniq.116930)"},{"name":"Z","sexp":"(:fv _uniq.116930)"},{"name":"D","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝¹","sexp":"((:c CategoryT...
(:app (:c CategoryTheory.Subobject.Factors) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit 2) (:arg :implicit 3) (:arg :explicit 4 (:app (:c Inf.inf) (:arg :implicit-type 0 (:app (:c CategoryTheory.Subobject) (:arg :im...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.116930","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.116933","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Catego...
{"children":[{"source":"exact","sourceEnd":16380,"sourceStart":16375,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":16384,"sourceStart":16381,"tag":"atom"},{"children":[{"children":[{"source":"_","sourceEnd":16385,"sourceStart":16384,"tag":"atom"}],"kind":"Lean.Parser.Term.hole","source":"_","sourceEnd":16385,"so...
[]
[{"source":"⟨_, pullback.lift_snd_assoc _ _ hg₂ _⟩","source_end":16425,"source_start":16381,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.116930","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.116933","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inte...
154
7
exact
true
1
15
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
db1a287dde8cdee7c5597ff3527b961e84a6a18540169f5cc14eb988adec1506
76a9acbb487574133dfc86efc3f4a67451696a8decdb3cc1323e730108ee493b
311eabb57e51e4e2cad00bac454fdee1116d0298e8c30c0e180a43563e35bb35
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,211
Nat.even_xor_odd'
Mathlib/Algebra/Ring/Parity.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨k, rfl⟩ | ⟨k, rfl⟩ := <a>Nat.even_or_odd</a> n <;> use k
F : Type u_1 α : Type u_2 β : Type u_3 R : Type u_4 m n✝ n : ℕ ⊢ ∃ k, Xor' (n = 2 * k) (n = 2 * k + 1)
((:c Exists) (:c Nat) (:lambda k (:c Nat) ((:c Xor') ((:c Eq) (:c Nat) (:fv _uniq.44565) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2))) 0)) ((:c Eq) (:c Nat) (:fv _uniq.44565) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat...
[{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"(:c Nat)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"}]
(:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda k :explicit (:c Nat) (:app (:c Xor') (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44363","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44366","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"obtain","sourceEnd":10188,"sourceStart":10182,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":10192,"sourceStart":10189,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{...
[]
[{"source":"even_or_odd n","source_end":10233,"source_start":10220,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨k, rfl⟩ | ⟨k, rfl⟩","source_end":10216,"source_start":10189,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"},{"source":"k","source_end":10243,"source_start":10242,"syntax_kind":"ident"},{"source":"two_mu...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44363","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44366","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
126
2
branch_opener
false
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
507f4c14f341ca27e02713d5e6b2706d09d2fac28a2e80d2603b44e4c7586de6
6dc39c1b35326abd5be974fde0ce9ac55410ee4b90d982b9aefd19b000d76445
333f05412a27bffcaeca103026b6bfbb2d2442079ac3b8126497be18184371f6
e8c3f6d2c676f26b10fc1e169fa7fcd42a91e4c7a061ac2af002e5e1bace47a9
cat-searcher/leandojo-benchmark-4-random
test
2,212
Nat.even_xor_odd'
Mathlib/Algebra/Ring/Parity.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simpa only [← <a>two_mul</a>, <a>eq_self_iff_true</a>, <a>xor_true</a>] using (<a>Nat.succ_ne_self</a> (2 * k)).<a>Ne.symm</a>
case h F : Type u_1 α : Type u_2 β : Type u_3 R : Type u_4 m n k : ℕ ⊢ Xor' (k + k = 2 * k) (k + k = 2 * k + 1)
((:c Xor') ((:c Eq) (:c Nat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.44622) (:fv _uniq.44622)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2))) (:fv _uniq.44622))) ...
[{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Nat)"}]
(:app (:c Xor') (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44363","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44366","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":10254,"sourceStart":10249,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind...
[]
[{"source":"two_mul","source_end":10272,"source_start":10265,"syntax_kind":"ident"},{"source":"eq_self_iff_true","source_end":10290,"source_start":10274,"syntax_kind":"ident"},{"source":"xor_true","source_end":10300,"source_start":10292,"syntax_kind":"ident"},{"source":"(succ_ne_self (2 * k)).symm","source_end":10335,"...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44363","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44366","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
126
11
exact
true
1
7
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d2b55a783ffa27142448d4610d74de69db82fe0dd70f0b41398552f34ae1e154
3dba280ca30b51fb56e397d876ca40d3dea5b17257fc009d716b08c8a50eb401
9af22927aa4984f97f0afbd0c5a861b56238bd68f4b9011fded8926bc37e31ed
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,213
Nat.even_xor_odd'
Mathlib/Algebra/Ring/Parity.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simpa only [<a>xor_true</a>, <a>xor_comm</a>] using (<a>Nat.succ_ne_self</a> _)
case h F : Type u_1 α : Type u_2 β : Type u_3 R : Type u_4 m n k : ℕ ⊢ Xor' (2 * k + 1 = 2 * k) (2 * k + 1 = 2 * k + 1)
((:c Xor') ((:c Eq) (:c Nat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) ((:c Distrib.toAdd) (:c Nat) ((:c NonUnitalNonAssocSemiring.toDistrib) (:c Nat) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:c Nat) ((:c Semiring.toNonAssocSemiring) (:c Nat) (:c Nat.instSemiring)))))) ((:c HMul.hMul...
[{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Nat)"}]
(:app (:c Xor') (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44363","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44366","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":10346,"sourceStart":10341,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind...
[]
[{"source":"xor_true","source_end":10361,"source_start":10353,"syntax_kind":"ident"},{"source":"xor_comm","source_end":10371,"source_start":10363,"syntax_kind":"ident"},{"source":"(succ_ne_self _)","source_end":10395,"source_start":10379,"syntax_kind":"Lean.Parser.Term.paren"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44363","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44366","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
126
16
exact
true
1
7
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
86f3e0ee521c2440e28a0b8244e50cb62cb2d690db6752a6107cc6aa8152749c
f4a1bc90ea38662535d1a597b882f085dbc89eb3904d59ae726a2375c80c1979
7fe864fdd1551870fa308bb83ee7e23ba9736f08e14ec81ac27430fa00183c82
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,214
LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer
Mathlib/Algebra/Lie/Engel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨x, hx₁, hx₂⟩ := <a>SetLike.exists_of_lt</a> hK₂
R : Type u₁ L : Type u₂ L₂ : Type u₃ M : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K < K.normalizer ⊢...
case intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K...
((:c Exists) ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) (:lambda K' ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) ((:c And) ((:c LieAlgebra.IsEngelian) (:fv _uniq.62747) ((:c Subtype) (:f...
[{"name":"R","sexp":"(:sort (+ u₁ 1))"},{"name":"L","sexp":"(:sort (+ u₂ 1))"},{"name":"L₂","sexp":"(:sort (+ u₃ 1))"},{"name":"M","sexp":"(:sort (+ u₄ 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.62747))"},{"name":"inst✝⁷","sexp":"((:c LieRing) (:fv _uniq.62749))"},{"name":"inst✝⁶","sexp":"((:c LieAlgebra)...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c LieSubalgebra) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"obtain","sourceEnd":9942,"sourceStart":9936,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":9946,"sourceStart":9943,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":9...
[]
[{"source":"SetLike.exists_of_lt hK₂","source_end":9994,"source_start":9968,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨x, hx₁, hx₂⟩","source_end":9964,"source_start":9943,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
30
4
exact
true
1
16
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2c20d44d6b360a6e0b1e7d6f2017de51d8d250831b502938fbaf25459f81ea7f
12069dfdcb3ba55e5ec97f7f5441e7231ae5a2504cef3bde12e99ab67381c02d
a5da9d0398b9fb65a2d5fb4fdb869024c0a5e65682c0f57f29b371e4fd382cae
938c6aec1a854ef1b83b06d1db55680333cedb2bc11312d5254eba28c2a382a3
cat-searcher/leandojo-benchmark-4-random
test
2,215
LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer
Mathlib/Algebra/Lie/Engel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
let K' : <a>LieSubalgebra</a> R L := { (R ∙ x) ⊔ (K : <a>Submodule</a> R L) with lie_mem' := fun {y z} => <a>LieSubalgebra.lie_mem_sup_of_mem_normalizer</a> hx₁ }
case intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K...
case intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K...
((:c Exists) ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) (:lambda K' ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) ((:c And) ((:c LieAlgebra.IsEngelian) (:fv _uniq.62747) ((:c Subtype) (:f...
[{"name":"R","sexp":"(:sort (+ u₁ 1))"},{"name":"L","sexp":"(:sort (+ u₂ 1))"},{"name":"L₂","sexp":"(:sort (+ u₃ 1))"},{"name":"M","sexp":"(:sort (+ u₄ 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.62747))"},{"name":"inst✝⁷","sexp":"((:c LieRing) (:fv _uniq.62749))"},{"name":"inst✝⁶","sexp":"((:c LieAlgebra)...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c LieSubalgebra) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"let","sourceEnd":10000,"sourceStart":9997,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"K'","sourceEnd":10003,"sourceStart":10001,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":1000...
[]
[{"source":"LieSubalgebra R L","source_end":10023,"source_start":10006,"syntax_kind":"Lean.Parser.Term.app"},{"source":"{ (R ∙ x) ⊔ (K : Submodule R L) with\n lie_mem' := fun {y z} => LieSubalgebra.lie_mem_sup_of_mem_normalizer hx₁ }","source_end":10154,"source_start":10031,"syntax_kind":"Lean.Parser.Term.structIn...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
30
5
exact
true
1
19
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d5ae877506fa704f8be07707cd74f783e3e7cba97fc1e225e2ed73772ae62989
938c6aec1a854ef1b83b06d1db55680333cedb2bc11312d5254eba28c2a382a3
30921a59b61759001de51144c779e0a57f30a298f471a2f272c1081915f864aa
80da85245e2b8f49173d87923d3403da92215911d9f497a2664b440366fcaa47
cat-searcher/leandojo-benchmark-4-random
test
2,216
LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer
Mathlib/Algebra/Lie/Engel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have hxK' : x ∈ K' := <a>Submodule.mem_sup_left</a> (<a>Submodule.subset_span</a> (<a>Set.mem_singleton</a> _))
case intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K...
case intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K...
((:c Exists) ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) (:lambda K' ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) ((:c And) ((:c LieAlgebra.IsEngelian) (:fv _uniq.62747) ((:c Subtype) (:f...
[{"name":"R","sexp":"(:sort (+ u₁ 1))"},{"name":"L","sexp":"(:sort (+ u₂ 1))"},{"name":"L₂","sexp":"(:sort (+ u₃ 1))"},{"name":"M","sexp":"(:sort (+ u₄ 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.62747))"},{"name":"inst✝⁷","sexp":"((:c LieRing) (:fv _uniq.62749))"},{"name":"inst✝⁶","sexp":"((:c LieAlgebra)...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c LieSubalgebra) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"have","sourceEnd":10161,"sourceStart":10157,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hxK'","sourceEnd":10166,"sourceStart":10162,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hxK'","sourceEnd":10166,"sourceStart":10162,"tag":...
[]
[{"source":"x ∈ K'","source_end":10177,"source_start":10169,"syntax_kind":"«term_∈_»"},{"source":"Submodule.mem_sup_left (Submodule.subset_span (Set.mem_singleton _))","source_end":10249,"source_start":10181,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
30
6
exact
true
1
20
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4e67d6886264800fb85252ef326b7dcc030d65eb9b4f9da7626da5be20d8663f
80da85245e2b8f49173d87923d3403da92215911d9f497a2664b440366fcaa47
89b58da9710ca43878be3997501930984bf9ebfb146e4a3c58a5c9f365a6fba0
5ecbe38bc3eac6d8e38964e82d7d65e7f51195516a22485d69688219ffc9131b
cat-searcher/leandojo-benchmark-4-random
test
2,217
LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer
Mathlib/Algebra/Lie/Engel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have hKK' : K ≤ K' := (<a>LieSubalgebra.coe_submodule_le_coe_submodule</a> K K').<a>Iff.mp</a> <a>le_sup_right</a>
case intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K...
case intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K...
((:c Exists) ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) (:lambda K' ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) ((:c And) ((:c LieAlgebra.IsEngelian) (:fv _uniq.62747) ((:c Subtype) (:f...
[{"name":"R","sexp":"(:sort (+ u₁ 1))"},{"name":"L","sexp":"(:sort (+ u₂ 1))"},{"name":"L₂","sexp":"(:sort (+ u₃ 1))"},{"name":"M","sexp":"(:sort (+ u₄ 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.62747))"},{"name":"inst✝⁷","sexp":"((:c LieRing) (:fv _uniq.62749))"},{"name":"inst✝⁶","sexp":"((:c LieAlgebra)...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c LieSubalgebra) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"have","sourceEnd":10256,"sourceStart":10252,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hKK'","sourceEnd":10261,"sourceStart":10257,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hKK'","sourceEnd":10261,"sourceStart":10257,"tag":...
[]
[{"source":"K ≤ K'","source_end":10272,"source_start":10264,"syntax_kind":"«term_≤_»"},{"source":"(LieSubalgebra.coe_submodule_le_coe_submodule K K').mp le_sup_right","source_end":10343,"source_start":10276,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
30
7
exact
true
1
21
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9520b714ffa4cecaf71857c52587ee9bea0ae67f47b08e12d277f97ab00ce529
5ecbe38bc3eac6d8e38964e82d7d65e7f51195516a22485d69688219ffc9131b
67e932699d13bc70a9ce46c3522249c7f9c5531ff1c26a93c729a174feb393b0
8b532e88d818e6ca19b2d9b78f0ffc42e5ab45ee57ae108bef8d3514cf849c80
cat-searcher/leandojo-benchmark-4-random
test
2,218
LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer
Mathlib/Algebra/Lie/Engel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have hK' : K' ≤ K.normalizer := by rw [← <a>LieSubalgebra.coe_submodule_le_coe_submodule</a>] exact <a>sup_le</a> ((<a>Submodule.span_singleton_le_iff_mem</a> _ _).<a>Iff.mpr</a> hx₁) hK₂.le
case intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K...
case intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K...
((:c Exists) ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) (:lambda K' ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) ((:c And) ((:c LieAlgebra.IsEngelian) (:fv _uniq.62747) ((:c Subtype) (:f...
[{"name":"R","sexp":"(:sort (+ u₁ 1))"},{"name":"L","sexp":"(:sort (+ u₂ 1))"},{"name":"L₂","sexp":"(:sort (+ u₃ 1))"},{"name":"M","sexp":"(:sort (+ u₄ 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.62747))"},{"name":"inst✝⁷","sexp":"((:c LieRing) (:fv _uniq.62749))"},{"name":"inst✝⁶","sexp":"((:c LieAlgebra)...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c LieSubalgebra) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"have","sourceEnd":10350,"sourceStart":10346,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hK'","sourceEnd":10354,"sourceStart":10351,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hK'","sourceEnd":10354,"sourceStart":10351,"tag":"n...
[]
[{"source":"K' ≤ K.normalizer","source_end":10376,"source_start":10357,"syntax_kind":"«term_≤_»"},{"source":"LieSubalgebra.coe_submodule_le_coe_submodule","source_end":10439,"source_start":10395,"syntax_kind":"ident"},{"source":"sup_le ((Submodule.span_singleton_le_iff_mem _ _).mpr hx₁) hK₂.le","source_end":10520,"sour...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
30
8
exact
true
1
22
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ea0c0335a63882f7e29dba52e6922b277986eca8206509073e38cd3b0d1e3660
8b532e88d818e6ca19b2d9b78f0ffc42e5ab45ee57ae108bef8d3514cf849c80
947767711818ad54ad753cac2c84c1945b0810c6ddb32516a6de1c06e3b743a8
9e4b64af8b182a59adc5a8f28e638262bf3d77f351a1b413069045cccd32c8f9
cat-searcher/leandojo-benchmark-4-random
test
2,219
LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer
Mathlib/Algebra/Lie/Engel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨K', ?_, lt_iff_le_and_ne.mpr ⟨hKK', fun contra => hx₂ (contra.symm ▸ hxK')⟩⟩
case intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K...
case intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K...
((:c Exists) ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) (:lambda K' ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) ((:c And) ((:c LieAlgebra.IsEngelian) (:fv _uniq.62747) ((:c Subtype) (:f...
[{"name":"R","sexp":"(:sort (+ u₁ 1))"},{"name":"L","sexp":"(:sort (+ u₂ 1))"},{"name":"L₂","sexp":"(:sort (+ u₃ 1))"},{"name":"M","sexp":"(:sort (+ u₄ 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.62747))"},{"name":"inst✝⁷","sexp":"((:c LieRing) (:fv _uniq.62749))"},{"name":"inst✝⁶","sexp":"((:c LieAlgebra)...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c LieSubalgebra) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"refine","sourceEnd":10529,"sourceStart":10523,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":10533,"sourceStart":10530,"tag":"atom"},{"children":[{"contextIndex":20,"semanticRole":"local","source":"K'","sourceEnd":10535,"sourceStart":10533,"tag":"identifier"},{"source":",","sourceEnd":1053...
[]
[{"source":"⟨K', ?_, lt_iff_le_and_ne.mpr ⟨hKK', fun contra => hx₂ (contra.symm ▸ hxK')⟩⟩","source_end":10619,"source_start":10530,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
30
14
exact
true
1
23
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
26810a4f2643cb74062ba10f7718290d5d3dc2b1df9fb9656e56053f72141a99
9e4b64af8b182a59adc5a8f28e638262bf3d77f351a1b413069045cccd32c8f9
589061c1c83c64c8a3ede2c5d78c867aeaf96c6fa0ba292c90347b756e1b1f8b
f911cc744399f219b64efce5d00e88d97a790fbe2ca8687acd2689fbc68d3979
cat-searcher/leandojo-benchmark-4-random
test
2,220
LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer
Mathlib/Algebra/Lie/Engel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro M _i1 _i2 _i3 _i4 h
case intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K...
case intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M✝ : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M✝ inst✝² : Module R M✝ inst✝¹ : LieRingModule L M✝ inst✝ : LieModule R L M✝ K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK...
((:c LieAlgebra.IsEngelian) (:fv _uniq.62747) ((:c Subtype) (:fv _uniq.62749) (:lambda x (:fv _uniq.62749) ((:c Membership.mem) (:fv _uniq.62749) ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) ((:c SetLike.instMembership) ((:c LieSubalgebra) (:fv _uniq.627...
[{"name":"R","sexp":"(:sort (+ u₁ 1))"},{"name":"L","sexp":"(:sort (+ u₂ 1))"},{"name":"L₂","sexp":"(:sort (+ u₃ 1))"},{"name":"M","sexp":"(:sort (+ u₄ 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.62747))"},{"name":"inst✝⁷","sexp":"((:c LieRing) (:fv _uniq.62749))"},{"name":"inst✝⁶","sexp":"((:c LieAlgebra)...
(:app (:c LieAlgebra.IsEngelian) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c LieSubalgebra) (:arg :explicit 0 (:fv FV0)) (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"intro","sourceEnd":10627,"sourceStart":10622,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"M","sourceEnd":10629,"sourceStart":10628,"tag":"identifier"},{"semanticRole":"scoped_local","source":"_i1","sourceEnd":10633,"sourceStart":10630,"tag":"identifier"},{"semanticRole":"s...
[{"role":"fresh_name","source":"M","source_end":10629,"source_start":10628,"syntax_kind":"ident"},{"role":"fresh_name","source":"_i1","source_end":10633,"source_start":10630,"syntax_kind":"ident"},{"role":"fresh_name","source":"_i2","source_end":10637,"source_start":10634,"syntax_kind":"ident"},{"role":"fresh_name","so...
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
30
15
exact
true
1
23
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3ad3702877d63cad2e2d33e8e6e4ef2b5cb9f7e81a5515db5c2f791355dd0ea8
f911cc744399f219b64efce5d00e88d97a790fbe2ca8687acd2689fbc68d3979
a4164a9a74324274358524d6f38e6e55d98a3bfa3612f604980dc743cc34775f
7e2f63cf807639c38aeb7685b96d0898202bef651fd02d9e066c20b135819c57
cat-searcher/leandojo-benchmark-4-random
test
2,221
LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer
Mathlib/Algebra/Lie/Engel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨I, hI₁ : (I : <a>LieSubalgebra</a> R K') = <a>LieSubalgebra.ofLe</a> hKK'⟩ := <a>LieSubalgebra.exists_nested_lieIdeal_ofLe_normalizer</a> hKK' hK'
case intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M✝ : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M✝ inst✝² : Module R M✝ inst✝¹ : LieRingModule L M✝ inst✝ : LieModule R L M✝ K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK...
case intro.intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M✝ : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M✝ inst✝² : Module R M✝ inst✝¹ : LieRingModule L M✝ inst✝ : LieModule R L M✝ K : LieSubalgebra R L hK₁ : IsEngelian R...
((:c LieModule.IsNilpotent) (:fv _uniq.62747) ((:c Subtype) (:fv _uniq.62749) (:lambda x (:fv _uniq.62749) ((:c Membership.mem) (:fv _uniq.62749) ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) ((:c SetLike.instMembership) ((:c LieSubalgebra) (:fv _uniq.627...
[{"name":"R","sexp":"(:sort (+ u₁ 1))"},{"name":"L","sexp":"(:sort (+ u₂ 1))"},{"name":"L₂","sexp":"(:sort (+ u₃ 1))"},{"name":"M✝","sexp":"(:sort (+ u₄ 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.62747))"},{"name":"inst✝⁷","sexp":"((:c LieRing) (:fv _uniq.62749))"},{"name":"inst✝⁶","sexp":"((:c LieAlgebra...
(:app (:c LieModule.IsNilpotent) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c LieSubalgebra) (:arg :explicit 0 (:fv FV0)) (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"obtain","sourceEnd":10656,"sourceStart":10650,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":10660,"sourceStart":10657,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"I","sourceEn...
[]
[{"source":"LieSubalgebra.exists_nested_lieIdeal_ofLe_normalizer hKK' hK'","source_end":10793,"source_start":10732,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨I, hI₁ : (I : LieSubalgebra R K') = LieSubalgebra.ofLe hKK'⟩","source_end":10724,"source_start":10657,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
30
16
exact
true
1
29
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5139c43bebfb0e96d04ba75e0ff19d977060ba329e6d4675b77dc98b21eb00d9
7e2f63cf807639c38aeb7685b96d0898202bef651fd02d9e066c20b135819c57
07a2d88a7ffa988bd01fd7973000a016c8a6f0e9113c204e639b757ecd88a1f4
1ff714bd8672ce3034702266187b16b73ff5be0434f8920e3e2e041427b983ee
cat-searcher/leandojo-benchmark-4-random
test
2,222
LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer
Mathlib/Algebra/Lie/Engel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have hI₂ : (R ∙ (⟨x, hxK'⟩ : K')) ⊔ (LieSubmodule.toSubmodule I) = ⊤ := by rw [← <a>LieIdeal.coe_to_lieSubalgebra_to_submodule</a> R K' I, hI₁] apply <a>Submodule.map_injective_of_injective</a> (K' : <a>Submodule</a> R L).<a>Submodule.injective_subtype</a> simp
case intro.intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M✝ : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M✝ inst✝² : Module R M✝ inst✝¹ : LieRingModule L M✝ inst✝ : LieModule R L M✝ K : LieSubalgebra R L hK₁ : IsEngelian R...
case intro.intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M✝ : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M✝ inst✝² : Module R M✝ inst✝¹ : LieRingModule L M✝ inst✝ : LieModule R L M✝ K : LieSubalgebra R L hK₁ : IsEngelian R...
((:c LieModule.IsNilpotent) (:fv _uniq.62747) ((:c Subtype) (:fv _uniq.62749) (:lambda x (:fv _uniq.62749) ((:c Membership.mem) (:fv _uniq.62749) ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) ((:c SetLike.instMembership) ((:c LieSubalgebra) (:fv _uniq.627...
[{"name":"R","sexp":"(:sort (+ u₁ 1))"},{"name":"L","sexp":"(:sort (+ u₂ 1))"},{"name":"L₂","sexp":"(:sort (+ u₃ 1))"},{"name":"M✝","sexp":"(:sort (+ u₄ 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.62747))"},{"name":"inst✝⁷","sexp":"((:c LieRing) (:fv _uniq.62749))"},{"name":"inst✝⁶","sexp":"((:c LieAlgebra...
(:app (:c LieModule.IsNilpotent) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c LieSubalgebra) (:arg :explicit 0 (:fv FV0)) (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"have","sourceEnd":10800,"sourceStart":10796,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hI₂","sourceEnd":10806,"sourceStart":10801,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hI₂","sourceEnd":10806,"sourceStart":10801,"tag":"n...
[]
[{"source":"(R ∙ (⟨x, hxK'⟩ : K')) ⊔ (LieSubmodule.toSubmodule I) = ⊤","source_end":10876,"source_start":10809,"syntax_kind":"«term_=_»"},{"source":"LieIdeal.coe_to_lieSubalgebra_to_submodule R K' I","source_end":10944,"source_start":10895,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hI₁","source_end":10951,"source...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
30
17
exact
true
1
31
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4003376f605bc7f5045637d659ece71da0c9d238c4f06d455a94f4ca15d4c5c7
1ff714bd8672ce3034702266187b16b73ff5be0434f8920e3e2e041427b983ee
1830600c0f5aaef53f01dd7e5d64d41f81c3d4195d3cd1490f8ad20d0de219e5
6ca17912e6c84412d2e4070bbe9a8907ea7a977e7f791c51b4c83b0909aa132c
cat-searcher/leandojo-benchmark-4-random
test
2,223
LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer
Mathlib/Algebra/Lie/Engel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have e : K ≃ₗ⁅R⁆ I := (<a>LieSubalgebra.equivOfLe</a> hKK').<a>LieEquiv.trans</a> (<a>LieEquiv.ofEq</a> _ _ ((<a>LieSubalgebra.coe_set_eq</a> _ _).<a>Iff.mpr</a> hI₁.symm))
case intro.intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M✝ : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M✝ inst✝² : Module R M✝ inst✝¹ : LieRingModule L M✝ inst✝ : LieModule R L M✝ K : LieSubalgebra R L hK₁ : IsEngelian R...
case intro.intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M✝ : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M✝ inst✝² : Module R M✝ inst✝¹ : LieRingModule L M✝ inst✝ : LieModule R L M✝ K : LieSubalgebra R L hK₁ : IsEngelian R...
((:c LieModule.IsNilpotent) (:fv _uniq.62747) ((:c Subtype) (:fv _uniq.62749) (:lambda x (:fv _uniq.62749) ((:c Membership.mem) (:fv _uniq.62749) ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) ((:c SetLike.instMembership) ((:c LieSubalgebra) (:fv _uniq.627...
[{"name":"R","sexp":"(:sort (+ u₁ 1))"},{"name":"L","sexp":"(:sort (+ u₂ 1))"},{"name":"L₂","sexp":"(:sort (+ u₃ 1))"},{"name":"M✝","sexp":"(:sort (+ u₄ 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.62747))"},{"name":"inst✝⁷","sexp":"((:c LieRing) (:fv _uniq.62749))"},{"name":"inst✝⁶","sexp":"((:c LieAlgebra...
(:app (:c LieModule.IsNilpotent) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c LieSubalgebra) (:arg :explicit 0 (:fv FV0)) (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"have","sourceEnd":11054,"sourceStart":11050,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"e","sourceEnd":11056,"sourceStart":11055,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"e","sourceEnd":11056,"sourceStart":11055,"tag":"node"...
[]
[{"source":"K ≃ₗ⁅R⁆ I","source_end":11076,"source_start":11059,"syntax_kind":"«term_≃ₗ⁅_⁆_»"},{"source":"(LieSubalgebra.equivOfLe hKK').trans\n (LieEquiv.ofEq _ _ ((LieSubalgebra.coe_set_eq _ _).mpr hI₁.symm))","source_end":11194,"source_start":11084,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
30
25
exact
true
1
32
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d19a88862d716dbe7ac11cb85763893b3d72a36b94d7d49ed0d4e6dc69562220
6ca17912e6c84412d2e4070bbe9a8907ea7a977e7f791c51b4c83b0909aa132c
591b5dc9cb7994931b88cc47342b164a119fbde1c331fa3fd4c4a90cf09f7dbe
2e447db3fae7b573646399c47fa3efbe8da5766047e2a8f8ca845cd70e22a777
cat-searcher/leandojo-benchmark-4-random
test
2,224
LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer
Mathlib/Algebra/Lie/Engel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have hI₃ : <a>LieAlgebra.IsEngelian</a> R I := e.isEngelian_iff.mp hK₁
case intro.intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M✝ : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M✝ inst✝² : Module R M✝ inst✝¹ : LieRingModule L M✝ inst✝ : LieModule R L M✝ K : LieSubalgebra R L hK₁ : IsEngelian R...
case intro.intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M✝ : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M✝ inst✝² : Module R M✝ inst✝¹ : LieRingModule L M✝ inst✝ : LieModule R L M✝ K : LieSubalgebra R L hK₁ : IsEngelian R...
((:c LieModule.IsNilpotent) (:fv _uniq.62747) ((:c Subtype) (:fv _uniq.62749) (:lambda x (:fv _uniq.62749) ((:c Membership.mem) (:fv _uniq.62749) ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) ((:c SetLike.instMembership) ((:c LieSubalgebra) (:fv _uniq.627...
[{"name":"R","sexp":"(:sort (+ u₁ 1))"},{"name":"L","sexp":"(:sort (+ u₂ 1))"},{"name":"L₂","sexp":"(:sort (+ u₃ 1))"},{"name":"M✝","sexp":"(:sort (+ u₄ 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.62747))"},{"name":"inst✝⁷","sexp":"((:c LieRing) (:fv _uniq.62749))"},{"name":"inst✝⁶","sexp":"((:c LieAlgebra...
(:app (:c LieModule.IsNilpotent) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c LieSubalgebra) (:arg :explicit 0 (:fv FV0)) (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"have","sourceEnd":11201,"sourceStart":11197,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hI₃","sourceEnd":11207,"sourceStart":11202,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hI₃","sourceEnd":11207,"sourceStart":11202,"tag":"n...
[]
[{"source":"LieAlgebra.IsEngelian R I","source_end":11235,"source_start":11210,"syntax_kind":"Lean.Parser.Term.app"},{"source":"e.isEngelian_iff.mp hK₁","source_end":11264,"source_start":11239,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
30
26
exact
true
1
33
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
371988f062d61d8674e79b08f218fe94667626f4ef7c2c682cfe52ddd7f63d49
2e447db3fae7b573646399c47fa3efbe8da5766047e2a8f8ca845cd70e22a777
c54645aefc1be344bfbbb98ee63a38d5d1c5fec98d2b0a05d3fbb22cf19058df
150359fb9a3a2e5d0311aa8d06a525b34e427fba39e23d717757f1e21097c201
cat-searcher/leandojo-benchmark-4-random
test
2,225
LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer
Mathlib/Algebra/Lie/Engel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>LieSubmodule.isNilpotentOfIsNilpotentSpanSupEqTop</a> hI₂ (h _) (hI₃ _ fun x => h x)
case intro.intro.intro R : Type u₁ L : Type u₂ L₂ : Type u₃ M✝ : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M✝ inst✝² : Module R M✝ inst✝¹ : LieRingModule L M✝ inst✝ : LieModule R L M✝ K : LieSubalgebra R L hK₁ : IsEngelian R...
((:c LieModule.IsNilpotent) (:fv _uniq.62747) ((:c Subtype) (:fv _uniq.62749) (:lambda x (:fv _uniq.62749) ((:c Membership.mem) (:fv _uniq.62749) ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) ((:c SetLike.instMembership) ((:c LieSubalgebra) (:fv _uniq.627...
[{"name":"R","sexp":"(:sort (+ u₁ 1))"},{"name":"L","sexp":"(:sort (+ u₂ 1))"},{"name":"L₂","sexp":"(:sort (+ u₃ 1))"},{"name":"M✝","sexp":"(:sort (+ u₄ 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.62747))"},{"name":"inst✝⁷","sexp":"((:c LieRing) (:fv _uniq.62749))"},{"name":"inst✝⁶","sexp":"((:c LieAlgebra...
(:app (:c LieModule.IsNilpotent) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c LieSubalgebra) (:arg :explicit 0 (:fv FV0)) (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"exact","sourceEnd":11272,"sourceStart":11267,"tag":"atom"},{"children":[{"name":"LieSubmodule.isNilpotentOfIsNilpotentSpanSupEqTop","semanticRole":"global","source":"LieSubmodule.isNilpotentOfIsNilpotentSpanSupEqTop","sourceEnd":11322,"sourceStart":11273,"tag":"identifier"},{"children":[{"contex...
[]
[{"source":"LieSubmodule.isNilpotentOfIsNilpotentSpanSupEqTop hI₂ (h _) (hI₃ _ fun x => h x)","source_end":11357,"source_start":11273,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
30
27
exact
true
1
34
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ba82e8e6795a7728949ab57c6237e0fe4e5b5caad6212e82e54fe9b01dd3bc40
150359fb9a3a2e5d0311aa8d06a525b34e427fba39e23d717757f1e21097c201
945522b8a4258e2e2a04e1e466f52b4ad63f9ef96230e0f514bb10552447d1e0
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,226
LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer
Mathlib/Algebra/Lie/Engel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>LieSubalgebra.coe_submodule_le_coe_submodule</a>]
R : Type u₁ L : Type u₂ L₂ : Type u₃ M : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K < K.normalizer x...
R : Type u₁ L : Type u₂ L₂ : Type u₃ M : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K < K.normalizer x...
((:c LE.le) ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) ((:c Preorder.toLE) ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) ((:c PartialOrder.toPreorder) ((:c LieSubalgebra) (:fv _uniq.62747...
[{"name":"R","sexp":"(:sort (+ u₁ 1))"},{"name":"L","sexp":"(:sort (+ u₂ 1))"},{"name":"L₂","sexp":"(:sort (+ u₃ 1))"},{"name":"M","sexp":"(:sort (+ u₄ 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.62747))"},{"name":"inst✝⁷","sexp":"((:c LieRing) (:fv _uniq.62749))"},{"name":"inst✝⁶","sexp":"((:c LieAlgebra)...
(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c LieSubalgebra) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-o...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"rw","sourceEnd":10389,"sourceStart":10387,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10391,"sourceStart":10390,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":10394,"sourceSt...
[]
[{"source":"LieSubalgebra.coe_submodule_le_coe_submodule","source_end":10439,"source_start":10395,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
30
10
exact
true
1
22
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
dad5d754a327166f2f4b7502630eb9423770baa7a50d6399bf917d6ab99d690f
acf975a507fd9549fcf3ec77a429239f406177e5beb906cd792e5606bbbee0e6
97e72e33006c17f356d3912eaff32592bcc58087f0b0fecb5a479cfb7f79f50b
ba3614623928a43818f3558de530f3666c45ae45f235525a0d83e7d792bee112
cat-searcher/leandojo-benchmark-4-random
test
2,227
LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer
Mathlib/Algebra/Lie/Engel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>sup_le</a> ((<a>Submodule.span_singleton_le_iff_mem</a> _ _).<a>Iff.mpr</a> hx₁) hK₂.le
R : Type u₁ L : Type u₂ L₂ : Type u₃ M : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K < K.normalizer x...
((:c LE.le) ((:c Submodule) (:fv _uniq.62747) (:fv _uniq.62749) ((:c CommSemiring.toSemiring) (:fv _uniq.62747) ((:c CommRing.toCommSemiring) (:fv _uniq.62747) (:fv _uniq.62756))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.62749) ((:c LieRing.toAddCommGroup) (:fv _uniq.62749) (:fv _uniq.62759))) ((:c LieAlgebra.toMo...
[{"name":"R","sexp":"(:sort (+ u₁ 1))"},{"name":"L","sexp":"(:sort (+ u₂ 1))"},{"name":"L₂","sexp":"(:sort (+ u₃ 1))"},{"name":"M","sexp":"(:sort (+ u₄ 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.62747))"},{"name":"inst✝⁷","sexp":"((:c LieRing) (:fv _uniq.62749))"},{"name":"inst✝⁶","sexp":"((:c LieAlgebra)...
(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (: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 FV1))))) (:arg :instance 4 (:instance...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"exact","sourceEnd":10450,"sourceStart":10445,"tag":"atom"},{"children":[{"name":"sup_le","semanticRole":"global","source":"sup_le","sourceEnd":10457,"sourceStart":10451,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":10459,"sourceStart":10458,"tag":"atom"},{"children":[{"...
[]
[{"source":"sup_le ((Submodule.span_singleton_le_iff_mem _ _).mpr hx₁) hK₂.le","source_end":10520,"source_start":10451,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
30
13
exact
true
1
22
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c951f79436f38570b1e0ca1570a56cbdf95f7e5458105faca95deef5df6dfa51
ba3614623928a43818f3558de530f3666c45ae45f235525a0d83e7d792bee112
de0cff94d0a558f5d3432d57f595d100db9539f256ee2585e66b6abcacd76e27
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,228
LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer
Mathlib/Algebra/Lie/Engel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>LieIdeal.coe_to_lieSubalgebra_to_submodule</a> R K' I, hI₁]
R : Type u₁ L : Type u₂ L₂ : Type u₃ M✝ : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M✝ inst✝² : Module R M✝ inst✝¹ : LieRingModule L M✝ inst✝ : LieModule R L M✝ K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K < K.normali...
R : Type u₁ L : Type u₂ L₂ : Type u₃ M✝ : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M✝ inst✝² : Module R M✝ inst✝¹ : LieRingModule L M✝ inst✝ : LieModule R L M✝ K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K < K.normali...
((:c Eq) ((:c Submodule) (:fv _uniq.62747) ((:c Subtype) (:fv _uniq.62749) (:lambda x (:fv _uniq.62749) ((:c Membership.mem) (:fv _uniq.62749) ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) ((:c SetLike.instMembership) ((:c LieSubalgebra) (:fv _uniq.62747)...
[{"name":"R","sexp":"(:sort (+ u₁ 1))"},{"name":"L","sexp":"(:sort (+ u₂ 1))"},{"name":"L₂","sexp":"(:sort (+ u₃ 1))"},{"name":"M✝","sexp":"(:sort (+ u₄ 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.62747))"},{"name":"inst✝⁷","sexp":"((:c LieRing) (:fv _uniq.62749))"},{"name":"inst✝⁶","sexp":"((:c LieAlgebra...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c LieSubalgebra) (:arg...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"rw","sourceEnd":10889,"sourceStart":10887,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10891,"sourceStart":10890,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":10894,"sourceSt...
[]
[{"source":"LieIdeal.coe_to_lieSubalgebra_to_submodule R K' I","source_end":10944,"source_start":10895,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hI₁","source_end":10951,"source_start":10946,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
30
19
exact
true
1
31
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3f92bbabae6048b8f529f4f5e9d8c92b3e7eef165ab8d5d326e5d86410c2743a
d5bf6d601a8564449322f87756272c3cc4dfd4ac95d1c3f8cac2ee0e82e321fb
e73647b51bd8561503b44b8cb7f3bde47b27090cd5dce5489725f0d9b96a1b8e
f6868a9d7825234a08565f23c38b79a28af582e81636b9a3b2410e762a177ff7
cat-searcher/leandojo-benchmark-4-random
test
2,229
LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer
Mathlib/Algebra/Lie/Engel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>Submodule.map_injective_of_injective</a> (K' : <a>Submodule</a> R L).<a>Submodule.injective_subtype</a>
R : Type u₁ L : Type u₂ L₂ : Type u₃ M✝ : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M✝ inst✝² : Module R M✝ inst✝¹ : LieRingModule L M✝ inst✝ : LieModule R L M✝ K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K < K.normali...
case a R : Type u₁ L : Type u₂ L₂ : Type u₃ M✝ : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M✝ inst✝² : Module R M✝ inst✝¹ : LieRingModule L M✝ inst✝ : LieModule R L M✝ K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K < K....
((:c Eq) ((:c Submodule) (:fv _uniq.62747) ((:c Subtype) (:fv _uniq.62749) (:lambda x (:fv _uniq.62749) ((:c Membership.mem) (:fv _uniq.62749) ((:c LieSubalgebra) (:fv _uniq.62747) (:fv _uniq.62749) (:fv _uniq.62756) (:fv _uniq.62759) (:fv _uniq.62776)) ((:c SetLike.instMembership) ((:c LieSubalgebra) (:fv _uniq.62747)...
[{"name":"R","sexp":"(:sort (+ u₁ 1))"},{"name":"L","sexp":"(:sort (+ u₂ 1))"},{"name":"L₂","sexp":"(:sort (+ u₃ 1))"},{"name":"M✝","sexp":"(:sort (+ u₄ 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.62747))"},{"name":"inst✝⁷","sexp":"((:c LieRing) (:fv _uniq.62749))"},{"name":"inst✝⁶","sexp":"((:c LieAlgebra...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c LieSubalgebra) (:arg...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"apply","sourceEnd":10962,"sourceStart":10957,"tag":"atom"},{"children":[{"name":"Submodule.map_injective_of_injective","semanticRole":"global","source":"Submodule.map_injective_of_injective","sourceEnd":10999,"sourceStart":10963,"tag":"identifier"},{"children":[{"children":[{"children":[{"source...
[]
[{"source":"Submodule.map_injective_of_injective (K' : Submodule R L).injective_subtype","source_end":11038,"source_start":10963,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
30
23
exact
true
1
31
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5d8a1606e8ca56e1451d34d80cd0a685992625d4afcf68cf8bf9643282ca3e38
f6868a9d7825234a08565f23c38b79a28af582e81636b9a3b2410e762a177ff7
75b43a7bee5d23f6aef8872f015ddfc6738da07642b6ebca3e344bce5e86484e
f026907e64c3c48a8c6f9066e773f8048f9ef28d3e3f491575d102a69904ec52
cat-searcher/leandojo-benchmark-4-random
test
2,230
LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer
Mathlib/Algebra/Lie/Engel.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
case a R : Type u₁ L : Type u₂ L₂ : Type u₃ M✝ : Type u₄ inst✝⁸ : CommRing R inst✝⁷ : LieRing L inst✝⁶ : LieAlgebra R L inst✝⁵ : LieRing L₂ inst✝⁴ : LieAlgebra R L₂ inst✝³ : AddCommGroup M✝ inst✝² : Module R M✝ inst✝¹ : LieRingModule L M✝ inst✝ : LieModule R L M✝ K : LieSubalgebra R L hK₁ : IsEngelian R ↥K hK₂ : K < K....
((:c Eq) ((:c Submodule) (:fv _uniq.62747) (:fv _uniq.62749) ((:c CommSemiring.toSemiring) (:fv _uniq.62747) ((:c CommRing.toCommSemiring) (:fv _uniq.62747) (:fv _uniq.62756))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.62749) ((:c LieRing.toAddCommGroup) (:fv _uniq.62749) (:fv _uniq.62759))) ((:c LieAlgebra.toModul...
[{"name":"R","sexp":"(:sort (+ u₁ 1))"},{"name":"L","sexp":"(:sort (+ u₂ 1))"},{"name":"L₂","sexp":"(:sort (+ u₃ 1))"},{"name":"M✝","sexp":"(:sort (+ u₄ 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.62747))"},{"name":"inst✝⁷","sexp":"((:c LieRing) (:fv _uniq.62749))"},{"name":"inst✝⁶","sexp":"((:c LieAlgebra...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (: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 FV1))))) (:arg :instance 4 (:instance-of...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62747","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"simp","sourceEnd":11047,"sourceStart":11043,"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.62747","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
30
24
exact
true
1
31
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b39ca152a0732464505c7d316bf63374068c533cbaf55af09a8a5f57f184b326
f026907e64c3c48a8c6f9066e773f8048f9ef28d3e3f491575d102a69904ec52
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,231
SimpleGraph.Walk.length_edges
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>SimpleGraph.Walk.edges</a>]
V : Type u V' : Type v V'' : Type w G : SimpleGraph V G' : SimpleGraph V' G'' : SimpleGraph V'' u v : V p : G.Walk u v ⊢ p.edges.length = p.length
((:c Eq) (:c Nat) ((:c List.length) ((:c Sym2) (:fv _uniq.72538)) ((:c SimpleGraph.Walk.edges) (:fv _uniq.72538) (:fv _uniq.72545) (:fv _uniq.72593) (:fv _uniq.72594) (:fv _uniq.72595))) ((:c SimpleGraph.Walk.length) (:fv _uniq.72538) (:fv _uniq.72545) (:fv _uniq.72593) (:fv _uniq.72594) (:fv _uniq.72595)))
[{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"V'","sexp":"(:sort (+ v 1))"},{"name":"V''","sexp":"(:sort (+ w 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.72538))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.72540))"},{"name":"G''","sexp":"((:c SimpleGraph) (:fv _uniq.72542))"},{"name":"u","sexp":"(:...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c List.length) (:arg :implicit-type 0 (:app (:c Sym2) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c SimpleGraph.Walk.edges) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :implicit 2) (:arg :implicit 3) (:arg :explicit 4 (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72538","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.72540","is_instance":false,"is_let":false,"name":"V'","sexp":"(:sort Type)"},{"binder_role":":implicit","co...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":32635,"sourceStart":32631,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...
[]
[{"source":"edges","source_end":32642,"source_start":32637,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72538","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.72540","is_instance":false,"is_let":false,"user_name":"V'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
240
2
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
841f8912c2c5970e30b13995e23a86630c82cc420fa2d475fee72ae897141fcb
e8c6ddafaeaa9a9482ef9d8ad7e86adad9f6cf0d9d782ea9e09ccc728d8db74b
43f45518f3f6d562e411102f49e637b66fc5fe08abb9072add5912494d6e8a20
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,232
CategoryTheory.Limits.Sigma.map_id
Mathlib/CategoryTheory/Limits/Shapes/Products.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
ext
β : Type w α : Type w₂ γ : Type w₃ C : Type u inst✝¹ : Category.{v, u} C f : α → C inst✝ : HasCoproduct f ⊢ (map fun a => 𝟙 (f a)) = 𝟙 (∐ f)
case h β : Type w α : Type w₂ γ : Type w₃ C : Type u inst✝¹ : Category.{v, u} C f : α → C inst✝ : HasCoproduct f b✝ : α ⊢ (ι f b✝ ≫ map fun a => 𝟙 (f a)) = ι f b✝ ≫ 𝟙 (∐ f)
((:c Eq) ((:c Quiver.Hom) (:fv _uniq.185966) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.185966) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.185966) (:fv _uniq.185969))) ((:c CategoryTheory.Limits.sigmaObj) (:fv _uniq.185962) (:fv _uniq.185966) (:fv _uniq.185969) (:fv _uniq.186343) (:fv _uniq....
[{"name":"β","sexp":"(:sort (+ w 1))"},{"name":"α","sexp":"(:sort (+ w₂ 1))"},{"name":"γ","sexp":"(:sort (+ w₃ 1))"},{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.185966))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.185962) (:fv _uniq.185966))"},{"name":"inst✝",...
(: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 CategoryTheory.Limits.sigmaObj) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV3)) (:arg :instance 2...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.185960","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.185962","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"ext","sourceEnd":19936,"sourceStart":19933,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":19936,"sourceStart":19933,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.185960","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.185962","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
100
4
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
566d24962660fa8dda1f9ce9d31f8b3fdc05180516231277eccd26c63581f8f3
88cc026121eb1574e5ef537ba22ce9912709dabc94930ca3fb160e03d7500eb9
a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de
3b6ef4f15423f9d9c15d3f6bddac4138b19de4e829059921163598cb645ac3f6
cat-searcher/leandojo-benchmark-4-random
test
2,233
CategoryTheory.Limits.Sigma.map_id
Mathlib/CategoryTheory/Limits/Shapes/Products.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
case h β : Type w α : Type w₂ γ : Type w₃ C : Type u inst✝¹ : Category.{v, u} C f : α → C inst✝ : HasCoproduct f b✝ : α ⊢ (ι f b✝ ≫ map fun a => 𝟙 (f a)) = ι f b✝ ≫ 𝟙 (∐ f)
((:c Eq) ((:c Quiver.Hom) (:fv _uniq.185966) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.185966) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.185966) (:fv _uniq.185969))) ((:fv _uniq.186343) (:fv _uniq.186429)) ((:c CategoryTheory.Limits.sigmaObj) (:fv _uniq.185962) (:fv _uniq.185966) (:fv _uni...
[{"name":"β","sexp":"(:sort (+ w 1))"},{"name":"α","sexp":"(:sort (+ w₂ 1))"},{"name":"γ","sexp":"(:sort (+ w₃ 1))"},{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.185966))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.185962) (:fv _uniq.185966))"},{"name":"inst✝",...
(: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 (:fv FV6) (:arg :explicit 0 (:fv FV8)))) (:arg :explicit 3 (:app (:c CategoryTheory.Limits.sigmaObj) (:arg :implicit-type...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.185960","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.185962","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"simp","sourceEnd":19942,"sourceStart":19938,"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.185960","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.185962","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
100
6
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
fbbf126ed793d89e4603a3313be368e5cd0dfecaf0835142f823fb0d712bc60f
3b6ef4f15423f9d9c15d3f6bddac4138b19de4e829059921163598cb645ac3f6
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,234
Polynomial.exists_forall_norm_le
Mathlib/Topology/Algebra/Polynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Polynomial.eq_C_of_degree_le_zero</a> (<a>le_of_not_gt</a> hp0)]
α : Type u_1 R : Type u_2 inst✝² : NormedRing R inst✝¹ : IsAbsoluteValue norm inst✝ : ProperSpace R p : R[X] hp0 : ¬0 < p.degree ⊢ ∀ (y : R), ‖eval (p.coeff 0) p‖ ≤ ‖eval y p‖
α : Type u_1 R : Type u_2 inst✝² : NormedRing R inst✝¹ : IsAbsoluteValue norm inst✝ : ProperSpace R p : R[X] hp0 : ¬0 < p.degree ⊢ ∀ (y : R), ‖eval ((C (p.coeff 0)).coeff 0) (C (p.coeff 0))‖ ≤ ‖eval y (C (p.coeff 0))‖
(:forall y (:fv _uniq.24227) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.24227) ((:c NormedRing.toNorm) (:fv _uniq.24227) (:fv _uniq.24230)) ((:c Polynomial.eval) (:fv _uniq.24227) ((:c Ring.toSemiring) (:fv _uniq.24227) ((:c NormedRing.toRing) (:fv _uniq.24227) (:fv _uniq.24230))) ((:c Polynomial...
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(:forall y :explicit (:fv FV1) (: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 FV1)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV1))))) (:arg :...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24224","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24227","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"rw","sourceEnd":6345,"sourceStart":6343,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6347,"sourceStart":6346,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Polynom...
[]
[{"source":"eq_C_of_degree_le_zero (le_of_not_gt hp0)","source_end":6388,"source_start":6347,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24224","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24227","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
38
4
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
55ca56cb3b4289d0228c7bc84fd68a2c9209fea09d24f0fae1114c9dc6d627e7
647fa470d41f98247844fa80a4b860d4fa5902a044df0311616d76be90b02b15
762cb1f84d221b158fd6256380cc6e1147ebe106194c8bdfcf9753fcc289da0b
06a02bdf54a4d283312c9bb7c4b68ab6f817a5526cc936376af4fe3d75e7d2c9
cat-searcher/leandojo-benchmark-4-random
test
2,235
Polynomial.exists_forall_norm_le
Mathlib/Topology/Algebra/Polynomial.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
α : Type u_1 R : Type u_2 inst✝² : NormedRing R inst✝¹ : IsAbsoluteValue norm inst✝ : ProperSpace R p : R[X] hp0 : ¬0 < p.degree ⊢ ∀ (y : R), ‖eval ((C (p.coeff 0)).coeff 0) (C (p.coeff 0))‖ ≤ ‖eval y (C (p.coeff 0))‖
(:forall y (:fv _uniq.24227) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.24227) ((:c NormedRing.toNorm) (:fv _uniq.24227) (:fv _uniq.24230)) ((:c Polynomial.eval) (:fv _uniq.24227) ((:c Ring.toSemiring) (:fv _uniq.24227) ((:c NormedRing.toRing) (:fv _uniq.24227) (:fv _uniq.24230))) ((:c Polynomial...
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(:forall y :explicit (:fv FV1) (: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 FV1)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV1))))) (:arg :...
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{"children":[{"source":"simp","sourceEnd":6395,"sourceStart":6391,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24224","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24227","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
38
8
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7d532ee0ba2cb8c7de86ee3ac9faaa91a8c5bfd1ec7cbde67581ea2ed14e4f87
06a02bdf54a4d283312c9bb7c4b68ab6f817a5526cc936376af4fe3d75e7d2c9
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,236
Pi.mulSingle_comm
Mathlib/Algebra/Group/Pi/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>Pi.mulSingle_apply</a>, <a>eq_comm</a>]
I : Type u α : Type u_1 β : Type u_2 γ : Type u_3 f : I → Type v₁ g : I → Type v₂ h : I → Type v₃ x✝ y : (i : I) → f i i✝ : I inst✝⁴ : DecidableEq I inst✝³ : (i : I) → One (f i) inst✝² : (i : I) → One (g i) inst✝¹ : (i : I) → One (h i) inst✝ : One β i : I x : β i' : I ⊢ mulSingle i x i' = mulSingle i' x i
((:c Eq) (:fv _uniq.19616) ((:c Pi.mulSingle) (:fv _uniq.19610) (:lambda _ (:fv _uniq.19610) (:fv _uniq.19616)) (:fv _uniq.19652) (:lambda i (:fv _uniq.19610) (:fv _uniq.19885)) (:fv _uniq.19886) (:fv _uniq.19887) (:fv _uniq.19888)) ((:c Pi.mulSingle) (:fv _uniq.19610) (:lambda _ (:fv _uniq.19610) (:fv _uniq.19616)) (:...
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(:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Pi.mulSingle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :instance 2 (:instance-of (:app (:c DecidableEq) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:forall i :explicit (:fv FV0) (:app (:c One) (:arg :expli...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.19610","is_instance":false,"is_let":false,"name":"I","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.19613","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
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[]
[{"source":"mulSingle_apply","source_end":14533,"source_start":14518,"syntax_kind":"ident"},{"source":"eq_comm","source_end":14542,"source_start":14535,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.19610","is_instance":false,"is_let":false,"user_name":"I"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.19613","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
169
2
exact
true
1
18
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8eeae78c4e2137f7624c1e2191f1d0f0fe42030b71c844007ca1ed1c11164a66
566b2e4c16fddfeb9e9912911f66153c9e6e050a51d9680df984d5a6fcf5a683
bbe5cf69d68f3bc99b7e649caf97b7e4e1ac8556bfb884a1594b0afe3970002d
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,237
aux_add
Mathlib/Analysis/Convex/Strong.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simpa [<a>neg_div</a>] using <a>_private.Mathlib.Analysis.Convex.Strong.0.aux_sub</a> (E := E) (m := -m) ha hb hab
E : Type u_1 inst✝¹ : NormedAddCommGroup E inst✝ : InnerProductSpace ℝ E φ ψ : ℝ → ℝ s : Set E a b m : ℝ x y : E f : E → ℝ ha : 0 ≤ a hb : 0 ≤ b hab : a + b = 1 ⊢ a * (f x + m / 2 * ‖x‖ ^ 2) + b * (f y + m / 2 * ‖y‖ ^ 2) - m / 2 * ‖a • x + b • y‖ ^ 2 = a * f x + b * f y + m / 2 * a * b * ‖x - y‖ ^ 2
((:c Eq) (:c Real) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.364166) ((:c HAdd.hA...
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(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HSub.hSub) (: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 HSub) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea...
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{"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":8018,"sourceStart":8013,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":...
[]
[{"source":"neg_div","source_end":8027,"source_start":8020,"syntax_kind":"ident"},{"source":"aux_sub (E := E) (m := -m) ha hb hab","source_end":8071,"source_start":8035,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.364137","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.364140","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index...
36
2
exact
true
1
15
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f5a3ef2b4940cc72f1e763ca4037a04283119cbfbabb8b28deab60a97e5b15e4
5e1fb0d9f90f97bccc4b8ffa60cad0563008f63929bac98888da9e11265275d5
cb110e9650048edc394f686457a6466f9661edcbbad604aa70ce0c45599038b9
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,238
OrderRingHom.cancel_left
Mathlib/Algebra/Order/Hom/Ring.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>OrderRingHom.comp_apply</a>, h, <a>OrderRingHom.comp_apply</a>]
F : Type u_1 α : Type u_2 β : Type u_3 γ : Type u_4 δ : Type u_5 inst✝⁷ : NonAssocSemiring α inst✝⁶ : Preorder α inst✝⁵ : NonAssocSemiring β inst✝⁴ : Preorder β inst✝³ : NonAssocSemiring γ inst✝² : Preorder γ inst✝¹ : NonAssocSemiring δ inst✝ : Preorder δ f : β →+*o γ g₁ g₂ : α →+*o β hf : Injective ⇑f h : f.comp g₁ = ...
((:c Eq) (:fv _uniq.26090) ((:c DFunLike.coe) ((:c OrderRingHom) (:fv _uniq.26087) (:fv _uniq.26090) (:fv _uniq.26102) (:fv _uniq.26105) (:fv _uniq.26108) (:fv _uniq.26111)) (:fv _uniq.26087) (:lambda _ (:fv _uniq.26087) (:fv _uniq.26090)) ((:c OrderRingHom.instFunLike) (:fv _uniq.26087) (:fv _uniq.26090) (:fv _uniq.26...
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(:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c OrderRingHom) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c NonAssocSemiring) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 3 (:instance-of (...
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{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":11429,"sourceStart":11427,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11431,"sourceStart":11430,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"...
[]
[{"source":"comp_apply","source_end":11445,"source_start":11435,"syntax_kind":"ident"},{"source":"h","source_end":11448,"source_start":11447,"syntax_kind":"ident"},{"source":"comp_apply","source_end":11460,"source_start":11450,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.26081","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26084","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
96
2
exact
true
1
19
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f8271a5559e113470e1191dd05e8fa8829a1cf70bc0b2ff699adb469974606bf
810ee4ba0a05ddf8b51ec38e2aa0d5c418f65676e8704c737b20818158ff5bc7
fdca56573bf495f2328209e8b177e72167b08ff22d847d2ee55a150ad0ba6789
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,239
LinearIndependent.image_subtype
Mathlib/LinearAlgebra/LinearIndependent.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>Subtype.range_coe</a> (s := s)] at hf_inj
ι : Type u' ι' : Type u_1 R : Type u_2 K : Type u_3 M : Type u_4 M' : Type u_5 M'' : Type u_6 V : Type u V' : Type u_7 v : ι → M inst✝⁶ : Ring R inst✝⁵ : AddCommGroup M inst✝⁴ : AddCommGroup M' inst✝³ : AddCommGroup M'' inst✝² : Module R M inst✝¹ : Module R M' inst✝ : Module R M'' a b : R x y : M s : Set M f : M →ₗ[R] ...
ι : Type u' ι' : Type u_1 R : Type u_2 K : Type u_3 M : Type u_4 M' : Type u_5 M'' : Type u_6 V : Type u V' : Type u_7 v : ι → M inst✝⁶ : Ring R inst✝⁵ : AddCommGroup M inst✝⁴ : AddCommGroup M' inst✝³ : AddCommGroup M'' inst✝² : Module R M inst✝¹ : Module R M' inst✝ : Module R M'' a b : R x y : M s : Set M f : M →ₗ[R] ...
((:c LinearIndependent) ((:c Set.Elem) (:fv _uniq.543813) ((:c Set.image) (:fv _uniq.543810) (:fv _uniq.543813) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.543804) (:fv _uniq.543804) ((:c Ring.toSemiring) (:fv _uniq.543804) (:fv _uniq.543828)) ((:c Ring.toSemiring) (:fv _uniq.543804) (:fv _uniq.543828)) ((:c RingHom....
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(:app (:c LinearIndependent) (:arg :implicit-type 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:app (:c Set.image) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:fv FV5)) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type ...
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{"children":[{"source":"rw","sourceEnd":52928,"sourceStart":52926,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":52930,"sourceStart":52929,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":52933,"sourceSt...
[]
[{"source":"hf_inj","source_end":52971,"source_start":52965,"syntax_kind":"ident"},{"source":"Subtype.range_coe (s := s)","source_end":52960,"source_start":52934,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.543798","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.543801","is_instance":false,"is_let":false,"user_name":"ι'"},{"binder_role":":implicit","context_index":2,"internal_name":"...
203
4
exact
true
1
25
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
592788f29e1b239e6c8df76b75151424bfdece1fa7e7024d58fd877fe28c578d
78272cb6e4c8b511f04924015bf3771623541217145b79a65ecda7e0a30fd420
d577bd1f5d88abbe0b85b0a753b6027392112fa6ee16227536531372901a8d04
4f1718055356829e50fd5f59e6242aed8641fa781bd878b92e72cf29b8653e5a
cat-searcher/leandojo-benchmark-4-random
test
2,240
LinearIndependent.image_subtype
Mathlib/LinearAlgebra/LinearIndependent.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine (hs.map hf_inj).<a>LinearIndependent.to_subtype_range'</a> ?_
ι : Type u' ι' : Type u_1 R : Type u_2 K : Type u_3 M : Type u_4 M' : Type u_5 M'' : Type u_6 V : Type u V' : Type u_7 v : ι → M inst✝⁶ : Ring R inst✝⁵ : AddCommGroup M inst✝⁴ : AddCommGroup M' inst✝³ : AddCommGroup M'' inst✝² : Module R M inst✝¹ : Module R M' inst✝ : Module R M'' a b : R x y : M s : Set M f : M →ₗ[R] ...
ι : Type u' ι' : Type u_1 R : Type u_2 K : Type u_3 M : Type u_4 M' : Type u_5 M'' : Type u_6 V : Type u V' : Type u_7 v : ι → M inst✝⁶ : Ring R inst✝⁵ : AddCommGroup M inst✝⁴ : AddCommGroup M' inst✝³ : AddCommGroup M'' inst✝² : Module R M inst✝¹ : Module R M' inst✝ : Module R M'' a b : R x y : M s : Set M f : M →ₗ[R] ...
((:c LinearIndependent) ((:c Set.Elem) (:fv _uniq.543813) ((:c Set.image) (:fv _uniq.543810) (:fv _uniq.543813) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.543804) (:fv _uniq.543804) ((:c Ring.toSemiring) (:fv _uniq.543804) (:fv _uniq.543828)) ((:c Ring.toSemiring) (:fv _uniq.543804) (:fv _uniq.543828)) ((:c RingHom....
[{"name":"ι","sexp":"(:sort (+ u' 1))"},{"name":"ι'","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"K","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"M'","sexp":"(:sort (+ u_5 1))"},{"name":"M''","sexp":"(:sort (+ u_6 1))"},{"name":"V","sexp":"(:sort (+ u 1))"...
(:app (:c LinearIndependent) (:arg :implicit-type 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:app (:c Set.image) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:fv FV5)) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.543798","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.543801","is_instance":false,"is_let":false,"name":"ι'","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"refine","sourceEnd":52980,"sourceStart":52974,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":52982,"sourceStart":52981,"tag":"atom"},{"children":[{"source":"hs.map","sourceEnd":52988,"sourceStart":52982,"tag":"identifier"},{"children":[{"contextIndex":25,"semantic...
[]
[{"source":"(hs.map hf_inj).to_subtype_range' ?_","source_end":53017,"source_start":52981,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.543798","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.543801","is_instance":false,"is_let":false,"user_name":"ι'"},{"binder_role":":implicit","context_index":2,"internal_name":"...
203
7
exact
true
1
25
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4bac82f7da2ab1f48d9b7cceca0adf9a57a65540676f7c686aa3d3d28003cb76
4f1718055356829e50fd5f59e6242aed8641fa781bd878b92e72cf29b8653e5a
56599f5241ad9637c7f97571eec3c5dba12c1a53448db0a28f93a67f9b15a482
cd0112ffe0213067a432645b01ee020372a6c5af4f506cd9f415b7244ddcf709
cat-searcher/leandojo-benchmark-4-random
test
2,241
LinearIndependent.image_subtype
Mathlib/LinearAlgebra/LinearIndependent.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>Set.range_comp</a> f]
ι : Type u' ι' : Type u_1 R : Type u_2 K : Type u_3 M : Type u_4 M' : Type u_5 M'' : Type u_6 V : Type u V' : Type u_7 v : ι → M inst✝⁶ : Ring R inst✝⁵ : AddCommGroup M inst✝⁴ : AddCommGroup M' inst✝³ : AddCommGroup M'' inst✝² : Module R M inst✝¹ : Module R M' inst✝ : Module R M'' a b : R x y : M s : Set M f : M →ₗ[R] ...
((:c Eq) ((:c Set) (:fv _uniq.543813)) ((:c Set.range) (:fv _uniq.543813) ((:c Set.Elem) (:fv _uniq.543810) (:fv _uniq.548139)) ((:c Function.comp) ((:c Set.Elem) (:fv _uniq.543810) (:fv _uniq.548139)) (:fv _uniq.543810) (:fv _uniq.543813) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.543804) (:fv _uniq.543804) ((:c Ri...
[{"name":"ι","sexp":"(:sort (+ u' 1))"},{"name":"ι'","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"K","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"M'","sexp":"(:sort (+ u_5 1))"},{"name":"M''","sexp":"(:sort (+ u_6 1))"},{"name":"V","sexp":"(:sort (+ u 1))"...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :explicit 1 (:app (:c Set.range) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:fv FV22)))) (:arg :explicit 2 (:app (:c Function.comp) (:arg :impli...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.543798","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.543801","is_instance":false,"is_let":false,"name":"ι'","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"simp","sourceEnd":53024,"sourceStart":53020,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":53026,"sourceStart":53025,"tag":"a...
[]
[{"source":"Set.range_comp f","source_end":53042,"source_start":53026,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.543798","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.543801","is_instance":false,"is_let":false,"user_name":"ι'"},{"binder_role":":implicit","context_index":2,"internal_name":"...
203
8
exact
true
1
25
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e998148de9ef80eb84db77b01f5aceb3ae55834585e3535bb5a0b5e11473debc
cd0112ffe0213067a432645b01ee020372a6c5af4f506cd9f415b7244ddcf709
f951f369619ceb6507f52e74ec892a8a4a473a75eef0670ac238c6c4224795d2
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,242
OrdinalApprox.lfpApprox_mem_fixedPoints_of_eq
Mathlib/SetTheory/Ordinal/FixedPointApproximants.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have lfpApprox_mem_fixedPoint : <a>OrdinalApprox.lfpApprox</a> f x a ∈ <a>Function.fixedPoints</a> f := by rw [<a>Function.mem_fixedPoints_iff</a>, ← <a>OrdinalApprox.lfpApprox_add_one</a> f x h_init] exact <a>Monotone.eq_of_le_of_le</a> (<a>OrdinalApprox.lfpApprox_monotone</a> f x) h_fab (<a>SuccOrder.le_succ</a> a) (...
α : Type u inst✝ : CompleteLattice α f : α →o α x : α a b c : Ordinal.{u} h_init : x ≤ f x h_ab : a < b h_ac : a ≤ c h_fab : lfpApprox f x a = lfpApprox f x b ⊢ lfpApprox f x c ∈ fixedPoints ⇑f
α : Type u inst✝ : CompleteLattice α f : α →o α x : α a b c : Ordinal.{u} h_init : x ≤ f x h_ab : a < b h_ac : a ≤ c h_fab : lfpApprox f x a = lfpApprox f x b lfpApprox_mem_fixedPoint : lfpApprox f x a ∈ fixedPoints ⇑f ⊢ lfpApprox f x c ∈ fixedPoints ⇑f
((:c Membership.mem) (:fv _uniq.11201) ((:c Set) (:fv _uniq.11201)) ((:c Set.instMembership) (:fv _uniq.11201)) ((:c OrdinalApprox.lfpApprox) (:fv _uniq.11201) (:fv _uniq.11204) (:fv _uniq.11365) (:fv _uniq.11367) (:fv _uniq.11879)) ((:c Function.fixedPoints) (:fv _uniq.11201) ((:c DFunLike.coe) ((:c OrderHom) (:fv _un...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c CompleteLattice) (:fv _uniq.11201))"},{"name":"f","sexp":"((:c OrderHom) (:fv _uniq.11201) (:fv _uniq.11201) ((:c PartialOrder.toPreorder) (:fv _uniq.11201) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.11201) ((:c CompleteLattice.toCompleteSe...
(: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 :explicit 3 (:app (:c OrdinalApprox...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11201","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11204","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CompleteLattice) (:arg :...
{"children":[{"source":"have","sourceEnd":5774,"sourceStart":5770,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"lfpApprox_mem_fixedPoint","sourceEnd":5799,"sourceStart":5775,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"lfpApprox_mem_fixedPoint","sourceE...
[]
[{"source":"lfpApprox f x a ∈ fixedPoints f","source_end":5841,"source_start":5808,"syntax_kind":"«term_∈_»"},{"source":"mem_fixedPoints_iff","source_end":5875,"source_start":5856,"syntax_kind":"ident"},{"source":"lfpApprox_add_one f x h_init","source_end":5909,"source_start":5881,"syntax_kind":"Lean.Parser.Term.app"},...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11201","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11204","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":2,"interna...
19
4
exact
true
1
11
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7405b348c1673e0bb3c26cfde26541f76098a85206dae3a19d0ef5a3d9ed55d8
85de749ab7ef6d1fcc95fd6baeb362a0fff2df23a7e0e481ee8920541f6dded9
89454862b5166f53b4ac05f582493ac54efebe0d5a699582a397f82e46b50363
a3321459994c18e9831ae9e91305e1928d13ea63eb1047687aab9b3f7724a95d
cat-searcher/leandojo-benchmark-4-random
test
2,243
OrdinalApprox.lfpApprox_mem_fixedPoints_of_eq
Mathlib/SetTheory/Ordinal/FixedPointApproximants.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>OrdinalApprox.lfpApprox_eq_of_mem_fixedPoints</a> f x h_init]
α : Type u inst✝ : CompleteLattice α f : α →o α x : α a b c : Ordinal.{u} h_init : x ≤ f x h_ab : a < b h_ac : a ≤ c h_fab : lfpApprox f x a = lfpApprox f x b lfpApprox_mem_fixedPoint : lfpApprox f x a ∈ fixedPoints ⇑f ⊢ lfpApprox f x c ∈ fixedPoints ⇑f
α : Type u inst✝ : CompleteLattice α f : α →o α x : α a b c : Ordinal.{u} h_init : x ≤ f x h_ab : a < b h_ac : a ≤ c h_fab : lfpApprox f x a = lfpApprox f x b lfpApprox_mem_fixedPoint : lfpApprox f x a ∈ fixedPoints ⇑f ⊢ lfpApprox f x ?m.12529 ∈ fixedPoints ⇑f case h_ab α : Type u inst✝ : CompleteLattice α f : α →o α x...
((:c Membership.mem) (:fv _uniq.11201) ((:c Set) (:fv _uniq.11201)) ((:c Set.instMembership) (:fv _uniq.11201)) ((:c OrdinalApprox.lfpApprox) (:fv _uniq.11201) (:fv _uniq.11204) (:fv _uniq.11365) (:fv _uniq.11367) (:fv _uniq.11879)) ((:c Function.fixedPoints) (:fv _uniq.11201) ((:c DFunLike.coe) ((:c OrderHom) (:fv _un...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c CompleteLattice) (:fv _uniq.11201))"},{"name":"f","sexp":"((:c OrderHom) (:fv _uniq.11201) (:fv _uniq.11201) ((:c PartialOrder.toPreorder) (:fv _uniq.11201) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.11201) ((:c CompleteLattice.toCompleteSe...
(: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 :explicit 3 (:app (:c OrdinalApprox...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11201","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11204","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CompleteLattice) (:arg :...
{"children":[{"source":"rw","sourceEnd":6039,"sourceStart":6037,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6041,"sourceStart":6040,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Ordinal...
[]
[{"source":"lfpApprox_eq_of_mem_fixedPoints f x h_init","source_end":6083,"source_start":6041,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11201","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11204","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":2,"interna...
19
11
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b6a7b3e3cd727d987c308be46c49821d7b1380196a2ddf0ef61e80cdc1820ee0
a3321459994c18e9831ae9e91305e1928d13ea63eb1047687aab9b3f7724a95d
31413ee785f12fef6b7a7d164a7a842a5e1a799136a5cf7c2416f43f3b49916d
5693ef8c969c8cd223a5d505ad72f448776196bc3d85779c17c3f383757b2026
cat-searcher/leandojo-benchmark-4-random
test
2,244
OrdinalApprox.lfpApprox_mem_fixedPoints_of_eq
Mathlib/SetTheory/Ordinal/FixedPointApproximants.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Function.mem_fixedPoints_iff</a>, ← <a>OrdinalApprox.lfpApprox_add_one</a> f x h_init]
α : Type u inst✝ : CompleteLattice α f : α →o α x : α a b c : Ordinal.{u} h_init : x ≤ f x h_ab : a < b h_ac : a ≤ c h_fab : lfpApprox f x a = lfpApprox f x b ⊢ lfpApprox f x a ∈ fixedPoints ⇑f
α : Type u inst✝ : CompleteLattice α f : α →o α x : α a b c : Ordinal.{u} h_init : x ≤ f x h_ab : a < b h_ac : a ≤ c h_fab : lfpApprox f x a = lfpApprox f x b ⊢ lfpApprox f x (a + 1) = lfpApprox f x a
((:c Membership.mem) (:fv _uniq.11201) ((:c Set) (:fv _uniq.11201)) ((:c Set.instMembership) (:fv _uniq.11201)) ((:c OrdinalApprox.lfpApprox) (:fv _uniq.11201) (:fv _uniq.11204) (:fv _uniq.11365) (:fv _uniq.11367) (:fv _uniq.11877)) ((:c Function.fixedPoints) (:fv _uniq.11201) ((:c DFunLike.coe) ((:c OrderHom) (:fv _un...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c CompleteLattice) (:fv _uniq.11201))"},{"name":"f","sexp":"((:c OrderHom) (:fv _uniq.11201) (:fv _uniq.11201) ((:c PartialOrder.toPreorder) (:fv _uniq.11201) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.11201) ((:c CompleteLattice.toCompleteSe...
(: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 :explicit 3 (:app (:c OrdinalApprox...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11201","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11204","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CompleteLattice) (:arg :...
{"children":[{"source":"rw","sourceEnd":5854,"sourceStart":5852,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5856,"sourceStart":5855,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Function.mem_fixedPo...
[]
[{"source":"mem_fixedPoints_iff","source_end":5875,"source_start":5856,"syntax_kind":"ident"},{"source":"lfpApprox_add_one f x h_init","source_end":5909,"source_start":5881,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11201","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11204","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":2,"interna...
19
6
exact
true
1
11
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a2a015783eda634f90a5cecbcfc5e387d7f7afbd1a1ba8fda4425a8158d4e6dc
75dcf586d5c851f49e40f4c92ce9c310de6faef6edbc4e2a170e9c7191015d4b
e3a0290de221b6f25d119dba62fd4df34f2b2eaa93b6cb70d79ffddacc667960
00cc1f9db57fdf563dcadaa373952261bab2dfe8fefa260639ffb59b57c49578
cat-searcher/leandojo-benchmark-4-random
test
2,245
OrdinalApprox.lfpApprox_mem_fixedPoints_of_eq
Mathlib/SetTheory/Ordinal/FixedPointApproximants.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>Monotone.eq_of_le_of_le</a> (<a>OrdinalApprox.lfpApprox_monotone</a> f x) h_fab (<a>SuccOrder.le_succ</a> a) (<a>SuccOrder.succ_le_of_lt</a> h_ab)
α : Type u inst✝ : CompleteLattice α f : α →o α x : α a b c : Ordinal.{u} h_init : x ≤ f x h_ab : a < b h_ac : a ≤ c h_fab : lfpApprox f x a = lfpApprox f x b ⊢ lfpApprox f x (a + 1) = lfpApprox f x a
((:c Eq) (:fv _uniq.11201) ((:c OrdinalApprox.lfpApprox) (:fv _uniq.11201) (:fv _uniq.11204) (:fv _uniq.11365) (:fv _uniq.11367) ((:c HAdd.hAdd) (:c Ordinal) (:c Ordinal) (:c Ordinal) ((:c instHAdd) (:c Ordinal) (:c Ordinal.add)) (:fv _uniq.11877) ((:c OfNat.ofNat) (:c Ordinal) (:lit 1) ((:c One.toOfNat1) (:c Ordinal) ...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c CompleteLattice) (:fv _uniq.11201))"},{"name":"f","sexp":"((:c OrderHom) (:fv _uniq.11201) (:fv _uniq.11201) ((:c PartialOrder.toPreorder) (:fv _uniq.11201) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.11201) ((:c CompleteLattice.toCompleteSe...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c OrdinalApprox.lfpApprox) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CompleteLattice) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :explicit 4 (:app (:c HAdd.hAd...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11201","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11204","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CompleteLattice) (:arg :...
{"children":[{"source":"exact","sourceEnd":5920,"sourceStart":5915,"tag":"atom"},{"children":[{"name":"Monotone.eq_of_le_of_le","semanticRole":"global","source":"Monotone.eq_of_le_of_le","sourceEnd":5944,"sourceStart":5921,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":5946,"sourceStart":5945,"...
[]
[{"source":"Monotone.eq_of_le_of_le (lfpApprox_monotone f x)\n h_fab (SuccOrder.le_succ a) (SuccOrder.succ_le_of_lt h_ab)","source_end":6034,"source_start":5921,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11201","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11204","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":2,"interna...
19
10
exact
true
1
11
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1f721c36ce7fac6622c478f12f9f604972a4cce9c81ff6496b20835afdf7e992
00cc1f9db57fdf563dcadaa373952261bab2dfe8fefa260639ffb59b57c49578
1ee8ef217d9e0c2924cc63dfd5cf4bdb7ee3e950faf7082d104b16df8ea0b7a6
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,246
OrdinalApprox.lfpApprox_mem_fixedPoints_of_eq
Mathlib/SetTheory/Ordinal/FixedPointApproximants.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact lfpApprox_mem_fixedPoint
α : Type u inst✝ : CompleteLattice α f : α →o α x : α a b c : Ordinal.{u} h_init : x ≤ f x h_ab : a < b h_ac : a ≤ c h_fab : lfpApprox f x a = lfpApprox f x b lfpApprox_mem_fixedPoint : lfpApprox f x a ∈ fixedPoints ⇑f ⊢ lfpApprox f x ?m.12529 ∈ fixedPoints ⇑f
((:c Membership.mem) (:fv _uniq.11201) ((:c Set) (:fv _uniq.11201)) ((:c Set.instMembership) (:fv _uniq.11201)) ((:c OrdinalApprox.lfpApprox) (:fv _uniq.11201) (:fv _uniq.11204) (:fv _uniq.11365) (:fv _uniq.11367) (:mv _uniq.12529)) ((:c Function.fixedPoints) (:fv _uniq.11201) ((:c DFunLike.coe) ((:c OrderHom) (:fv _un...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c CompleteLattice) (:fv _uniq.11201))"},{"name":"f","sexp":"((:c OrderHom) (:fv _uniq.11201) (:fv _uniq.11201) ((:c PartialOrder.toPreorder) (:fv _uniq.11201) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.11201) ((:c CompleteLattice.toCompleteSe...
(: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 :explicit 3 (:app (:c OrdinalApprox...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11201","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11204","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CompleteLattice) (:arg :...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":6095,"sourceStart":6090,"tag":"atom"},{"contextIndex":12,"semanticRole":"local","source":"lfpApprox_mem_fixedPoint","sourceEnd":6120,"sourceStart":6096,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact lfpApprox_mem_f...
[]
[{"source":"lfpApprox_mem_fixedPoint","source_end":6120,"source_start":6096,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11201","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11204","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":2,"interna...
19
16
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ea87e72af1caf9d4217bed233e901541e83fc7bdc0ee117837ac217eef401b8a
eae441924c8446bd52cadf14c67cedb6bc67fc22f407e6a3fc797dd9c5ca55fc
ff3569c8070d79418bc651ca286191f1f46ab7fd6a2d540f3a0dd3e2c5cb6b72
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,247
OrdinalApprox.lfpApprox_mem_fixedPoints_of_eq
Mathlib/SetTheory/Ordinal/FixedPointApproximants.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact h_ac
case h_ab α : Type u inst✝ : CompleteLattice α f : α →o α x : α a b c : Ordinal.{u} h_init : x ≤ f x h_ab : a < b h_ac : a ≤ c h_fab : lfpApprox f x a = lfpApprox f x b lfpApprox_mem_fixedPoint : lfpApprox f x a ∈ fixedPoints ⇑f ⊢ a ≤ c
((:c LE.le) (:c Ordinal) ((:c Preorder.toLE) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) (:fv _uniq.11877) (:fv _uniq.11879))
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c CompleteLattice) (:fv _uniq.11201))"},{"name":"f","sexp":"((:c OrderHom) (:fv _uniq.11201) (:fv _uniq.11201) ((:c PartialOrder.toPreorder) (:fv _uniq.11201) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.11201) ((:c CompleteLattice.toCompleteSe...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Ordinal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Ordinal))))) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:fv FV7)))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11201","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11204","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CompleteLattice) (:arg :...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":6131,"sourceStart":6126,"tag":"atom"},{"contextIndex":10,"semanticRole":"local","source":"h_ac","sourceEnd":6136,"sourceStart":6132,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact h_ac","sourceEnd":6136,"sourceStart...
[]
[{"source":"h_ac","source_end":6136,"source_start":6132,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11201","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11204","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":2,"interna...
19
21
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
cb76afa8dc91b5b43e6595ed129b30f18fa173d06c9ba3f7be46c6bd1128c228
d4b52ccb7b5f8adccb356877030f0b906874b306c0c71063cfef854959cd406d
fb8615d64eca734b8c56406fe7e1e568f0afabb66d4dd666b382d996052b9727
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,248
OrdinalApprox.lfpApprox_mem_fixedPoints_of_eq
Mathlib/SetTheory/Ordinal/FixedPointApproximants.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact lfpApprox_mem_fixedPoint
case h α : Type u inst✝ : CompleteLattice α f : α →o α x : α a b c : Ordinal.{u} h_init : x ≤ f x h_ab : a < b h_ac : a ≤ c h_fab : lfpApprox f x a = lfpApprox f x b lfpApprox_mem_fixedPoint : lfpApprox f x a ∈ fixedPoints ⇑f ⊢ lfpApprox f x a ∈ fixedPoints ⇑f
((:c Membership.mem) (:fv _uniq.11201) ((:c Set) (:fv _uniq.11201)) ((:c Set.instMembership) (:fv _uniq.11201)) ((:c OrdinalApprox.lfpApprox) (:fv _uniq.11201) (:fv _uniq.11204) (:fv _uniq.11365) (:fv _uniq.11367) (:fv _uniq.11877)) ((:c Function.fixedPoints) (:fv _uniq.11201) ((:c DFunLike.coe) ((:c OrderHom) (:fv _un...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c CompleteLattice) (:fv _uniq.11201))"},{"name":"f","sexp":"((:c OrderHom) (:fv _uniq.11201) (:fv _uniq.11201) ((:c PartialOrder.toPreorder) (:fv _uniq.11201) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.11201) ((:c CompleteLattice.toCompleteSe...
(: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 :explicit 3 (:app (:c OrdinalApprox...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11201","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11204","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CompleteLattice) (:arg :...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":6147,"sourceStart":6142,"tag":"atom"},{"contextIndex":12,"semanticRole":"local","source":"lfpApprox_mem_fixedPoint","sourceEnd":6172,"sourceStart":6148,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact lfpApprox_mem_f...
[]
[{"source":"lfpApprox_mem_fixedPoint","source_end":6172,"source_start":6148,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11201","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11204","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":2,"interna...
19
26
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f8c5097fccd102c5278482be486c6ef6ab5a0a3a95d73ad9f92f89ad2af12d4e
cae31d65ff7e862fe99c10b5457e68543e7c4ef531ffb9c0769d371b30fa8bcb
ff3569c8070d79418bc651ca286191f1f46ab7fd6a2d540f3a0dd3e2c5cb6b72
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,249
Substring.Valid.prevn
.lake/packages/batteries/Batteries/Data/String/Lemmas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
let ⟨l, m, r, h⟩ := h.validFor
m₂ m₁ : List Char x✝ : Substring h : x✝.Valid e : x✝.toString.data = m₁.reverse ++ m₂ ⊢ ∀ (n : Nat), x✝.prevn n { byteIdx := utf8Len m₁ } = { byteIdx := utf8Len (List.drop n m₁) }
m₂ m₁ : List Char x✝ : Substring h✝ : x✝.Valid e : x✝.toString.data = m₁.reverse ++ m₂ l m r : List Char h : ValidFor l m r x✝ ⊢ ∀ (n : Nat), x✝.prevn n { byteIdx := utf8Len m₁ } = { byteIdx := utf8Len (List.drop n m₁) }
(:forall n (:c Nat) ((:c Eq) (:c String.Pos) ((:c Substring.prevn) (:fv _uniq.173700) 0 ((:c String.Pos.mk) ((:c String.utf8Len) (:fv _uniq.173660)))) ((:c String.Pos.mk) ((:c String.utf8Len) ((:c List.drop) (:c Char) 0 (:fv _uniq.173660))))))
[{"name":"m₂","sexp":"((:c List) (:c Char))"},{"name":"m₁","sexp":"((:c List) (:c Char))"},{"name":"x✝","sexp":"(:c Substring)"},{"name":"h","sexp":"((:c Substring.Valid) (:fv _uniq.173700))"},{"name":"e","sexp":"((:c Eq) ((:c List) (:c Char)) ((:c String.data) ((:c Substring.toString) (:fv _uniq.173700))) ((:c HAppend...
(:forall n :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:c String.Pos)) (:arg :explicit 1 (:app (:c Substring.prevn) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 0) (:arg :explicit 2 (:app (:c String.Pos.mk) (:arg :explicit 0 (:app (:c String.utf8Len) (:arg :explicit 0 (:fv FV2)))))))) (:arg :explicit 2 (...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.173659","is_instance":false,"is_let":false,"name":"m₂","sexp":"(:app (:c List) (:arg :explicit 0 (:c Char)))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.173660","is_instance":false,"is_let":false,"name":"m₁","sexp":"(:app (:c...
{"children":[{"source":"let","sourceEnd":44118,"sourceStart":44115,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":44122,"sourceStart":44119,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"l","sourceEnd":44123,"sourceStart":44122,"tag":"identifier"},{"source":",","sour...
[]
[{"source":"h.validFor","source_end":44149,"source_start":44139,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.173659","is_instance":false,"is_let":false,"user_name":"m₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.173660","is_instance":false,"is_let":false,"user_name":"m₁"},{"binder_role":":explicit","context_index":3,"internal_name":...
199
4
exact
true
1
5
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8687253fe585e82f16dc077acd84b43fed8717df8126536b0458e2c47bfaa85d
f6b4b5f79cd5617fc7b135d44eb69d879d12b85a9f22dab33220af998e1039ab
c4a49969f9a49164bed59ac3215a4a63ece5d31aa7353ba2b8ab74698e084917
8419462ac8a93c48da88c463c7f40186fb569384dea0233ad6b6df0a29dd69e9
cat-searcher/leandojo-benchmark-4-random
test
2,250
Substring.Valid.prevn
.lake/packages/batteries/Batteries/Data/String/Lemmas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [h.toString] at e
m₂ m₁ : List Char x✝ : Substring h✝ : x✝.Valid e : x✝.toString.data = m₁.reverse ++ m₂ l m r : List Char h : ValidFor l m r x✝ ⊢ ∀ (n : Nat), x✝.prevn n { byteIdx := utf8Len m₁ } = { byteIdx := utf8Len (List.drop n m₁) }
m₂ m₁ : List Char x✝ : Substring h✝ : x✝.Valid l m r : List Char h : ValidFor l m r x✝ e : m = m₁.reverse ++ m₂ ⊢ ∀ (n : Nat), x✝.prevn n { byteIdx := utf8Len m₁ } = { byteIdx := utf8Len (List.drop n m₁) }
(:forall n (:c Nat) ((:c Eq) (:c String.Pos) ((:c Substring.prevn) (:fv _uniq.173700) 0 ((:c String.Pos.mk) ((:c String.utf8Len) (:fv _uniq.173660)))) ((:c String.Pos.mk) ((:c String.utf8Len) ((:c List.drop) (:c Char) 0 (:fv _uniq.173660))))))
[{"name":"m₂","sexp":"((:c List) (:c Char))"},{"name":"m₁","sexp":"((:c List) (:c Char))"},{"name":"x✝","sexp":"(:c Substring)"},{"name":"h✝","sexp":"((:c Substring.Valid) (:fv _uniq.173700))"},{"name":"e","sexp":"((:c Eq) ((:c List) (:c Char)) ((:c String.data) ((:c Substring.toString) (:fv _uniq.173700))) ((:c HAppen...
(:forall n :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:c String.Pos)) (:arg :explicit 1 (:app (:c Substring.prevn) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 0) (:arg :explicit 2 (:app (:c String.Pos.mk) (:arg :explicit 0 (:app (:c String.utf8Len) (:arg :explicit 0 (:fv FV2)))))))) (:arg :explicit 2 (...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.173659","is_instance":false,"is_let":false,"name":"m₂","sexp":"(:app (:c List) (:arg :explicit 0 (:c Char)))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.173660","is_instance":false,"is_let":false,"name":"m₁","sexp":"(:app (:c...
{"children":[{"source":"simp","sourceEnd":44158,"sourceStart":44154,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":44163,"sourceStart":44159,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":441...
[]
[{"source":"h.toString","source_end":44175,"source_start":44165,"syntax_kind":"ident"},{"source":"e","source_end":44181,"source_start":44180,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.173659","is_instance":false,"is_let":false,"user_name":"m₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.173660","is_instance":false,"is_let":false,"user_name":"m₁"},{"binder_role":":explicit","context_index":3,"internal_name":...
199
5
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
195fdd7561a7ea6941773e6af03bf57cfa7038cc0ccfe373173f88f20034058e
8419462ac8a93c48da88c463c7f40186fb569384dea0233ad6b6df0a29dd69e9
4476e7a5af0943d2d57b94c7f2fbe87e3a58460521bac5dcd57f61d0c1eba4dd
160c64eb9f8ecc2b46b9268681faa9b5319a519ebd588b93d698bc60ffaa4ce7
cat-searcher/leandojo-benchmark-4-random
test
2,251
Substring.Valid.prevn
.lake/packages/batteries/Batteries/Data/String/Lemmas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
subst e
m₂ m₁ : List Char x✝ : Substring h✝ : x✝.Valid l m r : List Char h : ValidFor l m r x✝ e : m = m₁.reverse ++ m₂ ⊢ ∀ (n : Nat), x✝.prevn n { byteIdx := utf8Len m₁ } = { byteIdx := utf8Len (List.drop n m₁) }
m₂ m₁ : List Char x✝ : Substring h✝ : x✝.Valid l r : List Char h : ValidFor l (m₁.reverse ++ m₂) r x✝ ⊢ ∀ (n : Nat), x✝.prevn n { byteIdx := utf8Len m₁ } = { byteIdx := utf8Len (List.drop n m₁) }
(:forall n (:c Nat) ((:c Eq) (:c String.Pos) ((:c Substring.prevn) (:fv _uniq.173700) 0 ((:c String.Pos.mk) ((:c String.utf8Len) (:fv _uniq.173660)))) ((:c String.Pos.mk) ((:c String.utf8Len) ((:c List.drop) (:c Char) 0 (:fv _uniq.173660))))))
[{"name":"m₂","sexp":"((:c List) (:c Char))"},{"name":"m₁","sexp":"((:c List) (:c Char))"},{"name":"x✝","sexp":"(:c Substring)"},{"name":"h✝","sexp":"((:c Substring.Valid) (:fv _uniq.173700))"},{"name":"l","sexp":"((:c List) (:c Char))"},{"name":"m","sexp":"((:c List) (:c Char))"},{"name":"r","sexp":"((:c List) (:c Cha...
(:forall n :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:c String.Pos)) (:arg :explicit 1 (:app (:c Substring.prevn) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 0) (:arg :explicit 2 (:app (:c String.Pos.mk) (:arg :explicit 0 (:app (:c String.utf8Len) (:arg :explicit 0 (:fv FV2)))))))) (:arg :explicit 2 (...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.173659","is_instance":false,"is_let":false,"name":"m₂","sexp":"(:app (:c List) (:arg :explicit 0 (:c Char)))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.173660","is_instance":false,"is_let":false,"name":"m₁","sexp":"(:app (:c...
{"children":[{"source":"subst","sourceEnd":44188,"sourceStart":44183,"tag":"atom"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"e","sourceEnd":44190,"sourceStart":44189,"tag":"identifier"}],"kind":"null","source":"e","sourceEnd":44190,"sourceStart":44189,"tag":"node"}],"kind":"Lean.Parser.Tactic.subs...
[]
[{"source":"e","source_end":44190,"source_start":44189,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.173659","is_instance":false,"is_let":false,"user_name":"m₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.173660","is_instance":false,"is_let":false,"user_name":"m₁"},{"binder_role":":explicit","context_index":3,"internal_name":...
199
7
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1fa367554978b2fd3e0866a7ae30663c1d2c82d10b8683ac220c449e14206a8e
160c64eb9f8ecc2b46b9268681faa9b5319a519ebd588b93d698bc60ffaa4ce7
9f87dce166543dae54bdf0d93e7bf67fad5e58e02009c37a2d8eb8b1f30b1ce7
449295677364e21ff82c423cf4ce6f16a38e089c297f22cf9670d85d9d063e07
cat-searcher/leandojo-benchmark-4-random
test
2,252
Substring.Valid.prevn
.lake/packages/batteries/Batteries/Data/String/Lemmas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [h.prevn]
m₂ m₁ : List Char x✝ : Substring h✝ : x✝.Valid l r : List Char h : ValidFor l (m₁.reverse ++ m₂) r x✝ ⊢ ∀ (n : Nat), x✝.prevn n { byteIdx := utf8Len m₁ } = { byteIdx := utf8Len (List.drop n m₁) }
(:forall n (:c Nat) ((:c Eq) (:c String.Pos) ((:c Substring.prevn) (:fv _uniq.173700) 0 ((:c String.Pos.mk) ((:c String.utf8Len) (:fv _uniq.173660)))) ((:c String.Pos.mk) ((:c String.utf8Len) ((:c List.drop) (:c Char) 0 (:fv _uniq.173660))))))
[{"name":"m₂","sexp":"((:c List) (:c Char))"},{"name":"m₁","sexp":"((:c List) (:c Char))"},{"name":"x✝","sexp":"(:c Substring)"},{"name":"h✝","sexp":"((:c Substring.Valid) (:fv _uniq.173700))"},{"name":"l","sexp":"((:c List) (:c Char))"},{"name":"r","sexp":"((:c List) (:c Char))"},{"name":"h","sexp":"((:c Substring.Val...
(:forall n :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:c String.Pos)) (:arg :explicit 1 (:app (:c Substring.prevn) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 0) (:arg :explicit 2 (:app (:c String.Pos.mk) (:arg :explicit 0 (:app (:c String.utf8Len) (:arg :explicit 0 (:fv FV2)))))))) (:arg :explicit 2 (...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.173659","is_instance":false,"is_let":false,"name":"m₂","sexp":"(:app (:c List) (:arg :explicit 0 (:c Char)))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.173660","is_instance":false,"is_let":false,"name":"m₁","sexp":"(:app (:c...
{"children":[{"source":"simp","sourceEnd":44196,"sourceStart":44192,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":44198,"sourceStart":44197,"tag":"a...
[]
[{"source":"h.prevn","source_end":44205,"source_start":44198,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.173659","is_instance":false,"is_let":false,"user_name":"m₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.173660","is_instance":false,"is_let":false,"user_name":"m₁"},{"binder_role":":explicit","context_index":3,"internal_name":...
199
9
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f755b00951bc196ca53254cace00a76962534472e1ce2fc0dd752f503c1bd64d
449295677364e21ff82c423cf4ce6f16a38e089c297f22cf9670d85d9d063e07
7872f6d55c93b76ca9a90da06889e382bab9ed99e508d27540eef5bd1e6a2113
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,253
Multiset.count_sub
Mathlib/Data/Multiset/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
revert s
α : Type u_1 β : Type v γ : Type u_2 inst✝ : DecidableEq α s✝ : Multiset α a : α s t : Multiset α ⊢ count a (s - t) = count a s - count a t
α : Type u_1 β : Type v γ : Type u_2 inst✝ : DecidableEq α s : Multiset α a : α t : Multiset α ⊢ ∀ (s : Multiset α), count a (s - t) = count a s - count a t
((:c Eq) (:c Nat) ((:c Multiset.count) (:fv _uniq.260224) (:fv _uniq.260236) (:fv _uniq.260394) ((:c HSub.hSub) ((:c Multiset) (:fv _uniq.260224)) ((:c Multiset) (:fv _uniq.260224)) ((:c Multiset) (:fv _uniq.260224)) ((:c instHSub) ((:c Multiset) (:fv _uniq.260224)) ((:c Multiset.instSub) (:fv _uniq.260224) (:fv _uniq....
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.260224))"},{"name":"s✝","sexp":"((:c Multiset) (:fv _uniq.260224))"},{"name":"a","sexp":"(:fv _uniq.260224)"},{"name":"s","sexp":"((:c Multiset) (:f...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Multiset.count) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c DecidableEq) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV6)) (:arg :explicit 3 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:app (:c Multise...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260224","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260226","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"revert","sourceEnd":105748,"sourceStart":105742,"tag":"atom"},{"children":[{"contextIndex":7,"semanticRole":"local","source":"s","sourceEnd":105750,"sourceStart":105749,"tag":"identifier"}],"kind":"null","source":"s","sourceEnd":105750,"sourceStart":105749,"tag":"node"}],"kind":"Lean.Parser.Tact...
[]
[{"source":"s","source_end":105750,"source_start":105749,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260224","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260226","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
911
4
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d2247c42bd26f28fa4858b87a7a22c759f7308c1a6e01a775bd63802258fb82b
8ac67eea7cbb22f3ce8dd2beae4d633579e3ea4e184eefe9072d530bfce481d4
b37b47f9fe8783b250609ec127a37bd5d88eda143550c28c2142e63c7a954722
21eb5abf61d8af9d63667c991488214e60bcf66c3af62d5403e6555ff9a72532
cat-searcher/leandojo-benchmark-4-random
test
2,254
Multiset.count_sub
Mathlib/Data/Multiset/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine <a>Multiset.induction_on</a> t (by simp) fun b t IH s => ?_
α : Type u_1 β : Type v γ : Type u_2 inst✝ : DecidableEq α s : Multiset α a : α t : Multiset α ⊢ ∀ (s : Multiset α), count a (s - t) = count a s - count a t
α : Type u_1 β : Type v γ : Type u_2 inst✝ : DecidableEq α s✝ : Multiset α a : α t✝ : Multiset α b : α t : Multiset α IH : ∀ (s : Multiset α), count a (s - t) = count a s - count a t s : Multiset α ⊢ count a (s - b ::ₘ t) = count a s - count a (b ::ₘ t)
(:forall s ((:c Multiset) (:fv _uniq.260224)) ((:c Eq) (:c Nat) ((:c Multiset.count) (:fv _uniq.260224) (:fv _uniq.260236) (:fv _uniq.260394) ((:c HSub.hSub) ((:c Multiset) (:fv _uniq.260224)) ((:c Multiset) (:fv _uniq.260224)) ((:c Multiset) (:fv _uniq.260224)) ((:c instHSub) ((:c Multiset) (:fv _uniq.260224)) ((:c Mu...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.260224))"},{"name":"s","sexp":"((:c Multiset) (:fv _uniq.260224))"},{"name":"a","sexp":"(:fv _uniq.260224)"},{"name":"t","sexp":"((:c Multiset) (:fv...
(:forall s :explicit (:app (:c Multiset) (:arg :explicit 0 (:fv FV0))) (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Multiset.count) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c DecidableEq) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV6)) (:arg :e...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260224","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260226","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"refine","sourceEnd":105758,"sourceStart":105752,"tag":"atom"},{"children":[{"name":"Multiset.induction_on","semanticRole":"global","source":"Multiset.induction_on","sourceEnd":105780,"sourceStart":105759,"tag":"identifier"},{"children":[{"contextIndex":7,"semanticRole":"local","source":"t","sour...
[]
[{"source":"Multiset.induction_on t (by simp) fun b t IH s => ?_","source_end":105811,"source_start":105759,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260224","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260226","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
911
6
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8e6436e62c29ea71350943de1154b5337aa172ba10b9e9d69de594e29b52a443
21eb5abf61d8af9d63667c991488214e60bcf66c3af62d5403e6555ff9a72532
d7b681d6316c4afa2c7c492db44247659fb8d39f2b14e642ff98e8d9f54bb89f
11f9638dd382887502a71e60382f5741462a590d24dc8570d0eb8578bbc3e951
cat-searcher/leandojo-benchmark-4-random
test
2,255
Multiset.count_sub
Mathlib/Data/Multiset/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Multiset.sub_cons</a>, IH]
α : Type u_1 β : Type v γ : Type u_2 inst✝ : DecidableEq α s✝ : Multiset α a : α t✝ : Multiset α b : α t : Multiset α IH : ∀ (s : Multiset α), count a (s - t) = count a s - count a t s : Multiset α ⊢ count a (s - b ::ₘ t) = count a s - count a (b ::ₘ t)
α : Type u_1 β : Type v γ : Type u_2 inst✝ : DecidableEq α s✝ : Multiset α a : α t✝ : Multiset α b : α t : Multiset α IH : ∀ (s : Multiset α), count a (s - t) = count a s - count a t s : Multiset α ⊢ count a (s.erase b) - count a t = count a s - count a (b ::ₘ t)
((:c Eq) (:c Nat) ((:c Multiset.count) (:fv _uniq.260224) (:fv _uniq.260236) (:fv _uniq.260394) ((:c HSub.hSub) ((:c Multiset) (:fv _uniq.260224)) ((:c Multiset) (:fv _uniq.260224)) ((:c Multiset) (:fv _uniq.260224)) ((:c instHSub) ((:c Multiset) (:fv _uniq.260224)) ((:c Multiset.instSub) (:fv _uniq.260224) (:fv _uniq....
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.260224))"},{"name":"s✝","sexp":"((:c Multiset) (:fv _uniq.260224))"},{"name":"a","sexp":"(:fv _uniq.260224)"},{"name":"t✝","sexp":"((:c Multiset) (:...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Multiset.count) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c DecidableEq) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV6)) (:arg :explicit 3 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:app (:c Multise...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260224","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260226","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"rw","sourceEnd":105816,"sourceStart":105814,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":105818,"sourceStart":105817,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Multiset.sub...
[]
[{"source":"sub_cons","source_end":105826,"source_start":105818,"syntax_kind":"ident"},{"source":"IH","source_end":105830,"source_start":105828,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260224","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260226","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
911
12
exact
true
1
11
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5b676d12fd2d34b51ac4ef5a934a8de48e891dc65ce343e98b0116867befa25a
11f9638dd382887502a71e60382f5741462a590d24dc8570d0eb8578bbc3e951
053e5db8302d7c08b4d9721c69fcb8aa440dc91e3619e2e9f553dcdfc2b5f66f
c439ec44937de62c08abe1f3c2ae1e70dd663d018f13e3231be49c1b8e9e36cb
cat-searcher/leandojo-benchmark-4-random
test
2,256
Multiset.count_sub
Mathlib/Data/Multiset/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rcases <a>Decidable.eq_or_ne</a> a b with rfl | ab
α : Type u_1 β : Type v γ : Type u_2 inst✝ : DecidableEq α s✝ : Multiset α a : α t✝ : Multiset α b : α t : Multiset α IH : ∀ (s : Multiset α), count a (s - t) = count a s - count a t s : Multiset α ⊢ count a (s.erase b) - count a t = count a s - count a (b ::ₘ t)
case inl α : Type u_1 β : Type v γ : Type u_2 inst✝ : DecidableEq α s✝ : Multiset α a : α t✝ t : Multiset α IH : ∀ (s : Multiset α), count a (s - t) = count a s - count a t s : Multiset α ⊢ count a (s.erase a) - count a t = count a s - count a (a ::ₘ t) case inr α : Type u_1 β : Type v γ : Type u_2 inst✝ : DecidableEq ...
((:c Eq) (:c Nat) ((:c HSub.hSub) (:c Nat) (:c Nat) (:c Nat) ((:c instHSub) (:c Nat) (:c instSubNat)) ((:c Multiset.count) (:fv _uniq.260224) (:fv _uniq.260236) (:fv _uniq.260394) ((:c Multiset.erase) (:fv _uniq.260224) (:fv _uniq.260236) (:fv _uniq.260438) (:fv _uniq.260428))) ((:c Multiset.count) (:fv _uniq.260224) (...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.260224))"},{"name":"s✝","sexp":"((:c Multiset) (:fv _uniq.260224))"},{"name":"a","sexp":"(:fv _uniq.260224)"},{"name":"t✝","sexp":"((:c Multiset) (:...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HSub.hSub) (: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 HSub) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260224","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260226","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"rcases","sourceEnd":105840,"sourceStart":105834,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Decidable.eq_or_ne","semanticRole":"global","source":"Decidable.eq_or_ne","sourceEnd":105859,"sourceStart":105841,"tag":"identifier...
[]
[{"source":"Decidable.eq_or_ne a b","source_end":105863,"source_start":105841,"syntax_kind":"Lean.Parser.Term.app"},{"source":"rfl | ab","source_end":105877,"source_start":105869,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260224","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260226","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
911
16
exact
true
1
11
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
50f30c4124ec059f4173b01ee830ccd14b8259f51fb0d308c98ae232cd8a2944
c439ec44937de62c08abe1f3c2ae1e70dd663d018f13e3231be49c1b8e9e36cb
38752e89bbecd6074605fed937354ddb8049614196973417e48c4f1369cd57d2
045efc1f1a45211c0e010b1651f5034821e6a714396664ca222d1e7017b1863a
cat-searcher/leandojo-benchmark-4-random
test
2,257
Multiset.count_sub
Mathlib/Data/Multiset/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
α : Type u_1 β : Type v γ : Type u_2 inst✝ : DecidableEq α s : Multiset α a : α t : Multiset α ⊢ ∀ (s : Multiset α), count a (s - 0) = count a s - count a 0
(:forall s ((:c Multiset) (:fv _uniq.260224)) ((:c Eq) (:c Nat) ((:c Multiset.count) (:fv _uniq.260224) (:fv _uniq.260236) (:fv _uniq.260394) ((:c HSub.hSub) ((:c Multiset) (:fv _uniq.260224)) ((:c Multiset) (:fv _uniq.260224)) ((:c Multiset) (:fv _uniq.260224)) ((:c instHSub) ((:c Multiset) (:fv _uniq.260224)) ((:c Mu...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.260224))"},{"name":"s","sexp":"((:c Multiset) (:fv _uniq.260224))"},{"name":"a","sexp":"(:fv _uniq.260224)"},{"name":"t","sexp":"((:c Multiset) (:fv...
(:forall s :explicit (:app (:c Multiset) (:arg :explicit 0 (:fv FV0))) (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Multiset.count) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c DecidableEq) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV6)) (:arg :e...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260224","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260226","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":105791,"sourceStart":105787,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","so...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260224","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260226","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
911
9
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
bc95c04396d901ef67ae30035cb24e61f878716098bbeb9567febdeb34879216
48f02af489fccfade58912a0a99c9722547d2d68a048391f566e8bd5a63c3d9d
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,258
Multiset.count_sub
Mathlib/Data/Multiset/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Multiset.count_erase_self</a>, <a>Multiset.count_cons_self</a>, <a>Nat.sub_sub</a>, <a>add_comm</a>]
case inl α : Type u_1 β : Type v γ : Type u_2 inst✝ : DecidableEq α s✝ : Multiset α a : α t✝ t : Multiset α IH : ∀ (s : Multiset α), count a (s - t) = count a s - count a t s : Multiset α ⊢ count a (s.erase a) - count a t = count a s - count a (a ::ₘ t)
((:c Eq) (:c Nat) ((:c HSub.hSub) (:c Nat) (:c Nat) (:c Nat) ((:c instHSub) (:c Nat) (:c instSubNat)) ((:c Multiset.count) (:fv _uniq.260224) (:fv _uniq.260236) (:fv _uniq.260394) ((:c Multiset.erase) (:fv _uniq.260224) (:fv _uniq.260236) (:fv _uniq.260438) (:fv _uniq.260394))) ((:c Multiset.count) (:fv _uniq.260224) (...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.260224))"},{"name":"s✝","sexp":"((:c Multiset) (:fv _uniq.260224))"},{"name":"a","sexp":"(:fv _uniq.260224)"},{"name":"t✝","sexp":"((:c Multiset) (:...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HSub.hSub) (: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 HSub) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260224","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260226","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":105885,"sourceStart":105883,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":105887,"sourceStart":105886,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source"...
[]
[{"source":"count_erase_self","source_end":105903,"source_start":105887,"syntax_kind":"ident"},{"source":"count_cons_self","source_end":105920,"source_start":105905,"syntax_kind":"ident"},{"source":"Nat.sub_sub","source_end":105933,"source_start":105922,"syntax_kind":"ident"},{"source":"add_comm","source_end":105943,"s...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260224","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260226","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
911
19
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
fe1c1d10e013f6553ba96283ff17f30e069e9f3e6e955e34bf620bf6ebfd6c5f
ce8d42a3af04e424e4153ca03c3fd47afd4f01ee405424f0f26adf2404a00761
bf67a35c2ae7df7976422df05a8fe49813a4a122a2ea3106dd2bdaeaeb21834c
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,259
Multiset.count_sub
Mathlib/Data/Multiset/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Multiset.count_erase_of_ne</a> ab, <a>Multiset.count_cons_of_ne</a> ab]
case inr α : Type u_1 β : Type v γ : Type u_2 inst✝ : DecidableEq α s✝ : Multiset α a : α t✝ : Multiset α b : α t : Multiset α IH : ∀ (s : Multiset α), count a (s - t) = count a s - count a t s : Multiset α ab : a ≠ b ⊢ count a (s.erase b) - count a t = count a s - count a (b ::ₘ t)
((:c Eq) (:c Nat) ((:c HSub.hSub) (:c Nat) (:c Nat) (:c Nat) ((:c instHSub) (:c Nat) (:c instSubNat)) ((:c Multiset.count) (:fv _uniq.260224) (:fv _uniq.260236) (:fv _uniq.260394) ((:c Multiset.erase) (:fv _uniq.260224) (:fv _uniq.260236) (:fv _uniq.260438) (:fv _uniq.260428))) ((:c Multiset.count) (:fv _uniq.260224) (...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.260224))"},{"name":"s✝","sexp":"((:c Multiset) (:fv _uniq.260224))"},{"name":"a","sexp":"(:fv _uniq.260224)"},{"name":"t✝","sexp":"((:c Multiset) (:...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HSub.hSub) (: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 HSub) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260224","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260226","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":105952,"sourceStart":105950,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":105954,"sourceStart":105953,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source"...
[]
[{"source":"count_erase_of_ne ab","source_end":105974,"source_start":105954,"syntax_kind":"Lean.Parser.Term.app"},{"source":"count_cons_of_ne ab","source_end":105995,"source_start":105976,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260224","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260226","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
911
29
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e96c1a354445d456a3827277bf2ef9fd561f4908d46767d29cacb77cd74df2a0
d8686fd4442e8a67718b98972f57535c7297e371ed1430904603a1904facb545
81398d105273e029aa8d3a13bd49f3ead64bc803ba1d73e0885f99b7f85faab6
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,260
List.prod_map_erase
Mathlib/Algebra/BigOperators/Group/List.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain rfl | ⟨ne, h⟩ := <a>List.eq_or_ne_mem_of_mem</a> h
ι : Type u_1 α : Type u_2 β : Type u_3 M : Type u_4 N : Type u_5 P : Type u_6 G : Type u_7 inst✝¹ : CommMonoid M a✝ : M l✝ l₁ l₂ : List M inst✝ : DecidableEq α f : α → M a b : α l : List α h : a ∈ b :: l ⊢ f a * (map f ((b :: l).erase a)).prod = (map f (b :: l)).prod
case inl ι : Type u_1 α : Type u_2 β : Type u_3 M : Type u_4 N : Type u_5 P : Type u_6 G : Type u_7 inst✝¹ : CommMonoid M a✝ : M l✝ l₁ l₂ : List M inst✝ : DecidableEq α f : α → M a : α l : List α h : a ∈ a :: l ⊢ f a * (map f ((a :: l).erase a)).prod = (map f (a :: l)).prod case inr.intro ι : Type u_1 α : Type u_2 β : ...
((:c Eq) (:fv _uniq.35942) ((:c HMul.hMul) (:fv _uniq.35942) (:fv _uniq.35942) (:fv _uniq.35942) ((:c instHMul) (:fv _uniq.35942) ((:c MulOneClass.toMul) (:fv _uniq.35942) ((:c Monoid.toMulOneClass) (:fv _uniq.35942) ((:c CommMonoid.toMonoid) (:fv _uniq.35942) (:fv _uniq.35954))))) ((:fv _uniq.36378) (:fv _uniq.36379))...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"N","sexp":"(:sort (+ u_5 1))"},{"name":"P","sexp":"(:sort (+ u_6 1))"},{"name":"G","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝¹","sexp":"((:c CommMonoi...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35933","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35936","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"obtain","sourceEnd":16814,"sourceStart":16808,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":16818,"sourceStart":16815,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl","sourceEnd":16818,"sou...
[]
[{"source":"List.eq_or_ne_mem_of_mem h","source_end":16862,"source_start":16836,"syntax_kind":"Lean.Parser.Term.app"},{"source":"rfl | ⟨ne, h⟩","source_end":16832,"source_start":16815,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35933","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35936","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
132
4
exact
true
1
18
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9a2fcc9e6213edf4ff7339dcfdf0666cae2fcbbfd09efeb5f317ab16ed8aae5b
043cf0661a1e8543c4908185ad3c79542d0acebb16c9230a627d3234c5bb6268
108a3868df6ad292dc81964295a3356d1a850b69048b3a38c427e520f2d1d723
f8721a4372160c4c976a16f11cf03911952b123c2d75e685b98bdc081976f01a
cat-searcher/leandojo-benchmark-4-random
test
2,261
List.prod_map_erase
Mathlib/Algebra/BigOperators/Group/List.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>List.map</a>, <a>List.erase_cons_head</a>, <a>List.prod_cons</a>]
case inl ι : Type u_1 α : Type u_2 β : Type u_3 M : Type u_4 N : Type u_5 P : Type u_6 G : Type u_7 inst✝¹ : CommMonoid M a✝ : M l✝ l₁ l₂ : List M inst✝ : DecidableEq α f : α → M a : α l : List α h : a ∈ a :: l ⊢ f a * (map f ((a :: l).erase a)).prod = (map f (a :: l)).prod
((:c Eq) (:fv _uniq.35942) ((:c HMul.hMul) (:fv _uniq.35942) (:fv _uniq.35942) (:fv _uniq.35942) ((:c instHMul) (:fv _uniq.35942) ((:c MulOneClass.toMul) (:fv _uniq.35942) ((:c Monoid.toMulOneClass) (:fv _uniq.35942) ((:c CommMonoid.toMonoid) (:fv _uniq.35942) (:fv _uniq.35954))))) ((:fv _uniq.36378) (:fv _uniq.36379))...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"N","sexp":"(:sort (+ u_5 1))"},{"name":"P","sexp":"(:sort (+ u_6 1))"},{"name":"G","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝¹","sexp":"((:c CommMonoi...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35933","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35936","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":16874,"sourceStart":16870,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":16879,"sourceStart":16875,"tag":"atom"}],"kind"...
[]
[{"source":"map","source_end":16884,"source_start":16881,"syntax_kind":"ident"},{"source":"erase_cons_head","source_end":16901,"source_start":16886,"syntax_kind":"ident"},{"source":"prod_cons","source_end":16912,"source_start":16903,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35933","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35936","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
132
7
exact
true
1
17
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
aca401b47ce3dde95f40184ea13e8e262c1a3a40225ab2beab98ffaf43884e88
dbfad5dd9f9b9832f45ca887d6818b504b9e9072548f536dac76abfc28c4ec05
8a64d7174b609852433e0ad2d971bc8f5704c57b2e74503ace5a40c9973a5642
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,262
List.prod_map_erase
Mathlib/Algebra/BigOperators/Group/List.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>List.map</a>, <a>List.erase_cons_tail</a> _ (<a>not_beq_of_ne</a> ne.symm), <a>List.prod_cons</a>, prod_map_erase _ h, <a>mul_left_comm</a> (f a) (f b)]
case inr.intro ι : Type u_1 α : Type u_2 β : Type u_3 M : Type u_4 N : Type u_5 P : Type u_6 G : Type u_7 inst✝¹ : CommMonoid M a✝ : M l✝ l₁ l₂ : List M inst✝ : DecidableEq α f : α → M a b : α l : List α h✝ : a ∈ b :: l ne : a ≠ b h : a ∈ l ⊢ f a * (map f ((b :: l).erase a)).prod = (map f (b :: l)).prod
((:c Eq) (:fv _uniq.35942) ((:c HMul.hMul) (:fv _uniq.35942) (:fv _uniq.35942) (:fv _uniq.35942) ((:c instHMul) (:fv _uniq.35942) ((:c MulOneClass.toMul) (:fv _uniq.35942) ((:c Monoid.toMulOneClass) (:fv _uniq.35942) ((:c CommMonoid.toMonoid) (:fv _uniq.35942) (:fv _uniq.35954))))) ((:fv _uniq.36378) (:fv _uniq.36379))...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"N","sexp":"(:sort (+ u_5 1))"},{"name":"P","sexp":"(:sort (+ u_6 1))"},{"name":"G","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝¹","sexp":"((:c CommMonoi...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35933","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35936","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":16925,"sourceStart":16921,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":16930,"sourceStart":16926,"tag":"atom"}],"kind"...
[]
[{"source":"map","source_end":16935,"source_start":16932,"syntax_kind":"ident"},{"source":"erase_cons_tail _ (not_beq_of_ne ne.symm)","source_end":16978,"source_start":16937,"syntax_kind":"Lean.Parser.Term.app"},{"source":"prod_cons","source_end":16989,"source_start":16980,"syntax_kind":"ident"},{"source":"prod_map_era...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35933","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35936","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
132
12
exact
true
1
20
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d119e5d1c311a4f744abe63347c4b611cbb724dd2059638fc30980a796e56ae8
51332cedb7e2e49de1da9c04fa51d21365388b617ba8d882b9cc094863262f28
3fae1135e70bd748fc21648af3a77bbc0c78d54fb8d8a2294ff5d5a3f44625d9
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,263
SzemerediRegularity.initialBound_le_bound
Mathlib/Combinatorics/SimpleGraph/Regularity/Bound.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
positivity
α : Type u_1 inst✝¹ : DecidableEq α inst✝ : Fintype α P : Finpartition univ u : Finset α ε : ℝ l : ℕ ⊢ 0 < 16 ^ stepBound^[⌊4 / ε ^ 5⌋₊] (initialBound ε l)
((:c LT.lt) (:c Nat) (:c instLTNat) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))) ((: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 16) ((:c instOfNatNat) (:lit 16))) ((:c Nat.iterate) (:c...
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(:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Nat)) (:arg :explici...
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{"children":[{"children":[{"children":[{"children":[{"source":"positivity","sourceEnd":10008,"sourceStart":9998,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":10008,"sourceStart":9998,"tag":"node"}],"kind":"null","source":"positivity","sourceEnd":10008,"sourceStart":9998,...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90839","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.90846","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":...
62
2
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
91da790a23c7542b5c1f5651cbe86d4561e7209f7196014736f9c11335b8a904
7d19ae31860a52f700d4ab9dd048d89842b5896124cc7597fd8f93a020c49fb9
bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
2,264
Polynomial.coeff_eq_zero_of_lt_natTrailingDegree
Mathlib/Algebra/Polynomial/Degree/TrailingDegree.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>Polynomial.coeff_eq_zero_of_lt_trailingDegree</a>
R : Type u S : Type v a b : R n✝ m : ℕ inst✝ : Semiring R p✝ q r p : R[X] n : ℕ h : n < p.natTrailingDegree ⊢ p.coeff n = 0
case h R : Type u S : Type v a b : R n✝ m : ℕ inst✝ : Semiring R p✝ q r p : R[X] n : ℕ h : n < p.natTrailingDegree ⊢ ↑n < p.trailingDegree
((:c Eq) (:fv _uniq.25261) ((:c Polynomial.coeff) (:fv _uniq.25261) (:fv _uniq.25274) (:fv _uniq.25537) (:fv _uniq.25538)) ((:c OfNat.ofNat) (:fv _uniq.25261) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.25261) ((:c MonoidWithZero.toZero) (:fv _uniq.25261) ((:c Semiring.toMonoidWithZero) (:fv _uniq.25261) (:fv _uniq.25274))...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.25261)"},{"name":"b","sexp":"(:fv _uniq.25261)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.25261))"},{"name":"p✝","sexp":"((:c Polynomial) (:...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Polynomial.coeff) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV11)) (:arg :explicit 3 (:fv FV12)))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25261","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25263","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"apply","sourceEnd":11455,"sourceStart":11450,"tag":"atom"},{"name":"Polynomial.coeff_eq_zero_of_lt_trailingDegree","semanticRole":"global","source":"coeff_eq_zero_of_lt_trailingDegree","sourceEnd":11490,"sourceStart":11456,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply co...
[]
[{"source":"coeff_eq_zero_of_lt_trailingDegree","source_end":11490,"source_start":11456,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25261","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25263","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
91
4
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
64f3ae8c7d8d10bc94831f0e5665e81978cf248b0fede8c7aeb29aeb1fd142de
8e9a0e9c851e28007548e4637621c9f08ae1e3ea3d84f27534b2ef9afe1696b8
fe22172a6896988d41e766949518c196a87ba0213e112020606258fd713ac397
fa57262047caf1098313d92d60e80142a4974c97a128b8483a542061c424cb0b
cat-searcher/leandojo-benchmark-4-random
test
2,265
Polynomial.coeff_eq_zero_of_lt_natTrailingDegree
Mathlib/Algebra/Polynomial/Degree/TrailingDegree.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
by_cases hp : p = 0
case h R : Type u S : Type v a b : R n✝ m : ℕ inst✝ : Semiring R p✝ q r p : R[X] n : ℕ h : n < p.natTrailingDegree ⊢ ↑n < p.trailingDegree
case pos R : Type u S : Type v a b : R n✝ m : ℕ inst✝ : Semiring R p✝ q r p : R[X] n : ℕ h : n < p.natTrailingDegree hp : p = 0 ⊢ ↑n < p.trailingDegree case neg R : Type u S : Type v a b : R n✝ m : ℕ inst✝ : Semiring R p✝ q r p : R[X] n : ℕ h : n < p.natTrailingDegree hp : ¬p = 0 ⊢ ↑n < p.trailingDegree
((:c LT.lt) (:c ENat) ((:c Preorder.toLT) (:c ENat) ((:c PartialOrder.toPreorder) (:c ENat) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENat) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENat) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENat) ((:c CompleteLinearOrder.toCompletelyDistribLattic...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.25261)"},{"name":"b","sexp":"(:fv _uniq.25261)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.25261))"},{"name":"p✝","sexp":"((:c Polynomial) (:...
(:app (:c LT.lt) (:arg :implicit-type 0 (:c ENat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENat))))) (:arg :explicit 2 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c ENat)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c ENat))))) (:arg :explicit 2 (:fv FV12)))) (:ar...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25261","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25263","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"by_cases","sourceEnd":11501,"sourceStart":11493,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hp","sourceEnd":11504,"sourceStart":11502,"tag":"identifier"},{"source":":","sourceEnd":11506,"sourceStart":11505,"tag":"atom"}],"kind":"null","source":"hp :","sourceEnd":11506,"so...
[]
[{"source":"p = 0","source_end":11512,"source_start":11507,"syntax_kind":"«term_=_»"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25261","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25263","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
91
5
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
56328b3ad5c3bf55af015f1fc22af09a376d577c060aee2997dd2a1ec1449bdd
fa57262047caf1098313d92d60e80142a4974c97a128b8483a542061c424cb0b
0360ef17e452ddf4c3ea41fb2a418d04798c080760edfba35c28026c92f77893
190328885fe52872de38faae40400d19f84837401e61c94cce6598322164c786