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iCogLabs-Dev
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Mathlib-Normalized-Sexpr

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cat-searcher/leandojo-benchmark-4-random
test
1,353
Finset.gcd_union
Mathlib/Algebra/GCDMonoid/Finset.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Finset.empty_union</a>, <a>Finset.gcd_empty</a>, <a>gcd_zero_left</a>, <a>Finset.normalize_gcd</a>]
ι : Type u_1 α : Type u_2 β : Type u_3 γ : Type u_4 inst✝² : CancelCommMonoidWithZero α inst✝¹ : NormalizedGCDMonoid α s s₁ s₂ : Finset β f : β → α inst✝ : DecidableEq β ⊢ (∅ ∪ s₂).gcd f = GCDMonoid.gcd (∅.gcd f) (s₂.gcd f)
((:c Eq) (:fv _uniq.12367) ((:c Finset.gcd) (:fv _uniq.12367) (:fv _uniq.12370) (:fv _uniq.12376) (:fv _uniq.12385) ((:c Union.union) ((:c Finset) (:fv _uniq.12370)) ((:c Finset.instUnion) (:fv _uniq.12370) (:fv _uniq.12532)) ((:c EmptyCollection.emptyCollection) ((:c Finset) (:fv _uniq.12370)) ((:c Finset.instEmptyCol...
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(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Finset.gcd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c CancelCommMonoidWithZero) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c NormalizedGCDMonoid) (...
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[]
[{"source":"empty_union","source_end":6076,"source_start":6065,"syntax_kind":"ident"},{"source":"gcd_empty","source_end":6087,"source_start":6078,"syntax_kind":"ident"},{"source":"gcd_zero_left","source_end":6102,"source_start":6089,"syntax_kind":"ident"},{"source":"normalize_gcd","source_end":6117,"source_start":6104,...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12364","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12367","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
64
2
exact
true
1
11
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2f3f998e52a551f887ef33198f787908a8865057e2a57bd4a8d7cd3f2c6d48d4
09c0b3c7114262ef4b8ddcc62d4e201f9b02db5dce656ef3d0d6dfa51085768d
14e1a7f4336d88bc23cdefde6a50eaabda7051bd9ea19157be63b4a8a05a55dc
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,354
Finset.gcd_union
Mathlib/Algebra/GCDMonoid/Finset.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Finset.insert_union</a>, <a>Finset.gcd_insert</a>, <a>Finset.gcd_insert</a>, ih, <a>gcd_assoc</a>]
ι : Type u_1 α : Type u_2 β : Type u_3 γ : Type u_4 inst✝² : CancelCommMonoidWithZero α inst✝¹ : NormalizedGCDMonoid α s✝ s₁ s₂ : Finset β f : β → α inst✝ : DecidableEq β a : β s : Finset β x✝ : a ∉ s ih : (s ∪ s₂).gcd f = GCDMonoid.gcd (s.gcd f) (s₂.gcd f) ⊢ (insert a s ∪ s₂).gcd f = GCDMonoid.gcd ((insert a s).gcd f)...
((:c Eq) (:fv _uniq.12367) ((:c Finset.gcd) (:fv _uniq.12367) (:fv _uniq.12370) (:fv _uniq.12376) (:fv _uniq.12385) ((:c Union.union) ((:c Finset) (:fv _uniq.12370)) ((:c Finset.instUnion) (:fv _uniq.12370) (:fv _uniq.12532)) ((:c Insert.insert) (:fv _uniq.12370) ((:c Finset) (:fv _uniq.12370)) ((:c Finset.instInsert) ...
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(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Finset.gcd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c CancelCommMonoidWithZero) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c NormalizedGCDMonoid) (...
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[]
[{"source":"insert_union","source_end":6160,"source_start":6148,"syntax_kind":"ident"},{"source":"gcd_insert","source_end":6172,"source_start":6162,"syntax_kind":"ident"},{"source":"gcd_insert","source_end":6184,"source_start":6174,"syntax_kind":"ident"},{"source":"ih","source_end":6188,"source_start":6186,"syntax_kind...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12364","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12367","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
64
12
exact
true
1
15
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d5517bc80757d6908a5a5241033cbe90209e24933f97867eab4578b6c17310d7
31a3f176d4a7dac6d82d5cd5d5991c768261cbaad8ac666527b42d7d5f4bd720
ce54155655cabb42a2fea89a20116d6dd01f4b717fd79dcbd22b77031276c4f3
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,355
Real.sqrt_sq
Mathlib/Data/Real/Sqrt.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>sq</a>, <a>Real.sqrt_mul_self</a> h]
x y : ℝ h : 0 ≤ x ⊢ √(x ^ 2) = x
((:c Eq) (:c Real) ((:c Real.sqrt) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNatPow) (:c Real) (:c Real.instMonoid))) (:fv _uniq.28807) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2))))) (:fv _uniq.28807))
[{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"h","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.28807))"}]
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Real.sqrt) (:arg :explicit 0 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c Real)) (:arg :explicit ...
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[]
[{"source":"sq","source_end":7680,"source_start":7678,"syntax_kind":"ident"},{"source":"sqrt_mul_self h","source_end":7697,"source_start":7682,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.28807","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28809","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":explicit","context_index":3,"internal_name":"_un...
80
2
exact
true
1
3
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
cfe3b7c61a525cc96a77df121d5aad2df59aa4ec8382962cb0a2197be0dd6982
6111be3b91be1b5fe5d3cf78d8c374dfa3347f745ba5da225f03425bbd92fb5d
6fdb35fcbc2e46445425672f0177e5cbfa2f3eaa4f9eb072a5fd26fe2424d083
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,356
Finset.insert_sdiff_cancel
Mathlib/Data/Finset/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Finset.insert_sdiff_of_not_mem</a> _ ha, <a>Finset.sdiff_self</a>, <a>LawfulSingleton.insert_emptyc_eq</a>]
α : Type u_1 β : Type u_2 γ : Type u_3 inst✝ : DecidableEq α s t u v : Finset α a b : α ha : a ∉ s ⊢ insert a s \ s = {a}
((:c Eq) ((:c Finset) (:fv _uniq.145289)) ((:c SDiff.sdiff) ((:c Finset) (:fv _uniq.145289)) ((:c Finset.instSDiff) (:fv _uniq.145289) (:fv _uniq.145302)) ((:c Insert.insert) (:fv _uniq.145289) ((:c Finset) (:fv _uniq.145289)) ((:c Finset.instInsert) (:fv _uniq.145289) (:fv _uniq.145302)) (:fv _uniq.145318) (:fv _uniq....
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.145289))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.145289))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.145289))"},{"name":"u","sexp":"((:c ...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c SDiff.sdiff) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c SDiff) (:arg :explicit 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0))))))) (:...
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{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":90783,"sourceStart":90781,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":90785,"sourceStart":90784,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",...
[]
[{"source":"insert_sdiff_of_not_mem _ ha","source_end":90813,"source_start":90785,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Finset.sdiff_self","source_end":90832,"source_start":90815,"syntax_kind":"ident"},{"source":"insert_emptyc_eq","source_end":90850,"source_start":90834,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.145289","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.145292","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
866
2
exact
true
1
11
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f2aab12ef8153f3167158ec6077d9fcdbc10b6b1722837d0588c48624552fa6e
dfda0a5d25c1eb1bcee19dd212cef95bb917a19e158cb5a7e7895fc6482d17a0
d2b49500301baf9a07d52d764c0bb477222da6f47025494b600c50d8600c966e
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,357
ContMDiff.codRestrict_sphere
Mathlib/Geometry/Manifold/Instances/Sphere.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>contMDiff_iff_target</a>]
E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCorners I M n : ...
E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCorners I M n : ...
((:c ContMDiff) (:c Real) ((:c DenselyNormedField.toNontriviallyNormedField) (:c Real) (:c Real.denselyNormedField)) (:fv _uniq.530932) (:fv _uniq.530935) (:fv _uniq.531044) (:fv _uniq.531047) (:fv _uniq.531050) (:fv _uniq.531092) (:fv _uniq.531095) (:fv _uniq.531098) (:fv _uniq.531110) ((:c EuclideanSpace) (:c Real) (...
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(:app (:c ContMDiff) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:c Real))))) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV3))))) (:arg :instance 4 (:instance-of (:app ...
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[]
[{"source":"contMDiff_iff_target","source_end":22595,"source_start":22575,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":instance-implicit","context_index...
82
4
exact
true
1
19
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4a2acbf4f953b5324cf52a3297408313509e8268ca34895f8cfe90c1447ac9f4
02c0be7f9870cefea2d8893ad3a9dc1cb3aac480099697c0e5978940a336a8c4
f98b52963b5d89774ce3c1fdc41e601e4e8ee7dd9527c58e669ef9efd0282ade
3ac35254b9e00d6bc3a331da44dde12cca832e7429b72c34a3124fcc764e41d0
cat-searcher/leandojo-benchmark-4-random
test
1,358
ContMDiff.codRestrict_sphere
Mathlib/Geometry/Manifold/Instances/Sphere.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨<a>continuous_induced_rng</a>.2 hf.continuous, ?_⟩
E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCorners I M n : ...
E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCorners I M n : ...
((:c And) ((:c Continuous) (:fv _uniq.531095) ((:c Set.Elem) (:fv _uniq.530913) ((:c Metric.sphere) (:fv _uniq.530913) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:fv _uniq.530913) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.530913) (:fv _uniq.530916))) ((:c OfNat.ofNat) (:fv _uniq.530913) (:lit ...
[{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.530913))"},{"name":"inst✝⁷","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.530913) (:c Real.RCLike) (:fv _uniq.530916))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c NormedAddCommGroup) ...
(:app (:c And) (:arg :explicit 0 (:app (:c Continuous) (:arg :implicit-type 0 (:fv FV9)) (:arg :implicit-type 1 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Metric.sphere) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NormedAddCommGroup) (...
{"children":[{"source":"refine","sourceEnd":22605,"sourceStart":22599,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":22609,"sourceStart":22606,"tag":"atom"},{"children":[{"children":[{"children":[{"name":"continuous_induced_rng","semanticRole":"global","source":"continuous_induced_rng","sourceEnd":22631,"sourceSt...
[]
[{"source":"⟨continuous_induced_rng.2 hf.continuous, ?_⟩","source_end":22654,"source_start":22606,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":instance-implicit","context_index...
82
7
exact
true
1
19
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
fdf35e6c00c7ec08650c64dc7af1b2bf85d76a6e285fdfd7c56b20e6da2467e7
3ac35254b9e00d6bc3a331da44dde12cca832e7429b72c34a3124fcc764e41d0
24babd915bc53512bc028502e38573a7e56cb92b9bb490ee70fc129cb8e65bfc
71e647698acfb6b178a66b6b13ae8d72dfabf3a678b87da34e61f8dd9219820f
cat-searcher/leandojo-benchmark-4-random
test
1,359
ContMDiff.codRestrict_sphere
Mathlib/Geometry/Manifold/Instances/Sphere.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro v
E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCorners I M n : ...
E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCorners I M n : ...
(:forall y ((:c Set.Elem) (:fv _uniq.530913) ((:c Metric.sphere) (:fv _uniq.530913) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:fv _uniq.530913) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.530913) (:fv _uniq.530916))) ((:c OfNat.ofNat) (:fv _uniq.530913) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.5...
[{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.530913))"},{"name":"inst✝⁷","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.530913) (:c Real.RCLike) (:fv _uniq.530916))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c NormedAddCommGroup) ...
(:forall y :explicit (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Metric.sphere) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV0)) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NormedAddCommGroup) (...
{"children":[{"source":"intro","sourceEnd":22662,"sourceStart":22657,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"v","sourceEnd":22664,"sourceStart":22663,"tag":"identifier"}],"kind":"null","source":"v","sourceEnd":22664,"sourceStart":22663,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source...
[{"role":"fresh_name","source":"v","source_end":22664,"source_start":22663,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":instance-implicit","context_index...
82
8
exact
true
1
19
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
391af4bd0e19227dcd3d6a47e936004839851e65581380f93ceb4d5dc497aa21
71e647698acfb6b178a66b6b13ae8d72dfabf3a678b87da34e61f8dd9219820f
3596acaa6acfe4c01b9cc7dd779de0e8423ddd9e6be047a7bfe7145f056d17d0
071f308198640a0cc244af76e18952d44f80956e2aa3f6f53a1fef0e93a2cb5e
cat-searcher/leandojo-benchmark-4-random
test
1,361
ContMDiff.codRestrict_sphere
Mathlib/Geometry/Manifold/Instances/Sphere.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have h : <a>ContDiffOn</a> ℝ ⊤ _ <a>Set.univ</a> := U.contDiff.contDiffOn
E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCorners I M n : ...
E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCorners I M n : ...
((:c ContMDiffOn) (:c Real) ((:c DenselyNormedField.toNontriviallyNormedField) (:c Real) (:c Real.denselyNormedField)) (:fv _uniq.530932) (:fv _uniq.530935) (:fv _uniq.531044) (:fv _uniq.531047) (:fv _uniq.531050) (:fv _uniq.531092) (:fv _uniq.531095) (:fv _uniq.531098) (:fv _uniq.531110) ((:c EuclideanSpace) (:c Real)...
[{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.530913))"},{"name":"inst✝⁷","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.530913) (:c Real.RCLike) (:fv _uniq.530916))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c NormedAddCommGroup) ...
(:app (:c ContMDiffOn) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:c Real))))) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV3))))) (:arg :instance 4 (:instance-of (:ap...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NormedAddCommGroup) (...
{"children":[{"source":"have","sourceEnd":22882,"sourceStart":22878,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":22884,"sourceStart":22883,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":22884,"sourceStart":22883,"tag":"node"...
[]
[{"source":"ContDiffOn ℝ ⊤ _ Set.univ","source_end":22916,"source_start":22887,"syntax_kind":"Lean.Parser.Term.app"},{"source":"U.contDiff.contDiffOn","source_end":22941,"source_start":22920,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":instance-implicit","context_index...
82
10
exact
true
1
21
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
76755420d310a31bffcb9b24d245f47d6bd9bf0fa75582b1a6314c6b352460ec
6de4e972d32d5417396c92da7069efe50f3ce2a5b2637f4c934a3eec6539401b
9bb035d9b428099c5118213a546479688b0d8d450bbe4456a3c76250f0fc1ed4
b1645fcb4276c117058f7d861fc686b527f86f2376c1149d93fab263feb616a8
cat-searcher/leandojo-benchmark-4-random
test
1,362
ContMDiff.codRestrict_sphere
Mathlib/Geometry/Manifold/Instances/Sphere.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have H₁ := (h.comp' <a>contDiffOn_stereoToFun</a>).<a>ContDiffOn.contMDiffOn</a>
E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCorners I M n : ...
E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCorners I M n : ...
((:c ContMDiffOn) (:c Real) ((:c DenselyNormedField.toNontriviallyNormedField) (:c Real) (:c Real.denselyNormedField)) (:fv _uniq.530932) (:fv _uniq.530935) (:fv _uniq.531044) (:fv _uniq.531047) (:fv _uniq.531050) (:fv _uniq.531092) (:fv _uniq.531095) (:fv _uniq.531098) (:fv _uniq.531110) ((:c EuclideanSpace) (:c Real)...
[{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.530913))"},{"name":"inst✝⁷","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.530913) (:c Real.RCLike) (:fv _uniq.530916))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c NormedAddCommGroup) ...
(:app (:c ContMDiffOn) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:c Real))))) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV3))))) (:arg :instance 4 (:instance-of (:ap...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NormedAddCommGroup) (...
{"children":[{"source":"have","sourceEnd":22948,"sourceStart":22944,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"H₁","sourceEnd":22953,"sourceStart":22949,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"H₁","sourceEnd":22953,"sourceStart":22949,"tag":"nod...
[]
[{"source":"(h.comp' contDiffOn_stereoToFun).contMDiffOn","source_end":23001,"source_start":22957,"syntax_kind":"Lean.Parser.Term.proj"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":instance-implicit","context_index...
82
11
exact
true
1
22
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
766c716f7ac1ef10da3682c73103a34bc9a2a9792b2e89f64b6188285447ed4c
b1645fcb4276c117058f7d861fc686b527f86f2376c1149d93fab263feb616a8
a9427993a98f1d1b57b3c54b78ebcdd088279c9361d9e0c9da2f63942e2d28c5
172d536398432d8680528345d87c2c3f40c13cdd8868cb07a8b38f334a9d7516
cat-searcher/leandojo-benchmark-4-random
test
1,363
ContMDiff.codRestrict_sphere
Mathlib/Geometry/Manifold/Instances/Sphere.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have H₂ : <a>ContMDiffOn</a> _ _ _ _ <a>Set.univ</a> := hf.contMDiffOn
E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCorners I M n : ...
E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCorners I M n : ...
((:c ContMDiffOn) (:c Real) ((:c DenselyNormedField.toNontriviallyNormedField) (:c Real) (:c Real.denselyNormedField)) (:fv _uniq.530932) (:fv _uniq.530935) (:fv _uniq.531044) (:fv _uniq.531047) (:fv _uniq.531050) (:fv _uniq.531092) (:fv _uniq.531095) (:fv _uniq.531098) (:fv _uniq.531110) ((:c EuclideanSpace) (:c Real)...
[{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.530913))"},{"name":"inst✝⁷","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.530913) (:c Real.RCLike) (:fv _uniq.530916))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c NormedAddCommGroup) ...
(:app (:c ContMDiffOn) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:c Real))))) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV3))))) (:arg :instance 4 (:instance-of (:ap...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NormedAddCommGroup) (...
{"children":[{"source":"have","sourceEnd":23008,"sourceStart":23004,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"H₂","sourceEnd":23013,"sourceStart":23009,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"H₂","sourceEnd":23013,"sourceStart":23009,"tag":"nod...
[]
[{"source":"ContMDiffOn _ _ _ _ Set.univ","source_end":23044,"source_start":23016,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hf.contMDiffOn","source_end":23062,"source_start":23048,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":instance-implicit","context_index...
82
12
exact
true
1
23
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a9606e29ae628f79dff7786b4b042e02cdf36b752f1732fc1c9c25c8903d24bf
172d536398432d8680528345d87c2c3f40c13cdd8868cb07a8b38f334a9d7516
9a9f329f3f03fde524f652d838f0b687fce847d35e1772a60135daa2d03d1252
63a49b0448f3f2d4f1fdbbb816755ba2407294ae039d5447e83b5fd27ee8218d
cat-searcher/leandojo-benchmark-4-random
test
1,364
ContMDiff.codRestrict_sphere
Mathlib/Geometry/Manifold/Instances/Sphere.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
convert (H₁.of_le <a>le_top</a>).<a>ContMDiffOn.comp'</a> H₂ using 1
E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCorners I M n : ...
case h.e'_23 E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCor...
((:c ContMDiffOn) (:c Real) ((:c DenselyNormedField.toNontriviallyNormedField) (:c Real) (:c Real.denselyNormedField)) (:fv _uniq.530932) (:fv _uniq.530935) (:fv _uniq.531044) (:fv _uniq.531047) (:fv _uniq.531050) (:fv _uniq.531092) (:fv _uniq.531095) (:fv _uniq.531098) (:fv _uniq.531110) ((:c EuclideanSpace) (:c Real)...
[{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.530913))"},{"name":"inst✝⁷","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.530913) (:c Real.RCLike) (:fv _uniq.530916))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c NormedAddCommGroup) ...
(:app (:c ContMDiffOn) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:c Real))))) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV3))))) (:arg :instance 4 (:instance-of (:ap...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NormedAddCommGroup) (...
{"children":[{"source":"convert","sourceEnd":23072,"sourceStart":23065,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":23074,"sourceStart":23073,"tag":"atom"},{"children":[{"sourc...
[]
[{"source":"(H₁.of_le le_top).comp' H₂","source_end":23103,"source_start":23073,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":instance-implicit","context_index...
82
13
exact
true
1
24
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
236140fb113812ed12507f9f9f96cab123220b955930a7d32a44a0572b8de841
63a49b0448f3f2d4f1fdbbb816755ba2407294ae039d5447e83b5fd27ee8218d
50949465812b837cca21e2218c5db9ba454a4058e1126fadd62b3fe7631421fe
b26b6c4a2718061be77016657f2edeeeac9cd32e1592b891ee02e1e14a7ba549
cat-searcher/leandojo-benchmark-4-random
test
1,365
ContMDiff.codRestrict_sphere
Mathlib/Geometry/Manifold/Instances/Sphere.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
ext x
case h.e'_23 E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCor...
case h.e'_23.h E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithC...
((:c Eq) ((:c Set) (:fv _uniq.531095)) ((:c Set.preimage) (:fv _uniq.531095) ((:c Set.Elem) (:fv _uniq.530913) ((:c Metric.sphere) (:fv _uniq.530913) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:fv _uniq.530913) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.530913) (:fv _uniq.530916))) ((:c OfNat.o...
[{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.530913))"},{"name":"inst✝⁷","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.530913) (:c Real.RCLike) (:fv _uniq.530916))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c NormedAddCommGroup) ...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV9)))) (:arg :explicit 1 (:app (:c Set.preimage) (:arg :implicit-type 0 (:fv FV9)) (:arg :implicit-type 1 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Metric.sphere) (:arg :implicit-type 0 (:fv FV0)) (:arg :...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NormedAddCommGroup) (...
{"children":[{"source":"ext","sourceEnd":23117,"sourceStart":23114,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":23119,"sourceStart":23118,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":23119,"sourceStart":23118,"tag...
[{"role":"fresh_name","source":"x","source_end":23119,"source_start":23118,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":instance-implicit","context_index...
82
14
exact
true
1
24
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a1f8775329342b2070e16fe2cd4c544353cb168e68ebb141c95870bfb0781ef0
b26b6c4a2718061be77016657f2edeeeac9cd32e1592b891ee02e1e14a7ba549
ee522618587c4a8062e9541e92fad69d5c6e7dbdf5366e9d82c63ebe3c1e08c5
5d79e067a9d3b513ffae21f6944c2ddab30db22c585d31b29a470ec481f1cdc0
cat-searcher/leandojo-benchmark-4-random
test
1,366
ContMDiff.codRestrict_sphere
Mathlib/Geometry/Manifold/Instances/Sphere.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have hfxv : f x = -↑v ↔ ⟪f x, -↑v⟫_ℝ = 1 := by have hfx : ‖f x‖ = 1 := by simpa using hf' x rw [<a>inner_eq_one_iff_of_norm_one</a> hfx] exact <a>norm_eq_of_mem_sphere</a> (-v)
case h.e'_23.h E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithC...
case h.e'_23.h E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithC...
((:c Iff) ((:c Membership.mem) (:fv _uniq.531095) ((:c Set) (:fv _uniq.531095)) ((:c Set.instMembership) (:fv _uniq.531095)) (:fv _uniq.553619) ((:c Set.preimage) (:fv _uniq.531095) ((:c Set.Elem) (:fv _uniq.530913) ((:c Metric.sphere) (:fv _uniq.530913) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:fv _uniq.53091...
[{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.530913))"},{"name":"inst✝⁷","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.530913) (:c Real.RCLike) (:fv _uniq.530916))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c NormedAddCommGroup) ...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV9)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV9)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV9)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV9))))))) (:arg :e...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NormedAddCommGroup) (...
{"children":[{"source":"have","sourceEnd":23126,"sourceStart":23122,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hfxv","sourceEnd":23131,"sourceStart":23127,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hfxv","sourceEnd":23131,"sourceStart":23127,"tag":...
[]
[{"source":"f x = -↑v ↔ ⟪f x, -↑v⟫_ℝ = 1","source_end":23174,"source_start":23134,"syntax_kind":"«term_↔_»"},{"source":"‖f x‖ = 1","source_end":23209,"source_start":23196,"syntax_kind":"«term_=_»"},{"source":"hf' x","source_end":23233,"source_start":23228,"syntax_kind":"Lean.Parser.Term.app"},{"source":"inner_eq_one_if...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":instance-implicit","context_index...
82
15
exact
true
1
25
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3d3f25d3f4d6ea3d8b1ec4d1c108411010ea31fd58f08d48b2c479a447ae2fb4
5d79e067a9d3b513ffae21f6944c2ddab30db22c585d31b29a470ec481f1cdc0
a8d7a6a01cd259ddf117a903aae1d1eeb7f13428861041ce8f069a6049354e7b
167081168f5e5dfee38250f642fd95edeae88145c5c7a0ccebc7cf3b2fd1e51d
cat-searcher/leandojo-benchmark-4-random
test
1,367
ContMDiff.codRestrict_sphere
Mathlib/Geometry/Manifold/Instances/Sphere.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
dsimp [<a>chartAt</a>, <a>Set.codRestrict</a>, <a>ChartedSpace.chartAt</a>]
case h.e'_23.h E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithC...
case h.e'_23.h E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithC...
((:c Iff) ((:c Membership.mem) (:fv _uniq.531095) ((:c Set) (:fv _uniq.531095)) ((:c Set.instMembership) (:fv _uniq.531095)) (:fv _uniq.553619) ((:c Set.preimage) (:fv _uniq.531095) ((:c Set.Elem) (:fv _uniq.530913) ((:c Metric.sphere) (:fv _uniq.530913) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:fv _uniq.53091...
[{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.530913))"},{"name":"inst✝⁷","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.530913) (:c Real.RCLike) (:fv _uniq.530916))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c NormedAddCommGroup) ...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV9)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV9)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV9)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV9))))))) (:arg :e...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NormedAddCommGroup) (...
{"children":[{"source":"dsimp","sourceEnd":23351,"sourceStart":23346,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":23353,"sourceStart":23352,"tag":"...
[]
[{"source":"chartAt","source_end":23360,"source_start":23353,"syntax_kind":"ident"},{"source":"Set.codRestrict","source_end":23377,"source_start":23362,"syntax_kind":"ident"},{"source":"ChartedSpace.chartAt","source_end":23399,"source_start":23379,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":instance-implicit","context_index...
82
24
exact
true
1
26
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e5f3a285ddb62caad4964eb8190b1b1c79e28396e38df1cb5d9e352b00170713
167081168f5e5dfee38250f642fd95edeae88145c5c7a0ccebc7cf3b2fd1e51d
52427bf4af9e464d636cdd53c043c9ab5380c5f1c0d3de4f1a3fd8a6a2a45ae4
9700d9674e6f532ced2704acfa95411e8a9be6eb365e157a9e2774cb810ea39e
cat-searcher/leandojo-benchmark-4-random
test
1,368
ContMDiff.codRestrict_sphere
Mathlib/Geometry/Manifold/Instances/Sphere.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>not_iff_not</a>, <a>Subtype.ext_iff</a>, hfxv, <a>real_inner_comm</a>]
case h.e'_23.h E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithC...
((:c Iff) ((:c Membership.mem) (:fv _uniq.531095) ((:c Set) (:fv _uniq.531095)) ((:c Set.instMembership) (:fv _uniq.531095)) (:fv _uniq.553619) ((:c Inter.inter) ((:c Set) (:fv _uniq.531095)) ((:c Set.instInter) (:fv _uniq.531095)) ((:c Set.preimage) (:fv _uniq.531095) ((:c Set.Elem) (:fv _uniq.530913) ((:c Metric.sphe...
[{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.530913))"},{"name":"inst✝⁷","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.530913) (:c Real.RCLike) (:fv _uniq.530916))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c NormedAddCommGroup) ...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV9)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV9)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV9)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV9))))))) (:arg :e...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NormedAddCommGroup) (...
{"children":[{"source":"simp","sourceEnd":23407,"sourceStart":23403,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":23409,"sourceStart":23408,"tag":"a...
[]
[{"source":"not_iff_not","source_end":23420,"source_start":23409,"syntax_kind":"ident"},{"source":"Subtype.ext_iff","source_end":23437,"source_start":23422,"syntax_kind":"ident"},{"source":"hfxv","source_end":23443,"source_start":23439,"syntax_kind":"ident"},{"source":"real_inner_comm","source_end":23460,"source_start"...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":instance-implicit","context_index...
82
25
exact
true
1
26
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d45ab49648258bfaf3ce8c43425d69064d9efab44dcffe02522b1c3275aac2cd
9700d9674e6f532ced2704acfa95411e8a9be6eb365e157a9e2774cb810ea39e
478caf8ea41a2336fa8a8bfebd497c2e75a231cb2bba0364e92cac933732bb1c
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,369
ContMDiff.codRestrict_sphere
Mathlib/Geometry/Manifold/Instances/Sphere.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have hfx : ‖f x‖ = 1 := by simpa using hf' x
E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCorners I M n : ...
E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCorners I M n : ...
((:c Iff) ((:c Eq) (:fv _uniq.530913) ((:fv _uniq.533860) (:fv _uniq.553619)) ((:c Neg.neg) (:fv _uniq.530913) ((:c NegZeroClass.toNeg) (:fv _uniq.530913) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.530913) ((:c SubtractionMonoid.toSubNegZeroMonoid) (:fv _uniq.530913) ((:c SubtractionCommMonoid.toSubtractionMonoid...
[{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.530913))"},{"name":"inst✝⁷","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.530913) (:c Real.RCLike) (:fv _uniq.530916))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c NormedAddCommGroup) ...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:fv FV17) (:arg :explicit 0 (:fv FV25)))) (:arg :explicit 2 (:app (:c Neg.neg) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:ap...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NormedAddCommGroup) (...
{"children":[{"source":"have","sourceEnd":23189,"sourceStart":23185,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hfx","sourceEnd":23193,"sourceStart":23190,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hfx","sourceEnd":23193,"sourceStart":23190,"tag":"n...
[]
[{"source":"‖f x‖ = 1","source_end":23209,"source_start":23196,"syntax_kind":"«term_=_»"},{"source":"hf' x","source_end":23233,"source_start":23228,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":instance-implicit","context_index...
82
17
exact
true
1
25
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5384ddf1fc4de4356383346154a286e28e34e25cee268c1f360d58e832022525
036d180ea6854c72fc423229d6f5fa9d50bdc76d98e7ad5196732a5612d8cf99
6ceba1dcfdef652a4b17904965f095f95b452d338c55f7b481df2f15353b2ebb
b1aaa8ed4c107a9fa5a804b471035511d1ab9c24318f3225ccf24efe8b29c3e6
cat-searcher/leandojo-benchmark-4-random
test
1,370
ContMDiff.codRestrict_sphere
Mathlib/Geometry/Manifold/Instances/Sphere.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>inner_eq_one_iff_of_norm_one</a> hfx]
E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCorners I M n : ...
E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCorners I M n : ...
((:c Iff) ((:c Eq) (:fv _uniq.530913) ((:fv _uniq.533860) (:fv _uniq.553619)) ((:c Neg.neg) (:fv _uniq.530913) ((:c NegZeroClass.toNeg) (:fv _uniq.530913) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.530913) ((:c SubtractionMonoid.toSubNegZeroMonoid) (:fv _uniq.530913) ((:c SubtractionCommMonoid.toSubtractionMonoid...
[{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.530913))"},{"name":"inst✝⁷","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.530913) (:c Real.RCLike) (:fv _uniq.530916))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c NormedAddCommGroup) ...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:fv FV17) (:arg :explicit 0 (:fv FV25)))) (:arg :explicit 2 (:app (:c Neg.neg) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:ap...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NormedAddCommGroup) (...
{"children":[{"source":"rw","sourceEnd":23240,"sourceStart":23238,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":23242,"sourceStart":23241,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"inn...
[]
[{"source":"inner_eq_one_iff_of_norm_one hfx","source_end":23274,"source_start":23242,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":instance-implicit","context_index...
82
20
exact
true
1
26
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2737cd3266d7a13fc0f881591f2194bd389019143adc61d52b9b30227c952a30
b1aaa8ed4c107a9fa5a804b471035511d1ab9c24318f3225ccf24efe8b29c3e6
a22c6b233da86a09a462f9beac9ec1f202710e400ccdf5c16653597dff88d047
2e020dc36ab1a3001e340390855e4d4dcadbada516b7399425fcbdac89ba0d5d
cat-searcher/leandojo-benchmark-4-random
test
1,371
ContMDiff.codRestrict_sphere
Mathlib/Geometry/Manifold/Instances/Sphere.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>norm_eq_of_mem_sphere</a> (-v)
E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCorners I M n : ...
((:c Eq) (:c Real) ((:c Norm.norm) (:fv _uniq.530913) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.530913) (:fv _uniq.530916)) ((:c Neg.neg) (:fv _uniq.530913) ((:c NegZeroClass.toNeg) (:fv _uniq.530913) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.530913) ((:c SubtractionMonoid.toSubNegZeroMonoid) (:fv _uniq.530913)...
[{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.530913))"},{"name":"inst✝⁷","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.530913) (:c Real.RCLike) (:fv _uniq.530916))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c NormedAddCommGroup) ...
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Neg.neg) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Neg) (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NormedAddCommGroup) (...
{"children":[{"source":"exact","sourceEnd":23285,"sourceStart":23280,"tag":"atom"},{"children":[{"name":"norm_eq_of_mem_sphere","semanticRole":"global","source":"norm_eq_of_mem_sphere","sourceEnd":23307,"sourceStart":23286,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":23309,"sourceStart":23308...
[]
[{"source":"norm_eq_of_mem_sphere (-v)\n -- Porting note: unfold more","source_end":23312,"source_start":23286,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":instance-implicit","context_index...
82
23
exact
true
1
26
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5d7bc436723f8dcb870971092d958cbbd8c62cfd8aa81cf8a038adec5362c3be
2e020dc36ab1a3001e340390855e4d4dcadbada516b7399425fcbdac89ba0d5d
3f29cacb57053ea88d858d96c4d9a50a7f78bcbfdcc294ad41d1a1a8c6aebf3d
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,372
ContMDiff.codRestrict_sphere
Mathlib/Geometry/Manifold/Instances/Sphere.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simpa using hf' x
E : Type u_1 inst✝⁸ : NormedAddCommGroup E inst✝⁷ : InnerProductSpace ℝ E F : Type u_2 inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F H : Type u_3 inst✝⁴ : TopologicalSpace H I : ModelWithCorners ℝ F H M : Type u_4 inst✝³ : TopologicalSpace M inst✝² : ChartedSpace H M inst✝¹ : SmoothManifoldWithCorners I M n : ...
((:c Eq) (:c Real) ((:c Norm.norm) (:fv _uniq.530913) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.530913) (:fv _uniq.530916)) ((:fv _uniq.533860) (:fv _uniq.553619))) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))))
[{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.530913))"},{"name":"inst✝⁷","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.530913) (:c Real.RCLike) (:fv _uniq.530916))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁶","sexp":"((:c NormedAddCommGroup) ...
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:fv FV17) (:arg :explicit 0 (:fv FV25)))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :im...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NormedAddCommGroup) (...
{"children":[{"source":"simpa","sourceEnd":23221,"sourceStart":23216,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"ch...
[]
[{"source":"hf' x","source_end":23233,"source_start":23228,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.530913","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.530916","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":instance-implicit","context_index...
82
19
exact
true
1
25
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a34c763e9c69124d5a6889bcd1664ae2e32561e123eda42359f2c2e1cf65199b
9d15b387f5542009d36d12f3342143aca15f034f9cca7f3ce1eb58c88ffa1d1b
f66bb84f1cb8eef64e85d128d7eaf019b890256925d1de12b5c7905d9191b8f0
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,375
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
set L : <a>Sublattice</a> α := ⟨<a>latticeClosure</a> (s ∪ t), <a>isSublattice_latticeClosure</a>.1, <a>isSublattice_latticeClosure</a>.2⟩
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α ⊢ (∑ a ∈ s, f₁ a) * ∑ a ∈ t, f₂ a ≤ (∑ a...
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
((:c LE.le) (:fv _uniq.193645) ((:c Preorder.toLE) (:fv _uniq.193645) ((:c PartialOrder.toPreorder) (:fv _uniq.193645) ((:c StrictOrderedSemiring.toPartialOrder) (:fv _uniq.193645) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.193645) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.1...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _un...
(: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 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"set","sourceEnd":15119,"sourceStart":15116,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"semanticRole":"scoped_local","source":"L","sourceEnd":15121,"sourceStart":15120,"tag":"identifier"},{"children":[{"source":":","sourceEnd":15123,"sourceStart":15122,"tag...
[]
[{"source":"Sublattice α","source_end":15137,"source_start":15124,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨latticeClosure (s ∪ t), isSublattice_latticeClosure.1,\n isSublattice_latticeClosure.2⟩","source_end":15237,"source_start":15141,"syntax_kind":"Lean.Parser.Term.anonymousCtor"},{"source":"L","source_en...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal...
23
7
exact
true
1
20
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
083ddba896409e70eecbc3e563b15e18a8e6f3d6f0942ceaeeb5cce28d897a31
7fb7d08fe12a898c4f9d1d32a05013e4388261031ffb094e429f327b07cc8318
0656e524c8607e20a089d0d81e145a02e97ac26d85436538a89c6de59a680054
37e74256fba3eff0dbefc61068209d19401777c7835a0147c62c1d259ca7ffb2
cat-searcher/leandojo-benchmark-4-random
test
1,376
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have : <a>Finite</a> L := (s.finite_toSet.union t.finite_toSet).latticeClosure.to_subtype
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
((:c LE.le) (:fv _uniq.193645) ((:c Preorder.toLE) (:fv _uniq.193645) ((:c PartialOrder.toPreorder) (:fv _uniq.193645) ((:c StrictOrderedSemiring.toPartialOrder) (:fv _uniq.193645) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.193645) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.1...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _un...
(: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 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"have","sourceEnd":15244,"sourceStart":15240,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":15245,"sourceStart":15245,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":15245,"sourceStart":15245,"tag":"node"}],"kind":"Lean.Parser.Term.hav...
[]
[{"source":"Finite L","source_end":15255,"source_start":15247,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(s.finite_toSet.union t.finite_toSet).latticeClosure.to_subtype","source_end":15322,"source_start":15259,"syntax_kind":"Lean.Parser.Term.proj"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal...
23
8
exact
true
1
21
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f2ec7e442cf3d5760644e71a206fac55e1e3a43e97a60b5ee8571b8ea6e29212
37e74256fba3eff0dbefc61068209d19401777c7835a0147c62c1d259ca7ffb2
7c497914f8d9a2c2e24b41928bb6b7f2222b6f2a880458afa79cb9830c3b4e06
def6148014912921cfbfe2ac0326903a4bdfdbb19f1751f3fbef529b73ada988
cat-searcher/leandojo-benchmark-4-random
test
1,377
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
set s' : <a>Finset</a> L := s.preimage (↑) Subtype.coe_injective.injOn
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
((:c LE.le) (:fv _uniq.193645) ((:c Preorder.toLE) (:fv _uniq.193645) ((:c PartialOrder.toPreorder) (:fv _uniq.193645) ((:c StrictOrderedSemiring.toPartialOrder) (:fv _uniq.193645) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.193645) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.1...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _un...
(: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 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"set","sourceEnd":15328,"sourceStart":15325,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"semanticRole":"scoped_local","source":"s'","sourceEnd":15331,"sourceStart":15329,"tag":"identifier"},{"children":[{"source":":","sourceEnd":15333,"sourceStart":15332,"ta...
[]
[{"source":"Finset L","source_end":15342,"source_start":15334,"syntax_kind":"Lean.Parser.Term.app"},{"source":"s.preimage (↑) Subtype.coe_injective.injOn","source_end":15390,"source_start":15346,"syntax_kind":"Lean.Parser.Term.app"},{"source":"s'","source_end":15331,"source_start":15329,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal...
23
9
exact
true
1
22
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f5a31d6862742483df6f43beebb267f17e7ee962f498e920f66487b5a67bb03f
def6148014912921cfbfe2ac0326903a4bdfdbb19f1751f3fbef529b73ada988
c7394f220d22c7c68cbf31fc6ddd5615096a22e3158cac19a6c308dbbfe96c5e
053a6ab1835e138e648ac5b6616cc71d360e56bcbc9ccec21ea5c0a568dcb76b
cat-searcher/leandojo-benchmark-4-random
test
1,378
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
set t' : <a>Finset</a> L := t.preimage (↑) Subtype.coe_injective.injOn
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
((:c LE.le) (:fv _uniq.193645) ((:c Preorder.toLE) (:fv _uniq.193645) ((:c PartialOrder.toPreorder) (:fv _uniq.193645) ((:c StrictOrderedSemiring.toPartialOrder) (:fv _uniq.193645) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.193645) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.1...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _un...
(: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 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"set","sourceEnd":15396,"sourceStart":15393,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"semanticRole":"scoped_local","source":"t'","sourceEnd":15399,"sourceStart":15397,"tag":"identifier"},{"children":[{"source":":","sourceEnd":15401,"sourceStart":15400,"ta...
[]
[{"source":"Finset L","source_end":15410,"source_start":15402,"syntax_kind":"Lean.Parser.Term.app"},{"source":"t.preimage (↑) Subtype.coe_injective.injOn","source_end":15458,"source_start":15414,"syntax_kind":"Lean.Parser.Term.app"},{"source":"t'","source_end":15399,"source_start":15397,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal...
23
10
exact
true
1
23
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
24a8895cffcb003f5afaa2dac88e4b13b7ad6f507af6dc08ecac2d1e25bf6952
053a6ab1835e138e648ac5b6616cc71d360e56bcbc9ccec21ea5c0a568dcb76b
4f32a95c6ab9a92bcc95908b88b5e88e89beef73070a43abce901faec16460cc
fd08fcabb15c7207c609f1f1922a556ecc157b8cef8c1e8f8a46d75b48767e13
cat-searcher/leandojo-benchmark-4-random
test
1,379
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have hs' : s'.map ⟨L.subtype, <a>Subtype.coe_injective</a>⟩ = s := by simp [s', <a>Finset.map_eq_image</a>, <a>Finset.image_preimage</a>, <a>Finset.filter_eq_self</a>] exact fun a ha ↦ <a>subset_latticeClosure</a> <| <a>Set.subset_union_left</a> ha
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
((:c LE.le) (:fv _uniq.193645) ((:c Preorder.toLE) (:fv _uniq.193645) ((:c PartialOrder.toPreorder) (:fv _uniq.193645) ((:c StrictOrderedSemiring.toPartialOrder) (:fv _uniq.193645) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.193645) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.1...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _un...
(: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 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"have","sourceEnd":15465,"sourceStart":15461,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hs'","sourceEnd":15469,"sourceStart":15466,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hs'","sourceEnd":15469,"sourceStart":15466,"tag":"n...
[]
[{"source":"s'.map ⟨L.subtype, Subtype.coe_injective⟩ = s","source_end":15521,"source_start":15472,"syntax_kind":"«term_=_»"},{"source":"s'","source_end":15540,"source_start":15538,"syntax_kind":"ident"},{"source":"map_eq_image","source_end":15554,"source_start":15542,"syntax_kind":"ident"},{"source":"image_preimage","...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal...
23
11
exact
true
1
24
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
21632a46f41fafbbae42ba63d2a2cfde53109539764a590e46c49cc7b86ad20b
fd08fcabb15c7207c609f1f1922a556ecc157b8cef8c1e8f8a46d75b48767e13
48ab6f50fe8eca88e3ce8775ec8e1e71edae08c8701ae4162614cd62dff58bf5
0e2d2957cfe8829bfc1add5489e8194ecd43dc7350dee43e4ac1fc7158f60001
cat-searcher/leandojo-benchmark-4-random
test
1,380
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have ht' : t'.map ⟨L.subtype, <a>Subtype.coe_injective</a>⟩ = t := by simp [t', <a>Finset.map_eq_image</a>, <a>Finset.image_preimage</a>, <a>Finset.filter_eq_self</a>] exact fun a ha ↦ <a>subset_latticeClosure</a> <| <a>Set.subset_union_right</a> ha
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
((:c LE.le) (:fv _uniq.193645) ((:c Preorder.toLE) (:fv _uniq.193645) ((:c PartialOrder.toPreorder) (:fv _uniq.193645) ((:c StrictOrderedSemiring.toPartialOrder) (:fv _uniq.193645) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.193645) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.1...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _un...
(: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 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"have","sourceEnd":15667,"sourceStart":15663,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"ht'","sourceEnd":15671,"sourceStart":15668,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"ht'","sourceEnd":15671,"sourceStart":15668,"tag":"n...
[]
[{"source":"t'.map ⟨L.subtype, Subtype.coe_injective⟩ = t","source_end":15723,"source_start":15674,"syntax_kind":"«term_=_»"},{"source":"t'","source_end":15742,"source_start":15740,"syntax_kind":"ident"},{"source":"map_eq_image","source_end":15756,"source_start":15744,"syntax_kind":"ident"},{"source":"image_preimage","...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal...
23
15
exact
true
1
25
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f8d2b776a19c13b85bb83133ce50929d4bb6abc9caaacb5239c9432ef45d79d4
0e2d2957cfe8829bfc1add5489e8194ecd43dc7350dee43e4ac1fc7158f60001
780653dd1936222b1d72b40c79b7bb2dcf54f7aeefcee69f7bb531352220a77d
11e1261a0d54bedee1c5b4c16e6d2994a0193bda96f02df156b8e0f89a130db7
cat-searcher/leandojo-benchmark-4-random
test
1,381
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
clear_value s' t'
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
((:c LE.le) (:fv _uniq.193645) ((:c Preorder.toLE) (:fv _uniq.193645) ((:c PartialOrder.toPreorder) (:fv _uniq.193645) ((:c StrictOrderedSemiring.toPartialOrder) (:fv _uniq.193645) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.193645) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.1...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _un...
(: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 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"clear_value","sourceEnd":15877,"sourceStart":15866,"tag":"atom"},{"children":[{"contextIndex":23,"semanticRole":"local","source":"s'","sourceEnd":15880,"sourceStart":15878,"tag":"identifier"},{"contextIndex":24,"semanticRole":"local","source":"t'","sourceEnd":15883,"sourceStart":15881,"tag":"ide...
[]
[{"source":"s'","source_end":15880,"source_start":15878,"syntax_kind":"ident"},{"source":"t'","source_end":15883,"source_start":15881,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal...
23
19
exact
true
1
26
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3ac4f4bc3c35445167d32600178cb83920fb2049f190744df98460fcdfb9bb08
11e1261a0d54bedee1c5b4c16e6d2994a0193bda96f02df156b8e0f89a130db7
6e10fd1664b5b02783584c00020a948985e2643b898b9ae2a08bd84f8df6bcc0
95047bf5300201e57b12caee73639e6d1b592e61ec87fd9d445ad07059b5b42b
cat-searcher/leandojo-benchmark-4-random
test
1,382
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨β, _, _, g, hg⟩ := <a>exists_birkhoff_representation</a> L
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
case intro.intro.intro.intro α : Type u_1 β✝ : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β✝ inst✝¹ : ExistsAddOfLE β✝ f f₁ f₂ f₃ f₄ g✝ μ : α → β✝ inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Su...
((:c LE.le) (:fv _uniq.193645) ((:c Preorder.toLE) (:fv _uniq.193645) ((:c PartialOrder.toPreorder) (:fv _uniq.193645) ((:c StrictOrderedSemiring.toPartialOrder) (:fv _uniq.193645) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.193645) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.1...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _un...
(: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 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"obtain","sourceEnd":15892,"sourceStart":15886,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":15896,"sourceStart":15893,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"β","sourceEn...
[]
[{"source":"exists_birkhoff_representation L","source_end":15950,"source_start":15918,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨β, _, _, g, hg⟩","source_end":15914,"source_start":15893,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal...
23
20
exact
true
1
26
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1b20f65a362f30bddf6813ac93646271723b9079a968be95a813a45925f5a50a
95047bf5300201e57b12caee73639e6d1b592e61ec87fd9d445ad07059b5b42b
50b4dbd2f4fd821c64d5949c8a6b988d03fb193425317324f99973291b81f460
e87bc8a2e95910f64a911d7262870d06f1a8595d41e61e9c5848f11b43055f46
cat-searcher/leandojo-benchmark-4-random
test
1,383
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have := <a>_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.four_functions_theorem_aux</a> (<a>Function.extend</a> g (f₁ ∘ (↑)) 0) (<a>Function.extend</a> g (f₂ ∘ (↑)) 0) (<a>Function.extend</a> g (f₃ ∘ (↑)) 0) (<a>Function.extend</a> g (f₄ ∘ (↑)) 0) (<a>Function.extend_nonneg</a> (fun _ ↦ h₁ _) <a>le_rfl</a>) ...
case intro.intro.intro.intro α : Type u_1 β✝ : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β✝ inst✝¹ : ExistsAddOfLE β✝ f f₁ f₂ f₃ f₄ g✝ μ : α → β✝ inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Su...
case intro.intro.intro.intro.refine_2 α : Type u_1 β✝ : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β✝ inst✝¹ : ExistsAddOfLE β✝ f f₁ f₂ f₃ f₄ g✝ μ : α → β✝ inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset...
((:c LE.le) (:fv _uniq.193645) ((:c Preorder.toLE) (:fv _uniq.193645) ((:c PartialOrder.toPreorder) (:fv _uniq.193645) ((:c StrictOrderedSemiring.toPartialOrder) (:fv _uniq.193645) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.193645) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.1...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _u...
(: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 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β✝","sexp":"(:sort Type)"},{"binder_role":":instance-im...
{"children":[{"source":"have","sourceEnd":15957,"sourceStart":15953,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":15958,"sourceStart":15958,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":15958,"sourceStart":15958,"tag":"node"}],"kind":"Lean.Parser.Term.hav...
[]
[{"source":"four_functions_theorem_aux (extend g (f₁ ∘ (↑)) 0) (extend g (f₂ ∘ (↑)) 0)\n (extend g (f₃ ∘ (↑)) 0) (extend g (f₄ ∘ (↑)) 0) (extend_nonneg (fun _ ↦ h₁ _) le_rfl)\n (extend_nonneg (fun _ ↦ h₂ _) le_rfl) (extend_nonneg (fun _ ↦ h₃ _) le_rfl)\n (extend_nonneg (fun _ ↦ h₄ _) le_rfl) ?_ (s'.map ⟨g, hg⟩...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β✝"},{"binder_role":":instance-implicit","context_index":2,"interna...
23
21
exact
true
1
31
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
eadf3f4ed21f7277be4b706c9ba3a7b9e8c001e46ad623c75b56d939abc780ed
e87bc8a2e95910f64a911d7262870d06f1a8595d41e61e9c5848f11b43055f46
2bbf6d869871af1c7bd5356f0f46cac80f555b1f43814595e48be0b8a8440fb3
c2d402426e64d04daee7dc938dbfd6abaa2874038c598ab4c4ab1f35994b69da
cat-searcher/leandojo-benchmark-4-random
test
1,384
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro s t
case intro.intro.intro.intro.refine_1 α : Type u_1 β✝ : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β✝ inst✝¹ : ExistsAddOfLE β✝ f f₁ f₂ f₃ f₄ g✝ μ : α → β✝ inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset...
case intro.intro.intro.intro.refine_1 α : Type u_1 β✝ : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β✝ inst✝¹ : ExistsAddOfLE β✝ f f₁ f₂ f₃ f₄ g✝ μ : α → β✝ inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s✝ t✝ : Fins...
(:forall s ((:c Finset) (:fv _uniq.205584)) (:forall t ((:c Finset) (:fv _uniq.205584)) ((:c LE.le) (:fv _uniq.193645) ((:c Preorder.toLE) (:fv _uniq.193645) ((:c PartialOrder.toPreorder) (:fv _uniq.193645) ((:c StrictOrderedSemiring.toPartialOrder) (:fv _uniq.193645) ((:c LinearOrderedSemiring.toStrictOrderedSemiring)...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _u...
(:forall s :explicit (:app (:c Finset) (:arg :explicit 0 (:fv FV27))) (:forall t :explicit (:app (:c Finset) (:arg :explicit 0 (:fv FV27))) (: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 (:app (:c HMul.hMul) (:arg :impli...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β✝","sexp":"(:sort Type)"},{"binder_role":":instance-im...
{"children":[{"source":"rintro","sourceEnd":16467,"sourceStart":16461,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"s","sourceEnd":16469,"sourceStart":16468,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"s","sourceEnd":16469,"sourceStart":16468,"...
[{"role":"fresh_name","source":"s","source_end":16469,"source_start":16468,"syntax_kind":"ident"},{"role":"fresh_name","source":"t","source_end":16471,"source_start":16470,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β✝"},{"binder_role":":instance-implicit","context_index":2,"interna...
23
27
exact
true
1
31
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
fd6f0eaa8118fac86b939bedd5eb63eb29908570cdbb55d7f7954b9100b4a86e
10df65e931f3f9dd917abe60dd164ffec021b84d1f064413f98292c999da48c3
5ac2a51a2bd1d1a6a2cbaba0c582bde4dab1dee36c1ba3ee6d0790818f0058c2
1d900d9a242589fb4b21f46855f34aa024abb3195d2970ee7d8f8ddc50157b86
cat-searcher/leandojo-benchmark-4-random
test
1,385
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [s', <a>Finset.map_eq_image</a>, <a>Finset.image_preimage</a>, <a>Finset.filter_eq_self</a>]
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
((:c Eq) ((:c Finset) (:fv _uniq.193642)) ((:c Finset.map) ((:c Subtype) (:fv _uniq.193642) (:lambda x (:fv _uniq.193642) ((:c Membership.mem) (:fv _uniq.193642) ((:c Sublattice) (:fv _uniq.193642) ((:c DistribLattice.toLattice) (:fv _uniq.193642) (:fv _uniq.193648))) ((:c SetLike.instMembership) ((:c Sublattice) (:fv ...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _un...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Finset.map) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :im...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"simp","sourceEnd":15536,"sourceStart":15532,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15538,"sourceStart":15537,"tag":"a...
[]
[{"source":"s'","source_end":15540,"source_start":15538,"syntax_kind":"ident"},{"source":"map_eq_image","source_end":15554,"source_start":15542,"syntax_kind":"ident"},{"source":"image_preimage","source_end":15570,"source_start":15556,"syntax_kind":"ident"},{"source":"filter_eq_self","source_end":15586,"source_start":15...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal...
23
13
exact
true
1
24
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
80ba632a8332b2452c6d868fed30c4e40d7eca315c529aae3ab5eb0f6bafdaac
4fdae2939a338b45b5d4cf48dccc3fc9b8e21ef6148641c54c804357a7f45b9b
13bc68e531d9204068b6a1e4fcf3333edba404a485064cc6dadaf1560831bfdb
e9a69337f1b6ec21a3d2eb1c00026231108bb5786fe08ebbbf88bc716fdc9fd7
cat-searcher/leandojo-benchmark-4-random
test
1,386
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact fun a ha ↦ <a>subset_latticeClosure</a> <| <a>Set.subset_union_left</a> ha
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
(:forall x (:fv _uniq.193642) (:forall _ ((:c Membership.mem) (:fv _uniq.193642) ((:c Finset) (:fv _uniq.193642)) ((:c Finset.instMembership) (:fv _uniq.193642)) 0 (:fv _uniq.195878)) ((:c Membership.mem) (:fv _uniq.193642) ((:c Sublattice) (:fv _uniq.193642) ((:c DistribLattice.toLattice) (:fv _uniq.193642) (:fv _uniq...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _un...
(:forall x :explicit (:fv FV0) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"exact","sourceEnd":15597,"sourceStart":15592,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":15601,"sourceStart":15598,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":15603,"sourceStart":15602,"tag":"identifier"},{"semanticRole":"scoped_loca...
[]
[{"source":"fun a ha ↦ subset_latticeClosure <| Set.subset_union_left ha","source_end":15660,"source_start":15598,"syntax_kind":"Lean.Parser.Term.fun"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal...
23
14
exact
true
1
24
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0390f27752a7f22dee8c4c3c174a527feb1b5e42cb6e1d8385b02d6ba3d1fcfa
e9a69337f1b6ec21a3d2eb1c00026231108bb5786fe08ebbbf88bc716fdc9fd7
17d97fbad4230670071007c06fe07104b5b87c1780cd6880a94328ab7b7ecf95
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,387
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [t', <a>Finset.map_eq_image</a>, <a>Finset.image_preimage</a>, <a>Finset.filter_eq_self</a>]
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
((:c Eq) ((:c Finset) (:fv _uniq.193642)) ((:c Finset.map) ((:c Subtype) (:fv _uniq.193642) (:lambda x (:fv _uniq.193642) ((:c Membership.mem) (:fv _uniq.193642) ((:c Sublattice) (:fv _uniq.193642) ((:c DistribLattice.toLattice) (:fv _uniq.193642) (:fv _uniq.193648))) ((:c SetLike.instMembership) ((:c Sublattice) (:fv ...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _un...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Finset.map) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :im...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"simp","sourceEnd":15738,"sourceStart":15734,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15740,"sourceStart":15739,"tag":"a...
[]
[{"source":"t'","source_end":15742,"source_start":15740,"syntax_kind":"ident"},{"source":"map_eq_image","source_end":15756,"source_start":15744,"syntax_kind":"ident"},{"source":"image_preimage","source_end":15772,"source_start":15758,"syntax_kind":"ident"},{"source":"filter_eq_self","source_end":15788,"source_start":15...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal...
23
17
exact
true
1
25
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f36cb7f49edf0e7cb2c45ec51879dcb4472da55ea5b0e2cb1328c4448d05e079
8e5f34e6e5d1bd0ca074cbfc52e60aebfac86c254df00f757b0d20bf153c1789
f5f5a8a5c101111db39892a2884a5b979bb182e676301634fd0c766db9ba5ea7
73d87ca383ccd4283787546b44d9625c0c625b9f11bd617ddb7b71bee4c0ace4
cat-searcher/leandojo-benchmark-4-random
test
1,388
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact fun a ha ↦ <a>subset_latticeClosure</a> <| <a>Set.subset_union_right</a> ha
α : Type u_1 β : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β inst✝¹ : ExistsAddOfLE β f f₁ f₂ f₃ f₄ g μ : α → β inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset α L : Sublattice α := { carrier := lattice...
(:forall x (:fv _uniq.193642) (:forall _ ((:c Membership.mem) (:fv _uniq.193642) ((:c Finset) (:fv _uniq.193642)) ((:c Finset.instMembership) (:fv _uniq.193642)) 0 (:fv _uniq.195879)) ((:c Membership.mem) (:fv _uniq.193642) ((:c Sublattice) (:fv _uniq.193642) ((:c DistribLattice.toLattice) (:fv _uniq.193642) (:fv _uniq...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _un...
(:forall x :explicit (:fv FV0) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"exact","sourceEnd":15799,"sourceStart":15794,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":15803,"sourceStart":15800,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":15805,"sourceStart":15804,"tag":"identifier"},{"semanticRole":"scoped_loca...
[]
[{"source":"fun a ha ↦ subset_latticeClosure <| Set.subset_union_right ha","source_end":15863,"source_start":15800,"syntax_kind":"Lean.Parser.Term.fun"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal...
23
18
exact
true
1
25
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b4b47e43ad96fa5df3348267c2132dd034f71485ed8351ad61b590ed1db21d78
73d87ca383ccd4283787546b44d9625c0c625b9f11bd617ddb7b71bee4c0ace4
df843f6d7d3908261318c4b5a157ea6651adb5981fc493e1d688f19d1fd3d30c
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,389
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simpa only [← hs', ← ht', ← <a>Finset.map_sups</a>, ← <a>Finset.map_infs</a>, <a>Finset.sum_map</a>, <a>Function.Embedding.coeFn_mk</a>, hg.extend_apply] using this
case intro.intro.intro.intro.refine_2 α : Type u_1 β✝ : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β✝ inst✝¹ : ExistsAddOfLE β✝ f f₁ f₂ f₃ f₄ g✝ μ : α → β✝ inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s t : Finset...
((:c LE.le) (:fv _uniq.193645) ((:c Preorder.toLE) (:fv _uniq.193645) ((:c PartialOrder.toPreorder) (:fv _uniq.193645) ((:c StrictOrderedSemiring.toPartialOrder) (:fv _uniq.193645) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.193645) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.1...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _u...
(: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 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β✝","sexp":"(:sort Type)"},{"binder_role":":instance-im...
{"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":16343,"sourceStart":16338,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind...
[]
[{"source":"hs'","source_end":16357,"source_start":16354,"syntax_kind":"ident"},{"source":"ht'","source_end":16366,"source_start":16363,"syntax_kind":"ident"},{"source":"map_sups","source_end":16380,"source_start":16372,"syntax_kind":"ident"},{"source":"map_infs","source_end":16394,"source_start":16386,"syntax_kind":"i...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β✝"},{"binder_role":":instance-implicit","context_index":2,"interna...
23
24
exact
true
1
32
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
51028ea321425734802fc600ebe7735f7c60f4d1487218d1f53e22cb32a69021
b0bcb1a410d4a3076fc2425493b25d8356c4b35941afdeb13e402835c69abdd7
44976e2b0db8515ef2ae2436685ab6d762a66cede57db210c8a8efe9fe8ceaa4
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,390
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨a, rfl⟩ | hs := <a>em</a> (∃ a, g a = s)
case intro.intro.intro.intro.refine_1 α : Type u_1 β✝ : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β✝ inst✝¹ : ExistsAddOfLE β✝ f f₁ f₂ f₃ f₄ g✝ μ : α → β✝ inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s✝ t✝ : Fins...
case intro.intro.intro.intro.refine_1.inl.intro α : Type u_1 β✝ : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β✝ inst✝¹ : ExistsAddOfLE β✝ f f₁ f₂ f₃ f₄ g✝ μ : α → β✝ inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s ...
((:c LE.le) (:fv _uniq.193645) ((:c Preorder.toLE) (:fv _uniq.193645) ((:c PartialOrder.toPreorder) (:fv _uniq.193645) ((:c StrictOrderedSemiring.toPartialOrder) (:fv _uniq.193645) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.193645) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.1...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _u...
(: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 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β✝","sexp":"(:sort Type)"},{"binder_role":":instance-im...
{"children":[{"source":"obtain","sourceEnd":16492,"sourceStart":16486,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":16496,"sourceStart":16493,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEn...
[]
[{"source":"em (∃ a, g a = s)","source_end":16533,"source_start":16514,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨a, rfl⟩ | hs","source_end":16510,"source_start":16493,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β✝"},{"binder_role":":instance-implicit","context_index":2,"interna...
23
31
exact
true
1
33
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d10ae7b2444b0790c49805b5da5e3ff105a28e5f8cf4143f3e9bcdcfd90b3eac
1d900d9a242589fb4b21f46855f34aa024abb3195d2970ee7d8f8ddc50157b86
5ebcefa6b6566aa342306348aaf8826427bf11fac44d9b97a5901f990c55a9e7
02098f52079fe3fcf9fb19e319a3ad551f952f6342046d9ad4edd58c2b658bc6
cat-searcher/leandojo-benchmark-4-random
test
1,391
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨b, rfl⟩ | ht := <a>em</a> (∃ b, g b = t)
case intro.intro.intro.intro.refine_1.inl.intro α : Type u_1 β✝ : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β✝ inst✝¹ : ExistsAddOfLE β✝ f f₁ f₂ f₃ f₄ g✝ μ : α → β✝ inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s ...
case intro.intro.intro.intro.refine_1.inl.intro.inl.intro α : Type u_1 β✝ : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β✝ inst✝¹ : ExistsAddOfLE β✝ f f₁ f₂ f₃ f₄ g✝ μ : α → β✝ inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ ...
((:c LE.le) (:fv _uniq.193645) ((:c Preorder.toLE) (:fv _uniq.193645) ((:c PartialOrder.toPreorder) (:fv _uniq.193645) ((:c StrictOrderedSemiring.toPartialOrder) (:fv _uniq.193645) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.193645) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.1...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _u...
(: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 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β✝","sexp":"(:sort Type)"},{"binder_role":":instance-im...
{"children":[{"source":"obtain","sourceEnd":16545,"sourceStart":16539,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":16549,"sourceStart":16546,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"b","sourceEn...
[]
[{"source":"em (∃ b, g b = t)","source_end":16586,"source_start":16567,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨b, rfl⟩ | ht","source_end":16563,"source_start":16546,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β✝"},{"binder_role":":instance-implicit","context_index":2,"interna...
23
36
exact
true
1
33
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9419b221e0ed7599da93b4d252c996a139e424899312114dbea558bbb9bd210c
081ca320da7e05caf0bdf0ef7aefbfb0036924375d28340c44f28a9938569be4
c7edc5171ef0acb7cdf5b5d1edf09c64988748580c1d19b822f2ae543d635328
e3ada55a4971e847e95302b7b355ee208208dccf80383ff3fe1849acb3f6efa1
cat-searcher/leandojo-benchmark-4-random
test
1,392
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp_rw [← <a>Finset.sup_eq_union</a>, ← <a>Finset.inf_eq_inter</a>, ← <a>SupHomClass.map_sup</a>, ← <a>InfHomClass.map_inf</a>, hg.extend_apply]
case intro.intro.intro.intro.refine_1.inl.intro.inl.intro α : Type u_1 β✝ : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β✝ inst✝¹ : ExistsAddOfLE β✝ f f₁ f₂ f₃ f₄ g✝ μ : α → β✝ inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ ...
case intro.intro.intro.intro.refine_1.inl.intro.inl.intro α : Type u_1 β✝ : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β✝ inst✝¹ : ExistsAddOfLE β✝ f f₁ f₂ f₃ f₄ g✝ μ : α → β✝ inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ ...
((:c LE.le) (:fv _uniq.193645) ((:c Preorder.toLE) (:fv _uniq.193645) ((:c PartialOrder.toPreorder) (:fv _uniq.193645) ((:c StrictOrderedSemiring.toPartialOrder) (:fv _uniq.193645) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.193645) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.1...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _u...
(: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 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β✝","sexp":"(:sort Type)"},{"binder_role":":instance-im...
{"children":[{"source":"simp_rw","sourceEnd":16601,"sourceStart":16594,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16603,"sourceStart":16602,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":16606,"sou...
[]
[{"source":"sup_eq_union","source_end":16619,"source_start":16607,"syntax_kind":"ident"},{"source":"inf_eq_inter","source_end":16637,"source_start":16625,"syntax_kind":"ident"},{"source":"map_sup","source_end":16650,"source_start":16643,"syntax_kind":"ident"},{"source":"map_inf","source_end":16663,"source_start":16656,...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β✝"},{"binder_role":":instance-implicit","context_index":2,"interna...
23
41
exact
true
1
33
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8f2e6fc4e22640fda062513800893bd6efb69757d1e290be127174886df54af9
5dae411db05c2318e9d17e1f61f160464a723eb7497e3daf3bcca68d2a680b03
2dc451a1d25b9fcfc481e2fa892a1c5c4a489f6749e5f0025e8863b784facea7
e0cf574742a6354cf26849a4bc2166d3e0001ba2cf70b1804cc91ebe1688a02d
cat-searcher/leandojo-benchmark-4-random
test
1,393
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact h _ _
case intro.intro.intro.intro.refine_1.inl.intro.inl.intro α : Type u_1 β✝ : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β✝ inst✝¹ : ExistsAddOfLE β✝ f f₁ f₂ f₃ f₄ g✝ μ : α → β✝ inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ ...
((:c LE.le) (:fv _uniq.193645) ((:c Preorder.toLE) (:fv _uniq.193645) ((:c PartialOrder.toPreorder) (:fv _uniq.193645) ((:c StrictOrderedSemiring.toPartialOrder) (:fv _uniq.193645) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.193645) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.1...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _u...
(: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 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β✝","sexp":"(:sort Type)"},{"binder_role":":instance-im...
{"children":[{"source":"exact","sourceEnd":16693,"sourceStart":16688,"tag":"atom"},{"children":[{"contextIndex":18,"semanticRole":"local","source":"h","sourceEnd":16695,"sourceStart":16694,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":16697,"sourceStart":16696,"tag":"atom"}],"kind":"Lean.Parse...
[]
[{"source":"h _ _","source_end":16699,"source_start":16694,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β✝"},{"binder_role":":instance-implicit","context_index":2,"interna...
23
48
exact
true
1
33
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a38be4b1b36c03e2dba3630af173b566184287b4e2bfc4eac683d8d8dc15c6e9
e0cf574742a6354cf26849a4bc2166d3e0001ba2cf70b1804cc91ebe1688a02d
2d81fb1c3eb782ecc8a2b11f8a65fdb5a26dfb0ed1fdffb13c710b1c24b0efaa
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,394
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simpa [<a>Function.extend_apply'</a> _ _ _ ht] using <a>mul_nonneg</a> (<a>Function.extend_nonneg</a> (fun a : L ↦ h₃ a) <a>le_rfl</a> _) (<a>Function.extend_nonneg</a> (fun a : L ↦ h₄ a) <a>le_rfl</a> _)
case intro.intro.intro.intro.refine_1.inl.intro.inr α : Type u_1 β✝ : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β✝ inst✝¹ : ExistsAddOfLE β✝ f f₁ f₂ f₃ f₄ g✝ μ : α → β✝ inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b...
((:c LE.le) (:fv _uniq.193645) ((:c Preorder.toLE) (:fv _uniq.193645) ((:c PartialOrder.toPreorder) (:fv _uniq.193645) ((:c StrictOrderedSemiring.toPartialOrder) (:fv _uniq.193645) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.193645) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.1...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _u...
(: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 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β✝","sexp":"(:sort Type)"},{"binder_role":":instance-im...
{"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":16712,"sourceStart":16707,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind...
[]
[{"source":"extend_apply' _ _ _ ht","source_end":16736,"source_start":16714,"syntax_kind":"Lean.Parser.Term.app"},{"source":"mul_nonneg\n (extend_nonneg (fun a : L ↦ h₃ a) le_rfl _) (extend_nonneg (fun a : L ↦ h₄ a) le_rfl _)","source_end":16858,"source_start":16744,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β✝"},{"binder_role":":instance-implicit","context_index":2,"interna...
23
51
exact
true
1
34
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
89d0d3ef9a89fa94ea64c809c7812a8e37ff4f51788fb3f2c7762400ed4d04eb
36502996bdf0497a54045adea6b41322c6b4862ea46da9ac2b0d5a72a07a7ecb
26142688824ec60e03d00312ecfca9e8d9249343d0644b275a32fcc95ddfbafe
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,395
four_functions_theorem
Mathlib/Combinatorics/SetFamily/FourFunctions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simpa [<a>Function.extend_apply'</a> _ _ _ hs] using <a>mul_nonneg</a> (<a>Function.extend_nonneg</a> (fun a : L ↦ h₃ a) <a>le_rfl</a> _) (<a>Function.extend_nonneg</a> (fun a : L ↦ h₄ a) <a>le_rfl</a> _)
case intro.intro.intro.intro.refine_1.inr α : Type u_1 β✝ : Type u_2 inst✝³ : DistribLattice α inst✝² : LinearOrderedCommSemiring β✝ inst✝¹ : ExistsAddOfLE β✝ f f₁ f₂ f₃ f₄ g✝ μ : α → β✝ inst✝ : DecidableEq α h₁ : 0 ≤ f₁ h₂ : 0 ≤ f₂ h₃ : 0 ≤ f₃ h₄ : 0 ≤ f₄ h : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b) s✝ t✝ : ...
((:c LE.le) (:fv _uniq.193645) ((:c Preorder.toLE) (:fv _uniq.193645) ((:c PartialOrder.toPreorder) (:fv _uniq.193645) ((:c StrictOrderedSemiring.toPartialOrder) (:fv _uniq.193645) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.193645) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.1...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c DistribLattice) (:fv _uniq.193642))"},{"name":"inst✝²","sexp":"((:c LinearOrderedCommSemiring) (:fv _uniq.193645))"},{"name":"inst✝¹","sexp":"((:c ExistsAddOfLE) (:fv _uniq.193645) ((:c Distrib.toAdd) (:fv _u...
(: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 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"name":"β✝","sexp":"(:sort Type)"},{"binder_role":":instance-im...
{"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":16869,"sourceStart":16864,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind...
[]
[{"source":"extend_apply' _ _ _ hs","source_end":16893,"source_start":16871,"syntax_kind":"Lean.Parser.Term.app"},{"source":"mul_nonneg\n (extend_nonneg (fun a : L ↦ h₃ a) le_rfl _) (extend_nonneg (fun a : L ↦ h₄ a) le_rfl _)","source_end":17013,"source_start":16901,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193642","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193645","is_instance":false,"is_let":false,"user_name":"β✝"},{"binder_role":":instance-implicit","context_index":2,"interna...
23
56
exact
true
1
34
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
32a436b0d011cf06d9bde79c5ae216b8d700201d8db11a443285262736bd003d
c306ba01dd3cd81c4f5d29699c6f8707c76db2fac6ba66174188db479c5faa97
b236949267039d0600eefc70535caae3e101926a9320361792f700b4c7619a37
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,396
CategoryTheory.GrothendieckTopology.WEqualsLocallyBijective.mk'
Mathlib/CategoryTheory/Sites/LocallyBijective.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>CategoryTheory.GrothendieckTopology.W_iff</a>, ← <a>CategoryTheory.Sheaf.isLocallyBijective_iff_isIso</a>, ← <a>CategoryTheory.Presheaf.isLocallyInjective_comp_iff</a> J f (<a>CategoryTheory.toSheafify</a> J Q), ← <a>CategoryTheory.Presheaf.isLocallySurjective_comp_iff</a> J f (<a>CategoryTheory.toSheafify</a> J...
C : Type u inst✝⁷ : Category.{v, u} C J : GrothendieckTopology C A : Type u' inst✝⁶ : Category.{v', u'} A inst✝⁵ : ConcreteCategory A inst✝⁴ : HasWeakSheafify J A inst✝³ : (forget A).ReflectsIsomorphisms inst✝² : J.HasSheafCompose (forget A) inst✝¹ : ∀ (P : Cᵒᵖ ⥤ A), Presheaf.IsLocallyInjective J (CategoryTheory.toShea...
((:c Iff) ((:c CategoryTheory.GrothendieckTopology.W) (:fv _uniq.18109) (:fv _uniq.18112) (:fv _uniq.18127) (:fv _uniq.18129) (:fv _uniq.18132) (:fv _uniq.19480) (:fv _uniq.19483) (:fv _uniq.19486)) ((:c And) ((:c CategoryTheory.Presheaf.IsLocallyInjective) (:fv _uniq.18109) (:fv _uniq.18112) (:fv _uniq.18129) (:fv _un...
[{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝⁷","sexp":"((:c CategoryTheory.Category) (:fv _uniq.18109))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.18109) (:fv _uniq.18112))"},{"name":"A","sexp":"(:sort (+ u' 1))"},{"name":"inst✝⁶","sexp":"((:c CategoryTheory.Category) (:fv _uniq...
(:app (:c Iff) (:arg :explicit 0 (:app (:c CategoryTheory.GrothendieckTopology.W) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :implicit-type 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18109","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18112","is_instance":true,"is_let":false,"name":"inst✝⁷","sexp":"(:app (:c CategoryTheory.Category...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":5332,"sourceStart":5330,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5334,"sourceStart":5333,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag...
[]
[{"source":"W_iff","source_end":5339,"source_start":5334,"syntax_kind":"ident"},{"source":"Sheaf.isLocallyBijective_iff_isIso","source_end":5379,"source_start":5345,"syntax_kind":"ident"},{"source":"Presheaf.isLocallyInjective_comp_iff J f (CategoryTheory.toSheafify J Q)","source_end":5463,"source_start":5391,"syntax_k...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18109","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18112","is_instance":true,"is_let":false,"user_name":"inst✝⁷"},{"binder_role":":explicit","context_index":2,"intern...
29
2
exact
true
1
14
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
391cb4608fa3748e1fd913a619793c3f5283face445c235510242ca33a94d9a2
186d2321dda76d9a37fe5bbd4a9726236d03a058d420db6a3f181ecb37721c8e
01335a3ba2bb3f8e6220ae5a1ab3622c0560dafbe033b0af18d8fdb9cccd6fee
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,397
LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegenerate
Mathlib/LinearAlgebra/BilinearForm/Orthogonal.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have : W ⊓ B.orthogonal W = ⊥ := by rw [<a>eq_bot_iff</a>] intro x hx obtain ⟨hx₁, hx₂⟩ := <a>Submodule.mem_inf</a>.1 hx refine <a>Subtype.mk_eq_mk</a>.1 (b₂ ⟨x, hx₁⟩ ?_) rintro ⟨n, hn⟩ simp only [<a>LinearMap.BilinForm.restrict_apply</a>, <a>LinearMap.domRestrict_apply</a>] exact b₁ n x (b₁ x n (b₁ n x (hx₂ n hn)))
R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : BilinForm R₁ M₁ ...
R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : BilinForm R₁ M₁ ...
((:c IsCompl) ((:c Submodule) (:fv _uniq.227969) (:fv _uniq.227966) ((:c DivisionSemiring.toSemiring) (:fv _uniq.227969) ((:c Semifield.toDivisionSemiring) (:fv _uniq.227969) ((:c Field.toSemifield) (:fv _uniq.227969) (:fv _uniq.227972)))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.227966) (:fv _uniq.227975)) (:fv _...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c CommSemiring) (:fv _uniq.227145))"},{"name":"inst✝¹⁰","sexp":"((:c AddCommMonoid) (:fv _uniq.227148))"},{"name":"inst✝⁹","sexp":"((:c Module) (:fv _uniq.227145) (:fv _uniq.227148) ((:c CommSemiring.toSemiring...
(:app (:c IsCompl) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV11)) (:arg :explicit 1 (:fv FV10)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV11))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV10))))) (:arg :instance 4 (:in...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"have","sourceEnd":16784,"sourceStart":16780,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":16785,"sourceStart":16785,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":16785,"sourceStart":16785,"tag":"node"}],"kind":"Lean.Parser.Term.hav...
[]
[{"source":"W ⊓ B.orthogonal W = ⊥","source_end":16813,"source_start":16787,"syntax_kind":"«term_=_»"},{"source":"eq_bot_iff","source_end":16838,"source_start":16828,"syntax_kind":"ident"},{"source":"mem_inf.1 hx","source_end":16900,"source_start":16888,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨hx₁, hx₂⟩","sour...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal...
84
4
exact
true
1
25
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c844d1cd3a948176891f30c1a2067534528b75b3d9d3731da601250080366681
5666daa92a0aed6e5d29188501bb2a0db433d32eba733ca70e2c22aba1a008e1
ae38cc55c3b2a18de7ab57bbd7e57609afe72d3748bec81865f56b0eb3febf1d
539818eb1d375c5e08328664f2e48de41ce52eb2ddaffc750962b06a32406a57
cat-searcher/leandojo-benchmark-4-random
test
1,398
LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegenerate
Mathlib/LinearAlgebra/BilinearForm/Orthogonal.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine <a>IsCompl.of_eq</a> this (<a>Submodule.eq_top_of_finrank_eq</a> <| (<a>Submodule.finrank_le</a> _).<a>LE.le.antisymm</a> ?_)
R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : BilinForm R₁ M₁ ...
R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : BilinForm R₁ M₁ ...
((:c IsCompl) ((:c Submodule) (:fv _uniq.227969) (:fv _uniq.227966) ((:c DivisionSemiring.toSemiring) (:fv _uniq.227969) ((:c Semifield.toDivisionSemiring) (:fv _uniq.227969) ((:c Field.toSemifield) (:fv _uniq.227969) (:fv _uniq.227972)))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.227966) (:fv _uniq.227975)) (:fv _...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c CommSemiring) (:fv _uniq.227145))"},{"name":"inst✝¹⁰","sexp":"((:c AddCommMonoid) (:fv _uniq.227148))"},{"name":"inst✝⁹","sexp":"((:c Module) (:fv _uniq.227145) (:fv _uniq.227148) ((:c CommSemiring.toSemiring...
(:app (:c IsCompl) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV11)) (:arg :explicit 1 (:fv FV10)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV11))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV10))))) (:arg :instance 4 (:in...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"refine","sourceEnd":17091,"sourceStart":17085,"tag":"atom"},{"children":[{"name":"IsCompl.of_eq","semanticRole":"global","source":"IsCompl.of_eq","sourceEnd":17105,"sourceStart":17092,"tag":"identifier"},{"children":[{"contextIndex":26,"semanticRole":"local","source":"this","sourceEnd":17110,"so...
[]
[{"source":"IsCompl.of_eq this (eq_top_of_finrank_eq <| (finrank_le _).antisymm ?_)","source_end":17163,"source_start":17092,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal...
84
15
exact
true
1
26
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
fd128fcd8d1b7e2ebdf9c854137fb8082a084a916cb5cf0f3c17d5ae42775781
539818eb1d375c5e08328664f2e48de41ce52eb2ddaffc750962b06a32406a57
25b305006c379403240425e9ab3f9b0128b599b4251b5f57f0e87f90457e6115
0427eab554f0497056dc2fa7515dc9b81e0510523b5125a8ced24ea0348f6ec2
cat-searcher/leandojo-benchmark-4-random
test
1,399
LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegenerate
Mathlib/LinearAlgebra/BilinearForm/Orthogonal.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
conv_rhs => rw [← <a>add_zero</a> (<a>FiniteDimensional.finrank</a> K _)]
R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : BilinForm R₁ M₁ ...
R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : BilinForm R₁ M₁ ...
((:c LE.le) (:c Nat) ((:c Preorder.toLE) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring)))) ((:c FiniteDimensional.finrank) (:fv _uniq.227969) (:fv _uniq.227966) ((:c Ring.toSemiring) (:fv _uniq.227969) ((:c DivisionRing.toRing) (:fv...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c CommSemiring) (:fv _uniq.227145))"},{"name":"inst✝¹⁰","sexp":"((:c AddCommMonoid) (:fv _uniq.227148))"},{"name":"inst✝⁹","sexp":"((:c Module) (:fv _uniq.227145) (:fv _uniq.227148) ((:c CommSemiring.toSemiring...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c FiniteDimensional.finrank) (:arg :explicit 0 (:fv FV11)) (:arg :explicit 1 (:fv FV10)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"conv_rhs","sourceEnd":17174,"sourceStart":17166,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":"=>","sourceEnd":17177,"sourceStart":17175,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"sou...
[]
[{"source":"add_zero (finrank K _)","source_end":17208,"source_start":17186,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal...
84
16
exact
true
1
26
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c1b40fe9ea84670c89a9262ea483e9a8901b0015ce48e57604195cd277e8702c
0427eab554f0497056dc2fa7515dc9b81e0510523b5125a8ced24ea0348f6ec2
8c6995c68f2f34940f7c4934a14a74e1e1a43c1a2d0d68f27053701831942f77
4fe8d12c45d92b26eb65cc2e73ec0e1d6302f74e89b3bdddf25a90e30605dacf
cat-searcher/leandojo-benchmark-4-random
test
1,400
LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegenerate
Mathlib/LinearAlgebra/BilinearForm/Orthogonal.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>finrank_bot</a> K V, ← this, <a>Submodule.finrank_sup_add_finrank_inf_eq</a>, <a>LinearMap.BilinForm.finrank_add_finrank_orthogonal</a> b₁]
R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : BilinForm R₁ M₁ ...
R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : BilinForm R₁ M₁ ...
((:c LE.le) (:c Nat) ((:c Preorder.toLE) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring)))) ((:c FiniteDimensional.finrank) (:fv _uniq.227969) (:fv _uniq.227966) ((:c Ring.toSemiring) (:fv _uniq.227969) ((:c DivisionRing.toRing) (:fv...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c CommSemiring) (:fv _uniq.227145))"},{"name":"inst✝¹⁰","sexp":"((:c AddCommMonoid) (:fv _uniq.227148))"},{"name":"inst✝⁹","sexp":"((:c Module) (:fv _uniq.227145) (:fv _uniq.227148) ((:c CommSemiring.toSemiring...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c FiniteDimensional.finrank) (:arg :explicit 0 (:fv FV11)) (:arg :explicit 1 (:fv FV10)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"rw","sourceEnd":17214,"sourceStart":17212,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":17216,"sourceStart":17215,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":17219,"sourceSt...
[]
[{"source":"finrank_bot K V","source_end":17235,"source_start":17220,"syntax_kind":"Lean.Parser.Term.app"},{"source":"this","source_end":17245,"source_start":17241,"syntax_kind":"ident"},{"source":"finrank_sup_add_finrank_inf_eq","source_end":17277,"source_start":17247,"syntax_kind":"ident"},{"source":"finrank_add_finr...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal...
84
21
exact
true
1
26
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5671e5d0ee272bdbadd7c5464527bbf08698fc100be848f012c8a73eac97050b
4fe8d12c45d92b26eb65cc2e73ec0e1d6302f74e89b3bdddf25a90e30605dacf
b10ce3d0e666aaba42a982d6c1186c1bc01846fe285aec1313f7a46a00668c32
881a52dbc992f25d3832295ae417b1f55075ddcc7322aae4625e80edebb18ff5
cat-searcher/leandojo-benchmark-4-random
test
1,401
LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegenerate
Mathlib/LinearAlgebra/BilinearForm/Orthogonal.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>le_self_add</a>
R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : BilinForm R₁ M₁ ...
((:c LE.le) (:c Nat) ((:c Preorder.toLE) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring)))) ((:c FiniteDimensional.finrank) (:fv _uniq.227969) (:fv _uniq.227966) ((:c Ring.toSemiring) (:fv _uniq.227969) ((:c DivisionRing.toRing) (:fv...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c CommSemiring) (:fv _uniq.227145))"},{"name":"inst✝¹⁰","sexp":"((:c AddCommMonoid) (:fv _uniq.227148))"},{"name":"inst✝⁹","sexp":"((:c Module) (:fv _uniq.227145) (:fv _uniq.227148) ((:c CommSemiring.toSemiring...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c FiniteDimensional.finrank) (:arg :explicit 0 (:fv FV11)) (:arg :explicit 1 (:fv FV10)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"exact","sourceEnd":17327,"sourceStart":17322,"tag":"atom"},{"name":"le_self_add","semanticRole":"global","source":"le_self_add","sourceEnd":17339,"sourceStart":17328,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact le_self_add","sourceEnd":17339,"sourceStart":17322,"tag":"n...
[]
[{"source":"le_self_add","source_end":17339,"source_start":17328,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal...
84
27
exact
true
1
26
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
94e3e8112594b2a0bc9c2b5723f6786f492b1b3d458008a7aeab261b13e5e1b3
881a52dbc992f25d3832295ae417b1f55075ddcc7322aae4625e80edebb18ff5
911fac57591b11ba9ab1c28152a15ddef018c2af2eddf9e1c47ff1e50158c0ae
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,402
LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegenerate
Mathlib/LinearAlgebra/BilinearForm/Orthogonal.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>eq_bot_iff</a>]
R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : BilinForm R₁ M₁ ...
R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : BilinForm R₁ M₁ ...
((:c Eq) ((:c Submodule) (:fv _uniq.227969) (:fv _uniq.227966) ((:c DivisionSemiring.toSemiring) (:fv _uniq.227969) ((:c Semifield.toDivisionSemiring) (:fv _uniq.227969) ((:c Field.toSemifield) (:fv _uniq.227969) (:fv _uniq.227972)))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.227966) (:fv _uniq.227975)) (:fv _uniq....
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c CommSemiring) (:fv _uniq.227145))"},{"name":"inst✝¹⁰","sexp":"((:c AddCommMonoid) (:fv _uniq.227148))"},{"name":"inst✝⁹","sexp":"((:c Module) (:fv _uniq.227145) (:fv _uniq.227148) ((:c CommSemiring.toSemiring...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV11)) (:arg :explicit 1 (:fv FV10)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV11))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV10))))) (:arg :instance 4 (:instanc...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"rw","sourceEnd":16826,"sourceStart":16824,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16828,"sourceStart":16827,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"eq_bot_iff","sem...
[]
[{"source":"eq_bot_iff","source_end":16838,"source_start":16828,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal...
84
6
exact
true
1
25
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1830de70fa3dfff3d5931b46aee581dda1c38bfacaf7b6b6abdef525147aa0fd
47566bb58a3e6049c7be8126bb98c83bdbf545c184fa28efafd5ad85a3096aba
f8fee02dab21bbb817b652394c160668f7dfb7c0d7fb2ea19ccdc0b593b35a7b
471d11aad0e123c5e11b05037d623e798c633a82ed1d3928debf6f199b3b389a
cat-searcher/leandojo-benchmark-4-random
test
1,403
LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegenerate
Mathlib/LinearAlgebra/BilinearForm/Orthogonal.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro x hx
R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : BilinForm R₁ M₁ ...
R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : BilinForm R₁ M₁ ...
((:c LE.le) ((:c Submodule) (:fv _uniq.227969) (:fv _uniq.227966) ((:c DivisionSemiring.toSemiring) (:fv _uniq.227969) ((:c Semifield.toDivisionSemiring) (:fv _uniq.227969) ((:c Field.toSemifield) (:fv _uniq.227969) (:fv _uniq.227972)))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.227966) (:fv _uniq.227975)) (:fv _un...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c CommSemiring) (:fv _uniq.227145))"},{"name":"inst✝¹⁰","sexp":"((:c AddCommMonoid) (:fv _uniq.227148))"},{"name":"inst✝⁹","sexp":"((:c Module) (:fv _uniq.227145) (:fv _uniq.227148) ((:c CommSemiring.toSemiring...
(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV11)) (:arg :explicit 1 (:fv FV10)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV11))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV10))))) (:arg :instance 4 (:inst...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"intro","sourceEnd":16849,"sourceStart":16844,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":16851,"sourceStart":16850,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hx","sourceEnd":16854,"sourceStart":16852,"tag":"identifier"}],"kind":"null","sou...
[{"role":"fresh_name","source":"x","source_end":16851,"source_start":16850,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":16854,"source_start":16852,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal...
84
9
exact
true
1
25
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ff5a65a720891d22cb9a678ace5927831f6ed0c69982bcb03d9ae067e9968c6f
471d11aad0e123c5e11b05037d623e798c633a82ed1d3928debf6f199b3b389a
65777af1f444837568ec00c3040db2bdc96178d91d8bf83037116b747be939ac
4ef23ca51cea0b43a6759394b418f2d444318a79e84d8878ce79b39f7fcbe157
cat-searcher/leandojo-benchmark-4-random
test
1,404
LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegenerate
Mathlib/LinearAlgebra/BilinearForm/Orthogonal.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨hx₁, hx₂⟩ := <a>Submodule.mem_inf</a>.1 hx
R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : BilinForm R₁ M₁ ...
case intro R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : Bilin...
((:c Membership.mem) (:fv _uniq.227966) ((:c Submodule) (:fv _uniq.227969) (:fv _uniq.227966) ((:c DivisionSemiring.toSemiring) (:fv _uniq.227969) ((:c Semifield.toDivisionSemiring) (:fv _uniq.227969) ((:c Field.toSemifield) (:fv _uniq.227969) (:fv _uniq.227972)))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.227966) ...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c CommSemiring) (:fv _uniq.227145))"},{"name":"inst✝¹⁰","sexp":"((:c AddCommMonoid) (:fv _uniq.227148))"},{"name":"inst✝⁹","sexp":"((:c Module) (:fv _uniq.227145) (:fv _uniq.227148) ((:c CommSemiring.toSemiring...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV10)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV11)) (:arg :explicit 1 (:fv FV10)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV11))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explic...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"obtain","sourceEnd":16865,"sourceStart":16859,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":16869,"sourceStart":16866,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hx₁","source...
[]
[{"source":"mem_inf.1 hx","source_end":16900,"source_start":16888,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨hx₁, hx₂⟩","source_end":16884,"source_start":16866,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal...
84
10
exact
true
1
27
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a9f7241c4bdc0f91908923f195779f7fac271fdec72ca8d7d500374a0f806479
4ef23ca51cea0b43a6759394b418f2d444318a79e84d8878ce79b39f7fcbe157
c33f5b2a0da3afa9f8583263a7a74312455d353888fde23e0e8803955fc1b787
677c355621266c33e4b0d5279028b0e5c44f6eb82c080b65eb9a3f50a1c4675a
cat-searcher/leandojo-benchmark-4-random
test
1,405
LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegenerate
Mathlib/LinearAlgebra/BilinearForm/Orthogonal.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine <a>Subtype.mk_eq_mk</a>.1 (b₂ ⟨x, hx₁⟩ ?_)
case intro R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : Bilin...
case intro R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : Bilin...
((:c Membership.mem) (:fv _uniq.227966) ((:c Submodule) (:fv _uniq.227969) (:fv _uniq.227966) ((:c DivisionSemiring.toSemiring) (:fv _uniq.227969) ((:c Semifield.toDivisionSemiring) (:fv _uniq.227969) ((:c Field.toSemifield) (:fv _uniq.227969) (:fv _uniq.227972)))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.227966) ...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c CommSemiring) (:fv _uniq.227145))"},{"name":"inst✝¹⁰","sexp":"((:c AddCommMonoid) (:fv _uniq.227148))"},{"name":"inst✝⁹","sexp":"((:c Module) (:fv _uniq.227145) (:fv _uniq.227148) ((:c CommSemiring.toSemiring...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV10)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV11)) (:arg :explicit 1 (:fv FV10)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV11))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explic...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"refine","sourceEnd":16911,"sourceStart":16905,"tag":"atom"},{"children":[{"children":[{"name":"Subtype.mk_eq_mk","semanticRole":"global","source":"Subtype.mk_eq_mk","sourceEnd":16928,"sourceStart":16912,"tag":"identifier"},{"source":".","sourceEnd":16929,"sourceStart":16928,"tag":"atom"},{"child...
[]
[{"source":"Subtype.mk_eq_mk.1 (b₂ ⟨x, hx₁⟩ ?_)","source_end":16955,"source_start":16912,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal...
84
11
exact
true
1
29
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a7cd0dc04b7a30d5fe5a50984bcdb2dd110ec11f8d6af345a294b48f883bb655
677c355621266c33e4b0d5279028b0e5c44f6eb82c080b65eb9a3f50a1c4675a
10b7e883a9012c660387d3be87ffe4e6835890f8da382da207ba26d8fc247879
c93d252c91005e6035a77c6179e5aaf5eefc4c6cd846954c34ef31acb55f1e34
cat-searcher/leandojo-benchmark-4-random
test
1,406
LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegenerate
Mathlib/LinearAlgebra/BilinearForm/Orthogonal.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro ⟨n, hn⟩
case intro R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : Bilin...
case intro.mk R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : Bi...
(:forall n ((:c Subtype) (:fv _uniq.227966) (:lambda x (:fv _uniq.227966) ((:c Membership.mem) (:fv _uniq.227966) ((:c Submodule) (:fv _uniq.227969) (:fv _uniq.227966) ((:c CommSemiring.toSemiring) (:fv _uniq.227969) ((:c Semifield.toCommSemiring) (:fv _uniq.227969) ((:c Field.toSemifield) (:fv _uniq.227969) (:fv _uniq...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c CommSemiring) (:fv _uniq.227145))"},{"name":"inst✝¹⁰","sexp":"((:c AddCommMonoid) (:fv _uniq.227148))"},{"name":"inst✝⁹","sexp":"((:c Module) (:fv _uniq.227145) (:fv _uniq.227148) ((:c CommSemiring.toSemiring...
(:forall n :explicit (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV10)) (:arg :explicit 1 (:lambda x :explicit (:fv FV10) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV10)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV11)) (:arg :explicit 1 (:fv FV10)) (:arg :instance 2 (:instance-o...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"rintro","sourceEnd":16966,"sourceStart":16960,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":16970,"sourceStart":16967,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"n","sourceEnd":16971,"sou...
[{"role":"fresh_name","source":"n","source_end":16971,"source_start":16970,"syntax_kind":"ident"},{"role":"fresh_name","source":"hn","source_end":16975,"source_start":16973,"syntax_kind":"ident"}]
[{"source":"⟨n, hn⟩","source_end":16978,"source_start":16967,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal...
84
12
exact
true
1
29
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d9cc6c438363d7c271acf30d8d5b1ec2247cf212caaebdce66375378f631c596
c93d252c91005e6035a77c6179e5aaf5eefc4c6cd846954c34ef31acb55f1e34
b1661b55bfa8efbb02ebaefe6af7583985026f054d9fdb3e1f0a8aadafc185cf
9ba75e4122ba1db50dc78036a3de72a2dbbee98174cbc06a08f22f1fb70dcd60
cat-searcher/leandojo-benchmark-4-random
test
1,407
LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegenerate
Mathlib/LinearAlgebra/BilinearForm/Orthogonal.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>LinearMap.BilinForm.restrict_apply</a>, <a>LinearMap.domRestrict_apply</a>]
case intro.mk R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : Bi...
case intro.mk R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : Bi...
((:c Eq) (:fv _uniq.227969) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.227969) (:fv _uniq.227969) ((:c CommSemiring.toSemiring) (:fv _uniq.227969) ((:c Semifield.toCommSemiring) (:fv _uniq.227969) ((:c Field.toSemifield) (:fv _uniq.227969) (:fv _uniq.227972)))) ((:c CommSemiring.toSemiring) (:fv _uniq.227969) ((:c S...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c CommSemiring) (:fv _uniq.227145))"},{"name":"inst✝¹⁰","sexp":"((:c AddCommMonoid) (:fv _uniq.227148))"},{"name":"inst✝⁹","sexp":"((:c Module) (:fv _uniq.227145) (:fv _uniq.227148) ((:c CommSemiring.toSemiring...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV11)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV11)) (:arg :implicit-type 1 (:fv FV11)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV11))))) (:arg :instance 3 (:instance-o...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"simp","sourceEnd":16987,"sourceStart":16983,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":16992,"sourceStart":16988,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":169...
[]
[{"source":"restrict_apply","source_end":17008,"source_start":16994,"syntax_kind":"ident"},{"source":"domRestrict_apply","source_end":17027,"source_start":17010,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal...
84
13
exact
true
1
31
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
895db776e51879de4c8a67af13920a7e62a811679de5c546847797c6f9c56fc2
9ba75e4122ba1db50dc78036a3de72a2dbbee98174cbc06a08f22f1fb70dcd60
b72d758b5807761e319a51130c70908fe745414beed106f079b1063843fa64d8
eb838a6c70d0803e975c8f02c92b34cceb648edffc8a23a32669e514d40028f3
cat-searcher/leandojo-benchmark-4-random
test
1,408
LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegenerate
Mathlib/LinearAlgebra/BilinearForm/Orthogonal.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact b₁ n x (b₁ x n (b₁ n x (hx₂ n hn)))
case intro.mk R : Type u_1 M : Type u_2 inst✝¹¹ : CommSemiring R inst✝¹⁰ : AddCommMonoid M inst✝⁹ : Module R M R₁ : Type u_3 M₁ : Type u_4 inst✝⁸ : CommRing R₁ inst✝⁷ : AddCommGroup M₁ inst✝⁶ : Module R₁ M₁ V : Type u_5 K : Type u_6 inst✝⁵ : Field K inst✝⁴ : AddCommGroup V inst✝³ : Module K V B✝ : BilinForm R M B₁ : Bi...
((:c Eq) (:fv _uniq.227969) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.227969) (:fv _uniq.227969) ((:c CommSemiring.toSemiring) (:fv _uniq.227969) ((:c Semifield.toCommSemiring) (:fv _uniq.227969) ((:c Field.toSemifield) (:fv _uniq.227969) (:fv _uniq.227972)))) ((:c CommSemiring.toSemiring) (:fv _uniq.227969) ((:c S...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c CommSemiring) (:fv _uniq.227145))"},{"name":"inst✝¹⁰","sexp":"((:c AddCommMonoid) (:fv _uniq.227148))"},{"name":"inst✝⁹","sexp":"((:c Module) (:fv _uniq.227145) (:fv _uniq.227148) ((:c CommSemiring.toSemiring...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV11)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV11)) (:arg :implicit-type 1 (:fv FV11)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV11))))) (:arg :instance 3 (:instance-o...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"exact","sourceEnd":17038,"sourceStart":17033,"tag":"atom"},{"children":[{"contextIndex":24,"semanticRole":"local","source":"b₁","sourceEnd":17043,"sourceStart":17039,"tag":"identifier"},{"children":[{"contextIndex":30,"semanticRole":"local","source":"n","sourceEnd":17045,"sourceStart":17044,"tag...
[]
[{"source":"b₁ n x (b₁ x n (b₁ n x (hx₂ n hn)))","source_end":17082,"source_start":17039,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227145","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227148","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal...
84
14
exact
true
1
31
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
90a7652e50c71349dd6543de8bcb90f1e66f9b17b4b81e2c977d2ddabc72f2d5
eb838a6c70d0803e975c8f02c92b34cceb648edffc8a23a32669e514d40028f3
c98d39150440916538a0dacf3cb949400dbd9b3f6cd49a489722715b2be2e6ff
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,409
WeierstrassCurve.Affine.equation_negAdd
Mathlib/AlgebraicGeometry/EllipticCurve/Affine.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>WeierstrassCurve.Affine.equation_add_iff</a>, <a>WeierstrassCurve.Affine.addPolynomial_slope</a> h₁ h₂ hxy]
R : Type u inst✝¹ : CommRing R W✝ : Affine R F : Type u inst✝ : Field F W : Affine F x₁ x₂ y₁ y₂ : F h₁ : W.Equation x₁ y₁ h₂ : W.Equation x₂ y₂ hxy : x₁ = x₂ → y₁ ≠ W.negY x₂ y₂ ⊢ W.Equation (W.addX x₁ x₂ (W.slope x₁ x₂ y₁ y₂)) (W.negAddY x₁ x₂ y₁ (W.slope x₁ x₂ y₁ y₂))
R : Type u inst✝¹ : CommRing R W✝ : Affine R F : Type u inst✝ : Field F W : Affine F x₁ x₂ y₁ y₂ : F h₁ : W.Equation x₁ y₁ h₂ : W.Equation x₂ y₂ hxy : x₁ = x₂ → y₁ ≠ W.negY x₂ y₂ ⊢ eval (W.addX x₁ x₂ (W.slope x₁ x₂ y₁ y₂)) (-((X - C x₁) * (X - C x₂) * (X - C (W.addX x₁ x₂ (W.slope x₁ x₂ y₁ y₂))))) = 0
((:c WeierstrassCurve.Affine.Equation) (:fv _uniq.416682) ((:c EuclideanDomain.toCommRing) (:fv _uniq.416682) ((:c Field.toEuclideanDomain) (:fv _uniq.416682) (:fv _uniq.416685))) (:fv _uniq.416688) ((:c WeierstrassCurve.Affine.addX) (:fv _uniq.416682) ((:c EuclideanDomain.toCommRing) (:fv _uniq.416682) ((:c Field.toEu...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.416674))"},{"name":"W✝","sexp":"((:c WeierstrassCurve.Affine) (:fv _uniq.416674))"},{"name":"F","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c Field) (:fv _uniq.416682))"},{"name":"W","sexp":"((:c WeierstrassCurve.Affine) ...
(:app (:c WeierstrassCurve.Affine.Equation) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:app (:c WeierstrassCurve.Affine.addX) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.416674","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.416677","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CommRing) (:arg :expl...
{"children":[{"source":"rw","sourceEnd":28647,"sourceStart":28645,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28649,"sourceStart":28648,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"WeierstrassCurve...
[]
[{"source":"equation_add_iff","source_end":28665,"source_start":28649,"syntax_kind":"ident"},{"source":"addPolynomial_slope h₁ h₂ hxy","source_end":28700,"source_start":28667,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.416674","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.416677","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"inte...
143
4
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
6db4eccb135ff470464ec498c26a0cd9e9c5b45e4be1fccd80728f72768fd3c3
11a65e3b4d4fb83291eb5a37f6648ccc91eccefc8be918ed2d3bae96a3769d7d
39bd033104e2d2d6f7ceca5b25450f8f9a1a5d07c87662f3e04ee7950201ec3a
3430f1d3f7ad242efcb373ea7abc3993afca77f32e3ec6b065eb388846fe0123
cat-searcher/leandojo-benchmark-4-random
test
1,410
WeierstrassCurve.Affine.equation_negAdd
Mathlib/AlgebraicGeometry/EllipticCurve/Affine.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
eval_simp
R : Type u inst✝¹ : CommRing R W✝ : Affine R F : Type u inst✝ : Field F W : Affine F x₁ x₂ y₁ y₂ : F h₁ : W.Equation x₁ y₁ h₂ : W.Equation x₂ y₂ hxy : x₁ = x₂ → y₁ ≠ W.negY x₂ y₂ ⊢ eval (W.addX x₁ x₂ (W.slope x₁ x₂ y₁ y₂)) (-((X - C x₁) * (X - C x₂) * (X - C (W.addX x₁ x₂ (W.slope x₁ x₂ y₁ y₂))))) = 0
R : Type u inst✝¹ : CommRing R W✝ : Affine R F : Type u inst✝ : Field F W : Affine F x₁ x₂ y₁ y₂ : F h₁ : W.Equation x₁ y₁ h₂ : W.Equation x₂ y₂ hxy : x₁ = x₂ → y₁ ≠ W.negY x₂ y₂ ⊢ -((W.addX x₁ x₂ (W.slope x₁ x₂ y₁ y₂) - x₁) * (W.addX x₁ x₂ (W.slope x₁ x₂ y₁ y₂) - x₂) * (W.addX x₁ x₂ (W.slope x₁ x₂ y₁ y₂) - W.a...
((:c Eq) (:fv _uniq.416682) ((:c Polynomial.eval) (:fv _uniq.416682) ((:c CommSemiring.toSemiring) (:fv _uniq.416682) ((:c CommRing.toCommSemiring) (:fv _uniq.416682) ((:c EuclideanDomain.toCommRing) (:fv _uniq.416682) ((:c Field.toEuclideanDomain) (:fv _uniq.416682) (:fv _uniq.416685))))) ((:c WeierstrassCurve.Affine....
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.416674))"},{"name":"W✝","sexp":"((:c WeierstrassCurve.Affine) (:fv _uniq.416674))"},{"name":"F","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c Field) (:fv _uniq.416682))"},{"name":"W","sexp":"((:c WeierstrassCurve.Affine) ...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c Polynomial.eval) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c WeierstrassCurve.Affine.addX) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.416674","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.416677","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CommRing) (:arg :expl...
{"children":[{"source":"eval_simp","sourceEnd":28713,"sourceStart":28704,"tag":"atom"}],"kind":"tacticEval_simp._@.Mathlib.AlgebraicGeometry.EllipticCurve.Affine._hyg.835","source":"eval_simp","sourceEnd":28713,"sourceStart":28704,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.416674","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.416677","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"inte...
143
8
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1b111ab80da9f0ff7eca2ae473676ade7187d1fd9a7f32468f37aedef63180bc
3430f1d3f7ad242efcb373ea7abc3993afca77f32e3ec6b065eb388846fe0123
1a08cc32d11c678fc984ef2ad6fb811b1750c281f285f873fc1ff01dd9b10d94
afbbc15f90294d350f997f409a830e01008eb9bfcfd71da266162ea07fa1fc63
cat-searcher/leandojo-benchmark-4-random
test
1,411
WeierstrassCurve.Affine.equation_negAdd
Mathlib/AlgebraicGeometry/EllipticCurve/Affine.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>neg_eq_zero</a>, <a>sub_self</a>, <a>MulZeroClass.mul_zero</a>]
R : Type u inst✝¹ : CommRing R W✝ : Affine R F : Type u inst✝ : Field F W : Affine F x₁ x₂ y₁ y₂ : F h₁ : W.Equation x₁ y₁ h₂ : W.Equation x₂ y₂ hxy : x₁ = x₂ → y₁ ≠ W.negY x₂ y₂ ⊢ -((W.addX x₁ x₂ (W.slope x₁ x₂ y₁ y₂) - x₁) * (W.addX x₁ x₂ (W.slope x₁ x₂ y₁ y₂) - x₂) * (W.addX x₁ x₂ (W.slope x₁ x₂ y₁ y₂) - W.a...
((:c Eq) (:fv _uniq.416682) ((:c Neg.neg) (:fv _uniq.416682) ((:c Ring.toNeg) (:fv _uniq.416682) ((:c DivisionRing.toRing) (:fv _uniq.416682) ((:c Field.toDivisionRing) (:fv _uniq.416682) (:fv _uniq.416685)))) ((:c HMul.hMul) (:fv _uniq.416682) (:fv _uniq.416682) (:fv _uniq.416682) ((:c instHMul) (:fv _uniq.416682) ((:...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.416674))"},{"name":"W✝","sexp":"((:c WeierstrassCurve.Affine) (:fv _uniq.416674))"},{"name":"F","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c Field) (:fv _uniq.416682))"},{"name":"W","sexp":"((:c WeierstrassCurve.Affine) ...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c Neg.neg) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.416674","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.416677","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CommRing) (:arg :expl...
{"children":[{"source":"rw","sourceEnd":28718,"sourceStart":28716,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28720,"sourceStart":28719,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"neg_eq_zero","se...
[]
[{"source":"neg_eq_zero","source_end":28731,"source_start":28720,"syntax_kind":"ident"},{"source":"sub_self","source_end":28741,"source_start":28733,"syntax_kind":"ident"},{"source":"mul_zero","source_end":28751,"source_start":28743,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.416674","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.416677","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"inte...
143
9
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a57207eb1cac3f532bac775937295223a7ce7c58bb9efd8976e0234330a87c4a
afbbc15f90294d350f997f409a830e01008eb9bfcfd71da266162ea07fa1fc63
54cd40a719038a669a84b5e42b45b162cf150e9a947dc1f563f23d0c695484ee
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,412
mul_eq_of_eq_inv_mul₀
Mathlib/Algebra/GroupWithZero/Units/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rwa [← <a>eq_inv_mul_iff_mul_eq₀</a>]
α : Type u_1 M₀ : Type u_2 G₀ : Type u_3 M₀' : Type u_4 G₀' : Type u_5 F : Type u_6 F' : Type u_7 inst✝¹ : MonoidWithZero M₀ inst✝ : GroupWithZero G₀ a b c d : G₀ m n : ℕ hb : b ≠ 0 h : b = a⁻¹ * c ⊢ a * b = c
α : Type u_1 M₀ : Type u_2 G₀ : Type u_3 M₀' : Type u_4 G₀' : Type u_5 F : Type u_6 F' : Type u_7 inst✝¹ : MonoidWithZero M₀ inst✝ : GroupWithZero G₀ a b c d : G₀ m n : ℕ hb : b ≠ 0 h : b = a⁻¹ * c ⊢ a ≠ 0
((:c Eq) (:fv _uniq.23545) ((:c HMul.hMul) (:fv _uniq.23545) (:fv _uniq.23545) (:fv _uniq.23545) ((:c instHMul) (:fv _uniq.23545) ((:c MulZeroClass.toMul) (:fv _uniq.23545) ((:c MulZeroOneClass.toMulZeroClass) (:fv _uniq.23545) ((:c MonoidWithZero.toMulZeroOneClass) (:fv _uniq.23545) ((:c GroupWithZero.toMonoidWithZero...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"M₀","sexp":"(:sort (+ u_2 1))"},{"name":"G₀","sexp":"(:sort (+ u_3 1))"},{"name":"M₀'","sexp":"(:sort (+ u_4 1))"},{"name":"G₀'","sexp":"(:sort (+ u_5 1))"},{"name":"F","sexp":"(:sort (+ u_6 1))"},{"name":"F'","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝¹","sexp":"((:c Mo...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23539","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23542","is_instance":false,"is_let":false,"name":"M₀","sexp":"(:sort Type)"},{"binder_role":":implicit","co...
{"children":[{"source":"rwa","sourceEnd":12794,"sourceStart":12791,"tag":"atom"},{"children":[{"source":"[","sourceEnd":12796,"sourceStart":12795,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":12799,"sourceStart":12796,"tag":"atom"}],"kind":"token.«← »","source"...
[]
[{"source":"eq_inv_mul_iff_mul_eq₀","source_end":12824,"source_start":12800,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23539","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23542","is_instance":false,"is_let":false,"user_name":"M₀"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
124
4
exact
true
1
17
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7ce540c25fb038f17ba38dfb84ddfe78446d2108d947d89a43d5d7ba519f098a
0ab718f2c81c9ce4ebaef6d62b0ee6291959a2265d053f9a037845cd3766e517
4ae115fac2db6ed112d4f167c9708f738bc0552ae6c95b3e08964b23b1ec5331
8f99b35c3e96cb27c4dad8f88781a7d92922c18a264cc4f619fcf6c4a6c51a64
cat-searcher/leandojo-benchmark-4-random
test
1,413
mul_eq_of_eq_inv_mul₀
Mathlib/Algebra/GroupWithZero/Units/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro rfl
α : Type u_1 M₀ : Type u_2 G₀ : Type u_3 M₀' : Type u_4 G₀' : Type u_5 F : Type u_6 F' : Type u_7 inst✝¹ : MonoidWithZero M₀ inst✝ : GroupWithZero G₀ a b c d : G₀ m n : ℕ hb : b ≠ 0 h : b = a⁻¹ * c ⊢ a ≠ 0
α : Type u_1 M₀ : Type u_2 G₀ : Type u_3 M₀' : Type u_4 G₀' : Type u_5 F : Type u_6 F' : Type u_7 inst✝¹ : MonoidWithZero M₀ inst✝ : GroupWithZero G₀ b c d : G₀ m n : ℕ hb : b ≠ 0 h : b = 0⁻¹ * c ⊢ False
((:c Ne) (:fv _uniq.23545) (:fv _uniq.23565) ((:c OfNat.ofNat) (:fv _uniq.23545) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.23545) ((:c MonoidWithZero.toZero) (:fv _uniq.23545) ((:c GroupWithZero.toMonoidWithZero) (:fv _uniq.23545) (:fv _uniq.23563))))))
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"M₀","sexp":"(:sort (+ u_2 1))"},{"name":"G₀","sexp":"(:sort (+ u_3 1))"},{"name":"M₀'","sexp":"(:sort (+ u_4 1))"},{"name":"G₀'","sexp":"(:sort (+ u_5 1))"},{"name":"F","sexp":"(:sort (+ u_6 1))"},{"name":"F'","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝¹","sexp":"((:c Mo...
(:app (:c Ne) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:fv FV9)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:lit 0))))))))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23539","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23542","is_instance":false,"is_let":false,"name":"M₀","sexp":"(:sort Type)"},{"binder_role":":implicit","co...
{"children":[{"source":"rintro","sourceEnd":12833,"sourceStart":12827,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":12837,"sourceStart":12834,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl","sourceEnd":12837,"sourceStart":128...
[]
[{"source":"rfl","source_end":12837,"source_start":12834,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23539","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23542","is_instance":false,"is_let":false,"user_name":"M₀"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
124
8
exact
true
1
17
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2addf345fd3f02828837dc77795363b4cf13792e8b8f480b8f4c05e8e29df6a1
8f99b35c3e96cb27c4dad8f88781a7d92922c18a264cc4f619fcf6c4a6c51a64
09e128cd6787f35d3c063b643315aff1382388dafa4e55b6546fbf9dcecb02da
b74c1159e154a05392addfd644bc690bc435adb45f1249acd64220bbb4e12a99
cat-searcher/leandojo-benchmark-4-random
test
1,414
mul_eq_of_eq_inv_mul₀
Mathlib/Algebra/GroupWithZero/Units/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [hb] at h
α : Type u_1 M₀ : Type u_2 G₀ : Type u_3 M₀' : Type u_4 G₀' : Type u_5 F : Type u_6 F' : Type u_7 inst✝¹ : MonoidWithZero M₀ inst✝ : GroupWithZero G₀ b c d : G₀ m n : ℕ hb : b ≠ 0 h : b = 0⁻¹ * c ⊢ False
(:c False)
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"M₀","sexp":"(:sort (+ u_2 1))"},{"name":"G₀","sexp":"(:sort (+ u_3 1))"},{"name":"M₀'","sexp":"(:sort (+ u_4 1))"},{"name":"G₀'","sexp":"(:sort (+ u_5 1))"},{"name":"F","sexp":"(:sort (+ u_6 1))"},{"name":"F'","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝¹","sexp":"((:c Mo...
(:c False)
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23539","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23542","is_instance":false,"is_let":false,"name":"M₀","sexp":"(:sort Type)"},{"binder_role":":implicit","co...
{"children":[{"source":"simp","sourceEnd":12843,"sourceStart":12839,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12845,"sourceStart":12844,"tag":"a...
[]
[{"source":"hb","source_end":12847,"source_start":12845,"syntax_kind":"ident"},{"source":"h","source_end":12853,"source_start":12852,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23539","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23542","is_instance":false,"is_let":false,"user_name":"M₀"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
124
10
exact
true
1
16
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
45ac4777a6f5ebb26c663273c747e5a3f859ae400e74b855eaff85d5816fac86
b74c1159e154a05392addfd644bc690bc435adb45f1249acd64220bbb4e12a99
5e29effcf5e430c88eef45f6aba58d02ddb7a45181dc9ba5727dacb89a9163e9
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,415
RingHom.rangeS_top_iff_surjective
Mathlib/Algebra/Ring/Subsemiring/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>RingHom.coe_rangeS</a>, <a>Subsemiring.coe_top</a>]
R : Type u S : Type v T : Type w inst✝⁷ : NonAssocSemiring R M : Submonoid R inst✝⁶ : NonAssocSemiring S inst✝⁵ inst✝⁴ : NonAssocSemiring T s : Subsemiring R σR : Type u_1 σS : Type u_2 inst✝³ : SetLike σR R inst✝² : SetLike σS S inst✝¹ : SubsemiringClass σR R inst✝ : SubsemiringClass σS S f : R →+* S ⊢ ↑f.rangeS = ↑⊤ ...
((:c Iff) ((:c Eq) ((:c Set) (:fv _uniq.158754)) ((:c SetLike.coe) ((:c Subsemiring) (:fv _uniq.158754) (:fv _uniq.158784)) (:fv _uniq.158754) ((:c Subsemiring.instSetLike) (:fv _uniq.158754) (:fv _uniq.158784)) ((:c RingHom.rangeS) (:fv _uniq.158752) (:fv _uniq.158754) (:fv _uniq.158759) (:fv _uniq.158784) (:fv _uniq....
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"inst✝⁷","sexp":"((:c NonAssocSemiring) (:fv _uniq.158752))"},{"name":"M","sexp":"((:c Submonoid) (:fv _uniq.158752) ((:c MulZeroOneClass.toMulOneClass) (:fv _uniq.158752) ((:c NonAssocSemiring.toM...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c SetLike.coe) (:arg :implicit-type 0 (:app (:c Subsemiring) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c NonAssocSemiring) (:arg :explicit 0 (:fv FV1))...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.158752","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.158754","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":47169,"sourceStart":47167,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":47171,"sourceStart":47170,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",...
[]
[{"source":"coe_rangeS","source_end":47181,"source_start":47171,"syntax_kind":"ident"},{"source":"coe_top","source_end":47190,"source_start":47183,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.158752","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.158754","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
384
2
exact
true
1
16
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0d7a0c1d1e78ee3defd06a8e06800be2f62d8773a3930e3f06526d34feada6b3
99fe3d7d4a22684fc57b7e5fc5a6d77e4b4af1718f7fba84916ee0c8fd23f855
cc1b401ce4adcc3f2ad72c71cfdd03b1171ec1012beba3f2a25814e675765450
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,416
Real.rpow_add_nat'
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Real.rpow_add'</a> hx h, <a>Real.rpow_natCast</a>]
x y z : ℝ n : ℕ hx : 0 ≤ x h : y + ↑n ≠ 0 ⊢ x ^ (y + ↑n) = x ^ y * x ^ n
((:c Eq) (:c Real) ((:c HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) (:fv _uniq.77488) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) (:fv _uniq.77490) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.77494)))) ((:c HM...
[{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"z","sexp":"(:c Real)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hx","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.77488))"},{"name":"h","sexp":"((:...
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HPow.hPow) (: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 HPow) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77488","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.77490","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"},{"binder_role":":implicit","context_i...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":18981,"sourceStart":18979,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":18983,"sourceStart":18982,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",...
[]
[{"source":"rpow_add' hx h","source_end":18997,"source_start":18983,"syntax_kind":"Lean.Parser.Term.app"},{"source":"rpow_natCast","source_end":19011,"source_start":18999,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77488","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.77490","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
139
2
exact
true
1
6
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5b9082e98f66534ca69721c9faa57691863dd179ad11c6e55075b3d75ea7789c
4fa64e21720a4a93bd561d394c5c6e6d048cd23da26df6bd0e3612a0b742904e
bf6480082d17aa4431fb62f5eaede92d1a741a87d9d59f216ee3b122ee3c7c02
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,417
IsPGroup.comap_of_ker_isPGroup
Mathlib/GroupTheory/PGroup.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro g
p : ℕ G : Type u_1 inst✝¹ : Group G H : Subgroup G hH : IsPGroup p ↥H K : Type u_2 inst✝ : Group K ϕ : K →* G hϕ : IsPGroup p ↥ϕ.ker ⊢ IsPGroup p ↥(Subgroup.comap ϕ H)
p : ℕ G : Type u_1 inst✝¹ : Group G H : Subgroup G hH : IsPGroup p ↥H K : Type u_2 inst✝ : Group K ϕ : K →* G hϕ : IsPGroup p ↥ϕ.ker g : ↥(Subgroup.comap ϕ H) ⊢ ∃ k, g ^ p ^ k = 1
((:c IsPGroup) (:fv _uniq.68461) ((:c Subtype) (:fv _uniq.69781) (:lambda x (:fv _uniq.69781) ((:c Membership.mem) (:fv _uniq.69781) ((:c Subgroup) (:fv _uniq.69781) (:fv _uniq.69782)) ((:c SetLike.instMembership) ((:c Subgroup) (:fv _uniq.69781) (:fv _uniq.69782)) (:fv _uniq.69781) ((:c Subgroup.instSetLike) (:fv _uni...
[{"name":"p","sexp":"(:c Nat)"},{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.68464))"},{"name":"H","sexp":"((:c Subgroup) (:fv _uniq.68464) (:fv _uniq.68467))"},{"name":"hH","sexp":"((:c IsPGroup) (:fv _uniq.68461) ((:c Subtype) (:fv _uniq.68464) (:lambda x (:fv _uniq.68464) (...
(:app (:c IsPGroup) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:lambda x :explicit (:fv FV6) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1 (:app (:c Subgroup) (:arg :explicit 0 (:fv FV6)) (:arg :instance 1 (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68461","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68464","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit"...
{"children":[{"source":"intro","sourceEnd":12595,"sourceStart":12590,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"g","sourceEnd":12597,"sourceStart":12596,"tag":"identifier"}],"kind":"null","source":"g","sourceEnd":12597,"sourceStart":12596,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source...
[{"role":"fresh_name","source":"g","source_end":12597,"source_start":12596,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68461","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68464","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
69
4
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3f2e32a3e5ed24c870323fdff643e2e6309f9470acce22ff07dded079fd3fa13
71495c4beec2eceb49bc0c276a4c756da07dca6b6b4cf4dca632cbf5b488662d
d28ef5e161473bac03b6a7d518df015e5aa75f837a38fc378a1b75baf75d8fe0
ad521d24e66aa508013d5e5bfd376d3e6730430867b88a2c4ce15571bb0d4ff6
cat-searcher/leandojo-benchmark-4-random
test
1,418
IsPGroup.comap_of_ker_isPGroup
Mathlib/GroupTheory/PGroup.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨j, hj⟩ := hH ⟨ϕ g.1, g.2⟩
p : ℕ G : Type u_1 inst✝¹ : Group G H : Subgroup G hH : IsPGroup p ↥H K : Type u_2 inst✝ : Group K ϕ : K →* G hϕ : IsPGroup p ↥ϕ.ker g : ↥(Subgroup.comap ϕ H) ⊢ ∃ k, g ^ p ^ k = 1
case intro p : ℕ G : Type u_1 inst✝¹ : Group G H : Subgroup G hH : IsPGroup p ↥H K : Type u_2 inst✝ : Group K ϕ : K →* G hϕ : IsPGroup p ↥ϕ.ker g : ↥(Subgroup.comap ϕ H) j : ℕ hj : ⟨ϕ ↑g, ⋯⟩ ^ p ^ j = 1 ⊢ ∃ k, g ^ p ^ k = 1
((:c Exists) (:c Nat) (:lambda k (:c Nat) ((:c Eq) ((:c Subtype) (:fv _uniq.69781) (:lambda x (:fv _uniq.69781) ((:c Membership.mem) (:fv _uniq.69781) ((:c Subgroup) (:fv _uniq.69781) (:fv _uniq.69782)) ((:c SetLike.instMembership) ((:c Subgroup) (:fv _uniq.69781) (:fv _uniq.69782)) (:fv _uniq.69781) ((:c Subgroup.inst...
[{"name":"p","sexp":"(:c Nat)"},{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.68464))"},{"name":"H","sexp":"((:c Subgroup) (:fv _uniq.68464) (:fv _uniq.68467))"},{"name":"hH","sexp":"((:c IsPGroup) (:fv _uniq.68461) ((:c Subtype) (:fv _uniq.68464) (:lambda x (:fv _uniq.68464) (...
(:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda k :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:lambda x :explicit (:fv FV6) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68461","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68464","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit"...
{"children":[{"source":"obtain","sourceEnd":12606,"sourceStart":12600,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":12610,"sourceStart":12607,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"j","sourceEn...
[]
[{"source":"hH ⟨ϕ g.1, g.2⟩","source_end":12642,"source_start":12622,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨j, hj⟩","source_end":12618,"source_start":12607,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68461","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68464","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
69
5
exact
true
1
10
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f5f11bb842b6a91a0b78eb800ff8d0e4cdf088f3148784a9a269a8e0b8365741
ad521d24e66aa508013d5e5bfd376d3e6730430867b88a2c4ce15571bb0d4ff6
d02e0b6c19afd2a157c3454c927118693457032df92a6c8866a5768d6a188c81
9fe40f101152b2f25dbc3715d7c58976a669aa9e6cdda805bf49895c95d62896
cat-searcher/leandojo-benchmark-4-random
test
1,419
IsPGroup.comap_of_ker_isPGroup
Mathlib/GroupTheory/PGroup.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Subtype.ext_iff</a>, H.coe_pow, <a>Subtype.coe_mk</a>, ← ϕ.map_pow] at hj
case intro p : ℕ G : Type u_1 inst✝¹ : Group G H : Subgroup G hH : IsPGroup p ↥H K : Type u_2 inst✝ : Group K ϕ : K →* G hϕ : IsPGroup p ↥ϕ.ker g : ↥(Subgroup.comap ϕ H) j : ℕ hj : ⟨ϕ ↑g, ⋯⟩ ^ p ^ j = 1 ⊢ ∃ k, g ^ p ^ k = 1
case intro p : ℕ G : Type u_1 inst✝¹ : Group G H : Subgroup G hH : IsPGroup p ↥H K : Type u_2 inst✝ : Group K ϕ : K →* G hϕ : IsPGroup p ↥ϕ.ker g : ↥(Subgroup.comap ϕ H) j : ℕ hj : ϕ (↑g ^ p ^ j) = ↑1 ⊢ ∃ k, g ^ p ^ k = 1
((:c Exists) (:c Nat) (:lambda k (:c Nat) ((:c Eq) ((:c Subtype) (:fv _uniq.69781) (:lambda x (:fv _uniq.69781) ((:c Membership.mem) (:fv _uniq.69781) ((:c Subgroup) (:fv _uniq.69781) (:fv _uniq.69782)) ((:c SetLike.instMembership) ((:c Subgroup) (:fv _uniq.69781) (:fv _uniq.69782)) (:fv _uniq.69781) ((:c Subgroup.inst...
[{"name":"p","sexp":"(:c Nat)"},{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.68464))"},{"name":"H","sexp":"((:c Subgroup) (:fv _uniq.68464) (:fv _uniq.68467))"},{"name":"hH","sexp":"((:c IsPGroup) (:fv _uniq.68461) ((:c Subtype) (:fv _uniq.68464) (:lambda x (:fv _uniq.68464) (...
(:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda k :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:lambda x :explicit (:fv FV6) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68461","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68464","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit"...
{"children":[{"source":"rw","sourceEnd":12647,"sourceStart":12645,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12649,"sourceStart":12648,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Subtype.ext_iff"...
[]
[{"source":"Subtype.ext_iff","source_end":12664,"source_start":12649,"syntax_kind":"ident"},{"source":"hj","source_end":12714,"source_start":12712,"syntax_kind":"ident"},{"source":"H.coe_pow","source_end":12675,"source_start":12666,"syntax_kind":"ident"},{"source":"Subtype.coe_mk","source_end":12691,"source_start":1267...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68461","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68464","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
69
6
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d8ce97484a1ff1062a1475394d62c817451a402f2da542e0504c79575d254770
9fe40f101152b2f25dbc3715d7c58976a669aa9e6cdda805bf49895c95d62896
2fd2f49f436a601d8219422761aa8bd2aaf503f15d7e332bc02384df08577152
1aa2c7c1d77241cf91abad482380f7ccf34c232196822142d17d41a74fac72f0
cat-searcher/leandojo-benchmark-4-random
test
1,420
IsPGroup.comap_of_ker_isPGroup
Mathlib/GroupTheory/PGroup.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨k, hk⟩ := hϕ ⟨g.1 ^ p ^ j, hj⟩
case intro p : ℕ G : Type u_1 inst✝¹ : Group G H : Subgroup G hH : IsPGroup p ↥H K : Type u_2 inst✝ : Group K ϕ : K →* G hϕ : IsPGroup p ↥ϕ.ker g : ↥(Subgroup.comap ϕ H) j : ℕ hj : ϕ (↑g ^ p ^ j) = ↑1 ⊢ ∃ k, g ^ p ^ k = 1
case intro.intro p : ℕ G : Type u_1 inst✝¹ : Group G H : Subgroup G hH : IsPGroup p ↥H K : Type u_2 inst✝ : Group K ϕ : K →* G hϕ : IsPGroup p ↥ϕ.ker g : ↥(Subgroup.comap ϕ H) j : ℕ hj : ϕ (↑g ^ p ^ j) = ↑1 k : ℕ hk : ⟨↑g ^ p ^ j, hj⟩ ^ p ^ k = 1 ⊢ ∃ k, g ^ p ^ k = 1
((:c Exists) (:c Nat) (:lambda k (:c Nat) ((:c Eq) ((:c Subtype) (:fv _uniq.69781) (:lambda x (:fv _uniq.69781) ((:c Membership.mem) (:fv _uniq.69781) ((:c Subgroup) (:fv _uniq.69781) (:fv _uniq.69782)) ((:c SetLike.instMembership) ((:c Subgroup) (:fv _uniq.69781) (:fv _uniq.69782)) (:fv _uniq.69781) ((:c Subgroup.inst...
[{"name":"p","sexp":"(:c Nat)"},{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.68464))"},{"name":"H","sexp":"((:c Subgroup) (:fv _uniq.68464) (:fv _uniq.68467))"},{"name":"hH","sexp":"((:c IsPGroup) (:fv _uniq.68461) ((:c Subtype) (:fv _uniq.68464) (:lambda x (:fv _uniq.68464) (...
(:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda k :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:lambda x :explicit (:fv FV6) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68461","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68464","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit"...
{"children":[{"source":"obtain","sourceEnd":12723,"sourceStart":12717,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":12727,"sourceStart":12724,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"k","sourceEn...
[]
[{"source":"hϕ ⟨g.1 ^ p ^ j, hj⟩","source_end":12764,"source_start":12739,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨k, hk⟩","source_end":12735,"source_start":12724,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68461","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68464","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
69
12
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
496893c148163db277fd35ee8fadd88d46ff2b40236cfd38147648bc0f393e0f
1aa2c7c1d77241cf91abad482380f7ccf34c232196822142d17d41a74fac72f0
a351f1620b824d5ad98eecde75dfc97e53d8cf4917688e30324a68e7ee0815ec
9285a3b382a5ade243bed5c2df470646a272e4abe18a5be2d6f1f82f91be8709
cat-searcher/leandojo-benchmark-4-random
test
1,421
IsPGroup.comap_of_ker_isPGroup
Mathlib/GroupTheory/PGroup.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Subtype.ext_iff</a>, ϕ.ker.coe_pow, <a>Subtype.coe_mk</a>, ← <a>pow_mul</a>, ← <a>pow_add</a>] at hk
case intro.intro p : ℕ G : Type u_1 inst✝¹ : Group G H : Subgroup G hH : IsPGroup p ↥H K : Type u_2 inst✝ : Group K ϕ : K →* G hϕ : IsPGroup p ↥ϕ.ker g : ↥(Subgroup.comap ϕ H) j : ℕ hj : ϕ (↑g ^ p ^ j) = ↑1 k : ℕ hk : ⟨↑g ^ p ^ j, hj⟩ ^ p ^ k = 1 ⊢ ∃ k, g ^ p ^ k = 1
case intro.intro p : ℕ G : Type u_1 inst✝¹ : Group G H : Subgroup G hH : IsPGroup p ↥H K : Type u_2 inst✝ : Group K ϕ : K →* G hϕ : IsPGroup p ↥ϕ.ker g : ↥(Subgroup.comap ϕ H) j : ℕ hj : ϕ (↑g ^ p ^ j) = ↑1 k : ℕ hk : ↑g ^ p ^ (j + k) = ↑1 ⊢ ∃ k, g ^ p ^ k = 1
((:c Exists) (:c Nat) (:lambda k (:c Nat) ((:c Eq) ((:c Subtype) (:fv _uniq.69781) (:lambda x (:fv _uniq.69781) ((:c Membership.mem) (:fv _uniq.69781) ((:c Subgroup) (:fv _uniq.69781) (:fv _uniq.69782)) ((:c SetLike.instMembership) ((:c Subgroup) (:fv _uniq.69781) (:fv _uniq.69782)) (:fv _uniq.69781) ((:c Subgroup.inst...
[{"name":"p","sexp":"(:c Nat)"},{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.68464))"},{"name":"H","sexp":"((:c Subgroup) (:fv _uniq.68464) (:fv _uniq.68467))"},{"name":"hH","sexp":"((:c IsPGroup) (:fv _uniq.68461) ((:c Subtype) (:fv _uniq.68464) (:lambda x (:fv _uniq.68464) (...
(:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda k :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:lambda x :explicit (:fv FV6) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68461","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68464","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit"...
{"children":[{"source":"rw","sourceEnd":12769,"sourceStart":12767,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12771,"sourceStart":12770,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Subtype.ext_iff"...
[]
[{"source":"Subtype.ext_iff","source_end":12786,"source_start":12771,"syntax_kind":"ident"},{"source":"hk","source_end":12851,"source_start":12849,"syntax_kind":"ident"},{"source":"ϕ.ker.coe_pow","source_end":12802,"source_start":12788,"syntax_kind":"ident"},{"source":"Subtype.coe_mk","source_end":12818,"source_start":...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68461","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68464","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
69
13
exact
true
1
14
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3dcb6dbc1d655591da962be203e6033f34fe79677704a9d8a6d04fd233d220bf
9285a3b382a5ade243bed5c2df470646a272e4abe18a5be2d6f1f82f91be8709
7e4c570d2c44d72653cad9cb546ccc92977cda1f6e3d04f7b3bd18ba7934da12
37487c15a317364e53182ccfb9837dcb7d07860e636942ea95087c0f4e1dd5ad
cat-searcher/leandojo-benchmark-4-random
test
1,422
IsPGroup.comap_of_ker_isPGroup
Mathlib/GroupTheory/PGroup.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact ⟨j + k, by rwa [<a>Subtype.ext_iff</a>, (H.comap ϕ).<a>Subgroup.coe_pow</a>]⟩
case intro.intro p : ℕ G : Type u_1 inst✝¹ : Group G H : Subgroup G hH : IsPGroup p ↥H K : Type u_2 inst✝ : Group K ϕ : K →* G hϕ : IsPGroup p ↥ϕ.ker g : ↥(Subgroup.comap ϕ H) j : ℕ hj : ϕ (↑g ^ p ^ j) = ↑1 k : ℕ hk : ↑g ^ p ^ (j + k) = ↑1 ⊢ ∃ k, g ^ p ^ k = 1
((:c Exists) (:c Nat) (:lambda k (:c Nat) ((:c Eq) ((:c Subtype) (:fv _uniq.69781) (:lambda x (:fv _uniq.69781) ((:c Membership.mem) (:fv _uniq.69781) ((:c Subgroup) (:fv _uniq.69781) (:fv _uniq.69782)) ((:c SetLike.instMembership) ((:c Subgroup) (:fv _uniq.69781) (:fv _uniq.69782)) (:fv _uniq.69781) ((:c Subgroup.inst...
[{"name":"p","sexp":"(:c Nat)"},{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.68464))"},{"name":"H","sexp":"((:c Subgroup) (:fv _uniq.68464) (:fv _uniq.68467))"},{"name":"hH","sexp":"((:c IsPGroup) (:fv _uniq.68461) ((:c Subtype) (:fv _uniq.68464) (:lambda x (:fv _uniq.68464) (...
(:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda k :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:lambda x :explicit (:fv FV6) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68461","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68464","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit"...
{"children":[{"source":"exact","sourceEnd":12859,"sourceStart":12854,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":12863,"sourceStart":12860,"tag":"atom"},{"children":[{"children":[{"contextIndex":11,"semanticRole":"local","source":"j","sourceEnd":12864,"sourceStart":12863,"tag":"identifier"},{"source":"+","sour...
[]
[{"source":"⟨j + k, by rwa [Subtype.ext_iff, (H.comap ϕ).coe_pow]⟩","source_end":12919,"source_start":12860,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68461","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68464","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
69
20
exact
true
1
14
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2a60add787ce0a77f96cdd31d96215ad083efe40001f3845c079caca17b09546
37487c15a317364e53182ccfb9837dcb7d07860e636942ea95087c0f4e1dd5ad
1765a4680b40bf5ca9688d2fd347d82c399224605177f6a02a9b81d3a9fefad5
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,423
IsPGroup.comap_of_ker_isPGroup
Mathlib/GroupTheory/PGroup.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rwa [<a>Subtype.ext_iff</a>, (H.comap ϕ).<a>Subgroup.coe_pow</a>]
p : ℕ G : Type u_1 inst✝¹ : Group G H : Subgroup G hH : IsPGroup p ↥H K : Type u_2 inst✝ : Group K ϕ : K →* G hϕ : IsPGroup p ↥ϕ.ker g : ↥(Subgroup.comap ϕ H) j : ℕ hj : ϕ (↑g ^ p ^ j) = ↑1 k : ℕ hk : ↑g ^ p ^ (j + k) = ↑1 ⊢ g ^ p ^ (j + k) = 1
((:c Eq) ((:c Subtype) (:fv _uniq.69781) (:lambda x (:fv _uniq.69781) ((:c Membership.mem) (:fv _uniq.69781) ((:c Subgroup) (:fv _uniq.69781) (:fv _uniq.69782)) ((:c SetLike.instMembership) ((:c Subgroup) (:fv _uniq.69781) (:fv _uniq.69782)) (:fv _uniq.69781) ((:c Subgroup.instSetLike) (:fv _uniq.69781) (:fv _uniq.6978...
[{"name":"p","sexp":"(:c Nat)"},{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.68464))"},{"name":"H","sexp":"((:c Subgroup) (:fv _uniq.68464) (:fv _uniq.68467))"},{"name":"hH","sexp":"((:c IsPGroup) (:fv _uniq.68461) ((:c Subtype) (:fv _uniq.68464) (:lambda x (:fv _uniq.68464) (...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:lambda x :explicit (:fv FV6) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1 (:app (:c Subgroup) (:arg :explicit 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c Group) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68461","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68464","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit"...
{"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":12876,"sourceStart":12873,"tag":"atom"},{"children":[{"source":"[","sourceEnd":12878,"sourceStart":12877,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Subtype.ext_iff","semanticRole"...
[]
[{"source":"Subtype.ext_iff","source_end":12893,"source_start":12878,"syntax_kind":"ident"},{"source":"(H.comap ϕ).coe_pow","source_end":12915,"source_start":12895,"syntax_kind":"Lean.Parser.Term.proj"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68461","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68464","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
69
23
exact
true
1
14
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
07672f7be96c83ad11ea80d5c99fd258463a15c2aa75528d9800b7a28b0222b1
0ca9c35fc747a24ed118eaeefbdf1501887f5d90870023270d9a0562670e3d41
fbc97ac16e05dbc72cd43fed9f7ca6c831c2649457a2a496d6e6d6103aa6f86b
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,424
Equiv.piCongr'_symm_apply_symm_apply
Mathlib/Logic/Equiv/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>Equiv.piCongr'</a>, <a>Equiv.piCongr_apply_apply</a>]
α : Sort u_1 β : Sort u_2 W : α → Sort w Z : β → Sort z h₁ : α ≃ β h₂ : (b : β) → W (h₁.symm b) ≃ Z b f : (b : β) → Z b b : β ⊢ (h₁.piCongr' h₂).symm f (h₁.symm b) = (h₂ b).symm (f b)
((:c Eq) ((:fv _uniq.119157) ((:c DFunLike.coe) ((:c Equiv) (:fv _uniq.119153) (:fv _uniq.119144)) (:fv _uniq.119153) (:lambda _ (:fv _uniq.119153) (:fv _uniq.119144)) ((:c Equiv.instFunLike) (:fv _uniq.119153) (:fv _uniq.119144)) ((:c Equiv.symm) (:fv _uniq.119144) (:fv _uniq.119153) (:fv _uniq.119165)) (:fv _uniq.119...
[{"name":"α","sexp":"(:sort u_1)"},{"name":"β","sexp":"(:sort u_2)"},{"name":"W","sexp":"(:forall _ (:fv _uniq.119144) (:sort w))"},{"name":"Z","sexp":"(:forall _ (:fv _uniq.119153) (:sort z))"},{"name":"h₁","sexp":"((:c Equiv) (:fv _uniq.119144) (:fv _uniq.119153))"},{"name":"h₂","sexp":"(:forall b (:fv _uniq.119153) ...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:fv FV2) (:arg :explicit 0 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Equiv) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV0)))) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c FunLike) (:arg :explicit 0 (:a...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119144","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119153","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":82904,"sourceStart":82900,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...
[]
[{"source":"piCongr'","source_end":82914,"source_start":82906,"syntax_kind":"ident"},{"source":"piCongr_apply_apply","source_end":82935,"source_start":82916,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119144","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119153","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
587
2
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ba960c5263b004fab0bb552bc0534179733bdc3a96c9720b0f98ee6d93b5a0c8
5cf49aaf30f14b3f0131c85dca4044fb5a1b611bbc097074ca4d3b7cb8b0f789
d8e73efb706ffc673d73d5c455e6292339fe89bbf5bf5c16542f0e5aa642439f
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,425
FormalMultilinearSeries.compPartialSumTarget_tendsto_atTop
Mathlib/Analysis/Analytic/Composition.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>Monotone.tendsto_atTop_finset</a>
𝕜 : Type u_1 E : Type u_2 F : Type u_3 G : Type u_4 H : Type u_5 inst✝⁸ : NontriviallyNormedField 𝕜 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G inst✝¹ : NormedAddCommGroup H inst✝ : NormedSpace ...
case h 𝕜 : Type u_1 E : Type u_2 F : Type u_3 G : Type u_4 H : Type u_5 inst✝⁸ : NontriviallyNormedField 𝕜 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G inst✝¹ : NormedAddCommGroup H inst✝ : Norme...
((:c Filter.Tendsto) (:c Nat) ((:c Finset) ((:c Sigma) (:c Nat) (:lambda n (:c Nat) ((:c Composition) 0)))) (:lambda N (:c Nat) ((:c FormalMultilinearSeries.compPartialSumTarget) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))) 0 0)) ((:c Filter.atTop) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"H","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.594860))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCo...
(:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:app (:c Sigma) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c Composition) (:arg :explicit 0 0)))))))) (:arg :explicit 2 (:lambda N :explicit (:c Nat) (:app...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"apply","sourceEnd":35754,"sourceStart":35749,"tag":"atom"},{"name":"Monotone.tendsto_atTop_finset","semanticRole":"global","source":"Monotone.tendsto_atTop_finset","sourceEnd":35784,"sourceStart":35755,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Monotone.tendsto_atTop_...
[]
[{"source":"Monotone.tendsto_atTop_finset","source_end":35784,"source_start":35755,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
114
4
exact
true
1
14
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
31a66458e51be37f7770ad687ef6179fc0d09e45eacd0221a0bc745e3dc2fcea
d83b37958f3365b73c15e91ed3fd287c4405d4d74e0582b5913f41da9c7b1435
4ede3a86af3fdf2b34479658b4c291b46e4ec4020e806bca3ea2eb8a61ccc009
bae927cf103e32b5c60699bea9cc9fa56df9fabeafbe1b2a35e4886a06655f64
cat-searcher/leandojo-benchmark-4-random
test
1,426
FormalMultilinearSeries.compPartialSumTarget_tendsto_atTop
Mathlib/Analysis/Analytic/Composition.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro m n hmn a ha
case h 𝕜 : Type u_1 E : Type u_2 F : Type u_3 G : Type u_4 H : Type u_5 inst✝⁸ : NontriviallyNormedField 𝕜 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G inst✝¹ : NormedAddCommGroup H inst✝ : Norme...
case h 𝕜 : Type u_1 E : Type u_2 F : Type u_3 G : Type u_4 H : Type u_5 inst✝⁸ : NontriviallyNormedField 𝕜 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G inst✝¹ : NormedAddCommGroup H inst✝ : Norme...
((:c Monotone) (:c Nat) ((:c Finset) ((:c Sigma) (:c Nat) (:lambda n (:c Nat) ((:c Composition) 0)))) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))) ((:c PartialOrder.toPreorder) ((:c Finset) ((:c Sigma) (:c Nat) (:lambda n (:c Nat) ((:c C...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"H","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.594860))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCo...
(:app (:c Monotone) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:app (:c Sigma) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c Composition) (:arg :explicit 0 0)))))))) (:arg :instance 2 (:instance-of (:app (:c Preorder) (:arg :...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"intro","sourceEnd":35795,"sourceStart":35790,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"m","sourceEnd":35797,"sourceStart":35796,"tag":"identifier"},{"semanticRole":"scoped_local","source":"n","sourceEnd":35799,"sourceStart":35798,"tag":"identifier"},{"semanticRole":"sco...
[{"role":"fresh_name","source":"m","source_end":35797,"source_start":35796,"syntax_kind":"ident"},{"role":"fresh_name","source":"n","source_end":35799,"source_start":35798,"syntax_kind":"ident"},{"role":"fresh_name","source":"hmn","source_end":35803,"source_start":35800,"syntax_kind":"ident"},{"role":"fresh_name","sour...
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
114
9
exact
true
1
14
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f3c3a2259210f48970d3a32b3b0ca8a5c6506f1127f6812b0b2db715d619887c
7868725b58406a3a5f2cf4b1de76ef85befaee433dbb02ab34687ae4891b76fa
0d943cb5c1c44f656b1b8c22d34e690911c632112febddfec81ff64bdba7459c
6d2f041f9ec2f18202d745d8edb21b562768645ba8cb4d4b6c89bed5011523a9
cat-searcher/leandojo-benchmark-4-random
test
1,427
FormalMultilinearSeries.compPartialSumTarget_tendsto_atTop
Mathlib/Analysis/Analytic/Composition.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have : ∀ i, i < m → i < n := fun i hi => <a>lt_of_lt_of_le</a> hi hmn
case h 𝕜 : Type u_1 E : Type u_2 F : Type u_3 G : Type u_4 H : Type u_5 inst✝⁸ : NontriviallyNormedField 𝕜 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G inst✝¹ : NormedAddCommGroup H inst✝ : Norme...
case h 𝕜 : Type u_1 E : Type u_2 F : Type u_3 G : Type u_4 H : Type u_5 inst✝⁸ : NontriviallyNormedField 𝕜 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G inst✝¹ : NormedAddCommGroup H inst✝ : Norme...
((:c Membership.mem) ((:c Sigma) (:c Nat) (:lambda n (:c Nat) ((:c Composition) 0))) ((:c Finset) ((:c Sigma) (:c Nat) (:lambda n (:c Nat) ((:c Composition) 0)))) ((:c Finset.instMembership) ((:c Sigma) (:c Nat) (:lambda n (:c Nat) ((:c Composition) 0)))) (:fv _uniq.595584) ((:lambda N (:c Nat) ((:c FormalMultilinearSe...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"H","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.594860))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCo...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Sigma) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c Composition) (:arg :explicit 0 0)))))) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:app (:c Sigma) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"have","sourceEnd":35817,"sourceStart":35813,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":35818,"sourceStart":35818,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":35818,"sourceStart":35818,"tag":"node"}],"kind":"Lean.Parser.Term.hav...
[]
[{"source":"∀ i, i < m → i < n","source_end":35842,"source_start":35820,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"fun i hi => lt_of_lt_of_le hi hmn","source_end":35879,"source_start":35846,"syntax_kind":"Lean.Parser.Term.fun"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
114
10
exact
true
1
19
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8e18e68a428b79ba03d3bb5de1a3e6d9ee40ec19564d5ee607fd6af93d2ddea0
6d2f041f9ec2f18202d745d8edb21b562768645ba8cb4d4b6c89bed5011523a9
70c2627889bb145c3e8b947c8e79a0c3a8b4c524fec327b9ef1479cbdf6f27f9
51fb3334548b213b1a6f011be5a48045ba434921e3bdc84c77e5cb9414e79477
cat-searcher/leandojo-benchmark-4-random
test
1,428
FormalMultilinearSeries.compPartialSumTarget_tendsto_atTop
Mathlib/Analysis/Analytic/Composition.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
aesop
case h 𝕜 : Type u_1 E : Type u_2 F : Type u_3 G : Type u_4 H : Type u_5 inst✝⁸ : NontriviallyNormedField 𝕜 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G inst✝¹ : NormedAddCommGroup H inst✝ : Norme...
((:c Membership.mem) ((:c Sigma) (:c Nat) (:lambda n (:c Nat) ((:c Composition) 0))) ((:c Finset) ((:c Sigma) (:c Nat) (:lambda n (:c Nat) ((:c Composition) 0)))) ((:c Finset.instMembership) ((:c Sigma) (:c Nat) (:lambda n (:c Nat) ((:c Composition) 0)))) (:fv _uniq.595584) ((:lambda N (:c Nat) ((:c FormalMultilinearSe...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"H","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.594860))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCo...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Sigma) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c Composition) (:arg :explicit 0 0)))))) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:app (:c Sigma) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"aesop","sourceEnd":35889,"sourceStart":35884,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Aesop.Frontend.Parser.aesopTactic","source":"aesop","sourceEnd":35889,"sourceStart":35884,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
114
11
exact
true
1
20
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7d5b03de44fc97006753d885333e269486cd68cf0670114f4cc8c7e2bbac3a10
51fb3334548b213b1a6f011be5a48045ba434921e3bdc84c77e5cb9414e79477
bf61abd9c8c94e02103733c96be27852844483acbf580158f224257e620356a8
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,429
FormalMultilinearSeries.compPartialSumTarget_tendsto_atTop
Mathlib/Analysis/Analytic/Composition.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro ⟨n, c⟩
case h' 𝕜 : Type u_1 E : Type u_2 F : Type u_3 G : Type u_4 H : Type u_5 inst✝⁸ : NontriviallyNormedField 𝕜 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G inst✝¹ : NormedAddCommGroup H inst✝ : Norm...
case h'.mk 𝕜 : Type u_1 E : Type u_2 F : Type u_3 G : Type u_4 H : Type u_5 inst✝⁸ : NontriviallyNormedField 𝕜 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G inst✝¹ : NormedAddCommGroup H inst✝ : N...
(:forall x ((:c Sigma) (:c Nat) (:lambda n (:c Nat) ((:c Composition) 0))) ((:c Exists) (:c Nat) (:lambda n (:c Nat) ((:c Membership.mem) ((:c Sigma) (:c Nat) (:lambda n (:c Nat) ((:c Composition) 0))) ((:c Finset) ((:c Sigma) (:c Nat) (:lambda n (:c Nat) ((:c Composition) 0)))) ((:c Finset.instMembership) ((:c Sigma) ...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"H","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.594860))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCo...
(:forall x :explicit (:app (:c Sigma) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c Composition) (:arg :explicit 0 0))))) (:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c Membership.mem) (:arg :implicit-type 0 (:app...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"rintro","sourceEnd":35901,"sourceStart":35895,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":35905,"sourceStart":35902,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"n","sourceEnd":35906,"sou...
[{"role":"fresh_name","source":"n","source_end":35906,"source_start":35905,"syntax_kind":"ident"},{"role":"fresh_name","source":"c","source_end":35909,"source_start":35908,"syntax_kind":"ident"}]
[{"source":"⟨n, c⟩","source_end":35912,"source_start":35902,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
114
16
exact
true
1
14
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1f9018fbcb377acce319adb30c65c39337aeba213d13efc36912401ba7447654
d722e261b8dbfb32cbb53c4d4bf6b4a214245dacf55d79d7d8e08a6206bfabb4
1b56e3e58cfdb438b88f5df5526b23af30307946b6decf590dffa3562f96a4a2
d348eb883f192c92890143c4221904e303b87fb079457e83d1d34a24b48aa74d
cat-searcher/leandojo-benchmark-4-random
test
1,430
FormalMultilinearSeries.compPartialSumTarget_tendsto_atTop
Mathlib/Analysis/Analytic/Composition.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>FormalMultilinearSeries.mem_compPartialSumTarget_iff</a>]
case h'.mk 𝕜 : Type u_1 E : Type u_2 F : Type u_3 G : Type u_4 H : Type u_5 inst✝⁸ : NontriviallyNormedField 𝕜 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G inst✝¹ : NormedAddCommGroup H inst✝ : N...
case h'.mk 𝕜 : Type u_1 E : Type u_2 F : Type u_3 G : Type u_4 H : Type u_5 inst✝⁸ : NontriviallyNormedField 𝕜 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G inst✝¹ : NormedAddCommGroup H inst✝ : N...
((:c Exists) (:c Nat) (:lambda n (:c Nat) ((:c Membership.mem) ((:c Sigma) (:c Nat) (:lambda n (:c Nat) ((:c Composition) 0))) ((:c Finset) ((:c Sigma) (:c Nat) (:lambda n (:c Nat) ((:c Composition) 0)))) ((:c Finset.instMembership) ((:c Sigma) (:c Nat) (:lambda n (:c Nat) ((:c Composition) 0)))) ((:c Sigma.mk) (:c Nat...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"H","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.594860))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCo...
(:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Sigma) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c Composition) (:arg :explicit 0 0)))))) (:arg :implicit-type 1 (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"simp","sourceEnd":35921,"sourceStart":35917,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":35926,"sourceStart":35922,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":359...
[]
[{"source":"mem_compPartialSumTarget_iff","source_end":35956,"source_start":35928,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
114
17
exact
true
1
16
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
92940a93d28646bf3765bf96f815396415cca598efdc4f6068b4d4a9861042f5
d348eb883f192c92890143c4221904e303b87fb079457e83d1d34a24b48aa74d
796a504c4bb9da746e3803ec3a9460e3853d0679ab5327510e6ea7f1f780ca0d
e6ba3c54ee7e584689c23185e43e4b15fdf00309881db1b79837c83c1e8a0cd4
cat-searcher/leandojo-benchmark-4-random
test
1,431
FormalMultilinearSeries.compPartialSumTarget_tendsto_atTop
Mathlib/Analysis/Analytic/Composition.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨n, hn⟩ : <a>BddAbove</a> ((Finset.univ.image fun i : <a>Fin</a> c.length => c.blocksFun i) : <a>Set</a> ℕ) := <a>Finset.bddAbove</a> _
case h'.mk 𝕜 : Type u_1 E : Type u_2 F : Type u_3 G : Type u_4 H : Type u_5 inst✝⁸ : NontriviallyNormedField 𝕜 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G inst✝¹ : NormedAddCommGroup H inst✝ : N...
case h'.mk.intro 𝕜 : Type u_1 E : Type u_2 F : Type u_3 G : Type u_4 H : Type u_5 inst✝⁸ : NontriviallyNormedField 𝕜 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G inst✝¹ : NormedAddCommGroup H ins...
((:c Exists) (:c Nat) (:lambda n (:c Nat) ((:c And) ((:c LE.le) (:c Nat) (:c instLENat) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))) ((:c Composition.length) (:fv _uniq.601179) (:fv _uniq.601180))) ((:c And) ((:c LT.lt) (:c Nat) (:c instLTNat) ((:c Composition.length) (:fv _uniq.601179) (:fv _uniq....
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"H","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.594860))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCo...
(:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c And) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"obtain","sourceEnd":35968,"sourceStart":35962,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":35972,"sourceStart":35969,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"n","sourceEn...
[]
[{"source":"BddAbove ((Finset.univ.image fun i : Fin c.length => c.blocksFun i) : Set ℕ)","source_end":36061,"source_start":35983,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Finset.bddAbove _","source_end":36088,"source_start":36071,"syntax_kind":"Lean.Parser.Term.app"},{"source":"obtain","source_end":35968,"sourc...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
114
18
exact
true
1
16
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c7a3c6ea2eace167c8831f0f6910aeb4eb3843448d7fdbe7d32725f3a167402f
e6ba3c54ee7e584689c23185e43e4b15fdf00309881db1b79837c83c1e8a0cd4
a14bb2e06b45e00f34dbfee21509dc24e03714ea6597fff2ab1ee0fa18308707
af654a84777a8621aeb991017c27392f02f27498554da765b8a1fc9988b17853
cat-searcher/leandojo-benchmark-4-random
test
1,432
FormalMultilinearSeries.compPartialSumTarget_tendsto_atTop
Mathlib/Analysis/Analytic/Composition.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨<a>Max.max</a> n c.length + 1, <a>bot_le</a>, <a>lt_of_le_of_lt</a> (<a>le_max_right</a> n c.length) (<a>lt_add_one</a> _), fun j => <a>lt_of_le_of_lt</a> (<a>le_trans</a> ?_ (<a>le_max_left</a> _ _)) (<a>lt_add_one</a> _)⟩
case h'.mk.intro 𝕜 : Type u_1 E : Type u_2 F : Type u_3 G : Type u_4 H : Type u_5 inst✝⁸ : NontriviallyNormedField 𝕜 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G inst✝¹ : NormedAddCommGroup H ins...
case h'.mk.intro 𝕜 : Type u_1 E : Type u_2 F : Type u_3 G : Type u_4 H : Type u_5 inst✝⁸ : NontriviallyNormedField 𝕜 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G inst✝¹ : NormedAddCommGroup H ins...
((:c Exists) (:c Nat) (:lambda n (:c Nat) ((:c And) ((:c LE.le) (:c Nat) (:c instLENat) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))) ((:c Composition.length) (:fv _uniq.601179) (:fv _uniq.601180))) ((:c And) ((:c LT.lt) (:c Nat) (:c instLTNat) ((:c Composition.length) (:fv _uniq.601179) (:fv _uniq....
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"H","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.594860))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCo...
(:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c And) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"refine","sourceEnd":36099,"sourceStart":36093,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":36109,"sourceStart":36106,"tag":"atom"},{"children":[{"children":[{"children":[{"name":"Max.max","semanticRole":"global","source":"max","sourceEnd":36112,"sourceStart":36109,"tag":"identifier"},{"c...
[]
[{"source":"⟨max n c.length + 1, bot_le, lt_of_le_of_lt (le_max_right n c.length) (lt_add_one _), fun j =>\n lt_of_le_of_lt (le_trans ?_ (le_max_left _ _)) (lt_add_one _)⟩","source_end":36275,"source_start":36106,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
114
19
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d595a45bab0ea402b0914ce304d51fb70386a2e9c752783cd08d0e53d7acc498
af654a84777a8621aeb991017c27392f02f27498554da765b8a1fc9988b17853
7845090242809ebdec879b2959e239c3deab652d404d8dc4fbd6ff28032196d8
ab12caeb63469b36925c2d0f3f25e8e19c306120fa68105a6cbbb0dea960c301
cat-searcher/leandojo-benchmark-4-random
test
1,433
FormalMultilinearSeries.compPartialSumTarget_tendsto_atTop
Mathlib/Analysis/Analytic/Composition.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply hn
case h'.mk.intro 𝕜 : Type u_1 E : Type u_2 F : Type u_3 G : Type u_4 H : Type u_5 inst✝⁸ : NontriviallyNormedField 𝕜 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G inst✝¹ : NormedAddCommGroup H ins...
case h'.mk.intro.a 𝕜 : Type u_1 E : Type u_2 F : Type u_3 G : Type u_4 H : Type u_5 inst✝⁸ : NontriviallyNormedField 𝕜 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G inst✝¹ : NormedAddCommGroup H i...
((:c LE.le) (:c Nat) ((:c Preorder.toLE) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring)))) ((:c Composition.blocksFun) (:fv _uniq.601179) (:fv _uniq.601180) (:fv _uniq.603318)) (:fv _uniq.601936))
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"H","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.594860))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCo...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Composition.blocksFun) (:arg :implicit 0) (:arg :explicit 1 (:fv FV16)) (:arg :explicit 2 (:fv FV19)))) (:arg :explicit 3 (:fv FV17)))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"apply","sourceEnd":36285,"sourceStart":36280,"tag":"atom"},{"contextIndex":18,"semanticRole":"local","source":"hn","sourceEnd":36288,"sourceStart":36286,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply hn","sourceEnd":36288,"sourceStart":36280,"tag":"node"}
[]
[{"source":"hn","source_end":36288,"source_start":36286,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
114
20
exact
true
1
19
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e276c0c3cdfa35c8081e5c18fe001118991edab8747eaf14a670c890b3eb4bde
ab12caeb63469b36925c2d0f3f25e8e19c306120fa68105a6cbbb0dea960c301
75f6b7f153463982c6a7328298ef359e82d0af652980ea7c9f8e42cdfaf512dc
f15965a51b84533680b781a56b207b583e5fe344df4b707f0317f6b94e7cdd55
cat-searcher/leandojo-benchmark-4-random
test
1,434
FormalMultilinearSeries.compPartialSumTarget_tendsto_atTop
Mathlib/Analysis/Analytic/Composition.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>Finset.mem_image_of_mem</a>, <a>Finset.mem_coe</a>, <a>Finset.mem_univ</a>]
case h'.mk.intro.a 𝕜 : Type u_1 E : Type u_2 F : Type u_3 G : Type u_4 H : Type u_5 inst✝⁸ : NontriviallyNormedField 𝕜 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G inst✝¹ : NormedAddCommGroup H i...
((:c Membership.mem) (:c Nat) ((:c Set) (:c Nat)) ((:c Set.instMembership) (:c Nat)) ((:c Composition.blocksFun) (:fv _uniq.601179) (:fv _uniq.601180) (:fv _uniq.603318)) ((:c Finset.toSet) (:c Nat) ((:c Finset.image) ((:c Fin) ((:c Composition.length) (:fv _uniq.601179) (:fv _uniq.601180))) (:c Nat) (:c instDecidableE...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"H","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.594860))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCo...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Nat)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 3 (:app (:c Composition.block...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"simp","sourceEnd":36297,"sourceStart":36293,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":36302,"sourceStart":36298,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":363...
[]
[{"source":"Finset.mem_image_of_mem","source_end":36327,"source_start":36304,"syntax_kind":"ident"},{"source":"Finset.mem_coe","source_end":36343,"source_start":36329,"syntax_kind":"ident"},{"source":"Finset.mem_univ","source_end":36360,"source_start":36345,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.594860","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.594863","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
114
21
exact
true
1
19
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0095323698811ff54e9ffbda4998b26151d0ddb0113ba9fde3b3754ba37ad69f
f15965a51b84533680b781a56b207b583e5fe344df4b707f0317f6b94e7cdd55
3cae1f13c94faeba2cc5b298d0f49044863838307e319d298ece627377a97445
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,435
CategoryTheory.congrArg_mpr_hom_right
Mathlib/CategoryTheory/EqToHom.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
cases q
C : Type u₁ inst✝ : Category.{v₁, u₁} C β : Sort u_1 X Y Z : C p : X ⟶ Y q : Z = Y ⊢ ⋯.mpr p = p ≫ eqToHom ⋯
case refl C : Type u₁ inst✝ : Category.{v₁, u₁} C β : Sort u_1 X Y : C p : X ⟶ Y ⊢ ⋯.mpr p = p ≫ eqToHom ⋯
((:c Eq) ((:c Quiver.Hom) (:fv _uniq.6791) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.6791) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.6791) (:fv _uniq.6794))) (:fv _uniq.6967) (:fv _uniq.6969)) ((:c Eq.mpr) ((:c Quiver.Hom) (:fv _uniq.6791) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv ...
[{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.6791))"},{"name":"β","sexp":"(:sort u_1)"},{"name":"X","sexp":"(:fv _uniq.6791)"},{"name":"Y","sexp":"(:fv _uniq.6791)"},{"name":"Z","sexp":"(:fv _uniq.6791)"},{"name":"p","sexp":"((:c Quiver.Hom) (:fv _uniq.6791) (...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV4)) (:arg :explicit 3 (:fv FV6)))) (:arg :explicit 1 (:app (:c Eq.mpr) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:ar...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6791","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.6794","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Category) (...
{"children":[{"source":"cases","sourceEnd":5846,"sourceStart":5841,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":8,"semanticRole":"local","source":"q","sourceEnd":5848,"sourceStart":5847,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","source...
[]
[{"source":"q","source_end":5848,"source_start":5847,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6791","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.6794","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"internal_...
24
4
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
87bf78b481e3a1563b43e2850cfab1c40bae53423c2cba4fec4a60ed8cc4d796
1c3e55cbf4e7a63eaf0cdb687a67331e54abf3772807f8b67de166ea1e2e2dbf
f725bcce21086eeed54dc140fda8b5e0c35222bddcd8dc07f2944aef76b3f4d3
bc84535abe5d2bac49c9638a4afe9aa448d137c856fdacff0ca43cb63a6420c0
cat-searcher/leandojo-benchmark-4-random
test
1,436
CategoryTheory.congrArg_mpr_hom_right
Mathlib/CategoryTheory/EqToHom.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
case refl C : Type u₁ inst✝ : Category.{v₁, u₁} C β : Sort u_1 X Y : C p : X ⟶ Y ⊢ ⋯.mpr p = p ≫ eqToHom ⋯
((:c Eq) ((:c Quiver.Hom) (:fv _uniq.6791) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.6791) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.6791) (:fv _uniq.6794))) (:fv _uniq.6967) (:fv _uniq.6968)) ((:c Eq.mpr) ((:c Quiver.Hom) (:fv _uniq.6791) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv ...
[{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.6791))"},{"name":"β","sexp":"(:sort u_1)"},{"name":"X","sexp":"(:fv _uniq.6791)"},{"name":"Y","sexp":"(:fv _uniq.6791)"},{"name":"p","sexp":"((:c Quiver.Hom) (:fv _uniq.6791) ((:c CategoryTheory.CategoryStruct.toQui...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV4)) (:arg :explicit 3 (:fv FV5)))) (:arg :explicit 1 (:app (:c Eq.mpr) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:ar...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6791","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.6794","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Category) (...
{"children":[{"source":"simp","sourceEnd":5855,"sourceStart":5851,"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.6791","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.6794","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"internal_...
24
5
exact
true
1
6
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
af09ef325196c91cb711b6d079f0941e176581dca47832b2b50ab9e53965c12e
bc84535abe5d2bac49c9638a4afe9aa448d137c856fdacff0ca43cb63a6420c0
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,437
Irrational.neg
Mathlib/Data/Real/Irrational.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rwa [<a>neg_neg</a>]
q : ℚ x y : ℝ h : Irrational x ⊢ Irrational (- -x)
((:c Irrational) ((:c Neg.neg) (:c Real) (:c Real.instNeg) ((:c Neg.neg) (:c Real) (:c Real.instNeg) (:fv _uniq.16284))))
[{"name":"q","sexp":"(:c Rat)"},{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"h","sexp":"((:c Irrational) (:fv _uniq.16284))"}]
(:app (:c Irrational) (:arg :explicit 0 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Real))))...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16282","is_instance":false,"is_let":false,"name":"q","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16284","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":implicit","context_in...
{"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":11738,"sourceStart":11735,"tag":"atom"},{"children":[{"source":"[","sourceEnd":11740,"sourceStart":11739,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"neg_neg","semanticRole":"global...
[]
[{"source":"neg_neg","source_end":11747,"source_start":11740,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16282","is_instance":false,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16284","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
89
2
exact
true
1
4
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
95dc8d6854f95cf788dcaa4f1066e626d3e0563c905a556a20fc35426480a206
027f0bb5a2b96cef72065ba0e3f137fb41e16a02a28b07a06d0bee89144e20a4
ea0a158937ff5accc6e944d13dc539c045f1af51b4244b97cf093c5a97b227a6
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,438
CategoryTheory.shift_shiftFunctorCompIsoId_inv_app
Mathlib/CategoryTheory/Shift/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>neg_eq_of_add_eq_zero_left</a> h, <a>add_right_neg</a>]
C : Type u A : Type u_1 inst✝² : Category.{v, u} C inst✝¹ : AddGroup A inst✝ : HasShift C A X✝ Y : C f : X✝ ⟶ Y n m : A h : n + m = 0 X : C ⊢ m + n = 0
((:c Eq) (:fv _uniq.178411) ((:c HAdd.hAdd) (:fv _uniq.178411) (:fv _uniq.178411) (:fv _uniq.178411) ((:c instHAdd) (:fv _uniq.178411) ((:c AddSemigroup.toAdd) (:fv _uniq.178411) ((:c AddMonoid.toAddSemigroup) (:fv _uniq.178411) ((:c SubNegMonoid.toAddMonoid) (:fv _uniq.178411) ((:c AddGroup.toSubNegMonoid) (:fv _uniq....
[{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"A","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.178408))"},{"name":"inst✝¹","sexp":"((:c AddGroup) (:fv _uniq.178411))"},{"name":"inst✝","sexp":"((:c CategoryTheory.HasShift) (:fv _uniq.178408) (:fv _uniq.178411) (:fv _uniq...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.178408","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.178411","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":23292,"sourceStart":23290,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":23294,"sourceStart":23293,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"...
[]
[{"source":"neg_eq_of_add_eq_zero_left h","source_end":23326,"source_start":23298,"syntax_kind":"Lean.Parser.Term.app"},{"source":"add_right_neg","source_end":23341,"source_start":23328,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.178408","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.178411","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":instance-implicit","context_index":2,"internal...
130
2
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9b0ec687bb4cef08435648b099c8f8a93ccad0244f318aa8dcb8fd05e348f8a7
224f8425166ede54f36a134b692feae9386311662be7c7d91b2884f00645cb41
cc2f1cb68f745d4930368a41e6e9771e3095efbe956c2b01feeb8435265a7ad3
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,439
CategoryTheory.shift_shiftFunctorCompIsoId_inv_app
Mathlib/CategoryTheory/Shift/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>CategoryTheory.cancel_mono</a> (((<a>CategoryTheory.shiftFunctorCompIsoId</a> C n m h).hom.app X)⟦n⟧'), ← <a>CategoryTheory.Functor.map_comp</a>, <a>CategoryTheory.Iso.inv_hom_id_app</a>, <a>CategoryTheory.Functor.map_id</a>, <a>CategoryTheory.shift_shiftFunctorCompIsoId_hom_app</a>, <a>CategoryTheory.Iso.inv_...
C : Type u A : Type u_1 inst✝² : Category.{v, u} C inst✝¹ : AddGroup A inst✝ : HasShift C A X✝ Y : C f : X✝ ⟶ Y n m : A h : n + m = 0 X : C ⊢ (shiftFunctor C n).map ((shiftFunctorCompIsoId C n m h).inv.app X) = (shiftFunctorCompIsoId C m n ⋯).inv.app ((shiftFunctor C n).obj X)
C : Type u A : Type u_1 inst✝² : Category.{v, u} C inst✝¹ : AddGroup A inst✝ : HasShift C A X✝ Y : C f : X✝ ⟶ Y n m : A h : n + m = 0 X : C ⊢ 𝟙 ((shiftFunctor C n).obj ((𝟭 C).obj X)) = 𝟙 ((𝟭 C).obj ((shiftFunctor C n).obj X))
((:c Eq) ((:c Quiver.Hom) (:fv _uniq.178408) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.178408) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.178408) (:fv _uniq.178414))) ((:c Prefunctor.obj) (:fv _uniq.178408) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.178408) ((:c CategoryTheory....
[{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"A","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.178408))"},{"name":"inst✝¹","sexp":"((:c AddGroup) (:fv _uniq.178411))"},{"name":"inst✝","sexp":"((:c CategoryTheory.HasShift) (:fv _uniq.178408) (:fv _uniq.178411) (:fv _uniq...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c 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.178408","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.178411","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"rw","sourceEnd":23375,"sourceStart":23373,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":23377,"sourceStart":23376,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":23380,"sourceSt...
[]
[{"source":"cancel_mono (((shiftFunctorCompIsoId C n m h).hom.app X)⟦n⟧')","source_end":23446,"source_start":23381,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Functor.map_comp","source_end":23472,"source_start":23456,"syntax_kind":"ident"},{"source":"Iso.inv_hom_id_app","source_end":23492,"source_start":23474,"syn...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.178408","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.178411","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":instance-implicit","context_index":2,"internal...
130
12
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5285639e52fc05af6240c7fd469a6ece827624f0c305e8214a46eb62d7bbe32a
1835eaefb1c5aff05cb848f7aa31699e5930b453b9d585da7c09926a5f29b08f
a51b2811b11c713da1a6667855c918b0d4d5e6b88d563c8370f5174c48c36426
9ec741cc27340b3a34d82011db3e9ee635aaa581acdfdc1c52ce3fa1f6005070
cat-searcher/leandojo-benchmark-4-random
test
1,440
CategoryTheory.shift_shiftFunctorCompIsoId_inv_app
Mathlib/CategoryTheory/Shift/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rfl
C : Type u A : Type u_1 inst✝² : Category.{v, u} C inst✝¹ : AddGroup A inst✝ : HasShift C A X✝ Y : C f : X✝ ⟶ Y n m : A h : n + m = 0 X : C ⊢ 𝟙 ((shiftFunctor C n).obj ((𝟭 C).obj X)) = 𝟙 ((𝟭 C).obj ((shiftFunctor C n).obj X))
((:c Eq) ((:c Quiver.Hom) (:fv _uniq.178408) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.178408) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.178408) (:fv _uniq.178414))) ((:c Prefunctor.obj) (:fv _uniq.178408) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.178408) ((:c CategoryTheory....
[{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"A","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.178408))"},{"name":"inst✝¹","sexp":"((:c AddGroup) (:fv _uniq.178411))"},{"name":"inst✝","sexp":"((:c CategoryTheory.HasShift) (:fv _uniq.178408) (:fv _uniq.178411) (:fv _uniq...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c 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.178408","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.178411","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"rfl","sourceEnd":23576,"sourceStart":23573,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":23576,"sourceStart":23573,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.178408","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.178411","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":instance-implicit","context_index":2,"internal...
130
20
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d8205dcebc9bc1a8cf6ac666b4f7d61c4b506b2047a7e90d3fc7a051cae34b65
9ec741cc27340b3a34d82011db3e9ee635aaa581acdfdc1c52ce3fa1f6005070
5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,441
SimpleGraph.Walk.reverseAux_append
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
induction p with | <a>SimpleGraph.Walk.nil</a> => rfl | <a>SimpleGraph.Walk.cons</a> h _ ih => simp [ih (<a>SimpleGraph.Walk.cons</a> (G.symm h) q)]
V : Type u V' : Type v V'' : Type w G : SimpleGraph V G' : SimpleGraph V' G'' : SimpleGraph V'' u v w x : V p : G.Walk u v q : G.Walk u w r : G.Walk w x ⊢ (p.reverseAux q).append r = p.reverseAux (q.append r)
((:c Eq) ((:c SimpleGraph.Walk) (:fv _uniq.16853) (:fv _uniq.16860) (:fv _uniq.16961) (:fv _uniq.16963)) ((:c SimpleGraph.Walk.append) (:fv _uniq.16853) (:fv _uniq.16860) (:fv _uniq.16961) (:fv _uniq.16962) (:fv _uniq.16963) ((:c SimpleGraph.Walk.reverseAux) (:fv _uniq.16853) (:fv _uniq.16860) (:fv _uniq.16960) (:fv _u...
[{"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.16853))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.16855))"},{"name":"G''","sexp":"((:c SimpleGraph) (:fv _uniq.16857))"},{"name":"u","sexp":"(:...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c SimpleGraph.Walk) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV10)))) (:arg :explicit 1 (:app (:c SimpleGraph.Walk.append) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :implicit 2) (:arg ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16853","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16855","is_instance":false,"is_let":false,"name":"V'","sexp":"(:sort Type)"},{"binder_role":":implicit","co...
{"children":[{"children":[{"children":[{"children":[{"source":"induction","sourceEnd":12960,"sourceStart":12951,"tag":"atom"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"p","sourceEnd":12962,"sourceStart":12961,"tag":"identifier"}],"kind":"null","source":"p","sourceEnd":12962,"sourceStart":12961,"t...
[]
[{"source":"p","source_end":12962,"source_start":12961,"syntax_kind":"ident"},{"source":"nil","source_end":12975,"source_start":12972,"syntax_kind":"ident"},{"source":"cons","source_end":12991,"source_start":12987,"syntax_kind":"ident"},{"source":"ih (cons (G.symm h) q)","source_end":13030,"source_start":13008,"syntax_...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16853","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16855","is_instance":false,"is_let":false,"user_name":"V'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
88
2
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
24674cacb25fbb17498ae0693627ef939b369e31b829e2a4077f715978efa025
302629606ea97212fe567e44e1712ee680357ca23878805c1292e4748540279b
d548a26d5e639d86abea56cde79ff8926ca771123bb1504bbd044da3f451f9f3
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,442
SimpleGraph.Walk.reverseAux_append
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rfl
case nil V : Type u V' : Type v V'' : Type w G : SimpleGraph V G' : SimpleGraph V' G'' : SimpleGraph V'' u v w x : V r : G.Walk w x u✝ : V q : G.Walk u✝ w ⊢ (nil.reverseAux q).append r = nil.reverseAux (q.append r)
((:c Eq) ((:c SimpleGraph.Walk) (:fv _uniq.16853) (:fv _uniq.16860) (:fv _uniq.17006) (:fv _uniq.16963)) ((:c SimpleGraph.Walk.append) (:fv _uniq.16853) (:fv _uniq.16860) (:fv _uniq.17006) (:fv _uniq.16962) (:fv _uniq.16963) ((:c SimpleGraph.Walk.reverseAux) (:fv _uniq.16853) (:fv _uniq.16860) (:fv _uniq.17006) (:fv _u...
[{"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.16853))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.16855))"},{"name":"G''","sexp":"((:c SimpleGraph) (:fv _uniq.16857))"},{"name":"u","sexp":"(:...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c SimpleGraph.Walk) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV12)) (:arg :explicit 3 (:fv FV10)))) (:arg :explicit 1 (:app (:c SimpleGraph.Walk.append) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :implicit 2) (:arg...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16853","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16855","is_instance":false,"is_let":false,"name":"V'","sexp":"(:sort Type)"},{"binder_role":":implicit","co...
{"children":[{"children":[{"children":[{"children":[{"source":"rfl","sourceEnd":12982,"sourceStart":12979,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":12982,"sourceStart":12979,"tag":"node"}],"kind":"null","source":"rfl","sourceEnd":12982,"sourceStart":12979,"tag":"node"}],"kind":"Lea...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16853","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16855","is_instance":false,"is_let":false,"user_name":"V'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
88
7
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d00e5aa80d7d8e39e7068e65a95ef45afef1e486e2e68cdcede682546bc4b96f
4dc1435a1474d82a599b1da5a9878629966e4c926de1b79c2b4fa1ac1decc93e
5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,443
SimpleGraph.Walk.reverseAux_append
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [ih (<a>SimpleGraph.Walk.cons</a> (G.symm h) q)]
case cons V : Type u V' : Type v V'' : Type w G : SimpleGraph V G' : SimpleGraph V' G'' : SimpleGraph V'' u v w x : V r : G.Walk w x u✝ v✝ w✝ : V h : G.Adj u✝ v✝ p✝ : G.Walk v✝ w✝ ih : ∀ (q : G.Walk v✝ w), (p✝.reverseAux q).append r = p✝.reverseAux (q.append r) q : G.Walk u✝ w ⊢ ((cons h p✝).reverseAux q).append r = (c...
((:c Eq) ((:c SimpleGraph.Walk) (:fv _uniq.16853) (:fv _uniq.16860) (:fv _uniq.17064) (:fv _uniq.16963)) ((:c SimpleGraph.Walk.append) (:fv _uniq.16853) (:fv _uniq.16860) (:fv _uniq.17064) (:fv _uniq.16962) (:fv _uniq.16963) ((:c SimpleGraph.Walk.reverseAux) (:fv _uniq.16853) (:fv _uniq.16860) (:fv _uniq.17062) (:fv _u...
[{"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.16853))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.16855))"},{"name":"G''","sexp":"((:c SimpleGraph) (:fv _uniq.16857))"},{"name":"u","sexp":"(:...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c SimpleGraph.Walk) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV14)) (:arg :explicit 3 (:fv FV10)))) (:arg :explicit 1 (:app (:c SimpleGraph.Walk.append) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :implicit 2) (:arg...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16853","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16855","is_instance":false,"is_let":false,"name":"V'","sexp":"(:sort Type)"},{"binder_role":":implicit","co...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":13006,"sourceStart":13002,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...
[]
[{"source":"ih (cons (G.symm h) q)","source_end":13030,"source_start":13008,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16853","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16855","is_instance":false,"is_let":false,"user_name":"V'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
88
11
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
262fe93f3d9a43380f7d64a59864bbfdefe70e2d18cbcf98005df5f4964f612d
cb2d4b3e83339473aa53ebe9f6d16797255b13d2e0b26d5b0e94ac93afb4c8c4
0d514afb7793eed60f908bfc10cb79410178fa6018d24837390243406a0d4c08
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,444
MeromorphicAt.pow
Mathlib/Analysis/Analytic/Meromorphic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
induction' n with m hm
𝕜 : Type u_1 inst✝² : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹ : NormedAddCommGroup E inst✝ : NormedSpace 𝕜 E f : 𝕜 → 𝕜 x : 𝕜 hf : MeromorphicAt f x n : ℕ ⊢ MeromorphicAt (f ^ n) x
case zero 𝕜 : Type u_1 inst✝² : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹ : NormedAddCommGroup E inst✝ : NormedSpace 𝕜 E f : 𝕜 → 𝕜 x : 𝕜 hf : MeromorphicAt f x ⊢ MeromorphicAt (f ^ 0) x case succ 𝕜 : Type u_1 inst✝² : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹ : NormedAddCommGroup E inst✝ : NormedSpace �...
((:c MeromorphicAt) (:fv _uniq.61043) (:fv _uniq.61046) (:fv _uniq.61043) ((:c NonUnitalNormedRing.toNormedAddCommGroup) (:fv _uniq.61043) ((:c NonUnitalNormedCommRing.toNonUnitalNormedRing) (:fv _uniq.61043) ((:c NormedCommRing.toNonUnitalNormedCommRing) (:fv _uniq.61043) ((:c NormedField.toNormedCommRing) (:fv _uniq....
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NontriviallyNormedField) (:fv _uniq.61043))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.61049))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:fv _uniq.61043) (:fv _uniq.61049) ((:c Nontrivi...
(:app (:c MeromorphicAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61043","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61046","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NontriviallyNormedFiel...
{"children":[{"source":"induction'","sourceEnd":5809,"sourceStart":5799,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":9,"semanticRole":"local","source":"n","sourceEnd":5811,"sourceStart":5810,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","s...
[]
[{"source":"n","source_end":5811,"source_start":5810,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61043","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61046","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inter...
19
4
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3d3ec34b1f7b64931b025344b50b32ccf843ccd4bd48bd724e01c28b3493f836
0d0f3fe88259b441be932e88c38d1023d702493c0ddc1c50188505cfe5001090
feafd5200e5059126531d0113f973700138102609b8cfef0e4b3c2a4c7277291
3032bd89c7f15a93305a8c47843288e6dcc11a0529a70dbb8e0c5c49fee31431
cat-searcher/leandojo-benchmark-4-random
test
1,445
MeromorphicAt.pow
Mathlib/Analysis/Analytic/Meromorphic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simpa only [<a>Nat.zero_eq</a>, <a>pow_zero</a>] using <a>MeromorphicAt.const</a> 1 x
case zero 𝕜 : Type u_1 inst✝² : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹ : NormedAddCommGroup E inst✝ : NormedSpace 𝕜 E f : 𝕜 → 𝕜 x : 𝕜 hf : MeromorphicAt f x ⊢ MeromorphicAt (f ^ 0) x
((:c MeromorphicAt) (:fv _uniq.61043) (:fv _uniq.61046) (:fv _uniq.61043) ((:c NonUnitalNormedRing.toNormedAddCommGroup) (:fv _uniq.61043) ((:c NonUnitalNormedCommRing.toNonUnitalNormedRing) (:fv _uniq.61043) ((:c NormedCommRing.toNonUnitalNormedCommRing) (:fv _uniq.61043) ((:c NormedField.toNormedCommRing) (:fv _uniq....
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NontriviallyNormedField) (:fv _uniq.61043))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.61049))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:fv _uniq.61043) (:fv _uniq.61049) ((:c Nontrivi...
(:app (:c MeromorphicAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61043","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61046","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NontriviallyNormedFiel...
{"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":5832,"sourceStart":5827,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":...
[]
[{"source":"Nat.zero_eq","source_end":5850,"source_start":5839,"syntax_kind":"ident"},{"source":"pow_zero","source_end":5860,"source_start":5852,"syntax_kind":"ident"},{"source":"MeromorphicAt.const 1 x","source_end":5891,"source_start":5868,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61043","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61046","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inter...
19
7
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2c99e9601d8d4d409cfd01b6c9582cd6ab7400fedd4cad0e5d57349a818ee488
6a45ec5892ace2b3989c307df7aaed21d31720f34c9e2be15c173f8b12df56aa
59104f5c0ca4233e9fdda429394fbb362c9195921a0080a0f95b1e44850ad341
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,446
MeromorphicAt.pow
Mathlib/Analysis/Analytic/Meromorphic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simpa only [<a>pow_succ</a>] using hm.mul hf
case succ 𝕜 : Type u_1 inst✝² : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹ : NormedAddCommGroup E inst✝ : NormedSpace 𝕜 E f : 𝕜 → 𝕜 x : 𝕜 hf : MeromorphicAt f x m : ℕ hm : MeromorphicAt (f ^ m) x ⊢ MeromorphicAt (f ^ (m + 1)) x
((:c MeromorphicAt) (:fv _uniq.61043) (:fv _uniq.61046) (:fv _uniq.61043) ((:c NonUnitalNormedRing.toNormedAddCommGroup) (:fv _uniq.61043) ((:c NonUnitalNormedCommRing.toNonUnitalNormedRing) (:fv _uniq.61043) ((:c NormedCommRing.toNonUnitalNormedCommRing) (:fv _uniq.61043) ((:c NormedField.toNormedCommRing) (:fv _uniq....
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NontriviallyNormedField) (:fv _uniq.61043))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.61049))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:fv _uniq.61043) (:fv _uniq.61049) ((:c Nontrivi...
(:app (:c MeromorphicAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61043","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61046","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NontriviallyNormedFiel...
{"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":5902,"sourceStart":5897,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":...
[]
[{"source":"pow_succ","source_end":5917,"source_start":5909,"syntax_kind":"ident"},{"source":"hm.mul hf","source_end":5934,"source_start":5925,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61043","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61046","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inter...
19
12
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
acd600b6f8695e61ed9df8ee8eae3dac5596c16b5a52a99a3a3f13b07d90d04a
e74b5c734179efa5ad6ea9b2a12fc54dd88ee758c46cd5140c431a4a7e221d6b
40345b5853295a2f21482433b5b897adb06101decd5cb63eb7b5d1ba771635ab
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,447
Submodule.sup_orthogonal_of_completeSpace
Mathlib/Analysis/InnerProductSpace/Projection.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
convert <a>Submodule.sup_orthogonal_inf_of_completeSpace</a> (<a>le_top</a> : K ≤ ⊤) using 2
𝕜 : Type u_1 E : Type u_2 F : Type u_3 inst✝⁵ : _root_.RCLike 𝕜 inst✝⁴ : NormedAddCommGroup E inst✝³ : NormedAddCommGroup F inst✝² : InnerProductSpace 𝕜 E inst✝¹ : InnerProductSpace ℝ F K : Submodule 𝕜 E inst✝ : HasOrthogonalProjection K ⊢ K ⊔ Kᗮ = ⊤
case h.e'_2.h.e'_4 𝕜 : Type u_1 E : Type u_2 F : Type u_3 inst✝⁵ : _root_.RCLike 𝕜 inst✝⁴ : NormedAddCommGroup E inst✝³ : NormedAddCommGroup F inst✝² : InnerProductSpace 𝕜 E inst✝¹ : InnerProductSpace ℝ F K : Submodule 𝕜 E inst✝ : HasOrthogonalProjection K ⊢ Kᗮ = Kᗮ ⊓ ⊤
((:c Eq) ((:c Submodule) (:fv _uniq.637121) (:fv _uniq.637124) ((:c DivisionSemiring.toSemiring) (:fv _uniq.637121) ((:c Semifield.toDivisionSemiring) (:fv _uniq.637121) ((:c Field.toSemifield) (:fv _uniq.637121) ((:c NormedField.toField) (:fv _uniq.637121) ((:c DenselyNormedField.toNormedField) (:fv _uniq.637121) ((:c...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁵","sexp":"((:c RCLike) (:fv _uniq.637121))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.637124))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.63712...
(: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.637121","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.637124","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"convert","sourceEnd":38745,"sourceStart":38738,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Submodule.sup_orthogonal_inf_of_completeSpace","semanticRole":"global","source":"Submodule.sup_orthogon...
[]
[{"source":"Submodule.sup_orthogonal_inf_of_completeSpace (le_top : K ≤ ⊤)","source_end":38812,"source_start":38746,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.637121","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.637124","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
130
4
exact
true
1
10
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d3ced80df7e52df246328cdac62422ab2a8b1771339aaf07a453c0bfcf48efe4
3cfa706d9b0734c8912f4f2968cdd6aaafc47b903843d3a71f5bc12af987fba3
4aacab33e042cd71e8975e6cd8268be736e524e752ae55a637000c4f47667e84
1de89335e5ba54352d3465617d12cbaa2c3f4e153f255313b74852a49e00821a
cat-searcher/leandojo-benchmark-4-random
test
1,448
Submodule.sup_orthogonal_of_completeSpace
Mathlib/Analysis/InnerProductSpace/Projection.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
case h.e'_2.h.e'_4 𝕜 : Type u_1 E : Type u_2 F : Type u_3 inst✝⁵ : _root_.RCLike 𝕜 inst✝⁴ : NormedAddCommGroup E inst✝³ : NormedAddCommGroup F inst✝² : InnerProductSpace 𝕜 E inst✝¹ : InnerProductSpace ℝ F K : Submodule 𝕜 E inst✝ : HasOrthogonalProjection K ⊢ Kᗮ = Kᗮ ⊓ ⊤
((:c Eq) ((:c Submodule) (:fv _uniq.637121) (:fv _uniq.637124) ((:c DivisionSemiring.toSemiring) (:fv _uniq.637121) ((:c Semifield.toDivisionSemiring) (:fv _uniq.637121) ((:c Field.toSemifield) (:fv _uniq.637121) ((:c NormedField.toField) (:fv _uniq.637121) ((:c DenselyNormedField.toNormedField) (:fv _uniq.637121) ((:c...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁵","sexp":"((:c RCLike) (:fv _uniq.637121))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.637124))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.63712...
(: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.637121","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.637124","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"simp","sourceEnd":38827,"sourceStart":38823,"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.637121","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.637124","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
130
5
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8819b0fc98f9c555908ccc5401de77a53e413e00317e884a16ea6ebc996e6de9
1de89335e5ba54352d3465617d12cbaa2c3f4e153f255313b74852a49e00821a
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,449
Rat.cast_div_of_ne_zero
Mathlib/Data/Rat/Cast/Defs.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Rat.div_def'</a>, <a>Rat.cast_divInt_of_ne_zero</a>, <a>Rat.cast_def</a>, <a>Rat.cast_def</a>, <a>div_eq_mul_inv</a> (_ / _), <a>inv_div</a>, (<a>Int.commute_cast</a> _ _).<a>Commute.div_mul_div_comm</a> (<a>Nat.commute_cast</a> _ _)]
F : Type u_1 ι : Type u_2 α : Type u_3 β : Type u_4 inst✝ : DivisionRing α p q : ℚ hp : ↑p.den ≠ 0 hq : ↑q.num ≠ 0 ⊢ ↑(p / q) = ↑p / ↑q
F : Type u_1 ι : Type u_2 α : Type u_3 β : Type u_4 inst✝ : DivisionRing α p q : ℚ hp : ↑p.den ≠ 0 hq : ↑q.num ≠ 0 ⊢ ↑(p.num * ↑q.den) / ↑(↑p.den * q.num) = ↑p.num * ↑q.den / (↑p.den * ↑q.num) case b0 F : Type u_1 ι : Type u_2 α : Type u_3 β : Type u_4 inst✝ : DivisionRing α p q : ℚ hp : ↑p.den ≠ 0 hq : ↑q.num ≠ 0 ⊢ ↑(...
((:c Eq) (:fv _uniq.60096) ((:c Rat.cast) (:fv _uniq.60096) ((:c DivisionRing.toRatCast) (:fv _uniq.60096) (:fv _uniq.60102)) ((:c HDiv.hDiv) (:c Rat) (:c Rat) (:c Rat) ((:c instHDiv) (:c Rat) (:c Rat.instDiv)) (:fv _uniq.60104) (:fv _uniq.60106))) ((:c HDiv.hDiv) (:fv _uniq.60096) (:fv _uniq.60096) (:fv _uniq.60096) (...
[{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c DivisionRing) (:fv _uniq.60096))"},{"name":"p","sexp":"(:c Rat)"},{"name":"q","sexp":"(:c Rat)"},{"name":"hp","sexp":"((:c Ne) (:f...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Rat.cast) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c RatCast) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Rat)) (:arg :implicit-type 1 (:c Rat)) (:arg :impli...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60090","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60093","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"rw","sourceEnd":7898,"sourceStart":7896,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7900,"sourceStart":7899,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Rat.div_def'","seman...
[]
[{"source":"div_def'","source_end":7908,"source_start":7900,"syntax_kind":"ident"},{"source":"cast_divInt_of_ne_zero","source_end":7932,"source_start":7910,"syntax_kind":"ident"},{"source":"cast_def","source_end":7942,"source_start":7934,"syntax_kind":"ident"},{"source":"cast_def","source_end":7952,"source_start":7944,...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60090","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60093","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
50
4
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
885f674fff330a74117e17c0d6e8518dc42cd58d8fb150e574536e6f6ce47794
e3256d9a41e5e17bb5fcb5af26c80740f6c5cd72098c873ff6bb9c69f0460ca6
f5cdac84eb74b80b479a3f47aad64d50da42f2a73d849c005330574ad86e5e1a
dea99b85947b7a7a7f8fea351d73cfc2a4edfada72be849cb13dd0a6cb3f807b
cat-searcher/leandojo-benchmark-4-random
test
1,450
Rat.cast_div_of_ne_zero
Mathlib/Data/Rat/Cast/Defs.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
push_cast
F : Type u_1 ι : Type u_2 α : Type u_3 β : Type u_4 inst✝ : DivisionRing α p q : ℚ hp : ↑p.den ≠ 0 hq : ↑q.num ≠ 0 ⊢ ↑(p.num * ↑q.den) / ↑(↑p.den * q.num) = ↑p.num * ↑q.den / (↑p.den * ↑q.num)
F : Type u_1 ι : Type u_2 α : Type u_3 β : Type u_4 inst✝ : DivisionRing α p q : ℚ hp : ↑p.den ≠ 0 hq : ↑q.num ≠ 0 ⊢ ↑p.num * ↑q.den / (↑p.den * ↑q.num) = ↑p.num * ↑q.den / (↑p.den * ↑q.num)
((:c Eq) (:fv _uniq.60096) ((:c HDiv.hDiv) (:fv _uniq.60096) (:fv _uniq.60096) (:fv _uniq.60096) ((:c instHDiv) (:fv _uniq.60096) ((:c DivisionRing.toDiv) (:fv _uniq.60096) (:fv _uniq.60102))) ((:c Int.cast) (:fv _uniq.60096) ((:c Ring.toIntCast) (:fv _uniq.60096) ((:c DivisionRing.toRing) (:fv _uniq.60096) (:fv _uniq....
[{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c DivisionRing) (:fv _uniq.60096))"},{"name":"p","sexp":"(:c Rat)"},{"name":"q","sexp":"(:c Rat)"},{"name":"hp","sexp":"((:c Ne) (:f...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60090","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60093","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"push_cast","sourceEnd":8069,"sourceStart":8060,"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":[],...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60090","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60093","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
50
17
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
6510ae3fa34cc8ab2e3fb9e7fbf523e0432c67aa3fc0ce84f512eaf37d4fa4c3
bc1d6431d699465e3168d478e23e85966b9a632569eb47575eaa8a1a9c55663f
5189104d9b5e7264ce49402b63410b1cd440d29f098c6f68c6d5dbb0f8982ff0
e62c451ccf7e0ad5769888eee0611fdf31a0fcb8fe909634e7a4f63a98a311e7
cat-searcher/leandojo-benchmark-4-random
test
1,451
Rat.cast_div_of_ne_zero
Mathlib/Data/Rat/Cast/Defs.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rfl
F : Type u_1 ι : Type u_2 α : Type u_3 β : Type u_4 inst✝ : DivisionRing α p q : ℚ hp : ↑p.den ≠ 0 hq : ↑q.num ≠ 0 ⊢ ↑p.num * ↑q.den / (↑p.den * ↑q.num) = ↑p.num * ↑q.den / (↑p.den * ↑q.num)
((:c Eq) (:fv _uniq.60096) ((:c HDiv.hDiv) (:fv _uniq.60096) (:fv _uniq.60096) (:fv _uniq.60096) ((:c instHDiv) (:fv _uniq.60096) ((:c DivisionRing.toDiv) (:fv _uniq.60096) (:fv _uniq.60102))) ((:c HMul.hMul) (:fv _uniq.60096) (:fv _uniq.60096) (:fv _uniq.60096) ((:c instHMul) (:fv _uniq.60096) ((:c NonUnitalNonAssocRi...
[{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c DivisionRing) (:fv _uniq.60096))"},{"name":"p","sexp":"(:c Rat)"},{"name":"q","sexp":"(:c Rat)"},{"name":"hp","sexp":"((:c Ne) (:f...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60090","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60093","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"rfl","sourceEnd":8077,"sourceStart":8074,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":8077,"sourceStart":8074,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60090","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60093","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
50
18
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8cb42aca86e5aaa4cd4fac4c7e44512571fb8f13732365eeaa2886da5f7f000f
e62c451ccf7e0ad5769888eee0611fdf31a0fcb8fe909634e7a4f63a98a311e7
5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,452
Rat.cast_div_of_ne_zero
Mathlib/Data/Rat/Cast/Defs.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
push_cast
case b0 F : Type u_1 ι : Type u_2 α : Type u_3 β : Type u_4 inst✝ : DivisionRing α p q : ℚ hp : ↑p.den ≠ 0 hq : ↑q.num ≠ 0 ⊢ ↑(↑p.den * q.num) ≠ 0
case b0 F : Type u_1 ι : Type u_2 α : Type u_3 β : Type u_4 inst✝ : DivisionRing α p q : ℚ hp : ↑p.den ≠ 0 hq : ↑q.num ≠ 0 ⊢ ↑p.den * ↑q.num ≠ 0
((:c Ne) (:fv _uniq.60096) ((:c Int.cast) (:fv _uniq.60096) ((:c Ring.toIntCast) (:fv _uniq.60096) ((:c DivisionRing.toRing) (:fv _uniq.60096) (:fv _uniq.60102))) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (:c Int.instMul)) ((:c Nat.cast) (:c Int) (:c instNatCastInt) ((:c Rat.den) (:fv _uniq.601...
[{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c DivisionRing) (:fv _uniq.60096))"},{"name":"p","sexp":"(:c Rat)"},{"name":"q","sexp":"(:c Rat)"},{"name":"hp","sexp":"((:c Ne) (:f...
(:app (:c Ne) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Int.cast) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c IntCast) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:c Int)) (:arg :impli...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60090","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60093","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"push_cast","sourceEnd":8092,"sourceStart":8083,"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":[],...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60090","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60093","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
50
23
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1d5f6b8296a6bb225792fbda64f9c6725178af57be1bbebd9834117629e1b35c
8f50e881990b6479c59b9ad6448683d3b310fe24418a4f62895a234d4334d0b8
5189104d9b5e7264ce49402b63410b1cd440d29f098c6f68c6d5dbb0f8982ff0
6b431a05ec27f67a3413d07efe8ee768733c3f5faaf8847f9e801ca3839036a5
cat-searcher/leandojo-benchmark-4-random
test
1,453
Rat.cast_div_of_ne_zero
Mathlib/Data/Rat/Cast/Defs.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>mul_ne_zero</a> hp hq
case b0 F : Type u_1 ι : Type u_2 α : Type u_3 β : Type u_4 inst✝ : DivisionRing α p q : ℚ hp : ↑p.den ≠ 0 hq : ↑q.num ≠ 0 ⊢ ↑p.den * ↑q.num ≠ 0
((:c Ne) (:fv _uniq.60096) ((:c HMul.hMul) (:fv _uniq.60096) (:fv _uniq.60096) (:fv _uniq.60096) ((:c instHMul) (:fv _uniq.60096) ((:c NonUnitalNonAssocRing.toMul) (:fv _uniq.60096) ((:c NonAssocRing.toNonUnitalNonAssocRing) (:fv _uniq.60096) ((:c Ring.toNonAssocRing) (:fv _uniq.60096) ((:c DivisionRing.toRing) (:fv _u...
[{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c DivisionRing) (:fv _uniq.60096))"},{"name":"p","sexp":"(:c Rat)"},{"name":"q","sexp":"(:c Rat)"},{"name":"hp","sexp":"((:c Ne) (:f...
(:app (:c Ne) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV...
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{"children":[{"source":"exact","sourceEnd":8102,"sourceStart":8097,"tag":"atom"},{"children":[{"name":"mul_ne_zero","semanticRole":"global","source":"mul_ne_zero","sourceEnd":8114,"sourceStart":8103,"tag":"identifier"},{"children":[{"contextIndex":8,"semanticRole":"local","source":"hp","sourceEnd":8117,"sourceStart":81...
[]
[{"source":"mul_ne_zero hp hq","source_end":8120,"source_start":8103,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.60090","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60093","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
50
24
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a56813abaa4894d81ff929d7d07f9635422bafd88f7c13040aff8f3431b94a9f
6b431a05ec27f67a3413d07efe8ee768733c3f5faaf8847f9e801ca3839036a5
559ab6837734b60d0c750490cd87dced1a39a1b39a34226a6168f764c87b4d92
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,454
Complex.abs_cpow_of_ne_zero
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Complex.cpow_def_of_ne_zero</a> hz, <a>Complex.abs_exp</a>, <a>Complex.mul_re</a>, <a>Complex.log_re</a>, <a>Complex.log_im</a>, <a>Real.exp_sub</a>, <a>Real.rpow_def_of_pos</a> (abs.pos hz)]
z : ℂ hz : z ≠ 0 w : ℂ ⊢ abs (z ^ w) = abs z ^ w.re / rexp (z.arg * w.im)
((:c Eq) (:c Real) ((:c DFunLike.coe) ((:c AbsoluteValue) (:c Complex) (:c Real) (:c Complex.instSemiring) (:c Real.orderedSemiring)) (:c Complex) (:lambda _ (:c Complex) (:c Real)) ((:c AbsoluteValue.funLike) (:c Complex) (:c Real) (:c Complex.instSemiring) (:c Real.orderedSemiring)) (:c Complex.abs) ((:c HPow.hPow) (...
[{"name":"z","sexp":"(:c Complex)"},{"name":"hz","sexp":"((:c Ne) (:c Complex) (:fv _uniq.51766) ((:c OfNat.ofNat) (:c Complex) (:lit 0) ((:c Zero.toOfNat0) (:c Complex) (:c Complex.instZero))))"},{"name":"w","sexp":"(:c Complex)"}]
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AbsoluteValue) (:arg :explicit 0 (:c Complex)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Complex))))) (:arg :instance 3 (:instance-of (:...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.51766","is_instance":false,"is_let":false,"name":"z","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.51767","is_instance":false,"is_let":false,"name":"hz","sexp":"(:app (:c Ne) (:arg :implicit-type 0 (:c Comp...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":13197,"sourceStart":13195,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13199,"sourceStart":13198,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",...
[]
[{"source":"cpow_def_of_ne_zero hz","source_end":13221,"source_start":13199,"syntax_kind":"Lean.Parser.Term.app"},{"source":"abs_exp","source_end":13230,"source_start":13223,"syntax_kind":"ident"},{"source":"mul_re","source_end":13238,"source_start":13232,"syntax_kind":"ident"},{"source":"log_re","source_end":13246,"so...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.51766","is_instance":false,"is_let":false,"user_name":"z"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.51767","is_instance":false,"is_let":false,"user_name":"hz"},{"binder_role":":explicit","context_index":3,"internal_name":"_u...
99
2
exact
true
1
3
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a206e6eecbc057f438b824c5a55a457e673c9b3720f43b2ef27fb717311c2539
027ee2d18ba21ecdccf657d0451f0b4ec714f675a7c9747b518e3e16db240b71
ec652169f9367842508434320b5375ee173b47d4968324c8b6be2777c6ddb184
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,455
AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff
Mathlib/Algebra/Order/Rearrangement.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [← hfg.sum_smul_comp_perm_eq_sum_smul_iff hσ, <a>lt_iff_le_and_ne</a>, <a>eq_comm</a>, hfg.sum_smul_le_sum_smul_comp_perm hσ]
ι : Type u_1 α : Type u_2 β : Type u_3 inst✝³ : LinearOrderedRing α inst✝² : LinearOrderedAddCommGroup β inst✝¹ : Module α β inst✝ : OrderedSMul α β s : Finset ι σ : Perm ι f : ι → α g : ι → β hfg : AntivaryOn f g ↑s hσ : {x | σ x ≠ x} ⊆ ↑s ⊢ ∑ i ∈ s, f i • g i < ∑ i ∈ s, f i • g (σ i) ↔ ¬AntivaryOn f (g ∘ ⇑σ) ↑s
((:c Iff) ((:c LT.lt) (:fv _uniq.65346) ((:c Preorder.toLT) (:fv _uniq.65346) ((:c PartialOrder.toPreorder) (:fv _uniq.65346) ((:c OrderedAddCommGroup.toPartialOrder) (:fv _uniq.65346) ((:c LinearOrderedAddCommGroup.toOrderedAddCommGroup) (:fv _uniq.65346) (:fv _uniq.65352))))) ((:c Finset.sum) (:fv _uniq.65340) (:fv _...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c LinearOrderedRing) (:fv _uniq.65343))"},{"name":"inst✝²","sexp":"((:c LinearOrderedAddCommGroup) (:fv _uniq.65346))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.65...
(:app (:c Iff) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 (:app (:c Finset.sum) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c AddCommM...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65340","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65343","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":11668,"sourceStart":11664,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...
[]
[{"source":"hfg.sum_smul_comp_perm_eq_sum_smul_iff hσ","source_end":11716,"source_start":11674,"syntax_kind":"Lean.Parser.Term.app"},{"source":"lt_iff_le_and_ne","source_end":11734,"source_start":11718,"syntax_kind":"ident"},{"source":"eq_comm","source_end":11743,"source_start":11736,"syntax_kind":"ident"},{"source":"h...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65340","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65343","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
24
2
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
db7e7aabf959fe6fa25de158a3c584d18eabf11c4c1b0eb1af42b4cb2e01dcfa
a4d8c81fb9c4f49aeefd0218b5d6763a2d911bb1c0063719a4b04ae2b74ab7e5
77a4a1a269153ec7c3d72e6d6d1160e3467c2d59df7b268bd58bec97f5bc5adc
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981