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iCogLabs-Dev
/
Mathlib-Normalized-Sexpr

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cat-searcher/leandojo-benchmark-4-random
test
3,185
MeasureTheory.Measure.InnerRegularWRT.of_restrict
Mathlib/MeasureTheory/Measure/Regular.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>Monotone.directed_le</a> fun m n h ↦ <a>Set.inter_subset_inter_right</a> _ (hmono h)
α : Type u_1 β : Type u_2 inst✝¹ : MeasurableSpace α inst✝ : TopologicalSpace α μ✝ : Measure α p q : Set α → Prop U s✝ : Set α ε r✝ : ℝ≥0∞ μ : Measure α s : ℕ → Set α h : ∀ (n : ℕ), (μ.restrict (s n)).InnerRegularWRT p MeasurableSet hs : univ ⊆ ⋃ n, s n hmono : Monotone s F : Set α hF : MeasurableSet F r : ℝ≥0∞ hr : r ...
((:c Directed) ((:c Set) (:fv _uniq.92228)) (:c Nat) (:lambda _ ((:c Set) (:fv _uniq.92228)) (:lambda _ ((:c Set) (:fv _uniq.92228)) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.92228)) ((:c Set.instHasSubset) (:fv _uniq.92228)) 1 0))) (:lambda n (:c Nat) ((:c Inter.inter) ((:c Set) (:fv _uniq.92228)) ((:c Set.instInter...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.92228))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.92228))"},{"name":"μ✝","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.92228) (:fv _uniq.92234))"},{"name":"p","se...
(:app (:c Directed) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:c Nat)) (:arg :explicit 2 (:lambda _ :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:lambda _ :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c HasSubset.Subset) (:arg :implicit-type...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"exact","sourceEnd":32357,"sourceStart":32352,"tag":"atom"},{"children":[{"name":"Monotone.directed_le","semanticRole":"global","source":"Monotone.directed_le","sourceEnd":32378,"sourceStart":32358,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":32382,"sourceStart":32379...
[]
[{"source":"Monotone.directed_le fun m n h ↦ inter_subset_inter_right _ (hmono h)","source_end":32429,"source_start":32358,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
66
18
exact
true
1
21
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d4414ae4592399ca0c325f91c7ca441a3dd5716b0e821af654756bfc1730d100
55ceaac86f1f0d72174e03c857fa0bad0879f86cfdc8660ffb2b44dbb664a423
608c81f88949aeb83f02d4db23cfa57252411c4d08ba678e723a0d9b6aada4dd
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,186
Finset.sum_nat_mod
Mathlib/Algebra/BigOperators/Group/Finset.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Finset.sum</a>, <a>Multiset.map_map</a>]
ι : Type u_1 κ : Type u_2 α : Type u_3 β : Type u_4 γ : Type u_5 s✝ s₁ s₂ : Finset α a : α f✝ g : α → β s : Finset α n : ℕ f : α → ℕ ⊢ (Multiset.map (fun x => x % n) (Multiset.map (fun i => f i) s.val)).sum % n = (∑ i ∈ s, f i % n) % n
ι : Type u_1 κ : Type u_2 α : Type u_3 β : Type u_4 γ : Type u_5 s✝ s₁ s₂ : Finset α a : α f✝ g : α → β s : Finset α n : ℕ f : α → ℕ ⊢ (Multiset.map ((fun x => x % n) ∘ fun i => f i) s.val).sum % n = (Multiset.map (fun i => f i % n) s.val).sum % n
((:c Eq) (:c Nat) ((:c HMod.hMod) (:c Nat) (:c Nat) (:c Nat) ((:c instHMod) (:c Nat) (:c Nat.instMod)) ((:c Multiset.sum) (:c Nat) (:c Nat.instAddCommMonoid) ((:c Multiset.map) (:c Nat) (:c Nat) (:lambda _ (:c Nat) ((:c HMod.hMod) (:c Nat) (:c Nat) (:c Nat) ((:c instHMod) (:c Nat) (:c Nat.instMod)) 0 (:fv _uniq.341147)...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"κ","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"s✝","sexp":"((:c Finset) (:fv _uniq.340997))"},{"name":"s₁","sexp":"((:c Finset) (:fv _uniq.340997))"},{"name"...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HMod.hMod) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HMod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.340991","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.340994","is_instance":false,"is_let":false,"name":"κ","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"rw","sourceEnd":105754,"sourceStart":105752,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":105756,"sourceStart":105755,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.sum",...
[]
[{"source":"Finset.sum","source_end":105766,"source_start":105756,"syntax_kind":"ident"},{"source":"Multiset.map_map","source_end":105784,"source_start":105768,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.340991","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.340994","is_instance":false,"is_let":false,"user_name":"κ"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
637
4
exact
true
1
14
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
246a60316b5d0d2878b5dfd8bb6d4d3ecc179ef5c907dcfefa5e6a403dfb02f3
667f4ff433a0aa8ffcf6b72acdf6df479e5ee83ec68b82ebf4cdd9f1894597a1
78ace93d52ceadb2f06f47c56b48e5a82d682d8121f1115b553f3ffc447feacf
d0e7b139cf4125a8518295354ac99ec7f9a4a805804ef2c20d453eba79e4d8fa
cat-searcher/leandojo-benchmark-4-random
test
3,187
Finset.sum_nat_mod
Mathlib/Algebra/BigOperators/Group/Finset.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rfl
ι : Type u_1 κ : Type u_2 α : Type u_3 β : Type u_4 γ : Type u_5 s✝ s₁ s₂ : Finset α a : α f✝ g : α → β s : Finset α n : ℕ f : α → ℕ ⊢ (Multiset.map ((fun x => x % n) ∘ fun i => f i) s.val).sum % n = (Multiset.map (fun i => f i % n) s.val).sum % n
((:c Eq) (:c Nat) ((:c HMod.hMod) (:c Nat) (:c Nat) (:c Nat) ((:c instHMod) (:c Nat) (:c Nat.instMod)) ((:c Multiset.sum) (:c Nat) (:c Nat.instAddCommMonoid) ((:c Multiset.map) (:fv _uniq.340997) (:c Nat) ((:c Function.comp) (:fv _uniq.340997) (:c Nat) (:c Nat) (:lambda _ (:c Nat) ((:c HMod.hMod) (:c Nat) (:c Nat) (:c ...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"κ","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"s✝","sexp":"((:c Finset) (:fv _uniq.340997))"},{"name":"s₁","sexp":"((:c Finset) (:fv _uniq.340997))"},{"name"...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HMod.hMod) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HMod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.340991","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.340994","is_instance":false,"is_let":false,"name":"κ","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"rfl","sourceEnd":105790,"sourceStart":105787,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":105790,"sourceStart":105787,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.340991","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.340994","is_instance":false,"is_let":false,"user_name":"κ"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
637
9
exact
true
1
14
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
55f7e54d34ba3ce9c6d787cbd62cf9706a70216a4097d8353ec25eddc75f3a4f
d0e7b139cf4125a8518295354ac99ec7f9a4a805804ef2c20d453eba79e4d8fa
5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,188
Associates.dvdNotUnit_of_lt
Mathlib/Algebra/Associated.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
constructor
α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 inst✝ : CommMonoidWithZero α a b : Associates α hlt : a < b ⊢ DvdNotUnit a b
case left α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 inst✝ : CommMonoidWithZero α a b : Associates α hlt : a < b ⊢ a ≠ 0 case right α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 inst✝ : CommMonoidWithZero α a b : Associates α hlt : a < b ⊢ ∃ x, ¬IsUnit x ∧ b = a * x
((:c DvdNotUnit) ((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:fv _uniq.146275) ((:c CommMonoidWithZero.toMonoidWithZero) (:fv _uniq.146275) (:fv _uniq.146287)))) ((:c Associates.instCommMonoidWithZero) (:fv _uniq.146275) (:fv _uniq.146287)) (:fv _uniq.146457) (:fv _uniq.146458))
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c CommMonoidWithZero) (:fv _uniq.146275))"},{"name":"a","sexp":"((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:...
(:app (:c DvdNotUnit) (:arg :implicit-type 0 (:app (:c Associates) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c CommMonoidWithZero) (:arg :explicit 0 (:app (:c Associates) (:arg :explicit 0 (:fv FV0)) (:arg :in...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.146275","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.146278","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"constructor","sourceEnd":47258,"sourceStart":47247,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":47258,"sourceStart":47247,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.146275","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.146278","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
371
4
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
04e0191dd219f79e79a79c6f05d096a3235b46059935f0cefcc96273c16b8c34
cb0f28d7fabde71fc45a4f6fa031b526778a6aa57582865897ec3d96befffd31
e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068
3c9e0bb0384294dd87dd5e7fb60b3ab11e43c138cf0eccd74e71cd46ae9b1093
cat-searcher/leandojo-benchmark-4-random
test
3,189
Associates.dvdNotUnit_of_lt
Mathlib/Algebra/Associated.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rcases hlt with ⟨⟨x, rfl⟩, ndvd⟩
case right α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 inst✝ : CommMonoidWithZero α a b : Associates α hlt : a < b ⊢ ∃ x, ¬IsUnit x ∧ b = a * x
case right.intro.intro α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 inst✝ : CommMonoidWithZero α a : Associates α x : Associates α ndvd : ¬a * x ∣ a ⊢ ∃ x_1, ¬IsUnit x_1 ∧ a * x = a * x_1
((:c Exists) ((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:fv _uniq.146275) ((:c CommMonoidWithZero.toMonoidWithZero) (:fv _uniq.146275) (:fv _uniq.146287)))) (:lambda x ((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:fv _uniq.146275) ((:c CommMonoidWithZero.toMonoidWithZero) (...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c CommMonoidWithZero) (:fv _uniq.146275))"},{"name":"a","sexp":"((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Associates) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:lambda x :explicit (:app (:c Associates) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:ar...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.146275","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.146278","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"rcases","sourceEnd":47332,"sourceStart":47326,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":8,"semanticRole":"local","source":"hlt","sourceEnd":47336,"sourceStart":47333,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget",...
[]
[{"source":"hlt","source_end":47336,"source_start":47333,"syntax_kind":"ident"},{"source":"⟨⟨x, rfl⟩, ndvd⟩","source_end":47366,"source_start":47342,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.146275","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.146278","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
371
13
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c57642500e562b0e8bdbd9cc6d5c6cbc3e89f14f3c91534d0f2644090369208a
057050163acff2b6084719fd7ed627d5e82ab08713b1edf350ecc74b2945ac7c
3fe47b1ca72e6275d814b776c342887c731273000cee69ddc68b075b9bc97739
f18cec1aeb0ba4611122cbe0c7d25495f3203f57e42ba94739681c1dc13e3b50
cat-searcher/leandojo-benchmark-4-random
test
3,190
Associates.dvdNotUnit_of_lt
Mathlib/Algebra/Associated.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨x, ?_, <a>rfl</a>⟩
case right.intro.intro α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 inst✝ : CommMonoidWithZero α a : Associates α x : Associates α ndvd : ¬a * x ∣ a ⊢ ∃ x_1, ¬IsUnit x_1 ∧ a * x = a * x_1
case right.intro.intro α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 inst✝ : CommMonoidWithZero α a : Associates α x : Associates α ndvd : ¬a * x ∣ a ⊢ ¬IsUnit x
((:c Exists) ((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:fv _uniq.146275) ((:c CommMonoidWithZero.toMonoidWithZero) (:fv _uniq.146275) (:fv _uniq.146287)))) (:lambda x ((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:fv _uniq.146275) ((:c CommMonoidWithZero.toMonoidWithZero) (...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c CommMonoidWithZero) (:fv _uniq.146275))"},{"name":"a","sexp":"((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Associates) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:lambda x :explicit (:app (:c Associates) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:ar...
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{"children":[{"source":"refine","sourceEnd":47375,"sourceStart":47369,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":47379,"sourceStart":47376,"tag":"atom"},{"children":[{"contextIndex":7,"semanticRole":"local","source":"x","sourceEnd":47380,"sourceStart":47379,"tag":"identifier"},{"source":",","sourceEnd":47381,...
[]
[{"source":"⟨x, ?_, rfl⟩","source_end":47392,"source_start":47376,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.146275","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.146278","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
371
14
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
380296f04af2a44eccd4aaa2b56f63af98ec4b6c9cd2214ce00270a7080b9eb9
f18cec1aeb0ba4611122cbe0c7d25495f3203f57e42ba94739681c1dc13e3b50
fedd472257787e4861730e7934d9a0d26198753050e54e66721bd627bd85757e
952c42063d52deed0b54c264202f19a3e544d1bf9527099a4490e53f1e88c97a
cat-searcher/leandojo-benchmark-4-random
test
3,191
Associates.dvdNotUnit_of_lt
Mathlib/Algebra/Associated.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
contrapose! ndvd
case right.intro.intro α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 inst✝ : CommMonoidWithZero α a : Associates α x : Associates α ndvd : ¬a * x ∣ a ⊢ ¬IsUnit x
case right.intro.intro α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 inst✝ : CommMonoidWithZero α a : Associates α x : Associates α ndvd : IsUnit x ⊢ a * x ∣ a
((:c Not) ((:c IsUnit) ((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:fv _uniq.146275) ((:c CommMonoidWithZero.toMonoidWithZero) (:fv _uniq.146275) (:fv _uniq.146287)))) ((:c MonoidWithZero.toMonoid) ((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:fv _uniq.146275) ((:c CommMonoi...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c CommMonoidWithZero) (:fv _uniq.146275))"},{"name":"a","sexp":"((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:...
(:app (:c Not) (:arg :explicit 0 (:app (:c IsUnit) (:arg :implicit-type 0 (:app (:c Associates) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:app (:c Associates) (:arg :explicit 0 (:f...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.146275","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.146278","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"contrapose!","sourceEnd":47406,"sourceStart":47395,"tag":"atom"},{"children":[{"contextIndex":8,"semanticRole":"local","source":"ndvd","sourceEnd":47411,"sourceStart":47407,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"null","source":"ndvd","sourceEnd":47411...
[]
[{"source":"ndvd","source_end":47411,"source_start":47407,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.146275","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.146278","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
371
15
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
97d88e06a3fa43db620a1b0655b2fcbcfc65af59594e151d5add133f5da3d6a3
952c42063d52deed0b54c264202f19a3e544d1bf9527099a4490e53f1e88c97a
e33d41bcaf144a0c0d7c54e87b5cfa092e376e4dec9cb3754b8eeb0347d22fce
569f6b1368e279c819c0d6dc0d52fc39a180d601f3fa4b09868e3667260d67e2
cat-searcher/leandojo-benchmark-4-random
test
3,192
Associates.dvdNotUnit_of_lt
Mathlib/Algebra/Associated.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rcases ndvd with ⟨u, rfl⟩
case right.intro.intro α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 inst✝ : CommMonoidWithZero α a : Associates α x : Associates α ndvd : IsUnit x ⊢ a * x ∣ a
case right.intro.intro.intro α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 inst✝ : CommMonoidWithZero α a : Associates α u : (Associates α)ˣ ⊢ a * ↑u ∣ a
((:c Dvd.dvd) ((:c Associates) (:fv _uniq.146275) ((:c CommMonoid.toMonoid) (:fv _uniq.146275) ((:c CommMonoidWithZero.toCommMonoid) (:fv _uniq.146275) (:fv _uniq.146287)))) ((:c semigroupDvd) ((:c Associates) (:fv _uniq.146275) ((:c CommMonoid.toMonoid) (:fv _uniq.146275) ((:c CommMonoidWithZero.toCommMonoid) (:fv _un...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c CommMonoidWithZero) (:fv _uniq.146275))"},{"name":"a","sexp":"((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:...
(:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Associates) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Associates) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instanc...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.146275","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.146278","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"rcases","sourceEnd":47420,"sourceStart":47414,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":8,"semanticRole":"local","source":"ndvd","sourceEnd":47425,"sourceStart":47421,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget"...
[]
[{"source":"ndvd","source_end":47425,"source_start":47421,"syntax_kind":"ident"},{"source":"⟨u, rfl⟩","source_end":47443,"source_start":47431,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.146275","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.146278","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
371
16
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f19c6b3ddff7af32888e9344d8ac9cc92b85e278cd26480665937d541c779fcd
569f6b1368e279c819c0d6dc0d52fc39a180d601f3fa4b09868e3667260d67e2
3e4d7102ba2489ae0e4c88203fb7fe84c607ee45817cbd8f148547cbbf76b204
96a8d08833603ada1c7062b0b470ccf0638c7927da2a248f7af19c898b1d7418
cat-searcher/leandojo-benchmark-4-random
test
3,193
Associates.dvdNotUnit_of_lt
Mathlib/Algebra/Associated.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
case right.intro.intro.intro α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 inst✝ : CommMonoidWithZero α a : Associates α u : (Associates α)ˣ ⊢ a * ↑u ∣ a
((:c Dvd.dvd) ((:c Associates) (:fv _uniq.146275) ((:c CommMonoid.toMonoid) (:fv _uniq.146275) ((:c CommMonoidWithZero.toCommMonoid) (:fv _uniq.146275) (:fv _uniq.146287)))) ((:c semigroupDvd) ((:c Associates) (:fv _uniq.146275) ((:c CommMonoid.toMonoid) (:fv _uniq.146275) ((:c CommMonoidWithZero.toCommMonoid) (:fv _un...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c CommMonoidWithZero) (:fv _uniq.146275))"},{"name":"a","sexp":"((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:...
(:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Associates) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Associates) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instanc...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.146275","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.146278","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"simp","sourceEnd":47450,"sourceStart":47446,"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.146275","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.146278","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
371
17
exact
true
1
7
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
346a28ad617762b7ec1b64010a3fb8d8fb3c8575aceea543e8938671afc17a08
96a8d08833603ada1c7062b0b470ccf0638c7927da2a248f7af19c898b1d7418
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,194
Associates.dvdNotUnit_of_lt
Mathlib/Algebra/Associated.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro rfl
case left α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 inst✝ : CommMonoidWithZero α a b : Associates α hlt : a < b ⊢ a ≠ 0
case left α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 inst✝ : CommMonoidWithZero α b : Associates α hlt : 0 < b ⊢ False
((:c Ne) ((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:fv _uniq.146275) ((:c CommMonoidWithZero.toMonoidWithZero) (:fv _uniq.146275) (:fv _uniq.146287)))) (:fv _uniq.146457) ((:c OfNat.ofNat) ((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:fv _uniq.146275) ((:c CommMonoidWithZe...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c CommMonoidWithZero) (:fv _uniq.146275))"},{"name":"a","sexp":"((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:...
(:app (:c Ne) (:arg :implicit-type 0 (:app (:c Associates) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:fv FV6)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:app (:c Associates) (:arg :explicit 0 (:fv FV0)) (:ar...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.146275","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.146278","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"rintro","sourceEnd":47271,"sourceStart":47265,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":47275,"sourceStart":47272,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl","sourceEnd":47275,"sourceStart":472...
[]
[{"source":"rfl","source_end":47275,"source_start":47272,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.146275","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.146278","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
371
10
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5a57c362e100e36400c896e1d798354cc99e360d70588505ef7b47244f2c8379
e2d841aa65e56dea2deefb6c8624451fa57495a0229e756b77a9bf4978141b92
09e128cd6787f35d3c063b643315aff1382388dafa4e55b6546fbf9dcecb02da
d2bf27428a74259fcdba08808c10dfea1fde314209d902918b2ba3aea48f851d
cat-searcher/leandojo-benchmark-4-random
test
3,195
Associates.dvdNotUnit_of_lt
Mathlib/Algebra/Associated.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>not_lt_of_le</a> _ hlt
case left α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 inst✝ : CommMonoidWithZero α b : Associates α hlt : 0 < b ⊢ False
α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 inst✝ : CommMonoidWithZero α b : Associates α hlt : 0 < b ⊢ b ≤ 0
(:c False)
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c CommMonoidWithZero) (:fv _uniq.146275))"},{"name":"b","sexp":"((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:...
(:c False)
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.146275","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.146278","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"apply","sourceEnd":47285,"sourceStart":47280,"tag":"atom"},{"children":[{"name":"not_lt_of_le","semanticRole":"global","source":"not_lt_of_le","sourceEnd":47298,"sourceStart":47286,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":47300,"sourceStart":47299,"tag":"atom"}],"k...
[]
[{"source":"not_lt_of_le _ hlt","source_end":47304,"source_start":47286,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.146275","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.146278","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
371
11
exact
true
1
7
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f61c668579c04de27463e0e96055db8103293d8bdfcc15b3c3ff34faae50e406
d2bf27428a74259fcdba08808c10dfea1fde314209d902918b2ba3aea48f851d
854cb5196eb8170e995746332d04c103398a36ed7d7953bb9a6032d34606a0cb
1c02b89abb9992ebd881f38aaaf61a680aace7f44507f02856de68f5d7207353
cat-searcher/leandojo-benchmark-4-random
test
3,196
Associates.dvdNotUnit_of_lt
Mathlib/Algebra/Associated.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>dvd_zero</a>
α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 inst✝ : CommMonoidWithZero α b : Associates α hlt : 0 < b ⊢ b ≤ 0
((:c LE.le) ((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:fv _uniq.146275) ((:c CommMonoidWithZero.toMonoidWithZero) (:fv _uniq.146275) (:fv _uniq.146287)))) ((:c Preorder.toLE) ((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:fv _uniq.146275) ((:c CommMonoidWithZero.toMonoidWit...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c CommMonoidWithZero) (:fv _uniq.146275))"},{"name":"b","sexp":"((:c Associates) (:fv _uniq.146275) ((:c MonoidWithZero.toMonoid) (:...
(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Associates) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Associates) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-o...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.146275","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.146278","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"apply","sourceEnd":47314,"sourceStart":47309,"tag":"atom"},{"name":"dvd_zero","semanticRole":"global","source":"dvd_zero","sourceEnd":47323,"sourceStart":47315,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply dvd_zero","sourceEnd":47323,"sourceStart":47309,"tag":"node"}
[]
[{"source":"dvd_zero","source_end":47323,"source_start":47315,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.146275","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.146278","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
371
12
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5141ca9826f81c06d7b17a3affca4b3c7fd19752d5a758b43937a6590f7687ce
1c02b89abb9992ebd881f38aaaf61a680aace7f44507f02856de68f5d7207353
59868904e229e903cf6dad113e4415f9dd721539abaf8f1235d7a3ea1f76518f
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,197
exists_maximal_orthonormal
Mathlib/Analysis/InnerProductSpace/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have := <a>zorn_subset_nonempty</a> { b | <a>Orthonormal</a> 𝕜 (<a>Subtype.val</a> : b → E) } ?_ _ hs
𝕜 : Type u_1 E : Type u_2 F : Type u_3 inst✝⁴ : _root_.RCLike 𝕜 inst✝³ : NormedAddCommGroup E inst✝² : InnerProductSpace 𝕜 E inst✝¹ : NormedAddCommGroup F inst✝ : InnerProductSpace ℝ F ι : Type u_4 s : Set E hs : Orthonormal 𝕜 Subtype.val ⊢ ∃ w ⊇ s, Orthonormal 𝕜 Subtype.val ∧ ∀ u ⊇ w, Orthonormal 𝕜 Subtype.val →...
case refine_2 𝕜 : Type u_1 E : Type u_2 F : Type u_3 inst✝⁴ : _root_.RCLike 𝕜 inst✝³ : NormedAddCommGroup E inst✝² : InnerProductSpace 𝕜 E inst✝¹ : NormedAddCommGroup F inst✝ : InnerProductSpace ℝ F ι : Type u_4 s : Set E hs : Orthonormal 𝕜 Subtype.val this : ∃ m ∈ {b | Orthonormal 𝕜 Subtype.val}, s ⊆ m ∧ ∀ a ∈ {b...
((:c Exists) ((:c Set) (:fv _uniq.349704)) (:lambda w ((:c Set) (:fv _uniq.349704)) ((:c And) ((:c Superset) ((:c Set) (:fv _uniq.349704)) ((:c Set.instHasSubset) (:fv _uniq.349704)) 0 (:fv _uniq.349960)) ((:c And) ((:c Orthonormal) (:fv _uniq.349701) (:fv _uniq.349704) (:fv _uniq.349746) (:fv _uniq.349749) (:fv _uniq....
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁴","sexp":"((:c RCLike) (:fv _uniq.349701))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.349704))"},{"name":"inst✝²","sexp":"((:c InnerProductSpace) (:fv _uniq.349701...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:lambda w :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV1))) (:app (:c And) (:arg :explicit 0 (:app (:c Superset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instanc...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.349701","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.349704","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"have","sourceEnd":45535,"sourceStart":45531,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":45536,"sourceStart":45536,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":45536,"sourceStart":45536,"tag":"node"}],"kind":"Lean.Parser.Term.hav...
[]
[{"source":"zorn_subset_nonempty { b | Orthonormal 𝕜 (Subtype.val : b → E) } ?_ _ hs","source_end":45616,"source_start":45539,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.349701","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.349704","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
280
4
exact
true
1
11
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
acfaa21fe636920d3d73524bd5152cfea9bbea40e02eb6696a6a9a51d21b779f
e5d78194520c0100df111069fc62e71f2e88d0a36af7b28d4cc71f93d70fad0f
6992f478e25bc9b3b0e16ef086bca20f92ce7dffff29aaa46284ea7e8918b8a6
fc77869194fbe24c3885da9ec34e20fbdf11fe4fb425a06ec5132cd1463861d0
cat-searcher/leandojo-benchmark-4-random
test
3,198
exists_maximal_orthonormal
Mathlib/Analysis/InnerProductSpace/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨b, bi, sb, h⟩ := this
case refine_2 𝕜 : Type u_1 E : Type u_2 F : Type u_3 inst✝⁴ : _root_.RCLike 𝕜 inst✝³ : NormedAddCommGroup E inst✝² : InnerProductSpace 𝕜 E inst✝¹ : NormedAddCommGroup F inst✝ : InnerProductSpace ℝ F ι : Type u_4 s : Set E hs : Orthonormal 𝕜 Subtype.val this : ∃ m ∈ {b | Orthonormal 𝕜 Subtype.val}, s ⊆ m ∧ ∀ a ∈ {b...
case refine_2.intro.intro.intro 𝕜 : Type u_1 E : Type u_2 F : Type u_3 inst✝⁴ : _root_.RCLike 𝕜 inst✝³ : NormedAddCommGroup E inst✝² : InnerProductSpace 𝕜 E inst✝¹ : NormedAddCommGroup F inst✝ : InnerProductSpace ℝ F ι : Type u_4 s : Set E hs : Orthonormal 𝕜 Subtype.val b : Set E bi : b ∈ {b | Orthonormal 𝕜 Subtyp...
((:c Exists) ((:c Set) (:fv _uniq.349704)) (:lambda w ((:c Set) (:fv _uniq.349704)) ((:c And) ((:c Superset) ((:c Set) (:fv _uniq.349704)) ((:c Set.instHasSubset) (:fv _uniq.349704)) 0 (:fv _uniq.349960)) ((:c And) ((:c Orthonormal) (:fv _uniq.349701) (:fv _uniq.349704) (:fv _uniq.349746) (:fv _uniq.349749) (:fv _uniq....
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁴","sexp":"((:c RCLike) (:fv _uniq.349701))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.349704))"},{"name":"inst✝²","sexp":"((:c InnerProductSpace) (:fv _uniq.349701...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:lambda w :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV1))) (:app (:c And) (:arg :explicit 0 (:app (:c Superset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instanc...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.349701","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.349704","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"obtain","sourceEnd":45628,"sourceStart":45622,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":45632,"sourceStart":45629,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"b","sourceEn...
[]
[{"source":"this","source_end":45655,"source_start":45651,"syntax_kind":"ident"},{"source":"⟨b, bi, sb, h⟩","source_end":45647,"source_start":45629,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.349701","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.349704","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
280
9
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c6cf38f980c142c7e0c338966bda98893452680b4039a5e8e7a11aea1d71ca60
7d6c1d7add71dc8a7b5f00e55ce7c9ebb578f83148d60724cac2b38d34d15d64
285315c8458dbf560af310a20d42d3fb713effd0ea201e4602b3924729686534
a2b739ee205086e41ebd3ee3fa9ad830f9e8317735e6c546fec6f30cceea8c53
cat-searcher/leandojo-benchmark-4-random
test
3,199
exists_maximal_orthonormal
Mathlib/Analysis/InnerProductSpace/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨b, sb, bi, ?_⟩
case refine_2.intro.intro.intro 𝕜 : Type u_1 E : Type u_2 F : Type u_3 inst✝⁴ : _root_.RCLike 𝕜 inst✝³ : NormedAddCommGroup E inst✝² : InnerProductSpace 𝕜 E inst✝¹ : NormedAddCommGroup F inst✝ : InnerProductSpace ℝ F ι : Type u_4 s : Set E hs : Orthonormal 𝕜 Subtype.val b : Set E bi : b ∈ {b | Orthonormal 𝕜 Subtyp...
case refine_2.intro.intro.intro 𝕜 : Type u_1 E : Type u_2 F : Type u_3 inst✝⁴ : _root_.RCLike 𝕜 inst✝³ : NormedAddCommGroup E inst✝² : InnerProductSpace 𝕜 E inst✝¹ : NormedAddCommGroup F inst✝ : InnerProductSpace ℝ F ι : Type u_4 s : Set E hs : Orthonormal 𝕜 Subtype.val b : Set E bi : b ∈ {b | Orthonormal 𝕜 Subtyp...
((:c Exists) ((:c Set) (:fv _uniq.349704)) (:lambda w ((:c Set) (:fv _uniq.349704)) ((:c And) ((:c Superset) ((:c Set) (:fv _uniq.349704)) ((:c Set.instHasSubset) (:fv _uniq.349704)) 0 (:fv _uniq.349960)) ((:c And) ((:c Orthonormal) (:fv _uniq.349701) (:fv _uniq.349704) (:fv _uniq.349746) (:fv _uniq.349749) (:fv _uniq....
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁴","sexp":"((:c RCLike) (:fv _uniq.349701))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.349704))"},{"name":"inst✝²","sexp":"((:c InnerProductSpace) (:fv _uniq.349701...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:lambda w :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV1))) (:app (:c And) (:arg :explicit 0 (:app (:c Superset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instanc...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.349701","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.349704","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"refine","sourceEnd":45666,"sourceStart":45660,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":45670,"sourceStart":45667,"tag":"atom"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"b","sourceEnd":45671,"sourceStart":45670,"tag":"identifier"},{"source":",","sourceEnd":45672...
[]
[{"source":"⟨b, sb, bi, ?_⟩","source_end":45686,"source_start":45667,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.349701","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.349704","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
280
10
exact
true
1
15
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
01885beb3c41ce0f1cb7a7e94079c8473e851c0da635824872fdeb344558383b
a2b739ee205086e41ebd3ee3fa9ad830f9e8317735e6c546fec6f30cceea8c53
57a60a066004adf23243a851f9a28cef3c9a82cadccd05b18f6639b9f026969a
7e4bbaf7c3e1e6fa3e27cd090bd67a29d9898c1be978a22b37e3d12da3d2bf7e
cat-searcher/leandojo-benchmark-4-random
test
3,200
exists_maximal_orthonormal
Mathlib/Analysis/InnerProductSpace/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact fun u hus hu => h u hu hus
case refine_2.intro.intro.intro 𝕜 : Type u_1 E : Type u_2 F : Type u_3 inst✝⁴ : _root_.RCLike 𝕜 inst✝³ : NormedAddCommGroup E inst✝² : InnerProductSpace 𝕜 E inst✝¹ : NormedAddCommGroup F inst✝ : InnerProductSpace ℝ F ι : Type u_4 s : Set E hs : Orthonormal 𝕜 Subtype.val b : Set E bi : b ∈ {b | Orthonormal 𝕜 Subtyp...
(:forall u ((:c Set) (:fv _uniq.349704)) (:forall _ ((:c Superset) ((:c Set) (:fv _uniq.349704)) ((:c Set.instHasSubset) (:fv _uniq.349704)) 0 (:fv _uniq.350075)) (:forall _ ((:c Orthonormal) (:fv _uniq.349701) (:fv _uniq.349704) (:fv _uniq.349746) (:fv _uniq.349749) (:fv _uniq.349763) ((:c Subtype) (:fv _uniq.349704) ...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁴","sexp":"((:c RCLike) (:fv _uniq.349701))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.349704))"},{"name":"inst✝²","sexp":"((:c InnerProductSpace) (:fv _uniq.349701...
(:forall u :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV1))) (:forall _ :explicit (:app (:c Superset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 2 0) (:a...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.349701","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.349704","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"exact","sourceEnd":45696,"sourceStart":45691,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":45700,"sourceStart":45697,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"u","sourceEnd":45702,"sourceStart":45701,"tag":"identifier"},{"semanticRole":"scoped_loca...
[]
[{"source":"fun u hus hu => h u hu hus","source_end":45723,"source_start":45697,"syntax_kind":"Lean.Parser.Term.fun"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.349701","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.349704","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
280
11
exact
true
1
15
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
093e422655ed9fb119d19113bb82da643601d1e1f0f5a978d60ec383cbd858eb
7e4bbaf7c3e1e6fa3e27cd090bd67a29d9898c1be978a22b37e3d12da3d2bf7e
0508377367882c568067f0fd632d9bb47c311d83dfa5d1dbff35a89f0396e4cb
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,201
exists_maximal_orthonormal
Mathlib/Analysis/InnerProductSpace/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine fun c hc cc _c0 => ⟨⋃₀ c, ?_, ?_⟩
case refine_1 𝕜 : Type u_1 E : Type u_2 F : Type u_3 inst✝⁴ : _root_.RCLike 𝕜 inst✝³ : NormedAddCommGroup E inst✝² : InnerProductSpace 𝕜 E inst✝¹ : NormedAddCommGroup F inst✝ : InnerProductSpace ℝ F ι : Type u_4 s : Set E hs : Orthonormal 𝕜 Subtype.val ⊢ ∀ c ⊆ {b | Orthonormal 𝕜 Subtype.val}, IsChain (fun x x_...
case refine_1.refine_1 𝕜 : Type u_1 E : Type u_2 F : Type u_3 inst✝⁴ : _root_.RCLike 𝕜 inst✝³ : NormedAddCommGroup E inst✝² : InnerProductSpace 𝕜 E inst✝¹ : NormedAddCommGroup F inst✝ : InnerProductSpace ℝ F ι : Type u_4 s : Set E hs : Orthonormal 𝕜 Subtype.val c : Set (Set E) hc : c ⊆ {b | Orthonormal 𝕜 Subtype.v...
(:forall c ((:c Set) ((:c Set) (:fv _uniq.349704))) (:forall _ ((:c HasSubset.Subset) ((:c Set) ((:c Set) (:fv _uniq.349704))) ((:c Set.instHasSubset) ((:c Set) (:fv _uniq.349704))) 0 ((:c setOf) ((:c Set) (:fv _uniq.349704)) (:lambda b ((:c Set) (:fv _uniq.349704)) ((:c Orthonormal) (:fv _uniq.349701) (:fv _uniq.34970...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁴","sexp":"((:c RCLike) (:fv _uniq.349701))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.349704))"},{"name":"inst✝²","sexp":"((:c InnerProductSpace) (:fv _uniq.349701...
(:forall c :explicit (:app (:c Set) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))) (:forall _ :explicit (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explic...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.349701","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.349704","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"refine","sourceEnd":45735,"sourceStart":45729,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":45739,"sourceStart":45736,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"c","sourceEnd":45741,"sourceStart":45740,"tag":"identifier"},{"semanticRole":"scoped_loc...
[]
[{"source":"fun c hc cc _c0 => ⟨⋃₀ c, ?_, ?_⟩","source_end":45777,"source_start":45736,"syntax_kind":"Lean.Parser.Term.fun"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.349701","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.349704","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
280
16
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4116383277721529f138225cd9de83d0b6e63ab9f735bbcac1cae8bf5eb0d6f8
d280f7a3216904650780f23b006949b936628c8766bca2c2fa9d8e73306d295a
9d0ab604854a2c0de54e76f19844232de6f20c1e2d1a2d1e95a60c6f877f94b2
b22e406edf7f36d599bd3f8a97c6395807fe82edb3a92c7112cab7131d9bf445
cat-searcher/leandojo-benchmark-4-random
test
3,202
exists_maximal_orthonormal
Mathlib/Analysis/InnerProductSpace/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>orthonormal_sUnion_of_directed</a> cc.directedOn fun x xc => hc xc
case refine_1.refine_1 𝕜 : Type u_1 E : Type u_2 F : Type u_3 inst✝⁴ : _root_.RCLike 𝕜 inst✝³ : NormedAddCommGroup E inst✝² : InnerProductSpace 𝕜 E inst✝¹ : NormedAddCommGroup F inst✝ : InnerProductSpace ℝ F ι : Type u_4 s : Set E hs : Orthonormal 𝕜 Subtype.val c : Set (Set E) hc : c ⊆ {b | Orthonormal 𝕜 Subtype.v...
((:c Membership.mem) ((:c Set) (:fv _uniq.349704)) ((:c Set) ((:c Set) (:fv _uniq.349704))) ((:c Set.instMembership) ((:c Set) (:fv _uniq.349704))) ((:c Set.sUnion) (:fv _uniq.349704) (:fv _uniq.350159)) ((:c setOf) ((:c Set) (:fv _uniq.349704)) (:lambda b ((:c Set) (:fv _uniq.349704)) ((:c Orthonormal) (:fv _uniq.3497...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁴","sexp":"((:c RCLike) (:fv _uniq.349701))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.349704))"},{"name":"inst✝²","sexp":"((:c InnerProductSpace) (:fv _uniq.349701...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:a...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.349701","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.349704","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":45790,"sourceStart":45785,"tag":"atom"},{"children":[{"name":"orthonormal_sUnion_of_directed","semanticRole":"global","source":"orthonormal_sUnion_of_directed","sourceEnd":45821,"sourceStart":45791,"tag":"identifier"},{"children":[{"name"...
[]
[{"source":"orthonormal_sUnion_of_directed cc.directedOn fun x xc => hc xc","source_end":45853,"source_start":45791,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.349701","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.349704","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
280
19
exact
true
1
15
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f38e4ee07d565b9de2844cca1ecdfd83154f319396fc3bc5e1152c6936df8fc3
e5ba62f11f8b12fdd1234ddebbac53fe73da6ef0c6c83857f5b1f7e15f5dd670
7b22733bee934df3683fb6802be9285fb5299507ec73370d848551f0b4292e97
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,203
exists_maximal_orthonormal
Mathlib/Analysis/InnerProductSpace/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact fun _ => <a>Set.subset_sUnion_of_mem</a>
case refine_1.refine_2 𝕜 : Type u_1 E : Type u_2 F : Type u_3 inst✝⁴ : _root_.RCLike 𝕜 inst✝³ : NormedAddCommGroup E inst✝² : InnerProductSpace 𝕜 E inst✝¹ : NormedAddCommGroup F inst✝ : InnerProductSpace ℝ F ι : Type u_4 s : Set E hs : Orthonormal 𝕜 Subtype.val c : Set (Set E) hc : c ⊆ {b | Orthonormal 𝕜 Subtype.v...
(:forall s ((:c Set) (:fv _uniq.349704)) (:forall _ ((:c Membership.mem) ((:c Set) (:fv _uniq.349704)) ((:c Set) ((:c Set) (:fv _uniq.349704))) ((:c Set.instMembership) ((:c Set) (:fv _uniq.349704))) 0 (:fv _uniq.350159)) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.349704)) ((:c Set.instHasSubset) (:fv _uniq.349704)) 1...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁴","sexp":"((:c RCLike) (:fv _uniq.349701))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.349704))"},{"name":"inst✝²","sexp":"((:c InnerProductSpace) (:fv _uniq.349701...
(:forall s :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV1))) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))))) (:arg :instance 2 (:instance-of (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.349701","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.349704","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":45866,"sourceStart":45861,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":45870,"sourceStart":45867,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"_","sourceEnd":45872,"sourceStart":45871,"tag":"atom"}],"kind":"Lea...
[]
[{"source":"fun _ => Set.subset_sUnion_of_mem","source_end":45900,"source_start":45867,"syntax_kind":"Lean.Parser.Term.fun"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.349701","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.349704","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
280
24
exact
true
1
15
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
88b2c1a52f48dbe11824b939c1202ab4b9624d8ecd7f6ace124a1a1589806862
5c356a835fce9ed7287530d70b920bdb0b2ef02ab1d7316fa67deb5f7cb378af
d60f618a171009ddabffc6475f0205b41a3a9382d211a785c97d18fc4802fd9d
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,204
mem_segment_translate
Mathlib/Analysis/Convex/Segment.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp_rw [← <a>vadd_eq_add</a>, ← <a>vadd_segment</a>, <a>Set.vadd_mem_vadd_set_iff</a>]
𝕜 : Type u_1 E : Type u_2 F : Type u_3 G : Type u_4 ι : Type u_5 π : ι → Type u_6 inst✝⁵ : OrderedRing 𝕜 inst✝⁴ : AddCommGroup E inst✝³ : AddCommGroup F inst✝² : AddCommGroup G inst✝¹ : Module 𝕜 E inst✝ : Module 𝕜 F a x b c : E ⊢ a + x ∈ [a + b-[𝕜]a + c] ↔ x ∈ [b-[𝕜]c]
((:c Iff) ((:c Membership.mem) (:fv _uniq.121716) ((:c Set) (:fv _uniq.121716)) ((:c Set.instMembership) (:fv _uniq.121716)) ((:c HAdd.hAdd) (:fv _uniq.121716) (:fv _uniq.121716) (:fv _uniq.121716) ((:c instHAdd) (:fv _uniq.121716) ((:c AddCommMagma.toAdd) (:fv _uniq.121716) ((:c AddCommSemigroup.toAddCommMagma) (:fv _...
[{"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":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.121725) (:sort (+ u_6 1)))"},{"name":"inst✝⁵","sexp":"((:c OrderedRing) (:fv...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :e...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.121713","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.121716","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":10307,"sourceStart":10300,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10309,"sourceStart":10308,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children...
[]
[{"source":"vadd_eq_add","source_end":10324,"source_start":10313,"syntax_kind":"ident"},{"source":"vadd_segment","source_end":10342,"source_start":10330,"syntax_kind":"ident"},{"source":"vadd_mem_vadd_set_iff","source_end":10365,"source_start":10344,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.121713","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.121716","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
80
2
exact
true
1
16
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1608018a7943faa29e17e8aea9d12e267b9dcc884928a2fe8846f275bc726f20
45913154dc4221840c23c06a8a065986285d9e566a987d225d8495d2f94d4ad0
3b1e5b87fd32c01c572c71b6217154f919cb685446913e79c96bb9ac6b301a2f
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,205
IsBoundedLinearMap.snd
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine (<a>LinearMap.snd</a> 𝕜 E F).isLinear.with_bound 1 fun x => ?_
𝕜 : Type u_1 inst✝⁶ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E F : Type u_3 inst✝³ : NormedAddCommGroup F inst✝² : NormedSpace 𝕜 F G : Type u_4 inst✝¹ : NormedAddCommGroup G inst✝ : NormedSpace 𝕜 G ⊢ IsBoundedLinearMap 𝕜 fun x => x.2
𝕜 : Type u_1 inst✝⁶ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E F : Type u_3 inst✝³ : NormedAddCommGroup F inst✝² : NormedSpace 𝕜 F G : Type u_4 inst✝¹ : NormedAddCommGroup G inst✝ : NormedSpace 𝕜 G x : E × F ⊢ ‖(LinearMap.snd 𝕜 E F) x‖ ≤ 1 * ‖x‖
((:c IsBoundedLinearMap) (:fv _uniq.27522) ((:c NontriviallyNormedField.toNormedField) (:fv _uniq.27522) (:fv _uniq.27525)) ((:c Prod) (:fv _uniq.27528) (:fv _uniq.27642)) ((:c Prod.normedAddCommGroup) (:fv _uniq.27528) (:fv _uniq.27642) (:fv _uniq.27531) (:fv _uniq.27645)) ((:c Prod.normedSpace) (:fv _uniq.27522) (:fv...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁶","sexp":"((:c NontriviallyNormedField) (:fv _uniq.27522))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.27528))"},{"name":"inst✝⁴","sexp":"((:c NormedSpace) (:fv _uniq.27522) (:fv _uniq.27528) ((:c Nontriv...
(:app (:c IsBoundedLinearMap) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV5)))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explic...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27522","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.27525","is_instance":true,"is_let":false,"name":"inst✝⁶","sexp":"(:app (:c NontriviallyNormedFiel...
{"children":[{"source":"refine","sourceEnd":5520,"sourceStart":5514,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":5522,"sourceStart":5521,"tag":"atom"},{"children":[{"name":"LinearMap.snd","semanticRole":"global","source":"LinearMap.snd","sourceEnd":5535,"sourceStart":5522,"tag":"identi...
[]
[{"source":"(LinearMap.snd 𝕜 E F).isLinear.with_bound 1 fun x => ?_","source_end":5579,"source_start":5521,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27522","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.27525","is_instance":true,"is_let":false,"user_name":"inst✝⁶"},{"binder_role":":implicit","context_index":2,"inter...
24
4
exact
true
1
11
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a01f15038ea091c3720d2f2b083b37e3fdcad903b67f865a98257b317aec4e2e
be183d5717982a1e2731a965ef4b089f23cdebf699b5580f8303eb609295e165
d8bfa7f4f557cbedd7a17719cd0196dc6d1da262c3233fc224ab6f7e2d7c7bf2
29eb954ea81ead5a85913e5216c7062ad1fe9252b470269f8fa149d50e71c599
cat-searcher/leandojo-benchmark-4-random
test
3,206
IsBoundedLinearMap.snd
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>one_mul</a>]
𝕜 : Type u_1 inst✝⁶ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E F : Type u_3 inst✝³ : NormedAddCommGroup F inst✝² : NormedSpace 𝕜 F G : Type u_4 inst✝¹ : NormedAddCommGroup G inst✝ : NormedSpace 𝕜 G x : E × F ⊢ ‖(LinearMap.snd 𝕜 E F) x‖ ≤ 1 * ‖x‖
𝕜 : Type u_1 inst✝⁶ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E F : Type u_3 inst✝³ : NormedAddCommGroup F inst✝² : NormedSpace 𝕜 F G : Type u_4 inst✝¹ : NormedAddCommGroup G inst✝ : NormedSpace 𝕜 G x : E × F ⊢ ‖(LinearMap.snd 𝕜 E F) x‖ ≤ ‖x‖
((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.27642) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.27642) (:fv _uniq.27645)) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.27522) (:fv _uniq.27522) ((:c DivisionSemiring.toSemiring) (:fv _uniq.27522) ((:c Semifield.toDivisionSemiring) (:fv _uniq.27522) ((...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁶","sexp":"((:c NontriviallyNormedField) (:fv _uniq.27522))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.27528))"},{"name":"inst✝⁴","sexp":"((:c NormedSpace) (:fv _uniq.27522) (:fv _uniq.27528) ((:c Nontriv...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c DFunLike.c...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27522","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.27525","is_instance":true,"is_let":false,"name":"inst✝⁶","sexp":"(:app (:c NontriviallyNormedFiel...
{"children":[{"source":"rw","sourceEnd":5584,"sourceStart":5582,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5586,"sourceStart":5585,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"one_mul","semanticRo...
[]
[{"source":"one_mul","source_end":5593,"source_start":5586,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27522","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.27525","is_instance":true,"is_let":false,"user_name":"inst✝⁶"},{"binder_role":":implicit","context_index":2,"inter...
24
5
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
49a862bfd2586e602bd386ff1d0aca07ce2cfc471f0fe207b675e72be438e159
29eb954ea81ead5a85913e5216c7062ad1fe9252b470269f8fa149d50e71c599
18c3e98597a318bf9015f3d59a8918a79a527e2a3d6bbc4d287bd6db906f596d
262d0e75b99fde01e7ac670eca04211fb699c2b886ea390f6d3f30ffc64cc371
cat-searcher/leandojo-benchmark-4-random
test
3,207
IsBoundedLinearMap.snd
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>le_max_right</a> _ _
𝕜 : Type u_1 inst✝⁶ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E F : Type u_3 inst✝³ : NormedAddCommGroup F inst✝² : NormedSpace 𝕜 F G : Type u_4 inst✝¹ : NormedAddCommGroup G inst✝ : NormedSpace 𝕜 G x : E × F ⊢ ‖(LinearMap.snd 𝕜 E F) x‖ ≤ ‖x‖
((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.27642) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.27642) (:fv _uniq.27645)) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.27522) (:fv _uniq.27522) ((:c DivisionSemiring.toSemiring) (:fv _uniq.27522) ((:c Semifield.toDivisionSemiring) (:fv _uniq.27522) ((...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁶","sexp":"((:c NontriviallyNormedField) (:fv _uniq.27522))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.27528))"},{"name":"inst✝⁴","sexp":"((:c NormedSpace) (:fv _uniq.27522) (:fv _uniq.27528) ((:c Nontriv...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c DFunLike.c...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27522","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.27525","is_instance":true,"is_let":false,"name":"inst✝⁶","sexp":"(:app (:c NontriviallyNormedFiel...
{"children":[{"source":"exact","sourceEnd":5602,"sourceStart":5597,"tag":"atom"},{"children":[{"name":"le_max_right","semanticRole":"global","source":"le_max_right","sourceEnd":5615,"sourceStart":5603,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":5617,"sourceStart":5616,"tag":"atom"}],"kind":"...
[]
[{"source":"le_max_right _ _","source_end":5619,"source_start":5603,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27522","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.27525","is_instance":true,"is_let":false,"user_name":"inst✝⁶"},{"binder_role":":implicit","context_index":2,"inter...
24
8
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d69b720fea1127e32ea2c7e6eb8f138efc2a2ddc5772c3777a408cb2c739246b
262d0e75b99fde01e7ac670eca04211fb699c2b886ea390f6d3f30ffc64cc371
2ad46dfe2c7cb5059c824423c073b75d9d2ef3a5949a4c9015fb275a5dd8fa7e
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,214
HasDerivWithinAt.norm_sq
Mathlib/Analysis/InnerProductSpace/Calculus.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simpa using hf.hasFDerivWithinAt.norm_sq.hasDerivWithinAt
𝕜 : Type u_1 E : Type u_2 F : Type u_3 inst✝⁷ : _root_.RCLike 𝕜 inst✝⁶ : NormedAddCommGroup E inst✝⁵ : InnerProductSpace 𝕜 E inst✝⁴ : NormedAddCommGroup F inst✝³ : InnerProductSpace ℝ F inst✝² : NormedSpace ℝ E G : Type u_4 inst✝¹ : NormedAddCommGroup G inst✝ : NormedSpace ℝ G f✝ g : G → E f'✝ g' : G →L[ℝ] E s✝ : Se...
((:c HasDerivWithinAt) (:c Real) ((:c DenselyNormedField.toNontriviallyNormedField) (:c Real) (:c Real.denselyNormedField)) (:c Real) (:c Real.normedAddCommGroup) ((:c InnerProductSpace.toNormedSpace) (:c Real) (:c Real) (:c Real.RCLike) (:c Real.normedAddCommGroup) ((:c RCLike.innerProductSpace) (:c Real) (:c Real.RCL...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁷","sexp":"((:c RCLike) (:fv _uniq.195497))"},{"name":"inst✝⁶","sexp":"((:c NormedAddCommGroup) (:fv _uniq.195500))"},{"name":"inst✝⁵","sexp":"((:c InnerProductSpace) (:fv _uniq.195497...
(:app (:c HasDerivWithinAt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:c Real))))) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Real))))) (:arg :instance 4 (:instance-of...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.195497","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.195500","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":11613,"sourceStart":11608,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind...
[]
[{"source":"hf.hasFDerivWithinAt.norm_sq.hasDerivWithinAt","source_end":11665,"source_start":11620,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.195497","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.195500","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...
87
2
exact
true
1
24
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f31705e83dd9519f422a01a49f718130c7397994a126a499497e993f73a0dfa5
d98c5b976c6487fc7a16aa5f09c85f0524b190ea2f6cf043645cc81ad4a53e16
ee5b244fdeac66d6e0feb6dbea8fc5755e9b3588a8c0386129a00db28115f90b
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,215
FiniteDimensional.finrank_pi
Mathlib/LinearAlgebra/Dimension/Constructions.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>FiniteDimensional.finrank</a>]
R S : Type u M : Type v M' : Type v' M₁ : Type v ι✝ : Type w ι' : Type w' η : Type u₁' φ : η → Type u_1 inst✝¹³ : Ring R inst✝¹² : CommRing S inst✝¹¹ : AddCommGroup M inst✝¹⁰ : AddCommGroup M' inst✝⁹ : AddCommGroup M₁ inst✝⁸ : Module R M inst✝⁷ : Module R M' inst✝⁶ : Module R M₁ inst✝⁵ : StrongRankCondition R inst✝⁴ : ...
((:c Eq) (:c Nat) ((:c FiniteDimensional.finrank) (:fv _uniq.418266) (:forall _ (:fv _uniq.422173) (:fv _uniq.418266)) ((:c Ring.toSemiring) (:fv _uniq.418266) (:fv _uniq.418288)) ((:c Pi.addCommGroup) (:fv _uniq.422173) (:lambda _ (:fv _uniq.422173) (:fv _uniq.418266)) (:lambda i (:fv _uniq.422173) ((:c Ring.toAddComm...
[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ u 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"M'","sexp":"(:sort (+ v' 1))"},{"name":"M₁","sexp":"(:sort (+ v 1))"},{"name":"ι✝","sexp":"(:sort (+ w 1))"},{"name":"ι'","sexp":"(:sort (+ w' 1))"},{"name":"η","sexp":"(:sort (+ u₁' 1))"},{"name"...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c FiniteDimensional.finrank) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:forall _ :explicit (:fv FV23) (:fv FV0))) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c A...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.418266","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.418268","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":11979,"sourceStart":11975,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...
[]
[{"source":"finrank","source_end":11988,"source_start":11981,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.418266","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.418268","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
75
2
exact
true
1
24
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
792f6b6758f8b140c2927c9b879dba4fdf942bcb16847e385d78c03ce2caf624
7c6fc06b7a2b3159454cf1b67cf4887fcda5c0aa8ceeef9a0ad1bbd54ee891a1
88d159e2e1ef0941c18d15d03239651b0ac9e3e2bcaf0ebe386bacd2e50e64b8
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,216
isOpenMap_eval
Mathlib/Topology/Bases.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine (<a>isTopologicalBasis_pi</a> fun _ ↦ <a>TopologicalSpace.isTopologicalBasis_opens</a>).<a>TopologicalSpace.IsTopologicalBasis.isOpenMap_iff</a>.2 ?_
ι : Type u_1 π : ι → Type u_2 inst✝ : (i : ι) → TopologicalSpace (π i) i : ι ⊢ IsOpenMap (eval i)
ι : Type u_1 π : ι → Type u_2 inst✝ : (i : ι) → TopologicalSpace (π i) i : ι ⊢ ∀ s ∈ {S | ∃ U F, (∀ i ∈ F, U i ∈ {U | IsOpen U}) ∧ S = (↑F).pi U}, IsOpen (eval i '' s)
((:c IsOpenMap) (:forall x (:fv _uniq.98466) ((:fv _uniq.98471) 0)) ((:fv _uniq.98471) (:fv _uniq.98585)) ((:c Pi.topologicalSpace) (:fv _uniq.98466) (:fv _uniq.98471) (:fv _uniq.98479)) ((:fv _uniq.98479) (:fv _uniq.98585)) ((:c Function.eval) (:fv _uniq.98466) (:fv _uniq.98471) (:fv _uniq.98585)))
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.98466) (:sort (+ u_2 1)))"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.98466) ((:c TopologicalSpace) ((:fv _uniq.98471) 0)))"},{"name":"i","sexp":"(:fv _uniq.98466)"}]
(:app (:c IsOpenMap) (:arg :implicit-type 0 (:forall x :explicit (:fv FV0) (:app (:fv FV1) (:arg :explicit 0 0)))) (:arg :implicit-type 1 (:app (:fv FV1) (:arg :explicit 0 (:fv FV4)))) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:forall i :explicit (:fv FV0) (:app (:fv FV1) (:arg :exp...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98466","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98471","is_instance":false,"is_let":false,"name":"π","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"}...
{"children":[{"source":"refine","sourceEnd":34752,"sourceStart":34746,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"(","sourceEnd":34754,"sourceStart":34753,"tag":"atom"},{"children":[{"name":"isTopologicalBasis_pi","semanticRole":"global","source":"isTopologicalBasis_pi","sourceEnd":3477...
[]
[{"source":"(isTopologicalBasis_pi fun _ ↦ isTopologicalBasis_opens).isOpenMap_iff.2 ?_","source_end":34830,"source_start":34753,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98466","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98471","is_instance":false,"is_let":false,"user_name":"π"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
136
7
exact
true
1
4
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8b7e9bd11598b1f79680cee7f9310167cb260ee5e713ed6d46e119a12e8a7245
2b308631270c7980f49846ca6264e8ab149cc9eb4a4789e3727e7c12fa00ef15
7929f422de2ed6fdfe5a63b38c0ef9a1edd1a158332ce8959200bc41483edb92
17fa6511686e7bd4c731c707f7ec8cf4c75430fa47faf3bc100016d6bc83f019
cat-searcher/leandojo-benchmark-4-random
test
3,217
isOpenMap_eval
Mathlib/Topology/Bases.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro _ ⟨U, s, hU, rfl⟩
ι : Type u_1 π : ι → Type u_2 inst✝ : (i : ι) → TopologicalSpace (π i) i : ι ⊢ ∀ s ∈ {S | ∃ U F, (∀ i ∈ F, U i ∈ {U | IsOpen U}) ∧ S = (↑F).pi U}, IsOpen (eval i '' s)
case intro.intro.intro ι : Type u_1 π : ι → Type u_2 inst✝ : (i : ι) → TopologicalSpace (π i) i : ι U : (i : ι) → Set (π i) s : Finset ι hU : ∀ i ∈ s, U i ∈ {U | IsOpen U} ⊢ IsOpen (eval i '' (↑s).pi U)
(:forall s ((:c Set) (:forall i (:fv _uniq.98466) ((:fv _uniq.98471) 0))) (:forall _ ((:c Membership.mem) ((:c Set) (:forall i (:fv _uniq.98466) ((:fv _uniq.98471) 0))) ((:c Set) ((:c Set) (:forall i (:fv _uniq.98466) ((:fv _uniq.98471) 0)))) ((:c Set.instMembership) ((:c Set) (:forall i (:fv _uniq.98466) ((:fv _uniq.9...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.98466) (:sort (+ u_2 1)))"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.98466) ((:c TopologicalSpace) ((:fv _uniq.98471) 0)))"},{"name":"i","sexp":"(:fv _uniq.98466)"}]
(:forall s :explicit (:app (:c Set) (:arg :explicit 0 (:forall i :explicit (:fv FV0) (:app (:fv FV1) (:arg :explicit 0 0))))) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:forall i :explicit (:fv FV0) (:app (:fv FV1) (:arg :explicit 0 0)))))) (:arg :implicit-ty...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98466","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98471","is_instance":false,"is_let":false,"name":"π","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"}...
{"children":[{"source":"rintro","sourceEnd":34839,"sourceStart":34833,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"_","sourceEnd":34841,"sourceStart":34840,"tag":"atom"}],"kind":"Lean.Parser.Tactic.rcasesPat.ignore","source":"_","sourceEnd":34841,"sourceStart":34840,"tag":"node"}],"kind":"Lean.Parser...
[{"role":"fresh_name","source":"U","source_end":34846,"source_start":34845,"syntax_kind":"ident"},{"role":"fresh_name","source":"s","source_end":34849,"source_start":34848,"syntax_kind":"ident"},{"role":"fresh_name","source":"hU","source_end":34853,"source_start":34851,"syntax_kind":"ident"}]
[{"source":"⟨U, s, hU, rfl⟩","source_end":34861,"source_start":34842,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98466","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98471","is_instance":false,"is_let":false,"user_name":"π"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
136
8
exact
true
1
4
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
26681b78e84f6c6ca74e6df59600e0673e5ba02b63497007539d8771a862f560
17fa6511686e7bd4c731c707f7ec8cf4c75430fa47faf3bc100016d6bc83f019
76e9b459684f490e00c42c8e45b49efc937404e492dd81d362d367768ef1e83a
d304cf2b3fe5bbb385c6828e261e6b05f5accdb23c88040da98a63854acb6428
cat-searcher/leandojo-benchmark-4-random
test
3,218
isOpenMap_eval
Mathlib/Topology/Bases.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain h | h := ((s : <a>Set</a> ι).<a>Set.pi</a> U).<a>Set.eq_empty_or_nonempty</a>
case intro.intro.intro ι : Type u_1 π : ι → Type u_2 inst✝ : (i : ι) → TopologicalSpace (π i) i : ι U : (i : ι) → Set (π i) s : Finset ι hU : ∀ i ∈ s, U i ∈ {U | IsOpen U} ⊢ IsOpen (eval i '' (↑s).pi U)
case intro.intro.intro.inl ι : Type u_1 π : ι → Type u_2 inst✝ : (i : ι) → TopologicalSpace (π i) i : ι U : (i : ι) → Set (π i) s : Finset ι hU : ∀ i ∈ s, U i ∈ {U | IsOpen U} h : (↑s).pi U = ∅ ⊢ IsOpen (eval i '' (↑s).pi U) case intro.intro.intro.inr ι : Type u_1 π : ι → Type u_2 inst✝ : (i : ι) → TopologicalSpace (π ...
((:c IsOpen) ((:fv _uniq.98471) (:fv _uniq.98585)) ((:fv _uniq.98479) (:fv _uniq.98585)) ((:c Set.image) (:forall i (:fv _uniq.98466) ((:fv _uniq.98471) 0)) ((:fv _uniq.98471) (:fv _uniq.98585)) ((:c Function.eval) (:fv _uniq.98466) (:fv _uniq.98471) (:fv _uniq.98585)) ((:c Set.pi) (:fv _uniq.98466) (:fv _uniq.98471) (...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.98466) (:sort (+ u_2 1)))"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.98466) ((:c TopologicalSpace) ((:fv _uniq.98471) 0)))"},{"name":"i","sexp":"(:fv _uniq.98466)"},{"name":"U","sexp":"(:forall i (:fv _uniq.98466) ((:c Set) ((:fv _u...
(:app (:c IsOpen) (:arg :implicit-type 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV4)))) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV4))))))) (:arg :explicit 2 (:app (:c Set.image) (:arg :implicit-type 0 (:forall i :explicit (:fv FV0) (:app (:fv ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98466","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98471","is_instance":false,"is_let":false,"name":"π","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"}...
{"children":[{"source":"obtain","sourceEnd":34870,"sourceStart":34864,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":34872,"sourceStart":34871,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"h","sourceEnd":34872,"sourceS...
[]
[{"source":"((s : Set ι).pi U).eq_empty_or_nonempty","source_end":34920,"source_start":34880,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"h | h","source_end":34876,"source_start":34871,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98466","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98471","is_instance":false,"is_let":false,"user_name":"π"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
136
9
exact
true
1
7
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
401bec5d4a96a6a844e8fa7241d7a7df2fd219e39521dfc6c1af99f37eba7d92
d304cf2b3fe5bbb385c6828e261e6b05f5accdb23c88040da98a63854acb6428
96e49780a6fa1cc3f27b2279d9d492f04bc6cc1dd9b79c2eda2cabbd28866164
3be7f9c1df5fa237ea66c5bf795948dc1be11abde41e5404b5d4fe4eae35518a
cat-searcher/leandojo-benchmark-4-random
test
3,219
isOpenMap_eval
Mathlib/Topology/Bases.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
by_cases hi : i ∈ s
case intro.intro.intro.inr ι : Type u_1 π : ι → Type u_2 inst✝ : (i : ι) → TopologicalSpace (π i) i : ι U : (i : ι) → Set (π i) s : Finset ι hU : ∀ i ∈ s, U i ∈ {U | IsOpen U} h : ((↑s).pi U).Nonempty ⊢ IsOpen (eval i '' (↑s).pi U)
case pos ι : Type u_1 π : ι → Type u_2 inst✝ : (i : ι) → TopologicalSpace (π i) i : ι U : (i : ι) → Set (π i) s : Finset ι hU : ∀ i ∈ s, U i ∈ {U | IsOpen U} h : ((↑s).pi U).Nonempty hi : i ∈ s ⊢ IsOpen (eval i '' (↑s).pi U) case neg ι : Type u_1 π : ι → Type u_2 inst✝ : (i : ι) → TopologicalSpace (π i) i : ι U : (i : ...
((:c IsOpen) ((:fv _uniq.98471) (:fv _uniq.98585)) ((:fv _uniq.98479) (:fv _uniq.98585)) ((:c Set.image) (:forall i (:fv _uniq.98466) ((:fv _uniq.98471) 0)) ((:fv _uniq.98471) (:fv _uniq.98585)) ((:c Function.eval) (:fv _uniq.98466) (:fv _uniq.98471) (:fv _uniq.98585)) ((:c Set.pi) (:fv _uniq.98466) (:fv _uniq.98471) (...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.98466) (:sort (+ u_2 1)))"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.98466) ((:c TopologicalSpace) ((:fv _uniq.98471) 0)))"},{"name":"i","sexp":"(:fv _uniq.98466)"},{"name":"U","sexp":"(:forall i (:fv _uniq.98466) ((:c Set) ((:fv _u...
(:app (:c IsOpen) (:arg :implicit-type 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV4)))) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV4))))))) (:arg :explicit 2 (:app (:c Set.image) (:arg :implicit-type 0 (:forall i :explicit (:fv FV0) (:app (:fv ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98466","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98471","is_instance":false,"is_let":false,"name":"π","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"}...
{"children":[{"source":"by_cases","sourceEnd":34945,"sourceStart":34937,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hi","sourceEnd":34948,"sourceStart":34946,"tag":"identifier"},{"source":":","sourceEnd":34950,"sourceStart":34949,"tag":"atom"}],"kind":"null","source":"hi :","sourceEnd":34950,"so...
[]
[{"source":"i ∈ s","source_end":34958,"source_start":34951,"syntax_kind":"«term_∈_»"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98466","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98471","is_instance":false,"is_let":false,"user_name":"π"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
136
15
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9d4893f16bce38ef9493d5a46649aaaf1897f64e2a6874b3a43e9a157f697b78
51ec1010e995ab01cdef2f74da9cd51d4e1d0b688ba89ea9c0e3630887d1e002
b43b2fc3a66e17af24e49f7221f17d6a0f24410b8dc210d7d8952c968bb5e4ae
7187ae383f2cf5e5c406124c61aa13ce1a4be10f8c1770ca26972529881a9cfd
cat-searcher/leandojo-benchmark-4-random
test
3,220
isOpenMap_eval
Mathlib/Topology/Bases.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [h]
case intro.intro.intro.inl ι : Type u_1 π : ι → Type u_2 inst✝ : (i : ι) → TopologicalSpace (π i) i : ι U : (i : ι) → Set (π i) s : Finset ι hU : ∀ i ∈ s, U i ∈ {U | IsOpen U} h : (↑s).pi U = ∅ ⊢ IsOpen (eval i '' (↑s).pi U)
((:c IsOpen) ((:fv _uniq.98471) (:fv _uniq.98585)) ((:fv _uniq.98479) (:fv _uniq.98585)) ((:c Set.image) (:forall i (:fv _uniq.98466) ((:fv _uniq.98471) 0)) ((:fv _uniq.98471) (:fv _uniq.98585)) ((:c Function.eval) (:fv _uniq.98466) (:fv _uniq.98471) (:fv _uniq.98585)) ((:c Set.pi) (:fv _uniq.98466) (:fv _uniq.98471) (...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.98466) (:sort (+ u_2 1)))"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.98466) ((:c TopologicalSpace) ((:fv _uniq.98471) 0)))"},{"name":"i","sexp":"(:fv _uniq.98466)"},{"name":"U","sexp":"(:forall i (:fv _uniq.98466) ((:c Set) ((:fv _u...
(:app (:c IsOpen) (:arg :implicit-type 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV4)))) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV4))))))) (:arg :explicit 2 (:app (:c Set.image) (:arg :implicit-type 0 (:forall i :explicit (:fv FV0) (:app (:fv ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98466","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98471","is_instance":false,"is_let":false,"name":"π","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"}...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":34930,"sourceStart":34926,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...
[]
[{"source":"h","source_end":34933,"source_start":34932,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98466","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98471","is_instance":false,"is_let":false,"user_name":"π"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
136
12
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c94c9ef03e85aaec5b97f254271fa473326e120ecb26515bcbe24cfcc3e86999
af6814256d9a0f138c876c18d0c3b519cff58ab1c9d4b205b4d0e2fff079f98a
80b5426f4cd8afb2daab5c530b5abbdb5bd333c6b56653091017c22104b3e089
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,221
isOpenMap_eval
Mathlib/Topology/Bases.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Set.eval_image_pi</a> (mod_cast hi) h]
case pos ι : Type u_1 π : ι → Type u_2 inst✝ : (i : ι) → TopologicalSpace (π i) i : ι U : (i : ι) → Set (π i) s : Finset ι hU : ∀ i ∈ s, U i ∈ {U | IsOpen U} h : ((↑s).pi U).Nonempty hi : i ∈ s ⊢ IsOpen (eval i '' (↑s).pi U)
case pos ι : Type u_1 π : ι → Type u_2 inst✝ : (i : ι) → TopologicalSpace (π i) i : ι U : (i : ι) → Set (π i) s : Finset ι hU : ∀ i ∈ s, U i ∈ {U | IsOpen U} h : ((↑s).pi U).Nonempty hi : i ∈ s ⊢ IsOpen (U i)
((:c IsOpen) ((:fv _uniq.98471) (:fv _uniq.98585)) ((:fv _uniq.98479) (:fv _uniq.98585)) ((:c Set.image) (:forall i (:fv _uniq.98466) ((:fv _uniq.98471) 0)) ((:fv _uniq.98471) (:fv _uniq.98585)) ((:c Function.eval) (:fv _uniq.98466) (:fv _uniq.98471) (:fv _uniq.98585)) ((:c Set.pi) (:fv _uniq.98466) (:fv _uniq.98471) (...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.98466) (:sort (+ u_2 1)))"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.98466) ((:c TopologicalSpace) ((:fv _uniq.98471) 0)))"},{"name":"i","sexp":"(:fv _uniq.98466)"},{"name":"U","sexp":"(:forall i (:fv _uniq.98466) ((:c Set) ((:fv _u...
(:app (:c IsOpen) (:arg :implicit-type 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV4)))) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV4))))))) (:arg :explicit 2 (:app (:c Set.image) (:arg :implicit-type 0 (:forall i :explicit (:fv FV0) (:app (:fv ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98466","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98471","is_instance":false,"is_let":false,"name":"π","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"}...
{"children":[{"source":"rw","sourceEnd":34966,"sourceStart":34964,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":34968,"sourceStart":34967,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Set...
[]
[{"source":"eval_image_pi (mod_cast hi) h","source_end":34997,"source_start":34968,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98466","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98471","is_instance":false,"is_let":false,"user_name":"π"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
136
20
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4f55eafe0e8b0ce73e27dee40d94509a9e596170e10b630e1725583e349b9a67
aa24436b2229e7afe74641d96d9228ff1306325631f79ca09382cfc3dba85dbe
60dc2c794c7587f4067de01561bfb959c0258c77a68e52f8d3547924cf623f44
dc5fb4292730e509d220a2bc72d7939240549f8625d9c031a31e762f96750eea
cat-searcher/leandojo-benchmark-4-random
test
3,222
isOpenMap_eval
Mathlib/Topology/Bases.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact hU _ hi
case pos ι : Type u_1 π : ι → Type u_2 inst✝ : (i : ι) → TopologicalSpace (π i) i : ι U : (i : ι) → Set (π i) s : Finset ι hU : ∀ i ∈ s, U i ∈ {U | IsOpen U} h : ((↑s).pi U).Nonempty hi : i ∈ s ⊢ IsOpen (U i)
((:c IsOpen) ((:fv _uniq.98471) (:fv _uniq.98585)) ((:fv _uniq.98479) (:fv _uniq.98585)) ((:fv _uniq.98954) (:fv _uniq.98585)))
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.98466) (:sort (+ u_2 1)))"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.98466) ((:c TopologicalSpace) ((:fv _uniq.98471) 0)))"},{"name":"i","sexp":"(:fv _uniq.98466)"},{"name":"U","sexp":"(:forall i (:fv _uniq.98466) ((:c Set) ((:fv _u...
(:app (:c IsOpen) (:arg :implicit-type 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV4)))) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV4))))))) (:arg :explicit 2 (:app (:fv FV5) (:arg :explicit 0 (:fv FV4)))))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98466","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98471","is_instance":false,"is_let":false,"name":"π","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"}...
{"children":[{"source":"exact","sourceEnd":35008,"sourceStart":35003,"tag":"atom"},{"children":[{"contextIndex":7,"semanticRole":"local","source":"hU","sourceEnd":35011,"sourceStart":35009,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":35013,"sourceStart":35012,"tag":"atom"}],"kind":"Lean.Parse...
[]
[{"source":"hU _ hi","source_end":35016,"source_start":35009,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98466","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98471","is_instance":false,"is_let":false,"user_name":"π"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
136
23
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d508078e7aaee5eb237ac0d4ba4d1ea44661099f061b69bb23ce288918ea43e1
dc5fb4292730e509d220a2bc72d7939240549f8625d9c031a31e762f96750eea
34c7dd21444292b2b2b298e24beb331e74a530acd722f082f1766fd4694df582
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,223
isOpenMap_eval
Mathlib/Topology/Bases.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Set.eval_image_pi_of_not_mem</a> (mod_cast hi), <a>if_pos</a> h]
case neg ι : Type u_1 π : ι → Type u_2 inst✝ : (i : ι) → TopologicalSpace (π i) i : ι U : (i : ι) → Set (π i) s : Finset ι hU : ∀ i ∈ s, U i ∈ {U | IsOpen U} h : ((↑s).pi U).Nonempty hi : i ∉ s ⊢ IsOpen (eval i '' (↑s).pi U)
case neg ι : Type u_1 π : ι → Type u_2 inst✝ : (i : ι) → TopologicalSpace (π i) i : ι U : (i : ι) → Set (π i) s : Finset ι hU : ∀ i ∈ s, U i ∈ {U | IsOpen U} h : ((↑s).pi U).Nonempty hi : i ∉ s ⊢ IsOpen univ
((:c IsOpen) ((:fv _uniq.98471) (:fv _uniq.98585)) ((:fv _uniq.98479) (:fv _uniq.98585)) ((:c Set.image) (:forall i (:fv _uniq.98466) ((:fv _uniq.98471) 0)) ((:fv _uniq.98471) (:fv _uniq.98585)) ((:c Function.eval) (:fv _uniq.98466) (:fv _uniq.98471) (:fv _uniq.98585)) ((:c Set.pi) (:fv _uniq.98466) (:fv _uniq.98471) (...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.98466) (:sort (+ u_2 1)))"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.98466) ((:c TopologicalSpace) ((:fv _uniq.98471) 0)))"},{"name":"i","sexp":"(:fv _uniq.98466)"},{"name":"U","sexp":"(:forall i (:fv _uniq.98466) ((:c Set) ((:fv _u...
(:app (:c IsOpen) (:arg :implicit-type 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV4)))) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV4))))))) (:arg :explicit 2 (:app (:c Set.image) (:arg :implicit-type 0 (:forall i :explicit (:fv FV0) (:app (:fv ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98466","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98471","is_instance":false,"is_let":false,"name":"π","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"}...
{"children":[{"source":"rw","sourceEnd":35024,"sourceStart":35022,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":35026,"sourceStart":35025,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Set...
[]
[{"source":"eval_image_pi_of_not_mem (mod_cast hi)","source_end":35064,"source_start":35026,"syntax_kind":"Lean.Parser.Term.app"},{"source":"if_pos h","source_end":35074,"source_start":35066,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98466","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98471","is_instance":false,"is_let":false,"user_name":"π"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
136
28
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
93d382d81b8a4c311e6b035d8b79795379e8c212e50903ac0d1827ccf2f7272c
258b48828d96903fe5b312ddf2fc10f0d922d5d7bfd8b3cec42b7a13f9946bee
c1c4f64d59a8725c6cb85fdde20079919c66498f9cd8118f82a4461183835153
7813d894793a6f2a962ad53b836a67e6f482268bf316d792cf5298123f96e8c5
cat-searcher/leandojo-benchmark-4-random
test
3,224
isOpenMap_eval
Mathlib/Topology/Bases.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>isOpen_univ</a>
case neg ι : Type u_1 π : ι → Type u_2 inst✝ : (i : ι) → TopologicalSpace (π i) i : ι U : (i : ι) → Set (π i) s : Finset ι hU : ∀ i ∈ s, U i ∈ {U | IsOpen U} h : ((↑s).pi U).Nonempty hi : i ∉ s ⊢ IsOpen univ
((:c IsOpen) ((:fv _uniq.98471) (:fv _uniq.98585)) ((:fv _uniq.98479) (:fv _uniq.98585)) ((:c Set.univ) ((:fv _uniq.98471) (:fv _uniq.98585))))
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.98466) (:sort (+ u_2 1)))"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.98466) ((:c TopologicalSpace) ((:fv _uniq.98471) 0)))"},{"name":"i","sexp":"(:fv _uniq.98466)"},{"name":"U","sexp":"(:forall i (:fv _uniq.98466) ((:c Set) ((:fv _u...
(:app (:c IsOpen) (:arg :implicit-type 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV4)))) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV4))))))) (:arg :explicit 2 (:app (:c Set.univ) (:arg :implicit-type 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV4)...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98466","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98471","is_instance":false,"is_let":false,"name":"π","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"}...
{"children":[{"source":"exact","sourceEnd":35085,"sourceStart":35080,"tag":"atom"},{"name":"isOpen_univ","semanticRole":"global","source":"isOpen_univ","sourceEnd":35097,"sourceStart":35086,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact isOpen_univ","sourceEnd":35097,"sourceStart":35080,"tag":"n...
[]
[{"source":"isOpen_univ","source_end":35097,"source_start":35086,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98466","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98471","is_instance":false,"is_let":false,"user_name":"π"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
136
32
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3a821ce086258d2941f312da13d1a0f3f21b7dbcca519a8a69a79e7d46564e1e
7813d894793a6f2a962ad53b836a67e6f482268bf316d792cf5298123f96e8c5
6ee24aac0f47965f389ffcd8f5495f0e8763f03a7ec96d096ddc1a471f493d4e
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,225
tsum_sq_fourierCoeff
Mathlib/Analysis/Fourier/AddCircle.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp_rw [← <a>fourierBasis_repr</a>]
T : ℝ hT : Fact (0 < T) f : ↥(Lp ℂ 2 haarAddCircle) ⊢ ∑' (i : ℤ), ‖fourierCoeff (↑↑f) i‖ ^ 2 = ∫ (t : AddCircle T), ‖↑↑f t‖ ^ 2 ∂haarAddCircle
T : ℝ hT : Fact (0 < T) f : ↥(Lp ℂ 2 haarAddCircle) ⊢ ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 = ∫ (t : AddCircle T), ‖↑↑f t‖ ^ 2 ∂haarAddCircle
((:c Eq) (:c Real) ((:c tsum) (:c Real) (:c Real.instAddCommMonoid) ((:c UniformSpace.toTopologicalSpace) (:c Real) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.pseudoMetricSpace))) (:c Int) (:lambda i (:c Int) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNat...
[{"name":"T","sexp":"(:c Real)"},{"name":"hT","sexp":"((:c Fact) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.152383)))"},{"name":"f","sexp":"((:c Subtype) ((:c MeasureTheory.AEEqFun) ((:c AddCircle) (:c Real) (:c Real.instLine...
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c tsum) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Real))))) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Real))))) (:arg :implicit-type 3 ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"name":"T","sexp":"(:c Real)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"name":"hT","sexp":"(:app (:c Fact) (:arg :explicit 0 (:ap...
{"children":[{"source":"simp_rw","sourceEnd":20513,"sourceStart":20506,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":20515,"sourceStart":20514,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":20518,"sou...
[]
[{"source":"fourierBasis_repr","source_end":20536,"source_start":20519,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"user_name":"T"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"user_name":"hT"},{"binder_role":":explicit","context_index":3,"internal...
97
4
exact
true
1
3
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
98a4b14a4f589cb8fce50ab08b484b723f5af6b58d17decb71e46384d399ccc1
78d6d0d66fff0afab97001097b6fc0ee744fdf833de86cdc887654e87c4755ca
757a2948ec1187025c921cd9439eb621325a1ed91e61bac377a22310ede5b8f5
809b4a2b2f080daebf41acccbfe64ca1226ade99c6255337bb045d5557268a1e
cat-searcher/leandojo-benchmark-4-random
test
3,226
tsum_sq_fourierCoeff
Mathlib/Analysis/Fourier/AddCircle.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have H₁ : ‖fourierBasis.repr f‖ ^ 2 = ∑' i, ‖fourierBasis.repr f i‖ ^ 2 := by apply_mod_cast <a>lp.norm_rpow_eq_tsum</a> ?_ (fourierBasis.repr f) norm_num
T : ℝ hT : Fact (0 < T) f : ↥(Lp ℂ 2 haarAddCircle) ⊢ ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 = ∫ (t : AddCircle T), ‖↑↑f t‖ ^ 2 ∂haarAddCircle
T : ℝ hT : Fact (0 < T) f : ↥(Lp ℂ 2 haarAddCircle) H₁ : ‖fourierBasis.repr f‖ ^ 2 = ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 ⊢ ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 = ∫ (t : AddCircle T), ‖↑↑f t‖ ^ 2 ∂haarAddCircle
((:c Eq) (:c Real) ((:c tsum) (:c Real) (:c Real.instAddCommMonoid) ((:c UniformSpace.toTopologicalSpace) (:c Real) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.pseudoMetricSpace))) (:c Int) (:lambda i (:c Int) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNat...
[{"name":"T","sexp":"(:c Real)"},{"name":"hT","sexp":"((:c Fact) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.152383)))"},{"name":"f","sexp":"((:c Subtype) ((:c MeasureTheory.AEEqFun) ((:c AddCircle) (:c Real) (:c Real.instLine...
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c tsum) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Real))))) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Real))))) (:arg :implicit-type 3 ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"name":"T","sexp":"(:c Real)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"name":"hT","sexp":"(:app (:c Fact) (:arg :explicit 0 (:ap...
{"children":[{"source":"have","sourceEnd":20544,"sourceStart":20540,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"H₁","sourceEnd":20549,"sourceStart":20545,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"H₁","sourceEnd":20549,"sourceStart":20545,"tag":"nod...
[]
[{"source":"‖fourierBasis.repr f‖ ^ 2 = ∑' i, ‖fourierBasis.repr f i‖ ^ 2","source_end":20623,"source_start":20552,"syntax_kind":"«term_=_»"},{"source":"lp.norm_rpow_eq_tsum ?_ (fourierBasis.repr f)","source_end":20694,"source_start":20649,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"user_name":"T"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"user_name":"hT"},{"binder_role":":explicit","context_index":3,"internal...
97
7
exact
true
1
3
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3fcbc79c273ad537e22d1fa029e9f1e22a93c94c26cd5c7e55f2535fad260291
809b4a2b2f080daebf41acccbfe64ca1226ade99c6255337bb045d5557268a1e
45dbe7fd6962357e9fd60c985d42d383f20e506d292394e254d96fba64f366fe
b76c5c85ec37ac00d97bdf6bbff44da85b54eb3ae233ae92f90c9b2542732f0b
cat-searcher/leandojo-benchmark-4-random
test
3,227
tsum_sq_fourierCoeff
Mathlib/Analysis/Fourier/AddCircle.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have H₂ : ‖fourierBasis.repr f‖ ^ 2 = ‖f‖ ^ 2 := by simp
T : ℝ hT : Fact (0 < T) f : ↥(Lp ℂ 2 haarAddCircle) H₁ : ‖fourierBasis.repr f‖ ^ 2 = ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 ⊢ ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 = ∫ (t : AddCircle T), ‖↑↑f t‖ ^ 2 ∂haarAddCircle
T : ℝ hT : Fact (0 < T) f : ↥(Lp ℂ 2 haarAddCircle) H₁ : ‖fourierBasis.repr f‖ ^ 2 = ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 H₂ : ‖fourierBasis.repr f‖ ^ 2 = ‖f‖ ^ 2 ⊢ ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 = ∫ (t : AddCircle T), ‖↑↑f t‖ ^ 2 ∂haarAddCircle
((:c Eq) (:c Real) ((:c tsum) (:c Real) (:c Real.instAddCommMonoid) ((:c UniformSpace.toTopologicalSpace) (:c Real) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.pseudoMetricSpace))) (:c Int) (:lambda i (:c Int) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNat...
[{"name":"T","sexp":"(:c Real)"},{"name":"hT","sexp":"((:c Fact) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.152383)))"},{"name":"f","sexp":"((:c Subtype) ((:c MeasureTheory.AEEqFun) ((:c AddCircle) (:c Real) (:c Real.instLine...
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c tsum) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Real))))) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Real))))) (:arg :implicit-type 3 ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"name":"T","sexp":"(:c Real)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"name":"hT","sexp":"(:app (:c Fact) (:arg :explicit 0 (:ap...
{"children":[{"source":"have","sourceEnd":20714,"sourceStart":20710,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"H₂","sourceEnd":20719,"sourceStart":20715,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"H₂","sourceEnd":20719,"sourceStart":20715,"tag":"nod...
[]
[{"source":"‖fourierBasis.repr f‖ ^ 2 = ‖f‖ ^ 2","source_end":20765,"source_start":20722,"syntax_kind":"«term_=_»"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"user_name":"T"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"user_name":"hT"},{"binder_role":":explicit","context_index":3,"internal...
97
11
exact
true
1
4
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
795e7023b14cec71ce9eaf4c24226b6ceb7e7364246e21d0ffbd3b8fc935f8fe
b76c5c85ec37ac00d97bdf6bbff44da85b54eb3ae233ae92f90c9b2542732f0b
fa7d480a99673c897f388c4031221f2c2fe39b31b2c846d27b07d695a67621e4
8fcd1129182f143b3b288268f732c6370c9384afd2f5184e0f275b6ae04ba614
cat-searcher/leandojo-benchmark-4-random
test
3,228
tsum_sq_fourierCoeff
Mathlib/Analysis/Fourier/AddCircle.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have H₃ := <a>congr_arg</a> <a>RCLike.re</a> (@<a>MeasureTheory.L2.inner_def</a> (<a>AddCircle</a> T) ℂ ℂ _ _ _ _ _ f f)
T : ℝ hT : Fact (0 < T) f : ↥(Lp ℂ 2 haarAddCircle) H₁ : ‖fourierBasis.repr f‖ ^ 2 = ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 H₂ : ‖fourierBasis.repr f‖ ^ 2 = ‖f‖ ^ 2 ⊢ ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 = ∫ (t : AddCircle T), ‖↑↑f t‖ ^ 2 ∂haarAddCircle
T : ℝ hT : Fact (0 < T) f : ↥(Lp ℂ 2 haarAddCircle) H₁ : ‖fourierBasis.repr f‖ ^ 2 = ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 H₂ : ‖fourierBasis.repr f‖ ^ 2 = ‖f‖ ^ 2 H₃ : RCLike.re ⟪f, f⟫_ℂ = RCLike.re (∫ (a : AddCircle T), ⟪↑↑f a, ↑↑f a⟫_ℂ ∂haarAddCircle) ⊢ ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 = ∫ (t : AddCir...
((:c Eq) (:c Real) ((:c tsum) (:c Real) (:c Real.instAddCommMonoid) ((:c UniformSpace.toTopologicalSpace) (:c Real) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.pseudoMetricSpace))) (:c Int) (:lambda i (:c Int) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNat...
[{"name":"T","sexp":"(:c Real)"},{"name":"hT","sexp":"((:c Fact) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.152383)))"},{"name":"f","sexp":"((:c Subtype) ((:c MeasureTheory.AEEqFun) ((:c AddCircle) (:c Real) (:c Real.instLine...
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c tsum) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Real))))) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Real))))) (:arg :implicit-type 3 ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"name":"T","sexp":"(:c Real)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"name":"hT","sexp":"(:app (:c Fact) (:arg :explicit 0 (:ap...
{"children":[{"source":"have","sourceEnd":20783,"sourceStart":20779,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"H₃","sourceEnd":20788,"sourceStart":20784,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"H₃","sourceEnd":20788,"sourceStart":20784,"tag":"nod...
[]
[{"source":"congr_arg RCLike.re (@L2.inner_def (AddCircle T) ℂ ℂ _ _ _ _ _ f f)","source_end":20863,"source_start":20792,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"user_name":"T"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"user_name":"hT"},{"binder_role":":explicit","context_index":3,"internal...
97
14
exact
true
1
5
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2bd041d9a377e437675a1c0ffd71ebb5e2ef9def5f3b474787b1e60f73b198cf
8fcd1129182f143b3b288268f732c6370c9384afd2f5184e0f275b6ae04ba614
cbe5b4032d8ad784576b0bb97dc3ed77d5ca7baa53ac3b4d847e0c66fa5cb435
26dce92b7658e221e14feb1f9262511b06d6f840c3af773c68e9064d3abddb43
cat-searcher/leandojo-benchmark-4-random
test
3,229
tsum_sq_fourierCoeff
Mathlib/Analysis/Fourier/AddCircle.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>integral_re</a>] at H₃
T : ℝ hT : Fact (0 < T) f : ↥(Lp ℂ 2 haarAddCircle) H₁ : ‖fourierBasis.repr f‖ ^ 2 = ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 H₂ : ‖fourierBasis.repr f‖ ^ 2 = ‖f‖ ^ 2 H₃ : RCLike.re ⟪f, f⟫_ℂ = RCLike.re (∫ (a : AddCircle T), ⟪↑↑f a, ↑↑f a⟫_ℂ ∂haarAddCircle) ⊢ ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 = ∫ (t : AddCir...
T : ℝ hT : Fact (0 < T) f : ↥(Lp ℂ 2 haarAddCircle) H₁ : ‖fourierBasis.repr f‖ ^ 2 = ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 H₂ : ‖fourierBasis.repr f‖ ^ 2 = ‖f‖ ^ 2 H₃ : RCLike.re ⟪f, f⟫_ℂ = ∫ (x : AddCircle T), RCLike.re ⟪↑↑f x, ↑↑f x⟫_ℂ ∂haarAddCircle ⊢ ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 = ∫ (t : AddCircl...
((:c Eq) (:c Real) ((:c tsum) (:c Real) (:c Real.instAddCommMonoid) ((:c UniformSpace.toTopologicalSpace) (:c Real) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.pseudoMetricSpace))) (:c Int) (:lambda i (:c Int) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNat...
[{"name":"T","sexp":"(:c Real)"},{"name":"hT","sexp":"((:c Fact) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.152383)))"},{"name":"f","sexp":"((:c Subtype) ((:c MeasureTheory.AEEqFun) ((:c AddCircle) (:c Real) (:c Real.instLine...
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c tsum) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Real))))) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Real))))) (:arg :implicit-type 3 ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"name":"T","sexp":"(:c Real)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"name":"hT","sexp":"(:app (:c Fact) (:arg :explicit 0 (:ap...
{"children":[{"source":"rw","sourceEnd":20868,"sourceStart":20866,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":20870,"sourceStart":20869,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":20873,"sourceSt...
[]
[{"source":"integral_re","source_end":20885,"source_start":20874,"syntax_kind":"ident"},{"source":"H₃","source_end":20894,"source_start":20890,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"user_name":"T"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"user_name":"hT"},{"binder_role":":explicit","context_index":3,"internal...
97
15
exact
true
1
6
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7d1cf47f80f26ff23e1886e7ff406eea7344ec0d4febe95efe5b2ebd14e16d71
26dce92b7658e221e14feb1f9262511b06d6f840c3af773c68e9064d3abddb43
b5dfb85e8d060bc19e908acabf9fb20c98c952c95aab486147093f7e69dade45
73be7e78adef6c80f2188859785b88d21a249e1c44c6d08aad18b1674dd78b7e
cat-searcher/leandojo-benchmark-4-random
test
3,230
tsum_sq_fourierCoeff
Mathlib/Analysis/Fourier/AddCircle.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply_mod_cast <a>lp.norm_rpow_eq_tsum</a> ?_ (fourierBasis.repr f)
T : ℝ hT : Fact (0 < T) f : ↥(Lp ℂ 2 haarAddCircle) ⊢ ‖fourierBasis.repr f‖ ^ 2 = ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2
T : ℝ hT : Fact (0 < T) f : ↥(Lp ℂ 2 haarAddCircle) ⊢ 0 < ENNReal.toReal 2
((:c Eq) (:c Real) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNatPow) (:c Real) (:c Real.instMonoid))) ((:c Norm.norm) ((:c Subtype) ((:c PreLp) (:c Int) (:lambda _ (:c Int) (:c Complex)) (:lambda i (:c Int) ((:c NonUnitalNormedRing.toNormedAddCommGroup) (:c Complex) ((...
[{"name":"T","sexp":"(:c Real)"},{"name":"hT","sexp":"((:c Fact) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.152383)))"},{"name":"f","sexp":"((:c Subtype) ((:c MeasureTheory.AEEqFun) ((:c AddCircle) (:c Real) (:c Real.instLine...
(: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 Nat)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Real)...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"name":"T","sexp":"(:c Real)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"name":"hT","sexp":"(:app (:c Fact) (:arg :explicit 0 (:ap...
{"children":[{"source":"apply_mod_cast","sourceEnd":20648,"sourceStart":20634,"tag":"atom"},{"children":[{"name":"lp.norm_rpow_eq_tsum","semanticRole":"global","source":"lp.norm_rpow_eq_tsum","sourceEnd":20669,"sourceStart":20649,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":20671,"sourceStart...
[]
[{"source":"lp.norm_rpow_eq_tsum ?_ (fourierBasis.repr f)","source_end":20694,"source_start":20649,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"user_name":"T"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"user_name":"hT"},{"binder_role":":explicit","context_index":3,"internal...
97
9
exact
true
1
3
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
14906f428889131b024dde34cc27ab3b036381906074bb90ecbca0bc59e9158d
7faf18a3707ade7a749ab9c9bcc031513c5561ca24263d41c5c473a11c10c53a
df98af962b3d2d046a60a0c32873a07bfc1547ad1b2ed7eb218535de1541d98e
5c91f44b66b36b3ee92c9ac731e5b515e02afdb5706502d019da816c6ae7e7fb
cat-searcher/leandojo-benchmark-4-random
test
3,231
tsum_sq_fourierCoeff
Mathlib/Analysis/Fourier/AddCircle.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
norm_num
T : ℝ hT : Fact (0 < T) f : ↥(Lp ℂ 2 haarAddCircle) ⊢ 0 < ENNReal.toReal 2
((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c ENNReal.toReal) ((:c OfNat.ofNat) (:c ENNReal) (:lit 2) ((:c instOfNatAtLeastTwo) (:c ENNReal) (:lit 2) ((:c CanonicallyOrderedCommSemiring.toNatCast) (:c ENNReal) (:c ENNReal.instCanonica...
[{"name":"T","sexp":"(:c Real)"},{"name":"hT","sexp":"((:c Fact) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.152383)))"},{"name":"f","sexp":"((:c Subtype) ((:c MeasureTheory.AEEqFun) ((:c AddCircle) (:c Real) (:c Real.instLine...
(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"name":"T","sexp":"(:c Real)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"name":"hT","sexp":"(:app (:c Fact) (:arg :explicit 0 (:ap...
{"children":[{"source":"norm_num","sourceEnd":20707,"sourceStart":20699,"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"}],"kind":"Mathl...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"user_name":"T"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"user_name":"hT"},{"binder_role":":explicit","context_index":3,"internal...
97
10
exact
true
1
3
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4bacc9b21755496d9d617a48417430f7ba5bcd5a98802aa40ac0ab6d0c8442c7
5c91f44b66b36b3ee92c9ac731e5b515e02afdb5706502d019da816c6ae7e7fb
7c64df8336d5a348b5f037e1d91facb19224fdef00e798d5c48c07a184602a59
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,232
tsum_sq_fourierCoeff
Mathlib/Analysis/Fourier/AddCircle.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
T : ℝ hT : Fact (0 < T) f : ↥(Lp ℂ 2 haarAddCircle) H₁ : ‖fourierBasis.repr f‖ ^ 2 = ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 ⊢ ‖fourierBasis.repr f‖ ^ 2 = ‖f‖ ^ 2
((:c Eq) (:c Real) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNatPow) (:c Real) (:c Real.instMonoid))) ((:c Norm.norm) ((:c Subtype) ((:c PreLp) (:c Int) (:lambda _ (:c Int) (:c Complex)) (:lambda i (:c Int) ((:c NonUnitalNormedRing.toNormedAddCommGroup) (:c Complex) ((...
[{"name":"T","sexp":"(:c Real)"},{"name":"hT","sexp":"((:c Fact) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.152383)))"},{"name":"f","sexp":"((:c Subtype) ((:c MeasureTheory.AEEqFun) ((:c AddCircle) (:c Real) (:c Real.instLine...
(: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 Nat)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Real)...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"name":"T","sexp":"(:c Real)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"name":"hT","sexp":"(:app (:c Fact) (:arg :explicit 0 (:ap...
{"children":[{"source":"simp","sourceEnd":20776,"sourceStart":20772,"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.152383","is_instance":false,"is_let":false,"user_name":"T"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"user_name":"hT"},{"binder_role":":explicit","context_index":3,"internal...
97
13
exact
true
1
4
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5595770caa2f9f1196a7c5d7788941c25c585da6b4f6f5ef3e248e0e4836a731
e7b70ac2bdb497add92fdc446d0bc98cef2b8089382b626fa70a0cb8360c601b
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,233
tsum_sq_fourierCoeff
Mathlib/Analysis/Fourier/AddCircle.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [← <a>InnerProductSpace.norm_sq_eq_inner</a>] at H₃
T : ℝ hT : Fact (0 < T) f : ↥(Lp ℂ 2 haarAddCircle) H₁ : ‖fourierBasis.repr f‖ ^ 2 = ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 H₂ : ‖fourierBasis.repr f‖ ^ 2 = ‖f‖ ^ 2 H₃ : RCLike.re ⟪f, f⟫_ℂ = ∫ (x : AddCircle T), RCLike.re ⟪↑↑f x, ↑↑f x⟫_ℂ ∂haarAddCircle ⊢ ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 = ∫ (t : AddCircl...
T : ℝ hT : Fact (0 < T) f : ↥(Lp ℂ 2 haarAddCircle) H₁ : ‖fourierBasis.repr f‖ ^ 2 = ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 H₂ : ‖fourierBasis.repr f‖ ^ 2 = ‖f‖ ^ 2 H₃ : ‖f‖ ^ 2 = ∫ (x : AddCircle T), ‖↑↑f x‖ ^ 2 ∂haarAddCircle ⊢ ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 = ∫ (t : AddCircle T), ‖↑↑f t‖ ^ 2 ∂haarAdd...
((:c Eq) (:c Real) ((:c tsum) (:c Real) (:c Real.instAddCommMonoid) ((:c UniformSpace.toTopologicalSpace) (:c Real) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.pseudoMetricSpace))) (:c Int) (:lambda i (:c Int) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNat...
[{"name":"T","sexp":"(:c Real)"},{"name":"hT","sexp":"((:c Fact) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.152383)))"},{"name":"f","sexp":"((:c Subtype) ((:c MeasureTheory.AEEqFun) ((:c AddCircle) (:c Real) (:c Real.instLine...
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c tsum) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Real))))) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Real))))) (:arg :implicit-type 3 ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"name":"T","sexp":"(:c Real)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"name":"hT","sexp":"(:app (:c Fact) (:arg :explicit 0 (:ap...
{"children":[{"source":"simp","sourceEnd":20904,"sourceStart":20900,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":20909,"sourceStart":20905,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":209...
[]
[{"source":"norm_sq_eq_inner","source_end":20931,"source_start":20915,"syntax_kind":"ident"},{"source":"H₃","source_end":20940,"source_start":20936,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"user_name":"T"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"user_name":"hT"},{"binder_role":":explicit","context_index":3,"internal...
97
22
exact
true
1
6
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9a29953af837c87e6b7e68ff5efb74788fb50d0cf26fe0bc2922eeaae857309c
313de3e484c041fc59420553c8701d7e4fefad0e4bb0b51f5b2ca1db96980cf0
d97f5a8a8201bf65c27632fda915a4095299c0eee762415c8bcb7c6e2fa10218
2f975dee7be1cf8f0c47e978c9cb5b7941176abc22bbff156e568ced5f79d14b
cat-searcher/leandojo-benchmark-4-random
test
3,234
tsum_sq_fourierCoeff
Mathlib/Analysis/Fourier/AddCircle.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← H₁, H₂, H₃]
T : ℝ hT : Fact (0 < T) f : ↥(Lp ℂ 2 haarAddCircle) H₁ : ‖fourierBasis.repr f‖ ^ 2 = ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 H₂ : ‖fourierBasis.repr f‖ ^ 2 = ‖f‖ ^ 2 H₃ : ‖f‖ ^ 2 = ∫ (x : AddCircle T), ‖↑↑f x‖ ^ 2 ∂haarAddCircle ⊢ ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 = ∫ (t : AddCircle T), ‖↑↑f t‖ ^ 2 ∂haarAdd...
((:c Eq) (:c Real) ((:c tsum) (:c Real) (:c Real.instAddCommMonoid) ((:c UniformSpace.toTopologicalSpace) (:c Real) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.pseudoMetricSpace))) (:c Int) (:lambda i (:c Int) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNat...
[{"name":"T","sexp":"(:c Real)"},{"name":"hT","sexp":"((:c Fact) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.152383)))"},{"name":"f","sexp":"((:c Subtype) ((:c MeasureTheory.AEEqFun) ((:c AddCircle) (:c Real) (:c Real.instLine...
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c tsum) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Real))))) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Real))))) (:arg :implicit-type 3 ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"name":"T","sexp":"(:c Real)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"name":"hT","sexp":"(:app (:c Fact) (:arg :explicit 0 (:ap...
{"children":[{"source":"rw","sourceEnd":20947,"sourceStart":20945,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":20949,"sourceStart":20948,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":20952,"sourceSt...
[]
[{"source":"H₁","source_end":20957,"source_start":20953,"syntax_kind":"ident"},{"source":"H₂","source_end":20963,"source_start":20959,"syntax_kind":"ident"},{"source":"H₃","source_end":20969,"source_start":20965,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"user_name":"T"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"user_name":"hT"},{"binder_role":":explicit","context_index":3,"internal...
97
23
exact
true
1
6
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7b2a4bd3430cdc2d7623b82a0a0b3101a8ebb6fe6fd35c56dc65df36439bcb34
2f975dee7be1cf8f0c47e978c9cb5b7941176abc22bbff156e568ced5f79d14b
0b0d2209809d02e368ddcfc6b448e744d356fe2eab5570e361f95642ca8e2b1f
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,235
tsum_sq_fourierCoeff
Mathlib/Analysis/Fourier/AddCircle.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>MeasureTheory.L2.integrable_inner</a> f f
T : ℝ hT : Fact (0 < T) f : ↥(Lp ℂ 2 haarAddCircle) H₁ : ‖fourierBasis.repr f‖ ^ 2 = ∑' (i : ℤ), ‖↑(fourierBasis.repr f) i‖ ^ 2 H₂ : ‖fourierBasis.repr f‖ ^ 2 = ‖f‖ ^ 2 H₃ : RCLike.re ⟪f, f⟫_ℂ = RCLike.re (∫ (a : AddCircle T), ⟪↑↑f a, ↑↑f a⟫_ℂ ∂haarAddCircle) ⊢ Integrable (fun a => ⟪↑↑f a, ↑↑f a⟫_ℂ) haarAddCircle
((:c MeasureTheory.Integrable) (:c Complex) ((:c NonUnitalNormedRing.toNormedAddCommGroup) (:c Complex) ((:c NonUnitalNormedCommRing.toNonUnitalNormedRing) (:c Complex) ((:c NormedCommRing.toNonUnitalNormedCommRing) (:c Complex) ((:c NormedField.toNormedCommRing) (:c Complex) ((:c DenselyNormedField.toNormedField) (:c ...
[{"name":"T","sexp":"(:c Real)"},{"name":"hT","sexp":"((:c Fact) ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.152383)))"},{"name":"f","sexp":"((:c Subtype) ((:c MeasureTheory.AEEqFun) ((:c AddCircle) (:c Real) (:c Real.instLine...
(:app (:c MeasureTheory.Integrable) (:arg :implicit-type 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Complex))))) (:arg :implicit-type 2 (:app (:c AddCircle) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedAddCommGroup) (:a...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"name":"T","sexp":"(:c Real)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"name":"hT","sexp":"(:app (:c Fact) (:arg :explicit 0 (:ap...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":20981,"sourceStart":20976,"tag":"atom"},{"children":[{"name":"MeasureTheory.L2.integrable_inner","semanticRole":"global","source":"L2.integrable_inner","sourceEnd":21001,"sourceStart":20982,"tag":"identifier"},{"children":[{"contextIndex"...
[]
[{"source":"L2.integrable_inner f f","source_end":21005,"source_start":20982,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152383","is_instance":false,"is_let":false,"user_name":"T"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.152438","is_instance":true,"is_let":false,"user_name":"hT"},{"binder_role":":explicit","context_index":3,"internal...
97
30
exact
true
1
6
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2f000fae98d36930551730f46baf4a0f70749a89d864c758c2ded60d3766c92f
6f9694d9a7e2c49b79d8ec08491cde0d6b84f6b3c34afca73b1e5173a565ddc8
e8f734f00c9187d2e373ff7c88112f5f80d7ebf4fd0f10683511e277d770b9c3
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,236
GaussianInt.natCast_natAbs_norm
Mathlib/NumberTheory/Zsqrtd/GaussianInt.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>Int.cast_natCast</a>, <a>GaussianInt.abs_natCast_norm</a>]
α : Type u_1 inst✝ : Ring α x : ℤ[i] ⊢ ↑(norm x).natAbs = ↑(norm x)
((:c Eq) (:fv _uniq.28936) ((:c Nat.cast) (:fv _uniq.28936) ((:c Semiring.toNatCast) (:fv _uniq.28936) ((:c Ring.toSemiring) (:fv _uniq.28936) (:fv _uniq.28937))) ((:c Int.natAbs) ((:c Zsqrtd.norm) ((:c Neg.neg) (:c Int) (:c Int.instNegInt) ((:c OfNat.ofNat) (:c Int) (:lit 1) ((:c instOfNat) (:lit 1)))) (:fv _uniq.2893...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Ring) (:fv _uniq.28936))"},{"name":"x","sexp":"(:c GaussianInt)"}]
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Nat.cast) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Int.natAbs) (:arg :explicit 0 (:app (:c Zsqrtd.norm) (:arg :implicit 0) (:arg :explicit 1...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28936","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.28937","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Ring) (:arg :explicit 0 ...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":6677,"sourceStart":6675,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6679,"sourceStart":6678,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"sour...
[]
[{"source":"Int.cast_natCast","source_end":6699,"source_start":6683,"syntax_kind":"ident"},{"source":"abs_natCast_norm","source_end":6717,"source_start":6701,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28936","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.28937","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":3,"interna...
65
2
exact
true
1
3
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4dd1dc1dd85a049affce47b13ae7f17dfbe4b7bd0fe301bced478187b8ad23d4
7f1c2630ab67ab57fbd383dde4557025140c556412f29cc661d9f37baaf4c470
56b527f3289411e385c06ff1b1453499bbbfbb12b6870fc5502f2bf3fc180261
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,237
Basis.mem_submodule_iff'
Mathlib/LinearAlgebra/Basis.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>Finsupp.sum_fintype</a>, <a>Finsupp.equivFunOnFinite</a>]
ι : Type u_1 ι' : Type u_2 R : Type u_3 R₂ : Type u_4 K : Type u_5 M : Type u_6 M' : Type u_7 M'' : Type u_8 V : Type u V' : Type u_9 inst✝⁸ : Semiring R inst✝⁷ : AddCommMonoid M inst✝⁶ : Module R M inst✝⁵ : AddCommMonoid M' inst✝⁴ : Module R M' S : Type u_10 inst✝³ : Semiring S inst✝² : Module S M' inst✝¹ : SMulCommCl...
((:c Iff) ((:c Eq) (:fv _uniq.394326) (:fv _uniq.397672) ((:c Finsupp.sum) (:fv _uniq.394311) (:fv _uniq.394317) (:fv _uniq.394326) ((:c MonoidWithZero.toZero) (:fv _uniq.394317) ((:c Semiring.toMonoidWithZero) (:fv _uniq.394317) (:fv _uniq.394340))) (:fv _uniq.394343) ((:c DFunLike.coe) ((:c Equiv) (:forall _ (:fv _un...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"ι'","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"R₂","sexp":"(:sort (+ u_4 1))"},{"name":"K","sexp":"(:sort (+ u_5 1))"},{"name":"M","sexp":"(:sort (+ u_6 1))"},{"name":"M'","sexp":"(:sort (+ u_7 1))"},{"name":"M''","sexp":"(:sort (+ u_8 ...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:fv FV23)) (:arg :explicit 2 (:app (:c Finsupp.sum) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c Zero) (:arg :explicit 0 ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.394311","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.394314","is_instance":false,"is_let":false,"name":"ι'","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":39533,"sourceStart":39529,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...
[]
[{"source":"Finsupp.sum_fintype","source_end":39554,"source_start":39535,"syntax_kind":"ident"},{"source":"Finsupp.equivFunOnFinite","source_end":39580,"source_start":39556,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.394311","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.394314","is_instance":false,"is_let":false,"user_name":"ι'"},{"binder_role":":implicit","context_index":2,"internal_name":"...
294
2
exact
true
1
24
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f17f85272d025f124ecf664d587cf216e82c905098eb17eff2b2b6b66871dd7c
1aa70c5193890b27192fc2dc5a13ae1fe372451636846d535deca53c4351e46c
a2ec653513a5df552d0fef829e8c86b77c4804d03a0092bd8ba32b5d0f79eb3d
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,238
variationOnFromTo.monotoneOn
Mathlib/Analysis/BoundedVariation.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro b bs c cs bc
α : Type u_1 inst✝¹ : LinearOrder α E : Type u_2 inst✝ : PseudoEMetricSpace E f : α → E s : Set α hf : LocallyBoundedVariationOn f s a : α as : a ∈ s ⊢ MonotoneOn (variationOnFromTo f s a) s
α : Type u_1 inst✝¹ : LinearOrder α E : Type u_2 inst✝ : PseudoEMetricSpace E f : α → E s : Set α hf : LocallyBoundedVariationOn f s a : α as : a ∈ s b : α bs : b ∈ s c : α cs : c ∈ s bc : b ≤ c ⊢ variationOnFromTo f s a b ≤ variationOnFromTo f s a c
((:c MonotoneOn) (:fv _uniq.327444) (:c Real) ((:c PartialOrder.toPreorder) (:fv _uniq.327444) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.327444) ((:c Lattice.toSemilatticeInf) (:fv _uniq.327444) ((:c DistribLattice.toLattice) (:fv _uniq.327444) ((:c instDistribLatticeOfLinearOrder) (:fv _uniq.327444) (:fv _uniq.32...
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(:app (:c MonotoneOn) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c Real))))) (:arg :explicit 4 (:app (:c variationOnFromTo) (:arg :implicit...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.327444","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.327447","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrder) (:arg :e...
{"children":[{"source":"rintro","sourceEnd":37903,"sourceStart":37897,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"b","sourceEnd":37905,"sourceStart":37904,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"b","sourceEnd":37905,"sourceStart":37904,"...
[{"role":"fresh_name","source":"b","source_end":37905,"source_start":37904,"syntax_kind":"ident"},{"role":"fresh_name","source":"bs","source_end":37908,"source_start":37906,"syntax_kind":"ident"},{"role":"fresh_name","source":"c","source_end":37910,"source_start":37909,"syntax_kind":"ident"},{"role":"fresh_name","sourc...
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.327444","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.327447","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"inte...
108
4
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4199abd6af2c8d5fc80981b3039f6efc345b1b62448f9ec1757ff2e68d553eea
eb6c4be6ea25de1a94eacf53fa5e30ec8767e04e90fcc7022bed7e0b3a2078fb
c07b08aeda3e1d2aaa9e602195f7ceb2fbbb63e540bfe6c82876c091aca437f6
a68fe66815e8a34dc0dd28b38e983fd4c0a188bcc05fdc0855fb9596de181c79
cat-searcher/leandojo-benchmark-4-random
test
3,239
variationOnFromTo.monotoneOn
Mathlib/Analysis/BoundedVariation.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>variationOnFromTo.add</a> hf as bs cs]
α : Type u_1 inst✝¹ : LinearOrder α E : Type u_2 inst✝ : PseudoEMetricSpace E f : α → E s : Set α hf : LocallyBoundedVariationOn f s a : α as : a ∈ s b : α bs : b ∈ s c : α cs : c ∈ s bc : b ≤ c ⊢ variationOnFromTo f s a b ≤ variationOnFromTo f s a c
α : Type u_1 inst✝¹ : LinearOrder α E : Type u_2 inst✝ : PseudoEMetricSpace E f : α → E s : Set α hf : LocallyBoundedVariationOn f s a : α as : a ∈ s b : α bs : b ∈ s c : α cs : c ∈ s bc : b ≤ c ⊢ variationOnFromTo f s a b ≤ variationOnFromTo f s a b + variationOnFromTo f s b c
((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c variationOnFromTo) (:fv _uniq.327444) (:fv _uniq.327447) (:fv _uniq.327450) (:fv _uniq.327453) (:fv _uniq.327457) (:fv _uniq.327460) (:fv _uniq.328540) (:fv _uniq.328543)) ((:c variationOnFromTo) (:fv _uniq.327444) (:fv _uniq.327447) (:fv ...
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(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c variationOnFromTo) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrder) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.327444","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.327447","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrder) (:arg :e...
{"children":[{"source":"rw","sourceEnd":37921,"sourceStart":37919,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":37923,"sourceStart":37922,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":37926,"sourceSt...
[]
[{"source":"variationOnFromTo.add hf as bs cs","source_end":37960,"source_start":37927,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.327444","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.327447","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"inte...
108
5
exact
true
1
14
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
cb49dfef4bb0d3f5af3c95fdf6db507378b2722c9eb9b5877ee77b39d7a3767e
a68fe66815e8a34dc0dd28b38e983fd4c0a188bcc05fdc0855fb9596de181c79
83dbcbb523200a09e3af586bd94d39de90c83449d22d4b1f2cffda1b4f32c5a2
d40366f5c29cca2bceac97b279225d5c854119cac14fd855aa02eb89efaa7984
cat-searcher/leandojo-benchmark-4-random
test
3,240
variationOnFromTo.monotoneOn
Mathlib/Analysis/BoundedVariation.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>le_add_of_nonneg_right</a> (<a>variationOnFromTo.nonneg_of_le</a> f s bc)
α : Type u_1 inst✝¹ : LinearOrder α E : Type u_2 inst✝ : PseudoEMetricSpace E f : α → E s : Set α hf : LocallyBoundedVariationOn f s a : α as : a ∈ s b : α bs : b ∈ s c : α cs : c ∈ s bc : b ≤ c ⊢ variationOnFromTo f s a b ≤ variationOnFromTo f s a b + variationOnFromTo f s b c
((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c variationOnFromTo) (:fv _uniq.327444) (:fv _uniq.327447) (:fv _uniq.327450) (:fv _uniq.327453) (:fv _uniq.327457) (:fv _uniq.327460) (:fv _uniq.328540) (:fv _uniq.328543)) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Re...
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(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c variationOnFromTo) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrder) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.327444","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.327447","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrder) (:arg :e...
{"children":[{"source":"exact","sourceEnd":37969,"sourceStart":37964,"tag":"atom"},{"children":[{"name":"le_add_of_nonneg_right","semanticRole":"global","source":"le_add_of_nonneg_right","sourceEnd":37992,"sourceStart":37970,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":37994,"sourceStart":379...
[]
[{"source":"le_add_of_nonneg_right (variationOnFromTo.nonneg_of_le f s bc)","source_end":38032,"source_start":37970,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.327444","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.327447","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"inte...
108
8
exact
true
1
14
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
faae083c5f2c456553b3a6729376d1a1039e6c54ebb96ed229f723fb17681ffb
d40366f5c29cca2bceac97b279225d5c854119cac14fd855aa02eb89efaa7984
83e25cf99a9dafb98cd5514780e5d0d28550c7bc33df11e4ebdcaead213379d1
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,241
List.length_sigma
Mathlib/Algebra/BigOperators/Group/List.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>List.length_sigma'</a>]
ι : Type u_1 α : Type u_2 β : Type u_3 M : Type u_4 N : Type u_5 P : Type u_6 G : Type u_7 σ : α → Type u_8 l₁ : List α l₂ : (a : α) → List (σ a) ⊢ (l₁.sigma l₂).length = (map (fun a => (l₂ a).length) l₁).sum
((:c Eq) (:c Nat) ((:c List.length) ((:c Sigma) (:fv _uniq.73922) (:lambda a (:fv _uniq.73922) ((:fv _uniq.74077) 0))) ((:c List.sigma) (:fv _uniq.73922) (:fv _uniq.74077) (:fv _uniq.74078) (:fv _uniq.74079))) ((:c List.sum) (:c Nat) (:c instAddNat) ((:c AddRightCancelMonoid.toZero) (:c Nat) ((:c AddCancelMonoid.toAddR...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"N","sexp":"(:sort (+ u_5 1))"},{"name":"P","sexp":"(:sort (+ u_6 1))"},{"name":"G","sexp":"(:sort (+ u_7 1))"},{"name":"σ","sexp":"(:forall _ (:fv _un...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c List.length) (:arg :implicit-type 0 (:app (:c Sigma) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda a :explicit (:fv FV1) (:app (:fv FV8) (:arg :explicit 0 0)))))) (:arg :explicit 1 (:app (:c List.sigma) (:arg :implicit-type 0 (:fv...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73919","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.73922","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":29569,"sourceStart":29565,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...
[]
[{"source":"length_sigma'","source_end":29584,"source_start":29571,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73919","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.73922","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
238
2
exact
true
1
10
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
32c0466acb077e52622a9b210b219549beb1c9989ff7fa22cfd80016c31017b3
033e4dc5465d2e5454549a98d1752ad60f1b2ed013aa1f23b530b2d74018a517
6132398f0b28407341969bfde98db993b780c270bde1aac9d01c0c1993f94cc8
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,242
Polynomial.smeval_comp
Mathlib/Algebra/Polynomial/Smeval.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
induction p using <a>Polynomial.induction_on'</a> with | h_add r s hr hs => simp [<a>Polynomial.add_comp</a>, hr, hs, <a>Polynomial.smeval_add</a>] | h_monomial n a => simp [<a>Polynomial.smeval_monomial</a>, <a>Polynomial.smeval_C_mul</a>, <a>Polynomial.smeval_pow</a>]
R : Type u_1 inst✝⁶ : Semiring R p✝ : R[X] r : R p q : R[X] S : Type u_2 inst✝⁵ : NonAssocSemiring S inst✝⁴ : Module R S inst✝³ : IsScalarTower R S S inst✝² : SMulCommClass R S S inst✝¹ : Pow S ℕ inst✝ : NatPowAssoc S x : S ⊢ (p.comp q).smeval x = p.smeval (q.smeval x)
((:c Eq) (:fv _uniq.134690) ((:c Polynomial.smeval) (:fv _uniq.134660) (:fv _uniq.134663) ((:c Polynomial.comp) (:fv _uniq.134660) (:fv _uniq.134663) (:fv _uniq.134683) (:fv _uniq.134687)) (:fv _uniq.134690) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.134690) ((:c NonAssocSemiring.toNonUnitalNonAssocSemi...
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(:app (:c Eq) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Polynomial.smeval) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Polynomial.comp) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.134660","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.134663","is_instance":true,"is_let":false,"name":"inst✝⁶","sexp":"(:app (:c Semiring) (:arg :expl...
{"children":[{"children":[{"children":[{"children":[{"source":"induction","sourceEnd":10478,"sourceStart":10469,"tag":"atom"},{"children":[{"contextIndex":4,"semanticRole":"local","source":"p","sourceEnd":10480,"sourceStart":10479,"tag":"identifier"}],"kind":"null","source":"p","sourceEnd":10480,"sourceStart":10479,"ta...
[]
[{"source":"p","source_end":10480,"source_start":10479,"syntax_kind":"ident"},{"source":"Polynomial.induction_on'","source_end":10511,"source_start":10487,"syntax_kind":"ident"},{"source":"add_comp","source_end":10558,"source_start":10550,"syntax_kind":"ident"},{"source":"hr","source_end":10562,"source_start":10560,"sy...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.134660","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.134663","is_instance":true,"is_let":false,"user_name":"inst✝⁶"},{"binder_role":":implicit","context_index":2,"inte...
49
2
exact
true
1
14
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
6786cfc2a113f1027f3883fd16d08be761547d6f81b1117efe536c54d3278ef7
cf0b6828a127a4e22e2a5fd4c3a0914968a4a58a96e6823be509b6dbda40d5f6
d9bd219feafa91f2e5a81a1df9ce31c65ab14072a08147030f92c9215834d5a4
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,243
Polynomial.smeval_comp
Mathlib/Algebra/Polynomial/Smeval.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>Polynomial.add_comp</a>, hr, hs, <a>Polynomial.smeval_add</a>]
case h_add R : Type u_1 inst✝⁶ : Semiring R p✝ : R[X] r✝ : R p q : R[X] S : Type u_2 inst✝⁵ : NonAssocSemiring S inst✝⁴ : Module R S inst✝³ : IsScalarTower R S S inst✝² : SMulCommClass R S S inst✝¹ : Pow S ℕ inst✝ : NatPowAssoc S x : S r s : R[X] hr : (r.comp q).smeval x = r.smeval (q.smeval x) hs : (s.comp q).smeval x...
((:c Eq) (:fv _uniq.134690) ((:c Polynomial.smeval) (:fv _uniq.134660) (:fv _uniq.134663) ((:c Polynomial.comp) (:fv _uniq.134660) (:fv _uniq.134663) ((:c HAdd.hAdd) ((:c Polynomial) (:fv _uniq.134660) (:fv _uniq.134663)) ((:c Polynomial) (:fv _uniq.134660) (:fv _uniq.134663)) ((:c Polynomial) (:fv _uniq.134660) (:fv _...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁶","sexp":"((:c Semiring) (:fv _uniq.134660))"},{"name":"p✝","sexp":"((:c Polynomial) (:fv _uniq.134660) (:fv _uniq.134663))"},{"name":"r✝","sexp":"(:fv _uniq.134660)"},{"name":"p","sexp":"((:c Polynomial) (:fv _uniq.134660) (:fv _uniq.134663))"},{"name":"q","sexp"...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Polynomial.smeval) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Polynomial.comp) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.134660","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.134663","is_instance":true,"is_let":false,"name":"inst✝⁶","sexp":"(:app (:c Semiring) (:arg :expl...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":10548,"sourceStart":10544,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...
[]
[{"source":"add_comp","source_end":10558,"source_start":10550,"syntax_kind":"ident"},{"source":"hr","source_end":10562,"source_start":10560,"syntax_kind":"ident"},{"source":"hs","source_end":10566,"source_start":10564,"syntax_kind":"ident"},{"source":"smeval_add","source_end":10578,"source_start":10568,"syntax_kind":"i...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.134660","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.134663","is_instance":true,"is_let":false,"user_name":"inst✝⁶"},{"binder_role":":implicit","context_index":2,"inte...
49
7
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e0d3eed0f6e0e4188f8161ff6bdca3931c3ade46812206318cd61efc7b5c9380
0abbe194d9bbf915af6577916cf4069441c694bfed1a22b59609d1f84e23f4d1
fd765db91366dd0ea855a87c46e45c1490e5d5beb6427ac0d1588a7802f036f9
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,244
Polynomial.smeval_comp
Mathlib/Algebra/Polynomial/Smeval.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>Polynomial.smeval_monomial</a>, <a>Polynomial.smeval_C_mul</a>, <a>Polynomial.smeval_pow</a>]
case h_monomial R : Type u_1 inst✝⁶ : Semiring R p✝ : R[X] r : R p q : R[X] S : Type u_2 inst✝⁵ : NonAssocSemiring S inst✝⁴ : Module R S inst✝³ : IsScalarTower R S S inst✝² : SMulCommClass R S S inst✝¹ : Pow S ℕ inst✝ : NatPowAssoc S x : S n : ℕ a : R ⊢ (((monomial n) a).comp q).smeval x = ((monomial n) a).smeval (q.sm...
((:c Eq) (:fv _uniq.134690) ((:c Polynomial.smeval) (:fv _uniq.134660) (:fv _uniq.134663) ((:c Polynomial.comp) (:fv _uniq.134660) (:fv _uniq.134663) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.134660) (:fv _uniq.134660) (:fv _uniq.134663) (:fv _uniq.134663) ((:c RingHom.id) (:fv _uniq.134660) ((:c Semiring.toNonAsso...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁶","sexp":"((:c Semiring) (:fv _uniq.134660))"},{"name":"p✝","sexp":"((:c Polynomial) (:fv _uniq.134660) (:fv _uniq.134663))"},{"name":"r","sexp":"(:fv _uniq.134660)"},{"name":"p","sexp":"((:c Polynomial) (:fv _uniq.134660) (:fv _uniq.134663))"},{"name":"q","sexp":...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Polynomial.smeval) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Polynomial.comp) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance...
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.134660","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.134663","is_instance":true,"is_let":false,"name":"inst✝⁶","sexp":"(:app (:c Semiring) (:arg :expl...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":10610,"sourceStart":10606,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...
[]
[{"source":"smeval_monomial","source_end":10627,"source_start":10612,"syntax_kind":"ident"},{"source":"smeval_C_mul","source_end":10641,"source_start":10629,"syntax_kind":"ident"},{"source":"smeval_pow","source_end":10653,"source_start":10643,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.134660","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.134663","is_instance":true,"is_let":false,"user_name":"inst✝⁶"},{"binder_role":":implicit","context_index":2,"inte...
49
11
exact
true
1
16
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
de0d53d440ac614556c8611e64d29c735950877d837c43a26031a30e7022f57c
49942071663783cb40268e560dd797da3652a253e4fb811dd58e03c8b2e53cb7
a006f20abaa0843a20c1a78e18605d9444a83536293789c2648a33a84007a13d
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,245
Option.map_bind'
Mathlib/Data/Option/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
cases x <;> simp
α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 p : α → Prop f✝ : (a : α) → p a → β x✝ : Option α f : β → γ x : Option α g : α → Option β ⊢ Option.map f (x.bind g) = x.bind fun a => Option.map f (g a)
((:c Eq) ((:c Option) (:fv _uniq.12826)) ((:c Option.map) (:fv _uniq.12823) (:fv _uniq.12826) (:fv _uniq.12903) ((:c Option.bind) (:fv _uniq.12820) (:fv _uniq.12823) (:fv _uniq.12904) (:fv _uniq.12905))) ((:c Option.bind) (:fv _uniq.12820) (:fv _uniq.12826) (:fv _uniq.12904) (:lambda a (:fv _uniq.12820) ((:c Option.map...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.12820) (:sort 0))"},{"name":"f✝","sexp":"(:forall a (:fv _uniq.12820) (:forall _ ((:fv _uniq.12833) 0) (:fv _uniq.128...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Option) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:app (:c Option.map) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:app (:c Option.bind) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12820","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12823","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"cases","sourceEnd":6598,"sourceStart":6593,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":9,"semanticRole":"local","source":"x","sourceEnd":6600,"sourceStart":6599,"tag":"identifie...
[]
[{"source":"x","source_end":6600,"source_start":6599,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12820","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12823","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
58
2
exact
true
1
10
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8796ff10750b46fc75e70c09d1acbfc1384d37ab996bd898cb2276cccaa5fc27
a006b7638c77f65a974f4727db736c4211c32290fa45bbef82c8e3f8fd10c420
1479d62dc53e5d52a93b30aa5968d9b808b428caac57d1ecc852d7fc235694f5
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,246
SimpleGraph.cliqueFinset_map_of_equiv
Mathlib/Combinatorics/SimpleGraph/Clique.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
push_cast
α : Type u_1 β : Type u_2 G H : SimpleGraph α inst✝⁵ : Fintype α inst✝⁴ : DecidableEq α inst✝³ : DecidableRel G.Adj n✝ : ℕ a b c : α s : Finset α inst✝² : DecidableRel H.Adj inst✝¹ : Fintype β inst✝ : DecidableEq β e : α ≃ β n : ℕ ⊢ ↑((SimpleGraph.map e.toEmbedding G).cliqueFinset n) = ↑(map { toFun := map e.toEmbe...
α : Type u_1 β : Type u_2 G H : SimpleGraph α inst✝⁵ : Fintype α inst✝⁴ : DecidableEq α inst✝³ : DecidableRel G.Adj n✝ : ℕ a b c : α s : Finset α inst✝² : DecidableRel H.Adj inst✝¹ : Fintype β inst✝ : DecidableEq β e : α ≃ β n : ℕ ⊢ (SimpleGraph.map e.toEmbedding G).cliqueSet n = ⇑{ toFun := map e.toEmbedding, inj' := ...
((:c Eq) ((:c Set) ((:c Finset) (:fv _uniq.177028))) ((:c Finset.toSet) ((:c Finset) (:fv _uniq.177028)) ((:c SimpleGraph.cliqueFinset) (:fv _uniq.177028) ((:c SimpleGraph.map) (:fv _uniq.177025) (:fv _uniq.177028) ((:c Equiv.toEmbedding) (:fv _uniq.177025) (:fv _uniq.177028) (:fv _uniq.178105)) (:fv _uniq.177031)) (:f...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.177025))"},{"name":"H","sexp":"((:c SimpleGraph) (:fv _uniq.177025))"},{"name":"inst✝⁵","sexp":"((:c Fintype) (:fv _uniq.177025))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.1770...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV1)))))) (:arg :explicit 1 (:app (:c Finset.toSet) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c SimpleGraph.cliqueFinset) (:arg :implicit-type 0 (:fv FV1...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.177025","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.177028","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":explicit","c...
{"children":[{"source":"push_cast","sourceEnd":27896,"sourceStart":27887,"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.177025","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.177028","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":explicit","context_index":2,"internal_name":"_...
192
4
exact
true
1
17
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b54334cc3284360b026df4054c795d90716693c9599676241d7423549b5faaf8
bf543341066ebf2c3ff7f4f075ed5e228813b23b378484400916352b15fdbb7c
5189104d9b5e7264ce49402b63410b1cd440d29f098c6f68c6d5dbb0f8982ff0
88c41f441497f4940f8cfa21190705485860d510715a3f239345715846cf3308
cat-searcher/leandojo-benchmark-4-random
test
3,247
SimpleGraph.cliqueFinset_map_of_equiv
Mathlib/Combinatorics/SimpleGraph/Clique.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>SimpleGraph.cliqueSet_map_of_equiv</a> _ _ _
α : Type u_1 β : Type u_2 G H : SimpleGraph α inst✝⁵ : Fintype α inst✝⁴ : DecidableEq α inst✝³ : DecidableRel G.Adj n✝ : ℕ a b c : α s : Finset α inst✝² : DecidableRel H.Adj inst✝¹ : Fintype β inst✝ : DecidableEq β e : α ≃ β n : ℕ ⊢ (SimpleGraph.map e.toEmbedding G).cliqueSet n = ⇑{ toFun := map e.toEmbedding, inj' := ...
((:c Eq) ((:c Set) ((:c Finset) (:fv _uniq.177028))) ((:c SimpleGraph.cliqueSet) (:fv _uniq.177028) ((:c SimpleGraph.map) (:fv _uniq.177025) (:fv _uniq.177028) ((:c Equiv.toEmbedding) (:fv _uniq.177025) (:fv _uniq.177028) (:fv _uniq.178105)) (:fv _uniq.177031)) (:fv _uniq.178106)) ((:c Set.image) ((:c Finset) (:fv _uni...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.177025))"},{"name":"H","sexp":"((:c SimpleGraph) (:fv _uniq.177025))"},{"name":"inst✝⁵","sexp":"((:c Fintype) (:fv _uniq.177025))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.1770...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV1)))))) (:arg :explicit 1 (:app (:c SimpleGraph.cliqueSet) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c SimpleGraph.map) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.177025","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.177028","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":explicit","c...
{"children":[{"source":"exact","sourceEnd":27903,"sourceStart":27898,"tag":"atom"},{"children":[{"name":"SimpleGraph.cliqueSet_map_of_equiv","semanticRole":"global","source":"cliqueSet_map_of_equiv","sourceEnd":27926,"sourceStart":27904,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":27928,"sour...
[]
[{"source":"cliqueSet_map_of_equiv _ _ _","source_end":27932,"source_start":27904,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.177025","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.177028","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":explicit","context_index":2,"internal_name":"_...
192
6
exact
true
1
17
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
068122ba14e02f8ea11c3aa2b57d8dd9bcc1ff3733d4f07bf66d9e987132235a
88c41f441497f4940f8cfa21190705485860d510715a3f239345715846cf3308
b7838169849d09fc8bfcf550bddc99bb5fdd22653fa75859b21ca4408d453235
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,248
Submonoid.LocalizationMap.eq_iff_exists
Mathlib/GroupTheory/MonoidLocalization.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
replace h := <a>congr_arg</a> f.toMap h
M : Type u_1 inst✝² : CommMonoid M S : Submonoid M N : Type u_2 inst✝¹ : CommMonoid N P : Type u_3 inst✝ : CommMonoid P f : S.LocalizationMap N x y : M x✝ : ∃ c, ↑c * x = ↑c * y c : ↥S h : ↑c * x = ↑c * y ⊢ f.toMap x = f.toMap y
M : Type u_1 inst✝² : CommMonoid M S : Submonoid M N : Type u_2 inst✝¹ : CommMonoid N P : Type u_3 inst✝ : CommMonoid P f : S.LocalizationMap N x y : M x✝ : ∃ c, ↑c * x = ↑c * y c : ↥S h : f.toMap (↑c * x) = f.toMap (↑c * y) ⊢ f.toMap x = f.toMap y
((:c Eq) (:fv _uniq.124061) ((:c DFunLike.coe) ((:c MonoidHom) (:fv _uniq.123745) (:fv _uniq.124061) ((:c Monoid.toMulOneClass) (:fv _uniq.123745) ((:c CommMonoid.toMonoid) (:fv _uniq.123745) (:fv _uniq.123748))) ((:c Monoid.toMulOneClass) (:fv _uniq.124061) ((:c CommMonoid.toMonoid) (:fv _uniq.124061) (:fv _uniq.12406...
[{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CommMonoid) (:fv _uniq.123745))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.123745) ((:c Monoid.toMulOneClass) (:fv _uniq.123745) ((:c CommMonoid.toMonoid) (:fv _uniq.123745) (:fv _uniq.123748))))"},{"name":"N","sexp":"(:sort (+ u_2 1))"},{"nam...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MonoidHom) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c MulOneClass) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.123745","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.123748","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CommMonoid) (:arg :ex...
{"children":[{"source":"replace","sourceEnd":29297,"sourceStart":29290,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":29299,"sourceStart":29298,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":29299,"sourceStart":29298,"tag":"no...
[]
[{"source":"congr_arg f.toMap h","source_end":29322,"source_start":29303,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.123745","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.123748","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inte...
157
4
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
cacb082ce534f81c75e80555c341926c2a29aee06542f5c53dbf880650834473
7dec0427d78af7bc77ddd3b4c2f5730cf75d8362dd31bc85b0a3939bd6656d0e
daeaef48cfeeb72471b83a63d73d722782a7e254e8e5f1d8a1c8b6157fd28f6d
0b5caeaa59d31bba08217dff8f6130553e40f7d93e7353d60262b72cb74f06c8
cat-searcher/leandojo-benchmark-4-random
test
3,249
Submonoid.LocalizationMap.eq_iff_exists
Mathlib/GroupTheory/MonoidLocalization.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>map_mul</a>, <a>map_mul</a>] at h
M : Type u_1 inst✝² : CommMonoid M S : Submonoid M N : Type u_2 inst✝¹ : CommMonoid N P : Type u_3 inst✝ : CommMonoid P f : S.LocalizationMap N x y : M x✝ : ∃ c, ↑c * x = ↑c * y c : ↥S h : f.toMap (↑c * x) = f.toMap (↑c * y) ⊢ f.toMap x = f.toMap y
M : Type u_1 inst✝² : CommMonoid M S : Submonoid M N : Type u_2 inst✝¹ : CommMonoid N P : Type u_3 inst✝ : CommMonoid P f : S.LocalizationMap N x y : M x✝ : ∃ c, ↑c * x = ↑c * y c : ↥S h : f.toMap ↑c * f.toMap x = f.toMap ↑c * f.toMap y ⊢ f.toMap x = f.toMap y
((:c Eq) (:fv _uniq.124061) ((:c DFunLike.coe) ((:c MonoidHom) (:fv _uniq.123745) (:fv _uniq.124061) ((:c Monoid.toMulOneClass) (:fv _uniq.123745) ((:c CommMonoid.toMonoid) (:fv _uniq.123745) (:fv _uniq.123748))) ((:c Monoid.toMulOneClass) (:fv _uniq.124061) ((:c CommMonoid.toMonoid) (:fv _uniq.124061) (:fv _uniq.12406...
[{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CommMonoid) (:fv _uniq.123745))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.123745) ((:c Monoid.toMulOneClass) (:fv _uniq.123745) ((:c CommMonoid.toMonoid) (:fv _uniq.123745) (:fv _uniq.123748))))"},{"name":"N","sexp":"(:sort (+ u_2 1))"},{"nam...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MonoidHom) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c MulOneClass) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.123745","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.123748","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CommMonoid) (:arg :ex...
{"children":[{"source":"rw","sourceEnd":29329,"sourceStart":29327,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":29331,"sourceStart":29330,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"map_mul","semant...
[]
[{"source":"map_mul","source_end":29338,"source_start":29331,"syntax_kind":"ident"},{"source":"h","source_end":29353,"source_start":29352,"syntax_kind":"ident"},{"source":"map_mul","source_end":29347,"source_start":29340,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.123745","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.123748","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inte...
157
5
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2280498f8c9212d8a6ace0dc8629c6ee81ef5300127fdb9ca3751b57c156f131
0b5caeaa59d31bba08217dff8f6130553e40f7d93e7353d60262b72cb74f06c8
34fdcd9f81c0259eab80e4b0797f95b776987e1ca457c65edd424a6178830115
b192ef1306d55ffcf072b15615af8cd0c7f7c9440b71d75fa72df9facbd59321
cat-searcher/leandojo-benchmark-4-random
test
3,250
Submonoid.LocalizationMap.eq_iff_exists
Mathlib/GroupTheory/MonoidLocalization.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact (f.map_units c).mul_right_inj.mp h
M : Type u_1 inst✝² : CommMonoid M S : Submonoid M N : Type u_2 inst✝¹ : CommMonoid N P : Type u_3 inst✝ : CommMonoid P f : S.LocalizationMap N x y : M x✝ : ∃ c, ↑c * x = ↑c * y c : ↥S h : f.toMap ↑c * f.toMap x = f.toMap ↑c * f.toMap y ⊢ f.toMap x = f.toMap y
((:c Eq) (:fv _uniq.124061) ((:c DFunLike.coe) ((:c MonoidHom) (:fv _uniq.123745) (:fv _uniq.124061) ((:c Monoid.toMulOneClass) (:fv _uniq.123745) ((:c CommMonoid.toMonoid) (:fv _uniq.123745) (:fv _uniq.123748))) ((:c Monoid.toMulOneClass) (:fv _uniq.124061) ((:c CommMonoid.toMonoid) (:fv _uniq.124061) (:fv _uniq.12406...
[{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CommMonoid) (:fv _uniq.123745))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.123745) ((:c Monoid.toMulOneClass) (:fv _uniq.123745) ((:c CommMonoid.toMonoid) (:fv _uniq.123745) (:fv _uniq.123748))))"},{"name":"N","sexp":"(:sort (+ u_2 1))"},{"nam...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MonoidHom) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c MulOneClass) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.123745","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.123748","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CommMonoid) (:arg :ex...
{"children":[{"source":"exact","sourceEnd":29363,"sourceStart":29358,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":29365,"sourceStart":29364,"tag":"atom"},{"children":[{"source":"f.map_units","sourceEnd":29376,"sourceStart":29365,"tag":"identifier"},{"children":[{"contextIndex":12,"sema...
[]
[{"source":"(f.map_units c).mul_right_inj.mp h","source_end":29398,"source_start":29364,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.123745","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.123748","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inte...
157
9
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
04a6a1a3a92cc9809f2dba7766e17cce22b54099858d6234c4162251e2dc434b
b192ef1306d55ffcf072b15615af8cd0c7f7c9440b71d75fa72df9facbd59321
552bf7d4959236dd537a6ab49f944346669559a80794133b3e483bb735614e92
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,251
Set.Intersecting.exists_card_eq
Mathlib/Combinatorics/SetFamily/Intersecting.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have := hs.card_le
α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s : Finset α hs : (↑s).Intersecting ⊢ ∃ t, s ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersecting
α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s : Finset α hs : (↑s).Intersecting this : 2 * s.card ≤ Fintype.card α ⊢ ∃ t, s ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersecting
((:c Exists) ((:c Finset) (:fv _uniq.17339)) (:lambda t ((:c Finset) (:fv _uniq.17339)) ((:c And) ((:c HasSubset.Subset) ((:c Finset) (:fv _uniq.17339)) ((:c Finset.instHasSubset) (:fv _uniq.17339)) (:fv _uniq.17351) 0) ((:c And) ((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c i...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c BooleanAlgebra) (:fv _uniq.17339))"},{"name":"inst✝¹","sexp":"((:c Nontrivial) (:fv _uniq.17339))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.17339))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.17339))"},{"name":"hs","sexp":"((:c Set.Inters...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Finset) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :ins...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c BooleanAlgebra) (:arg :...
{"children":[{"source":"have","sourceEnd":8724,"sourceStart":8720,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":8725,"sourceStart":8725,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":8725,"sourceStart":8725,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","...
[]
[{"source":"hs.card_le","source_end":8738,"source_start":8728,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
50
4
exact
true
1
6
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
922fc5aadcf56cadfbd6037b7f54bc7a48969d79407876690b22b5b6e7b5fb6b
542ef3bca633693609dbe16e0ac8e6fbd68083b0c22b3a272a2df5fa2993209c
66d5874ce98c399bb12db18ce4f7f3ff34cc865f74ea0fc2e604bb57462a0f57
ea826e682bb80dc246b7e8936aef67a007a02a55b9701a366e045b5d1669ce64
cat-searcher/leandojo-benchmark-4-random
test
3,252
Set.Intersecting.exists_card_eq
Mathlib/Combinatorics/SetFamily/Intersecting.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>mul_comm</a>, ← <a>Nat.le_div_iff_mul_le'</a> <a>Nat.two_pos</a>] at this
α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s : Finset α hs : (↑s).Intersecting this : 2 * s.card ≤ Fintype.card α ⊢ ∃ t, s ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersecting
α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s : Finset α hs : (↑s).Intersecting this : s.card ≤ Fintype.card α / 2 ⊢ ∃ t, s ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersecting
((:c Exists) ((:c Finset) (:fv _uniq.17339)) (:lambda t ((:c Finset) (:fv _uniq.17339)) ((:c And) ((:c HasSubset.Subset) ((:c Finset) (:fv _uniq.17339)) ((:c Finset.instHasSubset) (:fv _uniq.17339)) (:fv _uniq.17351) 0) ((:c And) ((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c i...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c BooleanAlgebra) (:fv _uniq.17339))"},{"name":"inst✝¹","sexp":"((:c Nontrivial) (:fv _uniq.17339))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.17339))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.17339))"},{"name":"hs","sexp":"((:c Set.Inters...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Finset) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :ins...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c BooleanAlgebra) (:arg :...
{"children":[{"source":"rw","sourceEnd":8743,"sourceStart":8741,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8745,"sourceStart":8744,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"mul_comm","semanticR...
[]
[{"source":"mul_comm","source_end":8753,"source_start":8745,"syntax_kind":"ident"},{"source":"this","source_end":8802,"source_start":8798,"syntax_kind":"ident"},{"source":"Nat.le_div_iff_mul_le' Nat.two_pos","source_end":8793,"source_start":8759,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
50
5
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
16ea3fc4cb8b3fea205dd9d2b4abd0866691cc9ab5d59cee6b3bc276abd1afcf
ea826e682bb80dc246b7e8936aef67a007a02a55b9701a366e045b5d1669ce64
dbf9f6946ee2038bff62ca69db1684d28e88593aa9081395e0027afc34455f81
43ea354be5afe4647db6a1a6053ae97a50db73aefef14f5daf6c7f2570e8f1a5
cat-searcher/leandojo-benchmark-4-random
test
3,253
Set.Intersecting.exists_card_eq
Mathlib/Combinatorics/SetFamily/Intersecting.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
revert hs
α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s : Finset α hs : (↑s).Intersecting this : s.card ≤ Fintype.card α / 2 ⊢ ∃ t, s ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersecting
α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s : Finset α this : s.card ≤ Fintype.card α / 2 ⊢ (↑s).Intersecting → ∃ t, s ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersecting
((:c Exists) ((:c Finset) (:fv _uniq.17339)) (:lambda t ((:c Finset) (:fv _uniq.17339)) ((:c And) ((:c HasSubset.Subset) ((:c Finset) (:fv _uniq.17339)) ((:c Finset.instHasSubset) (:fv _uniq.17339)) (:fv _uniq.17351) 0) ((:c And) ((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c i...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c BooleanAlgebra) (:fv _uniq.17339))"},{"name":"inst✝¹","sexp":"((:c Nontrivial) (:fv _uniq.17339))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.17339))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.17339))"},{"name":"hs","sexp":"((:c Set.Inters...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Finset) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :ins...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c BooleanAlgebra) (:arg :...
{"children":[{"source":"revert","sourceEnd":8811,"sourceStart":8805,"tag":"atom"},{"children":[{"contextIndex":6,"semanticRole":"local","source":"hs","sourceEnd":8814,"sourceStart":8812,"tag":"identifier"}],"kind":"null","source":"hs","sourceEnd":8814,"sourceStart":8812,"tag":"node"}],"kind":"Lean.Parser.Tactic.revert"...
[]
[{"source":"hs","source_end":8814,"source_start":8812,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
50
9
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
df192355724dbb796604a793cbfeebc2d24bebebfa5f4a5354698356d2539ed7
43ea354be5afe4647db6a1a6053ae97a50db73aefef14f5daf6c7f2570e8f1a5
ac30c866e2debeb72e78b5bbbbbba329803b7a666a63dac0f60c2567a86b3c8a
6b0ffd34c52ea4a246f4c4bf80fd483d97059d5c16fb2aa2965f3fd16c977d83
cat-searcher/leandojo-benchmark-4-random
test
3,254
Set.Intersecting.exists_card_eq
Mathlib/Combinatorics/SetFamily/Intersecting.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine s.strongDownwardInductionOn ?_ this
α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s : Finset α this : s.card ≤ Fintype.card α / 2 ⊢ (↑s).Intersecting → ∃ t, s ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersecting
α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s : Finset α this : s.card ≤ Fintype.card α / 2 ⊢ ∀ (t₁ : Finset α), (∀ {t₂ : Finset α}, t₂.card ≤ Fintype.card α / 2 → t₁ ⊂ t₂ → (↑t₂).Intersecting → ∃ t, t₂ ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersecting) → ...
(:forall hs ((:c Set.Intersecting) (:fv _uniq.17339) ((:c Lattice.toSemilatticeInf) (:fv _uniq.17339) ((:c GeneralizedCoheytingAlgebra.toLattice) (:fv _uniq.17339) ((:c CoheytingAlgebra.toGeneralizedCoheytingAlgebra) (:fv _uniq.17339) ((:c BiheytingAlgebra.toCoheytingAlgebra) (:fv _uniq.17339) ((:c BooleanAlgebra.toBih...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c BooleanAlgebra) (:fv _uniq.17339))"},{"name":"inst✝¹","sexp":"((:c Nontrivial) (:fv _uniq.17339))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.17339))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.17339))"},{"name":"this","sexp":"((:c LE.le) (...
(:forall hs :explicit (:app (:c Set.Intersecting) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c SemilatticeInf) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c BooleanAlgebra) (:arg :...
{"children":[{"source":"refine","sourceEnd":8823,"sourceStart":8817,"tag":"atom"},{"children":[{"source":"s.strongDownwardInductionOn","sourceEnd":8851,"sourceStart":8824,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":8853,"sourceStart":8852,"tag":"atom"},{"children":[{"source":"_","sourceEnd":...
[]
[{"source":"s.strongDownwardInductionOn ?_ this","source_end":8859,"source_start":8824,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
50
10
exact
true
1
6
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4e12e18d1db9d1d22e8969f2bd1a48d32a07211a16f8dd06c0a48a2c0b1b5a14
6b0ffd34c52ea4a246f4c4bf80fd483d97059d5c16fb2aa2965f3fd16c977d83
bd6787df8d6c506da688e50fe559b427ccce5ec9f9ea71f330a15ee7637a4086
9563d2861c9f6443461619aa4789c07e25a1cf769c229053ff07584d14eae294
cat-searcher/leandojo-benchmark-4-random
test
3,255
Set.Intersecting.exists_card_eq
Mathlib/Combinatorics/SetFamily/Intersecting.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro s ih _hcard hs
α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s : Finset α this : s.card ≤ Fintype.card α / 2 ⊢ ∀ (t₁ : Finset α), (∀ {t₂ : Finset α}, t₂.card ≤ Fintype.card α / 2 → t₁ ⊂ t₂ → (↑t₂).Intersecting → ∃ t, t₂ ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersecting) → ...
α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s✝ : Finset α this : s✝.card ≤ Fintype.card α / 2 s : Finset α ih : ∀ {t₂ : Finset α}, t₂.card ≤ Fintype.card α / 2 → s ⊂ t₂ → (↑t₂).Intersecting → ∃ t, t₂ ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersecting _hcard : s.card ≤ F...
(:forall t₁ ((:c Finset) (:fv _uniq.17339)) (:forall _ (:forall t₂ ((:c Finset) (:fv _uniq.17339)) (:forall _ ((:c LE.le) (:c Nat) (:c instLENat) ((:c Finset.card) (:fv _uniq.17339) 0) ((:c HDiv.hDiv) (:c Nat) (:c Nat) (:c Nat) ((:c instHDiv) (:c Nat) (:c Nat.instDiv)) ((:c Fintype.card) (:fv _uniq.17339) (:fv _uniq.17...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c BooleanAlgebra) (:fv _uniq.17339))"},{"name":"inst✝¹","sexp":"((:c Nontrivial) (:fv _uniq.17339))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.17339))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.17339))"},{"name":"this","sexp":"((:c LE.le) (...
(:forall t₁ :explicit (:app (:c Finset) (:arg :explicit 0 (:fv FV0))) (:forall _ :explicit (:forall t₂ :implicit (:app (:c Finset) (:arg :explicit 0 (:fv FV0))) (:forall _ :explicit (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :expl...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c BooleanAlgebra) (:arg :...
{"children":[{"source":"rintro","sourceEnd":8868,"sourceStart":8862,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"s","sourceEnd":8870,"sourceStart":8869,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"s","sourceEnd":8870,"sourceStart":8869,"tag":"...
[{"role":"fresh_name","source":"s","source_end":8870,"source_start":8869,"syntax_kind":"ident"},{"role":"fresh_name","source":"ih","source_end":8873,"source_start":8871,"syntax_kind":"ident"},{"role":"fresh_name","source":"_hcard","source_end":8880,"source_start":8874,"syntax_kind":"ident"},{"role":"fresh_name","source...
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
50
11
exact
true
1
6
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
60238342e0ecd1eecc4ebd751d50279c5b026a628abc159c617acd1d5a35e5ae
9563d2861c9f6443461619aa4789c07e25a1cf769c229053ff07584d14eae294
742d9cdf5f3d77aba6b4fc90b063143beb0a242eed3f7556ba4306ed786fb1fd
1d00de4bac755807fcdd5b69b07d8258389d3e31602fbe4dd99896b8e2c62cc3
cat-searcher/leandojo-benchmark-4-random
test
3,256
Set.Intersecting.exists_card_eq
Mathlib/Combinatorics/SetFamily/Intersecting.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
by_cases h : ∀ t : <a>Finset</a> α, (t : <a>Set</a> α).<a>Set.Intersecting</a> → s ⊆ t → s = t
α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s✝ : Finset α this : s✝.card ≤ Fintype.card α / 2 s : Finset α ih : ∀ {t₂ : Finset α}, t₂.card ≤ Fintype.card α / 2 → s ⊂ t₂ → (↑t₂).Intersecting → ∃ t, t₂ ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersecting _hcard : s.card ≤ F...
case pos α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s✝ : Finset α this : s✝.card ≤ Fintype.card α / 2 s : Finset α ih : ∀ {t₂ : Finset α}, t₂.card ≤ Fintype.card α / 2 → s ⊂ t₂ → (↑t₂).Intersecting → ∃ t, t₂ ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersecting _hcard : s...
((:c Exists) ((:c Finset) (:fv _uniq.17339)) (:lambda t ((:c Finset) (:fv _uniq.17339)) ((:c And) ((:c HasSubset.Subset) ((:c Finset) (:fv _uniq.17339)) ((:c Finset.instHasSubset) (:fv _uniq.17339)) (:fv _uniq.17929) 0) ((:c And) ((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c i...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c BooleanAlgebra) (:fv _uniq.17339))"},{"name":"inst✝¹","sexp":"((:c Nontrivial) (:fv _uniq.17339))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.17339))"},{"name":"s✝","sexp":"((:c Finset) (:fv _uniq.17339))"},{"name":"this","sexp":"((:c LE.le) ...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Finset) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :ins...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c BooleanAlgebra) (:arg :...
{"children":[{"source":"by_cases","sourceEnd":8894,"sourceStart":8886,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":8896,"sourceStart":8895,"tag":"identifier"},{"source":":","sourceEnd":8898,"sourceStart":8897,"tag":"atom"}],"kind":"null","source":"h :","sourceEnd":8898,"sourceStart...
[]
[{"source":"∀ t : Finset α, (t : Set α).Intersecting → s ⊆ t → s = t","source_end":8965,"source_start":8899,"syntax_kind":"Lean.Parser.Term.forall"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
50
12
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d15f784e500f5dbc2feb44b07babff6ef7bcf2469cdc7e15267ff3894847d1e3
1d00de4bac755807fcdd5b69b07d8258389d3e31602fbe4dd99896b8e2c62cc3
9ee1964c1a59797fc945baed53e63babc6d372687590cf0c2c7ff9cdb332f099
5c90658f65e7cd40ac43be42c475a211e3ef60f1ebc85750d481202b00407492
cat-searcher/leandojo-benchmark-4-random
test
3,257
Set.Intersecting.exists_card_eq
Mathlib/Combinatorics/SetFamily/Intersecting.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
push_neg at h
case neg α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s✝ : Finset α this : s✝.card ≤ Fintype.card α / 2 s : Finset α ih : ∀ {t₂ : Finset α}, t₂.card ≤ Fintype.card α / 2 → s ⊂ t₂ → (↑t₂).Intersecting → ∃ t, t₂ ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersecting _hcard : s...
case neg α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s✝ : Finset α this : s✝.card ≤ Fintype.card α / 2 s : Finset α ih : ∀ {t₂ : Finset α}, t₂.card ≤ Fintype.card α / 2 → s ⊂ t₂ → (↑t₂).Intersecting → ∃ t, t₂ ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersecting _hcard : s...
((:c Exists) ((:c Finset) (:fv _uniq.17339)) (:lambda t ((:c Finset) (:fv _uniq.17339)) ((:c And) ((:c HasSubset.Subset) ((:c Finset) (:fv _uniq.17339)) ((:c Finset.instHasSubset) (:fv _uniq.17339)) (:fv _uniq.17929) 0) ((:c And) ((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c i...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c BooleanAlgebra) (:fv _uniq.17339))"},{"name":"inst✝¹","sexp":"((:c Nontrivial) (:fv _uniq.17339))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.17339))"},{"name":"s✝","sexp":"((:c Finset) (:fv _uniq.17339))"},{"name":"this","sexp":"((:c LE.le) ...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Finset) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :ins...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c BooleanAlgebra) (:arg :...
{"children":[{"source":"push_neg","sourceEnd":9038,"sourceStart":9030,"tag":"atom"},{"children":[{"children":[{"source":"at","sourceEnd":9041,"sourceStart":9039,"tag":"atom"},{"children":[{"children":[{"contextIndex":11,"semanticRole":"local","source":"h","sourceEnd":9043,"sourceStart":9042,"tag":"identifier"}],"kind":...
[]
[{"source":"h","source_end":9043,"source_start":9042,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
50
18
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
dfb97531daaad4b9ced7faf9cfc40e1942236176adf6da82dce5cca2b14b52b6
d97d68cfb7437ee6170c6a22c49ba374721c5fba5805c11986beb9a776ac7fda
888142542b13b584203b27fd6ef959458ac821a7b1559f58d4a1f52094bdaa53
8c1be4cd4097a72ac2fdab9235ffcac504f3c3a66d42c1c48d0e3da465d4a62d
cat-searcher/leandojo-benchmark-4-random
test
3,258
Set.Intersecting.exists_card_eq
Mathlib/Combinatorics/SetFamily/Intersecting.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨t, ht, hst⟩ := h
case neg α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s✝ : Finset α this : s✝.card ≤ Fintype.card α / 2 s : Finset α ih : ∀ {t₂ : Finset α}, t₂.card ≤ Fintype.card α / 2 → s ⊂ t₂ → (↑t₂).Intersecting → ∃ t, t₂ ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersecting _hcard : s...
case neg.intro.intro α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s✝ : Finset α this : s✝.card ≤ Fintype.card α / 2 s : Finset α ih : ∀ {t₂ : Finset α}, t₂.card ≤ Fintype.card α / 2 → s ⊂ t₂ → (↑t₂).Intersecting → ∃ t, t₂ ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersectin...
((:c Exists) ((:c Finset) (:fv _uniq.17339)) (:lambda t ((:c Finset) (:fv _uniq.17339)) ((:c And) ((:c HasSubset.Subset) ((:c Finset) (:fv _uniq.17339)) ((:c Finset.instHasSubset) (:fv _uniq.17339)) (:fv _uniq.17929) 0) ((:c And) ((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c i...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c BooleanAlgebra) (:fv _uniq.17339))"},{"name":"inst✝¹","sexp":"((:c Nontrivial) (:fv _uniq.17339))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.17339))"},{"name":"s✝","sexp":"((:c Finset) (:fv _uniq.17339))"},{"name":"this","sexp":"((:c LE.le) ...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Finset) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :ins...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c BooleanAlgebra) (:arg :...
{"children":[{"source":"obtain","sourceEnd":9052,"sourceStart":9046,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":9056,"sourceStart":9053,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"t","sourceEnd":9...
[]
[{"source":"h","source_end":9074,"source_start":9073,"syntax_kind":"ident"},{"source":"⟨t, ht, hst⟩","source_end":9069,"source_start":9053,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
50
19
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b6791b92832164c3ef072c42d18125dc19dd9755a210bcd9391f8460230011dd
8c1be4cd4097a72ac2fdab9235ffcac504f3c3a66d42c1c48d0e3da465d4a62d
c52718570652da583f00e9ca6876213d0fe43b8ff2a40633303aaca68c56dedd
4b22e5ca34909fff3567349163d9a55fc202ef237eb0ed3a6763ba95f76e4ff1
cat-searcher/leandojo-benchmark-4-random
test
3,259
Set.Intersecting.exists_card_eq
Mathlib/Combinatorics/SetFamily/Intersecting.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine (ih ?_ (<a>ssubset_iff_subset_ne</a>.2 hst) ht).<a>Exists.imp</a> fun u => <a>And.imp_left</a> hst.1.<a>HasSubset.Subset.trans</a>
case neg.intro.intro α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s✝ : Finset α this : s✝.card ≤ Fintype.card α / 2 s : Finset α ih : ∀ {t₂ : Finset α}, t₂.card ≤ Fintype.card α / 2 → s ⊂ t₂ → (↑t₂).Intersecting → ∃ t, t₂ ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersectin...
case neg.intro.intro α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s✝ : Finset α this : s✝.card ≤ Fintype.card α / 2 s : Finset α ih : ∀ {t₂ : Finset α}, t₂.card ≤ Fintype.card α / 2 → s ⊂ t₂ → (↑t₂).Intersecting → ∃ t, t₂ ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersectin...
((:c Exists) ((:c Finset) (:fv _uniq.17339)) (:lambda t ((:c Finset) (:fv _uniq.17339)) ((:c And) ((:c HasSubset.Subset) ((:c Finset) (:fv _uniq.17339)) ((:c Finset.instHasSubset) (:fv _uniq.17339)) (:fv _uniq.17929) 0) ((:c And) ((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c i...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c BooleanAlgebra) (:fv _uniq.17339))"},{"name":"inst✝¹","sexp":"((:c Nontrivial) (:fv _uniq.17339))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.17339))"},{"name":"s✝","sexp":"((:c Finset) (:fv _uniq.17339))"},{"name":"this","sexp":"((:c LE.le) ...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Finset) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :ins...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c BooleanAlgebra) (:arg :...
{"children":[{"source":"refine","sourceEnd":9083,"sourceStart":9077,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":9085,"sourceStart":9084,"tag":"atom"},{"children":[{"contextIndex":8,"semanticRole":"local","source":"ih","sourceEnd":9087,"sourceStart":9085,"tag":"identifier"},{"children"...
[]
[{"source":"(ih ?_ (_root_.ssubset_iff_subset_ne.2 hst) ht).imp fun u => And.imp_left hst.1.trans","source_end":9169,"source_start":9084,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
50
20
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
af4c13b0825661bfcf68f9f3c9605c1b2023272095eb28d2346dedfb90ae8343
4b22e5ca34909fff3567349163d9a55fc202ef237eb0ed3a6763ba95f76e4ff1
59c4d21640a82e74085cc08c2ff8cebd30e4aae3d827af69c4ba29e61466a348
83f0445a586a9b82eaeca3d206d0a76aa24b504228e37e9750194d74c5e00264
cat-searcher/leandojo-benchmark-4-random
test
3,260
Set.Intersecting.exists_card_eq
Mathlib/Combinatorics/SetFamily/Intersecting.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Nat.le_div_iff_mul_le'</a> <a>Nat.two_pos</a>, <a>mul_comm</a>]
case neg.intro.intro α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s✝ : Finset α this : s✝.card ≤ Fintype.card α / 2 s : Finset α ih : ∀ {t₂ : Finset α}, t₂.card ≤ Fintype.card α / 2 → s ⊂ t₂ → (↑t₂).Intersecting → ∃ t, t₂ ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersectin...
case neg.intro.intro α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s✝ : Finset α this : s✝.card ≤ Fintype.card α / 2 s : Finset α ih : ∀ {t₂ : Finset α}, t₂.card ≤ Fintype.card α / 2 → s ⊂ t₂ → (↑t₂).Intersecting → ∃ t, t₂ ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersectin...
((:c LE.le) (:c Nat) (:c instLENat) ((:c Finset.card) (:fv _uniq.17339) (:fv _uniq.18890)) ((:c HDiv.hDiv) (:c Nat) (:c Nat) (:c Nat) ((:c instHDiv) (:c Nat) (:c Nat.instDiv)) ((:c Fintype.card) (:fv _uniq.17339) (:fv _uniq.17348)) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c BooleanAlgebra) (:fv _uniq.17339))"},{"name":"inst✝¹","sexp":"((:c Nontrivial) (:fv _uniq.17339))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.17339))"},{"name":"s✝","sexp":"((:c Finset) (:fv _uniq.17339))"},{"name":"this","sexp":"((:c LE.le) ...
(: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 Finset.card) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV11)))) (:arg :explicit 3 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Nat)) (:arg :implici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c BooleanAlgebra) (:arg :...
{"children":[{"source":"rw","sourceEnd":9174,"sourceStart":9172,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9176,"sourceStart":9175,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Nat.le_...
[]
[{"source":"Nat.le_div_iff_mul_le' Nat.two_pos","source_end":9210,"source_start":9176,"syntax_kind":"Lean.Parser.Term.app"},{"source":"mul_comm","source_end":9220,"source_start":9212,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
50
21
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0ac10f4a7bd8b74ae35b145bd2945f907a092b07606b86f1a549254da721a67a
83f0445a586a9b82eaeca3d206d0a76aa24b504228e37e9750194d74c5e00264
73ae3b49d14642d17a4f7572659c3cec958899169e6456b63df63aae4c5ec543
53e17f159804efc3d49293143ac536c39e4470776e21fef4b1b3172ba679f8fe
cat-searcher/leandojo-benchmark-4-random
test
3,261
Set.Intersecting.exists_card_eq
Mathlib/Combinatorics/SetFamily/Intersecting.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact ht.card_le
case neg.intro.intro α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s✝ : Finset α this : s✝.card ≤ Fintype.card α / 2 s : Finset α ih : ∀ {t₂ : Finset α}, t₂.card ≤ Fintype.card α / 2 → s ⊂ t₂ → (↑t₂).Intersecting → ∃ t, t₂ ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersectin...
((:c LE.le) (:c Nat) (:c instLENat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) ((:c CommMagma.toMul) (:c Nat) ((:c CommSemigroup.toCommMagma) (:c Nat) (:c Nat.instCommSemigroup)))) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2))) ((:c Finset.card) (:fv _uniq.17339) (:fv _uniq.18...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c BooleanAlgebra) (:fv _uniq.17339))"},{"name":"inst✝¹","sexp":"((:c Nontrivial) (:fv _uniq.17339))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.17339))"},{"name":"s✝","sexp":"((:c Finset) (:fv _uniq.17339))"},{"name":"this","sexp":"((:c LE.le) ...
(: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 HMul.hMul) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c BooleanAlgebra) (:arg :...
{"children":[{"source":"exact","sourceEnd":9229,"sourceStart":9224,"tag":"atom"},{"name":"Set.Intersecting.card_le","semanticRole":"global","source":"ht.card_le","sourceEnd":9240,"sourceStart":9230,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact ht.card_le","sourceEnd":9240,"sourceStart":9224,"ta...
[]
[{"source":"ht.card_le","source_end":9240,"source_start":9230,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
50
25
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
21534983565d70ef478f4851a6d34c97eedc901261f3615129d30daaa58e0926
53e17f159804efc3d49293143ac536c39e4470776e21fef4b1b3172ba679f8fe
72a62cae4c25e073df11a2169dc7c5633f1cc89ed58ee3dec5b31771504f54b6
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,262
Set.Intersecting.exists_card_eq
Mathlib/Combinatorics/SetFamily/Intersecting.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact ⟨s, <a>Set.Subset.rfl</a>, hs.is_max_iff_card_eq.1 h, hs⟩
case pos α : Type u_1 inst✝² : BooleanAlgebra α inst✝¹ : Nontrivial α inst✝ : Fintype α s✝ : Finset α this : s✝.card ≤ Fintype.card α / 2 s : Finset α ih : ∀ {t₂ : Finset α}, t₂.card ≤ Fintype.card α / 2 → s ⊂ t₂ → (↑t₂).Intersecting → ∃ t, t₂ ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersecting _hcard : s...
((:c Exists) ((:c Finset) (:fv _uniq.17339)) (:lambda t ((:c Finset) (:fv _uniq.17339)) ((:c And) ((:c HasSubset.Subset) ((:c Finset) (:fv _uniq.17339)) ((:c Finset.instHasSubset) (:fv _uniq.17339)) (:fv _uniq.17929) 0) ((:c And) ((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c i...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c BooleanAlgebra) (:fv _uniq.17339))"},{"name":"inst✝¹","sexp":"((:c Nontrivial) (:fv _uniq.17339))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.17339))"},{"name":"s✝","sexp":"((:c Finset) (:fv _uniq.17339))"},{"name":"this","sexp":"((:c LE.le) ...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Finset) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :ins...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c BooleanAlgebra) (:arg :...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":8976,"sourceStart":8971,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":8980,"sourceStart":8977,"tag":"atom"},{"children":[{"contextIndex":7,"semanticRole":"local","source":"s","sourceEnd":8981,"sourceStart":8980,"tag":"identifier"},...
[]
[{"source":"⟨s, Subset.rfl, hs.is_max_iff_card_eq.1 h, hs⟩","source_end":9027,"source_start":8977,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17339","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.17342","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...
50
15
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a06a050988093f38bbc3647180656aab5a0c78dacc351e84756e8cd2214758bf
30b6748cd6a2245220f1fdf08d3324c09925cf09fa82a984ff89181cb16d0eea
d5a1840a4138ff3dd199cc793080cc1fa967fb147decfa24df1478e6b6b3d7f9
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,263
Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint
Mathlib/LinearAlgebra/AffineSpace/Combination.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub</a>, <a>Finset.weightedVSubOfPoint_apply_const</a>]
k : Type u_1 V : Type u_2 P : Type u_3 inst✝² : Ring k inst✝¹ : AddCommGroup V inst✝ : Module k V S : AffineSpace V P ι : Type u_4 s : Finset ι ι₂ : Type u_5 s₂ : Finset ι₂ w : ι → k p₂ : ι → P p₁ b : P ⊢ ∑ i ∈ s, w i • (p₁ -ᵥ p₂ i) = (∑ i ∈ s, w i) • (p₁ -ᵥ b) - (s.weightedVSubOfPoint p₂ b) w
((:c Eq) (:fv _uniq.85096) ((:c Finset.sum) (:fv _uniq.85784) (:fv _uniq.85096) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.85096) (:fv _uniq.85105)) (:fv _uniq.85787) (:lambda i (:fv _uniq.85784) ((:c HSMul.hSMul) (:fv _uniq.85093) (:fv _uniq.85096) (:fv _uniq.85096) ((:c instHSMul) (:fv _uniq.85093) (:fv _uniq.8509...
[{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.85093))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.85096))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.85093) (:fv _uniq.85096) ((:c...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Finset.sum) (:arg :implicit-type 0 (:fv FV7)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 3 (:fv FV8)) (:arg :explicit 4 (:lambda i :explicit (:fv FV...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.85093","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.85096","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":9374,"sourceStart":9372,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9376,"sourceStart":9375,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag...
[]
[{"source":"sum_smul_vsub_eq_weightedVSubOfPoint_sub","source_end":9416,"source_start":9376,"syntax_kind":"ident"},{"source":"weightedVSubOfPoint_apply_const","source_end":9449,"source_start":9418,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.85093","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.85096","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
37
2
exact
true
1
15
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
abd3aecdd16dbe9df23be34792700275d469c2ea30ab5c39b5f9afca6196dc28
ac12526ebf6b174dba3c0b813778124b48f141a1ec677ec9154c520f6ed79966
1cb3bc2708a91770ac2bcdcb51eace205cde43468411ea87961846fa97f0b408
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,264
MeasurableSpace.cardinal_generateMeasurable_le_continuum
Mathlib/MeasureTheory/MeasurableSpace/Card.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>Cardinal.continuum_power_aleph0</a>]
α : Type u s : Set (Set α) hs : #↑s ≤ 𝔠 ⊢ max (#↑s) 2 ^ ℵ₀ ≤ 𝔠
α : Type u s : Set (Set α) hs : #↑s ≤ 𝔠 ⊢ max (#↑s) 2 ^ ℵ₀ ≤ 𝔠 ^ ℵ₀
((:c LE.le) (:c Cardinal) ((:c Preorder.toLE) (:c Cardinal) ((:c PartialOrder.toPreorder) (:c Cardinal) (:c Cardinal.partialOrder))) ((:c HPow.hPow) (:c Cardinal) (:c Cardinal) (:c Cardinal) ((:c instHPow) (:c Cardinal) (:c Cardinal) (:c Cardinal.instPowCardinal)) ((:c Max.max) (:c Cardinal) ((:c CanonicallyLinearOrder...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"s","sexp":"((:c Set) ((:c Set) (:fv _uniq.22859)))"},{"name":"hs","sexp":"((:c LE.le) (:c Cardinal) (:c Cardinal.instLE) ((:c Cardinal.mk) ((:c Set.Elem) ((:c Set) (:fv _uniq.22859)) (:fv _uniq.23187))) (:c Cardinal.continuum))"}]
(:app (:c LE.le) (:arg :implicit-type 0 (:c Cardinal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Cardinal))))) (:arg :explicit 2 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Cardinal)) (:arg :implicit-type 1 (:c Cardinal)) (:arg :implicit-type 2 (:c Cardinal)) (:arg :instance 3 (:instance-o...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22859","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.23187","is_instance":false,"is_let":false,"name":"s","sexp":"(:app (:c Set) (:arg :explicit 0 (:app (:c Set...
{"children":[{"source":"rw","sourceEnd":9192,"sourceStart":9190,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9194,"sourceStart":9193,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":9197,"sourceStart":...
[]
[{"source":"continuum_power_aleph0","source_end":9220,"source_start":9198,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22859","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.23187","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":3,"internal_name":"_un...
27
4
exact
true
1
3
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
589aac444747ab3c2931b7f377e154ea0217d2483dce163298441e9b97bae931
74a9f2a1740346a110f318ce50bb54a89c875b4ed39f28b97e7e099c131c7c7c
95c0b3b3731b646edd99799b018541cc83f6298a8c477dfd5b8c2deb17c19d35
2ab1b01a3513bd344deac2b98c30b6a900e44acf9ce54881a5c33f290695ad9e
cat-searcher/leandojo-benchmark-4-random
test
3,265
MeasurableSpace.cardinal_generateMeasurable_le_continuum
Mathlib/MeasureTheory/MeasurableSpace/Card.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact mod_cast <a>Cardinal.power_le_power_right</a> (<a>max_le</a> hs (<a>Cardinal.nat_lt_continuum</a> 2).<a>LT.lt.le</a>)
α : Type u s : Set (Set α) hs : #↑s ≤ 𝔠 ⊢ max (#↑s) 2 ^ ℵ₀ ≤ 𝔠 ^ ℵ₀
((:c LE.le) (:c Cardinal) ((:c Preorder.toLE) (:c Cardinal) ((:c PartialOrder.toPreorder) (:c Cardinal) (:c Cardinal.partialOrder))) ((:c HPow.hPow) (:c Cardinal) (:c Cardinal) (:c Cardinal) ((:c instHPow) (:c Cardinal) (:c Cardinal) (:c Cardinal.instPowCardinal)) ((:c Max.max) (:c Cardinal) ((:c CanonicallyLinearOrder...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"s","sexp":"((:c Set) ((:c Set) (:fv _uniq.22859)))"},{"name":"hs","sexp":"((:c LE.le) (:c Cardinal) (:c Cardinal.instLE) ((:c Cardinal.mk) ((:c Set.Elem) ((:c Set) (:fv _uniq.22859)) (:fv _uniq.23187))) (:c Cardinal.continuum))"}]
(:app (:c LE.le) (:arg :implicit-type 0 (:c Cardinal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Cardinal))))) (:arg :explicit 2 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Cardinal)) (:arg :implicit-type 1 (:c Cardinal)) (:arg :implicit-type 2 (:c Cardinal)) (:arg :instance 3 (:instance-o...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22859","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.23187","is_instance":false,"is_let":false,"name":"s","sexp":"(:app (:c Set) (:arg :explicit 0 (:app (:c Set...
{"children":[{"source":"exact","sourceEnd":9233,"sourceStart":9228,"tag":"atom"},{"children":[{"source":"mod_cast","sourceEnd":9242,"sourceStart":9234,"tag":"atom"},{"children":[{"name":"Cardinal.power_le_power_right","semanticRole":"global","source":"power_le_power_right","sourceEnd":9263,"sourceStart":9243,"tag":"ide...
[]
[{"source":"mod_cast power_le_power_right (max_le hs (nat_lt_continuum 2).le)","source_end":9299,"source_start":9234,"syntax_kind":"Lean.modCast"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22859","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.23187","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":3,"internal_name":"_un...
27
7
exact
true
1
3
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
02b112652acc635f86da2df51d8b86021d701dc01c44ffa1e1a34950e9e71a3e
2ab1b01a3513bd344deac2b98c30b6a900e44acf9ce54881a5c33f290695ad9e
aba48575a1dd3640a94260dc4a10d5ca44dc798cc67023eed41107e01d7b9330
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,266
Fin.coe_of_injective_castLE_symm
Mathlib/Data/Fin/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>Fin.coe_castLE</a> h]
n✝ m n k : ℕ h : n ≤ k i : Fin k hi : i ∈ Set.range (castLE h) ⊢ ↑((Equiv.ofInjective (castLE h) ⋯).symm ⟨i, hi⟩) = ↑i
n✝ m n k : ℕ h : n ≤ k i : Fin k hi : i ∈ Set.range (castLE h) ⊢ ↑(castLE h ((Equiv.ofInjective (castLE h) ⋯).symm ⟨i, hi⟩)) = ↑i
((:c Eq) (:c Nat) ((:c Fin.val) (:fv _uniq.27420) ((:c DFunLike.coe) ((:c Equiv) ((:c Set.Elem) ((:c Fin) (:fv _uniq.27421)) ((:c Set.range) ((:c Fin) (:fv _uniq.27421)) ((:c Fin) (:fv _uniq.27420)) ((:c Fin.castLE) (:fv _uniq.27420) (:fv _uniq.27421) (:fv _uniq.27422)))) ((:c Fin) (:fv _uniq.27420))) ((:c Set.Elem) ((...
[{"name":"n✝","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c LE.le) (:c Nat) (:c instLENat) (:fv _uniq.27420) (:fv _uniq.27421))"},{"name":"i","sexp":"((:c Fin) (:fv _uniq.27421))"},{"name":"hi","sexp":"((:c Membership.mem) ((:c F...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Fin.val) (:arg :implicit 0) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Equiv) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:app (:c Fin) (:arg :explicit 0 (:fv FV4)))) (:arg :explicit 1 (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27028","is_instance":false,"is_let":false,"name":"n✝","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27030","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":implicit","context_in...
{"children":[{"source":"rw","sourceEnd":27607,"sourceStart":27605,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27609,"sourceStart":27608,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":27612,"sourceSt...
[]
[{"source":"coe_castLE h","source_end":27625,"source_start":27613,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27028","is_instance":false,"is_let":false,"user_name":"n✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27030","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":3,"internal_name":"_u...
293
4
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
258e095f9f812d9151b8bd26bf9b9ddcf173a6a027a830af670ce5b63a79ea65
eadf4611752406abfbc63587f5702fdba2eab7381814e16219a48a2a916e2308
6bee5d29c81df3548e945a113a7a8a3d72be28b5ee4c8fe3ca19170577467e7e
5f1ad58e38657effd0fe63e19f2118821de977c21cf959d69d446df2a0e68688
cat-searcher/leandojo-benchmark-4-random
test
3,267
Fin.coe_of_injective_castLE_symm
Mathlib/Data/Fin/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>congr_arg</a> <a>Fin.val</a> (<a>Equiv.apply_ofInjective_symm</a> _ _)
n✝ m n k : ℕ h : n ≤ k i : Fin k hi : i ∈ Set.range (castLE h) ⊢ ↑(castLE h ((Equiv.ofInjective (castLE h) ⋯).symm ⟨i, hi⟩)) = ↑i
((:c Eq) (:c Nat) ((:c Fin.val) (:fv _uniq.27421) ((:c Fin.castLE) (:fv _uniq.27420) (:fv _uniq.27421) (:fv _uniq.27422) ((:c DFunLike.coe) ((:c Equiv) ((:c Set.Elem) ((:c Fin) (:fv _uniq.27421)) ((:c Set.range) ((:c Fin) (:fv _uniq.27421)) ((:c Fin) (:fv _uniq.27420)) ((:c Fin.castLE) (:fv _uniq.27420) (:fv _uniq.2742...
[{"name":"n✝","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c LE.le) (:c Nat) (:c instLENat) (:fv _uniq.27420) (:fv _uniq.27421))"},{"name":"i","sexp":"((:c Fin) (:fv _uniq.27421))"},{"name":"hi","sexp":"((:c Membership.mem) ((:c F...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Fin.val) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Fin.castLE) (:arg :implicit 0) (:arg :implicit 1) (:arg :proof 2 (:proof-of (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27028","is_instance":false,"is_let":false,"name":"n✝","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27030","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":implicit","context_in...
{"children":[{"source":"exact","sourceEnd":27634,"sourceStart":27629,"tag":"atom"},{"children":[{"name":"congr_arg","semanticRole":"global","source":"congr_arg","sourceEnd":27644,"sourceStart":27635,"tag":"identifier"},{"children":[{"name":"Fin.val","semanticRole":"global","source":"Fin.val","sourceEnd":27652,"sourceSt...
[]
[{"source":"congr_arg Fin.val (Equiv.apply_ofInjective_symm _ _)","source_end":27687,"source_start":27635,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27028","is_instance":false,"is_let":false,"user_name":"n✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27030","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":3,"internal_name":"_u...
293
7
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8baaf0f9df9dee8975f6e5cb029f2e4390e715722251b855331f310e4278d438
5f1ad58e38657effd0fe63e19f2118821de977c21cf959d69d446df2a0e68688
bcad5b7f548f3b4565d0158629f6ae12f137871b1f854e44b2d9b362e38646fa
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,268
cfc_inv_id
Mathlib/Topology/ContinuousFunction/FunctionalCalculus.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>Ring.inverse_unit</a>]
R : Type u_1 A : Type u_2 p : A → Prop inst✝¹⁰ : Semifield R inst✝⁹ : StarRing R inst✝⁸ : MetricSpace R inst✝⁷ : TopologicalSemiring R inst✝⁶ : ContinuousStar R inst✝⁵ : HasContinuousInv₀ R inst✝⁴ : TopologicalSpace A inst✝³ : Ring A inst✝² : StarRing A inst✝¹ : Algebra R A inst✝ : ContinuousFunctionalCalculus R p f : ...
R : Type u_1 A : Type u_2 p : A → Prop inst✝¹⁰ : Semifield R inst✝⁹ : StarRing R inst✝⁸ : MetricSpace R inst✝⁷ : TopologicalSemiring R inst✝⁶ : ContinuousStar R inst✝⁵ : HasContinuousInv₀ R inst✝⁴ : TopologicalSpace A inst✝³ : Ring A inst✝² : StarRing A inst✝¹ : Algebra R A inst✝ : ContinuousFunctionalCalculus R p f : ...
((:c Eq) (:fv _uniq.485628) ((:c cfc) (:fv _uniq.485625) (:fv _uniq.485628) (:fv _uniq.485632) ((:c Semifield.toCommSemiring) (:fv _uniq.485625) (:fv _uniq.485635)) (:fv _uniq.485982) (:fv _uniq.485985) (:fv _uniq.486392) (:fv _uniq.487034) (:fv _uniq.487267) (:fv _uniq.487270) (:fv _uniq.487407) (:fv _uniq.487697) (:f...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.485628) (:sort 0))"},{"name":"inst✝¹⁰","sexp":"((:c Semifield) (:fv _uniq.485625))"},{"name":"inst✝⁹","sexp":"((:c StarRing) (:fv _uniq.485625) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c cfc) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c StarRing) (:arg :expli...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.485625","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.485628","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"rw","sourceEnd":31161,"sourceStart":31159,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":31163,"sourceStart":31162,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":31166,"sourceSt...
[]
[{"source":"Ring.inverse_unit","source_end":31184,"source_start":31167,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.485625","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.485628","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
90
4
exact
true
1
18
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f39b72c820d1e3635a2319b7072e575f3f8ac3105d53ffdec71cc753e43f9dff
d6497c29556aedd3364ab4e054d7735ba8a465d96261c05084b818273e695ef6
36475cf1b882f574b268ac85e9c2ea9f186bdf52206cc4dcb2f15b7b2f6b680a
2e6dd89bc67d4d301b625daee889da7a787ed4f6528b65953acb7896760947ae
cat-searcher/leandojo-benchmark-4-random
test
3,269
cfc_inv_id
Mathlib/Topology/ContinuousFunction/FunctionalCalculus.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
convert <a>cfc_inv</a> (<a>id</a> : R → R) (a : A) ?_
R : Type u_1 A : Type u_2 p : A → Prop inst✝¹⁰ : Semifield R inst✝⁹ : StarRing R inst✝⁸ : MetricSpace R inst✝⁷ : TopologicalSemiring R inst✝⁶ : ContinuousStar R inst✝⁵ : HasContinuousInv₀ R inst✝⁴ : TopologicalSpace A inst✝³ : Ring A inst✝² : StarRing A inst✝¹ : Algebra R A inst✝ : ContinuousFunctionalCalculus R p f : ...
case h.e'_3.h.e'_3 R : Type u_1 A : Type u_2 p : A → Prop inst✝¹⁰ : Semifield R inst✝⁹ : StarRing R inst✝⁸ : MetricSpace R inst✝⁷ : TopologicalSemiring R inst✝⁶ : ContinuousStar R inst✝⁵ : HasContinuousInv₀ R inst✝⁴ : TopologicalSpace A inst✝³ : Ring A inst✝² : StarRing A inst✝¹ : Algebra R A inst✝ : ContinuousFunction...
((:c Eq) (:fv _uniq.485628) ((:c cfc) (:fv _uniq.485625) (:fv _uniq.485628) (:fv _uniq.485632) ((:c Semifield.toCommSemiring) (:fv _uniq.485625) (:fv _uniq.485635)) (:fv _uniq.485982) (:fv _uniq.485985) (:fv _uniq.486392) (:fv _uniq.487034) (:fv _uniq.487267) (:fv _uniq.487270) (:fv _uniq.487407) (:fv _uniq.487697) (:f...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.485628) (:sort 0))"},{"name":"inst✝¹⁰","sexp":"((:c Semifield) (:fv _uniq.485625))"},{"name":"inst✝⁹","sexp":"((:c StarRing) (:fv _uniq.485625) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c cfc) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c StarRing) (:arg :expli...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.485625","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.485628","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"convert","sourceEnd":31195,"sourceStart":31188,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"cfc_inv","semanticRole":"global","source":"cfc_inv","sourceEnd":31203,"sourceStart":31196,"tag":"identi...
[]
[{"source":"cfc_inv (id : R → R) (a : A) ?_","source_end":31229,"source_start":31196,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.485625","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.485628","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
90
7
exact
true
1
18
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ea1d396943654f00c63d78a96c7b321e9113ebbf4deee8e3314181e8859adc70
2e6dd89bc67d4d301b625daee889da7a787ed4f6528b65953acb7896760947ae
596dff2cacd051da3dc24258fafc934d45e26af1b6aec2856ec43244566ce413
127323863f3f17e89b56214c9f584cf7dd0027a7ec163c455fbabc7cea98f16a
cat-searcher/leandojo-benchmark-4-random
test
3,270
cfc_inv_id
Mathlib/Topology/ContinuousFunction/FunctionalCalculus.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact (<a>cfc_id</a> R (a : A)).<a>Eq.symm</a>
case h.e'_3.h.e'_3 R : Type u_1 A : Type u_2 p : A → Prop inst✝¹⁰ : Semifield R inst✝⁹ : StarRing R inst✝⁸ : MetricSpace R inst✝⁷ : TopologicalSemiring R inst✝⁶ : ContinuousStar R inst✝⁵ : HasContinuousInv₀ R inst✝⁴ : TopologicalSpace A inst✝³ : Ring A inst✝² : StarRing A inst✝¹ : Algebra R A inst✝ : ContinuousFunction...
((:c Eq) (:fv _uniq.485628) ((:c Units.val) (:fv _uniq.485628) ((:c MonoidWithZero.toMonoid) (:fv _uniq.485628) ((:c Semiring.toMonoidWithZero) (:fv _uniq.485628) ((:c Ring.toSemiring) (:fv _uniq.485628) (:fv _uniq.487270)))) (:fv _uniq.488961)) ((:c cfc) (:fv _uniq.485625) (:fv _uniq.485628) (:fv _uniq.485632) ((:c Se...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.485628) (:sort 0))"},{"name":"inst✝¹⁰","sexp":"((:c Semifield) (:fv _uniq.485625))"},{"name":"inst✝⁹","sexp":"((:c StarRing) (:fv _uniq.485625) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Units.val) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV17)))) (:arg :explicit 2 (:app (:c cfc) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-ty...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.485625","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.485628","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":31240,"sourceStart":31235,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":31242,"sourceStart":31241,"tag":"atom"},{"children":[{"name":"cfc_id","semanticRole":"global","source":"cfc_id","sourceEnd":31248,"sourceStart":31...
[]
[{"source":"(cfc_id R (a : A)).symm","source_end":31264,"source_start":31241,"syntax_kind":"Lean.Parser.Term.proj"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.485625","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.485628","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
90
10
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
025ab1772191dcf2edbfb673d4679df35edcbc408f032d15c4245c487a953371
50bb4874c762996eb09541716fa3b7ac3ed47c079b0796a0796417dcd948cca7
ab88c4115170f5ac2db2390de55fee19d9b37f51640723fb89deed4109b66e5e
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,271
cfc_inv_id
Mathlib/Topology/ContinuousFunction/FunctionalCalculus.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro x hx rfl
R : Type u_1 A : Type u_2 p : A → Prop inst✝¹⁰ : Semifield R inst✝⁹ : StarRing R inst✝⁸ : MetricSpace R inst✝⁷ : TopologicalSemiring R inst✝⁶ : ContinuousStar R inst✝⁵ : HasContinuousInv₀ R inst✝⁴ : TopologicalSpace A inst✝³ : Ring A inst✝² : StarRing A inst✝¹ : Algebra R A inst✝ : ContinuousFunctionalCalculus R p f : ...
R : Type u_1 A : Type u_2 p : A → Prop inst✝¹⁰ : Semifield R inst✝⁹ : StarRing R inst✝⁸ : MetricSpace R inst✝⁷ : TopologicalSemiring R inst✝⁶ : ContinuousStar R inst✝⁵ : HasContinuousInv₀ R inst✝⁴ : TopologicalSpace A inst✝³ : Ring A inst✝² : StarRing A inst✝¹ : Algebra R A inst✝ : ContinuousFunctionalCalculus R p f : ...
(:forall x (:fv _uniq.485625) (:forall _ ((:c Membership.mem) (:fv _uniq.485625) ((:c Set) (:fv _uniq.485625)) ((:c Set.instMembership) (:fv _uniq.485625)) 0 ((:c spectrum) (:fv _uniq.485625) (:fv _uniq.485628) ((:c Semifield.toCommSemiring) (:fv _uniq.485625) (:fv _uniq.485635)) (:fv _uniq.487270) (:fv _uniq.487697) (...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.485628) (:sort 0))"},{"name":"inst✝¹⁰","sexp":"((:c Semifield) (:fv _uniq.485625))"},{"name":"inst✝⁹","sexp":"((:c StarRing) (:fv _uniq.485625) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:...
(:forall x :explicit (:fv FV0) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.485625","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.485628","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"rintro","sourceEnd":31276,"sourceStart":31270,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":31278,"sourceStart":31277,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":31278,"sourceStart":31277,"...
[{"role":"fresh_name","source":"hx","source_end":31281,"source_start":31279,"syntax_kind":"ident"}]
[{"source":"rfl","source_end":31285,"source_start":31282,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.485625","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.485628","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
90
17
exact
true
1
18
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
81333b8223cc942804c98c1e25a3576ca160dfa303120a2471ed6a2e1d4315d7
cdc9a81f668e45ad36bf212343a3856394febc31bf93acf602b8de6de7ee07d7
597dd298d81a456f797e8f2e478b593fb7e23fe9bb29d8d98005f2062920e95b
9ed6614bb435eea4e03463fbaa39aa091c3fc3b356706dd2d67830fd7afe697c
cat-searcher/leandojo-benchmark-4-random
test
3,272
cfc_inv_id
Mathlib/Topology/ContinuousFunction/FunctionalCalculus.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>spectrum.zero_not_mem</a> R a.isUnit hx
R : Type u_1 A : Type u_2 p : A → Prop inst✝¹⁰ : Semifield R inst✝⁹ : StarRing R inst✝⁸ : MetricSpace R inst✝⁷ : TopologicalSemiring R inst✝⁶ : ContinuousStar R inst✝⁵ : HasContinuousInv₀ R inst✝⁴ : TopologicalSpace A inst✝³ : Ring A inst✝² : StarRing A inst✝¹ : Algebra R A inst✝ : ContinuousFunctionalCalculus R p f : ...
(:c False)
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.485628) (:sort 0))"},{"name":"inst✝¹⁰","sexp":"((:c Semifield) (:fv _uniq.485625))"},{"name":"inst✝⁹","sexp":"((:c StarRing) (:fv _uniq.485625) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:...
(:c False)
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.485625","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.485628","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"source":"exact","sourceEnd":31295,"sourceStart":31290,"tag":"atom"},{"children":[{"name":"spectrum.zero_not_mem","semanticRole":"global","source":"spectrum.zero_not_mem","sourceEnd":31317,"sourceStart":31296,"tag":"identifier"},{"children":[{"contextIndex":0,"semanticRole":"local","source":"R","sourceEnd...
[]
[{"source":"spectrum.zero_not_mem R a.isUnit hx","source_end":31331,"source_start":31296,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.485625","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.485628","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
90
18
exact
true
1
19
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8004926a38bb35fc6317cd1fd601b863d5ac8b47d33d128e5911ba3da776d01f
9ed6614bb435eea4e03463fbaa39aa091c3fc3b356706dd2d67830fd7afe697c
b79d1bb220a8db5692bee2473bcbab693d788fc6a59f9e42bf7b8db759dcfa96
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,273
summable_of_ratio_norm_eventually_le
Mathlib/Analysis/SpecificLimits/Normed.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
by_cases hr₀ : 0 ≤ r
α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 h : ∀ᶠ (n : ℕ) in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖ ⊢ Summable f
case pos α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 h : ∀ᶠ (n : ℕ) in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖ hr₀ : 0 ≤ r ⊢ Summable f case neg α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α in...
((:c Summable) (:fv _uniq.181949) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.181949) ((:c SeminormedAddCommGroup.toAddCommGroup) (:fv _uniq.181949) (:fv _uniq.181950))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.181949) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.181949) ((:c SeminormedAddCommGr...
[{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.181949))"},{"name":"inst✝","sexp":"((:c CompleteSpace) (:fv _uniq.181949) ((:c PseudoMetricSp...
(:app (:c Summable) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV4))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 4 (:fv FV7)))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"by_cases","sourceEnd":30395,"sourceStart":30387,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hr₀","sourceEnd":30401,"sourceStart":30396,"tag":"identifier"},{"source":":","sourceEnd":30403,"sourceStart":30402,"tag":"atom"}],"kind":"null","source":"hr₀ :","sourceEnd":30403,"...
[]
[{"source":"0 ≤ r","source_end":30411,"source_start":30404,"syntax_kind":"«term_≤_»"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...
136
4
exact
true
1
10
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8f66b33c0c6288350568c07573ff512347d26bf966eaf4afc38dac71e49546e4
434536c297ce3974d509294ec3a95b4cc789a72762607b6472dafbcfeed7a92d
e21b0f5f370fd1f115926bcbef954e08c184f20c16c68595e1279e4f156940a3
75e25c90ad1bb37cdf608c067d29c8155f5e568bfaeba43646c195f883294a75
cat-searcher/leandojo-benchmark-4-random
test
3,274
summable_of_ratio_norm_eventually_le
Mathlib/Analysis/SpecificLimits/Normed.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Filter.eventually_atTop</a>] at h
case pos α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 h : ∀ᶠ (n : ℕ) in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖ hr₀ : 0 ≤ r ⊢ Summable f
case pos α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 h : ∃ a, ∀ b ≥ a, ‖f (b + 1)‖ ≤ r * ‖f b‖ hr₀ : 0 ≤ r ⊢ Summable f
((:c Summable) (:fv _uniq.181949) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.181949) ((:c SeminormedAddCommGroup.toAddCommGroup) (:fv _uniq.181949) (:fv _uniq.181950))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.181949) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.181949) ((:c SeminormedAddCommGr...
[{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.181949))"},{"name":"inst✝","sexp":"((:c CompleteSpace) (:fv _uniq.181949) ((:c PseudoMetricSp...
(:app (:c Summable) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV4))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 4 (:fv FV7)))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"rw","sourceEnd":30419,"sourceStart":30417,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":30421,"sourceStart":30420,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Filter.eventuall...
[]
[{"source":"eventually_atTop","source_end":30437,"source_start":30421,"syntax_kind":"ident"},{"source":"h","source_end":30443,"source_start":30442,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...
136
9
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
15a7239a933319e88bd9d69550209cc3db8f5eac2229a84ac714e6440d030b27
15a93fb8ba20e70a39cb5a3f09bc6a7500bdd87be8407b56991facd8560b32b8
50080ffe00226139f15de3b57490673bc85038c1c5fbcb8a559220b1ac2c6979
a0afa9cf856f62937e3056afba9a324633be9fd14fdc750ef4f9b22e6dd794c1
cat-searcher/leandojo-benchmark-4-random
test
3,275
summable_of_ratio_norm_eventually_le
Mathlib/Analysis/SpecificLimits/Normed.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rcases h with ⟨N, hN⟩
case pos α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 h : ∃ a, ∀ b ≥ a, ‖f (b + 1)‖ ≤ r * ‖f b‖ hr₀ : 0 ≤ r ⊢ Summable f
case pos.intro α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 hr₀ : 0 ≤ r N : ℕ hN : ∀ b ≥ N, ‖f (b + 1)‖ ≤ r * ‖f b‖ ⊢ Summable f
((:c Summable) (:fv _uniq.181949) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.181949) ((:c SeminormedAddCommGroup.toAddCommGroup) (:fv _uniq.181949) (:fv _uniq.181950))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.181949) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.181949) ((:c SeminormedAddCommGr...
[{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.181949))"},{"name":"inst✝","sexp":"((:c CompleteSpace) (:fv _uniq.181949) ((:c PseudoMetricSp...
(:app (:c Summable) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV4))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 4 (:fv FV7)))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"rcases","sourceEnd":30454,"sourceStart":30448,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":10,"semanticRole":"local","source":"h","sourceEnd":30456,"sourceStart":30455,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","...
[]
[{"source":"h","source_end":30456,"source_start":30455,"syntax_kind":"ident"},{"source":"⟨N, hN⟩","source_end":30473,"source_start":30462,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...
136
12
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
39b90710069f770725ce05239509a286430abf81b8af6c09adda634aa0280615
a0afa9cf856f62937e3056afba9a324633be9fd14fdc750ef4f9b22e6dd794c1
08d366f352189c5a5acf6c573404f4f0a758b5c000f6bb0b57be78e0fbb23527
181b8190abab0ae260fb02061c32bf5f61c7a2bcd3eb139f55094d1e578f09da
cat-searcher/leandojo-benchmark-4-random
test
3,276
summable_of_ratio_norm_eventually_le
Mathlib/Analysis/SpecificLimits/Normed.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← @<a>summable_nat_add_iff</a> α _ _ _ _ N]
case pos.intro α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 hr₀ : 0 ≤ r N : ℕ hN : ∀ b ≥ N, ‖f (b + 1)‖ ≤ r * ‖f b‖ ⊢ Summable f
case pos.intro α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 hr₀ : 0 ≤ r N : ℕ hN : ∀ b ≥ N, ‖f (b + 1)‖ ≤ r * ‖f b‖ ⊢ Summable fun n => f (n + N)
((:c Summable) (:fv _uniq.181949) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.181949) ((:c SeminormedAddCommGroup.toAddCommGroup) (:fv _uniq.181949) (:fv _uniq.181950))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.181949) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.181949) ((:c SeminormedAddCommGr...
[{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.181949))"},{"name":"inst✝","sexp":"((:c CompleteSpace) (:fv _uniq.181949) ((:c PseudoMetricSp...
(:app (:c Summable) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV4))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 4 (:fv FV7)))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"rw","sourceEnd":30480,"sourceStart":30478,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":30482,"sourceStart":30481,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":30485,"sourceSt...
[]
[{"source":"@summable_nat_add_iff α _ _ _ _ N","source_end":30520,"source_start":30486,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...
136
13
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4f48302a08cb9f9dfca607a34847e594b80e29b9224315abd3982f2ce186d40e
181b8190abab0ae260fb02061c32bf5f61c7a2bcd3eb139f55094d1e578f09da
530f08471d072dbc9ffd7d9f3f8afd2a2cd9c2b61545b07ad75dac978c276378
ce8c40bb5e00fa7fbc6862a9be7f2e5eca2faaae76958e780642bc6b19052277
cat-searcher/leandojo-benchmark-4-random
test
3,277
summable_of_ratio_norm_eventually_le
Mathlib/Analysis/SpecificLimits/Normed.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine .of_norm_bounded (fun n ↦ ‖f N‖ * r ^ n) (<a>Summable.mul_left</a> _ <| <a>summable_geometric_of_lt_one</a> hr₀ hr₁) fun n ↦ ?_
case pos.intro α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 hr₀ : 0 ≤ r N : ℕ hN : ∀ b ≥ N, ‖f (b + 1)‖ ≤ r * ‖f b‖ ⊢ Summable fun n => f (n + N)
case pos.intro α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 hr₀ : 0 ≤ r N : ℕ hN : ∀ b ≥ N, ‖f (b + 1)‖ ≤ r * ‖f b‖ n : ℕ ⊢ ‖f (n + N)‖ ≤ (fun n => ‖f N‖ * r ^ n) n
((:c Summable) (:fv _uniq.181949) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.181949) ((:c SeminormedAddCommGroup.toAddCommGroup) (:fv _uniq.181949) (:fv _uniq.181950))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.181949) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.181949) ((:c SeminormedAddCommGr...
[{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.181949))"},{"name":"inst✝","sexp":"((:c CompleteSpace) (:fv _uniq.181949) ((:c PseudoMetricSp...
(:app (:c Summable) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV4))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 4 (:lambda n :explicit (:c Nat) (:ap...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"refine","sourceEnd":30532,"sourceStart":30526,"tag":"atom"},{"children":[{"children":[{"source":".","sourceEnd":30534,"sourceStart":30533,"tag":"atom"},{"source":"of_norm_bounded","sourceEnd":30549,"sourceStart":30534,"tag":"identifier"}],"kind":"Lean.Parser.Term.dotIdent","source":".of_norm_bou...
[]
[{"source":".of_norm_bounded (fun n ↦ ‖f N‖ * r ^ n)\n (Summable.mul_left _ <| summable_geometric_of_lt_one hr₀ hr₁) fun n ↦ ?_","source_end":30664,"source_start":30533,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...
136
16
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
33f4f9975031a4e7677131a8508c589ff7aa9778f5846b47b1b970362d124cd6
ce8c40bb5e00fa7fbc6862a9be7f2e5eca2faaae76958e780642bc6b19052277
580bee3a2c729ca626ffd953137f7b6655aef908e7b976ee1546910a9ff87b8d
42310359b768fc347c547ebc42474d6af9e6f738a7133119c17595639ee6a881
cat-searcher/leandojo-benchmark-4-random
test
3,278
summable_of_ratio_norm_eventually_le
Mathlib/Analysis/SpecificLimits/Normed.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only
case pos.intro α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 hr₀ : 0 ≤ r N : ℕ hN : ∀ b ≥ N, ‖f (b + 1)‖ ≤ r * ‖f b‖ n : ℕ ⊢ ‖f (n + N)‖ ≤ (fun n => ‖f N‖ * r ^ n) n
case pos.intro α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 hr₀ : 0 ≤ r N : ℕ hN : ∀ b ≥ N, ‖f (b + 1)‖ ≤ r * ‖f b‖ n : ℕ ⊢ ‖f (n + N)‖ ≤ ‖f N‖ * r ^ n
((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.181949) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.181949) (:fv _uniq.181950)) ((:fv _uniq.181952) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.184107) (:fv _uniq.182397)))) ((:lambda n (:c Nat) ((:c ...
[{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.181949))"},{"name":"inst✝","sexp":"((:c CompleteSpace) (:fv _uniq.181949) ((:c PseudoMetricSp...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:fv FV7) (:ar...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"simp","sourceEnd":30673,"sourceStart":30669,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":30678,"sourceStart":30674,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":306...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...
136
17
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
204f0d64b3a1542e05fb6603d0aabf96df257aa2d227183eb56a3d6e9f6c32d6
42310359b768fc347c547ebc42474d6af9e6f738a7133119c17595639ee6a881
474d6f2fb64f6202b4a1fc099cb53cf41b343456b831e8c4f67099fd49f38f97
a71107c27a4e18bcbfc955a83e92451da745a84635d9baa96f9f4d7f1343c466
cat-searcher/leandojo-benchmark-4-random
test
3,279
summable_of_ratio_norm_eventually_le
Mathlib/Analysis/SpecificLimits/Normed.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
conv_rhs => rw [<a>mul_comm</a>, ← <a>zero_add</a> N]
case pos.intro α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 hr₀ : 0 ≤ r N : ℕ hN : ∀ b ≥ N, ‖f (b + 1)‖ ≤ r * ‖f b‖ n : ℕ ⊢ ‖f (n + N)‖ ≤ ‖f N‖ * r ^ n
case pos.intro α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 hr₀ : 0 ≤ r N : ℕ hN : ∀ b ≥ N, ‖f (b + 1)‖ ≤ r * ‖f b‖ n : ℕ ⊢ ‖f (n + N)‖ ≤ r ^ n * ‖f (0 + N)‖
((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.181949) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.181949) (:fv _uniq.181950)) ((:fv _uniq.181952) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.184107) (:fv _uniq.182397)))) ((:c HMul.hMul) (:c Real) ...
[{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.181949))"},{"name":"inst✝","sexp":"((:c CompleteSpace) (:fv _uniq.181949) ((:c PseudoMetricSp...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:fv FV7) (:ar...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"conv_rhs","sourceEnd":30691,"sourceStart":30683,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":"=>","sourceEnd":30694,"sourceStart":30692,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"sou...
[]
[{"source":"mul_comm","source_end":30707,"source_start":30699,"syntax_kind":"ident"},{"source":"zero_add N","source_end":30723,"source_start":30713,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...
136
18
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
51148df4691f5d8e68841b6394289d298193a6d4d6ce9ce224362bcb89670012
a71107c27a4e18bcbfc955a83e92451da745a84635d9baa96f9f4d7f1343c466
d66021481e471ba25f04a9ef06389b614ab3a8903bf6b3982466666aba75a159
83dfb53cd2de007daaf7ce3f18d849994e0c431d3acf72ccaa546f2a1f178a4c
cat-searcher/leandojo-benchmark-4-random
test
3,280
summable_of_ratio_norm_eventually_le
Mathlib/Analysis/SpecificLimits/Normed.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine <a>le_geom</a> (u := fun n ↦ ‖f (n + N)‖) hr₀ n fun i _ ↦ ?_
case pos.intro α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 hr₀ : 0 ≤ r N : ℕ hN : ∀ b ≥ N, ‖f (b + 1)‖ ≤ r * ‖f b‖ n : ℕ ⊢ ‖f (n + N)‖ ≤ r ^ n * ‖f (0 + N)‖
case pos.intro α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 hr₀ : 0 ≤ r N : ℕ hN : ∀ b ≥ N, ‖f (b + 1)‖ ≤ r * ‖f b‖ n i : ℕ x✝ : i < n ⊢ (fun n => ‖f (n + N)‖) (i + 1) ≤ r * (fun n => ‖f (n + N)‖) i
((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.181949) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.181949) (:fv _uniq.181950)) ((:fv _uniq.181952) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.184107) (:fv _uniq.182397)))) ((:c HMul.hMul) (:c Real) ...
[{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.181949))"},{"name":"inst✝","sexp":"((:c CompleteSpace) (:fv _uniq.181949) ((:c PseudoMetricSp...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:fv FV7) (:ar...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"refine","sourceEnd":30735,"sourceStart":30729,"tag":"atom"},{"children":[{"name":"le_geom","semanticRole":"global","source":"le_geom","sourceEnd":30743,"sourceStart":30736,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":30745,"sourceStart":30744,"tag":"atom"},{"source":"u...
[]
[{"source":"le_geom (u := fun n ↦ ‖f (n + N)‖) hr₀ n fun i _ ↦ ?_","source_end":30799,"source_start":30736,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...
136
24
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8827b7fca7c18c11be45b829f33d90cf855cb48e5c9fd6304706eb7b8f164741
83dfb53cd2de007daaf7ce3f18d849994e0c431d3acf72ccaa546f2a1f178a4c
a626ee1e76feffffdc0a2a975fb2ca8d5db669231dc6ca95a45ec613ace4ecf4
17ea7dbf082a298b36025d2c65680b5b26f8cb0f42ce2c9f6ffe75a2297e9d52
cat-searcher/leandojo-benchmark-4-random
test
3,281
summable_of_ratio_norm_eventually_le
Mathlib/Analysis/SpecificLimits/Normed.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
convert hN (i + N) (N.le_add_left i) using 3
case pos.intro α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 hr₀ : 0 ≤ r N : ℕ hN : ∀ b ≥ N, ‖f (b + 1)‖ ≤ r * ‖f b‖ n i : ℕ x✝ : i < n ⊢ (fun n => ‖f (n + N)‖) (i + 1) ≤ r * (fun n => ‖f (n + N)‖) i
case h.e'_3.h.e'_3.h.e'_1 α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 hr₀ : 0 ≤ r N : ℕ hN : ∀ b ≥ N, ‖f (b + 1)‖ ≤ r * ‖f b‖ n i : ℕ x✝ : i < n ⊢ i + 1 + N = i + N + 1
((:c LE.le) (:c Real) (:c Real.instLE) ((:lambda n (:c Nat) ((:c Norm.norm) (:fv _uniq.181949) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.181949) (:fv _uniq.181950)) ((:fv _uniq.181952) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) 0 (:fv _uniq.182397))))) ((:c HAdd.hAdd) (:c N...
[{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.181949))"},{"name":"inst✝","sexp":"((:c CompleteSpace) (:fv _uniq.181949) ((:c PseudoMetricSp...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:lambda n :explicit (:c Nat) (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV4))))) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"convert","sourceEnd":30811,"sourceStart":30804,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"hN","sourceEnd":30814,"sourceStart":30812,"tag":"identifier"...
[]
[{"source":"hN (i + N) (N.le_add_left i)","source_end":30840,"source_start":30812,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...
136
25
exact
true
1
15
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
18a43ee0db9ea9fac2e2f2c33a514433fff87509c3440ef1d5731d8fb65f32c1
17ea7dbf082a298b36025d2c65680b5b26f8cb0f42ce2c9f6ffe75a2297e9d52
55ff9cc18ce928c3512754f3eb8c3048b732e52ca3518bb45192473671142b56
7d6e9b47b954e0d16244273cae4edc1ed68b23627454a9f7e80101b043a34487
cat-searcher/leandojo-benchmark-4-random
test
3,282
summable_of_ratio_norm_eventually_le
Mathlib/Analysis/SpecificLimits/Normed.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
ac_rfl
case h.e'_3.h.e'_3.h.e'_1 α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 hr₀ : 0 ≤ r N : ℕ hN : ∀ b ≥ N, ‖f (b + 1)‖ ≤ r * ‖f b‖ n i : ℕ x✝ : i < n ⊢ i + 1 + N = i + N + 1
((:c Eq) (:c Nat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.184606) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) (:fv _uniq.182397)) ((:c HAdd.hAdd) (:c Nat) (:c...
[{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.181949))"},{"name":"inst✝","sexp":"((:c CompleteSpace) (:fv _uniq.181949) ((:c PseudoMetricSp...
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"ac_rfl","sourceEnd":30859,"sourceStart":30853,"tag":"atom"}],"kind":"Lean.Parser.Tactic.acRfl","source":"ac_rfl","sourceEnd":30859,"sourceStart":30853,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...
136
26
exact
true
1
15
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f90cf318386e995e6cf5f458bdfac290fb73a02e516f7a35a900edd9395cc214
7d6e9b47b954e0d16244273cae4edc1ed68b23627454a9f7e80101b043a34487
2dd78c9d090141d123f9af8735c699cf9192b0edec0d63080dd4083a3ed0b2a9
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,283
summable_of_ratio_norm_eventually_le
Mathlib/Analysis/SpecificLimits/Normed.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
push_neg at hr₀
case neg α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 h : ∀ᶠ (n : ℕ) in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖ hr₀ : ¬0 ≤ r ⊢ Summable f
case neg α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 h : ∀ᶠ (n : ℕ) in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖ hr₀ : r < 0 ⊢ Summable f
((:c Summable) (:fv _uniq.181949) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.181949) ((:c SeminormedAddCommGroup.toAddCommGroup) (:fv _uniq.181949) (:fv _uniq.181950))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.181949) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.181949) ((:c SeminormedAddCommGr...
[{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.181949))"},{"name":"inst✝","sexp":"((:c CompleteSpace) (:fv _uniq.181949) ((:c PseudoMetricSp...
(:app (:c Summable) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV4))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 4 (:fv FV7)))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"push_neg","sourceEnd":30873,"sourceStart":30865,"tag":"atom"},{"children":[{"children":[{"source":"at","sourceEnd":30876,"sourceStart":30874,"tag":"atom"},{"children":[{"children":[{"contextIndex":11,"semanticRole":"local","source":"hr₀","sourceEnd":30882,"sourceStart":30877,"tag":"identifier"}]...
[]
[{"source":"hr₀","source_end":30882,"source_start":30877,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...
136
31
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0ea8e8d5ee4388b5398aa9587b078959463b1fe2c832c70a313f4d6975e3bb93
8c602aa8d6a7181ce5dbd844a6331781429161182cf4a9970d165eafcb394843
1748b14fdcd5248e425918151823c7b921c1a9382c0cde636c8d877a3173f567
84cf94350b439406e18496ace243568f8bee494cc6f5acc58d772681bc349292
cat-searcher/leandojo-benchmark-4-random
test
3,284
summable_of_ratio_norm_eventually_le
Mathlib/Analysis/SpecificLimits/Normed.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine .of_norm_bounded_eventually_nat 0 <a>summable_zero</a> ?_
case neg α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 h : ∀ᶠ (n : ℕ) in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖ hr₀ : r < 0 ⊢ Summable f
case neg α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 h : ∀ᶠ (n : ℕ) in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖ hr₀ : r < 0 ⊢ ∀ᶠ (i : ℕ) in atTop, ‖f i‖ ≤ 0 i
((:c Summable) (:fv _uniq.181949) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.181949) ((:c SeminormedAddCommGroup.toAddCommGroup) (:fv _uniq.181949) (:fv _uniq.181950))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.181949) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.181949) ((:c SeminormedAddCommGr...
[{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.181949))"},{"name":"inst✝","sexp":"((:c CompleteSpace) (:fv _uniq.181949) ((:c PseudoMetricSp...
(:app (:c Summable) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV4))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 4 (:fv FV7)))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"refine","sourceEnd":30893,"sourceStart":30887,"tag":"atom"},{"children":[{"children":[{"source":".","sourceEnd":30895,"sourceStart":30894,"tag":"atom"},{"source":"of_norm_bounded_eventually_nat","sourceEnd":30925,"sourceStart":30895,"tag":"identifier"}],"kind":"Lean.Parser.Term.dotIdent","source...
[]
[{"source":".of_norm_bounded_eventually_nat 0 summable_zero ?_","source_end":30944,"source_start":30894,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...
136
32
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8f62ed361662cafac8928e39681b7e64697239d263e08290d3f56011c32d2ebe
84cf94350b439406e18496ace243568f8bee494cc6f5acc58d772681bc349292
5543364ae642ac9855b948025f365033ca3534fb64f2a5b6e3158687f5299a6d
43e5286a5a4f3a9761abbbf75e975dcd08be0591856f1cafc2d0683a38f1204e
cat-searcher/leandojo-benchmark-4-random
test
3,285
summable_of_ratio_norm_eventually_le
Mathlib/Analysis/SpecificLimits/Normed.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
filter_upwards [h] with _ hn
case neg α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 h : ∀ᶠ (n : ℕ) in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖ hr₀ : r < 0 ⊢ ∀ᶠ (i : ℕ) in atTop, ‖f i‖ ≤ 0 i
case h α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 h : ∀ᶠ (n : ℕ) in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖ hr₀ : r < 0 a✝ : ℕ hn : ‖f (a✝ + 1)‖ ≤ r * ‖f a✝‖ ⊢ ‖f a✝‖ ≤ 0 a✝
((:c Filter.Eventually) (:c Nat) (:lambda i (:c Nat) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.181949) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.181949) (:fv _uniq.181950)) ((:fv _uniq.181952) 0)) ((:c OfNat.ofNat) (:forall _ (:c Nat) (:c Real)) (:lit 0) ((:c Zero.toOfNat0) (:forall _ (:c N...
[{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.181949))"},{"name":"inst✝","sexp":"((:c CompleteSpace) (:fv _uniq.181949) ((:c PseudoMetricSp...
(:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda i :explicit (:c Nat) (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV4)) (:arg :i...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"filter_upwards","sourceEnd":30963,"sourceStart":30949,"tag":"atom"},{"children":[{"source":"[","sourceEnd":30965,"sourceStart":30964,"tag":"atom"},{"children":[{"contextIndex":10,"semanticRole":"local","source":"h","sourceEnd":30966,"sourceStart":30965,"tag":"identifier"}],"kind":"null","source"...
[]
[{"source":"h","source_end":30966,"source_start":30965,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...
136
33
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
82de6568f25c4d724dc8426ef57935528ecaa4412eea4b5a82149fa6df21c8ad
43e5286a5a4f3a9761abbbf75e975dcd08be0591856f1cafc2d0683a38f1204e
416d14a4e25f952cfc77e0b1da3fe008bebc8b87c4b4a41d2081a413aa790c9a
3574f75847f9df2b342b0a99bfc66b267397d8f5dc792423a2a1b9c0903902b0
cat-searcher/leandojo-benchmark-4-random
test
3,286
summable_of_ratio_norm_eventually_le
Mathlib/Analysis/SpecificLimits/Normed.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
by_contra! h
case h α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 h : ∀ᶠ (n : ℕ) in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖ hr₀ : r < 0 a✝ : ℕ hn : ‖f (a✝ + 1)‖ ≤ r * ‖f a✝‖ ⊢ ‖f a✝‖ ≤ 0 a✝
case h α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 h✝ : ∀ᶠ (n : ℕ) in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖ hr₀ : r < 0 a✝ : ℕ hn : ‖f (a✝ + 1)‖ ≤ r * ‖f a✝‖ h : 0 a✝ < ‖f a✝‖ ⊢ False
((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.181949) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.181949) (:fv _uniq.181950)) ((:fv _uniq.181952) (:fv _uniq.186090))) ((:c OfNat.ofNat) (:forall _ (:c Nat) (:c Real)) (:lit 0) ((:c Zero.toOfNat0) (:forall _ (:c Nat) (:c Real)) ((:c Pi.instZero) (:c...
[{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.181949))"},{"name":"inst✝","sexp":"((:c CompleteSpace) (:fv _uniq.181949) ((:c PseudoMetricSp...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:fv FV7) (:ar...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"by_contra!","sourceEnd":30992,"sourceStart":30982,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":30994,"sourceStart":30993,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"h","sourceEnd":30994,"sourceStart":30993,"tag":"node"}],"kind":"nul...
[]
[{"source":"h","source_end":30994,"source_start":30993,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...
136
34
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e1e66a9266bcc1676755e0889f80c7894395223ffb836c241d6b7afe36d3f76c
3574f75847f9df2b342b0a99bfc66b267397d8f5dc792423a2a1b9c0903902b0
d018fbf160751ebd05cfab27a8e0e427d28df991abdec4965b6930805cf6100d
8fb89a1c97e7fc5911a3e6855ff77949dfcfdbffe7b2d7bd7b5d881cb1de4b0a
cat-searcher/leandojo-benchmark-4-random
test
3,287
summable_of_ratio_norm_eventually_le
Mathlib/Analysis/SpecificLimits/Normed.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact not_lt.mpr (<a>norm_nonneg</a> _) (<a>lt_of_le_of_lt</a> hn <| <a>mul_neg_of_neg_of_pos</a> hr₀ h)
case h α✝ : Type u_1 β : Type u_2 ι : Type u_3 α : Type u_4 inst✝¹ : SeminormedAddCommGroup α inst✝ : CompleteSpace α f : ℕ → α r : ℝ hr₁ : r < 1 h✝ : ∀ᶠ (n : ℕ) in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖ hr₀ : r < 0 a✝ : ℕ hn : ‖f (a✝ + 1)‖ ≤ r * ‖f a✝‖ h : 0 a✝ < ‖f a✝‖ ⊢ False
(:c False)
[{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.181949))"},{"name":"inst✝","sexp":"((:c CompleteSpace) (:fv _uniq.181949) ((:c PseudoMetricSp...
(:c False)
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"exact","sourceEnd":31004,"sourceStart":30999,"tag":"atom"},{"children":[{"source":"not_lt.mpr","sourceEnd":31015,"sourceStart":31005,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":31017,"sourceStart":31016,"tag":"atom"},{"children":[{"name":"norm_nonneg","semanticRole":"...
[]
[{"source":"not_lt.mpr (norm_nonneg _) (lt_of_le_of_lt hn <| mul_neg_of_neg_of_pos hr₀ h)","source_end":31084,"source_start":31005,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.180681","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.180684","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...
136
35
exact
true
1
14
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e351df378098a86059ace2fdff4fc7eb10a4d0d9f91549cd9a8c9fce57e61d66
8fb89a1c97e7fc5911a3e6855ff77949dfcfdbffe7b2d7bd7b5d881cb1de4b0a
b4e655c648557934af99a1247a73fc75f67d8ae84db4a5bf76cc358c3eb2d934
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,288
CategoryTheory.whisker_eq
Mathlib/CategoryTheory/Category/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [w]
C : Type u inst✝ : Category.{v, u} C X Y Z : C f : X ⟶ Y g h : Y ⟶ Z w : g = h ⊢ f ≫ g = f ≫ h
((:c Eq) ((:c Quiver.Hom) (:fv _uniq.7700) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.7700) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.7700) (:fv _uniq.7703))) (:fv _uniq.7705) (:fv _uniq.7709)) ((:c CategoryTheory.CategoryStruct.comp) (:fv _uniq.7700) ((:c CategoryTheory.Category.toCategory...
[{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.7700))"},{"name":"X","sexp":"(:fv _uniq.7700)"},{"name":"Y","sexp":"(:fv _uniq.7700)"},{"name":"Z","sexp":"(:fv _uniq.7700)"},{"name":"f","sexp":"((:c Quiver.Hom) (:fv _uniq.7700) ((:c CategoryTheory.CategoryStruct.t...
(: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 FV2)) (:arg :explicit 3 (:fv FV4)))) (:arg :explicit 1 (:app (:c CategoryTheory.CategoryStruct.comp) (:arg :implicit-type ...
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{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":8692,"sourceStart":8690,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8694,"sourceStart":8693,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag...
[]
[{"source":"w","source_end":8695,"source_start":8694,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7700","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.7703","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"internal_...
40
2
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e017196038123efe51325cb07a2126d7092280ec630b46be785c879eb90f2db6
a86a644cca4e54568a8f28001a13daae58e4230002a3207f8d8ac075dce8b79b
d819edbb6843ab08e21642b6a1927ae90235adb22c2ca3784556bb1565fee53e
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
3,289
IntermediateField.AdjoinSimple.norm_gen_eq_one
Mathlib/RingTheory/Norm.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Algebra.norm_eq_one_of_not_exists_basis</a>]
R : Type u_1 S : Type u_2 T : Type u_3 inst✝⁷ : CommRing R inst✝⁶ : Ring S inst✝⁵ : Algebra R S K : Type u_4 L : Type u_5 F : Type u_6 inst✝⁴ : Field K inst✝³ : Field L inst✝² : Field F inst✝¹ : Algebra K L inst✝ : Algebra K F ι : Type w x : L hx : ¬IsIntegral K x ⊢ (norm K) (AdjoinSimple.gen K x) = 1
case h R : Type u_1 S : Type u_2 T : Type u_3 inst✝⁷ : CommRing R inst✝⁶ : Ring S inst✝⁵ : Algebra R S K : Type u_4 L : Type u_5 F : Type u_6 inst✝⁴ : Field K inst✝³ : Field L inst✝² : Field F inst✝¹ : Algebra K L inst✝ : Algebra K F ι : Type w x : L hx : ¬IsIntegral K x ⊢ ¬∃ s, Nonempty (Basis { x_1 // x_1 ∈ s } K ↥K⟮...
((:c Eq) (:fv _uniq.99697) ((:c DFunLike.coe) ((:c MonoidHom) ((:c Subtype) (:fv _uniq.99700) (:lambda x (:fv _uniq.99700) ((:c Membership.mem) (:fv _uniq.99700) ((:c IntermediateField) (:fv _uniq.99697) (:fv _uniq.99700) (:fv _uniq.99706) (:fv _uniq.99709) (:fv _uniq.99799)) ((:c SetLike.instMembership) ((:c Intermedi...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"T","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.99372))"},{"name":"inst✝⁶","sexp":"((:c Ring) (:fv _uniq.99375))"},{"name":"inst✝⁵","sexp":"((:c Algebra) (:fv _uniq.99372) (:fv _uniq.99375) ((:c C...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MonoidHom) (:arg :explicit 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV7)) (:arg :explicit 1 (:lambda x :explicit (:fv FV7) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV7)) (:arg ...
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{"children":[{"source":"rw","sourceEnd":8882,"sourceStart":8880,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8884,"sourceStart":8883,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Algebra.norm_eq_one_...
[]
[{"source":"norm_eq_one_of_not_exists_basis","source_end":8915,"source_start":8884,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.99372","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.99375","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
56
4
exact
true
1
17
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
cc39f38b83f63ca249ee4ce5e6c7bcaf71597c9b524829d0f8b29c49eb9bfa48
004bd85a2b8bdb0da9ccd7f68c3b7cd2f546c7092b2eb2de0df56da85f7379b2
bdd9a2d3166b52bb87cbd1854f2f624169fa076432b45393ef4fa848c7f96d3e
db0b1eacf7a9e16422b40e8f985278784b3228bb66e41f19ae66ea39da16807f
cat-searcher/leandojo-benchmark-4-random
test
3,290
IntermediateField.AdjoinSimple.norm_gen_eq_one
Mathlib/RingTheory/Norm.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
contrapose! hx
case h R : Type u_1 S : Type u_2 T : Type u_3 inst✝⁷ : CommRing R inst✝⁶ : Ring S inst✝⁵ : Algebra R S K : Type u_4 L : Type u_5 F : Type u_6 inst✝⁴ : Field K inst✝³ : Field L inst✝² : Field F inst✝¹ : Algebra K L inst✝ : Algebra K F ι : Type w x : L hx : ¬IsIntegral K x ⊢ ¬∃ s, Nonempty (Basis { x_1 // x_1 ∈ s } K ↥K⟮...
case h R : Type u_1 S : Type u_2 T : Type u_3 inst✝⁷ : CommRing R inst✝⁶ : Ring S inst✝⁵ : Algebra R S K : Type u_4 L : Type u_5 F : Type u_6 inst✝⁴ : Field K inst✝³ : Field L inst✝² : Field F inst✝¹ : Algebra K L inst✝ : Algebra K F ι : Type w x : L hx : ∃ s, Nonempty (Basis { x_1 // x_1 ∈ s } K ↥K⟮x⟯) ⊢ IsIntegral K ...
((:c Not) ((:c Exists) ((:c Finset) ((:c Subtype) (:fv _uniq.99700) (:lambda x (:fv _uniq.99700) ((:c Membership.mem) (:fv _uniq.99700) ((:c IntermediateField) (:fv _uniq.99697) (:fv _uniq.99700) (:fv _uniq.99706) (:fv _uniq.99709) (:fv _uniq.99799)) ((:c SetLike.instMembership) ((:c IntermediateField) (:fv _uniq.99697...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"T","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.99372))"},{"name":"inst✝⁶","sexp":"((:c Ring) (:fv _uniq.99375))"},{"name":"inst✝⁵","sexp":"((:c Algebra) (:fv _uniq.99372) (:fv _uniq.99375) ((:c C...
(:app (:c Not) (:arg :explicit 0 (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV7)) (:arg :explicit 1 (:lambda x :explicit (:fv FV7) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV7)) (:arg :implicit-type 1 (:app (:c IntermediateFie...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.99372","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.99375","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"contrapose!","sourceEnd":8930,"sourceStart":8919,"tag":"atom"},{"children":[{"contextIndex":17,"semanticRole":"local","source":"hx","sourceEnd":8933,"sourceStart":8931,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"null","source":"hx","sourceEnd":8933,"source...
[]
[{"source":"hx","source_end":8933,"source_start":8931,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.99372","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.99375","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
56
7
exact
true
1
17
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
58b816f4db67e3698f565dda5534aaebe7189ada0abe72faa51f3627976fb6a1
db0b1eacf7a9e16422b40e8f985278784b3228bb66e41f19ae66ea39da16807f
018b0b5d96b1fb0026063b130c132cd261885f9ccd265695980caf8fd87d4780
e70f212e17f38070fa6f7799b714153b22bc014dad8028ebbd49ab47daefa609