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cat-searcher/leandojo-benchmark-4-random | test | 2,368 | Finite.isDomain_to_isField | Mathlib/RingTheory/LittleWedderburn.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let _ := <a>littleWedderburn</a> D | case intro
D : Type u_1
inst✝² : Finite D
inst✝¹ : Ring D
inst✝ : IsDomain D
val✝ : Fintype D
x✝ : DivisionRing D := divisionRingOfIsDomain D
⊢ IsField D | case intro
D : Type u_1
inst✝² : Finite D
inst✝¹ : Ring D
inst✝ : IsDomain D
val✝ : Fintype D
x✝¹ : DivisionRing D := divisionRingOfIsDomain D
x✝ : Field D := littleWedderburn D
⊢ IsField D | ((:c IsField) (:fv _uniq.86192) ((:c Ring.toSemiring) (:fv _uniq.86192) (:fv _uniq.86194))) | [{"name":"D","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c Finite) (:fv _uniq.86192))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.86192))"},{"name":"inst✝","sexp":"((:c IsDomain) (:fv _uniq.86192) ((:c Ring.toSemiring) (:fv _uniq.86192) (:fv _uniq.86194)))"},{"name":"val✝","sexp":"((:c Fintype) (:fv _u... | (:app (:c IsField) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1)))))) | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.86192","is_instance":false,"is_let":false,"name":"D","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.86193","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Finite) (:arg :explicit... | {"children":[{"source":"let","sourceEnd":7979,"sourceStart":7976,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"_","sourceEnd":7981,"sourceStart":7980,"tag":"atom"}],"kind":"Lean.Parser.Term.hole","source":"_","sourceEnd":7981,"sourceStart":7980,"tag":"node"},{"children":[],"kind":"null","source":"","t... | [] | [{"source":"littleWedderburn D","source_end":8003,"source_start":7985,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.86192","is_instance":false,"is_let":false,"user_name":"D"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.86193","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":... | 18 | 9 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c7106358f2b6440b337251449b651b22d04ab9209b8620876d73eafab5629860 | 2bf0c5093a68299bf04e7be2f9f156b0714b58050103895e104574ba401062f3 | 9bd36bcd6f2f200bf02819875623d32789dda2ed4d1d87c3833ee8abea8cd340 | b76f4ec67513aaf9716c2df6e1798e0288c16af3e4e676d801747021071c515c |
cat-searcher/leandojo-benchmark-4-random | test | 2,369 | Finite.isDomain_to_isField | Mathlib/RingTheory/LittleWedderburn.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Field.toIsField</a> D | case intro
D : Type u_1
inst✝² : Finite D
inst✝¹ : Ring D
inst✝ : IsDomain D
val✝ : Fintype D
x✝¹ : DivisionRing D := divisionRingOfIsDomain D
x✝ : Field D := littleWedderburn D
⊢ IsField D | ((:c IsField) (:fv _uniq.86192) ((:c Ring.toSemiring) (:fv _uniq.86192) (:fv _uniq.86194))) | [{"name":"D","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c Finite) (:fv _uniq.86192))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.86192))"},{"name":"inst✝","sexp":"((:c IsDomain) (:fv _uniq.86192) ((:c Ring.toSemiring) (:fv _uniq.86192) (:fv _uniq.86194)))"},{"name":"val✝","sexp":"((:c Fintype) (:fv _u... | (:app (:c IsField) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1)))))) | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.86192","is_instance":false,"is_let":false,"name":"D","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.86193","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Finite) (:arg :explicit... | {"children":[{"source":"exact","sourceEnd":8011,"sourceStart":8006,"tag":"atom"},{"children":[{"name":"Field.toIsField","semanticRole":"global","source":"Field.toIsField","sourceEnd":8027,"sourceStart":8012,"tag":"identifier"},{"children":[{"contextIndex":1,"semanticRole":"local","source":"D","sourceEnd":8029,"sourceSt... | [] | [{"source":"Field.toIsField D","source_end":8029,"source_start":8012,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.86192","is_instance":false,"is_let":false,"user_name":"D"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.86193","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":... | 18 | 10 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d7b406f787e617ab820cc58a1ff3c9a3143ff05fa98748be8afbcb1838cd26aa | b76f4ec67513aaf9716c2df6e1798e0288c16af3e4e676d801747021071c515c | 74f8da49af1e276328639b03e48d618f008069889056779e06eec8a1e52dfadf | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,370 | Filter.iInf_principal_finite | Mathlib/Order/Filter/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | lift s to <a>Finset</a> ι using hs | α : Type u
β : Type v
γ : Type w
δ : Type u_1
ι✝ : Sort x
f✝ g : Filter α
s✝ t : Set α
ι : Type w
s : Set ι
hs : s.Finite
f : ι → Set α
⊢ ⨅ i ∈ s, 𝓟 (f i) = 𝓟 (⋂ i ∈ s, f i) | case intro
α : Type u
β : Type v
γ : Type w
δ : Type u_1
ι✝ : Sort x
f✝ g : Filter α
s✝ t : Set α
ι : Type w
f : ι → Set α
s : Finset ι
⊢ ⨅ i ∈ ↑s, 𝓟 (f i) = 𝓟 (⋂ i ∈ ↑s, f i) | ((:c Eq) ((:c Filter) (:fv _uniq.87921)) ((:c iInf) ((:c Filter) (:fv _uniq.87921)) (:fv _uniq.88136) ((:c CompleteLattice.toInfSet) ((:c Filter) (:fv _uniq.87921)) ((:c Filter.instCompleteLatticeFilter) (:fv _uniq.87921))) (:lambda i (:fv _uniq.88136) ((:c iInf) ((:c Filter) (:fv _uniq.87921)) ((:c Membership.mem) (:f... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"δ","sexp":"(:sort (+ u_1 1))"},{"name":"ι✝","sexp":"(:sort x)"},{"name":"f✝","sexp":"((:c Filter) (:fv _uniq.87921))"},{"name":"g","sexp":"((:c Filter) (:fv _uniq.87921))"},{"name":"s✝","sexp":"((... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c iInf) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:fv FV10)) (:arg :instance 2 (:instance-of (:app (:c InfSet) (:arg :explicit 0 (:app (:c Filter) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.87921","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.87923","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"lift","sourceEnd":50023,"sourceStart":50019,"tag":"atom"},{"contextIndex":11,"semanticRole":"local","source":"s","sourceEnd":50025,"sourceStart":50024,"tag":"identifier"},{"source":"to","sourceEnd":50028,"sourceStart":50026,"tag":"atom"},{"children":[{"name":"Finset","semanticRole":"global","sou... | [] | [{"source":"s","source_end":50025,"source_start":50024,"syntax_kind":"ident"},{"source":"Finset ι","source_end":50038,"source_start":50029,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hs","source_end":50047,"source_start":50045,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.87921","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.87923","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 327 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5f21dcb9a4a00b8dedba12a859d7e8fb281392a9ac7899543b11043716a909ca | 12b525739fbce5f2770404e9f9768957aed543e1dc626fa087b7279eedaa8794 | 7a47904265ebb9c8bd9ddabcdd8d10443f7b2c9fb42dfa2602668a2ee4941a0a | 6051037819280fafef318ac54b03b54657e8c109fd743acc66ea64fb5e1254de |
cat-searcher/leandojo-benchmark-4-random | test | 2,371 | Filter.iInf_principal_finite | Mathlib/Order/Filter/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact mod_cast <a>Filter.iInf_principal_finset</a> s f | case intro
α : Type u
β : Type v
γ : Type w
δ : Type u_1
ι✝ : Sort x
f✝ g : Filter α
s✝ t : Set α
ι : Type w
f : ι → Set α
s : Finset ι
⊢ ⨅ i ∈ ↑s, 𝓟 (f i) = 𝓟 (⋂ i ∈ ↑s, f i) | ((:c Eq) ((:c Filter) (:fv _uniq.87921)) ((:c iInf) ((:c Filter) (:fv _uniq.87921)) (:fv _uniq.88136) ((:c CompleteLattice.toInfSet) ((:c Filter) (:fv _uniq.87921)) ((:c Filter.instCompleteLatticeFilter) (:fv _uniq.87921))) (:lambda i (:fv _uniq.88136) ((:c iInf) ((:c Filter) (:fv _uniq.87921)) ((:c Membership.mem) (:f... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"δ","sexp":"(:sort (+ u_1 1))"},{"name":"ι✝","sexp":"(:sort x)"},{"name":"f✝","sexp":"((:c Filter) (:fv _uniq.87921))"},{"name":"g","sexp":"((:c Filter) (:fv _uniq.87921))"},{"name":"s✝","sexp":"((... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c iInf) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:fv FV10)) (:arg :instance 2 (:instance-of (:app (:c InfSet) (:arg :explicit 0 (:app (:c Filter) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.87921","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.87923","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":50055,"sourceStart":50050,"tag":"atom"},{"children":[{"source":"mod_cast","sourceEnd":50064,"sourceStart":50056,"tag":"atom"},{"children":[{"name":"Filter.iInf_principal_finset","semanticRole":"global","source":"iInf_principal_finset","sourceEnd":50086,"sourceStart":50065,"tag... | [] | [{"source":"mod_cast iInf_principal_finset s f","source_end":50090,"source_start":50056,"syntax_kind":"Lean.modCast"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.87921","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.87923","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 327 | 5 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e1c8e3936b842ead97283a6abee7a829a34b0ee95241233fd84b2fc100a763f4 | 6051037819280fafef318ac54b03b54657e8c109fd743acc66ea64fb5e1254de | ecd17c5a507c8ad1b2de39536d9cb04ffac8503595d56657dd8ca8d65b305c15 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,372 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h_summable : ∀ᵐ x ∂μ, <a>Summable</a> fun i : ℕ => f (i + 1) x - f i x := by have h1 : ∀ n, <a>MeasureTheory.snorm'</a> (fun x => ∑ i ∈ <a>Finset.range</a> (n + 1), ‖f (i + 1) x - f i x‖) p μ ≤ ∑' i, B i := <a>_private.Mathlib.MeasureTheory.Function.LpSpace.0.MeasureTheory.Lp.snorm'_sum_norm_sub_le_tsum_of_cauchy_... | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | ((:c Filter.Eventually) (:fv _uniq.766464) (:lambda x (:fv _uniq.766464) ((:c Exists) (:fv _uniq.766467) (:lambda l (:fv _uniq.766467) ((:c Filter.Tendsto) (:c Nat) (:fv _uniq.766467) (:lambda n (:c Nat) ((:fv _uniq.768013) 0 2)) ((:c Filter.atTop) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemir... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda l :explicit (:fv FV1) (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":79021,"sourceStart":79017,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h_summable","sourceEnd":79032,"sourceStart":79022,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h_summable","sourceEnd":79032,"sourceStart":... | [] | [{"source":"∀ᵐ x ∂μ, Summable fun i : ℕ => f (i + 1) x - f i x","source_end":79094,"source_start":79035,"syntax_kind":"MeasureTheory.«term∀ᵐ_∂_,_»"},{"source":"∀ n, snorm' (fun x => ∑ i ∈ Finset.range (n + 1), ‖f (i + 1) x - f i x‖) p μ ≤ ∑' i, B i","source_end":79224,"source_start":79121,"syntax_kind":"Lean.Parser.Ter... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 4 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6b1a6646f0a9447b918491130042e232f21415f6737f915fd40e254a4e24f87b | bcc59d6dbf834d14d6356f96a942fd21f393578549d3cf274d18ade72ed3cc4d | fb6bc930d988aabecc7e0dc69e469537b4350d023b19d73b1cb5dabb99209abf | d8b40438b82b37e218b1b65929412228a9618e7f869bc4b9c6a4da4d9c156e87 |
cat-searcher/leandojo-benchmark-4-random | test | 2,373 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h : ∀ᵐ x ∂μ, ∃ l : E, atTop.Tendsto (fun n => ∑ i ∈ <a>Finset.range</a> n, (f (i + 1) x - f i x)) (𝓝 l) := by refine h_summable.mono fun x hx => ?_ let hx_sum := hx.hasSum.tendsto_sum_nat exact ⟨∑' i, (f (i + 1) x - f i x), hx_sum⟩ | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | ((:c Filter.Eventually) (:fv _uniq.766464) (:lambda x (:fv _uniq.766464) ((:c Exists) (:fv _uniq.766467) (:lambda l (:fv _uniq.766467) ((:c Filter.Tendsto) (:c Nat) (:fv _uniq.766467) (:lambda n (:c Nat) ((:fv _uniq.768013) 0 2)) ((:c Filter.atTop) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemir... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda l :explicit (:fv FV1) (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":79943,"sourceStart":79939,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":79945,"sourceStart":79944,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":79945,"sourceStart":79944,"tag":"node"... | [] | [{"source":"∀ᵐ x ∂μ, ∃ l : E,\n atTop.Tendsto (fun n => ∑ i ∈ Finset.range n, (f (i + 1) x - f i x)) (𝓝 l)","source_end":80066,"source_start":79952,"syntax_kind":"MeasureTheory.«term∀ᵐ_∂_,_»"},{"source":"h_summable.mono fun x hx => ?_","source_end":80114,"source_start":80084,"syntax_kind":"Lean.Parser.Term.app"},... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 11 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 997167e37d51c75ca692629b75d15e30180d49a949864d80ec94940e46bf51ca | d8b40438b82b37e218b1b65929412228a9618e7f869bc4b9c6a4da4d9c156e87 | c00569938ff1610618cf6bfd8b84b487ad8e2dd6901ebdeb1e979eb49cf660e4 | 48f24cc8e5d97f28f34c0e8ef466a2f90133c9d1e7f699bf2c030df1e2f8bdc3 |
cat-searcher/leandojo-benchmark-4-random | test | 2,374 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine h.mono fun x hx => ?_ | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | ((:c Filter.Eventually) (:fv _uniq.766464) (:lambda x (:fv _uniq.766464) ((:c Exists) (:fv _uniq.766467) (:lambda l (:fv _uniq.766467) ((:c Filter.Tendsto) (:c Nat) (:fv _uniq.766467) (:lambda n (:c Nat) ((:fv _uniq.768013) 0 2)) ((:c Filter.atTop) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemir... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda l :explicit (:fv FV1) (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":80221,"sourceStart":80215,"tag":"atom"},{"children":[{"source":"h.mono","sourceEnd":80228,"sourceStart":80222,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":80232,"sourceStart":80229,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_lo... | [] | [{"source":"h.mono fun x hx => ?_","source_end":80243,"source_start":80222,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 16 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d3ab9a82fd124f9efc34bf30b7f4753ae50feb9b2b011b1813850f068a4574fe | 48f24cc8e5d97f28f34c0e8ef466a2f90133c9d1e7f699bf2c030df1e2f8bdc3 | 006ccc17282fb6d6edd2f31dd2163d4c462b2ae4168ef5cef18cae22178358c1 | ff7903ab89146f4110095128caa6a100af510f3b57996d43255f9d039a64ad5d |
cat-searcher/leandojo-benchmark-4-random | test | 2,375 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases' hx with l hx | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | case intro
α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ... | ((:c Exists) (:fv _uniq.766467) (:lambda l (:fv _uniq.766467) ((:c Filter.Tendsto) (:c Nat) (:fv _uniq.766467) (:lambda n (:c Nat) ((:fv _uniq.768013) 0 (:fv _uniq.773937))) ((:c Filter.atTop) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSe... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda l :explicit (:fv FV1) (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:lambda n :explicit (:c Nat) (:app (:fv FV15) (:arg :explicit 0 0) (:arg :explicit 1 (:fv FV24))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"cases'","sourceEnd":80252,"sourceStart":80246,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":25,"semanticRole":"local","source":"hx","sourceEnd":80255,"sourceStart":80253,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget",... | [] | [{"source":"hx","source_end":80255,"source_start":80253,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 17 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 95e210b453ab1dbfdd8525e060b719cb562f55e7d696e1a3226d6f056c8af612 | ff7903ab89146f4110095128caa6a100af510f3b57996d43255f9d039a64ad5d | 740ae5071d8589cf0abecbd208d99e41bc26ba8e4ded119dceaab4de4ac441a4 | 64296a766922572f0b63f5371c6e90e9a5c23ea80d0d0491145088571e0f66c6 |
cat-searcher/leandojo-benchmark-4-random | test | 2,376 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h_rw_sum : (fun n => ∑ i ∈ <a>Finset.range</a> n, (f (i + 1) x - f i x)) = fun n => f n x - f 0 x := by ext1 n change (∑ i ∈ <a>Finset.range</a> n, ((fun m => f m x) (i + 1) - (fun m => f m x) i)) = f n x - f 0 x rw [<a>Finset.sum_range_sub</a> (fun m => f m x)] | case intro
α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ... | case intro
α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ... | ((:c Exists) (:fv _uniq.766467) (:lambda l (:fv _uniq.766467) ((:c Filter.Tendsto) (:c Nat) (:fv _uniq.766467) (:lambda n (:c Nat) ((:fv _uniq.768013) 0 (:fv _uniq.773937))) ((:c Filter.atTop) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSe... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda l :explicit (:fv FV1) (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:lambda n :explicit (:c Nat) (:app (:fv FV15) (:arg :explicit 0 0) (:arg :explicit 1 (:fv FV24))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":80272,"sourceStart":80268,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h_rw_sum","sourceEnd":80281,"sourceStart":80273,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h_rw_sum","sourceEnd":80281,"sourceStart":8027... | [] | [{"source":"(fun n => ∑ i ∈ Finset.range n, (f (i + 1) x - f i x)) = fun n => f n x - f 0 x","source_end":80373,"source_start":80290,"syntax_kind":"«term_=_»"},{"source":"(∑ i ∈ Finset.range n, ((fun m => f m x) (i + 1) - (fun m => f m x) i)) = f n x - f 0 x","source_end":80499,"source_start":80408,"syntax_kind":"«term... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 18 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e351fe72da760a7b32988ccf23052d08a40f6c72c6bd1d19333b669308db6e6b | 64296a766922572f0b63f5371c6e90e9a5c23ea80d0d0491145088571e0f66c6 | b5329f656eecc8a021a71fb7d6056b7f8100cb1ef8fee82244e9ba357fe461c0 | af810007a66494626374edfd2a4983bd9467917f28c410f50b62cdcbde2f4aff |
cat-searcher/leandojo-benchmark-4-random | test | 2,377 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [h_rw_sum] at hx | case intro
α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ... | case intro
α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ... | ((:c Exists) (:fv _uniq.766467) (:lambda l (:fv _uniq.766467) ((:c Filter.Tendsto) (:c Nat) (:fv _uniq.766467) (:lambda n (:c Nat) ((:fv _uniq.768013) 0 (:fv _uniq.773937))) ((:c Filter.atTop) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSe... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda l :explicit (:fv FV1) (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:lambda n :explicit (:c Nat) (:app (:fv FV15) (:arg :explicit 0 0) (:arg :explicit 1 (:fv FV24))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":80551,"sourceStart":80549,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":80553,"sourceStart":80552,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":27,"seman... | [] | [{"source":"h_rw_sum","source_end":80561,"source_start":80553,"syntax_kind":"ident"},{"source":"hx","source_end":80568,"source_start":80566,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 25 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7b818f111e84921e8275062e773edde208b25f23ee7b79dc42a53d97629fb85e | af810007a66494626374edfd2a4983bd9467917f28c410f50b62cdcbde2f4aff | 0d0cfe8ef52068871d75a600b3261911b2262ae3e80d2be7600dab6e8109c3a1 | b67998fca962aa338af5859f6fb55029d0428c3559506bba981a77067a67ae4f |
cat-searcher/leandojo-benchmark-4-random | test | 2,378 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hf_rw : (fun n => f n x) = fun n => f n x - f 0 x + f 0 x := by ext1 n abel | case intro
α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ... | case intro
α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ... | ((:c Exists) (:fv _uniq.766467) (:lambda l (:fv _uniq.766467) ((:c Filter.Tendsto) (:c Nat) (:fv _uniq.766467) (:lambda n (:c Nat) ((:fv _uniq.768013) 0 (:fv _uniq.773937))) ((:c Filter.atTop) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSe... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda l :explicit (:fv FV1) (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:lambda n :explicit (:c Nat) (:app (:fv FV15) (:arg :explicit 0 0) (:arg :explicit 1 (:fv FV24))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":80575,"sourceStart":80571,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hf_rw","sourceEnd":80581,"sourceStart":80576,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hf_rw","sourceEnd":80581,"sourceStart":80576,"tag... | [] | [{"source":"(fun n => f n x) = fun n => f n x - f 0 x + f 0 x","source_end":80633,"source_start":80584,"syntax_kind":"«term_=_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 28 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ad68b81a64e26168bca0a204e1b5c175e5b8d95bd4835a59970f673298563891 | b67998fca962aa338af5859f6fb55029d0428c3559506bba981a77067a67ae4f | 203452013f75cd6328adb73fa0c9a8c8c8c95620163f0efbbb8159af8acce7ff | 8630632f39b110f443f07290a85b8e047786f1084d4d3c0e9cdc0b1f303a72c7 |
cat-searcher/leandojo-benchmark-4-random | test | 2,379 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hf_rw] | case intro
α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ... | case intro
α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ... | ((:c Exists) (:fv _uniq.766467) (:lambda l (:fv _uniq.766467) ((:c Filter.Tendsto) (:c Nat) (:fv _uniq.766467) (:lambda n (:c Nat) ((:fv _uniq.768013) 0 (:fv _uniq.773937))) ((:c Filter.atTop) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSe... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda l :explicit (:fv FV1) (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:lambda n :explicit (:c Nat) (:app (:fv FV15) (:arg :explicit 0 0) (:arg :explicit 1 (:fv FV24))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":80664,"sourceStart":80662,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":80666,"sourceStart":80665,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":28,"seman... | [] | [{"source":"hf_rw","source_end":80671,"source_start":80666,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 33 | exact | true | 1 | 28 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eaac3a95c6b4bddc0e7063643a4b1e9943d217640064cb2fc0168c3184ceace5 | 8630632f39b110f443f07290a85b8e047786f1084d4d3c0e9cdc0b1f303a72c7 | 1da8047e8c48a2edd8a4e5eab947d3b428b642a3936324be29b47dfc214eec84 | ffe182098d5a67d5e45c17458b25f93648d0541dd8d1534ecbfd965dbb282149 |
cat-searcher/leandojo-benchmark-4-random | test | 2,380 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨l + f 0 x, <a>Filter.Tendsto.add_const</a> _ hx⟩ | case intro
α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ... | ((:c Exists) (:fv _uniq.766467) (:lambda l (:fv _uniq.766467) ((:c Filter.Tendsto) (:c Nat) (:fv _uniq.766467) (:lambda n (:c Nat) ((:c HAdd.hAdd) (:fv _uniq.766467) (:fv _uniq.766467) (:fv _uniq.766467) ((:c instHAdd) (:fv _uniq.766467) ((:c AddCommMagma.toAdd) (:fv _uniq.766467) ((:c AddCommSemigroup.toAddCommMagma) ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda l :explicit (:fv FV1) (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:lambda n :explicit (:c Nat) (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":80680,"sourceStart":80675,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":80684,"sourceStart":80681,"tag":"atom"},{"children":[{"children":[{"contextIndex":25,"semanticRole":"local","source":"l","sourceEnd":80685,"sourceStart":80684,"tag":"identifier"},{"source":"+","sour... | [] | [{"source":"⟨l + f 0 x, Tendsto.add_const _ hx⟩","source_end":80720,"source_start":80681,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 36 | exact | true | 1 | 28 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cf6f08809fa7d654f30285001a414b1335dd685a0027620ea70af45aea50379c | ffe182098d5a67d5e45c17458b25f93648d0541dd8d1534ecbfd965dbb282149 | 732964695320b050938d95f91c2f815e5f58ef46e00e33638c80e43cecdaf399 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,381 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h1 : ∀ n, <a>MeasureTheory.snorm'</a> (fun x => ∑ i ∈ <a>Finset.range</a> (n + 1), ‖f (i + 1) x - f i x‖) p μ ≤ ∑' i, B i := <a>_private.Mathlib.MeasureTheory.Function.LpSpace.0.MeasureTheory.Lp.snorm'_sum_norm_sub_le_tsum_of_cauchy_snorm'</a> hf hp1 h_cau | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | ((:c Filter.Eventually) (:fv _uniq.766464) (:lambda x (:fv _uniq.766464) ((:c Summable) (:fv _uniq.766467) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.766467) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.766467) (:fv _uniq.766499))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.766467) ((:c PseudoMe... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Summable) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":79109,"sourceStart":79105,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h1","sourceEnd":79112,"sourceStart":79110,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h1","sourceEnd":79112,"sourceStart":79110,"tag":"nod... | [] | [{"source":"∀ n, snorm' (fun x => ∑ i ∈ Finset.range (n + 1), ‖f (i + 1) x - f i x‖) p μ ≤ ∑' i, B i","source_end":79224,"source_start":79121,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"snorm'_sum_norm_sub_le_tsum_of_cauchy_snorm' hf hp1 h_cau","source_end":79291,"source_start":79234,"syntax_kind":"Lean.Parser.... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 6 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4582db299a8fc2e95ba24ca85d23f77555ed25285b92a21731d8314593bcbafc | 6350c2a2eee9568231e4bafa9bce6cce18bd478ea6034ce06b18ffcccf295e78 | 6bd2f618f75af5205e9aa5e10f5afe778dcc54eb4ef19a8e3b8cc1888266d11b | 9fb1ebde3ee1a23a9627619e1a4bc024d144e96c14b5ec65e0e56accc41c83b0 |
cat-searcher/leandojo-benchmark-4-random | test | 2,382 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h2 : ∀ n, (∫⁻ a, (∑ i ∈ <a>Finset.range</a> (n + 1), ‖f (i + 1) a - f i a‖₊ : ℝ≥0∞) ^ p ∂μ) ≤ (∑' i, B i) ^ p := fun n => <a>_private.Mathlib.MeasureTheory.Function.LpSpace.0.MeasureTheory.Lp.lintegral_rpow_sum_coe_nnnorm_sub_le_rpow_tsum</a> hp1 n (h1 n) | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | ((:c Filter.Eventually) (:fv _uniq.766464) (:lambda x (:fv _uniq.766464) ((:c Summable) (:fv _uniq.766467) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.766467) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.766467) (:fv _uniq.766499))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.766467) ((:c PseudoMe... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Summable) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":79300,"sourceStart":79296,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h2","sourceEnd":79303,"sourceStart":79301,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h2","sourceEnd":79303,"sourceStart":79301,"tag":"nod... | [] | [{"source":"∀ n,\n (∫⁻ a, (∑ i ∈ Finset.range (n + 1), ‖f (i + 1) a - f i a‖₊ : ℝ≥0∞) ^ p ∂μ) ≤\n (∑' i, B i) ^ p","source_end":79456,"source_start":79312,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"fun n => lintegral_rpow_sum_coe_nnnorm_sub_le_rpow_tsum hp1 n (h1 n)","source_end":79534,"source_... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 7 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 85ea4d604ac9ba827d1f9bd68dbc73c29ca16a9da545f1c7d8b4c2e1fa8d3ab3 | 9fb1ebde3ee1a23a9627619e1a4bc024d144e96c14b5ec65e0e56accc41c83b0 | 8eb8e189decab8b1718e5c5bc22f5cd91a2ca3a99a48cbc717b9c41e85a1fba5 | 868895f4164aa8b8f7e0c4b948d7d4ea43fb7a0e091e815933c725a449d3f596 |
cat-searcher/leandojo-benchmark-4-random | test | 2,383 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h3 : (∫⁻ a, (∑' i, ‖f (i + 1) a - f i a‖₊ : ℝ≥0∞) ^ p ∂μ) ^ (1 / p) ≤ ∑' i, B i := <a>_private.Mathlib.MeasureTheory.Function.LpSpace.0.MeasureTheory.Lp.lintegral_rpow_tsum_coe_nnnorm_sub_le_tsum</a> hf hp1 h2 | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | ((:c Filter.Eventually) (:fv _uniq.766464) (:lambda x (:fv _uniq.766464) ((:c Summable) (:fv _uniq.766467) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.766467) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.766467) (:fv _uniq.766499))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.766467) ((:c PseudoMe... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Summable) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":79543,"sourceStart":79539,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h3","sourceEnd":79546,"sourceStart":79544,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h3","sourceEnd":79546,"sourceStart":79544,"tag":"nod... | [] | [{"source":"(∫⁻ a, (∑' i, ‖f (i + 1) a - f i a‖₊ : ℝ≥0∞) ^ p ∂μ) ^ (1 / p) ≤ ∑' i, B i","source_end":79648,"source_start":79549,"syntax_kind":"«term_≤_»"},{"source":"lintegral_rpow_tsum_coe_nnnorm_sub_le_tsum hf hp1 h2","source_end":79710,"source_start":79658,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 8 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 84e057256ee6ba8395fc5c9cdec5c11265d428851f08853f071277f4b0f3f881 | 868895f4164aa8b8f7e0c4b948d7d4ea43fb7a0e091e815933c725a449d3f596 | 91f05e7774b6c9b898373238fdb5b386815f70681fb309fd0dc2dd6e277c1236 | 4ae5ce36bacdbaa515dfbb487990bca47e2be124f9cb3dd622aeb80e6e3a52f7 |
cat-searcher/leandojo-benchmark-4-random | test | 2,384 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h4 : ∀ᵐ x ∂μ, (∑' i, ‖f (i + 1) x - f i x‖₊ : ℝ≥0∞) < ∞ := <a>_private.Mathlib.MeasureTheory.Function.LpSpace.0.MeasureTheory.Lp.tsum_nnnorm_sub_ae_lt_top</a> hf hp1 hB h3 | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | ((:c Filter.Eventually) (:fv _uniq.766464) (:lambda x (:fv _uniq.766464) ((:c Summable) (:fv _uniq.766467) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.766467) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.766467) (:fv _uniq.766499))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.766467) ((:c PseudoMe... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Summable) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":79719,"sourceStart":79715,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h4","sourceEnd":79722,"sourceStart":79720,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h4","sourceEnd":79722,"sourceStart":79720,"tag":"nod... | [] | [{"source":"∀ᵐ x ∂μ, (∑' i, ‖f (i + 1) x - f i x‖₊ : ℝ≥0∞) < ∞","source_end":79798,"source_start":79725,"syntax_kind":"MeasureTheory.«term∀ᵐ_∂_,_»"},{"source":"tsum_nnnorm_sub_ae_lt_top hf hp1 hB h3","source_end":79846,"source_start":79808,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 9 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e1e15ae04d73c952188d45b954fe81c9527727127255368f891e43643862cade | 4ae5ce36bacdbaa515dfbb487990bca47e2be124f9cb3dd622aeb80e6e3a52f7 | a961b36e7d445dce38bcd869957cf5f62359d0c16d575a7f264ffff71f63c3ca | ba0a5cc25ccd8f79de8f1ba88389cefaa41f1816756029cb7fbc7c4b6b7ad7af |
cat-searcher/leandojo-benchmark-4-random | test | 2,385 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact h4.mono fun x hx => .of_nnnorm <| ENNReal.tsum_coe_ne_top_iff_summable.mp hx.ne | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | ((:c Filter.Eventually) (:fv _uniq.766464) (:lambda x (:fv _uniq.766464) ((:c Summable) (:fv _uniq.766467) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.766467) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.766467) (:fv _uniq.766499))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.766467) ((:c PseudoMe... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Summable) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":79856,"sourceStart":79851,"tag":"atom"},{"children":[{"source":"h4.mono","sourceEnd":79864,"sourceStart":79857,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":79868,"sourceStart":79865,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_lo... | [] | [{"source":"h4.mono fun x hx => .of_nnnorm <| ENNReal.tsum_coe_ne_top_iff_summable.mp hx.ne","source_end":79936,"source_start":79857,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 10 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 635f54d131236a69e4d86de0ea2957b87c3e4f334b3b51224d0dd33461562741 | ba0a5cc25ccd8f79de8f1ba88389cefaa41f1816756029cb7fbc7c4b6b7ad7af | ac865ae99b30196587a43587a1e27c03a548d0cbb9b1b21506af294b06e3b481 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,386 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine h_summable.mono fun x hx => ?_ | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | ((:c Filter.Eventually) (:fv _uniq.766464) (:lambda x (:fv _uniq.766464) ((:c Exists) (:fv _uniq.766467) (:lambda l (:fv _uniq.766467) ((:c Filter.Tendsto) (:c Nat) (:fv _uniq.766467) (:lambda n (:c Nat) ((:c Finset.sum) (:c Nat) (:fv _uniq.766467) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.766467) ((:c NormedAddCom... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda l :explicit (:fv FV1) (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":80083,"sourceStart":80077,"tag":"atom"},{"children":[{"source":"h_summable.mono","sourceEnd":80099,"sourceStart":80084,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":80103,"sourceStart":80100,"tag":"atom"},{"children":[{"children":[{"semanticRole":"... | [] | [{"source":"h_summable.mono fun x hx => ?_","source_end":80114,"source_start":80084,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 13 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3d614701c44edbee1631cc1cde9b161d4907b34bb9b989b56f319ee93358988a | a37856f04531fb617658b800485b8ddafc038e3961c1794b4cd0ff38d8f20955 | 65b3e7fa584a8048fadf87d186a959330b6765ad42d02894976f2ace62fdb887 | 112efd62c1a60e962e9f688ae2414e451d2190922eb6a351c252e7f637e184dd |
cat-searcher/leandojo-benchmark-4-random | test | 2,387 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let hx_sum := hx.hasSum.tendsto_sum_nat | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | ((:c Exists) (:fv _uniq.766467) (:lambda l (:fv _uniq.766467) ((:c Filter.Tendsto) (:c Nat) (:fv _uniq.766467) (:lambda n (:c Nat) ((:c Finset.sum) (:c Nat) (:fv _uniq.766467) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.766467) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.766467) (:fv _uniq.766499))) ((:c Finse... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda l :explicit (:fv FV1) (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:lambda n :explicit (:c Nat) (:app (:c Finset.sum) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"let","sourceEnd":80122,"sourceStart":80119,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"hx_sum","sourceEnd":80129,"sourceStart":80123,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"nod... | [] | [{"source":"hx.hasSum.tendsto_sum_nat","source_end":80158,"source_start":80133,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 14 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 017c34ca292893406aa4410cf9e3424196b3556c24f9881659c58672a8876dc1 | 112efd62c1a60e962e9f688ae2414e451d2190922eb6a351c252e7f637e184dd | 5cfdfed2e54f691d24f5d108358e1b298df7a17c858a0b91ef30d669f128426f | 56b9fc4d60db76dc475e9f22e538841481207dcfddc3be02343f8b03bcc43b98 |
cat-searcher/leandojo-benchmark-4-random | test | 2,388 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨∑' i, (f (i + 1) x - f i x), hx_sum⟩ | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | ((:c Exists) (:fv _uniq.766467) (:lambda l (:fv _uniq.766467) ((:c Filter.Tendsto) (:c Nat) (:fv _uniq.766467) (:lambda n (:c Nat) ((:c Finset.sum) (:c Nat) (:fv _uniq.766467) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.766467) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.766467) (:fv _uniq.766499))) ((:c Finse... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda l :explicit (:fv FV1) (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:lambda n :explicit (:c Nat) (:app (:c Finset.sum) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":80168,"sourceStart":80163,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":80172,"sourceStart":80169,"tag":"atom"},{"children":[{"children":[{"source":"∑'","sourceEnd":80176,"sourceStart":80172,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_lo... | [] | [{"source":"⟨∑' i, (f (i + 1) x - f i x), hx_sum⟩","source_end":80212,"source_start":80169,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 15 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0db2f53393d31b05caccd58402847adc7641d3abd7b844d26d69a494a9b35dc4 | 56b9fc4d60db76dc475e9f22e538841481207dcfddc3be02343f8b03bcc43b98 | 7d2ecd7296cf57b5d1fa3de40eb8f4da49df6f3520297d771f737b19ca52be64 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,389 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext1 n | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | case h
α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
... | ((:c Eq) (:forall n (:c Nat) (:fv _uniq.766467)) (:lambda n (:c Nat) ((:c Finset.sum) (:c Nat) (:fv _uniq.766467) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.766467) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.766467) (:fv _uniq.766499))) ((:c Finset.range) 0) (:lambda i (:c Nat) ((:c HSub.hSub) (:fv _uniq.766... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Eq) (:arg :implicit-type 0 (:forall n :explicit (:c Nat) (:fv FV1))) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c Finset.sum) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"ext1","sourceEnd":80388,"sourceStart":80384,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"n","sourceEnd":80390,"sourceStart":80389,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"n","sourceEnd":80390,"sourceStart":80389,"ta... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 20 | exact | true | 1 | 26 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 07a1c8cf8be494bc2ee548c90f8a3e58249b306536dc82b4fc0c40062a987c60 | 4e92b7f9fcf072b9f82cebbc08635c0bea36fafab90bb6688dc808d62957c58d | eb101057332c519e7695348442cdeb94302ff7d70a2419ef7383a62b15c049e5 | 3f16fcb077344da074ca4eaf3deab009ef68af87804f39b6d2fb835bc717d428 |
cat-searcher/leandojo-benchmark-4-random | test | 2,390 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | change (∑ i ∈ <a>Finset.range</a> n, ((fun m => f m x) (i + 1) - (fun m => f m x) i)) = f n x - f 0 x | case h
α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
... | case h
α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
... | ((:c Eq) (:fv _uniq.766467) ((:c Finset.sum) (:c Nat) (:fv _uniq.766467) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.766467) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.766467) (:fv _uniq.766499))) ((:c Finset.range) (:fv _uniq.774442)) (:lambda i (:c Nat) ((:c HSub.hSub) (:fv _uniq.766467) (:fv _uniq.766467) ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Finset.sum) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 3 (:app (:c Finset.range) (:arg :explicit 0 (:fv FV27)))) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"change","sourceEnd":80401,"sourceStart":80395,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":80409,"sourceStart":80408,"tag":"atom"},{"children":[{"source":"∑","sourceEnd":80412,"sourceStart":80409,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source"... | [] | [{"source":"(∑ i ∈ Finset.range n, ((fun m => f m x) (i + 1) - (fun m => f m x) i)) = f n x - f 0 x","source_end":80499,"source_start":80408,"syntax_kind":"«term_=_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 21 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 09c7c3dcad241dd7fa6b5b5433fcb28692b28740e743e996c0a2e09977ac8f05 | 3f16fcb077344da074ca4eaf3deab009ef68af87804f39b6d2fb835bc717d428 | 6462478aa3c4b490496b56176bada720021698334e24b9c560ad9ecfd69af076 | cb3c3f11c3b11acb2212ab6055f3817407bc42a908f4faf4de4313aeb443185e |
cat-searcher/leandojo-benchmark-4-random | test | 2,391 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.sum_range_sub</a> (fun m => f m x)] | case h
α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
... | ((:c Eq) (:fv _uniq.766467) ((:c Finset.sum) (:c Nat) (:fv _uniq.766467) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.766467) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.766467) (:fv _uniq.766499))) ((:c Finset.range) (:fv _uniq.774442)) (:lambda i (:c Nat) ((:c HSub.hSub) (:fv _uniq.766467) (:fv _uniq.766467) ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Finset.sum) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 3 (:app (:c Finset.range) (:arg :explicit 0 (:fv FV27)))) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":80506,"sourceStart":80504,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":80508,"sourceStart":80507,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Fin... | [] | [{"source":"Finset.sum_range_sub (fun m => f m x)","source_end":80545,"source_start":80508,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 22 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c6e9b8d60fbc7f76422d829b03b9689717d7561a8aae2277b73999f01e1c7f87 | cb3c3f11c3b11acb2212ab6055f3817407bc42a908f4faf4de4313aeb443185e | 276907af605850a28d6d52e93a37bd814b18cf377da839fab596f427e6897c6c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,392 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext1 n | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
hB : ∑'... | case h
α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
... | ((:c Eq) (:forall n (:c Nat) (:fv _uniq.766467)) (:lambda n (:c Nat) ((:fv _uniq.768013) 0 (:fv _uniq.773937))) (:lambda n (:c Nat) ((:c HAdd.hAdd) (:fv _uniq.766467) (:fv _uniq.766467) (:fv _uniq.766467) ((:c instHAdd) (:fv _uniq.766467) ((:c AddCommMagma.toAdd) (:fv _uniq.766467) ((:c AddCommSemigroup.toAddCommMagma)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Eq) (:arg :implicit-type 0 (:forall n :explicit (:c Nat) (:fv FV1))) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:fv FV15) (:arg :explicit 0 0) (:arg :explicit 1 (:fv FV24))))) (:arg :explicit 2 (:lambda n :explicit (:c Nat) (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-typ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"ext1","sourceEnd":80648,"sourceStart":80644,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"n","sourceEnd":80650,"sourceStart":80649,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"n","sourceEnd":80650,"sourceStart":80649,"ta... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 30 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7342b466e0ab4ce64b0b40b059409b7f410f9b3154a2b3482b4e689fb983c0e6 | d6d8f44e9630dca9517548e89a02b2f76374ed0de2570f7347e6be72b8df0537 | eb101057332c519e7695348442cdeb94302ff7d70a2419ef7383a62b15c049e5 | 2a0b2421c3f54592454d715ed909a58017387400839449c637af20abcfa6886a |
cat-searcher/leandojo-benchmark-4-random | test | 2,393 | MeasureTheory.Lp.ae_tendsto_of_cauchy_snorm' | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | abel | case h
α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p✝ : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝³ : NormedAddCommGroup E
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedAddCommGroup G
inst✝ : CompleteSpace E
f : ℕ → α → E
p : ℝ
hf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ
hp1 : 1 ≤ p
B : ℕ → ℝ≥0∞
... | ((:c Eq) (:fv _uniq.766467) ((:fv _uniq.768013) (:fv _uniq.776059) (:fv _uniq.773937)) ((:c HAdd.hAdd) (:fv _uniq.766467) (:fv _uniq.766467) (:fv _uniq.766467) ((:c instHAdd) (:fv _uniq.766467) ((:c AddCommMagma.toAdd) (:fv _uniq.766467) ((:c AddCommSemigroup.toAddCommMagma) (:fv _uniq.766467) ((:c AddCommMonoid.toAddC... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.766464))"},{"name":"p✝","sexp":"(:c ENNRe... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:fv FV15) (:arg :explicit 0 (:fv FV28)) (:arg :explicit 1 (:fv FV24)))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"source":"abel","sourceEnd":80659,"sourceStart":80655,"tag":"atom"}],"kind":"Mathlib.Tactic.Abel.abel","source":"abel","sourceEnd":80659,"sourceStart":80655,"tag":"node"},{"children":[{"source":"abel","sourceEnd":80659,"sourceStart":80655,"tag":"atom"},{"children":[],"kind":"null","source":""... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.766464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.766467","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 415 | 31 | exact | true | 1 | 28 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 849beb01b108bf022b46e9bfbb09815c41416bfdc1830b4b2bc0108178268111 | 2a0b2421c3f54592454d715ed909a58017387400839449c637af20abcfa6886a | 324bb56ef283edb7fa79c8d409c2ad5eb1d996512cb7016350638a690bde5f58 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,394 | Ideal.isUnit_iff | Mathlib/RingTheory/Ideal/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Ideal.mul_top</a>, h] | R : Type u
ι : Type u_1
inst✝ : CommSemiring R
I✝ J K L I : Ideal R
h : I = ⊤
⊢ ⊤ = I * ⊤ | ((:c Eq) ((:c Ideal) (:fv _uniq.413107) ((:c CommSemiring.toSemiring) (:fv _uniq.413107) (:fv _uniq.413113))) ((:c Top.top) ((:c Ideal) (:fv _uniq.413107) ((:c CommSemiring.toSemiring) (:fv _uniq.413107) (:fv _uniq.413113))) ((:c Submodule.instTop) (:fv _uniq.413107) (:fv _uniq.413107) ((:c CommSemiring.toSemiring) (:f... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommSemiring) (:fv _uniq.413107))"},{"name":"I✝","sexp":"((:c Ideal) (:fv _uniq.413107) ((:c CommSemiring.toSemiring) (:fv _uniq.413107) (:fv _uniq.413113)))"},{"name":"J","sexp":"((:c Ideal) (:fv _uniq.413107) (... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c Top.top) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Sem... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.413107","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.413110","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":58704,"sourceStart":58702,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":58706,"sourceStart":58705,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"mul_top","source_end":58713,"source_start":58706,"syntax_kind":"ident"},{"source":"h","source_end":58716,"source_start":58715,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.413107","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.413110","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":instance-implicit","context_index":2,"internal... | 375 | 2 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5e68774de6434045191e4c7d84ed9968b5a9851c6af49390a21bd661cb2d7ba3 | de1bcba62aec3222c553b1061af3b202949231489f916dbcbab8e5be4eda9e05 | 91e9191c1a39a28c765fefc48c39e092b66648b980d9d4b03ba5dcb573bc41fc | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,395 | List.nodup_enum_map_fst | Mathlib/Data/List/Sigma.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>List.nodup_range</a>] | α : Type u
β : α → Type v
l✝ l₁ l₂ : List (Sigma β)
l : List α
⊢ (map Prod.fst l.enum).Nodup | ((:c List.Nodup) (:c Nat) ((:c List.map) ((:c Prod) (:c Nat) (:fv _uniq.42033)) (:c Nat) ((:c Prod.fst) (:c Nat) (:fv _uniq.42033)) ((:c List.enum) (:fv _uniq.42033) (:fv _uniq.42096)))) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:forall _ (:fv _uniq.42033) (:sort (+ v 1)))"},{"name":"l✝","sexp":"((:c List) ((:c Sigma) (:fv _uniq.42033) (:fv _uniq.42037)))"},{"name":"l₁","sexp":"((:c List) ((:c Sigma) (:fv _uniq.42033) (:fv _uniq.42037)))"},{"name":"l₂","sexp":"((:c List) ((:c Sigma) (... | (:app (:c List.Nodup) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c List.map) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:fv FV0)))) (:arg :implicit-type 1 (:c Nat)) (:arg :explicit 2 (:app (:c Prod.fst) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.42033","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42037","is_instance":false,"is_let":false,"name":"β","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"}... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":5937,"sourceStart":5933,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"List.nodup_range","source_end":5955,"source_start":5939,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.42033","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42037","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 51 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d14db92782b77433da2d790c6ebc1ea7c7b8305b7502f71fef105a7b77860932 | fd79947af90caa59bc81f47f2e779231e4d5a7f2b62c0cf6dc7553251201c7de | ed12d35cf041a30a6871d666e80ecc1280f08c73be5c3b3bbf142e43ac933d51 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,396 | Projectivization.Subspace.sup_span | Mathlib/LinearAlgebra/Projectivization/Subspace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Projectivization.Subspace.span_union</a>, <a>Projectivization.Subspace.span_coe</a>] | K : Type u_1
V : Type u_2
inst✝² : Field K
inst✝¹ : AddCommGroup V
inst✝ : Module K V
S : Set (ℙ K V)
W : Subspace K V
⊢ W ⊔ span S = span (↑W ∪ S) | ((:c Eq) ((:c Projectivization.Subspace) (:fv _uniq.38518) (:fv _uniq.38521) (:fv _uniq.38524) (:fv _uniq.38527) (:fv _uniq.39103)) ((:c Sup.sup) ((:c Projectivization.Subspace) (:fv _uniq.38518) (:fv _uniq.38521) (:fv _uniq.38524) (:fv _uniq.38527) (:fv _uniq.39103)) ((:c SemilatticeSup.toSup) ((:c Projectivization.Su... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.38518))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.38521))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.38518) (:fv _uniq.38521) ((:c DivisionSemiring.toSemiring) (:fv _uni... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Projectivization.Subspace) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38518","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38521","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":8458,"sourceStart":8456,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8460,"sourceStart":8459,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"span_union","source_end":8470,"source_start":8460,"syntax_kind":"ident"},{"source":"span_coe","source_end":8480,"source_start":8472,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38518","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38521","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 45 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3a7f2702de707b981a69703534cb1a9325e984c7bf8a1e7a6ca5078b6f9e3145 | 08786b5d95a330411d8e5e7a2b2c68344f62be85fee57e9ad905abaa32a17470 | 7432672e388a320e374799ab9f5060678608bc57417156c7978a173c7c6b9940 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,397 | FiniteDimensional.finrank_self | Mathlib/LinearAlgebra/Dimension/StrongRankCondition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | R : Type u
M : Type v
inst✝³ : Ring R
inst✝² : AddCommGroup M
inst✝¹ : Module R M
ι : Type w
ι' : Type w'
inst✝ : StrongRankCondition R
⊢ Module.rank R R = ↑1 | ((:c Eq) (:c Cardinal) ((:c Module.rank) (:fv _uniq.190371) (:fv _uniq.190371) ((:c Ring.toSemiring) (:fv _uniq.190371) (:fv _uniq.190376)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.190371) ((:c Ring.toAddCommGroup) (:fv _uniq.190371) (:fv _uniq.190376))) ((:c Semiring.toModule) (:fv _uniq.190371) ((:c Ring.toSemir... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.190371))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.190373))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.190371) (:fv _uniq.190373) ((:c Ring.toSemiring) (:fv _uniq.190371) (:... | (:app (:c Eq) (:arg :implicit-type 0 (:c Cardinal)) (:arg :explicit 1 (:app (:c Module.rank) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV0))... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.190371","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190373","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":20983,"sourceStart":20979,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","sour... | [] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.190371","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190373","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal... | 84 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | abcf7b3a0b17477b968aaee2d5026f0c8ff2a5fb6f421481359cc41d0cca35bf | 2a47cc36deea86ce28b92a3f4507dffe344b605e404c743a62c49296e20bbbdf | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,398 | Matrix.mem_range_scalar_iff_commute_stdBasisMatrix | Mathlib/Data/Matrix/Basis.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨fun ⟨r, hr⟩ i j _ => hr ▸ <a>Commute.symm</a> ?_, <a>Matrix.mem_range_scalar_of_commute_stdBasisMatrix</a>⟩ | l : Type u_1
m : Type u_2
n : Type u_3
R : Type u_4
α : Type u_5
inst✝⁴ : DecidableEq l
inst✝³ : DecidableEq m
inst✝² : DecidableEq n
inst✝¹ : Semiring α
inst✝ : Fintype n
M : Matrix n n α
⊢ M ∈ Set.range ⇑(scalar n) ↔ ∀ (i j : n), i ≠ j → Commute (stdBasisMatrix i j 1) M | l : Type u_1
m : Type u_2
n : Type u_3
R : Type u_4
α : Type u_5
inst✝⁴ : DecidableEq l
inst✝³ : DecidableEq m
inst✝² : DecidableEq n
inst✝¹ : Semiring α
inst✝ : Fintype n
M : Matrix n n α
x✝¹ : M ∈ Set.range ⇑(scalar n)
i j : n
x✝ : i ≠ j
r : α
hr : (scalar n) r = M
⊢ Commute ((scalar n) r) (stdBasisMatrix i j 1) | ((:c Iff) ((:c Membership.mem) ((:c Matrix) (:fv _uniq.62262) (:fv _uniq.62262) (:fv _uniq.62268)) ((:c Set) ((:c Matrix) (:fv _uniq.62262) (:fv _uniq.62262) (:fv _uniq.62268))) ((:c Set.instMembership) ((:c Matrix) (:fv _uniq.62262) (:fv _uniq.62262) (:fv _uniq.62268))) (:fv _uniq.63096) ((:c Set.range) ((:c Matrix) (... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"α","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.62256))"},{"name":"inst✝³","sexp":"((:c DecidableEq) (:fv _uniq.6... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV4)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV2))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62256","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62259","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":10133,"sourceStart":10127,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":10137,"sourceStart":10134,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":10140,"sourceStart":10137,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd... | [] | [{"source":"⟨fun ⟨r, hr⟩ i j _ => hr ▸ Commute.symm ?_, mem_range_scalar_of_commute_stdBasisMatrix⟩","source_end":10231,"source_start":10134,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62256","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62259","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 68 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b075ef1c195aceb8bbf6638f0815128e39a5009788e65b9e45f6c5bf31afbec9 | ff8c351e0aab754ef25399f9c631d5dba3883c6c23874dccbf2c0f939e6a0384 | fafa5a08fcb4cda5c8943afd350bd14d8ef58ed70a7880a4f20e2cd5a7b32135 | 01d0fe05ee537e69aa18ba7365166c5480c469df4ee71cc737f1f2fb93e61405 |
cat-searcher/leandojo-benchmark-4-random | test | 2,399 | Matrix.mem_range_scalar_iff_commute_stdBasisMatrix | Mathlib/Data/Matrix/Basis.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Matrix.scalar_commute_iff</a>] | l : Type u_1
m : Type u_2
n : Type u_3
R : Type u_4
α : Type u_5
inst✝⁴ : DecidableEq l
inst✝³ : DecidableEq m
inst✝² : DecidableEq n
inst✝¹ : Semiring α
inst✝ : Fintype n
M : Matrix n n α
x✝¹ : M ∈ Set.range ⇑(scalar n)
i j : n
x✝ : i ≠ j
r : α
hr : (scalar n) r = M
⊢ Commute ((scalar n) r) (stdBasisMatrix i j 1) | l : Type u_1
m : Type u_2
n : Type u_3
R : Type u_4
α : Type u_5
inst✝⁴ : DecidableEq l
inst✝³ : DecidableEq m
inst✝² : DecidableEq n
inst✝¹ : Semiring α
inst✝ : Fintype n
M : Matrix n n α
x✝¹ : M ∈ Set.range ⇑(scalar n)
i j : n
x✝ : i ≠ j
r : α
hr : (scalar n) r = M
⊢ r • stdBasisMatrix i j 1 = MulOpposite.op r • stdB... | ((:c Commute) ((:c Matrix) (:fv _uniq.62262) (:fv _uniq.62262) (:fv _uniq.62268)) ((:c Matrix.instMulOfFintypeOfAddCommMonoid) (:fv _uniq.62262) (:fv _uniq.62268) (:fv _uniq.62301) ((:c NonUnitalNonAssocSemiring.toMul) (:fv _uniq.62268) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.62268) ((:c Semiring.... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"α","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.62256))"},{"name":"inst✝³","sexp":"((:c DecidableEq) (:fv _uniq.6... | (:app (:c Commute) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV4)))) (:arg :instance 1 (:instance-of (:app (:c Mul) (:arg :explicit 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV4))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62256","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62259","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":10236,"sourceStart":10234,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10238,"sourceStart":10237,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Matrix.scalar_co... | [] | [{"source":"scalar_commute_iff","source_end":10256,"source_start":10238,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62256","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62259","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 68 | 5 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f5a20c1f1c22ad5496ea404e98298702f665dec1fac5d14733c3614c3cd94c39 | 01d0fe05ee537e69aa18ba7365166c5480c469df4ee71cc737f1f2fb93e61405 | eb8792d066135d55aa477c2cb61a87f003765a16d849499aabcd1138fc6078f7 | 12d9459a72e8369d485b8a90b4216265b932e01a5838f4e8dfb7160378a772ed |
cat-searcher/leandojo-benchmark-4-random | test | 2,400 | Matrix.mem_range_scalar_iff_commute_stdBasisMatrix | Mathlib/Data/Matrix/Basis.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | l : Type u_1
m : Type u_2
n : Type u_3
R : Type u_4
α : Type u_5
inst✝⁴ : DecidableEq l
inst✝³ : DecidableEq m
inst✝² : DecidableEq n
inst✝¹ : Semiring α
inst✝ : Fintype n
M : Matrix n n α
x✝¹ : M ∈ Set.range ⇑(scalar n)
i j : n
x✝ : i ≠ j
r : α
hr : (scalar n) r = M
⊢ r • stdBasisMatrix i j 1 = MulOpposite.op r • stdB... | ((:c Eq) ((:c Matrix) (:fv _uniq.62262) (:fv _uniq.62262) (:fv _uniq.62268)) ((:c HSMul.hSMul) (:fv _uniq.62268) ((:c Matrix) (:fv _uniq.62262) (:fv _uniq.62262) (:fv _uniq.62268)) ((:c Matrix) (:fv _uniq.62262) (:fv _uniq.62262) (:fv _uniq.62268)) ((:c instHSMul) (:fv _uniq.62268) ((:c Matrix) (:fv _uniq.62262) (:fv _... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"α","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.62256))"},{"name":"inst✝³","sexp":"((:c DecidableEq) (:fv _uniq.6... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV4)))) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:app (:c Matrix) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV2)) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62256","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62259","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":10264,"sourceStart":10260,"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.62256","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62259","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 68 | 8 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 094e398833192eb6f97048696c0ae8b39a0377d52a78257f87ffeab8cf74eb73 | 12d9459a72e8369d485b8a90b4216265b932e01a5838f4e8dfb7160378a772ed | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,401 | ProbabilityTheory.gaussianReal_map_add_const | Mathlib/Probability/Distributions/Gaussian.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases hv : v = 0 | μ : ℝ
v : ℝ≥0
y : ℝ
⊢ Measure.map (fun x => x + y) (gaussianReal μ v) = gaussianReal (μ + y) v | ((:c Eq) ((:c MeasureTheory.Measure) (:c Real) (:c Real.measurableSpace)) ((:c MeasureTheory.Measure.map) (:c Real) (:c Real) (:c Real.measurableSpace) (:c Real.measurableSpace) (:lambda _ (:c Real) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) 0 (:fv _uniq.251450))) ((:c Pro... | [{"name":"μ","sexp":"(:c Real)"},{"name":"v","sexp":"(:c NNReal)"},{"name":"y","sexp":"(:c Real)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 1 (:app (:c MeasureTheory.Measure.map) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"name":"μ","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"name":"v","sexp":"(:c NNReal)"},{"binder_role":":explicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"by_cases","sourceEnd":11500,"sourceStart":11492,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hv","sourceEnd":11503,"sourceStart":11501,"tag":"identifier"},{"source":":","sourceEnd":11505,"sourceStart":11504,"tag":"atom"}],"kind":"null... | [] | [{"source":"v = 0","source_end":11511,"source_start":11506,"syntax_kind":"«term_=_»"},{"source":"hv","source_end":11530,"source_start":11528,"syntax_kind":"ident"},{"source":"ne_eq","source_end":11537,"source_start":11532,"syntax_kind":"ident"},{"source":"not_true","source_end":11547,"source_start":11539,"syntax_kind":... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"user_name":"μ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"user_name":"v"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 40 | 2 | branch_opener | false | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8efdf9e1c25169e62570c213e0a6f3e4a3e781c6d192ef3998684643c21310b2 | 9fc1c55ff0c815467811d437b75db2af70dc2cda44a30acb5ca1c13d516ab098 | e8c97933cf3be16cabb6be2789975b0b9b9cdbc675e1df22fe0c1bb88b0a01a5 | d8c6f040e9f4d6ef6a13dae6c24dc4af9e7f2a0fffa9bc33c716bd304260c646 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,402 | ProbabilityTheory.gaussianReal_map_add_const | Mathlib/Probability/Distributions/Gaussian.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let e : ℝ ≃ᵐ ℝ := (<a>Homeomorph.addRight</a> y).symm.toMeasurableEquiv | case neg
μ : ℝ
v : ℝ≥0
y : ℝ
hv : ¬v = 0
⊢ Measure.map (fun x => x + y) (gaussianReal μ v) = gaussianReal (μ + y) v | case neg
μ : ℝ
v : ℝ≥0
y : ℝ
hv : ¬v = 0
e : ℝ ≃ᵐ ℝ := (Homeomorph.addRight y).symm.toMeasurableEquiv
⊢ Measure.map (fun x => x + y) (gaussianReal μ v) = gaussianReal (μ + y) v | ((:c Eq) ((:c MeasureTheory.Measure) (:c Real) (:c Real.measurableSpace)) ((:c MeasureTheory.Measure.map) (:c Real) (:c Real) (:c Real.measurableSpace) (:c Real.measurableSpace) (:lambda _ (:c Real) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) 0 (:fv _uniq.251450))) ((:c Pro... | [{"name":"μ","sexp":"(:c Real)"},{"name":"v","sexp":"(:c NNReal)"},{"name":"y","sexp":"(:c Real)"},{"name":"hv","sexp":"((:c Not) ((:c Eq) (:c NNReal) (:fv _uniq.251352) ((:c OfNat.ofNat) (:c NNReal) (:lit 0) ((:c Zero.toOfNat0) (:c NNReal) (:c instNNRealZero)))))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 1 (:app (:c MeasureTheory.Measure.map) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"name":"μ","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"name":"v","sexp":"(:c NNReal)"},{"binder_role":":explicit","conte... | {"children":[{"source":"let","sourceEnd":11636,"sourceStart":11633,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"e","sourceEnd":11638,"sourceStart":11637,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":1164... | [] | [{"source":"ℝ ≃ᵐ ℝ","source_end":11655,"source_start":11641,"syntax_kind":"«term_≃ᵐ_»"},{"source":"(Homeomorph.addRight y).symm.toMeasurableEquiv","source_end":11705,"source_start":11659,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"user_name":"μ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"user_name":"v"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 40 | 11 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73da4c7cd24bb782bf11fde93fcb61042208f3aad9548c84137876cb2525cb85 | 205bbcf1c0797039554eaa56a15d2d01f6e6d2f83661e5e15cbdc0852e8464fe | c2170c46e85533c347609a68858e694976f579d4479188188398fb206461d356 | 4df83a1e7ce45540dd8cf9e0be54f563221bbec14cb4e6ddc9a72b5be87f3250 |
cat-searcher/leandojo-benchmark-4-random | test | 2,403 | ProbabilityTheory.gaussianReal_map_add_const | Mathlib/Probability/Distributions/Gaussian.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have he' : ∀ x, <a>HasDerivAt</a> e ((fun _ ↦ 1) x) x := fun _ ↦ (<a>hasDerivAt_id</a> _).<a>HasDerivAt.sub_const</a> y | case neg
μ : ℝ
v : ℝ≥0
y : ℝ
hv : ¬v = 0
e : ℝ ≃ᵐ ℝ := (Homeomorph.addRight y).symm.toMeasurableEquiv
⊢ Measure.map (fun x => x + y) (gaussianReal μ v) = gaussianReal (μ + y) v | case neg
μ : ℝ
v : ℝ≥0
y : ℝ
hv : ¬v = 0
e : ℝ ≃ᵐ ℝ := (Homeomorph.addRight y).symm.toMeasurableEquiv
he' : ∀ (x : ℝ), HasDerivAt (⇑e) ((fun x => 1) x) x
⊢ Measure.map (fun x => x + y) (gaussianReal μ v) = gaussianReal (μ + y) v | ((:c Eq) ((:c MeasureTheory.Measure) (:c Real) (:c Real.measurableSpace)) ((:c MeasureTheory.Measure.map) (:c Real) (:c Real) (:c Real.measurableSpace) (:c Real.measurableSpace) (:lambda _ (:c Real) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) 0 (:fv _uniq.251450))) ((:c Pro... | [{"name":"μ","sexp":"(:c Real)"},{"name":"v","sexp":"(:c NNReal)"},{"name":"y","sexp":"(:c Real)"},{"name":"hv","sexp":"((:c Not) ((:c Eq) (:c NNReal) (:fv _uniq.251352) ((:c OfNat.ofNat) (:c NNReal) (:lit 0) ((:c Zero.toOfNat0) (:c NNReal) (:c instNNRealZero)))))"},{"name":"e","sexp":"((:c MeasurableEquiv) (:c Real) (... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 1 (:app (:c MeasureTheory.Measure.map) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"name":"μ","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"name":"v","sexp":"(:c NNReal)"},{"binder_role":":explicit","conte... | {"children":[{"source":"have","sourceEnd":11712,"sourceStart":11708,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"he'","sourceEnd":11716,"sourceStart":11713,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"he'","sourceEnd":11716,"sourceStart":11713,"tag":"n... | [] | [{"source":"∀ x, HasDerivAt e ((fun _ ↦ 1) x) x","source_end":11758,"source_start":11719,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"fun _ ↦ (hasDerivAt_id _).sub_const y","source_end":11801,"source_start":11762,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"user_name":"μ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"user_name":"v"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 40 | 12 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d1dd72840b7c70f4ec6a19f7fa6b96dfd4ab8ee28ab1d8d89e9fdbfc566e46b3 | 4df83a1e7ce45540dd8cf9e0be54f563221bbec14cb4e6ddc9a72b5be87f3250 | 1be1f544e23d60a7141ea9e7109640b6b173ea80c94de54a6c0fdd2263b04199 | c773fdce2ca769480baaeabee6928ba127dc1c1191906df89f88f052fc6caf47 |
cat-searcher/leandojo-benchmark-4-random | test | 2,404 | ProbabilityTheory.gaussianReal_map_add_const | Mathlib/Probability/Distributions/Gaussian.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | change (<a>ProbabilityTheory.gaussianReal</a> μ v).<a>MeasureTheory.Measure.map</a> e.symm = <a>ProbabilityTheory.gaussianReal</a> (μ + y) v | case neg
μ : ℝ
v : ℝ≥0
y : ℝ
hv : ¬v = 0
e : ℝ ≃ᵐ ℝ := (Homeomorph.addRight y).symm.toMeasurableEquiv
he' : ∀ (x : ℝ), HasDerivAt (⇑e) ((fun x => 1) x) x
⊢ Measure.map (fun x => x + y) (gaussianReal μ v) = gaussianReal (μ + y) v | case neg
μ : ℝ
v : ℝ≥0
y : ℝ
hv : ¬v = 0
e : ℝ ≃ᵐ ℝ := (Homeomorph.addRight y).symm.toMeasurableEquiv
he' : ∀ (x : ℝ), HasDerivAt (⇑e) ((fun x => 1) x) x
⊢ Measure.map (⇑e.symm) (gaussianReal μ v) = gaussianReal (μ + y) v | ((:c Eq) ((:c MeasureTheory.Measure) (:c Real) (:c Real.measurableSpace)) ((:c MeasureTheory.Measure.map) (:c Real) (:c Real) (:c Real.measurableSpace) (:c Real.measurableSpace) (:lambda _ (:c Real) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) 0 (:fv _uniq.251450))) ((:c Pro... | [{"name":"μ","sexp":"(:c Real)"},{"name":"v","sexp":"(:c NNReal)"},{"name":"y","sexp":"(:c Real)"},{"name":"hv","sexp":"((:c Not) ((:c Eq) (:c NNReal) (:fv _uniq.251352) ((:c OfNat.ofNat) (:c NNReal) (:lit 0) ((:c Zero.toOfNat0) (:c NNReal) (:c instNNRealZero)))))"},{"name":"e","sexp":"((:c MeasurableEquiv) (:c Real) (... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 1 (:app (:c MeasureTheory.Measure.map) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"name":"μ","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"name":"v","sexp":"(:c NNReal)"},{"binder_role":":explicit","conte... | {"children":[{"source":"change","sourceEnd":11810,"sourceStart":11804,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"(","sourceEnd":11812,"sourceStart":11811,"tag":"atom"},{"children":[{"name":"ProbabilityTheory.gaussianReal","semanticRole":"global","source":"gaussianReal","sourceEnd":1182... | [] | [{"source":"(gaussianReal μ v).map e.symm = gaussianReal (μ + y) v","source_end":11867,"source_start":11811,"syntax_kind":"«term_=_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"user_name":"μ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"user_name":"v"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 40 | 13 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 69e582aa987b05c4f9f90344ab2342c621b77c2468429005484b05845c49b108 | c773fdce2ca769480baaeabee6928ba127dc1c1191906df89f88f052fc6caf47 | ca13bddfa2022f901768ab5b2cfc3524ce3cc3a2fd8cff01572ac1b38088a2f7 | a5e21d85fc2c2cbc148d8776be20092713b77e292f3085cf048df6570a609f4b |
cat-searcher/leandojo-benchmark-4-random | test | 2,405 | ProbabilityTheory.gaussianReal_map_add_const | Mathlib/Probability/Distributions/Gaussian.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext s' hs' | case neg
μ : ℝ
v : ℝ≥0
y : ℝ
hv : ¬v = 0
e : ℝ ≃ᵐ ℝ := (Homeomorph.addRight y).symm.toMeasurableEquiv
he' : ∀ (x : ℝ), HasDerivAt (⇑e) ((fun x => 1) x) x
⊢ Measure.map (⇑e.symm) (gaussianReal μ v) = gaussianReal (μ + y) v | case neg.h
μ : ℝ
v : ℝ≥0
y : ℝ
hv : ¬v = 0
e : ℝ ≃ᵐ ℝ := (Homeomorph.addRight y).symm.toMeasurableEquiv
he' : ∀ (x : ℝ), HasDerivAt (⇑e) ((fun x => 1) x) x
s' : Set ℝ
hs' : MeasurableSet s'
⊢ (Measure.map (⇑e.symm) (gaussianReal μ v)) s' = (gaussianReal (μ + y) v) s' | ((:c Eq) ((:c MeasureTheory.Measure) (:c Real) (:c Real.measurableSpace)) ((:c MeasureTheory.Measure.map) (:c Real) (:c Real) (:c Real.measurableSpace) (:c Real.measurableSpace) ((:c DFunLike.coe) ((:c MeasurableEquiv) (:c Real) (:c Real) (:c Real.measurableSpace) (:c Real.measurableSpace)) (:c Real) (:lambda _ (:c Rea... | [{"name":"μ","sexp":"(:c Real)"},{"name":"v","sexp":"(:c NNReal)"},{"name":"y","sexp":"(:c Real)"},{"name":"hv","sexp":"((:c Not) ((:c Eq) (:c NNReal) (:fv _uniq.251352) ((:c OfNat.ofNat) (:c NNReal) (:lit 0) ((:c Zero.toOfNat0) (:c NNReal) (:c instNNRealZero)))))"},{"name":"e","sexp":"((:c MeasurableEquiv) (:c Real) (... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 1 (:app (:c MeasureTheory.Measure.map) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"name":"μ","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"name":"v","sexp":"(:c NNReal)"},{"binder_role":":explicit","conte... | {"children":[{"source":"ext","sourceEnd":11873,"sourceStart":11870,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"s'","sourceEnd":11876,"sourceStart":11874,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"s'","sourceEnd":11876,"sourceStart":11874,"t... | [{"role":"fresh_name","source":"s'","source_end":11876,"source_start":11874,"syntax_kind":"ident"},{"role":"fresh_name","source":"hs'","source_end":11880,"source_start":11877,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"user_name":"μ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"user_name":"v"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 40 | 14 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 53765496af1759ca8d10fda0cea7314ecd36497fbb1642b5ff240f65469d181b | a5e21d85fc2c2cbc148d8776be20092713b77e292f3085cf048df6570a609f4b | 08803bac64a0bfe4f8d5c75e786a9e2afe135aefbc2add15f6e432e7c28cab42 | 6d861b9bb0571272c9f1edf3fbbd4e73703afad821de70088bd8bcfefd36a3f5 |
cat-searcher/leandojo-benchmark-4-random | test | 2,406 | ProbabilityTheory.gaussianReal_map_add_const | Mathlib/Probability/Distributions/Gaussian.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasurableEquiv.gaussianReal_map_symm_apply</a> hv e he' hs'] | case neg.h
μ : ℝ
v : ℝ≥0
y : ℝ
hv : ¬v = 0
e : ℝ ≃ᵐ ℝ := (Homeomorph.addRight y).symm.toMeasurableEquiv
he' : ∀ (x : ℝ), HasDerivAt (⇑e) ((fun x => 1) x) x
s' : Set ℝ
hs' : MeasurableSet s'
⊢ (Measure.map (⇑e.symm) (gaussianReal μ v)) s' = (gaussianReal (μ + y) v) s' | case neg.h
μ : ℝ
v : ℝ≥0
y : ℝ
hv : ¬v = 0
e : ℝ ≃ᵐ ℝ := (Homeomorph.addRight y).symm.toMeasurableEquiv
he' : ∀ (x : ℝ), HasDerivAt (⇑e) ((fun x => 1) x) x
s' : Set ℝ
hs' : MeasurableSet s'
⊢ ENNReal.ofReal (∫ (x : ℝ) in s', |1| * gaussianPDFReal μ v (e x)) = (gaussianReal (μ + y) v) s' | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:c Real) (:c Real.measurableSpace)) ((:c Set) (:c Real)) (:lambda _ ((:c Set) (:c Real)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:c Real) (:c Real.measurableSpace)) ((:c MeasureTheory.Measure.map) (:c Real) (:c Real) (:c Real.measurabl... | [{"name":"μ","sexp":"(:c Real)"},{"name":"v","sexp":"(:c NNReal)"},{"name":"y","sexp":"(:c Real)"},{"name":"hv","sexp":"((:c Not) ((:c Eq) (:c NNReal) (:fv _uniq.251352) ((:c OfNat.ofNat) (:c NNReal) (:lit 0) ((:c Zero.toOfNat0) (:c NNReal) (:c instNNRealZero)))))"},{"name":"e","sexp":"((:c MeasurableEquiv) (:c Real) (... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c Real))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"name":"μ","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"name":"v","sexp":"(:c NNReal)"},{"binder_role":":explicit","conte... | {"children":[{"source":"rw","sourceEnd":11885,"sourceStart":11883,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11887,"sourceStart":11886,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Mea... | [] | [{"source":"MeasurableEquiv.gaussianReal_map_symm_apply hv e he' hs'","source_end":11943,"source_start":11887,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"user_name":"μ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"user_name":"v"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 40 | 15 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6046cfacf633cd61e3108661808f4d73f0b29425187c10d70c4de6674d541c4f | 6d861b9bb0571272c9f1edf3fbbd4e73703afad821de70088bd8bcfefd36a3f5 | 060e8502cf614c610b3e912980d8cf168773c6bb39087c8d1b02694d0a923029 | 5d988c708cea38b9f82d80fa81055eb69afded42b45ba63d04862be0285fbf12 |
cat-searcher/leandojo-benchmark-4-random | test | 2,407 | ProbabilityTheory.gaussianReal_map_add_const | Mathlib/Probability/Distributions/Gaussian.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>abs_neg</a>, <a>abs_one</a>, <a>MeasurableEquiv.coe_mk</a>, <a>Equiv.coe_fn_mk</a>, <a>one_mul</a>, <a>ne_eq</a>] | case neg.h
μ : ℝ
v : ℝ≥0
y : ℝ
hv : ¬v = 0
e : ℝ ≃ᵐ ℝ := (Homeomorph.addRight y).symm.toMeasurableEquiv
he' : ∀ (x : ℝ), HasDerivAt (⇑e) ((fun x => 1) x) x
s' : Set ℝ
hs' : MeasurableSet s'
⊢ ENNReal.ofReal (∫ (x : ℝ) in s', |1| * gaussianPDFReal μ v (e x)) = (gaussianReal (μ + y) v) s' | case neg.h
μ : ℝ
v : ℝ≥0
y : ℝ
hv : ¬v = 0
e : ℝ ≃ᵐ ℝ := (Homeomorph.addRight y).symm.toMeasurableEquiv
he' : ∀ (x : ℝ), HasDerivAt (⇑e) ((fun x => 1) x) x
s' : Set ℝ
hs' : MeasurableSet s'
⊢ ENNReal.ofReal (∫ (x : ℝ) in s', gaussianPDFReal μ v (e x)) = (gaussianReal (μ + y) v) s' | ((:c Eq) (:c ENNReal) ((:c ENNReal.ofReal) ((:c MeasureTheory.integral) (:c Real) (: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.RCLike))) ((:c MeasureTheory.MeasureSpace.toM... | [{"name":"μ","sexp":"(:c Real)"},{"name":"v","sexp":"(:c NNReal)"},{"name":"y","sexp":"(:c Real)"},{"name":"hv","sexp":"((:c Not) ((:c Eq) (:c NNReal) (:fv _uniq.251352) ((:c OfNat.ofNat) (:c NNReal) (:lit 0) ((:c Zero.toOfNat0) (:c NNReal) (:c instNNRealZero)))))"},{"name":"e","sexp":"((:c MeasurableEquiv) (:c Real) (... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c ENNReal.ofReal) (:arg :explicit 0 (:app (:c MeasureTheory.integral) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Real))))) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"name":"μ","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"name":"v","sexp":"(:c NNReal)"},{"binder_role":":explicit","conte... | {"children":[{"source":"simp","sourceEnd":11951,"sourceStart":11947,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":11956,"sourceStart":11952,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":119... | [] | [{"source":"abs_neg","source_end":11965,"source_start":11958,"syntax_kind":"ident"},{"source":"abs_one","source_end":11974,"source_start":11967,"syntax_kind":"ident"},{"source":"MeasurableEquiv.coe_mk","source_end":11998,"source_start":11976,"syntax_kind":"ident"},{"source":"Equiv.coe_fn_mk","source_end":12015,"source_... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"user_name":"μ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"user_name":"v"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 40 | 18 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 14fc59bc780e773ef9c2db99ca73dcf2e7e2a3e96d01870452cfcf45ade3ead9 | 5d988c708cea38b9f82d80fa81055eb69afded42b45ba63d04862be0285fbf12 | c1c5d120b29a936709d9fb65bcc3a248afb693e0b7f5bdf8cba2df3f16a22b44 | 568a3429e094646599806f79945167dacd7e7d9c27eb8a03bf785b60d08de799 |
cat-searcher/leandojo-benchmark-4-random | test | 2,408 | ProbabilityTheory.gaussianReal_map_add_const | Mathlib/Probability/Distributions/Gaussian.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>ProbabilityTheory.gaussianReal_apply_eq_integral</a> _ hv s'] | case neg.h
μ : ℝ
v : ℝ≥0
y : ℝ
hv : ¬v = 0
e : ℝ ≃ᵐ ℝ := (Homeomorph.addRight y).symm.toMeasurableEquiv
he' : ∀ (x : ℝ), HasDerivAt (⇑e) ((fun x => 1) x) x
s' : Set ℝ
hs' : MeasurableSet s'
⊢ ENNReal.ofReal (∫ (x : ℝ) in s', gaussianPDFReal μ v (e x)) = (gaussianReal (μ + y) v) s' | case neg.h
μ : ℝ
v : ℝ≥0
y : ℝ
hv : ¬v = 0
e : ℝ ≃ᵐ ℝ := (Homeomorph.addRight y).symm.toMeasurableEquiv
he' : ∀ (x : ℝ), HasDerivAt (⇑e) ((fun x => 1) x) x
s' : Set ℝ
hs' : MeasurableSet s'
⊢ ENNReal.ofReal (∫ (x : ℝ) in s', gaussianPDFReal μ v (e x)) =
ENNReal.ofReal (∫ (x : ℝ) in s', gaussianPDFReal (μ + y) v x) | ((:c Eq) (:c ENNReal) ((:c ENNReal.ofReal) ((:c MeasureTheory.integral) (:c Real) (: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.RCLike))) ((:c MeasureTheory.MeasureSpace.toM... | [{"name":"μ","sexp":"(:c Real)"},{"name":"v","sexp":"(:c NNReal)"},{"name":"y","sexp":"(:c Real)"},{"name":"hv","sexp":"((:c Not) ((:c Eq) (:c NNReal) (:fv _uniq.251352) ((:c OfNat.ofNat) (:c NNReal) (:lit 0) ((:c Zero.toOfNat0) (:c NNReal) (:c instNNRealZero)))))"},{"name":"e","sexp":"((:c MeasurableEquiv) (:c Real) (... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c ENNReal.ofReal) (:arg :explicit 0 (:app (:c MeasureTheory.integral) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Real))))) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"name":"μ","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"name":"v","sexp":"(:c NNReal)"},{"binder_role":":explicit","conte... | {"children":[{"source":"rw","sourceEnd":12037,"sourceStart":12035,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12039,"sourceStart":12038,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Pro... | [] | [{"source":"gaussianReal_apply_eq_integral _ hv s'","source_end":12077,"source_start":12039,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"user_name":"μ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"user_name":"v"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 40 | 19 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c2dca0402261e06044899f4c0890636e8563764887099953c7a79dfb5b6e0b86 | 568a3429e094646599806f79945167dacd7e7d9c27eb8a03bf785b60d08de799 | c01233f4bbe786b66a5cd9d03720f294535bd0b6139a685b9a5101fb45141a4b | 0a659d28d96c4a160157226681a1b4a1ee74b0c38b8f790f6dc446622b7d8218 |
cat-searcher/leandojo-benchmark-4-random | test | 2,409 | ProbabilityTheory.gaussianReal_map_add_const | Mathlib/Probability/Distributions/Gaussian.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [e, <a>ProbabilityTheory.gaussianPDFReal_sub</a> _ y, <a>Homeomorph.addRight</a>, ← <a>sub_eq_add_neg</a>] | case neg.h
μ : ℝ
v : ℝ≥0
y : ℝ
hv : ¬v = 0
e : ℝ ≃ᵐ ℝ := (Homeomorph.addRight y).symm.toMeasurableEquiv
he' : ∀ (x : ℝ), HasDerivAt (⇑e) ((fun x => 1) x) x
s' : Set ℝ
hs' : MeasurableSet s'
⊢ ENNReal.ofReal (∫ (x : ℝ) in s', gaussianPDFReal μ v (e x)) =
ENNReal.ofReal (∫ (x : ℝ) in s', gaussianPDFReal (μ + y) v x) | ((:c Eq) (:c ENNReal) ((:c ENNReal.ofReal) ((:c MeasureTheory.integral) (:c Real) (: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.RCLike))) ((:c MeasureTheory.MeasureSpace.toM... | [{"name":"μ","sexp":"(:c Real)"},{"name":"v","sexp":"(:c NNReal)"},{"name":"y","sexp":"(:c Real)"},{"name":"hv","sexp":"((:c Not) ((:c Eq) (:c NNReal) (:fv _uniq.251352) ((:c OfNat.ofNat) (:c NNReal) (:lit 0) ((:c Zero.toOfNat0) (:c NNReal) (:c instNNRealZero)))))"},{"name":"e","sexp":"((:c MeasurableEquiv) (:c Real) (... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c ENNReal.ofReal) (:arg :explicit 0 (:app (:c MeasureTheory.integral) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Real))))) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"name":"μ","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"name":"v","sexp":"(:c NNReal)"},{"binder_role":":explicit","conte... | {"children":[{"source":"simp","sourceEnd":12085,"sourceStart":12081,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12087,"sourceStart":12086,"tag":"a... | [] | [{"source":"e","source_end":12088,"source_start":12087,"syntax_kind":"ident"},{"source":"gaussianPDFReal_sub _ y","source_end":12113,"source_start":12090,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Homeomorph.addRight","source_end":12134,"source_start":12115,"syntax_kind":"ident"},{"source":"sub_eq_add_neg","sourc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"user_name":"μ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"user_name":"v"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 40 | 22 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8c5b77c6e42043124e42228d14522d47bfefbfecda08b444c137ab2790a6323a | 0a659d28d96c4a160157226681a1b4a1ee74b0c38b8f790f6dc446622b7d8218 | 7b1fd79e793039f9b97c5aacaa05f3eab7f87936129007e9d3b5eb6719682c9c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,410 | ProbabilityTheory.gaussianReal_map_add_const | Mathlib/Probability/Distributions/Gaussian.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [hv, <a>ne_eq</a>, <a>not_true</a>, <a>ProbabilityTheory.gaussianReal_zero_var</a>] | case pos
μ : ℝ
v : ℝ≥0
y : ℝ
hv : v = 0
⊢ Measure.map (fun x => x + y) (gaussianReal μ v) = gaussianReal (μ + y) v | case pos
μ : ℝ
v : ℝ≥0
y : ℝ
hv : v = 0
⊢ Measure.map (fun x => x + y) (Measure.dirac μ) = Measure.dirac (μ + y) | ((:c Eq) ((:c MeasureTheory.Measure) (:c Real) (:c Real.measurableSpace)) ((:c MeasureTheory.Measure.map) (:c Real) (:c Real) (:c Real.measurableSpace) (:c Real.measurableSpace) (:lambda _ (:c Real) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) 0 (:fv _uniq.251450))) ((:c Pro... | [{"name":"μ","sexp":"(:c Real)"},{"name":"v","sexp":"(:c NNReal)"},{"name":"y","sexp":"(:c Real)"},{"name":"hv","sexp":"((:c Eq) (:c NNReal) (:fv _uniq.251352) ((:c OfNat.ofNat) (:c NNReal) (:lit 0) ((:c Zero.toOfNat0) (:c NNReal) (:c instNNRealZero))))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 1 (:app (:c MeasureTheory.Measure.map) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"name":"μ","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"name":"v","sexp":"(:c NNReal)"},{"binder_role":":explicit","conte... | {"children":[{"source":"simp","sourceEnd":11521,"sourceStart":11517,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":11526,"sourceStart":11522,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":115... | [] | [{"source":"hv","source_end":11530,"source_start":11528,"syntax_kind":"ident"},{"source":"ne_eq","source_end":11537,"source_start":11532,"syntax_kind":"ident"},{"source":"not_true","source_end":11547,"source_start":11539,"syntax_kind":"ident"},{"source":"gaussianReal_zero_var","source_end":11570,"source_start":11549,"s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"user_name":"μ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"user_name":"v"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 40 | 9 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f3fdbe8a3f761b7582200d7be9623811a5e834026d56520b777178ab954e5050 | b3640f424c30e2fc1c12189d0479ba8858a0ea5677b762d299f36f6b85912d51 | 22e03e8dcd6765b6050d5fe6f4cb0399c692b7f30440cfa0fc251381355a2e1a | f06c1b9018df019afc504f75220b4327163e95ac35f632b2ac62fdfb777a05e1 |
cat-searcher/leandojo-benchmark-4-random | test | 2,411 | ProbabilityTheory.gaussianReal_map_add_const | Mathlib/Probability/Distributions/Gaussian.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>MeasureTheory.Measure.map_dirac</a> (measurable_id'.add_const _) _ | case pos
μ : ℝ
v : ℝ≥0
y : ℝ
hv : v = 0
⊢ Measure.map (fun x => x + y) (Measure.dirac μ) = Measure.dirac (μ + y) | ((:c Eq) ((:c MeasureTheory.Measure) (:c Real) (:c Real.measurableSpace)) ((:c MeasureTheory.Measure.map) (:c Real) (:c Real) (:c Real.measurableSpace) (:c Real.measurableSpace) (:lambda _ (:c Real) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) 0 (:fv _uniq.251450))) ((:c Mea... | [{"name":"μ","sexp":"(:c Real)"},{"name":"v","sexp":"(:c NNReal)"},{"name":"y","sexp":"(:c Real)"},{"name":"hv","sexp":"((:c Eq) (:c NNReal) (:fv _uniq.251352) ((:c OfNat.ofNat) (:c NNReal) (:lit 0) ((:c Zero.toOfNat0) (:c NNReal) (:c instNNRealZero))))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 1 (:app (:c MeasureTheory.Measure.map) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"name":"μ","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"name":"v","sexp":"(:c NNReal)"},{"binder_role":":explicit","conte... | {"children":[{"source":"exact","sourceEnd":11581,"sourceStart":11576,"tag":"atom"},{"children":[{"name":"MeasureTheory.Measure.map_dirac","semanticRole":"global","source":"Measure.map_dirac","sourceEnd":11599,"sourceStart":11582,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":11601,"sourceStart"... | [] | [{"source":"Measure.map_dirac (measurable_id'.add_const _) _","source_end":11630,"source_start":11582,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251350","is_instance":false,"is_let":false,"user_name":"μ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251352","is_instance":false,"is_let":false,"user_name":"v"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 40 | 10 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 58f8f3231cea0223f9256b37405e32be1e3bf610f2dea6080229ec89a59161d3 | f06c1b9018df019afc504f75220b4327163e95ac35f632b2ac62fdfb777a05e1 | 66c24e092b792c99e201ddfa0584c5f023677a06e28d1e7a37405bf5a67bfe97 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,412 | LipschitzWith.pow_end | Mathlib/Topology/EMetricSpace/Lipschitz.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>pow_zero</a>] using <a>LipschitzWith.id</a> | α : Type u
β : Type v
γ : Type w
ι : Type x
inst✝² : PseudoEMetricSpace α
inst✝¹ : PseudoEMetricSpace β
inst✝ : PseudoEMetricSpace γ
K✝ : ℝ≥0
f✝ : α → β
x y : α
r : ℝ≥0∞
f : Function.End α
K : ℝ≥0
h : LipschitzWith K f
⊢ LipschitzWith (K ^ 0) (f ^ 0) | ((:c LipschitzWith) (:fv _uniq.34427) (:fv _uniq.34427) (:fv _uniq.34436) (:fv _uniq.34436) ((:c HPow.hPow) (:c NNReal) (:c Nat) (:c NNReal) ((:c instHPow) (:c NNReal) (:c Nat) ((:c Monoid.toNatPow) (:c NNReal) ((:c MonoidWithZero.toMonoid) (:c NNReal) ((:c Semiring.toMonoidWithZero) (:c NNReal) (:c instNNRealSemiring)... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ x 1))"},{"name":"inst✝²","sexp":"((:c PseudoEMetricSpace) (:fv _uniq.34427))"},{"name":"inst✝¹","sexp":"((:c PseudoEMetricSpace) (:fv _uniq.34429))"},{"name":"inst✝","sexp":"(... | (:app (:c LipschitzWith) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c PseudoEMetricSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c PseudoEMetricSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 4 (:app (:c HPow.hPow) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34427","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.34429","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":15000,"sourceStart":14995,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"pow_zero","source_end":15015,"source_start":15007,"syntax_kind":"ident"},{"source":"LipschitzWith.id","source_end":15039,"source_start":15023,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34427","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.34429","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 94 | 2 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9620e7cefe3ab19fb59c948ab9a9cf2390565a8ead3cc5996d300d54982a7788 | c35110752d5902f57735c66671dca6ea37b37b980dffd94af00597f21dbb44ed | ead3fd709e0e0ccb23ac43f325cdaf34df26876f8aca1abd598cf1441eb853d0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,413 | LipschitzWith.pow_end | Mathlib/Topology/EMetricSpace/Lipschitz.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>pow_succ</a>, <a>pow_succ</a>] | α : Type u
β : Type v
γ : Type w
ι : Type x
inst✝² : PseudoEMetricSpace α
inst✝¹ : PseudoEMetricSpace β
inst✝ : PseudoEMetricSpace γ
K✝ : ℝ≥0
f✝ : α → β
x y : α
r : ℝ≥0∞
f : Function.End α
K : ℝ≥0
h : LipschitzWith K f
n : ℕ
⊢ LipschitzWith (K ^ (n + 1)) (f ^ (n + 1)) | α : Type u
β : Type v
γ : Type w
ι : Type x
inst✝² : PseudoEMetricSpace α
inst✝¹ : PseudoEMetricSpace β
inst✝ : PseudoEMetricSpace γ
K✝ : ℝ≥0
f✝ : α → β
x y : α
r : ℝ≥0∞
f : Function.End α
K : ℝ≥0
h : LipschitzWith K f
n : ℕ
⊢ LipschitzWith (K ^ n * K) (f ^ n * f) | ((:c LipschitzWith) (:fv _uniq.34427) (:fv _uniq.34427) (:fv _uniq.34436) (:fv _uniq.34436) ((:c HPow.hPow) (:c NNReal) (:c Nat) (:c NNReal) ((:c instHPow) (:c NNReal) (:c Nat) ((:c Monoid.toNatPow) (:c NNReal) ((:c MonoidWithZero.toMonoid) (:c NNReal) ((:c Semiring.toMonoidWithZero) (:c NNReal) (:c instNNRealSemiring)... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ x 1))"},{"name":"inst✝²","sexp":"((:c PseudoEMetricSpace) (:fv _uniq.34427))"},{"name":"inst✝¹","sexp":"((:c PseudoEMetricSpace) (:fv _uniq.34429))"},{"name":"inst✝","sexp":"(... | (:app (:c LipschitzWith) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c PseudoEMetricSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c PseudoEMetricSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 4 (:app (:c HPow.hPow) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34427","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.34429","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":15062,"sourceStart":15060,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15064,"sourceStart":15063,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"pow_succ","seman... | [] | [{"source":"pow_succ","source_end":15072,"source_start":15064,"syntax_kind":"ident"},{"source":"pow_succ","source_end":15082,"source_start":15074,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34427","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.34429","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 94 | 9 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 77077eaf337a2285c0bae147c0703460012d89e577075fefe7c514bfdf4ae8df | fb8194d89e3adf089b4a55fda17758d7e620f62d440dc21d16510c0d86a939cc | 4ef32bb1f0ad7f77bfe26b400176f41df469a0180f5cf533014dc097cce8402e | be6642edf1deed243df624fdc9c32efae16f89a0f1b7009e08170995211580c8 |
cat-searcher/leandojo-benchmark-4-random | test | 2,414 | LipschitzWith.pow_end | Mathlib/Topology/EMetricSpace/Lipschitz.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (LipschitzWith.pow_end h n).<a>LipschitzWith.mul_end</a> h | α : Type u
β : Type v
γ : Type w
ι : Type x
inst✝² : PseudoEMetricSpace α
inst✝¹ : PseudoEMetricSpace β
inst✝ : PseudoEMetricSpace γ
K✝ : ℝ≥0
f✝ : α → β
x y : α
r : ℝ≥0∞
f : Function.End α
K : ℝ≥0
h : LipschitzWith K f
n : ℕ
⊢ LipschitzWith (K ^ n * K) (f ^ n * f) | ((:c LipschitzWith) (:fv _uniq.34427) (:fv _uniq.34427) (:fv _uniq.34436) (:fv _uniq.34436) ((:c HMul.hMul) (:c NNReal) (:c NNReal) (:c NNReal) ((:c instHMul) (:c NNReal) ((:c MulOneClass.toMul) (:c NNReal) ((:c Monoid.toMulOneClass) (:c NNReal) ((:c MonoidWithZero.toMonoid) (:c NNReal) ((:c Semiring.toMonoidWithZero) ... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ x 1))"},{"name":"inst✝²","sexp":"((:c PseudoEMetricSpace) (:fv _uniq.34427))"},{"name":"inst✝¹","sexp":"((:c PseudoEMetricSpace) (:fv _uniq.34429))"},{"name":"inst✝","sexp":"(... | (:app (:c LipschitzWith) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c PseudoEMetricSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c PseudoEMetricSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 4 (:app (:c HMul.hMul) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34427","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.34429","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":15093,"sourceStart":15088,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":15095,"sourceStart":15094,"tag":"atom"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"LipschitzWith.pow_end","sourceEnd":15116,"sourceStart":15095,"tag":... | [] | [{"source":"(LipschitzWith.pow_end h n).mul_end h","source_end":15131,"source_start":15094,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34427","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.34429","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 94 | 13 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3b65e7281d96cf6f6a60d6b4120ccd1c40d3bf22eb0fc546ea2b3928a59691a1 | be6642edf1deed243df624fdc9c32efae16f89a0f1b7009e08170995211580c8 | 8b87995dc5f872eef41c2727445eb4135abac66f1f8abe11295ebc734b194a31 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,415 | YoungDiagram.mk_mem_col_iff | Mathlib/Combinatorics/Young/YoungDiagram.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>YoungDiagram.col</a>] | μ : YoungDiagram
i j : ℕ
⊢ (i, j) ∈ μ.col j ↔ (i, j) ∈ μ | ((:c Iff) ((:c Membership.mem) ((:c Prod) (:c Nat) (:c Nat)) ((:c Finset) ((:c Prod) (:c Nat) (:c Nat))) ((:c Finset.instMembership) ((:c Prod) (:c Nat) (:c Nat))) ((:c Prod.mk) (:c Nat) (:c Nat) (:fv _uniq.15615) (:fv _uniq.15616)) ((:c YoungDiagram.col) (:fv _uniq.15614) (:fv _uniq.15616))) ((:c Membership.mem) ((:c ... | [{"name":"μ","sexp":"(:c YoungDiagram)"},{"name":"i","sexp":"(:c Nat)"},{"name":"j","sexp":"(:c Nat)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)))))) (:arg :instance 2 (:instance-... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15614","is_instance":false,"is_let":false,"name":"μ","sexp":"(:c YoungDiagram)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.15615","is_instance":false,"is_let":false,"name":"i","sexp":"(:c Nat)"},{"binder_role":":implicit","co... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":12810,"sourceStart":12806,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"col","source_end":12815,"source_start":12812,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15614","is_instance":false,"is_let":false,"user_name":"μ"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.15615","is_instance":false,"is_let":false,"user_name":"i"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 93 | 2 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6b0fd63c411372a2736170525cd35e975b0bf11228228fd6c2400ab736191e3f | 5ad238a1795cb8d57ef92486cb45b183874e9cd6eaadd8159e342164efeb01a7 | 456b99bf63201f472fb01e649bfc4bdcb945e75abf34d6e9e683869c3ce8d7bb | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,416 | Finset.geomSum_ofColex_strictMono | Mathlib/Combinatorics/Colex.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨s⟩ ⟨t⟩ hst | α : Type u_1
β : Type u_2
s t : Finset ℕ
n : ℕ
hn : 2 ≤ n
⊢ StrictMono fun s => ∑ k ∈ s.ofColex, n ^ k | case toColex.toColex
α : Type u_1
β : Type u_2
s✝ t✝ : Finset ℕ
n : ℕ
hn : 2 ≤ n
s t : Finset ℕ
hst : { ofColex := s } < { ofColex := t }
⊢ (fun s => ∑ k ∈ s.ofColex, n ^ k) { ofColex := s } < (fun s => ∑ k ∈ s.ofColex, n ^ k) { ofColex := t } | ((:c StrictMono) ((:c Finset.Colex) (:c Nat)) (:c Nat) ((:c PartialOrder.toPreorder) ((:c Finset.Colex) (:c Nat)) ((:c Finset.Colex.instPartialOrder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring)))) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPar... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"((:c Finset) (:c Nat))"},{"name":"t","sexp":"((:c Finset) (:c Nat))"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c LE.le) (:c Nat) (:c instLENat) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit ... | (:app (:c StrictMono) (:arg :implicit-type 0 (:app (:c Finset.Colex) (:arg :explicit 0 (:c Nat)))) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:app (:c Finset.Colex) (:arg :explicit 0 (:c Nat))))))) (:arg :instance 3 (:instance-of (:app (:c Preorder) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.133850","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.133853","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rintro","sourceEnd":17991,"sourceStart":17985,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":17995,"sourceStart":17992,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"s","sourceEnd":17996,"sou... | [{"role":"fresh_name","source":"s","source_end":17996,"source_start":17995,"syntax_kind":"ident"},{"role":"fresh_name","source":"t","source_end":18004,"source_start":18003,"syntax_kind":"ident"},{"role":"fresh_name","source":"hst","source_end":18011,"source_start":18008,"syntax_kind":"ident"}] | [{"source":"⟨s⟩","source_end":17999,"source_start":17992,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"},{"source":"⟨t⟩","source_end":18007,"source_start":18000,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.133850","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.133853","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 81 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e0eabff22e74ed3b9678498a09bd941e9d1e7f7b294b71fe5e9bb7d08021ac86 | da269b72ee12c12ec68b98893be37373c3aea7080bc0faf8b3cff739c0dcaf7a | b145aafabf1799bf13f2ddc9636302791a75d5fa71eee075155a702f003c8a94 | 8f856362fe56660174d41c91799c839ae2a471fbdc055cdf004109f6fc582b0c |
cat-searcher/leandojo-benchmark-4-random | test | 2,417 | Finset.geomSum_ofColex_strictMono | Mathlib/Combinatorics/Colex.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.Colex.toColex_lt_toColex_iff_exists_forall_lt</a>] at hst | case toColex.toColex
α : Type u_1
β : Type u_2
s✝ t✝ : Finset ℕ
n : ℕ
hn : 2 ≤ n
s t : Finset ℕ
hst : { ofColex := s } < { ofColex := t }
⊢ (fun s => ∑ k ∈ s.ofColex, n ^ k) { ofColex := s } < (fun s => ∑ k ∈ s.ofColex, n ^ k) { ofColex := t } | case toColex.toColex
α : Type u_1
β : Type u_2
s✝ t✝ : Finset ℕ
n : ℕ
hn : 2 ≤ n
s t : Finset ℕ
hst : ∃ a ∈ t, a ∉ s ∧ ∀ b ∈ s, b ∉ t → b < a
⊢ (fun s => ∑ k ∈ s.ofColex, n ^ k) { ofColex := s } < (fun s => ∑ k ∈ s.ofColex, n ^ k) { ofColex := t } | ((:c LT.lt) (:c Nat) ((:c Preorder.toLT) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring)))) ((:lambda s ((:c Finset.Colex) (:c Nat)) ((:c Finset.sum) (:c Nat) (:c Nat) (:c Nat.instAddCommMonoid) ((:c Finset.Colex.ofColex) (:c Nat) 0)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s✝","sexp":"((:c Finset) (:c Nat))"},{"name":"t✝","sexp":"((:c Finset) (:c Nat))"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c LE.le) (:c Nat) (:c instLENat) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:li... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:lambda s :explicit (:app (:c Finset.Colex) (:arg :explicit 0 (:c Nat))) (:app (:c Finset.sum) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.133850","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.133853","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":18016,"sourceStart":18014,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":18018,"sourceStart":18017,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.Colex.toC... | [] | [{"source":"toColex_lt_toColex_iff_exists_forall_lt","source_end":18057,"source_start":18018,"syntax_kind":"ident"},{"source":"hst","source_end":18065,"source_start":18062,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.133850","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.133853","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 81 | 5 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c6f591125149bbdc216420547467841e95062341b7a82ba82fdcbab45cf9a9e2 | 8f856362fe56660174d41c91799c839ae2a471fbdc055cdf004109f6fc582b0c | fb6b83a60ceec7f1adc1df186b3efe894e455923ad00158434d4371ea00614e9 | c66bf69b9469e5eb20d8733f69e50ddcc22d17a1de3606482f2545eddb92f81b |
cat-searcher/leandojo-benchmark-4-random | test | 2,418 | Finset.geomSum_ofColex_strictMono | Mathlib/Combinatorics/Colex.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨a, hat, has, ha⟩ := hst | case toColex.toColex
α : Type u_1
β : Type u_2
s✝ t✝ : Finset ℕ
n : ℕ
hn : 2 ≤ n
s t : Finset ℕ
hst : ∃ a ∈ t, a ∉ s ∧ ∀ b ∈ s, b ∉ t → b < a
⊢ (fun s => ∑ k ∈ s.ofColex, n ^ k) { ofColex := s } < (fun s => ∑ k ∈ s.ofColex, n ^ k) { ofColex := t } | case toColex.toColex.intro.intro.intro
α : Type u_1
β : Type u_2
s✝ t✝ : Finset ℕ
n : ℕ
hn : 2 ≤ n
s t : Finset ℕ
a : ℕ
hat : a ∈ t
has : a ∉ s
ha : ∀ b ∈ s, b ∉ t → b < a
⊢ (fun s => ∑ k ∈ s.ofColex, n ^ k) { ofColex := s } < (fun s => ∑ k ∈ s.ofColex, n ^ k) { ofColex := t } | ((:c LT.lt) (:c Nat) ((:c Preorder.toLT) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring)))) ((:lambda s ((:c Finset.Colex) (:c Nat)) ((:c Finset.sum) (:c Nat) (:c Nat) (:c Nat.instAddCommMonoid) ((:c Finset.Colex.ofColex) (:c Nat) 0)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s✝","sexp":"((:c Finset) (:c Nat))"},{"name":"t✝","sexp":"((:c Finset) (:c Nat))"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c LE.le) (:c Nat) (:c instLENat) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:li... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:lambda s :explicit (:app (:c Finset.Colex) (:arg :explicit 0 (:c Nat))) (:app (:c Finset.sum) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.133850","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.133853","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"obtain","sourceEnd":18074,"sourceStart":18068,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":18078,"sourceStart":18075,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEn... | [] | [{"source":"hst","source_end":18103,"source_start":18100,"syntax_kind":"ident"},{"source":"⟨a, hat, has, ha⟩","source_end":18096,"source_start":18075,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.133850","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.133853","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 81 | 8 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 02f101a74709727c8a6ce2d78bef808aa83bf4fff4eef8947b4a3fa05df03b76 | c66bf69b9469e5eb20d8733f69e50ddcc22d17a1de3606482f2545eddb92f81b | 9d1d5fa0dfd429176a153311f3740118f0b350d32bf0030625052957b7c32914 | 3b9b7635bb8642384ec3c4a25528ad5ed0c2ffbcf00134ab1a9cad7dbd2b6a3b |
cat-searcher/leandojo-benchmark-4-random | test | 2,419 | Finset.geomSum_ofColex_strictMono | Mathlib/Combinatorics/Colex.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Finset.sum_sdiff_lt_sum_sdiff</a>] | case toColex.toColex.intro.intro.intro
α : Type u_1
β : Type u_2
s✝ t✝ : Finset ℕ
n : ℕ
hn : 2 ≤ n
s t : Finset ℕ
a : ℕ
hat : a ∈ t
has : a ∉ s
ha : ∀ b ∈ s, b ∉ t → b < a
⊢ (fun s => ∑ k ∈ s.ofColex, n ^ k) { ofColex := s } < (fun s => ∑ k ∈ s.ofColex, n ^ k) { ofColex := t } | case toColex.toColex.intro.intro.intro
α : Type u_1
β : Type u_2
s✝ t✝ : Finset ℕ
n : ℕ
hn : 2 ≤ n
s t : Finset ℕ
a : ℕ
hat : a ∈ t
has : a ∉ s
ha : ∀ b ∈ s, b ∉ t → b < a
⊢ ∑ i ∈ { ofColex := s }.ofColex \ { ofColex := t }.ofColex, n ^ i <
∑ i ∈ { ofColex := t }.ofColex \ { ofColex := s }.ofColex, n ^ i | ((:c LT.lt) (:c Nat) ((:c Preorder.toLT) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring)))) ((:lambda s ((:c Finset.Colex) (:c Nat)) ((:c Finset.sum) (:c Nat) (:c Nat) (:c Nat.instAddCommMonoid) ((:c Finset.Colex.ofColex) (:c Nat) 0)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s✝","sexp":"((:c Finset) (:c Nat))"},{"name":"t✝","sexp":"((:c Finset) (:c Nat))"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c LE.le) (:c Nat) (:c instLENat) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:li... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:lambda s :explicit (:app (:c Finset.Colex) (:arg :explicit 0 (:c Nat))) (:app (:c Finset.sum) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.133850","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.133853","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":18108,"sourceStart":18106,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":18110,"sourceStart":18109,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":18113,"sourceSt... | [] | [{"source":"sum_sdiff_lt_sum_sdiff","source_end":18136,"source_start":18114,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.133850","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.133853","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 81 | 9 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a78cb1b91e0145c6338914d67a5d4d1d194ccb9d0540c42774e4f29802efa367 | 3b9b7635bb8642384ec3c4a25528ad5ed0c2ffbcf00134ab1a9cad7dbd2b6a3b | eab552b39a1032dca07cbe95ee5f0893151039187899640024e216fcc4d5d04b | bd715a865e7d06f2dba81ebce40ffa79076eb65ce14acaef407591494bc83026 |
cat-searcher/leandojo-benchmark-4-random | test | 2,420 | Finset.geomSum_ofColex_strictMono | Mathlib/Combinatorics/Colex.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>Nat.geomSum_lt</a> hn <| by simpa).<a>LT.lt.trans_le</a> <| <a>Finset.single_le_sum</a> (fun _ _ ↦ by positivity) <| <a>Finset.mem_sdiff</a>.2 ⟨hat, has⟩ | case toColex.toColex.intro.intro.intro
α : Type u_1
β : Type u_2
s✝ t✝ : Finset ℕ
n : ℕ
hn : 2 ≤ n
s t : Finset ℕ
a : ℕ
hat : a ∈ t
has : a ∉ s
ha : ∀ b ∈ s, b ∉ t → b < a
⊢ ∑ i ∈ { ofColex := s }.ofColex \ { ofColex := t }.ofColex, n ^ i <
∑ i ∈ { ofColex := t }.ofColex \ { ofColex := s }.ofColex, n ^ i | ((:c LT.lt) (:c Nat) ((:c Preorder.toLT) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c OrderedAddCommMonoid.toPartialOrder) (:c Nat) ((:c OrderedCancelAddCommMonoid.toOrderedAddCommMonoid) (:c Nat) ((:c StrictOrderedSemiring.toOrderedCancelAddCommMonoid) (:c Nat) (:c Nat.instStrictOrderedSemiring)))))) ((:c Fins... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s✝","sexp":"((:c Finset) (:c Nat))"},{"name":"t✝","sexp":"((:c Finset) (:c Nat))"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c LE.le) (:c Nat) (:c instLENat) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:li... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Finset.sum) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Nat)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.133850","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.133853","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":18145,"sourceStart":18140,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":18147,"sourceStart":18146,"tag":"atom"},{"children":[{"children":[{"name":"Nat.geomSum_lt","semanticRole":"global","source":"Nat.geomSum_lt","sourceEnd":18161,"sourceStart"... | [] | [{"source":"(Nat.geomSum_lt hn <| by simpa).trans_le <| single_le_sum (fun _ _ ↦ by positivity) <|\n mem_sdiff.2 ⟨hat, has⟩","source_end":18265,"source_start":18146,"syntax_kind":"«term_<|_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.133850","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.133853","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 81 | 12 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9827c8de7bcd6c52ae848e7f3162cff7792a9de0a014b4daf18a435379db88c0 | bd715a865e7d06f2dba81ebce40ffa79076eb65ce14acaef407591494bc83026 | ef335e6e239175c06bf23cf95912308c98a9b4eac31df512c98b9ad18e2849ac | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,421 | Finset.geomSum_ofColex_strictMono | Mathlib/Combinatorics/Colex.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa | α : Type u_1
β : Type u_2
s✝ t✝ : Finset ℕ
n : ℕ
hn : 2 ≤ n
s t : Finset ℕ
a : ℕ
hat : a ∈ t
has : a ∉ s
ha : ∀ b ∈ s, b ∉ t → b < a
⊢ ∀ k ∈ { ofColex := s }.ofColex \ { ofColex := t }.ofColex, k < a | (:forall k (:c Nat) (:forall _ ((:c Membership.mem) (:c Nat) ((:c Finset) (:c Nat)) ((:c Finset.instMembership) (:c Nat)) 0 ((:c SDiff.sdiff) ((:c Finset) (:c Nat)) ((:c Finset.instSDiff) (:c Nat) (:c instDecidableEqNat)) ((:c Finset.Colex.ofColex) (:c Nat) ((:c Finset.Colex.toColex) (:c Nat) (:fv _uniq.134571))) ((:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s✝","sexp":"((:c Finset) (:c Nat))"},{"name":"t✝","sexp":"((:c Finset) (:c Nat))"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c LE.le) (:c Nat) (:c instLENat) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:li... | (:forall k :explicit (:c Nat) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:c Nat)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.133850","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.133853","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":18176,"sourceStart":18171,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.133850","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.133853","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 81 | 15 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9931b96b664c8adcdd4368f00d2ec6f2dbf0c60be4095d65756e45b8e2c33c87 | 0557fc3f81ca1fe01c61284ad9848ee36481053a8762096ed30520a223f762f2 | edfd421d35afd10931f43b505e9dca6d13b79f4a744024949fbf865064271c32 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,422 | Finset.geomSum_ofColex_strictMono | Mathlib/Combinatorics/Colex.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | α : Type u_1
β : Type u_2
s✝ t✝ : Finset ℕ
n : ℕ
hn : 2 ≤ n
s t : Finset ℕ
a : ℕ
hat : a ∈ t
has : a ∉ s
ha : ∀ b ∈ s, b ∉ t → b < a
x✝¹ : ℕ
x✝ : x✝¹ ∈ { ofColex := t }.ofColex \ { ofColex := s }.ofColex
⊢ 0 ≤ n ^ x✝¹ | ((:c LE.le) (:c Nat) ((:c Preorder.toLE) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c OrderedAddCommMonoid.toPartialOrder) (:c Nat) ((:c OrderedSemiring.toOrderedAddCommMonoid) (:c Nat) (:c Nat.instOrderedSemiring))))) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c Zero.toOfNat0) (:c Nat) ((:c AddMonoid.toZero) (:c N... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s✝","sexp":"((:c Finset) (:c Nat))"},{"name":"t✝","sexp":"((:c Finset) (:c Nat))"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c LE.le) (:c Nat) (:c instLENat) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:li... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Nat)) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.133850","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.133853","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"positivity","sourceEnd":18230,"sourceStart":18220,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":18230,"sourceStart":18220,"tag":"node"}],"kind":"null","source":"positivity","sourceEnd":18230,"sourceStart":182... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.133850","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.133853","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 81 | 20 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a568703a63a49646b463f8fc3cb8fb45bc83b0584f9135f32e592d37b1a077ca | 7a72e8778ef28aec4388392f53667006675066b8ae703535c4a0ccf4a67fe11c | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,423 | CategoryTheory.Functor.ShiftSequence.induced_shiftIso_hom_app_obj | Mathlib/CategoryTheory/Shift/InducedShiftSequence.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>CategoryTheory.Functor.ShiftSequence.induced.shiftIso_hom_app_obj</a> | C : Type u_1
D : Type u_2
A : Type u_3
inst✝⁹ : Category.{u_7, u_1} C
inst✝⁸ : Category.{u_6, u_2} D
inst✝⁷ : Category.{u_5, u_3} A
L : C ⥤ D
F : D ⥤ A
G : C ⥤ A
e : L ⋙ F ≅ G
M : Type u_4
inst✝⁶ : AddMonoid M
inst✝⁵ : HasShift C M
inst✝⁴ : HasShift D M
inst✝³ : L.CommShift M
inst✝² : G.ShiftSequence M
F' : M → D ⥤ A
e... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.48539) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.48539) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.48539) (:fv _uniq.48551))) ((:c Prefunctor.obj) (:fv _uniq.48536) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.48536) ((:c CategoryTheory.Catego... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"D","sexp":"(:sort (+ u_2 1))"},{"name":"A","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.48533))"},{"name":"inst✝⁸","sexp":"((:c CategoryTheory.Category) (:fv _uniq.48536))"},{"name":"inst✝⁷","sexp":"((:c CategoryTheory.Ca... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48533","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48536","is_instance":false,"is_let":false,"name":"D","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"apply","sourceEnd":5396,"sourceStart":5391,"tag":"atom"},{"name":"CategoryTheory.Functor.ShiftSequence.induced.shiftIso_hom_app_obj","semanticRole":"global","source":"induced.shiftIso_hom_app_obj","sourceEnd":5425,"sourceStart":5397,"tag":"identifier"}],"ki... | [] | [{"source":"induced.shiftIso_hom_app_obj","source_end":5425,"source_start":5397,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48533","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48536","is_instance":false,"is_let":false,"user_name":"D"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 16 | 2 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6aad24b5b0ab459be0bf7019e5f0c9413594859bfffaa84767367eaa26042f0d | 1e0a974fce491e552eab66c69ae9bc9b88ce2c7a2c7ea4e403fbbe323a1fa7c7 | 28171b421ff27567ceed1408b4e14e6da0335babe9abcde63cf81baec6acff10 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,424 | Polynomial.degree_eq_card_roots | Mathlib/Algebra/Polynomial/Splits.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Polynomial.degree_eq_natDegree</a> p_ne_zero, <a>Polynomial.natDegree_eq_card_roots</a> hsplit] | R : Type u_1
F : Type u
K : Type v
L : Type w
inst✝³ : CommRing R
inst✝² : Field K
inst✝¹ : Field L
inst✝ : Field F
i✝ : K →+* L
p : K[X]
i : K →+* L
p_ne_zero : p ≠ 0
hsplit : Splits i p
⊢ p.degree = ↑(Multiset.card (map i p).roots) | ((:c Eq) ((:c WithBot) (:c Nat)) ((:c Polynomial.degree) (:fv _uniq.72740) ((:c DivisionSemiring.toSemiring) (:fv _uniq.72740) ((:c Semifield.toDivisionSemiring) (:fv _uniq.72740) ((:c Field.toSemifield) (:fv _uniq.72740) (:fv _uniq.72748)))) (:fv _uniq.74283)) ((:c Nat.cast) ((:c WithBot) (:c Nat)) ((:c Semiring.toNat... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"F","sexp":"(:sort (+ u 1))"},{"name":"K","sexp":"(:sort (+ v 1))"},{"name":"L","sexp":"(:sort (+ w 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.72736))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.72740))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uni... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 (:fv FV10)))) (:arg :explicit 2 (:app (:c Nat.cast)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72736","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.72738","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":14061,"sourceStart":14059,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":14063,"sourceStart":14062,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"degree_eq_natDegree p_ne_zero","source_end":14092,"source_start":14063,"syntax_kind":"Lean.Parser.Term.app"},{"source":"natDegree_eq_card_roots hsplit","source_end":14124,"source_start":14094,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72736","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.72738","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 97 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cd165772d17f34cd6dc6fbc6d7314be0e1f7d3d63b3b82e77c748524435ac0fe | 2a38927b58d278b1de32102634b62e1d6d2b3ad4d0674a13b3214404fdcecce6 | 21afc64f0dc3b5434a9dbf70396e28017a1a69ff5bb3ad1cfd18b4b2919ff49e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,425 | UniformOnFun.uniformContinuous_toFun | Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>uniformContinuous_pi</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
s s' : Set α
x : α
p : Filter ι
g : ι → α
inst✝ : UniformSpace β
𝔖 : Set (Set α)
h : ⋃₀ 𝔖 = univ
⊢ UniformContinuous ⇑(toFun 𝔖) | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
s s' : Set α
x : α
p : Filter ι
g : ι → α
inst✝ : UniformSpace β
𝔖 : Set (Set α)
h : ⋃₀ 𝔖 = univ
⊢ ∀ (i : α), UniformContinuous fun x => (toFun 𝔖) x i | ((:c UniformContinuous) ((:c UniformOnFun) (:fv _uniq.77569) (:fv _uniq.77572) (:fv _uniq.77600)) (:forall _ (:fv _uniq.77569) (:fv _uniq.77572)) ((:c UniformOnFun.uniformSpace) (:fv _uniq.77569) (:fv _uniq.77572) (:fv _uniq.77596) (:fv _uniq.77600)) ((:c Pi.uniformSpace) (:fv _uniq.77569) (:lambda _ (:fv _uniq.77569) ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.77569))"},{"name":"s'","sexp":"((:c Set) (:fv _uniq.77569))"},{"name":"x","sexp":"(:fv _uniq.77569)"},{"name":"p","sex... | (:app (:c UniformContinuous) (:arg :implicit-type 0 (:app (:c UniformOnFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV10)))) (:arg :implicit-type 1 (:forall _ :explicit (:fv FV0) (:fv FV1))) (:arg :instance 2 (:instance-of (:app (:c UniformSpace) (:arg :explicit 0 (:app (:c Unif... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77569","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.77572","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":56396,"sourceStart":56394,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":56398,"sourceStart":56397,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"uniformContinuou... | [] | [{"source":"uniformContinuous_pi","source_end":56418,"source_start":56398,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77569","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.77572","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 173 | 4 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cf0e052d8ded28050cbe933b486d38036493f53f4378fe0ec13192a05a726bc5 | cab60e59ae86babbc8d5c8bff68fd0703f9163d8411e028a6d9b88bb6dc1a54a | e8e954437fd73de7297f715968c1fd079d1148943c69f5b00a66fe8840862919 | 9a6ea1cb8472d94418bd3ec03b4a595b2c8069cc0ad675bea29da7dce890a21e |
cat-searcher/leandojo-benchmark-4-random | test | 2,426 | UniformOnFun.uniformContinuous_toFun | Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>UniformOnFun.uniformContinuous_eval</a> h | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
s s' : Set α
x : α
p : Filter ι
g : ι → α
inst✝ : UniformSpace β
𝔖 : Set (Set α)
h : ⋃₀ 𝔖 = univ
⊢ ∀ (i : α), UniformContinuous fun x => (toFun 𝔖) x i | (:forall i (:fv _uniq.77569) ((:c UniformContinuous) ((:c UniformOnFun) (:fv _uniq.77569) (:fv _uniq.77572) (:fv _uniq.77600)) (:fv _uniq.77572) ((:c UniformOnFun.uniformSpace) (:fv _uniq.77569) (:fv _uniq.77572) (:fv _uniq.77596) (:fv _uniq.77600)) (:fv _uniq.77596) (:lambda x ((:c UniformOnFun) (:fv _uniq.77569) (:fv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.77569))"},{"name":"s'","sexp":"((:c Set) (:fv _uniq.77569))"},{"name":"x","sexp":"(:fv _uniq.77569)"},{"name":"p","sex... | (:forall i :explicit (:fv FV0) (:app (:c UniformContinuous) (:arg :implicit-type 0 (:app (:c UniformOnFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV10)))) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c UniformSpace) (:arg :explicit 0 (:app (:c Unifo... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77569","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.77572","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":56427,"sourceStart":56422,"tag":"atom"},{"children":[{"name":"UniformOnFun.uniformContinuous_eval","semanticRole":"global","source":"uniformContinuous_eval","sourceEnd":56450,"sourceStart":56428,"tag":"identifier"},{"children":[{"contextIndex":12,"semanticRole":"local","source... | [] | [{"source":"uniformContinuous_eval h","source_end":56452,"source_start":56428,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77569","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.77572","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 173 | 7 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f71231bc4b92aed1ba841584a83ec6f9f8bf6f16b7c123a05117f06a0cd7b42d | 9a6ea1cb8472d94418bd3ec03b4a595b2c8069cc0ad675bea29da7dce890a21e | 8f5219bcb69e7aa3d2bb0807cb6de59da84239835cf8da8de5cbb838c1ed9e2b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,429 | MeasureTheory.lintegral_tilted | Mathlib/MeasureTheory/Measure/Tilted.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>MeasureTheory.setLIntegral_univ</a>, <a>MeasureTheory.setLIntegral_tilted'</a> f g <a>MeasurableSet.univ</a>, <a>MeasureTheory.setLIntegral_univ</a>] | α : Type u_1
mα : MeasurableSpace α
μ : Measure α
f✝ f : α → ℝ
g : α → ℝ≥0∞
⊢ ∫⁻ (x : α), g x ∂μ.tilted f = ∫⁻ (x : α), ENNReal.ofReal (rexp (f x) / ∫ (x : α), rexp (f x) ∂μ) * g x ∂μ | ((:c Eq) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.46414) (:fv _uniq.46417) ((:c MeasureTheory.Measure.tilted) (:fv _uniq.46414) (:fv _uniq.46417) (:fv _uniq.46426) (:fv _uniq.46763)) (:lambda x (:fv _uniq.46414) ((:fv _uniq.46764) 0))) ((:c MeasureTheory.lintegral) (:fv _uniq.46414) (:fv _uniq.46417) (:fv ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.46414))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.46414) (:fv _uniq.46417))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.46414) (:c Real))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.46414) (:c Real))"},{"n... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure.tilted) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.46414","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.46417","is_instance":false,"is_let":false,"name":"mα","sexp":"(:app (:c MeasurableSpace) (:arg :explicit 0 ... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":8249,"sourceStart":8247,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8251,"sourceStart":8250,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"sour... | [] | [{"source":"setLIntegral_univ","source_end":8272,"source_start":8255,"syntax_kind":"ident"},{"source":"setLIntegral_tilted' f g MeasurableSet.univ","source_end":8317,"source_start":8274,"syntax_kind":"Lean.Parser.Term.app"},{"source":"setLIntegral_univ","source_end":8336,"source_start":8319,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.46414","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.46417","is_instance":false,"is_let":false,"user_name":"mα"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 26 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0087f5de47b273b6794ab2a67a030c1c480777dad1109e95393d39445271f767 | 2f3b924581647245460fd6ca65adcca9796e73e2199e66d2dd5457629146e4b7 | 387e61933ff2dc6a3f52a35c3b8d236389f140e2caee9ceaf2163b8361571775 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,430 | Nat.choose_two_right | Mathlib/Data/Nat/Choose/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction' n with n ih | n : ℕ
⊢ n.choose 2 = n * (n - 1) / 2 | ((:c Eq) (:c Nat) ((:c Nat.choose) (:fv _uniq.5876) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c HDiv.hDiv) (:c Nat) (:c Nat) (:c Nat) ((:c instHDiv) (:c Nat) (:c Nat.instDiv)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.5876) ((:c HSub.hSub)... | [{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.choose) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 2)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:lit 2... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.5876","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"induction'","sourceEnd":4003,"sourceStart":3993,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":1,"semanticRole":"local","source":"n","sourceEnd":4005,"sourceStart":4004,"tag":"identifier"}],"ki... | [] | [{"source":"n","source_end":4005,"source_start":4004,"syntax_kind":"ident"},{"source":"triangle_succ n","source_end":4050,"source_start":4035,"syntax_kind":"Lean.Parser.Term.app"},{"source":"choose","source_end":4058,"source_start":4052,"syntax_kind":"ident"},{"source":"ih","source_end":4062,"source_start":4060,"syntax... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.5876","is_instance":false,"is_let":false,"user_name":"n"}] | 23 | 2 | branch_opener | false | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f373d23c50a56d5491149165c58fb3c85aa84f2915f725608cfae8fabdf99e58 | 2052ee6f034c54e3fa34668a722f19f9cd4d97f5c5b179d7cb13f2e69e9ae9a0 | e9e977af13db95340b52852f9ed24a874f04a57e53bb9edd1a10e3351ff79078 | cf4176804ce8faa452b6bb71fc4ea1598e121183ad2ddb94ff5151fa58d7d7be | |
cat-searcher/leandojo-benchmark-4-random | test | 2,431 | Nat.choose_two_right | Mathlib/Data/Nat/Choose/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case zero
⊢ choose 0 2 = 0 * (0 - 1) / 2 | ((:c Eq) (:c Nat) ((:c Nat.choose) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c HDiv.hDiv) (:c Nat) (:c Nat) (:c Nat) ((:c instHDiv) (:c Nat) (:c Nat.instDiv)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) ... | [] | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.choose) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:lit 0))))))) (:arg :explicit 1 (:a... | [] | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":4025,"sourceStart":4021,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source... | [] | [] | [] | 23 | 7 | exact | true | 1 | 0 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 57cd945ecf228c05df1576ad3d638a2014e2a5c39450c3112d415ad6440d0be0 | 7c1c4130b1fd551d2264f203ef41e295819d5f70ffdd0889f3fc8d40845e1b9b | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,432 | Nat.choose_two_right | Mathlib/Data/Nat/Choose/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Nat.triangle_succ</a> n, <a>Nat.choose</a>, ih] | case succ
n : ℕ
ih : n.choose 2 = n * (n - 1) / 2
⊢ (n + 1).choose 2 = (n + 1) * (n + 1 - 1) / 2 | case succ
n : ℕ
ih : n.choose 2 = n * (n - 1) / 2
⊢ n.choose 1 + n * (n - 1) / 2 = n * (n - 1) / 2 + n | ((:c Eq) (:c Nat) ((:c Nat.choose) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.5893) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c HDiv.hDiv) (:c Nat) (:c Nat) (:c Nat) ((:c in... | [{"name":"n","sexp":"(:c Nat)"},{"name":"ih","sexp":"((:c Eq) (:c Nat) ((:c Nat.choose) (:fv _uniq.5893) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c HDiv.hDiv) (:c Nat) (:c Nat) (:c Nat) ((:c instHDiv) (:c Nat) (:c Nat.instDiv)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c N... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.choose) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.5893","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.5894","is_instance":false,"is_let":false,"name":"ih","sexp":"(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:ar... | {"children":[{"source":"rw","sourceEnd":4033,"sourceStart":4031,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4035,"sourceStart":4034,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Nat.tri... | [] | [{"source":"triangle_succ n","source_end":4050,"source_start":4035,"syntax_kind":"Lean.Parser.Term.app"},{"source":"choose","source_end":4058,"source_start":4052,"syntax_kind":"ident"},{"source":"ih","source_end":4062,"source_start":4060,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.5893","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.5894","is_instance":false,"is_let":false,"user_name":"ih"}] | 23 | 14 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2c511fa317f15753fefd0621289a57944752c300671558af51b70c322c6a1427 | 5d918c0e457e2535dedaa95af5e40873045090cdc7c18de461aab4bae0496687 | 95602349ccd9a0a689873599ee49f85bebcb6570f71b054d283701246512b58e | c53973163cb1fbcf880577f8d3db3111875b8e9ddbb2c3526d084e4f1cbce052 |
cat-searcher/leandojo-benchmark-4-random | test | 2,433 | Nat.choose_two_right | Mathlib/Data/Nat/Choose/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Nat.add_comm</a>] | case succ
n : ℕ
ih : n.choose 2 = n * (n - 1) / 2
⊢ n.choose 1 + n * (n - 1) / 2 = n * (n - 1) / 2 + n | ((:c Eq) (:c Nat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c Nat.choose) (:fv _uniq.5893) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) ((:c HDiv.hDiv) (:c Nat) (:c Nat) (:c Nat) ((:c instHDiv) (:c Nat) (:c Nat.instDiv)) ((:c HMul.hMul) (:c Nat) (:c Nat... | [{"name":"n","sexp":"(:c Nat)"},{"name":"ih","sexp":"((:c Eq) (:c Nat) ((:c Nat.choose) (:fv _uniq.5893) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c HDiv.hDiv) (:c Nat) (:c Nat) (:c Nat) ((:c instHDiv) (:c Nat) (:c Nat.instDiv)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c N... | (: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":":explicit","context_index":1,"internal_name":"_uniq.5893","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.5894","is_instance":false,"is_let":false,"name":"ih","sexp":"(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:ar... | {"children":[{"source":"simp","sourceEnd":4072,"sourceStart":4068,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4074,"sourceStart":4073,"tag":"atom"... | [] | [{"source":"Nat.add_comm","source_end":4086,"source_start":4074,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.5893","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.5894","is_instance":false,"is_let":false,"user_name":"ih"}] | 23 | 19 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cadf1c93492af48f8a1d86d460d061b1122f15a8cd6e9b85983995f880412bbd | c53973163cb1fbcf880577f8d3db3111875b8e9ddbb2c3526d084e4f1cbce052 | e28287607cf57c5c655996e9d411d223f288385fdba708b6504a3f8be927db07 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,434 | Vector.replicate_succ_to_snoc | Mathlib/Data/Vector/Snoc.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | clear xs | α : Type u_1
n : ℕ
xs : Vector α n
val : α
⊢ replicate (n + 1) val = (replicate n val).snoc val | α : Type u_1
n : ℕ
val : α
⊢ replicate (n + 1) val = (replicate n val).snoc val | ((:c Eq) ((:c Vector) (:fv _uniq.1557) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.1562) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) ((:c Vector.replicate) (:fv _uniq.1557) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c i... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"n","sexp":"(:c Nat)"},{"name":"xs","sexp":"((:c Vector) (:fv _uniq.1557) (:fv _uniq.1562))"},{"name":"val","sexp":"(:fv _uniq.1557)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Vector) (:arg :explicit 0 (:fv FV0)) (: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 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1557","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1562","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_i... | {"children":[{"source":"clear","sourceEnd":1525,"sourceStart":1520,"tag":"atom"},{"children":[{"contextIndex":2,"semanticRole":"local","source":"xs","sourceEnd":1528,"sourceStart":1526,"tag":"identifier"}],"kind":"null","source":"xs","sourceEnd":1528,"sourceStart":1526,"tag":"node"}],"kind":"Lean.Parser.Tactic.clear","... | [] | [{"source":"xs","source_end":1528,"source_start":1526,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1557","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1562","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq... | 11 | 4 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 00be4c518614cfab42a2da4fe6f90c86500a965c4ed832311f03d9967d80b4fb | 9598c4d6dad8e7a25d0f25bf65e92b2f6c94c84b1a465a152c29a34979b502a8 | eaaab7390377698486fc7de8a74077fca976638e9bcbe6b1d59a7795808fce8e | 5de16e0fd26e0faaa207274eb5a8b8f52cff32bf8b0b756e9c029bc784741d47 |
cat-searcher/leandojo-benchmark-4-random | test | 2,435 | Vector.replicate_succ_to_snoc | Mathlib/Data/Vector/Snoc.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction n with | zero => rfl | succ n ih => rw [<a>Vector.replicate_succ</a>] conv => rhs; rw [<a>Vector.replicate_succ</a>] rw [<a>Vector.snoc_cons</a>, ih] | α : Type u_1
n : ℕ
val : α
⊢ replicate (n + 1) val = (replicate n val).snoc val | ((:c Eq) ((:c Vector) (:fv _uniq.1557) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.1562) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) ((:c Vector.replicate) (:fv _uniq.1557) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c i... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"n","sexp":"(:c Nat)"},{"name":"val","sexp":"(:fv _uniq.1557)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Vector) (:arg :explicit 0 (:fv FV0)) (: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 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1557","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1562","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_i... | {"children":[{"source":"induction","sourceEnd":1540,"sourceStart":1531,"tag":"atom"},{"children":[{"contextIndex":1,"semanticRole":"local","source":"n","sourceEnd":1542,"sourceStart":1541,"tag":"identifier"}],"kind":"null","source":"n","sourceEnd":1542,"sourceStart":1541,"tag":"node"},{"children":[],"kind":"null","sour... | [] | [{"source":"n","source_end":1542,"source_start":1541,"syntax_kind":"ident"},{"source":"replicate_succ","source_end":1603,"source_start":1589,"syntax_kind":"ident"},{"source":"replicate_succ","source_end":1640,"source_start":1626,"syntax_kind":"ident"},{"source":"snoc_cons","source_end":1659,"source_start":1650,"syntax_... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1557","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1562","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 11 | 5 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f828f310ae2e91767971b75edcd2234d1d49e71965b2fba580f7934b8959c033 | 5de16e0fd26e0faaa207274eb5a8b8f52cff32bf8b0b756e9c029bc784741d47 | de5e6809e09a9fa71794cdcd40a8114fa2d38a72ccec369c7010734810bc5ae2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,436 | Vector.replicate_succ_to_snoc | Mathlib/Data/Vector/Snoc.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case zero
α : Type u_1
n : ℕ
val : α
⊢ replicate (0 + 1) val = (replicate 0 val).snoc val | ((:c Eq) ((:c Vector) (:fv _uniq.1557) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) ((:c Vector.replicate) (:fv _uniq.1557) ((:c HAdd.hAdd) (:c Nat... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"n","sexp":"(:c Nat)"},{"name":"val","sexp":"(:fv _uniq.1557)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Vector) (:arg :explicit 0 (:fv FV0)) (: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 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1557","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1562","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_i... | {"children":[{"children":[{"children":[{"children":[{"source":"rfl","sourceEnd":1563,"sourceStart":1560,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":1563,"sourceStart":1560,"tag":"node"}],"kind":"null","source":"rfl","sourceEnd":1563,"sourceStart":1560,"tag":"node"}],"kind":"Lean.Pars... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1557","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1562","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 11 | 8 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e585ed2bab47f71a774433cb5ffc6baa30f9fa3553d240532ec61c05e471799a | 60fa23bc72fdfdf05f63b1b657c9e2aa2d0996a8af654d7394a751d7d44dba9b | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,437 | Vector.replicate_succ_to_snoc | Mathlib/Data/Vector/Snoc.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Vector.replicate_succ</a>] | case succ
α : Type u_1
n✝ : ℕ
val : α
n : ℕ
ih : replicate (n + 1) val = (replicate n val).snoc val
⊢ replicate (n + 1 + 1) val = (replicate (n + 1) val).snoc val | case succ
α : Type u_1
n✝ : ℕ
val : α
n : ℕ
ih : replicate (n + 1) val = (replicate n val).snoc val
⊢ val ::ᵥ replicate (n + 1) val = (replicate (n + 1) val).snoc val | ((:c Eq) ((:c Vector) (:fv _uniq.1557) ((: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.1724) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) ((:c OfNat.ofNat) (:c Nat) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"val","sexp":"(:fv _uniq.1557)"},{"name":"n","sexp":"(:c Nat)"},{"name":"ih","sexp":"((:c Eq) ((:c Vector) (:fv _uniq.1557) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.1724) ((:c OfNat.ofN... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Vector) (:arg :explicit 0 (:fv FV0)) (: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 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1557","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1562","is_instance":false,"is_let":false,"name":"n✝","sexp":"(:c Nat)"},{"binder_role":":explicit","context_... | {"children":[{"source":"rw","sourceEnd":1587,"sourceStart":1585,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1589,"sourceStart":1588,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Vector.replicate_suc... | [] | [{"source":"replicate_succ","source_end":1603,"source_start":1589,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1557","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1562","is_instance":false,"is_let":false,"user_name":"n✝"},{"binder_role":":explicit","context_index":3,"internal_name":"_uni... | 11 | 14 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 12a65cea584e8e74cbc15ff52b6fd7a19233319accc480bea0399c132fbba71e | 657d9d4e02f666a4ac1d13190b4c50ad8d3ecaf2161460964db350e500a05fb8 | 56379fbcf75dcab542805db481d1030c8103bd2b56186ad7b381888f7d36dd58 | 78a2a9ec5cd6f57edeab09caf9ee0cfbec8d145526adb853700d9940f046911b |
cat-searcher/leandojo-benchmark-4-random | test | 2,438 | Vector.replicate_succ_to_snoc | Mathlib/Data/Vector/Snoc.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | conv => rhs; rw [<a>Vector.replicate_succ</a>] | case succ
α : Type u_1
n✝ : ℕ
val : α
n : ℕ
ih : replicate (n + 1) val = (replicate n val).snoc val
⊢ val ::ᵥ replicate (n + 1) val = (replicate (n + 1) val).snoc val | case succ
α : Type u_1
n✝ : ℕ
val : α
n : ℕ
ih : replicate (n + 1) val = (replicate n val).snoc val
⊢ val ::ᵥ replicate (n + 1) val = (val ::ᵥ replicate n val).snoc val | ((:c Eq) ((:c Vector) (:fv _uniq.1557) ((: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.1724) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) ((:c OfNat.ofNat) (:c Nat) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"val","sexp":"(:fv _uniq.1557)"},{"name":"n","sexp":"(:c Nat)"},{"name":"ih","sexp":"((:c Eq) ((:c Vector) (:fv _uniq.1557) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.1724) ((:c OfNat.ofN... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Vector) (:arg :explicit 0 (:fv FV0)) (: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 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1557","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1562","is_instance":false,"is_let":false,"name":"n✝","sexp":"(:c Nat)"},{"binder_role":":explicit","context_... | {"children":[{"source":"conv","sourceEnd":1613,"sourceStart":1609,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":"=>","sourceEnd":1616,"sourceStart":1614,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"rh... | [] | [{"source":"replicate_succ","source_end":1640,"source_start":1626,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1557","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1562","is_instance":false,"is_let":false,"user_name":"n✝"},{"binder_role":":explicit","context_index":3,"internal_name":"_uni... | 11 | 17 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e4f9de521fc80e5ed7d5afffc0bc6f06b206182ead8394f882340edc61512282 | 78a2a9ec5cd6f57edeab09caf9ee0cfbec8d145526adb853700d9940f046911b | eef205548a77422947c1e800551e98a69dcfdd264127134c6ef75ad8f7f90e58 | eca3f37a0eb89e0d94011bc95f500d420f3d20e401f08ead685d9a0e7b40b367 |
cat-searcher/leandojo-benchmark-4-random | test | 2,439 | Vector.replicate_succ_to_snoc | Mathlib/Data/Vector/Snoc.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Vector.snoc_cons</a>, ih] | case succ
α : Type u_1
n✝ : ℕ
val : α
n : ℕ
ih : replicate (n + 1) val = (replicate n val).snoc val
⊢ val ::ᵥ replicate (n + 1) val = (val ::ᵥ replicate n val).snoc val | ((:c Eq) ((:c Vector) (:fv _uniq.1557) ((: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.1724) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) ((:c OfNat.ofNat) (:c Nat) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"val","sexp":"(:fv _uniq.1557)"},{"name":"n","sexp":"(:c Nat)"},{"name":"ih","sexp":"((:c Eq) ((:c Vector) (:fv _uniq.1557) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.1724) ((:c OfNat.ofN... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Vector) (:arg :explicit 0 (:fv FV0)) (: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 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1557","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1562","is_instance":false,"is_let":false,"name":"n✝","sexp":"(:c Nat)"},{"binder_role":":explicit","context_... | {"children":[{"source":"rw","sourceEnd":1648,"sourceStart":1646,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1650,"sourceStart":1649,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Vector.snoc_cons","s... | [] | [{"source":"snoc_cons","source_end":1659,"source_start":1650,"syntax_kind":"ident"},{"source":"ih","source_end":1663,"source_start":1661,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1557","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1562","is_instance":false,"is_let":false,"user_name":"n✝"},{"binder_role":":explicit","context_index":3,"internal_name":"_uni... | 11 | 25 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2e9042f7f2a37b8fa9aa24e4d8e969a25ead17fd9bcf853cebd761daebe5ab24 | eca3f37a0eb89e0d94011bc95f500d420f3d20e401f08ead685d9a0e7b40b367 | fa76e11137ff87a85099f20eb2e595d57e0623b59497403da28458389563b91d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,440 | Computable.list_ofFn | Mathlib/Computability/Partrec.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>List.ofFn_zero</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
σ : Type u_4
inst✝³ : Primcodable α
inst✝² : Primcodable β
inst✝¹ : Primcodable γ
inst✝ : Primcodable σ
x✝¹ : Fin 0 → α → σ
x✝ : ∀ (i : Fin 0), Computable (x✝¹ i)
⊢ Computable fun a => List.ofFn fun i => x✝¹ i a | α : Type u_1
β : Type u_2
γ : Type u_3
σ : Type u_4
inst✝³ : Primcodable α
inst✝² : Primcodable β
inst✝¹ : Primcodable γ
inst✝ : Primcodable σ
x✝¹ : Fin 0 → α → σ
x✝ : ∀ (i : Fin 0), Computable (x✝¹ i)
⊢ Computable fun a => [] | ((:c Computable) (:fv _uniq.93934) ((:c List) (:fv _uniq.93943)) (:fv _uniq.93946) ((:c Primcodable.list) (:fv _uniq.93943) (:fv _uniq.93955)) (:lambda a (:fv _uniq.93934) ((:c List.ofFn) (:fv _uniq.93943) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))) (:lambda i ((:c Fin) ((:c OfNat.ofNat) (:c Nat) ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"σ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝³","sexp":"((:c Primcodable) (:fv _uniq.93934))"},{"name":"inst✝²","sexp":"((:c Primcodable) (:fv _uniq.93937))"},{"name":"inst✝¹","sexp":"((:c P... | (:app (:c Computable) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 2 (:instance-of (:app (:c Primcodable) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Primcodable) (:arg :explicit 0 (:app (:c List) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.93934","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93937","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":30641,"sourceStart":30637,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":30646,"sourceStart":30642,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":306... | [] | [{"source":"List.ofFn_zero","source_end":30662,"source_start":30648,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.93934","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93937","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 251 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dc228213e4f137a9628c28d1b8ff70fe4bfcc9efdb2d4ce0d69130d43628d96b | 2656bdeae4f5598d3345dfb188a72af70a5a2ada9d8387ad8d05c09aaa8da991 | eda5a59b0d6ff5c213103e491dda32f8658cb71ef038f2d2e8f5348b2c0f479a | 5ab261fa1002a0762d46786bce17bde426f24a6c5124b898778db8e320d77372 |
cat-searcher/leandojo-benchmark-4-random | test | 2,441 | Computable.list_ofFn | Mathlib/Computability/Partrec.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Computable.const</a> [] | α : Type u_1
β : Type u_2
γ : Type u_3
σ : Type u_4
inst✝³ : Primcodable α
inst✝² : Primcodable β
inst✝¹ : Primcodable γ
inst✝ : Primcodable σ
x✝¹ : Fin 0 → α → σ
x✝ : ∀ (i : Fin 0), Computable (x✝¹ i)
⊢ Computable fun a => [] | ((:c Computable) (:fv _uniq.93934) ((:c List) (:fv _uniq.93943)) (:fv _uniq.93946) ((:c Primcodable.list) (:fv _uniq.93943) (:fv _uniq.93955)) (:lambda a (:fv _uniq.93934) ((:c List.nil) (:fv _uniq.93943)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"σ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝³","sexp":"((:c Primcodable) (:fv _uniq.93934))"},{"name":"inst✝²","sexp":"((:c Primcodable) (:fv _uniq.93937))"},{"name":"inst✝¹","sexp":"((:c P... | (:app (:c Computable) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 2 (:instance-of (:app (:c Primcodable) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Primcodable) (:arg :explicit 0 (:app (:c List) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.93934","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93937","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":30673,"sourceStart":30668,"tag":"atom"},{"children":[{"name":"Computable.const","semanticRole":"global","source":"const","sourceEnd":30679,"sourceStart":30674,"tag":"identifier"},{"children":[{"children":[{"source":"[","sourceEnd":30681,"sourceStart":30680,"tag":"atom"},{"chil... | [] | [{"source":"const []","source_end":30682,"source_start":30674,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.93934","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93937","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 251 | 5 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 51aa0075d11afd7067fae7daeb3965b5cde3e6180d666694a7e4848934b730da | 5ab261fa1002a0762d46786bce17bde426f24a6c5124b898778db8e320d77372 | 38d657d0162ccc1a1039cf8b81468823f5e30586d3e30e7d0915ac7c5f601193 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,442 | Computable.list_ofFn | Mathlib/Computability/Partrec.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>List.ofFn_succ</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
σ : Type u_4
inst✝³ : Primcodable α
inst✝² : Primcodable β
inst✝¹ : Primcodable γ
inst✝ : Primcodable σ
n : ℕ
f : Fin (n + 1) → α → σ
hf : ∀ (i : Fin (n + 1)), Computable (f i)
⊢ Computable fun a => List.ofFn fun i => f i a | α : Type u_1
β : Type u_2
γ : Type u_3
σ : Type u_4
inst✝³ : Primcodable α
inst✝² : Primcodable β
inst✝¹ : Primcodable γ
inst✝ : Primcodable σ
n : ℕ
f : Fin (n + 1) → α → σ
hf : ∀ (i : Fin (n + 1)), Computable (f i)
⊢ Computable fun a => f 0 a :: List.ofFn fun i => f i.succ a | ((:c Computable) (:fv _uniq.93934) ((:c List) (:fv _uniq.93943)) (:fv _uniq.93946) ((:c Primcodable.list) (:fv _uniq.93943) (:fv _uniq.93955)) (:lambda a (:fv _uniq.93934) ((:c List.ofFn) (:fv _uniq.93943) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.94257) ((:c OfNat.o... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"σ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝³","sexp":"((:c Primcodable) (:fv _uniq.93934))"},{"name":"inst✝²","sexp":"((:c Primcodable) (:fv _uniq.93937))"},{"name":"inst✝¹","sexp":"((:c P... | (:app (:c Computable) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 2 (:instance-of (:app (:c Primcodable) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Primcodable) (:arg :explicit 0 (:app (:c List) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.93934","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93937","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":30714,"sourceStart":30710,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":30719,"sourceStart":30715,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":307... | [] | [{"source":"List.ofFn_succ","source_end":30735,"source_start":30721,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.93934","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93937","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 251 | 10 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 512ca373f2fbae935302e7f51e404d60f060f9bd89670327964d2293c21324c0 | cd798504e11601a67f2a2f3f77364416e4e43fef39e079d952b1e123673b71da | f5cf371b77b109a42ccf74f8e07800b03cb1128cfb570c1a68bc4b3a960d5897 | 81c5a0bf068f825d71c67316e1ffd092d8e8c468b248f710ebc814507c85d100 |
cat-searcher/leandojo-benchmark-4-random | test | 2,443 | Computable.list_ofFn | Mathlib/Computability/Partrec.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact list_cons.comp (hf 0) (list_ofFn fun i => hf i.succ) | α : Type u_1
β : Type u_2
γ : Type u_3
σ : Type u_4
inst✝³ : Primcodable α
inst✝² : Primcodable β
inst✝¹ : Primcodable γ
inst✝ : Primcodable σ
n : ℕ
f : Fin (n + 1) → α → σ
hf : ∀ (i : Fin (n + 1)), Computable (f i)
⊢ Computable fun a => f 0 a :: List.ofFn fun i => f i.succ a | ((:c Computable) (:fv _uniq.93934) ((:c List) (:fv _uniq.93943)) (:fv _uniq.93946) ((:c Primcodable.list) (:fv _uniq.93943) (:fv _uniq.93955)) (:lambda a (:fv _uniq.93934) ((:c List.cons) (:fv _uniq.93943) ((:fv _uniq.94258) ((:c OfNat.ofNat) ((:c Fin) ((:c Nat.succ) (:fv _uniq.94257))) (:lit 0) ((:c Fin.instOfNatOfNeZ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"σ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝³","sexp":"((:c Primcodable) (:fv _uniq.93934))"},{"name":"inst✝²","sexp":"((:c Primcodable) (:fv _uniq.93937))"},{"name":"inst✝¹","sexp":"((:c P... | (:app (:c Computable) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 2 (:instance-of (:app (:c Primcodable) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Primcodable) (:arg :explicit 0 (:app (:c List) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.93934","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93937","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":30746,"sourceStart":30741,"tag":"atom"},{"children":[{"source":"list_cons.comp","sourceEnd":30761,"sourceStart":30747,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":30763,"sourceStart":30762,"tag":"atom"},{"children":[{"contextIndex":11,"semanticRole":... | [] | [{"source":"list_cons.comp (hf 0) (list_ofFn fun i => hf i.succ)","source_end":30799,"source_start":30747,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.93934","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93937","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 251 | 11 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 97590f83378c5b0513f557fbcd0753d755be6a9d29f4eae75726f0cdf049a69d | 81c5a0bf068f825d71c67316e1ffd092d8e8c468b248f710ebc814507c85d100 | 1e9228b21af9a4082b1678e89ecdb8ebb54e613fc132b90893421a1773d8faab | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,444 | IsSquare.pow | Mathlib/Algebra/Group/Even.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨a, rfl⟩ | F : Type u_1
α : Type u_2
β : Type u_3
R : Type u_4
inst✝ : Monoid α
n✝ : ℕ
a : α
n : ℕ
⊢ IsSquare a → IsSquare (a ^ n) | case intro
F : Type u_1
α : Type u_2
β : Type u_3
R : Type u_4
inst✝ : Monoid α
n✝ n : ℕ
a : α
⊢ IsSquare ((a * a) ^ n) | (:forall _ ((:c IsSquare) (:fv _uniq.4470) ((:c MulOneClass.toMul) (:fv _uniq.4470) ((:c Monoid.toMulOneClass) (:fv _uniq.4470) (:fv _uniq.4479))) (:fv _uniq.4483)) ((:c IsSquare) (:fv _uniq.4470) ((:c MulOneClass.toMul) (:fv _uniq.4470) ((:c Monoid.toMulOneClass) (:fv _uniq.4470) (:fv _uniq.4479))) ((:c HPow.hPow) (:f... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c Monoid) (:fv _uniq.4470))"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"a","sexp":"(:fv _uniq.4470)"},{"name":"n","sexp":"(:c Nat)"}] | (:forall _ :explicit (:app (:c IsSquare) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Mul) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV6))) (:app (:c IsSquare) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Mul) (:arg :explicit 0 (:fv FV1))))) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4467","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4470","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"rintro","sourceEnd":4398,"sourceStart":4392,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":4402,"sourceStart":4399,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":4403,"sourceSt... | [{"role":"fresh_name","source":"a","source_end":4403,"source_start":4402,"syntax_kind":"ident"}] | [{"source":"⟨a, rfl⟩","source_end":4411,"source_start":4399,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4467","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4470","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 45 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0b0af0861fbbae877db621395fcfba9c676865af666d6d7d3658472b75248057 | d51b35b499ff042940afe9a28dcff0cee213dc4230091546fd3581fd8fbb689c | d95672bc52af15f4b67659d8adda0b269a766e8d73a28fc812fb1ff59e7917d0 | e93bd13e33a4c9567eb10625f926f705d14565d0b24f235c3a4ef875ef5b55a7 |
cat-searcher/leandojo-benchmark-4-random | test | 2,445 | IsSquare.pow | Mathlib/Algebra/Group/Even.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨a ^ n, (<a>Commute.refl</a> _).<a>Commute.mul_pow</a> _⟩ | case intro
F : Type u_1
α : Type u_2
β : Type u_3
R : Type u_4
inst✝ : Monoid α
n✝ n : ℕ
a : α
⊢ IsSquare ((a * a) ^ n) | ((:c IsSquare) (:fv _uniq.4470) ((:c MulOneClass.toMul) (:fv _uniq.4470) ((:c Monoid.toMulOneClass) (:fv _uniq.4470) (:fv _uniq.4479))) ((:c HPow.hPow) (:fv _uniq.4470) (:c Nat) (:fv _uniq.4470) ((:c instHPow) (:fv _uniq.4470) (:c Nat) ((:c Monoid.toNatPow) (:fv _uniq.4470) (:fv _uniq.4479))) ((:c HMul.hMul) (:fv _uniq... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c Monoid) (:fv _uniq.4470))"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"a","sexp":"(:fv _uniq.4470)"}] | (:app (:c IsSquare) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Mul) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HPow)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4467","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4470","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"exact","sourceEnd":4418,"sourceStart":4413,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":4422,"sourceStart":4419,"tag":"atom"},{"children":[{"children":[{"contextIndex":7,"semanticRole":"local","source":"a","sourceEnd":4423,"sourceStart":4422,"tag":"identifier"},{"source":"^","sourceEnd":... | [] | [{"source":"⟨a ^ n, (Commute.refl _).mul_pow _⟩","source_end":4458,"source_start":4419,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4467","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4470","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 45 | 6 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d2def3babc2f601aa68f4b6e051f24d6be651747f714231c4e915748acf47e8d | e93bd13e33a4c9567eb10625f926f705d14565d0b24f235c3a4ef875ef5b55a7 | 05a4a84f60ec945af092654a3db21cdba9bcf5fd2d9efc68690d5c6e8731fd6c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,446 | CategoryTheory.Limits.coequalizerComparison_map_desc | Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [← G.map_comp, w] | C : Type u
inst✝³ : Category.{v, u} C
X Y : C
f g : X ⟶ Y
D : Type u₂
inst✝² : Category.{v₂, u₂} D
G : C ⥤ D
inst✝¹ : HasCoequalizer f g
inst✝ : HasCoequalizer (G.map f) (G.map g)
Z : C
h : Y ⟶ Z
w : f ≫ h = g ≫ h
⊢ G.map f ≫ G.map h = G.map g ≫ G.map h | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.204724) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.204724) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.204724) (:fv _uniq.204727))) ((:c Prefunctor.obj) (:fv _uniq.204610) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.204610) ((:c CategoryTheory.... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.204610))"},{"name":"X","sexp":"(:fv _uniq.204610)"},{"name":"Y","sexp":"(:fv _uniq.204610)"},{"name":"f","sexp":"((:c Quiver.Hom) (:fv _uniq.204610) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.204610) ((... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV6))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.204610","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.204613","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Catego... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":57055,"sourceStart":57051,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":57060,"sourceStart":57056,"tag":"atom"}],"kind"... | [] | [{"source":"G.map_comp","source_end":57076,"source_start":57066,"syntax_kind":"ident"},{"source":"w","source_end":57079,"source_start":57078,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.204610","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.204613","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 332 | 2 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5082b8a899f1dbf8116aa3a0c7869031d5e8e512f6436c605d26d6a50d3e1ab1 | 6fcded2f583ade2c734b23aa8579312b8ff13f856daa23539616dc87ce5dafea | 7858f6e6e48835b792e1d02b33b4d04b48c1685c7125803bd1b603afbc57db99 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,447 | CategoryTheory.Limits.coequalizerComparison_map_desc | Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>CategoryTheory.Limits.coequalizer.hom_ext</a> | C : Type u
inst✝³ : Category.{v, u} C
X Y : C
f g : X ⟶ Y
D : Type u₂
inst✝² : Category.{v₂, u₂} D
G : C ⥤ D
inst✝¹ : HasCoequalizer f g
inst✝ : HasCoequalizer (G.map f) (G.map g)
Z : C
h : Y ⟶ Z
w : f ≫ h = g ≫ h
⊢ coequalizerComparison f g G ≫ G.map (coequalizer.desc h w) = coequalizer.desc (G.map h) ⋯ | case h
C : Type u
inst✝³ : Category.{v, u} C
X Y : C
f g : X ⟶ Y
D : Type u₂
inst✝² : Category.{v₂, u₂} D
G : C ⥤ D
inst✝¹ : HasCoequalizer f g
inst✝ : HasCoequalizer (G.map f) (G.map g)
Z : C
h : Y ⟶ Z
w : f ≫ h = g ≫ h
⊢ coequalizer.π (G.map f) (G.map g) ≫ coequalizerComparison f g G ≫ G.map (coequalizer.desc h w) =
... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.204724) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.204724) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.204724) (:fv _uniq.204727))) ((:c CategoryTheory.Limits.coequalizer) (:fv _uniq.204724) (:fv _uniq.204727) ((:c Prefunctor.obj) (:fv _uniq.204610) ((:c C... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.204610))"},{"name":"X","sexp":"(:fv _uniq.204610)"},{"name":"Y","sexp":"(:fv _uniq.204610)"},{"name":"f","sexp":"((:c Quiver.Hom) (:fv _uniq.204610) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.204610) ((... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV6))))) (:arg :explicit 2 (:app (:c CategoryTheory.Limits.coequalizer) (:arg :implicit-type 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c Catego... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.204610","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.204613","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Catego... | {"children":[{"source":"apply","sourceEnd":57095,"sourceStart":57090,"tag":"atom"},{"name":"CategoryTheory.Limits.coequalizer.hom_ext","semanticRole":"global","source":"coequalizer.hom_ext","sourceEnd":57115,"sourceStart":57096,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply coequalizer.hom_ext",... | [] | [{"source":"coequalizer.hom_ext","source_end":57115,"source_start":57096,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.204610","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.204613","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 332 | 9 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f255b49bda474505de80a296e59cd96e4ecf57a3b7f21858944dcda47b5bef89 | ecbd2476c2c7825250b99e0bba039263ce45fd79be2ed2be7d37de677252c43a | 69448cafe405d4f31af7e57a9ad9cfbe0c7b99f1a7564d55957a1263e0ef50e2 | e00101e04a4f322b4dbd5e308f29a996f2f689edbbb70a463834438769e7df3b |
cat-searcher/leandojo-benchmark-4-random | test | 2,448 | CategoryTheory.Limits.coequalizerComparison_map_desc | Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [← G.map_comp] | case h
C : Type u
inst✝³ : Category.{v, u} C
X Y : C
f g : X ⟶ Y
D : Type u₂
inst✝² : Category.{v₂, u₂} D
G : C ⥤ D
inst✝¹ : HasCoequalizer f g
inst✝ : HasCoequalizer (G.map f) (G.map g)
Z : C
h : Y ⟶ Z
w : f ≫ h = g ≫ h
⊢ coequalizer.π (G.map f) (G.map g) ≫ coequalizerComparison f g G ≫ G.map (coequalizer.desc h w) =
... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.204724) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.204724) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.204724) (:fv _uniq.204727))) ((:c Prefunctor.obj) (:fv _uniq.204610) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.204610) ((:c CategoryTheory.... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.204610))"},{"name":"X","sexp":"(:fv _uniq.204610)"},{"name":"Y","sexp":"(:fv _uniq.204610)"},{"name":"f","sexp":"((:c Quiver.Hom) (:fv _uniq.204610) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.204610) ((... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV6))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.204610","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.204613","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Catego... | {"children":[{"source":"simp","sourceEnd":57122,"sourceStart":57118,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":57124,"sourceStart":57123,"tag":"a... | [] | [{"source":"G.map_comp","source_end":57138,"source_start":57128,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.204610","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.204613","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 332 | 10 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 79b96ce51a6579e3fe094e67c13deaec4a0f0cca08dc972cc93c1ce795ef47c4 | e00101e04a4f322b4dbd5e308f29a996f2f689edbbb70a463834438769e7df3b | 9c641cccd254d0daa0178136d60c1c0e579ed418d19634a4fa0a9fad80827b6d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,449 | sbtw_one_zero_iff | Mathlib/Analysis/Convex/Between.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>sbtw_comm</a>, <a>sbtw_zero_one_iff</a>] | R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : OrderedRing R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
x : R
⊢ Sbtw R 1 x 0 ↔ x ∈ Set.Ioo 0 1 | ((:c Iff) ((:c Sbtw) (:fv _uniq.251972) (:fv _uniq.251972) (:fv _uniq.251972) (:fv _uniq.251987) ((:c OrderedAddCommGroup.toAddCommGroup) (:fv _uniq.251972) ((:c OrderedRing.toOrderedAddCommGroup) (:fv _uniq.251972) (:fv _uniq.251987))) ((:c Semiring.toModule) (:fv _uniq.251972) ((:c OrderedSemiring.toSemiring) (:fv _u... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c OrderedRing) (:fv _uniq.251972))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup) (:fv _un... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Sbtw) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c OrderedRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV0)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251972","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251975","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":17575,"sourceStart":17573,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":17577,"sourceStart":17576,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"sbtw_comm","source_end":17586,"source_start":17577,"syntax_kind":"ident"},{"source":"sbtw_zero_one_iff","source_end":17605,"source_start":17588,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251972","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.251975","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 151 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5df7fb333977cb8d28746d932fe0dfade011925cc42150efa0c4955c8c0f681c | f0981db821e413c3dce3f9ce1ff1621df278dbb1946d8d2024f045fa748ddfc7 | 6968fd386d4d4fee5f1c968dd5fbc279f02a6ef641f6d1b5a60bc1a2f1d740c9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,450 | CompositionSeries.isMaximal_eraseLast_last | Mathlib/Order/JordanHolder.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : s.length - 1 + 1 = s.length := by conv_rhs => rw [← <a>Nat.add_one_sub_one</a> s.length]; rw [<a>Nat.succ_sub</a> h] | X : Type u
inst✝¹ : Lattice X
inst✝ : JordanHolderLattice X
s : CompositionSeries X
h : 0 < s.length
⊢ IsMaximal (eraseLast s).last (last s) | X : Type u
inst✝¹ : Lattice X
inst✝ : JordanHolderLattice X
s : CompositionSeries X
h : 0 < s.length
this : s.length - 1 + 1 = s.length
⊢ IsMaximal (eraseLast s).last (last s) | ((:c JordanHolderLattice.IsMaximal) (:fv _uniq.21170) (:fv _uniq.21173) (:fv _uniq.21186) ((:c RelSeries.last) (:fv _uniq.21170) ((:c JordanHolderLattice.IsMaximal) (:fv _uniq.21170) (:fv _uniq.21173) (:fv _uniq.21186)) ((:c RelSeries.eraseLast) (:fv _uniq.21170) ((:c JordanHolderLattice.IsMaximal) (:fv _uniq.21170) (:... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Lattice) (:fv _uniq.21170))"},{"name":"inst✝","sexp":"((:c JordanHolderLattice) (:fv _uniq.21170) (:fv _uniq.21173))"},{"name":"s","sexp":"((:c CompositionSeries) (:fv _uniq.21170) (:fv _uniq.21173) (:fv _uniq.21186))"},{"name":"h","sexp":"((:c LT.lt)... | (:app (:c JordanHolderLattice.IsMaximal) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Lattice) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c JordanHolderLattice) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Lattice) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21170","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21173","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Lattice) (:arg :explici... | {"children":[{"source":"have","sourceEnd":13824,"sourceStart":13820,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":13825,"sourceStart":13825,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":13825,"sourceStart":13825,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"s.length - 1 + 1 = s.length","source_end":13854,"source_start":13827,"syntax_kind":"«term_=_»"},{"source":"Nat.add_one_sub_one s.length","source_end":13913,"source_start":13885,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Nat.succ_sub h","source_end":13934,"source_start":13920,"syntax_kind":"Lean.Parser... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21170","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21173","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 82 | 4 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f3322f2b64acdf6854e65484a0b9a75d28a602748c14ad0d7b0d855c3ae05671 | f0bd23e756dbf3c4caa8f78332b0be82c995a816842668cdda782b0dfdabde0e | 65364ea5fbd5f39b18755275ef25067332b0e7ccc063165d2c37e9170c70e87d | 955303cb099553e6e2e779f49c9942da7eef039388aacd74b831bea3666053d4 |
cat-searcher/leandojo-benchmark-4-random | test | 2,451 | CompositionSeries.isMaximal_eraseLast_last | Mathlib/Order/JordanHolder.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>RelSeries.last_eraseLast</a>, <a>RelSeries.last</a>] | X : Type u
inst✝¹ : Lattice X
inst✝ : JordanHolderLattice X
s : CompositionSeries X
h : 0 < s.length
this : s.length - 1 + 1 = s.length
⊢ IsMaximal (eraseLast s).last (last s) | X : Type u
inst✝¹ : Lattice X
inst✝ : JordanHolderLattice X
s : CompositionSeries X
h : 0 < s.length
this : s.length - 1 + 1 = s.length
⊢ IsMaximal (s.toFun ⟨s.length.pred, ⋯⟩) (s.toFun (Fin.last s.length)) | ((:c JordanHolderLattice.IsMaximal) (:fv _uniq.21170) (:fv _uniq.21173) (:fv _uniq.21186) ((:c RelSeries.last) (:fv _uniq.21170) ((:c JordanHolderLattice.IsMaximal) (:fv _uniq.21170) (:fv _uniq.21173) (:fv _uniq.21186)) ((:c RelSeries.eraseLast) (:fv _uniq.21170) ((:c JordanHolderLattice.IsMaximal) (:fv _uniq.21170) (:... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Lattice) (:fv _uniq.21170))"},{"name":"inst✝","sexp":"((:c JordanHolderLattice) (:fv _uniq.21170) (:fv _uniq.21173))"},{"name":"s","sexp":"((:c CompositionSeries) (:fv _uniq.21170) (:fv _uniq.21173) (:fv _uniq.21186))"},{"name":"h","sexp":"((:c LT.lt)... | (:app (:c JordanHolderLattice.IsMaximal) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Lattice) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c JordanHolderLattice) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Lattice) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21170","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21173","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Lattice) (:arg :explici... | {"children":[{"source":"rw","sourceEnd":13940,"sourceStart":13938,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13942,"sourceStart":13941,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"RelSeries.last_e... | [] | [{"source":"last_eraseLast","source_end":13956,"source_start":13942,"syntax_kind":"ident"},{"source":"last","source_end":13962,"source_start":13958,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21170","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21173","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 82 | 14 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 91e0de345876c4c9ed9137896101c351db735199b7028dc11fae51557c21f991 | 955303cb099553e6e2e779f49c9942da7eef039388aacd74b831bea3666053d4 | e11977d5370fa3664a54484834c352d2341c866b38fe83cdd19f427eb450f6f1 | de6b44a8c55a0312cd797b3a914a91adac769d519491ada691082d89afea1928 |
cat-searcher/leandojo-benchmark-4-random | test | 2,452 | CompositionSeries.isMaximal_eraseLast_last | Mathlib/Order/JordanHolder.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert s.step ⟨s.length - 1, by omega⟩ | X : Type u
inst✝¹ : Lattice X
inst✝ : JordanHolderLattice X
s : CompositionSeries X
h : 0 < s.length
this : s.length - 1 + 1 = s.length
⊢ IsMaximal (s.toFun ⟨s.length.pred, ⋯⟩) (s.toFun (Fin.last s.length)) | case h.e'_5.h.e'_4
X : Type u
inst✝¹ : Lattice X
inst✝ : JordanHolderLattice X
s : CompositionSeries X
h : 0 < s.length
this : s.length - 1 + 1 = s.length
⊢ Fin.last s.length = ⟨s.length - 1, ⋯⟩.succ | ((:c JordanHolderLattice.IsMaximal) (:fv _uniq.21170) (:fv _uniq.21173) (:fv _uniq.21186) ((:c RelSeries.toFun) (:fv _uniq.21170) ((:c JordanHolderLattice.IsMaximal) (:fv _uniq.21170) (:fv _uniq.21173) (:fv _uniq.21186)) (:fv _uniq.21302) ((:c Fin.mk) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Lattice) (:fv _uniq.21170))"},{"name":"inst✝","sexp":"((:c JordanHolderLattice) (:fv _uniq.21170) (:fv _uniq.21173))"},{"name":"s","sexp":"((:c CompositionSeries) (:fv _uniq.21170) (:fv _uniq.21173) (:fv _uniq.21186))"},{"name":"h","sexp":"((:c LT.lt)... | (:app (:c JordanHolderLattice.IsMaximal) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Lattice) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c JordanHolderLattice) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Lattice) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21170","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21173","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Lattice) (:arg :explici... | {"children":[{"source":"convert","sourceEnd":13973,"sourceStart":13966,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"s.step","sourceEnd":13980,"sourceStart":13974,"tag":"identifier"},{"children":[{"children":[{"source"... | [] | [{"source":"s.step ⟨s.length - 1, by omega⟩","source_end":14009,"source_start":13974,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21170","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21173","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 82 | 18 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0cb222af41e5ab5858afb84e16405d8a8841b99ca07588210e5f800436559a1a | de6b44a8c55a0312cd797b3a914a91adac769d519491ada691082d89afea1928 | 9cb4567aa5999e96ffc7fae1e0720e30d5600124256637581e0c178059fb65bf | 0c52fe32ecf1870fa328e44cebda19d7d4be8f50a7b6d20a36f1a80c8ee3f25f |
cat-searcher/leandojo-benchmark-4-random | test | 2,453 | CompositionSeries.isMaximal_eraseLast_last | Mathlib/Order/JordanHolder.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext | case h.e'_5.h.e'_4
X : Type u
inst✝¹ : Lattice X
inst✝ : JordanHolderLattice X
s : CompositionSeries X
h : 0 < s.length
this : s.length - 1 + 1 = s.length
⊢ Fin.last s.length = ⟨s.length - 1, ⋯⟩.succ | case h.e'_5.h.e'_4.h
X : Type u
inst✝¹ : Lattice X
inst✝ : JordanHolderLattice X
s : CompositionSeries X
h : 0 < s.length
this : s.length - 1 + 1 = s.length
⊢ ↑(Fin.last s.length) = ↑⟨s.length - 1, ⋯⟩.succ | ((:c Eq) ((:c Fin) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c RelSeries.length) (:fv _uniq.21170) ((:c JordanHolderLattice.IsMaximal) (:fv _uniq.21170) (:fv _uniq.21173) (:fv _uniq.21186)) (:fv _uniq.21302)) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Lattice) (:fv _uniq.21170))"},{"name":"inst✝","sexp":"((:c JordanHolderLattice) (:fv _uniq.21170) (:fv _uniq.21173))"},{"name":"s","sexp":"((:c CompositionSeries) (:fv _uniq.21170) (:fv _uniq.21173) (:fv _uniq.21186))"},{"name":"h","sexp":"((:c LT.lt)... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Fin) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21170","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21173","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Lattice) (:arg :explici... | {"children":[{"source":"ext","sourceEnd":14014,"sourceStart":14011,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":14014,"sourceStart":14011,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21170","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21173","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 82 | 25 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 30e845a8ff46447b8c3b5c6ae9ed7732e73a7f1c23f73674e410520a8d7487bd | 0c52fe32ecf1870fa328e44cebda19d7d4be8f50a7b6d20a36f1a80c8ee3f25f | a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de | 47932b47a52bfb78dd71a17c33e21dc3ef3197dcb81fe439189e88e117896ae1 |
cat-searcher/leandojo-benchmark-4-random | test | 2,454 | CompositionSeries.isMaximal_eraseLast_last | Mathlib/Order/JordanHolder.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [this] | case h.e'_5.h.e'_4.h
X : Type u
inst✝¹ : Lattice X
inst✝ : JordanHolderLattice X
s : CompositionSeries X
h : 0 < s.length
this : s.length - 1 + 1 = s.length
⊢ ↑(Fin.last s.length) = ↑⟨s.length - 1, ⋯⟩.succ | ((:c Eq) (:c Nat) ((:c Fin.val) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c RelSeries.length) (:fv _uniq.21170) ((:c JordanHolderLattice.IsMaximal) (:fv _uniq.21170) (:fv _uniq.21173) (:fv _uniq.21186)) (:fv _uniq.21302)) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Lattice) (:fv _uniq.21170))"},{"name":"inst✝","sexp":"((:c JordanHolderLattice) (:fv _uniq.21170) (:fv _uniq.21173))"},{"name":"s","sexp":"((:c CompositionSeries) (:fv _uniq.21170) (:fv _uniq.21173) (:fv _uniq.21186))"},{"name":"h","sexp":"((:c LT.lt)... | (: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.last) (:arg :explicit 0 (:app (:c RelSeries.length) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV4)))))))) (:arg :explicit 2 (:app (:c Fin.val) (:arg :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21170","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21173","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Lattice) (:arg :explici... | {"children":[{"source":"simp","sourceEnd":14020,"sourceStart":14016,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":14022,"sourceStart":14021,"tag":"a... | [] | [{"source":"this","source_end":14026,"source_start":14022,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21170","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21173","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 82 | 27 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 43dd75a6a2b8819f5d865015005852b59ac8fc4eaba74d936edf3dd25f150cbb | 47932b47a52bfb78dd71a17c33e21dc3ef3197dcb81fe439189e88e117896ae1 | 2739860bec7952c6457e85d62dcc82ff2a268ce0336906f3574a07be169573c0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,455 | CompositionSeries.isMaximal_eraseLast_last | Mathlib/Order/JordanHolder.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | conv_rhs => rw [← <a>Nat.add_one_sub_one</a> s.length]; rw [<a>Nat.succ_sub</a> h] | X : Type u
inst✝¹ : Lattice X
inst✝ : JordanHolderLattice X
s : CompositionSeries X
h : 0 < s.length
⊢ s.length - 1 + 1 = s.length | ((:c Eq) (:c Nat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HSub.hSub) (:c Nat) (:c Nat) (:c Nat) ((:c instHSub) (:c Nat) (:c instSubNat)) ((:c RelSeries.length) (:fv _uniq.21170) ((:c JordanHolderLattice.IsMaximal) (:fv _uniq.21170) (:fv _uniq.21173) (:fv _uniq.21186)) (:... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Lattice) (:fv _uniq.21170))"},{"name":"inst✝","sexp":"((:c JordanHolderLattice) (:fv _uniq.21170) (:fv _uniq.21173))"},{"name":"s","sexp":"((:c CompositionSeries) (:fv _uniq.21170) (:fv _uniq.21173) (:fv _uniq.21186))"},{"name":"h","sexp":"((:c LT.lt)... | (: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.21170","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21173","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Lattice) (:arg :explici... | {"children":[{"source":"conv_rhs","sourceEnd":13873,"sourceStart":13865,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":"=>","sourceEnd":13876,"sourceStart":13874,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"sou... | [] | [{"source":"Nat.add_one_sub_one s.length","source_end":13913,"source_start":13885,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Nat.succ_sub h","source_end":13934,"source_start":13920,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21170","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21173","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 82 | 6 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 682cc781680b68526dff2941bbf669f8073f541ca892d3b60c50e5cb6de69ca0 | 8ede7c2334ce3fd2c191c176f5b16d650c72185fc400fe17d7ebcfc8e6d987c3 | 07224b12a6accc180f5abd26334af271cbdcf5fc40f4c8be9bf7fe476478c29b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,456 | CompositionSeries.isMaximal_eraseLast_last | Mathlib/Order/JordanHolder.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | omega | X : Type u
inst✝¹ : Lattice X
inst✝ : JordanHolderLattice X
s : CompositionSeries X
h : 0 < s.length
this : s.length - 1 + 1 = s.length
⊢ s.length - 1 < s.length | ((:c LT.lt) (:c Nat) (:c instLTNat) ((:c HSub.hSub) (:c Nat) (:c Nat) (:c Nat) ((:c instHSub) (:c Nat) (:c instSubNat)) ((:c RelSeries.length) (:fv _uniq.21170) ((:c JordanHolderLattice.IsMaximal) (:fv _uniq.21170) (:fv _uniq.21173) (:fv _uniq.21186)) (:fv _uniq.21302)) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNa... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Lattice) (:fv _uniq.21170))"},{"name":"inst✝","sexp":"((:c JordanHolderLattice) (:fv _uniq.21170) (:fv _uniq.21173))"},{"name":"s","sexp":"((:c CompositionSeries) (:fv _uniq.21170) (:fv _uniq.21173) (:fv _uniq.21186))"},{"name":"h","sexp":"((:c LT.lt)... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HSub) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21170","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21173","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Lattice) (:arg :explici... | {"children":[{"children":[{"children":[{"children":[{"source":"omega","sourceEnd":14006,"sourceStart":14001,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.omega","source":"omega","sourceEnd":14006,"sourceStart":14001,"tag":"node"}],"kind":"null","source":"omega","source... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21170","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21173","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 82 | 21 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c600aa63d8a3f200d650a8f37a4060fda3402931b0b3e3ab65a7581bb8b13c80 | 69689dab4aad3c6a39c518092a70cb9c63fb9954da1475335511f335a703d6ce | 304b4a90a76a1cbe4c112e074b30e75181f54df43d60f883597457844293b341 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,457 | MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top | Mathlib/MeasureTheory/OuterMeasure/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>MeasureTheory.measure_iUnion_of_tendsto_zero</a> m <a>Filter.atTop</a> ?_ | α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
⊢ m (⋃ n, s n) = ⨆ n, m (s n) | α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
⊢ Tendsto (fun k => m ((⋃ n, s n) \ s k)) atTop (𝓝 0) | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806)) ((:c Set) (:fv _uniq.91806)) (:lambda _ ((:c Set) (:fv _uniq.91806)) (:c ENNReal)) ((:c MeasureTheory.OuterMeasure.instFunLikeSetENNReal) (:fv _uniq.91806)) (:fv _uniq.92513) ((:c Set.iUnion) (:fv _uniq.91806) (:c Nat) (:lambda... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m✝","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"m","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"s","sexp":"(:forall _ (:c Nat) ((:c Set) (:fv _uniq.91806)))"},{"name":"h_mono","... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.OuterMeasure) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c FunLi... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":13264,"sourceStart":13258,"tag":"atom"},{"children":[{"name":"MeasureTheory.measure_iUnion_of_tendsto_zero","semanticRole":"global","source":"measure_iUnion_of_tendsto_zero","sourceEnd":13295,"sourceStart":13265,"tag":"identifier"},{"children":[{"contextIndex":4,"semanticRole... | [] | [{"source":"measure_iUnion_of_tendsto_zero m atTop ?_","source_end":13306,"source_start":13265,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 79 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0bc9a1a9a9dbc80995a67824369f69e03cf5f3c2568fe47755a02c506d47d378 | fa1198afccfb359213e17c6ac5815d1f2aade754fdb1f28045f51df81b781d83 | e31e6ba78a1fe966153a9cf401688100e65366289f3b6f955650750b83182a5f | 49c6384af98e7fb9a26a2ff7c414bebe7b95536c360dd331f244979b9662f302 |
cat-searcher/leandojo-benchmark-4-random | test | 2,458 | MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top | Mathlib/MeasureTheory/OuterMeasure/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>tendsto_nhds_bot_mono'</a> (<a>ENNReal.tendsto_sum_nat_add</a> _ h0) fun n => ?_ | α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
⊢ Tendsto (fun k => m ((⋃ n, s n) \ s k)) atTop (𝓝 0) | α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
⊢ m ((⋃ n, s n) \ s n) ≤ ∑' (k : ℕ), m (s (k + n + 1) \ s (k + n)) | ((:c Filter.Tendsto) (:c Nat) (:c ENNReal) (:lambda k (:c Nat) ((:c DFunLike.coe) ((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806)) ((:c Set) (:fv _uniq.91806)) (:lambda _ ((:c Set) (:fv _uniq.91806)) (:c ENNReal)) ((:c MeasureTheory.OuterMeasure.instFunLikeSetENNReal) (:fv _uniq.91806)) (:fv _uniq.92513) ((:c SDiff.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m✝","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"m","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"s","sexp":"(:forall _ (:c Nat) ((:c Set) (:fv _uniq.91806)))"},{"name":"h_mono","... | (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:lambda k :explicit (:c Nat) (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.OuterMeasure) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":13315,"sourceStart":13309,"tag":"atom"},{"children":[{"name":"tendsto_nhds_bot_mono'","semanticRole":"global","source":"tendsto_nhds_bot_mono'","sourceEnd":13338,"sourceStart":13316,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":13340,"sourceStart":13... | [] | [{"source":"tendsto_nhds_bot_mono' (ENNReal.tendsto_sum_nat_add _ h0) fun n => ?_","source_end":13385,"source_start":13316,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 79 | 5 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ec105d149c0fb69fa7a408e971db9add61c51e9be95c312a14166e04128028a3 | 49c6384af98e7fb9a26a2ff7c414bebe7b95536c360dd331f244979b9662f302 | 078834f4426ab0ad8862b4235c9a1feb00a08e4d30f7467dbef7013c22961e15 | a2fb523f5448bfc9ab40529732ae9c287d6524082e224233fa72051625677573 |
cat-searcher/leandojo-benchmark-4-random | test | 2,459 | MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top | Mathlib/MeasureTheory/OuterMeasure/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (m.mono ?_).<a>LE.le.trans</a> (<a>MeasureTheory.measure_iUnion_le</a> _) | α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
⊢ m ((⋃ n, s n) \ s n) ≤ ∑' (k : ℕ), m (s (k + n + 1) \ s (k + n)) | α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
⊢ (⋃ n, s n) \ s n ⊆ ⋃ i, s (i + n + 1) \ s (i + n) | ((:c LE.le) ((:lambda _ (:c Nat) (:c ENNReal)) (:fv _uniq.93049)) ((:lambda i (:c Nat) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.toPartialOrder) (:c ENNReal) ((:c OrderedCommSemiring.toOrderedSemiring) (:c ENNReal) ((:c CanonicallyOrderedCommSemiring.toOrderedCommS... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m✝","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"m","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"s","sexp":"(:forall _ (:c Nat) ((:c Set) (:fv _uniq.91806)))"},{"name":"h_mono","... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:lambda _ :explicit (:c Nat) (:c ENNReal)) (:arg :explicit 0 (:fv FV8)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.OuterMeasure) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":13394,"sourceStart":13388,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":13396,"sourceStart":13395,"tag":"atom"},{"children":[{"source":"m.mono","sourceEnd":13402,"sourceStart":13396,"tag":"identifier"},{"children":[{"children":[{"source":"?","... | [] | [{"source":"(m.mono ?_).trans (measure_iUnion_le _)\n -- Current goal: `(⋃ k, s k) \\ s n ⊆ ⋃ k, s (k + n + 1) \\ s (k + n)`","source_end":13434,"source_start":13395,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 79 | 6 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3ffb28a48ba2f106c14127bc0537d531606ee5ac71776569fb59d96595ec05b0 | a2fb523f5448bfc9ab40529732ae9c287d6524082e224233fa72051625677573 | 5c9231fa63f3aff02fc88fa081150f7289bfe797246c1769a6a858fb3c6e45a6 | 7169c098138d6b26638508264353c22362f7690148d4ddfc18d406d131d5a992 |
cat-searcher/leandojo-benchmark-4-random | test | 2,460 | MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top | Mathlib/MeasureTheory/OuterMeasure/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h' : <a>Monotone</a> s := @<a>monotone_nat_of_le_succ</a> (<a>Set</a> α) _ _ h_mono | α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
⊢ (⋃ n, s n) \ s n ⊆ ⋃ i, s (i + n + 1) \ s (i + n) | α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
h' : Monotone s
⊢ (⋃ n, s n) \ s n ⊆ ⋃ i, s (i + n + 1) \ s (i + n) | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.91806)) ((:c Set.instHasSubset) (:fv _uniq.91806)) ((:c SDiff.sdiff) ((:c Set) (:fv _uniq.91806)) ((:c Set.instSDiff) (:fv _uniq.91806)) ((:c Set.iUnion) (:fv _uniq.91806) (:c Nat) (:lambda n (:c Nat) ((:fv _uniq.92514) 0))) ((:fv _uniq.92514) (:fv _uniq.93049))) ((:c Set.iUn... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m✝","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"m","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"s","sexp":"(:forall _ (:c Nat) ((:c Set) (:fv _uniq.91806)))"},{"name":"h_mono","... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:c SDiff.sdiff) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":13518,"sourceStart":13514,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h'","sourceEnd":13521,"sourceStart":13519,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h'","sourceEnd":13521,"sourceStart":13519,"tag":"nod... | [] | [{"source":"Monotone s","source_end":13534,"source_start":13524,"syntax_kind":"Lean.Parser.Term.app"},{"source":"@monotone_nat_of_le_succ (Set α) _ _ h_mono","source_end":13582,"source_start":13538,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 79 | 7 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6f97256fb81eb3f81232e849ec765a4d43a18a3633476f2d96f5f4a5e9926c36 | 7169c098138d6b26638508264353c22362f7690148d4ddfc18d406d131d5a992 | ec63572c405779c1dd697a019c8b97c1eab30ea2d0814ef60ab0de6e04ebcaeb | 08cd81effec08d8c39591cd7767cf6d9691181deaebad2f8ecb0bceb28c84e36 |
cat-searcher/leandojo-benchmark-4-random | test | 2,461 | MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top | Mathlib/MeasureTheory/OuterMeasure/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.diff_subset_iff</a>, <a>Set.iUnion_subset_iff</a>] | α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
h' : Monotone s
⊢ (⋃ n, s n) \ s n ⊆ ⋃ i, s (i + n + 1) \ s (i + n) | α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
h' : Monotone s
⊢ ∀ (i : ℕ), s i ⊆ s n ∪ ⋃ i, s (i + n + 1) \ s (i + n) | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.91806)) ((:c Set.instHasSubset) (:fv _uniq.91806)) ((:c SDiff.sdiff) ((:c Set) (:fv _uniq.91806)) ((:c Set.instSDiff) (:fv _uniq.91806)) ((:c Set.iUnion) (:fv _uniq.91806) (:c Nat) (:lambda n (:c Nat) ((:fv _uniq.92514) 0))) ((:fv _uniq.92514) (:fv _uniq.93049))) ((:c Set.iUn... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m✝","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"m","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"s","sexp":"(:forall _ (:c Nat) ((:c Set) (:fv _uniq.91806)))"},{"name":"h_mono","... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:c SDiff.sdiff) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":13589,"sourceStart":13585,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":13594,"sourceStart":13590,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":135... | [] | [{"source":"diff_subset_iff","source_end":13611,"source_start":13596,"syntax_kind":"ident"},{"source":"iUnion_subset_iff","source_end":13630,"source_start":13613,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 79 | 8 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b7927c9ba36cf24fb57d49d120444aab2aa71680fe202b72fd85342d9be08911 | 08cd81effec08d8c39591cd7767cf6d9691181deaebad2f8ecb0bceb28c84e36 | a0598f773f38c8a28002a88d55068bbd389a1d4ef01b5c8563947ca67d781a54 | 2ced9fedc4eb36c54803255df2747e992677a4a7b5acca97df6665025ee4f522 |
cat-searcher/leandojo-benchmark-4-random | test | 2,462 | MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top | Mathlib/MeasureTheory/OuterMeasure/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro i x hx | α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
h' : Monotone s
⊢ ∀ (i : ℕ), s i ⊆ s n ∪ ⋃ i, s (i + n + 1) \ s (i + n) | α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
h' : Monotone s
i : ℕ
x : α
hx : x ∈ s i
⊢ x ∈ s n ∪ ⋃ i, s (i + n + 1) \ s (i + n) | (:forall i (:c Nat) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.91806)) ((:c Set.instHasSubset) (:fv _uniq.91806)) ((:fv _uniq.92514) 0) ((:c Union.union) ((:c Set) (:fv _uniq.91806)) ((:c Set.instUnion) (:fv _uniq.91806)) ((:fv _uniq.92514) (:fv _uniq.93049)) ((:c Set.iUnion) (:fv _uniq.91806) (:c Nat) (:lambda i (:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m✝","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"m","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"s","sexp":"(:forall _ (:c Nat) ((:c Set) (:fv _uniq.91806)))"},{"name":"h_mono","... | (:forall i :explicit (:c Nat) (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:fv FV5) (:arg :explicit 0 0))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"intro","sourceEnd":13639,"sourceStart":13634,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"i","sourceEnd":13641,"sourceStart":13640,"tag":"identifier"},{"semanticRole":"scoped_local","source":"x","sourceEnd":13643,"sourceStart":13642,"tag":"identifier"},{"semanticRole":"sco... | [{"role":"fresh_name","source":"i","source_end":13641,"source_start":13640,"syntax_kind":"ident"},{"role":"fresh_name","source":"x","source_end":13643,"source_start":13642,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":13646,"source_start":13644,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 79 | 9 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 91fb7afc5196c15c35c49804a22b3be13405ce16e2abfa1a13965a32fba7c472 | 2ced9fedc4eb36c54803255df2747e992677a4a7b5acca97df6665025ee4f522 | 6579c04d6729cd02f9e3fb01b19a7947d7224f84cf9b2d9c66907f617af7b311 | 28dfb003dc294d3f2fadd409d66ba6a2d43485326b06afb69ae83a651feb3fde |
cat-searcher/leandojo-benchmark-4-random | test | 2,463 | MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top | Mathlib/MeasureTheory/OuterMeasure/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : ∃i, x ∈ s i := by exists i | α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
h' : Monotone s
i : ℕ
x : α
hx : x ∈ s i
⊢ x ∈ s n ∪ ⋃ i, s (i + n + 1) \ s (i + n) | α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
h' : Monotone s
i : ℕ
x : α
hx : x ∈ s i
this : ∃ i, x ∈ s i
⊢ x ∈ s n ∪ ⋃ i, s (i + n + 1) \ s (i + n) | ((:c Membership.mem) (:fv _uniq.91806) ((:c Set) (:fv _uniq.91806)) ((:c Set.instMembership) (:fv _uniq.91806)) (:fv _uniq.94775) ((:c Union.union) ((:c Set) (:fv _uniq.91806)) ((:c Set.instUnion) (:fv _uniq.91806)) ((:fv _uniq.92514) (:fv _uniq.93049)) ((:c Set.iUnion) (:fv _uniq.91806) (:c Nat) (:lambda i (:c Nat) ((... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m✝","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"m","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"s","sexp":"(:forall _ (:c Nat) ((:c Set) (:fv _uniq.91806)))"},{"name":"h_mono","... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV11)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":13653,"sourceStart":13649,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":13654,"sourceStart":13654,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":13654,"sourceStart":13654,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"∃i, x ∈ s i","source_end":13671,"source_start":13656,"syntax_kind":"«term∃_,_»"},{"source":"i","source_end":13686,"source_start":13685,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 79 | 10 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | acb4fc18193218523ab7f9322e11a4c24252dc82c9cd48b0253e24b409c30264 | 28dfb003dc294d3f2fadd409d66ba6a2d43485326b06afb69ae83a651feb3fde | eb9a69e307c29eab30e6cac5d20a4eaee89a81868d210619477e8034edd6f03d | bb14c9be920fade18bf2b4337a9f44219f3a438afffa27ff0833266e3a1cf0af |
cat-searcher/leandojo-benchmark-4-random | test | 2,464 | MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top | Mathlib/MeasureTheory/OuterMeasure/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>Nat.findX</a> this with ⟨j, hj, hlt⟩ | α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
h' : Monotone s
i : ℕ
x : α
hx : x ∈ s i
this : ∃ i, x ∈ s i
⊢ x ∈ s n ∪ ⋃ i, s (i + n + 1) \ s (i + n) | case mk.intro
α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
h' : Monotone s
i : ℕ
x : α
hx : x ∈ s i
this : ∃ i, x ∈ s i
j : ℕ
hj : x ∈ s j
hlt : ∀ m < j, x ∉ s m
⊢ x ∈ s n ∪ ⋃ i, s (i + n + 1) \ s (i + n) | ((:c Membership.mem) (:fv _uniq.91806) ((:c Set) (:fv _uniq.91806)) ((:c Set.instMembership) (:fv _uniq.91806)) (:fv _uniq.94775) ((:c Union.union) ((:c Set) (:fv _uniq.91806)) ((:c Set.instUnion) (:fv _uniq.91806)) ((:fv _uniq.92514) (:fv _uniq.93049)) ((:c Set.iUnion) (:fv _uniq.91806) (:c Nat) (:lambda i (:c Nat) ((... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m✝","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"m","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"s","sexp":"(:forall _ (:c Nat) ((:c Set) (:fv _uniq.91806)))"},{"name":"h_mono","... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV11)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rcases","sourceEnd":13695,"sourceStart":13689,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Nat.findX","semanticRole":"global","source":"Nat.findX","sourceEnd":13705,"sourceStart":13696,"tag":"identifier"},{"children":[{"cont... | [] | [{"source":"Nat.findX this","source_end":13710,"source_start":13696,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨j, hj, hlt⟩","source_end":13732,"source_start":13716,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 79 | 13 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cd6332698e906bc093848a5c1ae6560d83bbbcd262c6d29f54756581e113236d | bb14c9be920fade18bf2b4337a9f44219f3a438afffa27ff0833266e3a1cf0af | 5917ea6aaae9306d37810f6d5435023974ea6d58e7984b191b767916a161fceb | b09e3184313af60b9df699dfc4d4217e7cb4336c7db31f7cf3af13f9653e908d |
cat-searcher/leandojo-benchmark-4-random | test | 2,465 | MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top | Mathlib/MeasureTheory/OuterMeasure/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | clear hx i | case mk.intro
α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
h' : Monotone s
i : ℕ
x : α
hx : x ∈ s i
this : ∃ i, x ∈ s i
j : ℕ
hj : x ∈ s j
hlt : ∀ m < j, x ∉ s m
⊢ x ∈ s n ∪ ⋃ i, s (i + n + 1) \ s (i + n) | case mk.intro
α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
h' : Monotone s
x : α
this : ∃ i, x ∈ s i
j : ℕ
hj : x ∈ s j
hlt : ∀ m < j, x ∉ s m
⊢ x ∈ s n ∪ ⋃ i, s (i + n + 1) \ s (i + n) | ((:c Membership.mem) (:fv _uniq.91806) ((:c Set) (:fv _uniq.91806)) ((:c Set.instMembership) (:fv _uniq.91806)) (:fv _uniq.94775) ((:c Union.union) ((:c Set) (:fv _uniq.91806)) ((:c Set.instUnion) (:fv _uniq.91806)) ((:fv _uniq.92514) (:fv _uniq.93049)) ((:c Set.iUnion) (:fv _uniq.91806) (:c Nat) (:lambda i (:c Nat) ((... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m✝","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"m","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"s","sexp":"(:forall _ (:c Nat) ((:c Set) (:fv _uniq.91806)))"},{"name":"h_mono","... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV11)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"clear","sourceEnd":13740,"sourceStart":13735,"tag":"atom"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"hx","sourceEnd":13743,"sourceStart":13741,"tag":"identifier"},{"contextIndex":10,"semanticRole":"local","source":"i","sourceEnd":13745,"sourceStart":13744,"tag":"identifier... | [] | [{"source":"hx","source_end":13743,"source_start":13741,"syntax_kind":"ident"},{"source":"i","source_end":13745,"source_start":13744,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 79 | 14 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 23489a95ef1869435921e4f43a7718f37860bb7b9b6ba5c969766b82f1fe7ee3 | b09e3184313af60b9df699dfc4d4217e7cb4336c7db31f7cf3af13f9653e908d | 5c44936b0482cf11f6376cfbf75f27b74ba88022ae4772915d8c948d7bf2ad01 | 0f8d3685939a4e46477986046db40c8a1677d6ab589c0f43654bd81763480db7 |
cat-searcher/leandojo-benchmark-4-random | test | 2,466 | MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top | Mathlib/MeasureTheory/OuterMeasure/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>le_or_lt</a> j n with hjn | hnj | case mk.intro
α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
h' : Monotone s
x : α
this : ∃ i, x ∈ s i
j : ℕ
hj : x ∈ s j
hlt : ∀ m < j, x ∉ s m
⊢ x ∈ s n ∪ ⋃ i, s (i + n + 1) \ s (i + n) | case mk.intro.inl
α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
h' : Monotone s
x : α
this : ∃ i, x ∈ s i
j : ℕ
hj : x ∈ s j
hlt : ∀ m < j, x ∉ s m
hjn : j ≤ n
⊢ x ∈ s n ∪ ⋃ i, s (i + n + 1) \ s (i + n)
case mk.intro.inr
... | ((:c Membership.mem) (:fv _uniq.91806) ((:c Set) (:fv _uniq.91806)) ((:c Set.instMembership) (:fv _uniq.91806)) (:fv _uniq.94775) ((:c Union.union) ((:c Set) (:fv _uniq.91806)) ((:c Set.instUnion) (:fv _uniq.91806)) ((:fv _uniq.92514) (:fv _uniq.93049)) ((:c Set.iUnion) (:fv _uniq.91806) (:c Nat) (:lambda i (:c Nat) ((... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m✝","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"m","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"s","sexp":"(:forall _ (:c Nat) ((:c Set) (:fv _uniq.91806)))"},{"name":"h_mono","... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV10)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rcases","sourceEnd":13754,"sourceStart":13748,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"le_or_lt","semanticRole":"global","source":"le_or_lt","sourceEnd":13763,"sourceStart":13755,"tag":"identifier"},{"children":[{"contex... | [] | [{"source":"le_or_lt j n","source_end":13767,"source_start":13755,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hjn | hnj","source_end":13782,"source_start":13773,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 79 | 15 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 233e7611cfa979fdf4aa66c0b650fccfd4b6f5f93288190f14eca987a9124dad | 0f8d3685939a4e46477986046db40c8a1677d6ab589c0f43654bd81763480db7 | 016b7e47657108f4480fb89c393a74d6dfdc1fc105de484832c9917d112430f4 | 8c522341d3d998065ee1df0fff5dc7916ba0a76af670b427d4365da068deb622 |
cat-searcher/leandojo-benchmark-4-random | test | 2,467 | MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top | Mathlib/MeasureTheory/OuterMeasure/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : j - (n + 1) + n + 1 = j := by omega | case mk.intro.inr
α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
h' : Monotone s
x : α
this : ∃ i, x ∈ s i
j : ℕ
hj : x ∈ s j
hlt : ∀ m < j, x ∉ s m
hnj : n < j
⊢ x ∈ s n ∪ ⋃ i, s (i + n + 1) \ s (i + n) | case mk.intro.inr
α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
h' : Monotone s
x : α
this✝ : ∃ i, x ∈ s i
j : ℕ
hj : x ∈ s j
hlt : ∀ m < j, x ∉ s m
hnj : n < j
this : j - (n + 1) + n + 1 = j
⊢ x ∈ s n ∪ ⋃ i, s (i + n + 1... | ((:c Membership.mem) (:fv _uniq.91806) ((:c Set) (:fv _uniq.91806)) ((:c Set.instMembership) (:fv _uniq.91806)) (:fv _uniq.94775) ((:c Union.union) ((:c Set) (:fv _uniq.91806)) ((:c Set.instUnion) (:fv _uniq.91806)) ((:fv _uniq.92514) (:fv _uniq.93049)) ((:c Set.iUnion) (:fv _uniq.91806) (:c Nat) (:lambda i (:c Nat) ((... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m✝","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"m","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"s","sexp":"(:forall _ (:c Nat) ((:c Set) (:fv _uniq.91806)))"},{"name":"h_mono","... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV10)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":13819,"sourceStart":13815,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":13820,"sourceStart":13820,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":13820,"sourceStart":13820,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"j - (n + 1) + n + 1 = j","source_end":13845,"source_start":13822,"syntax_kind":"«term_=_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 79 | 21 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7981c8778622761fdf9c72e231661b0e531a4fbdd73007d30aa8ff4e133a471b | b9213f5ad2c46f16517bbd74e217222ef88891ca89211aa49f31c18737ec0ea2 | 38bc679f940bc26f3f37a79ece2e89716087ba3a8e06f71bc1263a333ceb1aeb | e131d854c9bc0af41ac37904ef7e6e9eea6639bb427814a4502d4f8062f46f32 |
cat-searcher/leandojo-benchmark-4-random | test | 2,468 | MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top | Mathlib/MeasureTheory/OuterMeasure/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Or.inr</a> (<a>Set.mem_iUnion</a>.2 ⟨j - (n + 1), ?_, hlt _ ?_⟩) | case mk.intro.inr
α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
h' : Monotone s
x : α
this✝ : ∃ i, x ∈ s i
j : ℕ
hj : x ∈ s j
hlt : ∀ m < j, x ∉ s m
hnj : n < j
this : j - (n + 1) + n + 1 = j
⊢ x ∈ s n ∪ ⋃ i, s (i + n + 1... | case mk.intro.inr.refine_1
α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
h' : Monotone s
x : α
this✝ : ∃ i, x ∈ s i
j : ℕ
hj : x ∈ s j
hlt : ∀ m < j, x ∉ s m
hnj : n < j
this : j - (n + 1) + n + 1 = j
⊢ x ∈ s (j - (n + 1)... | ((:c Membership.mem) (:fv _uniq.91806) ((:c Set) (:fv _uniq.91806)) ((:c Set.instMembership) (:fv _uniq.91806)) (:fv _uniq.94775) ((:c Union.union) ((:c Set) (:fv _uniq.91806)) ((:c Set.instUnion) (:fv _uniq.91806)) ((:fv _uniq.92514) (:fv _uniq.93049)) ((:c Set.iUnion) (:fv _uniq.91806) (:c Nat) (:lambda i (:c Nat) ((... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m✝","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"m","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"s","sexp":"(:forall _ (:c Nat) ((:c Set) (:fv _uniq.91806)))"},{"name":"h_mono","... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV10)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":13866,"sourceStart":13860,"tag":"atom"},{"children":[{"name":"Or.inr","semanticRole":"constructor","source":"Or.inr","sourceEnd":13873,"sourceStart":13867,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":13875,"sourceStart":13874,"tag":"atom"},{"childre... | [] | [{"source":"Or.inr (mem_iUnion.2 ⟨j - (n + 1), ?_, hlt _ ?_⟩)","source_end":13920,"source_start":13867,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 79 | 24 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ea27a5194a01e869541844fd10dc8614030cb5f9617cf9847dee3c18ed0c7e16 | e131d854c9bc0af41ac37904ef7e6e9eea6639bb427814a4502d4f8062f46f32 | 0e06b8dff9a463c0ac399963b35b68a515d2021c9633fe66981a077277762d32 | 1a6ccd6155712aad5037b2af5456a7b3aa7549924de62961ff4d508245238815 |
cat-searcher/leandojo-benchmark-4-random | test | 2,469 | MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top | Mathlib/MeasureTheory/OuterMeasure/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exists i | α : Type u_1
β : Type u_2
m✝ m : OuterMeasure α
s : ℕ → Set α
h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1)
h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤
n : ℕ
h' : Monotone s
i : ℕ
x : α
hx : x ∈ s i
⊢ ∃ i, x ∈ s i | ((:c Exists) (:c Nat) (:lambda i (:c Nat) ((:c Membership.mem) (:fv _uniq.91806) ((:c Set) (:fv _uniq.91806)) ((:c Set.instMembership) (:fv _uniq.91806)) (:fv _uniq.94775) ((:fv _uniq.92514) 0)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m✝","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"m","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"s","sexp":"(:forall _ (:c Nat) ((:c Set) (:fv _uniq.91806)))"},{"name":"h_mono","... | (:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda i :explicit (:c Nat) (: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 :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exists","sourceEnd":13684,"sourceStart":13678,"tag":"atom"},{"children":[{"contextIndex":10,"semanticRole":"local","source":"i","sourceEnd":13686,"sourceStart":13685,"tag":"identifier"}],"kind":"null","source":"i","sourceEnd":13686,"sourceStart":13685,"tag":"node"}],"kind":"Lean.Parser.Tactic.«t... | [] | [{"source":"i","source_end":13686,"source_start":13685,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 79 | 12 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4980820988662a6cc53d74f1f6f2f762f63915015841e5afa431b409c636d0e9 | 7b10c66e55e550a566a1cc59f30b63d5cbe913025350e88d2d07725856329f83 | 714420c0c88f0be625bb7208c7d93055f5e36d3623f6e2c6deb85a5295938615 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 |
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