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cat-searcher/leandojo-benchmark-4-random | test | 3,798 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | field_simp [hA, hB] | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c DivInvMonoid.toDiv) (:fv _uniq.2711) ((:c DivisionMonoid.toDivInvMonoid) (:fv _uniq.2711) ((:c DivisionCommMonoid.toDivisionMonoid) (:fv _uniq.2711) ((:c CommGroupWithZero.toDivisionCommMono... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"field_simp","sourceEnd":11069,"sourceStart":11059,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":"[","sourceEnd":11071,"sourceSt... | [] | [{"source":"hA","source_end":11073,"source_start":11071,"syntax_kind":"ident"},{"source":"hB","source_end":11077,"source_start":11075,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 155 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 17a89d8e807806470dda6bb69ab01eaba379ef2d41f68a2ef559b0cbdf5bc82d | 23ed73cbb20b71a3892913aa55779ed603e1e0725070a83214134d65ffa1e5b4 | abcf7402f5adf1ac4a7b9129bbe9fa85ffe44cd31d0df46c84ca4705ed28a9c4 | 8e73e5abdb4c40aed0bbc0c8e7449b8f6e0ef22c51e7d0dc7c4de5c237d6e045 |
cat-searcher/leandojo-benchmark-4-random | test | 3,799 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ac_rfl | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c DivInvMonoid.toDiv) (:fv _uniq.2711) ((:c DivisionMonoid.toDivInvMonoid) (:fv _uniq.2711) ((:c DivisionCommMonoid.toDivisionMonoid) (:fv _uniq.2711) ((:c CommGroupWithZero.toDivisionCommMono... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"ac_rfl","sourceEnd":11093,"sourceStart":11087,"tag":"atom"}],"kind":"Lean.Parser.Tactic.acRfl","source":"ac_rfl","sourceEnd":11093,"sourceStart":11087,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 156 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a941b0d6d51253724449f3a99e7b73d1038dd1a0cde2b1be3e70a3b2dc0edc70 | 8e73e5abdb4c40aed0bbc0c8e7449b8f6e0ef22c51e7d0dc7c4de5c237d6e045 | 2dd78c9d090141d123f9af8735c699cf9192b0edec0d63080dd4083a3ed0b2a9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,800 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>inv_eq_one_div</a>, hfr] | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.continuantsAux (n + 2)
pconts : Pair K := g.continuantsAux (n + 1)... | ((:c Not) ((:c Eq) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.IntFractPair.fr) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.IntFractPair.of) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.2736) ((:c Inv.inv) (:fv _uniq.2711) ((:c DivInvMonoid.toInv) (:fv _uniq.2711) ((:c DivisionRing.toDivInvMonoid) (:fv _u... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c GeneralizedContinuedFraction.IntFractPair.fr) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c GeneralizedContinuedFraction.IntFractPair.of) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:ins... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":11106,"sourceStart":11103,"tag":"atom"},{"children":[{"source":"[","sourceEnd":11108,"sourceStart":11107,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"inv_eq_one_div","semanticRole":... | [] | [{"source":"inv_eq_one_div","source_end":11122,"source_start":11108,"syntax_kind":"ident"},{"source":"hfr","source_end":11127,"source_start":11124,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 159 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8e9334efc30eccce2f1d01252b01a4440af4a28765cf7b8f8fd1457b2233f606 | b720c40f680e34648a04453b050ba8a15ec6e0cfd1df5213f61e5f5e4591c8fd | 9e7c62c078dd6f473d5ca0723eef361569b6465732c307dd1b95a6b518a243f9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,801 | ConvexOn.average_mem_epigraph | Mathlib/Analysis/Convex/Integral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have ht_mem : ∀ᵐ x ∂μ, (f x, g (f x)) ∈ {p : E × ℝ | p.1 ∈ s ∧ g p.1 ≤ p.2} := hfs.mono fun x hx => ⟨hx, <a>le_rfl</a>⟩ | α : Type u_1
E : Type u_2
F : Type u_3
m0 : MeasurableSpace α
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : CompleteSpace E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
μ : Measure α
s : Set E
t : Set α
f : α → E
g : E → ℝ
C : ℝ
inst✝¹ : IsFiniteMeasure μ
inst✝ : NeZ... | α : Type u_1
E : Type u_2
F : Type u_3
m0 : MeasurableSpace α
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : CompleteSpace E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
μ : Measure α
s : Set E
t : Set α
f : α → E
g : E → ℝ
C : ℝ
inst✝¹ : IsFiniteMeasure μ
inst✝ : NeZ... | ((:c Membership.mem) ((:c Prod) (:fv _uniq.23397) (:c Real)) ((:c Set) ((:c Prod) (:fv _uniq.23397) (:c Real))) ((:c Set.instMembership) ((:c Prod) (:fv _uniq.23397) (:c Real))) ((:c Prod.mk) (:fv _uniq.23397) (:c Real) ((:c MeasureTheory.average) (:fv _uniq.23394) (:fv _uniq.23397) (:fv _uniq.23403) (:fv _uniq.23406) ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.23394))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCommGroup) (:fv _uniq.23397))"},{"name":"inst✝⁶","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23394","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23397","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":5902,"sourceStart":5898,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"ht_mem","sourceEnd":5909,"sourceStart":5903,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"ht_mem","sourceEnd":5909,"sourceStart":5903,"tag":"n... | [] | [{"source":"∀ᵐ x ∂μ, (f x, g (f x)) ∈ {p : E × ℝ | p.1 ∈ s ∧ g p.1 ≤ p.2}","source_end":5991,"source_start":5912,"syntax_kind":"MeasureTheory.«term∀ᵐ_∂_,_»"},{"source":"hfs.mono fun x hx => ⟨hx, le_rfl⟩","source_end":6036,"source_start":5999,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23394","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23397","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 14 | 4 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1a9185b035e80e9accac7cfb267bb46819fee4bcb93a55cede4aa0a4bd62fde2 | 721d06c17c664be9a897814a190afcda499a9d7e7ed96abf9df06782fae7eb5e | 69a1f76661efc205f0a701d974be9c7fb1d32434fcc7c1da12ffd7e5714ce3be | 847b1a18b0a345e2beba86b31119253abb97c57a2dea464163699e65f1f366d2 |
cat-searcher/leandojo-benchmark-4-random | test | 3,802 | ConvexOn.average_mem_epigraph | Mathlib/Analysis/Convex/Integral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>MeasureTheory.average_pair</a> hfi hgi ▸ hg.convex_epigraph.average_mem (hsc.epigraph hgc) ht_mem (hfi.prod_mk hgi) | α : Type u_1
E : Type u_2
F : Type u_3
m0 : MeasurableSpace α
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : CompleteSpace E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
μ : Measure α
s : Set E
t : Set α
f : α → E
g : E → ℝ
C : ℝ
inst✝¹ : IsFiniteMeasure μ
inst✝ : NeZ... | ((:c Membership.mem) ((:c Prod) (:fv _uniq.23397) (:c Real)) ((:c Set) ((:c Prod) (:fv _uniq.23397) (:c Real))) ((:c Set.instMembership) ((:c Prod) (:fv _uniq.23397) (:c Real))) ((:c Prod.mk) (:fv _uniq.23397) (:c Real) ((:c MeasureTheory.average) (:fv _uniq.23394) (:fv _uniq.23397) (:fv _uniq.23403) (:fv _uniq.23406) ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.23394))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCommGroup) (:fv _uniq.23397))"},{"name":"inst✝⁶","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23394","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23397","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":6044,"sourceStart":6039,"tag":"atom"},{"children":[{"children":[{"name":"MeasureTheory.average_pair","semanticRole":"global","source":"average_pair","sourceEnd":6057,"sourceStart":6045,"tag":"identifier"},{"children":[{"contextIndex":23,"semanticRole":"local","source":"hfi","s... | [] | [{"source":"average_pair hfi hgi ▸\n hg.convex_epigraph.average_mem (hsc.epigraph hgc) ht_mem (hfi.prod_mk hgi)","source_end":6148,"source_start":6045,"syntax_kind":"Lean.Parser.Term.subst"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23394","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23397","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 14 | 5 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5307e9203d72b556ecd7474be25695fbeafbb903bbe369d3280b54a66da224a1 | 847b1a18b0a345e2beba86b31119253abb97c57a2dea464163699e65f1f366d2 | 0378a22de59ec7f376bfcf2ebc755898fdaf014e341132589bb4d09b91668f17 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,803 | StrictConcaveOn.eq_of_map_sum_eq | Mathlib/Analysis/Convex/Jensen.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_contra! | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
β : Type u_4
ι : Type u_5
inst✝⁵ : LinearOrderedField 𝕜
inst✝⁴ : AddCommGroup E
inst✝³ : OrderedAddCommGroup β
inst✝² : Module 𝕜 E
inst✝¹ : Module 𝕜 β
inst✝ : OrderedSMul 𝕜 β
s : Set E
f : E → β
t : Finset ι
w : ι → 𝕜
p : ι → E
v : 𝕜
q : E
hf : StrictConcaveOn 𝕜 s f
h₀ : ∀... | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
β : Type u_4
ι : Type u_5
inst✝⁵ : LinearOrderedField 𝕜
inst✝⁴ : AddCommGroup E
inst✝³ : OrderedAddCommGroup β
inst✝² : Module 𝕜 E
inst✝¹ : Module 𝕜 β
inst✝ : OrderedSMul 𝕜 β
s : Set E
f : E → β
t : Finset ι
w : ι → 𝕜
p : ι → E
v : 𝕜
q : E
hf : StrictConcaveOn 𝕜 s f
h₀ : ∀... | (:forall j (:fv _uniq.240921) (:forall _ ((:c Membership.mem) (:fv _uniq.240921) ((:c Finset) (:fv _uniq.240921)) ((:c Finset.instMembership) (:fv _uniq.240921)) 0 (:fv _uniq.242330)) (:forall k (:fv _uniq.240921) (:forall _ ((:c Membership.mem) (:fv _uniq.240921) ((:c Finset) (:fv _uniq.240921)) ((:c Finset.instMember... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁵","sexp":"((:c LinearOrderedField) (:fv _uniq.240909))"},{"name":"inst✝⁴","sexp":"((:c AddCommGroup) (:... | (:forall j :strict-implicit (:fv FV4) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV4)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV4)) (:arg :explicit 1 (:app (:c Finset) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.240909","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.240912","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"by_contra!","sourceEnd":9284,"sourceStart":9274,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"byContra!","source":"by_contra!","sourceEnd":9284,"sourceStart":9274,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.240909","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.240912","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 24 | 4 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 387277950f0e399d5f6b9e71742cd68cb73f751c1b6d46b19b3a42caa40a0f2b | 6d33d62fec79edd5cc07a36165877409f727326d74c200105959769b1b082388 | 570bb406836e3971c79364381ab24090f829035dbf76fc0cfa78cd39905d6297 | 4d6435fe41d287da49243653ecc910a1445c2b7aa2e614bb898c59f63ad517c1 |
cat-searcher/leandojo-benchmark-4-random | test | 3,804 | StrictConcaveOn.eq_of_map_sum_eq | Mathlib/Analysis/Convex/Jensen.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact h_eq.not_lt <| hf.lt_map_sum h₀ h₁ hmem this | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
β : Type u_4
ι : Type u_5
inst✝⁵ : LinearOrderedField 𝕜
inst✝⁴ : AddCommGroup E
inst✝³ : OrderedAddCommGroup β
inst✝² : Module 𝕜 E
inst✝¹ : Module 𝕜 β
inst✝ : OrderedSMul 𝕜 β
s : Set E
f : E → β
t : Finset ι
w : ι → 𝕜
p : ι → E
v : 𝕜
q : E
hf : StrictConcaveOn 𝕜 s f
h₀ : ∀... | (:c False) | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁵","sexp":"((:c LinearOrderedField) (:fv _uniq.240909))"},{"name":"inst✝⁴","sexp":"((:c AddCommGroup) (:... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.240909","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.240912","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"exact","sourceEnd":9291,"sourceStart":9286,"tag":"atom"},{"children":[{"source":"h_eq.not_lt","sourceEnd":9303,"sourceStart":9292,"tag":"identifier"},{"source":"<|","sourceEnd":9306,"sourceStart":9304,"tag":"atom"},{"children":[{"source":"hf.lt_map_sum","sourceEnd":9320,"sourceStart":9307,"tag":... | [] | [{"source":"h_eq.not_lt <| hf.lt_map_sum h₀ h₁ hmem this","source_end":9340,"source_start":9292,"syntax_kind":"«term_<|_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.240909","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.240912","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 24 | 6 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8d1bbf1c51a81de6867c76f46879643976e2d8784173e621529ba3e3a08cfec6 | 4d6435fe41d287da49243653ecc910a1445c2b7aa2e614bb898c59f63ad517c1 | a39a370c5e226b68fbc09ec170c90c66c0391bdadeb0bc86028f8fe6c3ae1feb | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,805 | Finsupp.card_Ico | Mathlib/Data/Finsupp/Interval.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.card_Ico_eq_card_Icc_sub_one</a>, <a>Finsupp.card_Icc</a>] | ι : Type u_1
α : Type u_2
inst✝² : PartialOrder α
inst✝¹ : Zero α
inst✝ : LocallyFiniteOrder α
f g : ι →₀ α
⊢ (Ico f g).card = ∏ i ∈ f.support ∪ g.support, (Icc (f i) (g i)).card - 1 | ((:c Eq) (:c Nat) ((:c Finset.card) ((:c Finsupp) (:fv _uniq.6259) (:fv _uniq.6262) (:fv _uniq.6268)) ((:c Finset.Ico) ((:c Finsupp) (:fv _uniq.6259) (:fv _uniq.6262) (:fv _uniq.6268)) ((:c Finsupp.preorder) (:fv _uniq.6259) (:fv _uniq.6262) (:fv _uniq.6268) ((:c PartialOrder.toPreorder) (:fv _uniq.6262) (:fv _uniq.626... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c PartialOrder) (:fv _uniq.6262))"},{"name":"inst✝¹","sexp":"((:c Zero) (:fv _uniq.6262))"},{"name":"inst✝","sexp":"((:c LocallyFiniteOrder) (:fv _uniq.6262) ((:c PartialOrder.toPreorder) (:fv _uniq.6262) (:fv _... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Finset.card) (:arg :implicit-type 0 (:app (:c Finsupp) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 1 (:app (:c Finset.Ico) (:arg :imp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6259","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6262","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":3980,"sourceStart":3978,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3982,"sourceStart":3981,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"card_Ico_eq_card_Icc_sub_one","source_end":4010,"source_start":3982,"syntax_kind":"ident"},{"source":"card_Icc","source_end":4020,"source_start":4012,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6259","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6262","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 32 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 57ece2883193b30ce8dbb0766a00d76ae75fe72688c3e99592927c7c69691f4e | ef5da7649ab08edd6f6bed4a34c1189184d417b0efb170ee8b4365deb480a4ca | 60142b8af3ed342850f9d7cd7c1d290bfdf520a18b876cd4971a5c4d91ac999d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,806 | neg_one_sq | Mathlib/Algebra/Ring/Commute.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>neg_sq</a>, <a>one_pow</a>] | α : Type u
β : Type v
γ : Type w
R : Type x
inst✝¹ : Monoid R
inst✝ : HasDistribNeg R
⊢ (-1) ^ 2 = 1 | ((:c Eq) (:fv _uniq.20296) ((:c HPow.hPow) (:fv _uniq.20296) (:c Nat) (:fv _uniq.20296) ((:c instHPow) (:fv _uniq.20296) (:c Nat) ((:c Monoid.toNatPow) (:fv _uniq.20296) (:fv _uniq.20299))) ((:c Neg.neg) (:fv _uniq.20296) ((:c InvolutiveNeg.toNeg) (:fv _uniq.20296) ((:c HasDistribNeg.toInvolutiveNeg) (:fv _uniq.20296) ... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"R","sexp":"(:sort (+ x 1))"},{"name":"inst✝¹","sexp":"((:c Monoid) (:fv _uniq.20296))"},{"name":"inst✝","sexp":"((:c HasDistribNeg) (:fv _uniq.20296) ((:c MulOneClass.toMul) (:fv _uniq.20296) ((:c... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:fv FV3)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20290","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20292","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":6480,"sourceStart":6476,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"neg_sq","source_end":6488,"source_start":6482,"syntax_kind":"ident"},{"source":"one_pow","source_end":6497,"source_start":6490,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20290","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20292","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 79 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 00a55e0768f3f63c046212c482e9e8b882a4f3727b8e77175478690bb7f31321 | 1c827a2bcac2876439b7ef22477440f79a2b942596ca4147d16d667dccbdbe90 | 06294a8e9beb3ee3e950eeb6d38ae8561c9f23bc5b61f55daf99028efc2911f5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,808 | Real.Angle.eq_iff_sign_eq_and_abs_toReal_eq | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases h with ⟨hs, hr⟩ | case refine_2
θ ψ : Angle
h : θ.sign = ψ.sign ∧ |θ.toReal| = |ψ.toReal|
⊢ θ = ψ | case refine_2.intro
θ ψ : Angle
hs : θ.sign = ψ.sign
hr : |θ.toReal| = |ψ.toReal|
⊢ θ = ψ | ((:c Eq) (:c Real.Angle) (:fv _uniq.222044) (:fv _uniq.222045)) | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"ψ","sexp":"(:c Real.Angle)"},{"name":"h","sexp":"((:c And) ((:c Eq) (:c SignType) ((:c Real.Angle.sign) (:fv _uniq.222044)) ((:c Real.Angle.sign) (:fv _uniq.222045))) ((:c Eq) (:c Real) ((:c abs) (:c Real) (:c Real.lattice) (:c Real.instAddGroup) ((:c Real.Angle.toReal) (... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"name":"ψ","sexp":"(:c Real.Angle)"},{"binder_role":":explic... | {"children":[{"source":"rcases","sourceEnd":42765,"sourceStart":42759,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":3,"semanticRole":"local","source":"h","sourceEnd":42767,"sourceStart":42766,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","s... | [] | [{"source":"h","source_end":42767,"source_start":42766,"syntax_kind":"ident"},{"source":"⟨hs, hr⟩","source_end":42785,"source_start":42773,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"user_name":"ψ"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 319 | 12 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9a806ac6699d48a3c78343a95812f5fc166a08fe6cb77a8ad7348d170a0a8a1e | 8b5587dca42cdb608991b17fdbc012abce5617f811e9d35b9c628000e156b192 | 5124b7731ee5fe648c16de4235775795c214394d77794058b855c91dc63ece66 | 83e72253572626882ed198e5bd9fb0d203d10235a19bbf2d3817b5366ffd7816 |
cat-searcher/leandojo-benchmark-4-random | test | 3,809 | Real.Angle.eq_iff_sign_eq_and_abs_toReal_eq | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>abs_eq_abs</a>] at hr | case refine_2.intro
θ ψ : Angle
hs : θ.sign = ψ.sign
hr : |θ.toReal| = |ψ.toReal|
⊢ θ = ψ | case refine_2.intro
θ ψ : Angle
hs : θ.sign = ψ.sign
hr : θ.toReal = ψ.toReal ∨ θ.toReal = -ψ.toReal
⊢ θ = ψ | ((:c Eq) (:c Real.Angle) (:fv _uniq.222044) (:fv _uniq.222045)) | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"ψ","sexp":"(:c Real.Angle)"},{"name":"hs","sexp":"((:c Eq) (:c SignType) ((:c Real.Angle.sign) (:fv _uniq.222044)) ((:c Real.Angle.sign) (:fv _uniq.222045)))"},{"name":"hr","sexp":"((:c Eq) (:c Real) ((:c abs) (:c Real) (:c Real.lattice) (:c Real.instAddGroup) ((:c Real.A... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"name":"ψ","sexp":"(:c Real.Angle)"},{"binder_role":":explic... | {"children":[{"source":"rw","sourceEnd":42790,"sourceStart":42788,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":42792,"sourceStart":42791,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"abs_eq_abs","sem... | [] | [{"source":"abs_eq_abs","source_end":42802,"source_start":42792,"syntax_kind":"ident"},{"source":"hr","source_end":42809,"source_start":42807,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"user_name":"ψ"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 319 | 13 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0e7d2e221db55bd5cc3f05c8fc46c3eaacf2fbdb3672f84df24b2095b1870bb7 | 83e72253572626882ed198e5bd9fb0d203d10235a19bbf2d3817b5366ffd7816 | 8cf8910911106312de2cbb1baf2e589faee2d536a2bc34a9d8ee47a6d250ccf9 | 71644d62ea0b0e62d1d55d38b10154d7ae95f0380e34d5343d898dc366fedb26 |
cat-searcher/leandojo-benchmark-4-random | test | 3,811 | Real.Angle.eq_iff_sign_eq_and_abs_toReal_eq | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro rfl | case refine_1
θ ψ : Angle
⊢ θ = ψ → θ.sign = ψ.sign ∧ |θ.toReal| = |ψ.toReal| | case refine_1
θ : Angle
⊢ θ.sign = θ.sign ∧ |θ.toReal| = |θ.toReal| | (:forall _ ((:c Eq) (:c Real.Angle) (:fv _uniq.222044) (:fv _uniq.222045)) ((:c And) ((:c Eq) (:c SignType) ((:c Real.Angle.sign) (:fv _uniq.222044)) ((:c Real.Angle.sign) (:fv _uniq.222045))) ((:c Eq) (:c Real) ((:c abs) (:c Real) (:c Real.lattice) (:c Real.instAddGroup) ((:c Real.Angle.toReal) (:fv _uniq.222044))) ((... | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"ψ","sexp":"(:c Real.Angle)"}] | (:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2))) (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c Real.Angle.sign) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 2 (:app (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"name":"ψ","sexp":"(:c Real.Angle)"}] | {"children":[{"source":"rintro","sourceEnd":42727,"sourceStart":42721,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":42731,"sourceStart":42728,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl","sourceEnd":42731,"sourceStart":427... | [] | [{"source":"rfl","source_end":42731,"source_start":42728,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"user_name":"ψ"}] | 319 | 10 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d95e4d10114cfe74a4574ed151f74a3f44cdf1458fabce291f09a644045f1692 | a5b99e079b7d1af3fcb5a4494de01ae00efcf3e53794ea189d216ec18978dff5 | 09e128cd6787f35d3c063b643315aff1382388dafa4e55b6546fbf9dcecb02da | 21310fe360866cddf668158672e4c8720a21454e9b248b7637d2ad870882470d |
cat-searcher/leandojo-benchmark-4-random | test | 3,812 | Real.Angle.eq_iff_sign_eq_and_abs_toReal_eq | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨<a>rfl</a>, <a>rfl</a>⟩ | case refine_1
θ : Angle
⊢ θ.sign = θ.sign ∧ |θ.toReal| = |θ.toReal| | ((:c And) ((:c Eq) (:c SignType) ((:c Real.Angle.sign) (:fv _uniq.222044)) ((:c Real.Angle.sign) (:fv _uniq.222044))) ((:c Eq) (:c Real) ((:c abs) (:c Real) (:c Real.lattice) (:c Real.instAddGroup) ((:c Real.Angle.toReal) (:fv _uniq.222044))) ((:c abs) (:c Real) (:c Real.lattice) (:c Real.instAddGroup) ((:c Real.Angle.... | [{"name":"θ","sexp":"(:c Real.Angle)"}] | (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c Real.Angle.sign) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 2 (:app (:c Real.Angle.sign) (:arg :explicit 0 (:fv FV1)))))) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"}] | {"children":[{"source":"exact","sourceEnd":42741,"sourceStart":42736,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":42745,"sourceStart":42742,"tag":"atom"},{"children":[{"name":"rfl","semanticRole":"global","source":"rfl","sourceEnd":42748,"sourceStart":42745,"tag":"identifier"},{"source":",","sourceEnd":42749,"s... | [] | [{"source":"⟨rfl, rfl⟩","source_end":42756,"source_start":42742,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"user_name":"θ"}] | 319 | 11 | exact | true | 1 | 1 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4c2c49105d759c763c5238cb1f8ec16239a0c0ba8be136fb79472a9b2046e6b0 | 21310fe360866cddf668158672e4c8720a21454e9b248b7637d2ad870882470d | 55a3315bfea033a898560566d82fa37a5f6f4561121f80c8d7462809550b8cdd | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,813 | Real.Angle.eq_iff_sign_eq_and_abs_toReal_eq | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Real.Angle.toReal_injective</a> hr | case refine_2.intro.inl
θ ψ : Angle
hs : θ.sign = ψ.sign
hr : θ.toReal = ψ.toReal
⊢ θ = ψ | ((:c Eq) (:c Real.Angle) (:fv _uniq.222044) (:fv _uniq.222045)) | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"ψ","sexp":"(:c Real.Angle)"},{"name":"hs","sexp":"((:c Eq) (:c SignType) ((:c Real.Angle.sign) (:fv _uniq.222044)) ((:c Real.Angle.sign) (:fv _uniq.222045)))"},{"name":"hr","sexp":"((:c Eq) (:c Real) ((:c Real.Angle.toReal) (:fv _uniq.222044)) ((:c Real.Angle.toReal) (:fv... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"name":"ψ","sexp":"(:c Real.Angle)"},{"binder_role":":explic... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":42847,"sourceStart":42842,"tag":"atom"},{"children":[{"name":"Real.Angle.toReal_injective","semanticRole":"global","source":"toReal_injective","sourceEnd":42864,"sourceStart":42848,"tag":"identifier"},{"children":[{"contextIndex":4,"seman... | [] | [{"source":"toReal_injective hr","source_end":42867,"source_start":42848,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"user_name":"ψ"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 319 | 19 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 48b5a0361e805fa90d1195e04dbaeee637ada2b6bcc86b092bcc33ad1d09e223 | 8bc61ca087042ad4314fc3ea84bdb525269c96184880cb8e4995e57d4e32668d | a096f05b67e5b794d7463ee318214c0745fa1526651f83f4c0a74ab54754887d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,814 | Real.Angle.eq_iff_sign_eq_and_abs_toReal_eq | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases h : θ = π | case refine_2.intro.inr
θ ψ : Angle
hs : θ.sign = ψ.sign
hr : θ.toReal = -ψ.toReal
⊢ θ = ψ | ((:c Eq) (:c Real.Angle) (:fv _uniq.222044) (:fv _uniq.222045)) | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"ψ","sexp":"(:c Real.Angle)"},{"name":"hs","sexp":"((:c Eq) (:c SignType) ((:c Real.Angle.sign) (:fv _uniq.222044)) ((:c Real.Angle.sign) (:fv _uniq.222045)))"},{"name":"hr","sexp":"((:c Eq) (:c Real) ((:c Real.Angle.toReal) (:fv _uniq.222044)) ((:c Neg.neg) (:c Real) ((:c... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"name":"ψ","sexp":"(:c Real.Angle)"},{"binder_role":":explic... | {"children":[{"children":[{"children":[{"children":[{"source":"by_cases","sourceEnd":42881,"sourceStart":42873,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":42883,"sourceStart":42882,"tag":"identifier"},{"source":":","sourceEnd":42885,"sourceStart":42884,"tag":"atom"}],"kind":"null"... | [] | [{"source":"θ = π","source_end":42893,"source_start":42886,"syntax_kind":"«term_=_»"},{"source":"h","source_end":42906,"source_start":42905,"syntax_kind":"ident"},{"source":"hr","source_end":42947,"source_start":42945,"syntax_kind":"ident"},{"source":"toReal_pi","source_end":42917,"source_start":42908,"syntax_kind":"id... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"user_name":"ψ"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 319 | 24 | branch_opener | false | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d0521d5bdf3e6c9bc63c8433637be5d9d086b6599c15523ed286be5bff0def78 | 2d837b7d3b9e9be9cfc65900344203e8e3d322664e0a2e14b54ee85203f28dfe | cfcd3d96baac9474ef8433e8a32d9467cf610b2a6c01c655dfd10a4d6a1f039b | 5ed1a79cc01466b0937fce232cb1b8430f7e21df52867b900f2003def2e4feba | |
cat-searcher/leandojo-benchmark-4-random | test | 3,815 | Real.Angle.eq_iff_sign_eq_and_abs_toReal_eq | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [h, <a>Real.Angle.toReal_pi</a>, ← <a>neg_eq_iff_eq_neg</a>] at hr | case pos
θ ψ : Angle
hs : θ.sign = ψ.sign
hr : θ.toReal = -ψ.toReal
h : θ = ↑π
⊢ θ = ψ | case pos
θ ψ : Angle
hs : θ.sign = ψ.sign
hr : -π = ψ.toReal
h : θ = ↑π
⊢ θ = ψ | ((:c Eq) (:c Real.Angle) (:fv _uniq.222044) (:fv _uniq.222045)) | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"ψ","sexp":"(:c Real.Angle)"},{"name":"hs","sexp":"((:c Eq) (:c SignType) ((:c Real.Angle.sign) (:fv _uniq.222044)) ((:c Real.Angle.sign) (:fv _uniq.222045)))"},{"name":"hr","sexp":"((:c Eq) (:c Real) ((:c Real.Angle.toReal) (:fv _uniq.222044)) ((:c Neg.neg) (:c Real) ((:c... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"name":"ψ","sexp":"(:c Real.Angle)"},{"binder_role":":explic... | {"children":[{"source":"rw","sourceEnd":42903,"sourceStart":42901,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":42905,"sourceStart":42904,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":5,"semant... | [] | [{"source":"h","source_end":42906,"source_start":42905,"syntax_kind":"ident"},{"source":"hr","source_end":42947,"source_start":42945,"syntax_kind":"ident"},{"source":"toReal_pi","source_end":42917,"source_start":42908,"syntax_kind":"ident"},{"source":"neg_eq_iff_eq_neg","source_end":42940,"source_start":42923,"syntax_k... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"user_name":"ψ"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 319 | 31 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1907590a675575c75e1b6db1ec2849e9ef5750be0304b430f26a326b8ca7bb64 | 965b91ef905b2d2bb33773bb50258647e0e747a712a86924cb974162b1ba6dde | 5fa59cc2cc80efc0c34a46cf91a663f66dabf988f87c11531906e7cb3607172d | 9b3c03704e9c90107114b975ede2fcead7f020fdf08b5a9f27b1669a36061814 |
cat-searcher/leandojo-benchmark-4-random | test | 3,816 | Real.Angle.eq_iff_sign_eq_and_abs_toReal_eq | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>False.elim</a> ((<a>Real.Angle.neg_pi_lt_toReal</a> ψ).<a>LT.lt.ne</a> hr) | case pos
θ ψ : Angle
hs : θ.sign = ψ.sign
hr : -π = ψ.toReal
h : θ = ↑π
⊢ θ = ψ | ((:c Eq) (:c Real.Angle) (:fv _uniq.222044) (:fv _uniq.222045)) | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"ψ","sexp":"(:c Real.Angle)"},{"name":"hs","sexp":"((:c Eq) (:c SignType) ((:c Real.Angle.sign) (:fv _uniq.222044)) ((:c Real.Angle.sign) (:fv _uniq.222045)))"},{"name":"hr","sexp":"((:c Eq) (:c Real) ((:c Neg.neg) (:c Real) ((:c InvolutiveNeg.toNeg) (:c Real) ((:c HasDist... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"name":"ψ","sexp":"(:c Real.Angle)"},{"binder_role":":explic... | {"children":[{"source":"exact","sourceEnd":42959,"sourceStart":42954,"tag":"atom"},{"children":[{"name":"False.elim","semanticRole":"global","source":"False.elim","sourceEnd":42970,"sourceStart":42960,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":42972,"sourceStart":42971,"tag":"atom"},{"child... | [] | [{"source":"False.elim ((neg_pi_lt_toReal ψ).ne hr)","source_end":43000,"source_start":42960,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"user_name":"ψ"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 319 | 36 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8774c6fe036ec8d5162e93d68ac71e73962b372bca751e351b6498ffddfa516f | 9b3c03704e9c90107114b975ede2fcead7f020fdf08b5a9f27b1669a36061814 | 52ec6f3cbea627a6883a1b17198c8fe35dd4289736dc443f4ac04794b7a9cced | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,817 | Real.Angle.eq_iff_sign_eq_and_abs_toReal_eq | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases h' : ψ = π | case neg
θ ψ : Angle
hs : θ.sign = ψ.sign
hr : θ.toReal = -ψ.toReal
h : ¬θ = ↑π
⊢ θ = ψ | ((:c Eq) (:c Real.Angle) (:fv _uniq.222044) (:fv _uniq.222045)) | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"ψ","sexp":"(:c Real.Angle)"},{"name":"hs","sexp":"((:c Eq) (:c SignType) ((:c Real.Angle.sign) (:fv _uniq.222044)) ((:c Real.Angle.sign) (:fv _uniq.222045)))"},{"name":"hr","sexp":"((:c Eq) (:c Real) ((:c Real.Angle.toReal) (:fv _uniq.222044)) ((:c Neg.neg) (:c Real) ((:c... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"name":"ψ","sexp":"(:c Real.Angle)"},{"binder_role":":explic... | {"children":[{"children":[{"children":[{"children":[{"source":"by_cases","sourceEnd":43016,"sourceStart":43008,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h'","sourceEnd":43019,"sourceStart":43017,"tag":"identifier"},{"source":":","sourceEnd":43021,"sourceStart":43020,"tag":"atom"}],"kind":"null... | [] | [{"source":"ψ = π","source_end":43029,"source_start":43022,"syntax_kind":"«term_=_»"},{"source":"h'","source_end":43045,"source_start":43043,"syntax_kind":"ident"},{"source":"hr","source_end":43063,"source_start":43061,"syntax_kind":"ident"},{"source":"toReal_pi","source_end":43056,"source_start":43047,"syntax_kind":"i... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"user_name":"ψ"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 319 | 39 | branch_opener | false | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 716b4b3035c50947b6629d43af56b710374a8b38c409e5e0bf8a4efe923f15ee | 0b75197ca6f2da6d2b9a6e7265c31c40388e0811e2816ccbda0b826f37834d51 | 88d692200a60f27546d03984caf3ed4f8c4291d408ccfce0549cb5d74f1761a8 | c65afc7616da1bf14cc2c5d9198aa02078cd98470cec9cf220e62ad523c53c85 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,818 | Real.Angle.eq_iff_sign_eq_and_abs_toReal_eq | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [h', <a>Real.Angle.toReal_pi</a>] at hr | case pos
θ ψ : Angle
hs : θ.sign = ψ.sign
hr : θ.toReal = -ψ.toReal
h : ¬θ = ↑π
h' : ψ = ↑π
⊢ θ = ψ | case pos
θ ψ : Angle
hs : θ.sign = ψ.sign
hr : θ.toReal = -π
h : ¬θ = ↑π
h' : ψ = ↑π
⊢ θ = ψ | ((:c Eq) (:c Real.Angle) (:fv _uniq.222044) (:fv _uniq.222045)) | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"ψ","sexp":"(:c Real.Angle)"},{"name":"hs","sexp":"((:c Eq) (:c SignType) ((:c Real.Angle.sign) (:fv _uniq.222044)) ((:c Real.Angle.sign) (:fv _uniq.222045)))"},{"name":"hr","sexp":"((:c Eq) (:c Real) ((:c Real.Angle.toReal) (:fv _uniq.222044)) ((:c Neg.neg) (:c Real) ((:c... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"name":"ψ","sexp":"(:c Real.Angle)"},{"binder_role":":explic... | {"children":[{"source":"rw","sourceEnd":43041,"sourceStart":43039,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":43043,"sourceStart":43042,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":6,"semant... | [] | [{"source":"h'","source_end":43045,"source_start":43043,"syntax_kind":"ident"},{"source":"hr","source_end":43063,"source_start":43061,"syntax_kind":"ident"},{"source":"toReal_pi","source_end":43056,"source_start":43047,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"user_name":"ψ"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 319 | 46 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dbd71f0deab3fcb346bcbaa556901815678af6c9ed38ba1b1aed8d6ac88cd33d | 2c5c776706a9f8bac85f3acf341408fc694d04e267032713dc50607ceea5951f | 52e0e227b5faac3c16cf0d2a8597793b21eec4aa8b56c61b99492a5605a1cfbb | ff887b759dc0c7946a520fad22bf8adfb89a63e16a22d69dba0165ed510ccd0c |
cat-searcher/leandojo-benchmark-4-random | test | 3,819 | Real.Angle.eq_iff_sign_eq_and_abs_toReal_eq | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>False.elim</a> ((<a>Real.Angle.neg_pi_lt_toReal</a> θ).<a>LT.lt.ne</a> hr.symm) | case pos
θ ψ : Angle
hs : θ.sign = ψ.sign
hr : θ.toReal = -π
h : ¬θ = ↑π
h' : ψ = ↑π
⊢ θ = ψ | ((:c Eq) (:c Real.Angle) (:fv _uniq.222044) (:fv _uniq.222045)) | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"ψ","sexp":"(:c Real.Angle)"},{"name":"hs","sexp":"((:c Eq) (:c SignType) ((:c Real.Angle.sign) (:fv _uniq.222044)) ((:c Real.Angle.sign) (:fv _uniq.222045)))"},{"name":"hr","sexp":"((:c Eq) (:c Real) ((:c Real.Angle.toReal) (:fv _uniq.222044)) ((:c Neg.neg) (:c Real) ((:c... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"name":"ψ","sexp":"(:c Real.Angle)"},{"binder_role":":explic... | {"children":[{"source":"exact","sourceEnd":43077,"sourceStart":43072,"tag":"atom"},{"children":[{"name":"False.elim","semanticRole":"global","source":"False.elim","sourceEnd":43088,"sourceStart":43078,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":43090,"sourceStart":43089,"tag":"atom"},{"child... | [] | [{"source":"False.elim ((neg_pi_lt_toReal θ).ne hr.symm)","source_end":43123,"source_start":43078,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"user_name":"ψ"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 319 | 50 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 62f052699cd4b097b94d0dd09c3e880290587f9666288afce92a0540042880f4 | ff887b759dc0c7946a520fad22bf8adfb89a63e16a22d69dba0165ed510ccd0c | fa1772248aaa3f939608e20b62b17cfa26008e3afb5e00675f6a2bb3290dd509 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,820 | Real.Angle.eq_iff_sign_eq_and_abs_toReal_eq | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Real.Angle.sign_toReal</a> h, ← <a>Real.Angle.sign_toReal</a> h', hr, <a>Left.sign_neg</a>, <a>SignType.neg_eq_self_iff</a>, <a>sign_eq_zero_iff</a>, <a>Real.Angle.toReal_eq_zero_iff</a>] at hs | case neg
θ ψ : Angle
hs : θ.sign = ψ.sign
hr : θ.toReal = -ψ.toReal
h : ¬θ = ↑π
h' : ¬ψ = ↑π
⊢ θ = ψ | case neg
θ ψ : Angle
hs : ψ = 0
hr : θ.toReal = -ψ.toReal
h : ¬θ = ↑π
h' : ¬ψ = ↑π
⊢ θ = ψ | ((:c Eq) (:c Real.Angle) (:fv _uniq.222044) (:fv _uniq.222045)) | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"ψ","sexp":"(:c Real.Angle)"},{"name":"hs","sexp":"((:c Eq) (:c SignType) ((:c Real.Angle.sign) (:fv _uniq.222044)) ((:c Real.Angle.sign) (:fv _uniq.222045)))"},{"name":"hr","sexp":"((:c Eq) (:c Real) ((:c Real.Angle.toReal) (:fv _uniq.222044)) ((:c Neg.neg) (:c Real) ((:c... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"name":"ψ","sexp":"(:c Real.Angle)"},{"binder_role":":explic... | {"children":[{"source":"rw","sourceEnd":43135,"sourceStart":43133,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":43137,"sourceStart":43136,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":43140,"sourceSt... | [] | [{"source":"hs","source_end":43281,"source_start":43279,"syntax_kind":"ident"},{"source":"sign_toReal h","source_end":43154,"source_start":43141,"syntax_kind":"Lean.Parser.Term.app"},{"source":"sign_toReal h'","source_end":43174,"source_start":43160,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hr","source_end":4317... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"user_name":"ψ"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 319 | 55 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f0c3b7b40b22bd20f994ed056c7f8c368ddc72f518c7201d1bfc5f2cdcbc5bde | 922a3b725a50dcafe8a194b33105d5c45be1d2e708e0b2949dccaa874dbe6072 | 84e1fec4be19e7cbfdb62fadc5c43f5be35bbcce8ad6a4aae7791acde0ecff71 | a5b230798fcbc419eec1185d7e8ad5df517b51641f0eb825362a62fd1f5d79a8 |
cat-searcher/leandojo-benchmark-4-random | test | 3,821 | Real.Angle.eq_iff_sign_eq_and_abs_toReal_eq | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hs, <a>Real.Angle.toReal_zero</a>, <a>neg_zero</a>, <a>Real.Angle.toReal_eq_zero_iff</a>] at hr | case neg
θ ψ : Angle
hs : ψ = 0
hr : θ.toReal = -ψ.toReal
h : ¬θ = ↑π
h' : ¬ψ = ↑π
⊢ θ = ψ | case neg
θ ψ : Angle
hs : ψ = 0
hr : θ = 0
h : ¬θ = ↑π
h' : ¬ψ = ↑π
⊢ θ = ψ | ((:c Eq) (:c Real.Angle) (:fv _uniq.222044) (:fv _uniq.222045)) | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"ψ","sexp":"(:c Real.Angle)"},{"name":"hs","sexp":"((:c Eq) (:c Real.Angle) (:fv _uniq.222045) ((:c OfNat.ofNat) (:c Real.Angle) (:lit 0) ((:c Zero.toOfNat0) (:c Real.Angle) ((:c NegZeroClass.toZero) (:c Real.Angle) ((:c SubNegZeroMonoid.toNegZeroClass) (:c Real.Angle) ((:... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"name":"ψ","sexp":"(:c Real.Angle)"},{"binder_role":":explic... | {"children":[{"source":"rw","sourceEnd":43292,"sourceStart":43290,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":43294,"sourceStart":43293,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":3,"semant... | [] | [{"source":"hs","source_end":43296,"source_start":43294,"syntax_kind":"ident"},{"source":"hr","source_end":43346,"source_start":43344,"syntax_kind":"ident"},{"source":"toReal_zero","source_end":43309,"source_start":43298,"syntax_kind":"ident"},{"source":"neg_zero","source_end":43319,"source_start":43311,"syntax_kind":"... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"user_name":"ψ"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 319 | 64 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5943b6dca0ec36b1385907bf78b5dd32bac2dee048c41688d5693e4be28d4b26 | a5b230798fcbc419eec1185d7e8ad5df517b51641f0eb825362a62fd1f5d79a8 | c45d7ed3b433df7356273c3e927cc1c11e623ddc7a22c3e57d3026340319aa79 | 77b8d57c0e1d182ed2913c743f9e4bfe43114a99b9f7585ff72c69bcd05ca10a |
cat-searcher/leandojo-benchmark-4-random | test | 3,822 | Real.Angle.eq_iff_sign_eq_and_abs_toReal_eq | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hr, hs] | case neg
θ ψ : Angle
hs : ψ = 0
hr : θ = 0
h : ¬θ = ↑π
h' : ¬ψ = ↑π
⊢ θ = ψ | ((:c Eq) (:c Real.Angle) (:fv _uniq.222044) (:fv _uniq.222045)) | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"ψ","sexp":"(:c Real.Angle)"},{"name":"hs","sexp":"((:c Eq) (:c Real.Angle) (:fv _uniq.222045) ((:c OfNat.ofNat) (:c Real.Angle) (:lit 0) ((:c Zero.toOfNat0) (:c Real.Angle) ((:c NegZeroClass.toZero) (:c Real.Angle) ((:c SubNegZeroMonoid.toNegZeroClass) (:c Real.Angle) ((:... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"name":"ψ","sexp":"(:c Real.Angle)"},{"binder_role":":explic... | {"children":[{"source":"rw","sourceEnd":43357,"sourceStart":43355,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":43359,"sourceStart":43358,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":4,"semant... | [] | [{"source":"hr","source_end":43361,"source_start":43359,"syntax_kind":"ident"},{"source":"hs","source_end":43365,"source_start":43363,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.222044","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.222045","is_instance":false,"is_let":false,"user_name":"ψ"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 319 | 70 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 74226a16f778297a4b822b4e41266cc15c3d12427b1055647fd20fc99becf9cc | 77b8d57c0e1d182ed2913c743f9e4bfe43114a99b9f7585ff72c69bcd05ca10a | 9b10182f28ea3eb8ddbed842c7fbd33621c6b0a14a035f45c42b7d2922a99d43 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,823 | Submodule.restrictScalars_mul | Mathlib/Algebra/Algebra/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>le_antisymm</a> | ι : Sort uι
R : Type u
inst✝⁹ : CommSemiring R
A✝ : Type v
inst✝⁸ : Semiring A✝
inst✝⁷ : Algebra R A✝
S T : Set A✝
M N P Q : Submodule R A✝
m n : A✝
A : Type u_1
B : Type u_2
C : Type u_3
inst✝⁶ : CommSemiring A
inst✝⁵ : CommSemiring B
inst✝⁴ : Semiring C
inst✝³ : Algebra A B
inst✝² : Algebra A C
inst✝¹ : Algebra B C
i... | case a
ι : Sort uι
R : Type u
inst✝⁹ : CommSemiring R
A✝ : Type v
inst✝⁸ : Semiring A✝
inst✝⁷ : Algebra R A✝
S T : Set A✝
M N P Q : Submodule R A✝
m n : A✝
A : Type u_1
B : Type u_2
C : Type u_3
inst✝⁶ : CommSemiring A
inst✝⁵ : CommSemiring B
inst✝⁴ : Semiring C
inst✝³ : Algebra A B
inst✝² : Algebra A C
inst✝¹ : Algebr... | ((:c Eq) ((:c Submodule) (:fv _uniq.145378) (:fv _uniq.145380) ((:c CommSemiring.toSemiring) (:fv _uniq.145378) (:fv _uniq.145381)) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.145380) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.145380) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.145380... | [{"name":"ι","sexp":"(:sort uι)"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝⁹","sexp":"((:c CommSemiring) (:fv _uniq.143522))"},{"name":"A✝","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁸","sexp":"((:c Semiring) (:fv _uniq.143527))"},{"name":"inst✝⁷","sexp":"((:c Algebra) (:fv _uniq.143522) (:fv _uniq.143527) (:fv... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV15)) (:arg :explicit 1 (:fv FV17)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV15))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV17))))) (:arg :instance 4 (:instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.143520","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.143522","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"apply","sourceEnd":12645,"sourceStart":12640,"tag":"atom"},{"name":"le_antisymm","semanticRole":"global","source":"le_antisymm","sourceEnd":12657,"sourceStart":12646,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply le_antisymm","sourceEnd":12657,"sourceStart":12640,"tag":"n... | [] | [{"source":"le_antisymm","source_end":12657,"source_start":12646,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.143520","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.143522","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal... | 95 | 4 | exact | true | 1 | 26 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9e7af58679d0c69e168a6a581185cecd0b5e37e1e8644550dda5ab8833c15456 | 405f5726e5990ec5dba0b894e01ca2e89194bdd6b52bafe44edffcbc88cfd2ad | 0abfddcb77ef175f592e63086534058d51fe8d6b63ac2fff9f69f045bc0962dc | c6a3c724223cac81f4b12a4442a6a7c4a72e4357383bbc15fdfa9c543aa87c55 |
cat-searcher/leandojo-benchmark-4-random | test | 3,824 | Submodule.restrictScalars_mul | Mathlib/Algebra/Algebra/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro x (hx : x ∈ I * J) | case a
ι : Sort uι
R : Type u
inst✝⁹ : CommSemiring R
A✝ : Type v
inst✝⁸ : Semiring A✝
inst✝⁷ : Algebra R A✝
S T : Set A✝
M N P Q : Submodule R A✝
m n : A✝
A : Type u_1
B : Type u_2
C : Type u_3
inst✝⁶ : CommSemiring A
inst✝⁵ : CommSemiring B
inst✝⁴ : Semiring C
inst✝³ : Algebra A B
inst✝² : Algebra A C
inst✝¹ : Algebr... | case a
ι : Sort uι
R : Type u
inst✝⁹ : CommSemiring R
A✝ : Type v
inst✝⁸ : Semiring A✝
inst✝⁷ : Algebra R A✝
S T : Set A✝
M N P Q : Submodule R A✝
m n : A✝
A : Type u_1
B : Type u_2
C : Type u_3
inst✝⁶ : CommSemiring A
inst✝⁵ : CommSemiring B
inst✝⁴ : Semiring C
inst✝³ : Algebra A B
inst✝² : Algebra A C
inst✝¹ : Algebr... | ((:c LE.le) ((:c Submodule) (:fv _uniq.145378) (:fv _uniq.145380) ((:c CommSemiring.toSemiring) (:fv _uniq.145378) (:fv _uniq.145381)) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.145380) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.145380) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.145... | [{"name":"ι","sexp":"(:sort uι)"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝⁹","sexp":"((:c CommSemiring) (:fv _uniq.143522))"},{"name":"A✝","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁸","sexp":"((:c Semiring) (:fv _uniq.143527))"},{"name":"inst✝⁷","sexp":"((:c Algebra) (:fv _uniq.143522) (:fv _uniq.143527) (:fv... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV15)) (:arg :explicit 1 (:fv FV17)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV15))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV17))))) (:arg :instance 4 (:inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.143520","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.143522","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"intro","sourceEnd":12668,"sourceStart":12663,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":12670,"sourceStart":12669,"tag":"identifier"},{"children":[{"source":"(","sourceEnd":12672,"sourceStart":12671,"tag":"atom"},{"semanticRole":"scoped_local","source":"hx... | [{"role":"fresh_name","source":"x","source_end":12670,"source_start":12669,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":12674,"source_start":12672,"syntax_kind":"ident"},{"role":"fresh_name","source":"x","source_end":12678,"source_start":12677,"syntax_kind":"ident"}] | [{"source":"x ∈ I * J","source_end":12688,"source_start":12677,"syntax_kind":"«term_∈_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.143520","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.143522","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal... | 95 | 9 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7e17a9f7a176ada58fff3f4620eb48d816aa378051881b75af51c3b6bbbe2c4d | 7f0a9cd18fcc225e1bcf6ef94fad5007db324cf7f4c4a3d1efea8fff3af321a2 | 1fcc4a0a52090648ce8146651ff79dc000db0af67bcc2045821e10ed81a743ba | cbada121229429d70bd95b0c5a76edd1ada93215110268e366c806bfa20fb69a |
cat-searcher/leandojo-benchmark-4-random | test | 3,825 | Submodule.restrictScalars_mul | Mathlib/Algebra/Algebra/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Submodule.mul_induction_on</a> hx ?_ ?_ | case a
ι : Sort uι
R : Type u
inst✝⁹ : CommSemiring R
A✝ : Type v
inst✝⁸ : Semiring A✝
inst✝⁷ : Algebra R A✝
S T : Set A✝
M N P Q : Submodule R A✝
m n : A✝
A : Type u_1
B : Type u_2
C : Type u_3
inst✝⁶ : CommSemiring A
inst✝⁵ : CommSemiring B
inst✝⁴ : Semiring C
inst✝³ : Algebra A B
inst✝² : Algebra A C
inst✝¹ : Algebr... | case a.refine_1
ι : Sort uι
R : Type u
inst✝⁹ : CommSemiring R
A✝ : Type v
inst✝⁸ : Semiring A✝
inst✝⁷ : Algebra R A✝
S T : Set A✝
M N P Q : Submodule R A✝
m n : A✝
A : Type u_1
B : Type u_2
C : Type u_3
inst✝⁶ : CommSemiring A
inst✝⁵ : CommSemiring B
inst✝⁴ : Semiring C
inst✝³ : Algebra A B
inst✝² : Algebra A C
inst✝¹... | ((:c Membership.mem) (:fv _uniq.145380) ((:c Submodule) (:fv _uniq.145378) (:fv _uniq.145380) ((:c CommSemiring.toSemiring) (:fv _uniq.145378) (:fv _uniq.145381)) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.145380) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.145380) ((:c Semiring.toNonA... | [{"name":"ι","sexp":"(:sort uι)"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝⁹","sexp":"((:c CommSemiring) (:fv _uniq.143522))"},{"name":"A✝","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁸","sexp":"((:c Semiring) (:fv _uniq.143527))"},{"name":"inst✝⁷","sexp":"((:c Algebra) (:fv _uniq.143522) (:fv _uniq.143527) (:fv... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV17)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV15)) (:arg :explicit 1 (:fv FV17)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV15))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.143520","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.143522","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":12700,"sourceStart":12694,"tag":"atom"},{"children":[{"name":"Submodule.mul_induction_on","semanticRole":"global","source":"Submodule.mul_induction_on","sourceEnd":12727,"sourceStart":12701,"tag":"identifier"},{"children":[{"contextIndex":28,"semanticRole":"local","source":"h... | [] | [{"source":"Submodule.mul_induction_on hx ?_ ?_","source_end":12736,"source_start":12701,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.143520","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.143522","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal... | 95 | 10 | exact | true | 1 | 28 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e83efc26e8da90d1342b3bc8d6b4d0b698fb8ff04f8491b4d12bd481d161fb4b | cbada121229429d70bd95b0c5a76edd1ada93215110268e366c806bfa20fb69a | 3c6e0c044876d3ca8358eb92f781cb212634d0a512267ec0dbf65382e398a843 | c3f9d6e57984e67a1098118ead1ef4856acd6fdd2f95ef92d5908bcb47046ec2 |
cat-searcher/leandojo-benchmark-4-random | test | 3,826 | Submodule.restrictScalars_mul | Mathlib/Algebra/Algebra/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun m hm n hn ↦ <a>Submodule.mul_mem_mul</a> hm hn | case a.refine_1
ι : Sort uι
R : Type u
inst✝⁹ : CommSemiring R
A✝ : Type v
inst✝⁸ : Semiring A✝
inst✝⁷ : Algebra R A✝
S T : Set A✝
M N P Q : Submodule R A✝
m n : A✝
A : Type u_1
B : Type u_2
C : Type u_3
inst✝⁶ : CommSemiring A
inst✝⁵ : CommSemiring B
inst✝⁴ : Semiring C
inst✝³ : Algebra A B
inst✝² : Algebra A C
inst✝¹... | (:forall m (:fv _uniq.145380) (:forall _ ((:c Membership.mem) (:fv _uniq.145380) ((:c Submodule) (:fv _uniq.145379) (:fv _uniq.145380) ((:c CommSemiring.toSemiring) (:fv _uniq.145379) (:fv _uniq.145382)) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.145380) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring... | [{"name":"ι","sexp":"(:sort uι)"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝⁹","sexp":"((:c CommSemiring) (:fv _uniq.143522))"},{"name":"A✝","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁸","sexp":"((:c Semiring) (:fv _uniq.143527))"},{"name":"inst✝⁷","sexp":"((:c Algebra) (:fv _uniq.143522) (:fv _uniq.143527) (:fv... | (:forall m :explicit (:fv FV17) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV17)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV16)) (:arg :explicit 1 (:fv FV17)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV16))))) (:arg :instance 3... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.143520","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.143522","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":12749,"sourceStart":12744,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":12753,"sourceStart":12750,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"m","sourceEnd":12755,"sourceStart":12754,"tag":"id... | [] | [{"source":"fun m hm n hn ↦ mul_mem_mul hm hn","source_end":12785,"source_start":12750,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.143520","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.143522","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal... | 95 | 13 | exact | true | 1 | 28 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7db6bda6d148686874f421272414279f6b301426f398270ab7cb0228383a324d | a495db137014f904694754e23d0f6c61a1baaea9e8be233a05db7c749e6f0871 | 92420f9fe65ea00c8d8dac4d7246157974f824939ae019cef923df4003cf50b7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,827 | Submodule.restrictScalars_mul | Mathlib/Algebra/Algebra/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun _ _ ↦ <a>AddMemClass.add_mem</a> | case a.refine_2
ι : Sort uι
R : Type u
inst✝⁹ : CommSemiring R
A✝ : Type v
inst✝⁸ : Semiring A✝
inst✝⁷ : Algebra R A✝
S T : Set A✝
M N P Q : Submodule R A✝
m n : A✝
A : Type u_1
B : Type u_2
C : Type u_3
inst✝⁶ : CommSemiring A
inst✝⁵ : CommSemiring B
inst✝⁴ : Semiring C
inst✝³ : Algebra A B
inst✝² : Algebra A C
inst✝¹... | (:forall x (:fv _uniq.145380) (:forall y (:fv _uniq.145380) (:forall _ ((:c Membership.mem) (:fv _uniq.145380) ((:c Submodule) (:fv _uniq.145378) (:fv _uniq.145380) ((:c CommSemiring.toSemiring) (:fv _uniq.145378) (:fv _uniq.145381)) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.145380) ((:c NonAssocSemiri... | [{"name":"ι","sexp":"(:sort uι)"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝⁹","sexp":"((:c CommSemiring) (:fv _uniq.143522))"},{"name":"A✝","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁸","sexp":"((:c Semiring) (:fv _uniq.143527))"},{"name":"inst✝⁷","sexp":"((:c Algebra) (:fv _uniq.143522) (:fv _uniq.143527) (:fv... | (:forall x :explicit (:fv FV17) (:forall y :explicit (:fv FV17) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV17)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV15)) (:arg :explicit 1 (:fv FV17)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.143520","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.143522","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":12798,"sourceStart":12793,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":12802,"sourceStart":12799,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"_","sourceEnd":12804,"sourceStart":12803,"tag":"atom"}],"kind":"Lea... | [] | [{"source":"fun _ _ ↦ add_mem","source_end":12818,"source_start":12799,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.143520","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.143522","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal... | 95 | 18 | exact | true | 1 | 28 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 70b6bd17667ab2b1ec7851c62e992170e10cbb0ddca6a0185f6e97c40721aba9 | 42edb94e841e40e7ff01276c140f0682267e7aba8f8d64436fe850c42019476c | 3fc339379df222e95b976201f14d7316678f735e843c2679a4795c768bbbe262 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,828 | Submodule.restrictScalars_mul | Mathlib/Algebra/Algebra/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact mul_le.mpr (fun _ hm _ hn ↦ <a>Submodule.mul_mem_mul</a> hm hn) | case a
ι : Sort uι
R : Type u
inst✝⁹ : CommSemiring R
A✝ : Type v
inst✝⁸ : Semiring A✝
inst✝⁷ : Algebra R A✝
S T : Set A✝
M N P Q : Submodule R A✝
m n : A✝
A : Type u_1
B : Type u_2
C : Type u_3
inst✝⁶ : CommSemiring A
inst✝⁵ : CommSemiring B
inst✝⁴ : Semiring C
inst✝³ : Algebra A B
inst✝² : Algebra A C
inst✝¹ : Algebr... | ((:c LE.le) ((:c Submodule) (:fv _uniq.145378) (:fv _uniq.145380) ((:c CommSemiring.toSemiring) (:fv _uniq.145378) (:fv _uniq.145381)) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.145380) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.145380) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.145... | [{"name":"ι","sexp":"(:sort uι)"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝⁹","sexp":"((:c CommSemiring) (:fv _uniq.143522))"},{"name":"A✝","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁸","sexp":"((:c Semiring) (:fv _uniq.143527))"},{"name":"inst✝⁷","sexp":"((:c Algebra) (:fv _uniq.143522) (:fv _uniq.143527) (:fv... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV15)) (:arg :explicit 1 (:fv FV17)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV15))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV17))))) (:arg :instance 4 (:inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.143520","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.143522","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":12829,"sourceStart":12824,"tag":"atom"},{"children":[{"source":"mul_le.mpr","sourceEnd":12840,"sourceStart":12830,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":12842,"sourceStart":12841,"tag":"atom"},{"children":... | [] | [{"source":"mul_le.mpr (fun _ hm _ hn ↦ mul_mem_mul hm hn)","source_end":12878,"source_start":12830,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.143520","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.143522","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal... | 95 | 23 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d4e939b3145598174ae33a41a6b9afb568f7a74cdbcd0ae320d7a7983a6d203f | b667afbddddf784338f8e7ffb3aed020f687cb9e0edf275b045fed17796f4876 | 2adb0defed8b7f3e05bb7c9c621ab49ca0437508cd213f03ef57e1af874a45a0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,829 | Subalgebra.iSupLift_of_mem | Mathlib/Algebra/Algebra/Subalgebra/Directed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp [<a>Subalgebra.iSupLift</a>, <a>Subalgebra.inclusion</a>] | R : Type u_1
A : Type u_2
B : Type u_3
inst✝⁵ : CommSemiring R
inst✝⁴ : Semiring A
inst✝³ : Algebra R A
inst✝² : Semiring B
inst✝¹ : Algebra R B
S : Subalgebra R A
ι : Type u_4
inst✝ : Nonempty ι
K : ι → Subalgebra R A
dir : Directed (fun x x_1 => x ≤ x_1) K
f : (i : ι) → ↥(K i) →ₐ[R] B
hf : ∀ (i j : ι) (h : K i ≤ K j)... | R : Type u_1
A : Type u_2
B : Type u_3
inst✝⁵ : CommSemiring R
inst✝⁴ : Semiring A
inst✝³ : Algebra R A
inst✝² : Semiring B
inst✝¹ : Algebra R B
S : Subalgebra R A
ι : Type u_4
inst✝ : Nonempty ι
K : ι → Subalgebra R A
dir : Directed (fun x x_1 => x ≤ x_1) K
f : (i : ι) → ↥(K i) →ₐ[R] B
hf : ∀ (i j : ι) (h : K i ≤ K j)... | ((:c Eq) (:fv _uniq.84441) ((:c DFunLike.coe) ((:c AlgHom) (:fv _uniq.84435) ((:c Subtype) (:fv _uniq.84438) (:lambda x (:fv _uniq.84438) ((:c Membership.mem) (:fv _uniq.84438) ((:c Subalgebra) (:fv _uniq.84435) (:fv _uniq.84438) (:fv _uniq.84444) (:fv _uniq.84447) (:fv _uniq.84472)) ((:c SetLike.instMembership) ((:c S... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁵","sexp":"((:c CommSemiring) (:fv _uniq.84435))"},{"name":"inst✝⁴","sexp":"((:c Semiring) (:fv _uniq.84438))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.84435) (:fv _uniq.84438... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AlgHom) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84435","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84438","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"dsimp","sourceEnd":3948,"sourceStart":3943,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3950,"sourceStart":3949,"tag":"atom... | [] | [{"source":"iSupLift","source_end":3958,"source_start":3950,"syntax_kind":"ident"},{"source":"inclusion","source_end":3969,"source_start":3960,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84435","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84438","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 20 | 4 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f5342ad9ae91ad780089a51401286df4d4ee0d0c0505653b9c5674dc5a7bfa82 | cfcc173fc4a12f472e47da4b7eabc5e04a6d99548214cf2c0f54e8b4c83b33fc | b48803cea57b32ce178383c1075400ae03132201d30da65229f99ee9073c5500 | 2305e2cc68d638f90d7f7600ca2ba5dcda8b95bbe1e3f7b94dffab7dcb804fb8 |
cat-searcher/leandojo-benchmark-4-random | test | 3,830 | Subalgebra.iSupLift_of_mem | Mathlib/Algebra/Algebra/Subalgebra/Directed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.iUnionLift_of_mem</a>] | R : Type u_1
A : Type u_2
B : Type u_3
inst✝⁵ : CommSemiring R
inst✝⁴ : Semiring A
inst✝³ : Algebra R A
inst✝² : Semiring B
inst✝¹ : Algebra R B
S : Subalgebra R A
ι : Type u_4
inst✝ : Nonempty ι
K : ι → Subalgebra R A
dir : Directed (fun x x_1 => x ≤ x_1) K
f : (i : ι) → ↥(K i) →ₐ[R] B
hf : ∀ (i j : ι) (h : K i ≤ K j)... | ((:c Eq) (:fv _uniq.84441) ((:c Set.iUnionLift) (:fv _uniq.84438) (:fv _uniq.84533) (:fv _uniq.84441) (:lambda i (:fv _uniq.84533) ((:c SetLike.coe) ((:c Subalgebra) (:fv _uniq.84435) (:fv _uniq.84438) (:fv _uniq.84444) (:fv _uniq.84447) (:fv _uniq.84472)) (:fv _uniq.84438) ((:c Subalgebra.instSetLike) (:fv _uniq.84435... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁵","sexp":"((:c CommSemiring) (:fv _uniq.84435))"},{"name":"inst✝⁴","sexp":"((:c Semiring) (:fv _uniq.84438))"},{"name":"inst✝³","sexp":"((:c Algebra) (:fv _uniq.84435) (:fv _uniq.84438... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Set.iUnionLift) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV9)) (:arg :implicit-type 2 (:fv FV2)) (:arg :explicit 3 (:lambda i :explicit (:fv FV9) (:app (:c SetLike.coe) (:arg :implicit-type 0 (:app (:c Subalgebra) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84435","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84438","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":3975,"sourceStart":3973,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3977,"sourceStart":3976,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.iUnionLift_of_me... | [] | [{"source":"Set.iUnionLift_of_mem","source_end":3998,"source_start":3977,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84435","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84438","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 20 | 5 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1a0ef106b076520b39d983020289cfe8f08a6a5e0c4b25a01bec34547b5aab69 | 2305e2cc68d638f90d7f7600ca2ba5dcda8b95bbe1e3f7b94dffab7dcb804fb8 | cca10b3d8eb832f0460e05ba9443c14e6936435eea55aeffe5d87a9bd54dc81b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,831 | Cardinal.lift_le_continuum | Mathlib/SetTheory/Cardinal/Continuum.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Cardinal.lift_continuum</a>.{v, u}, <a>Cardinal.lift_le</a>] | c : Cardinal.{u}
⊢ lift.{v, u} c ≤ 𝔠 ↔ c ≤ 𝔠 | ((:c Iff) ((:c LE.le) (:c Cardinal) (:c Cardinal.instLE) ((:c Cardinal.lift) (:fv _uniq.1839)) (:c Cardinal.continuum)) ((:c LE.le) (:c Cardinal) (:c Cardinal.instLE) (:fv _uniq.1839) (:c Cardinal.continuum))) | [{"name":"c","sexp":"(:c Cardinal)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c Cardinal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Cardinal))))) (:arg :explicit 2 (:app (:c Cardinal.lift) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 3 (:c Cardinal.continuum)))) (:arg :explicit 1 (:app (:c LE.... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1839","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Cardinal)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":1472,"sourceStart":1470,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1474,"sourceStart":1473,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"sour... | [] | [{"source":"lift_continuum.{v, u}","source_end":1499,"source_start":1478,"syntax_kind":"Lean.Parser.Term.explicitUniv"},{"source":"lift_le","source_end":1508,"source_start":1501,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1839","is_instance":false,"is_let":false,"user_name":"c"}] | 14 | 2 | exact | true | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ee420f8818ccb634cb8af7f82c33e5e1bd29d1938b246c29bba21216a43581ea | 0052525b3a9459086b30863cc0b408c3b2b1fcc01b67a40d0786403b6e100737 | 3416cbb315acc17c0eb0601fa2136ee5c3c467cd820b885503fb921551e7cb46 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,832 | Int.fract_add_int | Mathlib/Algebra/Order/Floor.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Int.fract</a>] | F : Type u_1
α : Type u_2
β : Type u_3
inst✝¹ : LinearOrderedRing α
inst✝ : FloorRing α
z : ℤ
a✝ a : α
m : ℤ
⊢ fract (a + ↑m) = fract a | F : Type u_1
α : Type u_2
β : Type u_3
inst✝¹ : LinearOrderedRing α
inst✝ : FloorRing α
z : ℤ
a✝ a : α
m : ℤ
⊢ a + ↑m - ↑⌊a + ↑m⌋ = fract a | ((:c Eq) (:fv _uniq.152857) ((:c Int.fract) (:fv _uniq.152857) (:fv _uniq.152863) (:fv _uniq.152871) ((:c HAdd.hAdd) (:fv _uniq.152857) (:fv _uniq.152857) (:fv _uniq.152857) ((:c instHAdd) (:fv _uniq.152857) ((:c Distrib.toAdd) (:fv _uniq.152857) ((:c NonUnitalNonAssocSemiring.toDistrib) (:fv _uniq.152857) ((:c NonUnit... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedRing) (:fv _uniq.152857))"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.152857) (:fv _uniq.152863))"},{"name":"z","sexp":"(:c Int)"},{"name":"a✝","se... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Int.fract) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c FloorRing) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152854","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.152857","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":32171,"sourceStart":32169,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32173,"sourceStart":32172,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Int.fract","sema... | [] | [{"source":"fract","source_end":32178,"source_start":32173,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152854","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.152857","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 288 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f9f671848f7b8a609df0afb82286776b8d03afed1ab518f1cacaa8b193c92948 | cb900011affaf81465aa3ce81c27d3ca3fc8f70fdb5a03eb4d4dcda100cab3e8 | acb829837a19b3bd7081a1a893c6cb2e1fe3b8ebece31751e7e8e1ca85fe5c9b | f05999a0ccda263224023d992e4c5105903a34863165256dbc4dfd5ce5ee6d8d |
cat-searcher/leandojo-benchmark-4-random | test | 3,833 | Int.fract_add_int | Mathlib/Algebra/Order/Floor.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | F : Type u_1
α : Type u_2
β : Type u_3
inst✝¹ : LinearOrderedRing α
inst✝ : FloorRing α
z : ℤ
a✝ a : α
m : ℤ
⊢ a + ↑m - ↑⌊a + ↑m⌋ = fract a | ((:c Eq) (:fv _uniq.152857) ((:c HSub.hSub) (:fv _uniq.152857) (:fv _uniq.152857) (:fv _uniq.152857) ((:c instHSub) (:fv _uniq.152857) ((:c Ring.toSub) (:fv _uniq.152857) ((:c StrictOrderedRing.toRing) (:fv _uniq.152857) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.152857) (:fv _uniq.152863))))) ((:c HAdd.hAd... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedRing) (:fv _uniq.152857))"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.152857) (:fv _uniq.152863))"},{"name":"z","sexp":"(:c Int)"},{"name":"a✝","se... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HSub) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152854","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.152857","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":32186,"sourceStart":32182,"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.152854","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.152857","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 288 | 7 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c440070cbc7412d80f28798e8c226776253d5e115c5bb54229ef7423256317ac | f05999a0ccda263224023d992e4c5105903a34863165256dbc4dfd5ce5ee6d8d | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,834 | exists_mem_frontier_infDist_compl_eq_dist | Mathlib/Analysis/NormedSpace/FiniteDimension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>Metric.exists_mem_closure_infDist_eq_dist</a> (<a>Set.nonempty_compl</a>.2 hs) x with ⟨y, hys, hyd⟩ | E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : FiniteDimensional ℝ E
x : E
s : Set E
hx : x ∈ s
hs : s ≠ univ
⊢ ∃ y ∈ frontier s, infDist x sᶜ = dist x y | case intro.intro
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : FiniteDimensional ℝ E
x : E
s : Set E
hx : x ∈ s
hs : s ≠ univ
y : E
hys : y ∈ closure sᶜ
hyd : infDist x sᶜ = dist x y
⊢ ∃ y ∈ frontier s, infDist x sᶜ = dist x y | ((:c Exists) (:fv _uniq.542830) (:lambda y (:fv _uniq.542830) ((:c And) ((:c Membership.mem) (:fv _uniq.542830) ((:c Set) (:fv _uniq.542830)) ((:c Set.instMembership) (:fv _uniq.542830)) 0 ((:c frontier) (:fv _uniq.542830) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.542830) ((:c PseudoMetricSpace.toUniformSpace) (... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.542830))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.542830) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.542830) (:fv _uniq.542831)))"},{"name":"inst✝","sexp... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda y :explicit (:fv FV1) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.542830","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.542831","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedAddCommGroup) (... | {"children":[{"source":"rcases","sourceEnd":34329,"sourceStart":34323,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Metric.exists_mem_closure_infDist_eq_dist","semanticRole":"global","source":"Metric.exists_mem_closure_infDist_eq_dist","sourceEnd":3... | [] | [{"source":"Metric.exists_mem_closure_infDist_eq_dist (nonempty_compl.2 hs) x","source_end":34395,"source_start":34330,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨y, hys, hyd⟩","source_end":34418,"source_start":34401,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.542830","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.542831","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 118 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | adfbb325b8c15f13d649d4c17b9df122bdc2bffc562e56cfbb1dd3a04dd60aaa | 04a3f525070691ae8c2ad6d2c338c8ddbbc067cf0f4986b4c27c20b3530b0796 | 0a80c3aadc926d5e2b84bd3dacdb1bfe2411e1133df386f1f712160c70a28962 | 4ff172912e9bebf5783ad15ae013b6899b36d34ea929068744af2a88b824f378 |
cat-searcher/leandojo-benchmark-4-random | test | 3,835 | exists_mem_frontier_infDist_compl_eq_dist | Mathlib/Analysis/NormedSpace/FiniteDimension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>closure_compl</a>] at hys | case intro.intro
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : FiniteDimensional ℝ E
x : E
s : Set E
hx : x ∈ s
hs : s ≠ univ
y : E
hys : y ∈ closure sᶜ
hyd : infDist x sᶜ = dist x y
⊢ ∃ y ∈ frontier s, infDist x sᶜ = dist x y | case intro.intro
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : FiniteDimensional ℝ E
x : E
s : Set E
hx : x ∈ s
hs : s ≠ univ
y : E
hys : y ∈ (interior s)ᶜ
hyd : infDist x sᶜ = dist x y
⊢ ∃ y ∈ frontier s, infDist x sᶜ = dist x y | ((:c Exists) (:fv _uniq.542830) (:lambda y (:fv _uniq.542830) ((:c And) ((:c Membership.mem) (:fv _uniq.542830) ((:c Set) (:fv _uniq.542830)) ((:c Set.instMembership) (:fv _uniq.542830)) 0 ((:c frontier) (:fv _uniq.542830) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.542830) ((:c PseudoMetricSpace.toUniformSpace) (... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.542830))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.542830) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.542830) (:fv _uniq.542831)))"},{"name":"inst✝","sexp... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda y :explicit (:fv FV1) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.542830","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.542831","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedAddCommGroup) (... | {"children":[{"source":"rw","sourceEnd":34423,"sourceStart":34421,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":34425,"sourceStart":34424,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"closure_compl","... | [] | [{"source":"closure_compl","source_end":34438,"source_start":34425,"syntax_kind":"ident"},{"source":"hys","source_end":34446,"source_start":34443,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.542830","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.542831","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 118 | 5 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 975e82671386f0f42800ab76ddddf6cb28a176f2d6dd5fbd300e1c4e8645eb81 | 4ff172912e9bebf5783ad15ae013b6899b36d34ea929068744af2a88b824f378 | 2b88a29b8f57faa124aa87121957c30ce370b850c71749a83062878f0dc611a1 | f7d7d5c7f773351a54ac51bf82ac40d2bdbb19cff66535c63726409ad4e76396 |
cat-searcher/leandojo-benchmark-4-random | test | 3,836 | exists_mem_frontier_infDist_compl_eq_dist | Mathlib/Analysis/NormedSpace/FiniteDimension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨y, ⟨<a>Metric.closedBall_infDist_compl_subset_closure</a> hx <| <a>Metric.mem_closedBall</a>.2 <| <a>ge_of_eq</a> ?_, hys⟩, hyd⟩ | case intro.intro
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : FiniteDimensional ℝ E
x : E
s : Set E
hx : x ∈ s
hs : s ≠ univ
y : E
hys : y ∈ (interior s)ᶜ
hyd : infDist x sᶜ = dist x y
⊢ ∃ y ∈ frontier s, infDist x sᶜ = dist x y | case intro.intro
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : FiniteDimensional ℝ E
x : E
s : Set E
hx : x ∈ s
hs : s ≠ univ
y : E
hys : y ∈ (interior s)ᶜ
hyd : infDist x sᶜ = dist x y
⊢ infDist x sᶜ = dist y x | ((:c Exists) (:fv _uniq.542830) (:lambda y (:fv _uniq.542830) ((:c And) ((:c Membership.mem) (:fv _uniq.542830) ((:c Set) (:fv _uniq.542830)) ((:c Set.instMembership) (:fv _uniq.542830)) 0 ((:c frontier) (:fv _uniq.542830) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.542830) ((:c PseudoMetricSpace.toUniformSpace) (... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.542830))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.542830) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.542830) (:fv _uniq.542831)))"},{"name":"inst✝","sexp... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda y :explicit (:fv FV1) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.542830","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.542831","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedAddCommGroup) (... | {"children":[{"source":"refine","sourceEnd":34455,"sourceStart":34449,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":34459,"sourceStart":34456,"tag":"atom"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"y","sourceEnd":34460,"sourceStart":34459,"tag":"identifier"},{"source":",","sourceEnd":34461,... | [] | [{"source":"⟨y, ⟨Metric.closedBall_infDist_compl_subset_closure hx <|\n Metric.mem_closedBall.2 <| ge_of_eq ?_, hys⟩, hyd⟩","source_end":34576,"source_start":34456,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.542830","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.542831","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 118 | 8 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 69bc45ef447b55c274e7446cf639c31f3b58a8e70ca58db24221124be7bcf7d8 | f7d7d5c7f773351a54ac51bf82ac40d2bdbb19cff66535c63726409ad4e76396 | 5948fb7b1085090b7e402f4d115cf0bf504f84ef0bac40cbb157c5ca99ab5827 | cd994ce35700d7877d8f742ffa37c220358a996832563dd5cdd2ce05e33440da |
cat-searcher/leandojo-benchmark-4-random | test | 3,837 | exists_mem_frontier_infDist_compl_eq_dist | Mathlib/Analysis/NormedSpace/FiniteDimension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>dist_comm</a>] | case intro.intro
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : FiniteDimensional ℝ E
x : E
s : Set E
hx : x ∈ s
hs : s ≠ univ
y : E
hys : y ∈ (interior s)ᶜ
hyd : infDist x sᶜ = dist x y
⊢ infDist x sᶜ = dist y x | ((:c Eq) (:c Real) ((:c Metric.infDist) (:fv _uniq.542830) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:fv _uniq.542830) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.542830) (:fv _uniq.542831))) (:fv _uniq.542834) ((:c HasCompl.compl) ((:c Set) (:fv _uniq.542830)) ((:c Set.instHasCompl) (:fv _uniq... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.542830))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.542830) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.542830) (:fv _uniq.542831)))"},{"name":"inst✝","sexp... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Metric.infDist) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:app (:c HasCompl.compl) (:arg :implicit-type 0 (:app... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.542830","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.542831","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedAddCommGroup) (... | {"children":[{"source":"rwa","sourceEnd":34582,"sourceStart":34579,"tag":"atom"},{"children":[{"source":"[","sourceEnd":34584,"sourceStart":34583,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"dist_comm","semanticRole":"global","source":"dist_comm","sourceEnd":34... | [] | [{"source":"dist_comm","source_end":34593,"source_start":34584,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.542830","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.542831","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 118 | 9 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ad72a7d5f7006eac03941d5fcd710875c82ac5f1005dfdff77f898db432ed99c | cd994ce35700d7877d8f742ffa37c220358a996832563dd5cdd2ce05e33440da | fecc0ef8d35c9e5231b11cc9c6144355cc1bfd19ee81bd5d08d0d8cdc403b4cd | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,838 | Multiset.product_cons | Mathlib/Data/Multiset/Bind.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>SProd.sprod</a>, <a>Multiset.product</a>] | α : Type u_1
β : Type v
γ : Type u_2
δ : Type u_3
a : α
b : β
s : Multiset α
t : Multiset β
⊢ s ×ˢ (b ::ₘ t) = map (fun a => (a, b)) s + s ×ˢ t | ((:c Eq) ((:c Multiset) ((:c Prod) (:fv _uniq.32518) (:fv _uniq.32520))) ((:c SProd.sprod) ((:c Multiset) (:fv _uniq.32518)) ((:c Multiset) (:fv _uniq.32520)) ((:c Multiset) ((:c Prod) (:fv _uniq.32518) (:fv _uniq.32520))) ((:c Multiset.instSProd) (:fv _uniq.32518) (:fv _uniq.32520)) (:fv _uniq.32533) ((:c Multiset.con... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"a","sexp":"(:fv _uniq.32518)"},{"name":"b","sexp":"(:fv _uniq.32520)"},{"name":"s","sexp":"((:c Multiset) (:fv _uniq.32518))"},{"name":"t","sexp":"((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))))) (:arg :explicit 1 (:app (:c SProd.sprod) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Multiset) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32518","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32520","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":11006,"sourceStart":11002,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"SProd.sprod","source_end":11019,"source_start":11008,"syntax_kind":"ident"},{"source":"product","source_end":11028,"source_start":11021,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32518","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32520","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 102 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 19ad0de5df6cf538b5387373db25363e13fde434e8c125678e70ed11c6ad3327 | 775f23cd16367e697462b6e82408c1c7eeea76de27495540194577640e92c899 | a043885f52cbf5503f99bfec3a2c23f16a23687f3d51fafa381b5b4027bbb02a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,839 | integrable_rpow_mul_exp_neg_mul_sq | Mathlib/Analysis/SpecialFunctions/Gaussian/GaussianIntegral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>MeasureTheory.integrableOn_univ</a>, ← @<a>Set.Iio_union_Ici</a> _ _ (0 : ℝ), <a>MeasureTheory.integrableOn_union</a>, <a>integrableOn_Ici_iff_integrableOn_Ioi</a>] | b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
⊢ Integrable (fun x => x ^ s * rexp (-b * x ^ 2)) volume | b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
⊢ IntegrableOn (fun x => x ^ s * rexp (-b * x ^ 2)) (Iio 0) volume ∧
IntegrableOn (fun x => x ^ s * rexp (-b * x ^ 2)) (Ioi 0) volume | ((:c MeasureTheory.Integrable) (:c Real) (:c Real.normedAddCommGroup) (:c Real) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)) (:lambda x (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Real) (:c Real... | [{"name":"b","sexp":"(:c Real)"},{"name":"hb","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.35780))"},{"name":"s","sexp":"(:c Real)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c Neg.neg) (:c Real) (:... | (:app (:c MeasureTheory.Integrable) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Real))))) (:arg :implicit-type 2 (:c Real)) (:arg :implicit 3) (:arg :explicit 4 (:lambda x :explicit (:c Real) (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real))... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"name":"hb","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real... | {"children":[{"source":"rw","sourceEnd":5762,"sourceStart":5760,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5764,"sourceStart":5763,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":5767,"sourceStart":... | [] | [{"source":"integrableOn_univ","source_end":5785,"source_start":5768,"syntax_kind":"ident"},{"source":"@Iio_union_Ici _ _ (0 : ℝ)","source_end":5819,"source_start":5791,"syntax_kind":"Lean.Parser.Term.app"},{"source":"integrableOn_union","source_end":5839,"source_start":5821,"syntax_kind":"ident"},{"source":"integrable... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"user_name":"hb"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 16 | 4 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c6664e12ea2099465e5b42257e3e53e3d46f85e5c4505fa5b435cc055a968f56 | 69434eaef3eda6a06021441185477515dd479943b0ab3cbe324e750430e68294 | 81ff5f0a61a254c4d35b70c5c4cfd21bbebe71df31be6b337e2d7fb9b66cd973 | 48f3d03807c40b5acce7d492eca564115d77082a6dd94cfed400fe973a0821c9 |
cat-searcher/leandojo-benchmark-4-random | test | 3,840 | integrable_rpow_mul_exp_neg_mul_sq | Mathlib/Analysis/SpecialFunctions/Gaussian/GaussianIntegral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨?_, <a>integrableOn_rpow_mul_exp_neg_mul_sq</a> hb hs⟩ | b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
⊢ IntegrableOn (fun x => x ^ s * rexp (-b * x ^ 2)) (Iio 0) volume ∧
IntegrableOn (fun x => x ^ s * rexp (-b * x ^ 2)) (Ioi 0) volume | b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
⊢ IntegrableOn (fun x => x ^ s * rexp (-b * x ^ 2)) (Iio 0) volume | ((:c And) ((:c MeasureTheory.IntegrableOn) (:c Real) (:c Real) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)) (:c Real.normedAddCommGroup) (:lambda x (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Re... | [{"name":"b","sexp":"(:c Real)"},{"name":"hb","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.35780))"},{"name":"s","sexp":"(:c Real)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c Neg.neg) (:c Real) (:... | (:app (:c And) (:arg :explicit 0 (:app (:c MeasureTheory.IntegrableOn) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Real))... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"name":"hb","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real... | {"children":[{"source":"refine","sourceEnd":5892,"sourceStart":5886,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":5896,"sourceStart":5893,"tag":"atom"},{"children":[{"children":[{"source":"?","sourceEnd":5897,"sourceStart":5896,"tag":"atom"},{"children":[{"source":"_","sourceEnd":5898,"sourceStart":5897,"tag":"a... | [] | [{"source":"⟨?_, integrableOn_rpow_mul_exp_neg_mul_sq hb hs⟩","source_end":5945,"source_start":5893,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"user_name":"hb"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 16 | 10 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 19a448b29b5bc3b42bfd782b901a82f62d712e5f194151fe369706cad9e35f61 | 48f3d03807c40b5acce7d492eca564115d77082a6dd94cfed400fe973a0821c9 | 1ab5f9fc02d29cd72a5f1c0741e3a2abaa7be567eaa103947028d48d3214dec6 | 638a3cea881564aaaba6eac28a3c385ef6a8e5b0d88547ae4c9972c0e6dc25c5 |
cat-searcher/leandojo-benchmark-4-random | test | 3,841 | integrable_rpow_mul_exp_neg_mul_sq | Mathlib/Analysis/SpecialFunctions/Gaussian/GaussianIntegral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← (<a>MeasureTheory.Measure.measurePreserving_neg</a> (<a>MeasureTheory.MeasureSpace.volume</a> : <a>MeasureTheory.Measure</a> ℝ)).<a>MeasureTheory.MeasurePreserving.integrableOn_comp_preimage</a> (<a>Homeomorph.neg</a> ℝ).<a>Homeomorph.measurableEmbedding</a>] | b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
⊢ IntegrableOn (fun x => x ^ s * rexp (-b * x ^ 2)) (Iio 0) volume | b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
⊢ IntegrableOn ((fun x => x ^ s * rexp (-b * x ^ 2)) ∘ Neg.neg) (Neg.neg ⁻¹' Iio 0) volume | ((:c MeasureTheory.IntegrableOn) (:c Real) (:c Real) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)) (:c Real.normedAddCommGroup) (:lambda x (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Real) (:c Re... | [{"name":"b","sexp":"(:c Real)"},{"name":"hb","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.35780))"},{"name":"s","sexp":"(:c Real)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c Neg.neg) (:c Real) (:... | (:app (:c MeasureTheory.IntegrableOn) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Real))))) (:arg :explicit 4 (:lambda x ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"name":"hb","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real... | {"children":[{"source":"rw","sourceEnd":5950,"sourceStart":5948,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5952,"sourceStart":5951,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":5955,"sourceStart":... | [] | [{"source":"(Measure.measurePreserving_neg (volume : Measure ℝ)).integrableOn_comp_preimage\n (Homeomorph.neg ℝ).measurableEmbedding","source_end":6084,"source_start":5956,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"user_name":"hb"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 16 | 11 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fdd7b92dc306c9d040eae4c42baf09f339e61e787e9e64b724806cc1e50a2bdb | 638a3cea881564aaaba6eac28a3c385ef6a8e5b0d88547ae4c9972c0e6dc25c5 | 5db2121a05d739f6e27ea21d0f47bbf8248b298a95bb9ea4b866c33f6e825939 | b713999af353e703ccc7d76a9aec239edb7b7db30d3ae602c586bdd8e9f634e5 |
cat-searcher/leandojo-benchmark-4-random | test | 3,842 | integrable_rpow_mul_exp_neg_mul_sq | Mathlib/Analysis/SpecialFunctions/Gaussian/GaussianIntegral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Function.comp</a>, <a>neg_sq</a>, <a>Set.neg_preimage</a>, <a>Set.preimage_neg_Iio</a>, <a>neg_neg</a>, <a>neg_zero</a>] | b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
⊢ IntegrableOn ((fun x => x ^ s * rexp (-b * x ^ 2)) ∘ Neg.neg) (Neg.neg ⁻¹' Iio 0) volume | b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
⊢ IntegrableOn (fun x => (-x) ^ s * rexp (-b * x ^ 2)) (Ioi 0) volume | ((:c MeasureTheory.IntegrableOn) (:c Real) (:c Real) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)) (:c Real.normedAddCommGroup) ((:c Function.comp) (:c Real) (:c Real) (:c Real) (:lambda x (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.in... | [{"name":"b","sexp":"(:c Real)"},{"name":"hb","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.35780))"},{"name":"s","sexp":"(:c Real)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c Neg.neg) (:c Real) (:... | (:app (:c MeasureTheory.IntegrableOn) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Real))))) (:arg :explicit 4 (:app (:c F... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"name":"hb","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real... | {"children":[{"source":"simp","sourceEnd":6092,"sourceStart":6088,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":6097,"sourceStart":6093,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":6097,"s... | [] | [{"source":"Function.comp","source_end":6112,"source_start":6099,"syntax_kind":"ident"},{"source":"neg_sq","source_end":6120,"source_start":6114,"syntax_kind":"ident"},{"source":"neg_preimage","source_end":6134,"source_start":6122,"syntax_kind":"ident"},{"source":"preimage_neg_Iio","source_end":6152,"source_start":6136... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"user_name":"hb"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 16 | 14 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c26a29157ba77486296166fc78e37af04a8281037012097cf3f4ee91d3e863c6 | b713999af353e703ccc7d76a9aec239edb7b7db30d3ae602c586bdd8e9f634e5 | 5f4e9811b065065aa93a6cdff9dfba86946bf50c9290911eeefc599384bf7841 | 2207dd291d9f3ac6f80ab03dbe21215dafa8db0b5b97a9501271f271b246e4c9 |
cat-searcher/leandojo-benchmark-4-random | test | 3,843 | integrable_rpow_mul_exp_neg_mul_sq | Mathlib/Analysis/SpecialFunctions/Gaussian/GaussianIntegral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>MeasureTheory.Integrable.mono'</a> (<a>integrableOn_rpow_mul_exp_neg_mul_sq</a> hb hs) | b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
⊢ IntegrableOn (fun x => (-x) ^ s * rexp (-b * x ^ 2)) (Ioi 0) volume | case hf
b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
⊢ AEStronglyMeasurable (fun x => (-x) ^ s * rexp (-b * x ^ 2)) (volume.restrict (Ioi 0))
case h
b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
⊢ ∀ᵐ (a : ℝ) ∂volume.restrict (Ioi 0), ‖(-a) ^ s * rexp (-b * a ^ 2)‖ ≤ a ^ s * rexp (-b * a ^ 2) | ((:c MeasureTheory.IntegrableOn) (:c Real) (:c Real) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)) (:c Real.normedAddCommGroup) (:lambda x (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Real) (:c Re... | [{"name":"b","sexp":"(:c Real)"},{"name":"hb","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.35780))"},{"name":"s","sexp":"(:c Real)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c Neg.neg) (:c Real) (:... | (:app (:c MeasureTheory.IntegrableOn) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Real))))) (:arg :explicit 4 (:lambda x ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"name":"hb","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real... | {"children":[{"source":"apply","sourceEnd":6180,"sourceStart":6175,"tag":"atom"},{"children":[{"name":"MeasureTheory.Integrable.mono'","semanticRole":"global","source":"Integrable.mono'","sourceEnd":6197,"sourceStart":6181,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":6199,"sourceStart":6198,"... | [] | [{"source":"Integrable.mono' (integrableOn_rpow_mul_exp_neg_mul_sq hb hs)","source_end":6242,"source_start":6181,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"user_name":"hb"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 16 | 15 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bdc03b9a0aae2c92dc53be6a3b90c0b43ad25e928401ab68c079164b6987c115 | 2207dd291d9f3ac6f80ab03dbe21215dafa8db0b5b97a9501271f271b246e4c9 | f5e6a8a973fd48ab0d7745f02b1b758fc0c4ff1b73e244fd17dc3406e7fb67f2 | 78b20f6ddd1ca6848d625f4c3f3aedd231f2781241155b7272cbf9c2541de484 |
cat-searcher/leandojo-benchmark-4-random | test | 3,844 | integrable_rpow_mul_exp_neg_mul_sq | Mathlib/Analysis/SpecialFunctions/Gaussian/GaussianIntegral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Measurable.aestronglyMeasurable</a> | case hf
b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
⊢ AEStronglyMeasurable (fun x => (-x) ^ s * rexp (-b * x ^ 2)) (volume.restrict (Ioi 0)) | case hf.hf
b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
⊢ Measurable fun x => (-x) ^ s * rexp (-b * x ^ 2) | ((:c MeasureTheory.AEStronglyMeasurable) (:c Real) (:c Real) ((:c UniformSpace.toTopologicalSpace) (:c Real) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:c Real) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:c Real) (:c Real.normedAddCommGroup))))) (:c Real.m... | [{"name":"b","sexp":"(:c Real)"},{"name":"hb","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.35780))"},{"name":"s","sexp":"(:c Real)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c Neg.neg) (:c Real) (:... | (:app (:c MeasureTheory.AEStronglyMeasurable) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Real))))) (:arg :implicit 3) (:arg :explicit 4 (:lambda x :explicit (:c Real) (:app (:c HMul.hMul) (:arg :implicit-type 0 (:... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"name":"hb","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real... | {"children":[{"source":"apply","sourceEnd":6253,"sourceStart":6248,"tag":"atom"},{"name":"Measurable.aestronglyMeasurable","semanticRole":"global","source":"Measurable.aestronglyMeasurable","sourceEnd":6285,"sourceStart":6254,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Measurable.aestronglyMe... | [] | [{"source":"Measurable.aestronglyMeasurable","source_end":6285,"source_start":6254,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"user_name":"hb"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 16 | 20 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f5a39a2004d3749fe696c00a3632119a6c693ef9421ecaf58cc511de34fff1be | 21b01e468eb352cd777dd3812ea0b0203ea0b469a6fdff6b9014bc77af465e03 | 0891544a731718f73af18fb641da7a028022c768d5bbddccb04f6592b8b08cd7 | af84615bc6cb84809fc05fe0e78094157de58373a7e6b994c95aec325967257d |
cat-searcher/leandojo-benchmark-4-random | test | 3,845 | integrable_rpow_mul_exp_neg_mul_sq | Mathlib/Analysis/SpecialFunctions/Gaussian/GaussianIntegral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (measurable_id'.neg.pow <a>measurable_const</a>).<a>Measurable.mul</a> ((measurable_id'.pow <a>measurable_const</a>).<a>Measurable.const_mul</a> (-b)).<a>Measurable.exp</a> | case hf.hf
b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
⊢ Measurable fun x => (-x) ^ s * rexp (-b * x ^ 2) | ((:c Measurable) (:c Real) (:c Real) (:c Real.measurableSpace) (:c Real.measurableSpace) (:lambda x (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) ((:c Neg.neg) (:c Re... | [{"name":"b","sexp":"(:c Real)"},{"name":"hb","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.35780))"},{"name":"s","sexp":"(:c Real)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c Neg.neg) (:c Real) (:... | (:app (:c Measurable) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c Real))))) (:arg :explicit 4 (:lambda x :explicit (:c Real)... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"name":"hb","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real... | {"children":[{"source":"exact","sourceEnd":6295,"sourceStart":6290,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":6297,"sourceStart":6296,"tag":"atom"},{"children":[{"source":"measurable_id'.neg.pow","sourceEnd":6319,"sourceStart":6297,"tag":"identifier"},{"children":[{"name":"measurable... | [] | [{"source":"(measurable_id'.neg.pow measurable_const).mul\n ((measurable_id'.pow measurable_const).const_mul (-b)).exp","source_end":6406,"source_start":6296,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"user_name":"hb"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 16 | 21 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5b39f949fe39ef75d0da71542b95933d35a4369c807e6c9468ab1b74728806c5 | af84615bc6cb84809fc05fe0e78094157de58373a7e6b994c95aec325967257d | 2735647065bc82424ed5c36ce711fe67ad71d76596dad88c90dd1c9a0e3abb4c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,846 | integrable_rpow_mul_exp_neg_mul_sq | Mathlib/Analysis/SpecialFunctions/Gaussian/GaussianIntegral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>MeasurableSet</a> (<a>Set.Ioi</a> (0 : ℝ)) := <a>measurableSet_Ioi</a> | case h
b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
⊢ ∀ᵐ (a : ℝ) ∂volume.restrict (Ioi 0), ‖(-a) ^ s * rexp (-b * a ^ 2)‖ ≤ a ^ s * rexp (-b * a ^ 2) | case h
b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
this : MeasurableSet (Ioi 0)
⊢ ∀ᵐ (a : ℝ) ∂volume.restrict (Ioi 0), ‖(-a) ^ s * rexp (-b * a ^ 2)‖ ≤ a ^ s * rexp (-b * a ^ 2) | ((:c Filter.Eventually) (:c Real) (:lambda a (:c Real) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:c Real) ((:c NormedAddCommGroup.toNorm) (:c Real) (:c Real.normedAddCommGroup)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Real) (:... | [{"name":"b","sexp":"(:c Real)"},{"name":"hb","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.35780))"},{"name":"s","sexp":"(:c Real)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c Neg.neg) (:c Real) (:... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda a :explicit (:c Real) (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:c Real)) (:arg ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"name":"hb","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real... | {"children":[{"source":"have","sourceEnd":6416,"sourceStart":6412,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":6417,"sourceStart":6417,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":6417,"sourceStart":6417,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"MeasurableSet (Ioi (0 : ℝ))","source_end":6448,"source_start":6419,"syntax_kind":"Lean.Parser.Term.app"},{"source":"measurableSet_Ioi","source_end":6469,"source_start":6452,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"user_name":"hb"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 16 | 26 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 874a72ca0ce084ff24f73fa67cc17b8b191a78e4e83aeee58df78cedde701d25 | 6767fa16c930dd679b701a436fdd4d22ee42036998f32403757d90b8072c454c | 9527ea2fc11f27d132526ec5ecd3cd71b126336482a586b7d455c58579300371 | 8323896dc8c65b05becee2196d1a83c071855158baa997cfe7e28e202460869f |
cat-searcher/leandojo-benchmark-4-random | test | 3,847 | integrable_rpow_mul_exp_neg_mul_sq | Mathlib/Analysis/SpecialFunctions/Gaussian/GaussianIntegral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards [<a>MeasureTheory.ae_restrict_mem</a> this] with x hx | case h
b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
this : MeasurableSet (Ioi 0)
⊢ ∀ᵐ (a : ℝ) ∂volume.restrict (Ioi 0), ‖(-a) ^ s * rexp (-b * a ^ 2)‖ ≤ a ^ s * rexp (-b * a ^ 2) | case h
b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
this : MeasurableSet (Ioi 0)
x : ℝ
hx : x ∈ Ioi 0
⊢ ‖(-x) ^ s * rexp (-b * x ^ 2)‖ ≤ x ^ s * rexp (-b * x ^ 2) | ((:c Filter.Eventually) (:c Real) (:lambda a (:c Real) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:c Real) ((:c NormedAddCommGroup.toNorm) (:c Real) (:c Real.normedAddCommGroup)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Real) (:... | [{"name":"b","sexp":"(:c Real)"},{"name":"hb","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.35780))"},{"name":"s","sexp":"(:c Real)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c Neg.neg) (:c Real) (:... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda a :explicit (:c Real) (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:c Real)) (:arg ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"name":"hb","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real... | {"children":[{"source":"filter_upwards","sourceEnd":6488,"sourceStart":6474,"tag":"atom"},{"children":[{"source":"[","sourceEnd":6490,"sourceStart":6489,"tag":"atom"},{"children":[{"children":[{"name":"MeasureTheory.ae_restrict_mem","semanticRole":"global","source":"ae_restrict_mem","sourceEnd":6505,"sourceStart":6490,... | [] | [{"source":"ae_restrict_mem this","source_end":6510,"source_start":6490,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"user_name":"hb"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 16 | 27 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 05a7352b9ae21f27722e15f4c4b755f997f604c834e335bf1eebec3164210dd8 | 8323896dc8c65b05becee2196d1a83c071855158baa997cfe7e28e202460869f | 033e3c8c7f98505deee56b2987c2dd57c90440374c44e983d0c623511ac8422a | b9f2bcb96d312f45c007f1cfbc32f8b41155d04183c9b373b0516cbb24e644e7 |
cat-searcher/leandojo-benchmark-4-random | test | 3,848 | integrable_rpow_mul_exp_neg_mul_sq | Mathlib/Analysis/SpecialFunctions/Gaussian/GaussianIntegral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h'x : 0 ≤ x := <a>le_of_lt</a> hx | case h
b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
this : MeasurableSet (Ioi 0)
x : ℝ
hx : x ∈ Ioi 0
⊢ ‖(-x) ^ s * rexp (-b * x ^ 2)‖ ≤ x ^ s * rexp (-b * x ^ 2) | case h
b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
this : MeasurableSet (Ioi 0)
x : ℝ
hx : x ∈ Ioi 0
h'x : 0 ≤ x
⊢ ‖(-x) ^ s * rexp (-b * x ^ 2)‖ ≤ x ^ s * rexp (-b * x ^ 2) | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:c Real) ((:c NormedAddCommGroup.toNorm) (:c Real) (:c Real.normedAddCommGroup)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.ins... | [{"name":"b","sexp":"(:c Real)"},{"name":"hb","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.35780))"},{"name":"s","sexp":"(:c Real)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c Neg.neg) (:c Real) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul)... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"name":"hb","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real... | {"children":[{"source":"have","sourceEnd":6530,"sourceStart":6526,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h'x","sourceEnd":6534,"sourceStart":6531,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h'x","sourceEnd":6534,"sourceStart":6531,"tag":"node"},... | [] | [{"source":"0 ≤ x","source_end":6544,"source_start":6537,"syntax_kind":"«term_≤_»"},{"source":"le_of_lt hx","source_end":6559,"source_start":6548,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"user_name":"hb"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 16 | 28 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7eb961c8a4ba36074f8bfd6f8c9be33f1267cf0d5ba485162c78b09b1e78f639 | b9f2bcb96d312f45c007f1cfbc32f8b41155d04183c9b373b0516cbb24e644e7 | b4223ae8fa1b9521eef88bd332bff09e5f8302a690d0cb90d1cc06e67af01947 | 0f3014799b181f262d92690cd26de565470b56fe363147bc891ade840d2b83a1 |
cat-searcher/leandojo-benchmark-4-random | test | 3,849 | integrable_rpow_mul_exp_neg_mul_sq | Mathlib/Analysis/SpecialFunctions/Gaussian/GaussianIntegral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Real.norm_eq_abs</a>, <a>abs_mul</a>, <a>abs_of_nonneg</a> (<a>Real.exp_pos</a> _).<a>LT.lt.le</a>] | case h
b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
this : MeasurableSet (Ioi 0)
x : ℝ
hx : x ∈ Ioi 0
h'x : 0 ≤ x
⊢ ‖(-x) ^ s * rexp (-b * x ^ 2)‖ ≤ x ^ s * rexp (-b * x ^ 2) | case h
b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
this : MeasurableSet (Ioi 0)
x : ℝ
hx : x ∈ Ioi 0
h'x : 0 ≤ x
⊢ |(-x) ^ s| * rexp (-b * x ^ 2) ≤ x ^ s * rexp (-b * x ^ 2) | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:c Real) ((:c NormedAddCommGroup.toNorm) (:c Real) (:c Real.normedAddCommGroup)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.ins... | [{"name":"b","sexp":"(:c Real)"},{"name":"hb","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.35780))"},{"name":"s","sexp":"(:c Real)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c Neg.neg) (:c Real) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul)... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"name":"hb","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real... | {"children":[{"source":"rw","sourceEnd":6566,"sourceStart":6564,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6568,"sourceStart":6567,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Real.norm_eq_abs","s... | [] | [{"source":"Real.norm_eq_abs","source_end":6584,"source_start":6568,"syntax_kind":"ident"},{"source":"abs_mul","source_end":6593,"source_start":6586,"syntax_kind":"ident"},{"source":"abs_of_nonneg (exp_pos _).le","source_end":6623,"source_start":6595,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"user_name":"hb"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 16 | 29 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7072759319be1e21d74ca5e94dd4a57b17597a6699f0ed28f82da51c0ea4688c | 0f3014799b181f262d92690cd26de565470b56fe363147bc891ade840d2b83a1 | bcd77c1c0fe7f7980d9c559b325ab703bc9460ac796d09373b4c36779c146b46 | f760c582acdc0ce9aaec82b591acdcb7dc8793de844056df50110b1c465a4f88 |
cat-searcher/leandojo-benchmark-4-random | test | 3,850 | integrable_rpow_mul_exp_neg_mul_sq | Mathlib/Analysis/SpecialFunctions/Gaussian/GaussianIntegral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>mul_le_mul_of_nonneg_right</a> _ (<a>Real.exp_pos</a> _).<a>LT.lt.le</a> | case h
b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
this : MeasurableSet (Ioi 0)
x : ℝ
hx : x ∈ Ioi 0
h'x : 0 ≤ x
⊢ |(-x) ^ s| * rexp (-b * x ^ 2) ≤ x ^ s * rexp (-b * x ^ 2) | b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
this : MeasurableSet (Ioi 0)
x : ℝ
hx : x ∈ Ioi 0
h'x : 0 ≤ x
⊢ |(-x) ^ s| ≤ x ^ s | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) ((:c NonUnitalNonAssocRing.toMul) (:c Real) ((:c NonAssocRing.toNonUnitalNonAssocRing) (:c Real) ((:c Ring.toNonAssocRing) (:c Real) ((:c StrictOrderedRing.toRing) (:c Real) ((:c LinearOrderedRing.toStrictOrder... | [{"name":"b","sexp":"(:c Real)"},{"name":"hb","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.35780))"},{"name":"s","sexp":"(:c Real)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c Neg.neg) (:c Real) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"name":"hb","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real... | {"children":[{"source":"apply","sourceEnd":6634,"sourceStart":6629,"tag":"atom"},{"children":[{"name":"mul_le_mul_of_nonneg_right","semanticRole":"global","source":"mul_le_mul_of_nonneg_right","sourceEnd":6661,"sourceStart":6635,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":6663,"sourceStart":... | [] | [{"source":"mul_le_mul_of_nonneg_right _ (exp_pos _).le","source_end":6678,"source_start":6635,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"user_name":"hb"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 16 | 34 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9cc95cdf8360b9af55069272d06ccbe6f5b65984d0f9bb27dd1576b917b53ca3 | f760c582acdc0ce9aaec82b591acdcb7dc8793de844056df50110b1c465a4f88 | 2eaa45e8aee0686e6e8458af0583ffe251162d4eed0385a232106bd739b3d6c4 | 17629c4651d4c39b39dee9701b53fc145347044b5e905b2e47d41ba384b9ad7a |
cat-searcher/leandojo-benchmark-4-random | test | 3,851 | integrable_rpow_mul_exp_neg_mul_sq | Mathlib/Analysis/SpecialFunctions/Gaussian/GaussianIntegral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [<a>abs_of_nonneg</a> h'x] using <a>Real.abs_rpow_le_abs_rpow</a> (-x) s | b : ℝ
hb : 0 < b
s : ℝ
hs : -1 < s
this : MeasurableSet (Ioi 0)
x : ℝ
hx : x ∈ Ioi 0
h'x : 0 ≤ x
⊢ |(-x) ^ s| ≤ x ^ s | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c abs) (:c Real) ((:c DistribLattice.toLattice) (:c Real) ((:c instDistribLatticeOfLinearOrder) (:c Real) ((:c LinearOrderedRing.toLinearOrder) (:c Real) (:c Real.instLinearOrderedRing)))) ((:c AddGroupWithOne.toAddGroup) (:c Real) ((:c Ring... | [{"name":"b","sexp":"(:c Real)"},{"name":"hb","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.35780))"},{"name":"s","sexp":"(:c Real)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c Neg.neg) (:c Real) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c abs) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Lattice) (:arg :explicit 0 (:c Real))))) (:arg :instance 2 (:instance-of (:app (:c... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"name":"hb","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real... | {"children":[{"source":"simpa","sourceEnd":6688,"sourceStart":6683,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"chil... | [] | [{"source":"abs_of_nonneg h'x","source_end":6707,"source_start":6690,"syntax_kind":"Lean.Parser.Term.app"},{"source":"abs_rpow_le_abs_rpow (-x) s","source_end":6742,"source_start":6715,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35780","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.35781","is_instance":false,"is_let":false,"user_name":"hb"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 16 | 35 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 91e6d0cd49469c3b2ca703c367c860a49edfcb4180eb7eab28134d3c92889e83 | 17629c4651d4c39b39dee9701b53fc145347044b5e905b2e47d41ba384b9ad7a | bff10427f2cf2c1b1f03d83f689203b910971823e9ad48ee07882881d86de42d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,852 | TopCat.Presheaf.covering_presieve_eq_self | Mathlib/Topology/Sheaves/SheafCondition/Sites.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | funext Z | X : TopCat
Y : Opens ↑X
R : Presieve Y
⊢ presieveOfCoveringAux (coveringOfPresieve Y R) Y = R | case h
X : TopCat
Y : Opens ↑X
R : Presieve Y
Z : Opens ↑X
⊢ presieveOfCoveringAux (coveringOfPresieve Y R) Y = R | ((:c Eq) ((:c CategoryTheory.Presieve) ((:c TopologicalSpace.Opens) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) (:fv _uniq.6119)) ((:c TopCat.topologicalSpace_coe) (:fv _uniq.6119))) ((:c Preorder.smallCategory) ((:c TopologicalSpace.Opens) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) (:fv _uniq.6119))... | [{"name":"X","sexp":"(:c TopCat)"},{"name":"Y","sexp":"((:c TopologicalSpace.Opens) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) (:fv _uniq.6119)) ((:c TopCat.topologicalSpace_coe) (:fv _uniq.6119)))"},{"name":"R","sexp":"((:c CategoryTheory.Presieve) ((:c TopologicalSpace.Opens) ((:c CategoryTheory.Bundled.α) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Presieve) (:arg :implicit-type 0 (:app (:c TopologicalSpace.Opens) (:arg :explicit 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:app (:c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6119","is_instance":false,"is_let":false,"name":"X","sexp":"(:c TopCat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.6723","is_instance":false,"is_let":false,"name":"Y","sexp":"(:app (:c TopologicalSpace.Opens) (:arg :explicit... | {"children":[{"source":"funext","sourceEnd":3715,"sourceStart":3709,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"Z","sourceEnd":3717,"sourceStart":3716,"tag":"identifier"}],"kind":"null","source":"Z","sourceEnd":3717,"sourceStart":3716,"tag":"node"}],"kind":"tacticFunext___","source":"funext Z","... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6119","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.6723","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 21 | 4 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 544cee3e72943038c685172b418b2bb7e4b89da1a8ded3e5689f98bc893fb4f8 | bd1ea12e6bf5b8833c887f7b6de7fe1b8166bc6fbbd5c9a5382f83d29f7bf867 | 518febe59f68422b23c8f1d31ff0789de678d41695a3a779704879a9705d4ea3 | 62b174de7d80e73ee971f8cf02a58548d84870e582ed433c6a42490bfbc094dd |
cat-searcher/leandojo-benchmark-4-random | test | 3,853 | TopCat.Presheaf.covering_presieve_eq_self | Mathlib/Topology/Sheaves/SheafCondition/Sites.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext f | case h
X : TopCat
Y : Opens ↑X
R : Presieve Y
Z : Opens ↑X
⊢ presieveOfCoveringAux (coveringOfPresieve Y R) Y = R | case h.h
X : TopCat
Y : Opens ↑X
R : Presieve Y
Z : Opens ↑X
f : Z ⟶ Y
⊢ f ∈ presieveOfCoveringAux (coveringOfPresieve Y R) Y ↔ f ∈ R | ((:c Eq) ((:c Set) ((:c Quiver.Hom) ((:c TopologicalSpace.Opens) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) (:fv _uniq.6119)) ((:c TopCat.topologicalSpace_coe) (:fv _uniq.6119))) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c TopologicalSpace.Opens) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) (:fv... | [{"name":"X","sexp":"(:c TopCat)"},{"name":"Y","sexp":"((:c TopologicalSpace.Opens) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) (:fv _uniq.6119)) ((:c TopCat.topologicalSpace_coe) (:fv _uniq.6119)))"},{"name":"R","sexp":"((:c CategoryTheory.Presieve) ((:c TopologicalSpace.Opens) ((:c CategoryTheory.Bundled.α) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:app (:c TopologicalSpace.Opens) (:arg :explicit 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6119","is_instance":false,"is_let":false,"name":"X","sexp":"(:c TopCat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.6723","is_instance":false,"is_let":false,"name":"Y","sexp":"(:app (:c TopologicalSpace.Opens) (:arg :explicit... | {"children":[{"source":"ext","sourceEnd":3723,"sourceStart":3720,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"f","sourceEnd":3725,"sourceStart":3724,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"f","sourceEnd":3725,"sourceStart":3724,"tag":"nod... | [{"role":"fresh_name","source":"f","source_end":3725,"source_start":3724,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6119","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.6723","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 21 | 5 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 70de2c100ef5144825fc6bee2073e151c8bdbd76457e21de99cf3ef082b59ee8 | 62b174de7d80e73ee971f8cf02a58548d84870e582ed433c6a42490bfbc094dd | 3ad5088d5027a93ac2d31f4b2dce30c355016245cd598d7cac08f019999d851b | c7cfa9adc33f90c402bbed8d8db953d7a2cf6afa4511e4e0a44eb46e43c6193f |
cat-searcher/leandojo-benchmark-4-random | test | 3,854 | TopCat.Presheaf.covering_presieve_eq_self | Mathlib/Topology/Sheaves/SheafCondition/Sites.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨fun ⟨⟨_, f', h⟩, <a>rfl</a>⟩ => by rwa [<a>Subsingleton.elim</a> f f'], fun h => ⟨⟨Z, f, h⟩, <a>rfl</a>⟩⟩ | case h.h
X : TopCat
Y : Opens ↑X
R : Presieve Y
Z : Opens ↑X
f : Z ⟶ Y
⊢ f ∈ presieveOfCoveringAux (coveringOfPresieve Y R) Y ↔ f ∈ R | ((:c Iff) ((:c Membership.mem) ((:c Quiver.Hom) ((:c TopologicalSpace.Opens) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) (:fv _uniq.6119)) ((:c TopCat.topologicalSpace_coe) (:fv _uniq.6119))) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c TopologicalSpace.Opens) ((:c CategoryTheory.Bundled.α) (:c Topologica... | [{"name":"X","sexp":"(:c TopCat)"},{"name":"Y","sexp":"((:c TopologicalSpace.Opens) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) (:fv _uniq.6119)) ((:c TopCat.topologicalSpace_coe) (:fv _uniq.6119)))"},{"name":"R","sexp":"((:c CategoryTheory.Presieve) ((:c TopologicalSpace.Opens) ((:c CategoryTheory.Bundled.α) ... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:app (:c TopologicalSpace.Opens) (:arg :explicit 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c TopologicalSp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6119","is_instance":false,"is_let":false,"name":"X","sexp":"(:c TopCat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.6723","is_instance":false,"is_let":false,"name":"Y","sexp":"(:app (:c TopologicalSpace.Opens) (:arg :explicit... | {"children":[{"source":"exact","sourceEnd":3733,"sourceStart":3728,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":3737,"sourceStart":3734,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":3740,"sourceStart":3737,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":3744,... | [] | [{"source":"⟨fun ⟨⟨_, f', h⟩, rfl⟩ => by rwa [Subsingleton.elim f f'], fun h => ⟨⟨Z, f, h⟩, rfl⟩⟩","source_end":3839,"source_start":3734,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6119","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.6723","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 21 | 6 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 95fbb0a2868803ff68910fff7c838e9313ff4e51c2c34b71838c06a033e1054c | c7cfa9adc33f90c402bbed8d8db953d7a2cf6afa4511e4e0a44eb46e43c6193f | 89bd361289dda4feb57d5e7d8e1fc11d3a2558388816d3f85967b7c57b7202c0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,855 | TopCat.Presheaf.covering_presieve_eq_self | Mathlib/Topology/Sheaves/SheafCondition/Sites.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>Subsingleton.elim</a> f f'] | X : TopCat
Y : Opens ↑X
R : Presieve Y
Z : Opens ↑X
f : Z ⟶ Y
x✝ : f ∈ presieveOfCoveringAux (coveringOfPresieve Y R) Y
f' : Z ⟶ Y
h : R f'
⊢ f ∈ R | ((:c Membership.mem) ((:c Quiver.Hom) ((:c TopologicalSpace.Opens) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) (:fv _uniq.6119)) ((:c TopCat.topologicalSpace_coe) (:fv _uniq.6119))) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c TopologicalSpace.Opens) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) (:... | [{"name":"X","sexp":"(:c TopCat)"},{"name":"Y","sexp":"((:c TopologicalSpace.Opens) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) (:fv _uniq.6119)) ((:c TopCat.topologicalSpace_coe) (:fv _uniq.6119)))"},{"name":"R","sexp":"((:c CategoryTheory.Presieve) ((:c TopologicalSpace.Opens) ((:c CategoryTheory.Bundled.α) ... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:app (:c TopologicalSpace.Opens) (:arg :explicit 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6119","is_instance":false,"is_let":false,"name":"X","sexp":"(:c TopCat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.6723","is_instance":false,"is_let":false,"name":"Y","sexp":"(:app (:c TopologicalSpace.Opens) (:arg :explicit... | {"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":3776,"sourceStart":3773,"tag":"atom"},{"children":[{"source":"[","sourceEnd":3778,"sourceStart":3777,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Subsingleton.elim","se... | [] | [{"source":"Subsingleton.elim f f'","source_end":3800,"source_start":3778,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6119","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.6723","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 21 | 9 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3ac63bafbc1a6df73d1f176089011ab42f2068f7d62bafe2e9e6c0fa826419fc | a916f4aa69ded3e4bd374641e93eff090c121de762e9adda9ad2827b5dd2dc6b | 0681a17d3af0dfc0aba89143a336b84d195f3b82371b22280acdac294d1938f9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,856 | Finset.prod_eq_prod_Ico_succ_bot | Mathlib/Algebra/BigOperators/Intervals.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have ha : a ∉ <a>Finset.Ico</a> (a + 1) b := by simp | α : Type u_1
M : Type u_2
inst✝ : CommMonoid M
s₂ s₁ s : Finset α
a✝ : α
g f✝ : α → M
a b : ℕ
hab : a < b
f : ℕ → M
⊢ ∏ k ∈ Ico a b, f k = f a * ∏ k ∈ Ico (a + 1) b, f k | α : Type u_1
M : Type u_2
inst✝ : CommMonoid M
s₂ s₁ s : Finset α
a✝ : α
g f✝ : α → M
a b : ℕ
hab : a < b
f : ℕ → M
ha : a ∉ Ico (a + 1) b
⊢ ∏ k ∈ Ico a b, f k = f a * ∏ k ∈ Ico (a + 1) b, f k | ((:c Eq) (:fv _uniq.30512) ((:c Finset.prod) (:c Nat) (:fv _uniq.30512) (:fv _uniq.30515) ((:c Finset.Ico) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))) (:c Nat.instLocallyFiniteOrder) (:fv _uniq.31693) (:fv _uniq.31694)) (:lambd... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommMonoid) (:fv _uniq.30512))"},{"name":"s₂","sexp":"((:c Finset) (:fv _uniq.30509))"},{"name":"s₁","sexp":"((:c Finset) (:fv _uniq.30509))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.30509))"},{"name":"a✝",... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Finset.prod) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 3 (:app (:c Finset.Ico) (:arg :implicit-type 0 (:c Nat)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30509","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30512","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"have","sourceEnd":4324,"sourceStart":4320,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"ha","sourceEnd":4327,"sourceStart":4325,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"ha","sourceEnd":4327,"sourceStart":4325,"tag":"node"},{"... | [] | [{"source":"a ∉ Ico (a + 1) b","source_end":4349,"source_start":4330,"syntax_kind":"«term_∉_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30509","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30512","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 42 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | de42ba3e28446eec28b61b7cbc79840aaeb5a45b2ef49023745b9d36840a4dfa | a1c0d1a3a34cafc166e71e292bbba350af29bf3c5d5de7cdaa1537046745413d | 7c0269b8c93f692aeb993da6a2328d45aff9a8801f34096bec72ccca471f2c7d | da7b52aed37534ea368a0fefc7f434ea884c2cd6b7959d6c66cfe4e92c75d03c |
cat-searcher/leandojo-benchmark-4-random | test | 3,857 | Finset.prod_eq_prod_Ico_succ_bot | Mathlib/Algebra/BigOperators/Intervals.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Finset.prod_insert</a> ha, <a>Nat.Ico_insert_succ_left</a> hab] | α : Type u_1
M : Type u_2
inst✝ : CommMonoid M
s₂ s₁ s : Finset α
a✝ : α
g f✝ : α → M
a b : ℕ
hab : a < b
f : ℕ → M
ha : a ∉ Ico (a + 1) b
⊢ ∏ k ∈ Ico a b, f k = f a * ∏ k ∈ Ico (a + 1) b, f k | ((:c Eq) (:fv _uniq.30512) ((:c Finset.prod) (:c Nat) (:fv _uniq.30512) (:fv _uniq.30515) ((:c Finset.Ico) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))) (:c Nat.instLocallyFiniteOrder) (:fv _uniq.31693) (:fv _uniq.31694)) (:lambd... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommMonoid) (:fv _uniq.30512))"},{"name":"s₂","sexp":"((:c Finset) (:fv _uniq.30509))"},{"name":"s₁","sexp":"((:c Finset) (:fv _uniq.30509))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.30509))"},{"name":"a✝",... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Finset.prod) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 3 (:app (:c Finset.Ico) (:arg :implicit-type 0 (:c Nat)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30509","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30512","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":4365,"sourceStart":4363,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4367,"sourceStart":4366,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":4370,"sourceStart":... | [] | [{"source":"prod_insert ha","source_end":4385,"source_start":4371,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Nat.Ico_insert_succ_left hab","source_end":4415,"source_start":4387,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30509","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30512","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 42 | 7 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f8626877dc63176cf3182896c9b801bb0a0b234bd5a4568dc1a38773ffa11aac | da7b52aed37534ea368a0fefc7f434ea884c2cd6b7959d6c66cfe4e92c75d03c | 5e84fab1eb7944091c9929c88a2e3be3bd469a9a5339ae77cd8cc11715502998 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,858 | Finset.prod_eq_prod_Ico_succ_bot | Mathlib/Algebra/BigOperators/Intervals.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | α : Type u_1
M : Type u_2
inst✝ : CommMonoid M
s₂ s₁ s : Finset α
a✝ : α
g f✝ : α → M
a b : ℕ
hab : a < b
f : ℕ → M
⊢ a ∉ Ico (a + 1) b | ((:c Not) ((:c Membership.mem) (:c Nat) ((:c Finset) (:c Nat)) ((:c Finset.instMembership) (:c Nat)) (:fv _uniq.31693) ((:c Finset.Ico) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))) (:c Nat.instLocallyFiniteOrder) ((:c HAdd.hAdd)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommMonoid) (:fv _uniq.30512))"},{"name":"s₂","sexp":"((:c Finset) (:fv _uniq.30509))"},{"name":"s₁","sexp":"((:c Finset) (:fv _uniq.30509))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.30509))"},{"name":"a✝",... | (:app (:c Not) (:arg :explicit 0 (: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 Nat))))))) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30509","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30512","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"simp","sourceEnd":4360,"sourceStart":4356,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30509","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30512","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 42 | 6 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 561c88300ca2d313ba1d06483c4219ca5b65e259f90b1137f66836758b99c5fe | 95a3a58a06885263d5b5f9a8e5fa20271f658e1898e27f43b46494e9f98350b0 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,859 | Orientation.oangle_add_left_eq_arccos_of_oangle_eq_pi_div_two | Mathlib/Geometry/Euclidean/Angle/Oriented/RightAngle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>neg_inj</a>, <a>Orientation.oangle_rev</a>, ← <a>Orientation.oangle_neg_orientation_eq_neg</a>, <a>neg_inj</a>] at h ⊢ | V : Type u_1
inst✝¹ : NormedAddCommGroup V
inst✝ : InnerProductSpace ℝ V
hd2 : Fact (finrank ℝ V = 2)
o : Orientation ℝ V (Fin 2)
x y : V
h : o.oangle x y = ↑(π / 2)
⊢ o.oangle (x + y) y = ↑(Real.arccos (‖y‖ / ‖x + y‖)) | V : Type u_1
inst✝¹ : NormedAddCommGroup V
inst✝ : InnerProductSpace ℝ V
hd2 : Fact (finrank ℝ V = 2)
o : Orientation ℝ V (Fin 2)
x y : V
h : (-o).oangle y x = ↑(π / 2)
⊢ (-o).oangle y (x + y) = ↑(Real.arccos (‖y‖ / ‖x + y‖)) | ((:c Eq) (:c Real.Angle) ((:c Orientation.oangle) (:fv _uniq.4869) (:fv _uniq.4872) (:fv _uniq.4885) (:fv _uniq.5168) (:fv _uniq.5861) ((:c HAdd.hAdd) (:fv _uniq.4869) (:fv _uniq.4869) (:fv _uniq.4869) ((:c instHAdd) (:fv _uniq.4869) ((:c AddCommMagma.toAdd) (:fv _uniq.4869) ((:c AddCommSemigroup.toAddCommMagma) (:fv _... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.4869))"},{"name":"inst✝","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.4869) (:c Real.RCLike) (:fv _uniq.4872))"},{"name":"hd2","sexp":"((:c Fact) ((:c Eq) (:c Nat) ((:c FiniteDimensional.finrank) (:c Real) (:fv... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:app (:c Orientation.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c InnerProductSpace) (:arg :explicit 0 (:c Real)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4869","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4872","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (:arg... | {"children":[{"source":"rw","sourceEnd":1836,"sourceStart":1834,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1838,"sourceStart":1837,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":1841,"sourceStart":... | [] | [{"source":"neg_inj","source_end":1849,"source_start":1842,"syntax_kind":"ident"},{"source":"h","source_end":1911,"source_start":1910,"syntax_kind":"ident"},{"source":"oangle_rev","source_end":1861,"source_start":1851,"syntax_kind":"ident"},{"source":"oangle_neg_orientation_eq_neg","source_end":1896,"source_start":1867... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4869","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4872","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":2,... | 12 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a683bbc9e53b2971bf5a39d723ce51eaa17447f9847c2fe4426a50453bb4b832 | 39fbe6a0083d6bcb26597268ede77153cddf0c2817125bdfe32a08cf683b7cde | f14a5e4d554b8004cc8f64e753b6e7a50625cf73fe5c27fad2b8d8ef0894688e | 620d6db731eedc35da3ffb0c57a8b9185318a898fd6a0747b675883e1ca9ca04 |
cat-searcher/leandojo-benchmark-4-random | test | 3,860 | Orientation.oangle_add_left_eq_arccos_of_oangle_eq_pi_div_two | Mathlib/Geometry/Euclidean/Angle/Oriented/RightAngle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>add_comm</a>] | V : Type u_1
inst✝¹ : NormedAddCommGroup V
inst✝ : InnerProductSpace ℝ V
hd2 : Fact (finrank ℝ V = 2)
o : Orientation ℝ V (Fin 2)
x y : V
h : (-o).oangle y x = ↑(π / 2)
⊢ (-o).oangle y (x + y) = ↑(Real.arccos (‖y‖ / ‖x + y‖)) | V : Type u_1
inst✝¹ : NormedAddCommGroup V
inst✝ : InnerProductSpace ℝ V
hd2 : Fact (finrank ℝ V = 2)
o : Orientation ℝ V (Fin 2)
x y : V
h : (-o).oangle y x = ↑(π / 2)
⊢ (-o).oangle y (y + x) = ↑(Real.arccos (‖y‖ / ‖y + x‖)) | ((:c Eq) (:c Real.Angle) ((:c Orientation.oangle) (:fv _uniq.4869) (:fv _uniq.4872) (:fv _uniq.4885) (:fv _uniq.5168) ((:c Neg.neg) ((:c Orientation) (:c Real) (:c Real.strictOrderedCommSemiring) (:fv _uniq.4869) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.4869) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.4869... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.4869))"},{"name":"inst✝","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.4869) (:c Real.RCLike) (:fv _uniq.4872))"},{"name":"hd2","sexp":"((:c Fact) ((:c Eq) (:c Nat) ((:c FiniteDimensional.finrank) (:c Real) (:fv... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:app (:c Orientation.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c InnerProductSpace) (:arg :explicit 0 (:c Real)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4869","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4872","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (:arg... | {"children":[{"source":"rw","sourceEnd":1920,"sourceStart":1918,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1922,"sourceStart":1921,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"add_comm","semanticR... | [] | [{"source":"add_comm","source_end":1930,"source_start":1922,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4869","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4872","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":2,... | 12 | 10 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 39daa9dfd8758d5a75e6c6a1c22e58c836dd859da689f82451ee92736e546629 | 620d6db731eedc35da3ffb0c57a8b9185318a898fd6a0747b675883e1ca9ca04 | 707f7395094bb37fad92bf71eb5cc4cfd5bf0547886ddb8474de13ffc18b39f4 | 58e2de6c658d78eaaf18a02a0eaa3bdd0a57f6482a733d934ba8ea932979f46b |
cat-searcher/leandojo-benchmark-4-random | test | 3,861 | Orientation.oangle_add_left_eq_arccos_of_oangle_eq_pi_div_two | Mathlib/Geometry/Euclidean/Angle/Oriented/RightAngle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (-o).<a>Orientation.oangle_add_right_eq_arccos_of_oangle_eq_pi_div_two</a> h | V : Type u_1
inst✝¹ : NormedAddCommGroup V
inst✝ : InnerProductSpace ℝ V
hd2 : Fact (finrank ℝ V = 2)
o : Orientation ℝ V (Fin 2)
x y : V
h : (-o).oangle y x = ↑(π / 2)
⊢ (-o).oangle y (y + x) = ↑(Real.arccos (‖y‖ / ‖y + x‖)) | ((:c Eq) (:c Real.Angle) ((:c Orientation.oangle) (:fv _uniq.4869) (:fv _uniq.4872) (:fv _uniq.4885) (:fv _uniq.5168) ((:c Neg.neg) ((:c Orientation) (:c Real) (:c Real.strictOrderedCommSemiring) (:fv _uniq.4869) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.4869) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.4869... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.4869))"},{"name":"inst✝","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.4869) (:c Real.RCLike) (:fv _uniq.4872))"},{"name":"hd2","sexp":"((:c Fact) ((:c Eq) (:c Nat) ((:c FiniteDimensional.finrank) (:c Real) (:fv... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:app (:c Orientation.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c InnerProductSpace) (:arg :explicit 0 (:c Real)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4869","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4872","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (:arg... | {"children":[{"source":"exact","sourceEnd":1939,"sourceStart":1934,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":1941,"sourceStart":1940,"tag":"atom"},{"children":[{"source":"-","sourceEnd":1942,"sourceStart":1941,"tag":"atom"},{"contextIndex":4,"semanticRole":"local","source":"o","sour... | [] | [{"source":"(-o).oangle_add_right_eq_arccos_of_oangle_eq_pi_div_two h","source_end":1997,"source_start":1940,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4869","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4872","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":2,... | 12 | 13 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1ba71a299f4787fdba0e9e85c91d7266c887c9fe368d587c54ffe353c58af310 | 58e2de6c658d78eaaf18a02a0eaa3bdd0a57f6482a733d934ba8ea932979f46b | 694a3463ffc907601ad968d91c752bdf1f27ae03185b880210eb2feed6ec459d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,862 | Real.mul_self_sqrt | Mathlib/Data/Real/Sqrt.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Real.sqrt</a>, ← <a>NNReal.coe_mul</a>, <a>NNReal.mul_self_sqrt</a>, <a>Real.coe_toNNReal</a> _ h] | x y : ℝ
h : 0 ≤ x
⊢ √x * √x = x | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c Real.sqrt) (:fv _uniq.25312)) ((:c Real.sqrt) (:fv _uniq.25312))) (:fv _uniq.25312)) | [{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"h","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.25312))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25312","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25314","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"},{"binder_role":":explicit","context_i... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":6091,"sourceStart":6089,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6093,"sourceStart":6092,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"Real.sqrt","source_end":6102,"source_start":6093,"syntax_kind":"ident"},{"source":"NNReal.coe_mul","source_end":6122,"source_start":6108,"syntax_kind":"ident"},{"source":"NNReal.mul_self_sqrt","source_end":6144,"source_start":6124,"syntax_kind":"ident"},{"source":"Real.coe_toNNReal _ h","source_end":6167,"s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25312","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25314","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 66 | 2 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bedc5ec28b06c3cdd6c7f773957ecf61e54f2b9e69d42ec9b8eb604f1684ce7f | 2d80a090adb0735dd4803ffbfc5adccf4223b54d462ce37e20241f6a19e8f280 | 551ddea8813f3fd1c7415244fd7626fe8408afb95d40211303c95b549221133d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,863 | Asymptotics.IsBigO.integrable | Mathlib/MeasureTheory/Integral/Asymptotics.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rewrite [← <a>MeasureTheory.integrableAtFilter_top</a>] at * | α : Type u_1
E : Type u_2
F : Type u_3
inst✝² : MeasurableSpace α
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedAddCommGroup F
f : α → E
g : α → F
a b : α
μ : Measure α
l : Filter α
hfm : AEStronglyMeasurable f μ
hf : f =O[⊤] g
hg : Integrable g μ
⊢ Integrable f μ | α : Type u_1
E : Type u_2
F : Type u_3
inst✝² : MeasurableSpace α
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedAddCommGroup F
f : α → E
g : α → F
a b : α
μ : Measure α
l : Filter α
hfm : AEStronglyMeasurable f μ
hf : f =O[⊤] g
hg : IntegrableAtFilter g ⊤ μ
⊢ IntegrableAtFilter f ⊤ μ | ((:c MeasureTheory.Integrable) (:fv _uniq.1873) (:fv _uniq.1882) (:fv _uniq.1870) (:fv _uniq.1879) (:fv _uniq.1889) (:fv _uniq.1906)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c MeasurableSpace) (:fv _uniq.1870))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1873))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.18... | (:app (:c MeasureTheory.Integrable) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:fv FV0)) (:arg :implicit 3) (:arg :explicit 4 (:fv FV6)) (:arg :explicit 5 (:fv FV10))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1870","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1873","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"rewrite","sourceEnd":2411,"sourceStart":2404,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2413,"sourceStart":2412,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":2416,"sourceSt... | [] | [{"source":"integrableAtFilter_top","source_end":2439,"source_start":2417,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1870","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1873","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 4 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e2681da7b3a97456b1c509adf6560715c8f83470681f3322d4a8d0d1064aa542 | 950028fd2b545ef297132e488d9926351075ef7ff5159b48a1b7895fe284c4af | c8f75e0b648ff3930a7c705293ab9aaaf57c9133d98b71bf02ce2f897745cb15 | dbd9ba8ae8209f228953141d15b7b2b1fe8406553e046a32054a374c763b565e |
cat-searcher/leandojo-benchmark-4-random | test | 3,864 | Asymptotics.IsBigO.integrable | Mathlib/MeasureTheory/Integral/Asymptotics.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hf.integrableAtFilter ⟨<a>Set.univ</a>, <a>Filter.univ_mem</a>, hfm.restrict⟩ hg | α : Type u_1
E : Type u_2
F : Type u_3
inst✝² : MeasurableSpace α
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedAddCommGroup F
f : α → E
g : α → F
a b : α
μ : Measure α
l : Filter α
hfm : AEStronglyMeasurable f μ
hf : f =O[⊤] g
hg : IntegrableAtFilter g ⊤ μ
⊢ IntegrableAtFilter f ⊤ μ | ((:c MeasureTheory.IntegrableAtFilter) (:fv _uniq.1870) (:fv _uniq.1873) (:fv _uniq.1879) (:fv _uniq.1882) (:fv _uniq.1889) ((:c Top.top) ((:c Filter) (:fv _uniq.1870)) ((:c Filter.instTop) (:fv _uniq.1870))) (:fv _uniq.1906)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c MeasurableSpace) (:fv _uniq.1870))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1873))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.18... | (:app (:c MeasureTheory.IntegrableAtFilter) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 4 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1870","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1873","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"exact","sourceEnd":2453,"sourceStart":2448,"tag":"atom"},{"children":[{"source":"hf.integrableAtFilter","sourceEnd":2475,"sourceStart":2454,"tag":"identifier"},{"children":[{"children":[{"source":"⟨","sourceEnd":2479,"sourceStart":2476,"tag":"atom"},{"children":[{"name":"Set.univ","semanticRole"... | [] | [{"source":"hf.integrableAtFilter ⟨univ, univ_mem, hfm.restrict⟩ hg","source_end":2513,"source_start":2454,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1870","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1873","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 4 | 7 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e333b58f45965030b0155bb7d06e9ff84b2355c693b11b1a036a926933d46cb4 | dbd9ba8ae8209f228953141d15b7b2b1fe8406553e046a32054a374c763b565e | e6d393ba3b91bb63f7f3bd6e09bb70796a992ebb9463cfd7ce2ef261a8ea1bfc | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,865 | Filter.frequently_iff_forall_eventually_exists_and | Mathlib/Order/Filter/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>and_not_self_iff</a>, <a>exists_false</a>] using H hp | α : Type u
β : Type v
γ : Type w
δ : Type u_1
ι : Sort x
p : α → Prop
f : Filter α
H : ∀ {q : α → Prop}, (∀ᶠ (x : α) in f, q x) → ∃ x, p x ∧ q x
hp : ∀ᶠ (x : α) in f, ¬(fun x => p x) x
⊢ False | (:c False) | [{"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":"p","sexp":"(:forall _ (:fv _uniq.101157) (:sort 0))"},{"name":"f","sexp":"((:c Filter) (:fv _uniq.101157))"},{"name":"H","se... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.101157","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.101159","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":61712,"sourceStart":61707,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"and_not_self_iff","source_end":61735,"source_start":61719,"syntax_kind":"ident"},{"source":"exists_false","source_end":61749,"source_start":61737,"syntax_kind":"ident"},{"source":"H hp","source_end":61761,"source_start":61757,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.101157","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.101159","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 429 | 2 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 35f89d9529bad4be8421986c893eaea27d26f389e6bf8d00fcc65cfb8c6633cb | 5beccf55423fba3cd8c36586bb3e521298f37e3f8667e926b8a0815e4bd9e06a | 6c4e922fdfec337be14bfee15d28877ccfa4477be084bb744d8918e642e9130c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,866 | Filter.extraction_forall_of_eventually' | Mathlib/Order/Filter/AtTopBot.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Filter.eventually_atTop</a>, h] | ι : Type u_1
ι' : Type u_2
α : Type u_3
β : Type u_4
γ : Type u_5
P : ℕ → ℕ → Prop
h : ∀ (n : ℕ), ∃ N, ∀ k ≥ N, P n k
⊢ ∀ (n : ℕ), ∀ᶠ (k : ℕ) in atTop, P n k | (:forall n (:c Nat) ((:c Filter.Eventually) (:c Nat) (:lambda k (:c Nat) ((:fv _uniq.73263) 1 0)) ((:c Filter.atTop) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring)))))) | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"ι'","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"P","sexp":"(:forall _ (:c Nat) (:forall _ (:c Nat) (:sort 0)))"},{"name":"h","sexp":"(:forall n (:c Nat) ((:c... | (:forall n :explicit (:c Nat) (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda k :explicit (:c Nat) (:app (:fv FV6) (:arg :explicit 0 1) (:arg :explicit 1 0)))) (:arg :explicit 2 (:app (:c Filter.atTop) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c Pr... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73048","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.73051","is_instance":false,"is_let":false,"name":"ι'","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":26300,"sourceStart":26296,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"eventually_atTop","source_end":26318,"source_start":26302,"syntax_kind":"ident"},{"source":"h","source_end":26321,"source_start":26320,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.73048","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.73051","is_instance":false,"is_let":false,"user_name":"ι'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 191 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a019880236a1ba7ebbdac61b8f70778be0db4d7f3c51b12bf81446bc945006a0 | a3cb2643a562f234ccfd74914021814c44f9cc2baac5fdd913ad8e329b3de9a8 | ffa06ada31d13f65f880488763d23a8c0d50673a90e6c71313a1c8ae406d275f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,867 | Matroid.restrict_eq_restrict_iff | Mathlib/Data/Matroid/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨fun h I hIX ↦ ?_, fun h ↦ <a>Matroid.eq_of_indep_iff_indep_forall</a> <a>rfl</a> fun I (hI : I ⊆ X) ↦ ?_⟩ | α : Type u_1
M✝ : Matroid α
R I J X✝ Y : Set α
M M' : Matroid α
X : Set α
⊢ M ↾ X = M' ↾ X ↔ ∀ I ⊆ X, M.Indep I ↔ M'.Indep I | case refine_1
α : Type u_1
M✝ : Matroid α
R I✝ J X✝ Y : Set α
M M' : Matroid α
X : Set α
h : M ↾ X = M' ↾ X
I : Set α
hIX : I ⊆ X
⊢ M.Indep I ↔ M'.Indep I
case refine_2
α : Type u_1
M✝ : Matroid α
R I✝ J X✝ Y : Set α
M M' : Matroid α
X : Set α
h : ∀ I ⊆ X, M.Indep I ↔ M'.Indep I
I : Set α
hI : I ⊆ X
⊢ (M ↾ X).Indep I ↔... | ((:c Iff) ((:c Eq) ((:c Matroid) (:fv _uniq.61338)) ((:c Matroid.restrict) (:fv _uniq.61338) (:fv _uniq.61411) (:fv _uniq.61413)) ((:c Matroid.restrict) (:fv _uniq.61338) (:fv _uniq.61412) (:fv _uniq.61413))) (:forall I ((:c Set) (:fv _uniq.61338)) (:forall _ ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.61338)) ((:c Set... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"M✝","sexp":"((:c Matroid) (:fv _uniq.61338))"},{"name":"R","sexp":"((:c Set) (:fv _uniq.61338))"},{"name":"I","sexp":"((:c Set) (:fv _uniq.61338))"},{"name":"J","sexp":"((:c Set) (:fv _uniq.61338))"},{"name":"X✝","sexp":"((:c Set) (:fv _uniq.61338))"},{"name":"Y","sexp"... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Matroid) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Matroid.restrict) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV8)) (:arg :explicit 2 (:fv FV10)))) (:arg :explicit 2 (:app (:c Matroid.restrict) (:arg :implic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61338","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61341","is_instance":false,"is_let":false,"name":"M✝","sexp":"(:app (:c Matroid) (:arg :explicit 0 (:fv FV0... | {"children":[{"source":"refine","sourceEnd":9514,"sourceStart":9508,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":9518,"sourceStart":9515,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":9521,"sourceStart":9518,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"h"... | [] | [{"source":"⟨fun h I hIX ↦ ?_, fun h ↦ eq_of_indep_iff_indep_forall rfl fun I (hI : I ⊆ X) ↦ ?_⟩","source_end":9611,"source_start":9515,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61338","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61341","is_instance":false,"is_let":false,"user_name":"M✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 27 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c5bf77076be8966247ee30d6f7a1f28c7ff48c3548681d00de0617fc8586ea41 | b8bbe40816b678b67d8e5963d1adb5f325a5ad7c2d4be49e1e134bf2b890277c | 8f13abbf0482a65f820e18cb87c986c0e0823a1148d611fe0ad224f4986ea1b7 | 6a992a5de3d5052d1a23c0548252b13d96a297a00ff175be48f4bfd0ba877a16 |
cat-searcher/leandojo-benchmark-4-random | test | 3,868 | Matroid.restrict_eq_restrict_iff | Mathlib/Data/Matroid/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Matroid.restrict_indep_iff</a>, <a>and_iff_left</a> hI, <a>Matroid.restrict_indep_iff</a>, <a>and_iff_left</a> hI, h _ hI] | case refine_2
α : Type u_1
M✝ : Matroid α
R I✝ J X✝ Y : Set α
M M' : Matroid α
X : Set α
h : ∀ I ⊆ X, M.Indep I ↔ M'.Indep I
I : Set α
hI : I ⊆ X
⊢ (M ↾ X).Indep I ↔ (M' ↾ X).Indep I | ((:c Iff) ((:c Matroid.Indep) (:fv _uniq.61338) ((:c Matroid.restrict) (:fv _uniq.61338) (:fv _uniq.61411) (:fv _uniq.61413)) (:fv _uniq.61502)) ((:c Matroid.Indep) (:fv _uniq.61338) ((:c Matroid.restrict) (:fv _uniq.61338) (:fv _uniq.61412) (:fv _uniq.61413)) (:fv _uniq.61502))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"M✝","sexp":"((:c Matroid) (:fv _uniq.61338))"},{"name":"R","sexp":"((:c Set) (:fv _uniq.61338))"},{"name":"I✝","sexp":"((:c Set) (:fv _uniq.61338))"},{"name":"J","sexp":"((:c Set) (:fv _uniq.61338))"},{"name":"X✝","sexp":"((:c Set) (:fv _uniq.61338))"},{"name":"Y","sexp... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Matroid.Indep) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Matroid.restrict) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV8)) (:arg :explicit 2 (:fv FV10)))) (:arg :explicit 2 (:fv FV12)))) (:arg :explicit 1 (:app (:c Matroid.Indep) (:arg :impli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61338","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61341","is_instance":false,"is_let":false,"name":"M✝","sexp":"(:app (:c Matroid) (:arg :explicit 0 (:fv FV0... | {"children":[{"source":"rw","sourceEnd":9761,"sourceStart":9759,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9763,"sourceStart":9762,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Matroid.restrict_ind... | [] | [{"source":"restrict_indep_iff","source_end":9781,"source_start":9763,"syntax_kind":"ident"},{"source":"and_iff_left hI","source_end":9798,"source_start":9783,"syntax_kind":"Lean.Parser.Term.app"},{"source":"restrict_indep_iff","source_end":9818,"source_start":9800,"syntax_kind":"ident"},{"source":"and_iff_left hI","so... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61338","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61341","is_instance":false,"is_let":false,"user_name":"M✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 27 | 16 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fda8dde7207108cbd618d9a1c803b9f97641512ba4723916a35bbffd35537b90 | 94ec80150eb7cc39b08730e3cf0bdf18e13d906637e97523f422f735fd63eda9 | 76371a0e0dba87eb73abf15c5c8488f9ced07e05aebdbbe45bbd7d7b9068ad65 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,869 | Matroid.restrict_eq_restrict_iff | Mathlib/Data/Matroid/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>and_iff_left</a> (a := (M.Indep I)) hIX, ← <a>and_iff_left</a> (a := (M'.Indep I)) hIX, ← <a>Matroid.restrict_indep_iff</a>, h, <a>Matroid.restrict_indep_iff</a>] | case refine_1
α : Type u_1
M✝ : Matroid α
R I✝ J X✝ Y : Set α
M M' : Matroid α
X : Set α
h : M ↾ X = M' ↾ X
I : Set α
hIX : I ⊆ X
⊢ M.Indep I ↔ M'.Indep I | ((:c Iff) ((:c Matroid.Indep) (:fv _uniq.61338) (:fv _uniq.61411) (:fv _uniq.61430)) ((:c Matroid.Indep) (:fv _uniq.61338) (:fv _uniq.61412) (:fv _uniq.61430))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"M✝","sexp":"((:c Matroid) (:fv _uniq.61338))"},{"name":"R","sexp":"((:c Set) (:fv _uniq.61338))"},{"name":"I✝","sexp":"((:c Set) (:fv _uniq.61338))"},{"name":"J","sexp":"((:c Set) (:fv _uniq.61338))"},{"name":"X✝","sexp":"((:c Set) (:fv _uniq.61338))"},{"name":"Y","sexp... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Matroid.Indep) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV8)) (:arg :explicit 2 (:fv FV12)))) (:arg :explicit 1 (:app (:c Matroid.Indep) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV9)) (:arg :explicit 2 (:fv FV12))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61338","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61341","is_instance":false,"is_let":false,"name":"M✝","sexp":"(:app (:c Matroid) (:arg :explicit 0 (:fv FV0... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":9619,"sourceStart":9617,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9621,"sourceStart":9620,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"sour... | [] | [{"source":"and_iff_left (a := (M.Indep I)) hIX","source_end":9660,"source_start":9625,"syntax_kind":"Lean.Parser.Term.app"},{"source":"and_iff_left (a := (M'.Indep I)) hIX","source_end":9702,"source_start":9666,"syntax_kind":"Lean.Parser.Term.app"},{"source":"restrict_indep_iff","source_end":9732,"source_start":9714,"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61338","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.61341","is_instance":false,"is_let":false,"user_name":"M✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 27 | 7 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6ca77e9257c69eb7962de0f5663373887587a78adb67a13e37c61a85b95ccb9c | 026e665f620b482ddbcbe982545e0c0e9067ac15d53759110ff805d0fb10b574 | 24e170befb6e31ef3229eac2f393936a9550eed416222b29c904ffc08fa62d9a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,870 | Part.some_inter_some | Mathlib/Data/Part.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Part.inter_def</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
inst✝ : Inter α
a b : α
⊢ some a ∩ some b = some (a ∩ b) | ((:c Eq) ((:c Part) (:fv _uniq.59979)) ((:c Inter.inter) ((:c Part) (:fv _uniq.59979)) ((:c Part.instInter) (:fv _uniq.59979) (:fv _uniq.60024)) ((:c Part.some) (:fv _uniq.59979) (:fv _uniq.60025)) ((:c Part.some) (:fv _uniq.59979) (:fv _uniq.60026))) ((:c Part.some) (:fv _uniq.59979) ((:c Inter.inter) (:fv _uniq.59979... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c Inter) (:fv _uniq.59979))"},{"name":"a","sexp":"(:fv _uniq.59979)"},{"name":"b","sexp":"(:fv _uniq.59979)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Part) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Part) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c Inter) (:arg :explicit 0 (:app (:c Part) (:arg :explicit 0 (:fv FV0))))))) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.59979","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.59982","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":32099,"sourceStart":32095,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"inter_def","source_end":32110,"source_start":32101,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.59979","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.59982","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 307 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c30caa7bfe92662517af17a75b0dcb3420ae292f6abaf7d78185178be33bc841 | 3709033da9ce449c6ee026d97abb9f5ce145b430ec1017ec0c11a7424917964c | de1e2aeae42103b4a201213f39e8db9d19775c1c7e14e48bba372121353f57b0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,871 | Finset.mem_inv_smul_finset_iff | Mathlib/Data/Finset/Pointwise.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Finset.smul_mem_smul_finset_iff</a> a, <a>smul_inv_smul</a>] | F : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
inst✝² : DecidableEq β
inst✝¹ : Group α
inst✝ : MulAction α β
s t : Finset β
a : α
b : β
⊢ b ∈ a⁻¹ • s ↔ a • b ∈ s | ((:c Iff) ((:c Membership.mem) (:fv _uniq.355230) ((:c Finset) (:fv _uniq.355230)) ((:c Finset.instMembership) (:fv _uniq.355230)) (:fv _uniq.355558) ((:c HSMul.hSMul) (:fv _uniq.355227) ((:c Finset) (:fv _uniq.355230)) ((:c Finset) (:fv _uniq.355230)) ((:c instHSMul) (:fv _uniq.355227) ((:c Finset) (:fv _uniq.355230))... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.355230))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.355227))"},{"name":"inst✝","sexp":"((:c MulAct... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV2))))))) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.355224","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.355227","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":82089,"sourceStart":82087,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":82091,"sourceStart":82090,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"smul_mem_smul_finset_iff a","source_end":82121,"source_start":82095,"syntax_kind":"Lean.Parser.Term.app"},{"source":"smul_inv_smul","source_end":82136,"source_start":82123,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.355224","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.355227","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 901 | 2 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 413ec16be3e305e4c879639823370d6e0ea49bafe172897801822c895b0959cf | db88b594ed0bed52725f490da49fac4951a700ddd7402c5a0e3c84db62350227 | 5a4b444d62540cf4fc75719c77469af5d890a46cee7b262137d4a493e3d9f008 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,872 | integral_comp_neg_Iic | Mathlib/MeasureTheory/Measure/Lebesgue/Integral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have A : <a>MeasurableEmbedding</a> fun x : ℝ => -x := (<a>Homeomorph.neg</a> ℝ).closedEmbedding.measurableEmbedding | E : Type u_1
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace ℝ E
c : ℝ
f : ℝ → E
⊢ ∫ (x : ℝ) in Iic c, f (-x) = ∫ (x : ℝ) in Ioi (-c), f x | E : Type u_1
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace ℝ E
c : ℝ
f : ℝ → E
A : MeasurableEmbedding fun x => -x
⊢ ∫ (x : ℝ) in Iic c, f (-x) = ∫ (x : ℝ) in Ioi (-c), f x | ((:c Eq) (:fv _uniq.12747) ((:c MeasureTheory.integral) (:c Real) (:fv _uniq.12747) (:fv _uniq.12748) (:fv _uniq.12749) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)) ((:c MeasureTheory.Measure.restrict) (:c Real) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Rea... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.12747))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.12747) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.12747) (:fv _uniq.12748)))"},{"name":"c","sexp":"(:c Re... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c MeasureTheory.integral) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c NormedSpace) (:a... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12747","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.12748","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (:a... | {"children":[{"source":"have","sourceEnd":4289,"sourceStart":4285,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"A","sourceEnd":4291,"sourceStart":4290,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"A","sourceEnd":4291,"sourceStart":4290,"tag":"node"},{"ch... | [] | [{"source":"MeasurableEmbedding fun x : ℝ => -x","source_end":4331,"source_start":4294,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(Homeomorph.neg ℝ).closedEmbedding.measurableEmbedding","source_end":4395,"source_start":4339,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12747","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.12748","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 17 | 4 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 50faf13ab1648b66eea535f9bd1df5c08e28f9326cedb0a55162f2ff20b06fa7 | a7697157b980e4ace3f2232ce1885f252c50021694a495959b834f2fde917216 | 0206a3fb6a6bd3ce9499c379cb5ced68ac3f7c6ff96256d7e58a067750dc8168 | 4d65194b6db1c4efddef524b0f955f02c037a1fe80ad6896a01c4e7bb1403df2 |
cat-searcher/leandojo-benchmark-4-random | test | 3,873 | integral_comp_neg_Iic | Mathlib/MeasureTheory/Measure/Lebesgue/Integral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have := <a>MeasurableEmbedding.setIntegral_map</a> (μ := <a>MeasureTheory.MeasureSpace.volume</a>) A f (<a>Set.Ici</a> (-c)) | E : Type u_1
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace ℝ E
c : ℝ
f : ℝ → E
A : MeasurableEmbedding fun x => -x
⊢ ∫ (x : ℝ) in Iic c, f (-x) = ∫ (x : ℝ) in Ioi (-c), f x | E : Type u_1
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace ℝ E
c : ℝ
f : ℝ → E
A : MeasurableEmbedding fun x => -x
this : ∫ (y : ℝ) in Ici (-c), f y ∂Measure.map (fun x => -x) volume = ∫ (x : ℝ) in (fun x => -x) ⁻¹' Ici (-c), f (-x)
⊢ ∫ (x : ℝ) in Iic c, f (-x) = ∫ (x : ℝ) in Ioi (-c), f x | ((:c Eq) (:fv _uniq.12747) ((:c MeasureTheory.integral) (:c Real) (:fv _uniq.12747) (:fv _uniq.12748) (:fv _uniq.12749) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)) ((:c MeasureTheory.Measure.restrict) (:c Real) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Rea... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.12747))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.12747) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.12747) (:fv _uniq.12748)))"},{"name":"c","sexp":"(:c Re... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c MeasureTheory.integral) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c NormedSpace) (:a... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12747","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.12748","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (:a... | {"children":[{"source":"have","sourceEnd":4402,"sourceStart":4398,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":4403,"sourceStart":4403,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":4403,"sourceStart":4403,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"MeasurableEmbedding.setIntegral_map (μ := volume) A f (Ici (-c))","source_end":4471,"source_start":4406,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12747","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.12748","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 17 | 5 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a2e4822447f779512b9a95137f31a299010a8b9421cfda8342c46f68d187a37e | 4d65194b6db1c4efddef524b0f955f02c037a1fe80ad6896a01c4e7bb1403df2 | 3f9dca1130837cc61d1e96e063564cf8ccf0926094bde0f64366aa92109e4402 | 64db753811b0b4edb15e2e9b2169d08ae9520bf395bc3507db27738112fea05f |
cat-searcher/leandojo-benchmark-4-random | test | 3,874 | integral_comp_neg_Iic | Mathlib/MeasureTheory/Measure/Lebesgue/Integral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.Measure.map_neg_eq_self</a> (<a>MeasureTheory.MeasureSpace.volume</a> : <a>MeasureTheory.Measure</a> ℝ)] at this | E : Type u_1
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace ℝ E
c : ℝ
f : ℝ → E
A : MeasurableEmbedding fun x => -x
this : ∫ (y : ℝ) in Ici (-c), f y ∂Measure.map (fun x => -x) volume = ∫ (x : ℝ) in (fun x => -x) ⁻¹' Ici (-c), f (-x)
⊢ ∫ (x : ℝ) in Iic c, f (-x) = ∫ (x : ℝ) in Ioi (-c), f x | E : Type u_1
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace ℝ E
c : ℝ
f : ℝ → E
A : MeasurableEmbedding fun x => -x
this : ∫ (y : ℝ) in Ici (-c), f y ∂volume = ∫ (x : ℝ) in (fun x => -x) ⁻¹' Ici (-c), f (-x)
⊢ ∫ (x : ℝ) in Iic c, f (-x) = ∫ (x : ℝ) in Ioi (-c), f x | ((:c Eq) (:fv _uniq.12747) ((:c MeasureTheory.integral) (:c Real) (:fv _uniq.12747) (:fv _uniq.12748) (:fv _uniq.12749) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)) ((:c MeasureTheory.Measure.restrict) (:c Real) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Rea... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.12747))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.12747) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.12747) (:fv _uniq.12748)))"},{"name":"c","sexp":"(:c Re... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c MeasureTheory.integral) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c NormedSpace) (:a... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12747","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.12748","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (:a... | {"children":[{"source":"rw","sourceEnd":4476,"sourceStart":4474,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4478,"sourceStart":4477,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Measure... | [] | [{"source":"this","source_end":4533,"source_start":4529,"syntax_kind":"ident"},{"source":"Measure.map_neg_eq_self (volume : Measure ℝ)","source_end":4524,"source_start":4478,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12747","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.12748","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 17 | 6 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6dccd0ddb431ff6460c2d05e7751ee5735a8d7c328f7f4f20629a96a18aad78a | 64db753811b0b4edb15e2e9b2169d08ae9520bf395bc3507db27738112fea05f | 086fa124cea8005dff4e542810d8561ef2e6bf1eb34f153a780226abe41a7192 | c08bee3ec436f8245ea02b76eb14ebe9a9affc975da00330b2242a5cc5452721 |
cat-searcher/leandojo-benchmark-4-random | test | 3,875 | integral_comp_neg_Iic | Mathlib/MeasureTheory/Measure/Lebesgue/Integral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [← <a>MeasureTheory.integral_Ici_eq_integral_Ioi</a>, this, <a>Set.neg_preimage</a>, <a>Set.preimage_neg_Ici</a>, <a>neg_neg</a>] | E : Type u_1
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace ℝ E
c : ℝ
f : ℝ → E
A : MeasurableEmbedding fun x => -x
this : ∫ (y : ℝ) in Ici (-c), f y ∂volume = ∫ (x : ℝ) in (fun x => -x) ⁻¹' Ici (-c), f (-x)
⊢ ∫ (x : ℝ) in Iic c, f (-x) = ∫ (x : ℝ) in Ioi (-c), f x | ((:c Eq) (:fv _uniq.12747) ((:c MeasureTheory.integral) (:c Real) (:fv _uniq.12747) (:fv _uniq.12748) (:fv _uniq.12749) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)) ((:c MeasureTheory.Measure.restrict) (:c Real) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Rea... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.12747))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.12747) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.12747) (:fv _uniq.12748)))"},{"name":"c","sexp":"(:c Re... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c MeasureTheory.integral) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c NormedSpace) (:a... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12747","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.12748","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (:a... | {"children":[{"source":"simp_rw","sourceEnd":4543,"sourceStart":4536,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4545,"sourceStart":4544,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":4548,"sourceSt... | [] | [{"source":"integral_Ici_eq_integral_Ioi","source_end":4577,"source_start":4549,"syntax_kind":"ident"},{"source":"this","source_end":4583,"source_start":4579,"syntax_kind":"ident"},{"source":"neg_preimage","source_end":4597,"source_start":4585,"syntax_kind":"ident"},{"source":"preimage_neg_Ici","source_end":4615,"sourc... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12747","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.12748","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 17 | 9 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4f0fcaafa07e4087bef50fd67d0b75e6505e6026849f637c9943b5ae25823d2e | c08bee3ec436f8245ea02b76eb14ebe9a9affc975da00330b2242a5cc5452721 | 5bb67335226e14e26aaa3d7feb9a5394321fc8d38befcfd0d6df96e7bf6f6d53 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,876 | Equiv.Perm.viaFintypeEmbedding_apply_not_mem_range | Mathlib/Logic/Equiv/Fintype.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>Equiv.Perm.viaFintypeEmbedding</a>, <a>Equiv.Perm.extendDomain_apply_not_subtype</a>] | α : Type u_1
β : Type u_2
inst✝¹ : Fintype α
inst✝ : DecidableEq β
e : Perm α
f : α ↪ β
b : β
h : b ∉ Set.range ⇑f
⊢ (e.viaFintypeEmbedding f) b = b | ((:c Eq) (:fv _uniq.10537) ((:c DFunLike.coe) ((:c Equiv.Perm) (:fv _uniq.10537)) (:fv _uniq.10537) (:lambda _ (:fv _uniq.10537) (:fv _uniq.10537)) ((:c Equiv.instFunLike) (:fv _uniq.10537) (:fv _uniq.10537)) ((:c Equiv.Perm.viaFintypeEmbedding) (:fv _uniq.10534) (:fv _uniq.10537) (:fv _uniq.10540) (:fv _uniq.10547) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.10534))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.10537))"},{"name":"e","sexp":"((:c Equiv.Perm) (:fv _uniq.10534))"},{"name":"f","sexp":"((:c Function.Embedding) (:fv _uniq.10... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Equiv.Perm) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c FunLike) (:arg :explicit 0 (:app (:c Equiv) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10534","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10537","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":3942,"sourceStart":3939,"tag":"atom"},{"children":[{"source":"[","sourceEnd":3944,"sourceStart":3943,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Equiv.Perm.viaFintypeEmbedding","se... | [] | [{"source":"Equiv.Perm.viaFintypeEmbedding","source_end":3974,"source_start":3944,"syntax_kind":"ident"},{"source":"Equiv.Perm.extendDomain_apply_not_subtype","source_end":4017,"source_start":3976,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10534","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10537","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 18 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f812bd6b76b4aa9bb318c9bddcf25315a51f6182907a6e51e654a6dc6b0c3aa5 | dd07cdcb2843140acf1bfca5d69d8219a5137dfa70aeef4b3313a66643fa71b7 | 02f397a0f4e86a95cb2ec3e8d2ca5577bdae458031fcbc13985fd590d22a046d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,877 | IsCyclic.unique_zpow_zmod | Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨n, rfl⟩ := ha x | α : Type u
a : α
inst✝² : Group α
inst✝¹ : DecidableEq α
inst✝ : Fintype α
ha : ∀ (x : α), x ∈ zpowers a
x : α
⊢ ∃! n, x = a ^ n.val | case intro
α : Type u
a : α
inst✝² : Group α
inst✝¹ : DecidableEq α
inst✝ : Fintype α
ha : ∀ (x : α), x ∈ zpowers a
n : ℤ
⊢ ∃! n_1, (fun x => a ^ x) n = a ^ n_1.val | ((:c ExistsUnique) ((:c ZMod) ((:c Fintype.card) (:fv _uniq.52777) (:fv _uniq.52794))) (:lambda n ((:c ZMod) ((:c Fintype.card) (:fv _uniq.52777) (:fv _uniq.52794))) ((:c Eq) (:fv _uniq.52777) (:fv _uniq.53266) ((:c HPow.hPow) (:fv _uniq.52777) (:c Nat) (:fv _uniq.52777) ((:c instHPow) (:fv _uniq.52777) (:c Nat) ((:c M... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"a","sexp":"(:fv _uniq.52777)"},{"name":"inst✝²","sexp":"((:c Group) (:fv _uniq.52777))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.52777))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.52777))"},{"name":"ha","sexp":"(:forall x (:fv _uniq.52777) ((:c Membe... | (:app (:c ExistsUnique) (:arg :implicit-type 0 (:app (:c ZMod) (:arg :explicit 0 (:app (:c Fintype.card) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Fintype) (:arg :explicit 0 (:fv FV0))))))))) (:arg :explicit 1 (:lambda n :explicit (:app (:c ZMod) (:arg :explicit 0 (:app (:c Fintype.card) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52777","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52779","is_instance":false,"is_let":false,"name":"a","sexp":"(:fv FV0)"},{"binder_role":":instance-implicit... | {"children":[{"source":"obtain","sourceEnd":17003,"sourceStart":16997,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":17007,"sourceStart":17004,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"n","sourceEn... | [] | [{"source":"ha x","source_end":17024,"source_start":17020,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨n, rfl⟩","source_end":17016,"source_start":17004,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52777","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52779","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 76 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dd2c8797b1ecb4791896f121b298ea8784260aad255e3b286daf1d7d26e61e13 | de90887521b950f55a5661a2f379d1a7d066f27665da4dc5ef0876038e914e3f | e019eb5ab49e6ddcb9d3a19bdeb7fd826b6999dedbad0efb3caea20d5bda2b3b | 63f2aa2485d0ce09c3887360437532b5dd8c91cb56613602b47ef6c27963c805 |
cat-searcher/leandojo-benchmark-4-random | test | 3,878 | IsCyclic.unique_zpow_zmod | Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨n, (?_ : a ^ n = _), fun y (hy : a ^ n = _) ↦ ?_⟩ | case intro
α : Type u
a : α
inst✝² : Group α
inst✝¹ : DecidableEq α
inst✝ : Fintype α
ha : ∀ (x : α), x ∈ zpowers a
n : ℤ
⊢ ∃! n_1, (fun x => a ^ x) n = a ^ n_1.val | case intro.refine_1
α : Type u
a : α
inst✝² : Group α
inst✝¹ : DecidableEq α
inst✝ : Fintype α
ha : ∀ (x : α), x ∈ zpowers a
n : ℤ
⊢ a ^ n = a ^ (↑n).val
case intro.refine_2
α : Type u
a : α
inst✝² : Group α
inst✝¹ : DecidableEq α
inst✝ : Fintype α
ha : ∀ (x : α), x ∈ zpowers a
n : ℤ
y : ZMod (Fintype.card α)
hy : a ^ ... | ((:c ExistsUnique) ((:c ZMod) ((:c Fintype.card) (:fv _uniq.52777) (:fv _uniq.52794))) (:lambda n ((:c ZMod) ((:c Fintype.card) (:fv _uniq.52777) (:fv _uniq.52794))) ((:c Eq) (:fv _uniq.52777) ((:lambda _ (:c Int) ((:c HPow.hPow) (:fv _uniq.52777) (:c Int) (:fv _uniq.52777) ((:c instHPow) (:fv _uniq.52777) (:c Int) ((:... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"a","sexp":"(:fv _uniq.52777)"},{"name":"inst✝²","sexp":"((:c Group) (:fv _uniq.52777))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.52777))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.52777))"},{"name":"ha","sexp":"(:forall x (:fv _uniq.52777) ((:c Membe... | (:app (:c ExistsUnique) (:arg :implicit-type 0 (:app (:c ZMod) (:arg :explicit 0 (:app (:c Fintype.card) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Fintype) (:arg :explicit 0 (:fv FV0))))))))) (:arg :explicit 1 (:lambda n :explicit (:app (:c ZMod) (:arg :explicit 0 (:app (:c Fintype.card) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52777","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52779","is_instance":false,"is_let":false,"name":"a","sexp":"(:fv FV0)"},{"binder_role":":instance-implicit... | {"children":[{"source":"refine","sourceEnd":17033,"sourceStart":17027,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":17037,"sourceStart":17034,"tag":"atom"},{"children":[{"contextIndex":7,"semanticRole":"local","source":"n","sourceEnd":17038,"sourceStart":17037,"tag":"identifier"},{"source":",","sourceEnd":17039,... | [] | [{"source":"⟨n, (?_ : a ^ n = _), fun y (hy : a ^ n = _) ↦ ?_⟩","source_end":17090,"source_start":17034,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52777","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52779","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 76 | 5 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0d49a5fa8df2720bb9d67756efdafdd4a692f3a36835cf7f33699a15fa659bc4 | 63f2aa2485d0ce09c3887360437532b5dd8c91cb56613602b47ef6c27963c805 | c913d98a7b9b714d1ad19f30062d3d916ef3e1d15eb93db46ed793ce3cf39c55 | 6afffbbc599deb3dd895019f5db0bcf9aca05510da6466c30d683b45a2eeec21 |
cat-searcher/leandojo-benchmark-4-random | test | 3,879 | IsCyclic.unique_zpow_zmod | Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>zpow_natCast</a>, <a>zpow_eq_zpow_iff_modEq</a>, <a>orderOf_eq_card_of_forall_mem_zpowers</a> ha, <a>Int.modEq_comm</a>, <a>Int.modEq_iff_add_fac</a>, ← <a>ZMod.intCast_eq_iff</a>] | case intro.refine_1
α : Type u
a : α
inst✝² : Group α
inst✝¹ : DecidableEq α
inst✝ : Fintype α
ha : ∀ (x : α), x ∈ zpowers a
n : ℤ
⊢ a ^ n = a ^ (↑n).val | ((:c Eq) (:fv _uniq.52777) ((:c HPow.hPow) (:fv _uniq.52777) (:c Int) (:fv _uniq.52777) ((:c instHPow) (:fv _uniq.52777) (:c Int) ((:c DivInvMonoid.Pow) (:fv _uniq.52777) ((:c Group.toDivInvMonoid) (:fv _uniq.52777) (:fv _uniq.52782)))) (:fv _uniq.52779) (:fv _uniq.53295)) ((:c HPow.hPow) (:fv _uniq.52777) (:c Nat) (:f... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"a","sexp":"(:fv _uniq.52777)"},{"name":"inst✝²","sexp":"((:c Group) (:fv _uniq.52777))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.52777))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.52777))"},{"name":"ha","sexp":"(:forall x (:fv _uniq.52777) ((:c Membe... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c Int)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Int)) (:arg :explicit 2 (:fv FV0)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52777","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52779","is_instance":false,"is_let":false,"name":"a","sexp":"(:fv FV0)"},{"binder_role":":instance-implicit... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":17098,"sourceStart":17096,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":17100,"sourceStart":17099,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"zpow_natCast","source_end":17116,"source_start":17104,"syntax_kind":"ident"},{"source":"zpow_eq_zpow_iff_modEq","source_end":17140,"source_start":17118,"syntax_kind":"ident"},{"source":"orderOf_eq_card_of_forall_mem_zpowers ha","source_end":17182,"source_start":17142,"syntax_kind":"Lean.Parser.Term.app"},{"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52777","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52779","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 76 | 8 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aef212d7a28f480b65548ea97b34dd79054dfcb428ee253c793f7b420459f779 | c0f40290c34e812a8861a5538de36e1b6a6d0c21c1f4eb8a6552ab7dd6876013 | de99a04f29c79621a863ed7d717bf4e8d4745eb7f98f236a517b1fbb8b1022a1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,880 | IsCyclic.unique_zpow_zmod | Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>zpow_natCast</a>, <a>zpow_eq_zpow_iff_modEq</a>, <a>orderOf_eq_card_of_forall_mem_zpowers</a> ha, ← <a>ZMod.intCast_eq_intCast_iff</a>] at hy | case intro.refine_2
α : Type u
a : α
inst✝² : Group α
inst✝¹ : DecidableEq α
inst✝ : Fintype α
ha : ∀ (x : α), x ∈ zpowers a
n : ℤ
y : ZMod (Fintype.card α)
hy : a ^ n = a ^ y.val
⊢ y = ↑n | case intro.refine_2
α : Type u
a : α
inst✝² : Group α
inst✝¹ : DecidableEq α
inst✝ : Fintype α
ha : ∀ (x : α), x ∈ zpowers a
n : ℤ
y : ZMod (Fintype.card α)
hy : ↑n = ↑↑y.val
⊢ y = ↑n | ((:c Eq) ((:c ZMod) ((:c Fintype.card) (:fv _uniq.52777) (:fv _uniq.52794))) (:fv _uniq.53542) ((:c Int.cast) ((:c ZMod) ((:c Fintype.card) (:fv _uniq.52777) (:fv _uniq.52794))) ((:c Ring.toIntCast) ((:c ZMod) ((:c Fintype.card) (:fv _uniq.52777) (:fv _uniq.52794))) ((:c CommRing.toRing) ((:c ZMod) ((:c Fintype.card) (... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"a","sexp":"(:fv _uniq.52777)"},{"name":"inst✝²","sexp":"((:c Group) (:fv _uniq.52777))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.52777))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.52777))"},{"name":"ha","sexp":"(:forall x (:fv _uniq.52777) ((:c Membe... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c ZMod) (:arg :explicit 0 (:app (:c Fintype.card) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Fintype) (:arg :explicit 0 (:fv FV0))))))))) (:arg :explicit 1 (:fv FV8)) (:arg :explicit 2 (:app (:c Int.cast) (:arg :implicit-type 0 (:app (:c ZMod) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52777","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52779","is_instance":false,"is_let":false,"name":"a","sexp":"(:fv FV0)"},{"binder_role":":instance-implicit... | {"children":[{"source":"rw","sourceEnd":17261,"sourceStart":17259,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":17263,"sourceStart":17262,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":17266,"sourceSt... | [] | [{"source":"zpow_natCast","source_end":17279,"source_start":17267,"syntax_kind":"ident"},{"source":"hy","source_end":17391,"source_start":17389,"syntax_kind":"ident"},{"source":"zpow_eq_zpow_iff_modEq","source_end":17303,"source_start":17281,"syntax_kind":"ident"},{"source":"orderOf_eq_card_of_forall_mem_zpowers ha","s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52777","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52779","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 76 | 22 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 270da4a71a61a318bb72c5cf5c65b0eb6529da975af509e59564561a9ecc5089 | 4911d48702b69fd9e43196403ecce3427d660a6fa6f3f2c05d0b74d460066735 | 78153936a080f3bf5906caaa8173535f82cb7e0df848baf3a88f78b37bc7c5b5 | a4e501803d10b8de560d1b4c29e22b5b4b11d9f148c758aaa8c9a3c51c566ec6 |
cat-searcher/leandojo-benchmark-4-random | test | 3,881 | IsCyclic.unique_zpow_zmod | Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [hy] | case intro.refine_2
α : Type u
a : α
inst✝² : Group α
inst✝¹ : DecidableEq α
inst✝ : Fintype α
ha : ∀ (x : α), x ∈ zpowers a
n : ℤ
y : ZMod (Fintype.card α)
hy : ↑n = ↑↑y.val
⊢ y = ↑n | ((:c Eq) ((:c ZMod) ((:c Fintype.card) (:fv _uniq.52777) (:fv _uniq.52794))) (:fv _uniq.53542) ((:c Int.cast) ((:c ZMod) ((:c Fintype.card) (:fv _uniq.52777) (:fv _uniq.52794))) ((:c Ring.toIntCast) ((:c ZMod) ((:c Fintype.card) (:fv _uniq.52777) (:fv _uniq.52794))) ((:c CommRing.toRing) ((:c ZMod) ((:c Fintype.card) (... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"a","sexp":"(:fv _uniq.52777)"},{"name":"inst✝²","sexp":"((:c Group) (:fv _uniq.52777))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.52777))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.52777))"},{"name":"ha","sexp":"(:forall x (:fv _uniq.52777) ((:c Membe... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c ZMod) (:arg :explicit 0 (:app (:c Fintype.card) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Fintype) (:arg :explicit 0 (:fv FV0))))))))) (:arg :explicit 1 (:fv FV8)) (:arg :explicit 2 (:app (:c Int.cast) (:arg :implicit-type 0 (:app (:c ZMod) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52777","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52779","is_instance":false,"is_let":false,"name":"a","sexp":"(:fv FV0)"},{"binder_role":":instance-implicit... | {"children":[{"source":"simp","sourceEnd":17400,"sourceStart":17396,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":17402,"sourceStart":17401,"tag":"a... | [] | [{"source":"hy","source_end":17404,"source_start":17402,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52777","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52779","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 76 | 28 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4894b387e9eac7034e60b8b23e201b6e7e890f34f9c67dd33a8f5d6ff119db74 | a4e501803d10b8de560d1b4c29e22b5b4b11d9f148c758aaa8c9a3c51c566ec6 | 2b03c6fa0d97965b3010a3cc79e50f72491584aefb1dd167b2724cabbf4cbe14 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,882 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | inhabit X | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
⊢ ∃ g, (∀ (y : Y), ∃ x₁ x₂, g y ∈ Icc (f x₁) (f x₂)) ∧ ⇑g ∘ e = ⇑f | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
⊢ ∃ g, (∀ (y : Y), ∃ x₁ x₂, g y ∈ Icc (f x₁) (f x₂)) ∧ ⇑g ∘ e = ⇑f | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"inhabit","sourceEnd":18834,"sourceStart":18827,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":0,"semanticRole":"local","source":"X","sourceEnd":18836,"sourceStart":18835,"tag":"identifier"}],"kind":"Lean.Elab.Tactic.inhabit","source":"inhabit X\n -- Put `a ... | [] | [{"source":"X\n -- Put `a = ⨅ x, f x` and `b = ⨆ x, f x`","source_end":18836,"source_start":18835,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d964f39b1182f4e55f1791d3549face12ff9f7e83741b27a7ce71735d1eab8ec | d13720b80fdccc6ae6db8b405c9e5e3b4dd2cb464eed9a9c3185aee592ee9664 | 6ce56ea3431481d4faf43872a7d820b694fafc16f1f23b02a87f736d4021be14 | edb8a4d7344bdfebf1819cac1cba139022b4f4afb39c3fe59d64a5c4b18abe45 |
cat-searcher/leandojo-benchmark-4-random | test | 3,883 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨a, ha⟩ : ∃ a, <a>IsGLB</a> (<a>Set.range</a> f) a := ⟨_, <a>isGLB_ciInf</a> f.isBounded_range.bddBelow⟩ | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
⊢ ∃ g, (∀ (y : Y), ∃ x₁ x₂, g y ∈ Icc (f x₁) (f x₂)) ∧ ⇑g ∘ e = ⇑f | case intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
⊢ ∃ g, (∀ (y : Y), ∃ x₁ x₂, g y ∈ Icc (f x₁) (f x₂)) ∧ ⇑g ∘ e = ⇑f | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"obtain","sourceEnd":18892,"sourceStart":18886,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":18896,"sourceStart":18893,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEn... | [] | [{"source":"∃ a, IsGLB (range f) a","source_end":18931,"source_start":18907,"syntax_kind":"«term∃_,_»"},{"source":"⟨_, isGLB_ciInf f.isBounded_range.bddBelow⟩","source_end":18982,"source_start":18935,"syntax_kind":"Lean.Parser.Term.anonymousCtor"},{"source":"obtain","source_end":18892,"source_start":18886,"syntax_kind"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 5 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a46fbc87664292fde732f4cc53abf5734824877a65ffe321ecda3c91ac4f9972 | edb8a4d7344bdfebf1819cac1cba139022b4f4afb39c3fe59d64a5c4b18abe45 | f846f4f943ea9fceab935b2397975042b672019ca2a648454fa059a284307e01 | bd1dbbfc53a16ebf668817bbd80dcbdef9b0e2d4a3527c7d47a47e94696b6482 |
cat-searcher/leandojo-benchmark-4-random | test | 3,884 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨b, hb⟩ : ∃ b, <a>IsLUB</a> (<a>Set.range</a> f) b := ⟨_, <a>isLUB_ciSup</a> f.isBounded_range.bddAbove⟩ | case intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
⊢ ∃ g, (∀ (y : Y), ∃ x₁ x₂, g y ∈ Icc (f x₁) (f x₂)) ∧ ⇑g ∘ e = ⇑f | case intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
⊢ ∃ g, (∀ (y : Y), ∃ x₁ x₂, g y ∈ Icc (f x₁) (f x... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"obtain","sourceEnd":18991,"sourceStart":18985,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":18995,"sourceStart":18992,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"b","sourceEn... | [] | [{"source":"∃ b, IsLUB (range f) b","source_end":19030,"source_start":19006,"syntax_kind":"«term∃_,_»"},{"source":"⟨_, isLUB_ciSup f.isBounded_range.bddAbove⟩\n -- Then `f x ∈ [a, b]` for all `x`","source_end":19081,"source_start":19034,"syntax_kind":"Lean.Parser.Term.anonymousCtor"},{"source":"obtain","source_end":18... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 6 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1bf0cc2dfa4868809852ef09baaca64d2a643a79b99929e57c9a3cc9a3dd9981 | bd1dbbfc53a16ebf668817bbd80dcbdef9b0e2d4a3527c7d47a47e94696b6482 | 8af83bf304915c1261d5db9c7b86e04541585e11cfe50f48aa1dd0d81bfe3bbc | 2f5c165006c8ece0e9b0a35aa9b1348f5a29bf36bf621774a489236a5a512de8 |
cat-searcher/leandojo-benchmark-4-random | test | 3,885 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hmem : ∀ x, f x ∈ <a>Set.Icc</a> a b := fun x => ⟨ha.1 ⟨x, <a>rfl</a>⟩, hb.1 ⟨x, <a>rfl</a>⟩⟩ | case intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
⊢ ∃ g, (∀ (y : Y), ∃ x₁ x₂, g y ∈ Icc (f x₁) (f x... | case intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
⊢ ∃ g, (∀ (y : Y)... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"have","sourceEnd":19127,"sourceStart":19123,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hmem","sourceEnd":19132,"sourceStart":19128,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hmem","sourceEnd":19132,"sourceStart":19128,"tag":... | [] | [{"source":"∀ x, f x ∈ Icc a b","source_end":19157,"source_start":19135,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"fun x => ⟨ha.1 ⟨x, rfl⟩, hb.1 ⟨x, rfl⟩⟩\n -- Rule out the trivial case `a = b`","source_end":19212,"source_start":19161,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 7 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7fb430053c89b407c2d748f07258b1797d5a2d203bf18ee392fc7fda06b1441b | 2f5c165006c8ece0e9b0a35aa9b1348f5a29bf36bf621774a489236a5a512de8 | d3020ac78ae1536eeefe8b27348563687fcea2c30bb3c1cbfea1254cd5b39339 | f1f1f2cad71a5ae340be79076f3735ca3a30aba56e8c794fc425df68c3e0a108 |
cat-searcher/leandojo-benchmark-4-random | test | 3,886 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hle : a ≤ b := (hmem <a>Inhabited.default</a>).1.<a>LE.le.trans</a> (hmem <a>Inhabited.default</a>).2 | case intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
⊢ ∃ g, (∀ (y : Y)... | case intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
⊢ ∃ g... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"have","sourceEnd":19258,"sourceStart":19254,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hle","sourceEnd":19262,"sourceStart":19259,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hle","sourceEnd":19262,"sourceStart":19259,"tag":"n... | [] | [{"source":"a ≤ b","source_end":19272,"source_start":19265,"syntax_kind":"«term_≤_»"},{"source":"(hmem default).1.trans (hmem default).2","source_end":19315,"source_start":19276,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 8 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 46a0cf6049a1f30d3f4d71daf4d26bd23c1115bf7f3d86f21cfd3b674455b8bf | f1f1f2cad71a5ae340be79076f3735ca3a30aba56e8c794fc425df68c3e0a108 | 35ef8bc14fe2443107d90a2d63db867f85c324abdb76f1d189fe110207971159 | 4df3b0fd11782666ee77944e322bbed72771e245f165ab634badc43dc090f616 |
cat-searcher/leandojo-benchmark-4-random | test | 3,887 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases hle.eq_or_lt with (rfl | hlt) | case intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
⊢ ∃ g... | case intro.intro.inl
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
hb : IsLUB (range ⇑f) a
hmem : ∀ (x : X), f x ∈ Icc a a
hle : a ≤ a
⊢ ∃ g, ... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rcases","sourceEnd":19324,"sourceStart":19318,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"LE.le.eq_or_lt","semanticRole":"global","source":"hle.eq_or_lt","sourceEnd":19337,"sourceStart":19325,"tag":"identifier"}],"kind":"Lean.Parser.Tac... | [] | [{"source":"hle.eq_or_lt","source_end":19337,"source_start":19325,"syntax_kind":"ident"},{"source":"(rfl | hlt)","source_end":19354,"source_start":19343,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 9 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0da9a248fc40c396f7bf70ad6d2d6f4a82d5763593b8c0932583e6b4cf6c3ca5 | 4df3b0fd11782666ee77944e322bbed72771e245f165ab634badc43dc090f616 | 01ce7e88519dfd2aef682e23d81fe5e3c1e328b124db8cf28aeaf137664a9c80 | 6119441b28049fbdb029aeb96ed8fd6c5825a3f7614bc0137c0ee8f9d6a159ed |
cat-searcher/leandojo-benchmark-4-random | test | 3,888 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | set c := (a + b) / 2 | case intro.intro.inr
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
h... | case intro.intro.inr
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
h... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"set","sourceEnd":19531,"sourceStart":19528,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"semanticRole":"scoped_local","source":"c","sourceEnd":19533,"sourceStart":19532,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":":="... | [] | [{"source":"(a + b) / 2","source_end":19548,"source_start":19537,"syntax_kind":"«term_/_»"},{"source":"c","source_end":19533,"source_start":19532,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 19 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1e2659e2b09c63e5506a0ec5b40ebda0f1c09c77c525fca05a6759a048c785db | 13fbe57fd209f7b8ab8146737f606f74bb9bb6200eb840f06b0aeb910e0585bc | 2fd553c3372dcae5ca9a2fa6bc8c7afacbcfbe89c36adcf5878982459f699013 | bfcf421d862f5cbe66fa7a849f31774952643e4829335df735a23c4de7edb7cf |
cat-searcher/leandojo-benchmark-4-random | test | 3,889 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hac : a < c := <a>left_lt_add_div_two</a>.2 hlt | case intro.intro.inr
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
h... | case intro.intro.inr
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
h... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"have","sourceEnd":19555,"sourceStart":19551,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hac","sourceEnd":19559,"sourceStart":19556,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hac","sourceEnd":19559,"sourceStart":19556,"tag":"n... | [] | [{"source":"a < c","source_end":19567,"source_start":19562,"syntax_kind":"«term_<_»"},{"source":"left_lt_add_div_two.2 hlt","source_end":19596,"source_start":19571,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 20 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 35b346ed2e69bdb135250b1e2e2cc0ead690ec693cb1e7b39d93c0d4ed41e3be | bfcf421d862f5cbe66fa7a849f31774952643e4829335df735a23c4de7edb7cf | f0548e23dfe2e0bc89a10f7568762e8a74bb542745e6964d19e794b477cdcae2 | 81cdd923cc2ff622c25d8d60323abe792dada9cd54a8757c9196cc52d93993d1 |
cat-searcher/leandojo-benchmark-4-random | test | 3,890 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hcb : c < b := <a>add_div_two_lt_right</a>.2 hlt | case intro.intro.inr
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
h... | case intro.intro.inr
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
h... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"have","sourceEnd":19603,"sourceStart":19599,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hcb","sourceEnd":19607,"sourceStart":19604,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hcb","sourceEnd":19607,"sourceStart":19604,"tag":"n... | [] | [{"source":"c < b","source_end":19615,"source_start":19610,"syntax_kind":"«term_<_»"},{"source":"add_div_two_lt_right.2 hlt","source_end":19645,"source_start":19619,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 21 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ab6bba08495afaa1cca5aa5c2ad3732f37f85ae872418a2a76044903c94e37c9 | 81cdd923cc2ff622c25d8d60323abe792dada9cd54a8757c9196cc52d93993d1 | 49b568becdbb07156aadf71671b3715894b9c5aacbb5740792d021beaf70dd69 | 5a23e2ae5f09ed5f3b3d1dfc4c2cf8469f3459792145c6cc1b60152195fc4824 |
cat-searcher/leandojo-benchmark-4-random | test | 3,891 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hsub : c - a = b - c := by field_simp [c] ring | case intro.intro.inr
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
h... | case intro.intro.inr
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
h... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"have","sourceEnd":19652,"sourceStart":19648,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hsub","sourceEnd":19657,"sourceStart":19653,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hsub","sourceEnd":19657,"sourceStart":19653,"tag":... | [] | [{"source":"c - a = b - c","source_end":19673,"source_start":19660,"syntax_kind":"«term_=_»"},{"source":"c","source_end":19697,"source_start":19696,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 22 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c065424e30d081a66ee1c82c6ccd2c05c0585b8dc7ce3bee42cfec58814186b3 | 5a23e2ae5f09ed5f3b3d1dfc4c2cf8469f3459792145c6cc1b60152195fc4824 | 7f1c02d76fd319c09d5f0efb52d76f7e4cf0c8655036fef78a95c09497004c82 | 7fd2149c157cc0e3b9ecd94c792560e2ab29ab1837e93feedd757fd8a98a1cfb |
cat-searcher/leandojo-benchmark-4-random | test | 3,892 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | choose xl hxl hgb using hg_mem | case intro.intro.inr.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
h... | case intro.intro.inr.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
h... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"choose","sourceEnd":22245,"sourceStart":22239,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"xl","sourceEnd":22248,"sourceStart":22246,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"xl","sourceEnd"... | [] | [{"source":"hg_mem","source_end":22269,"source_start":22263,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 96 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 94fa76219bbce670e7399d4b311ad016dced17acc63a4cd1b519f81a68a337a1 | a2968dbdcde80d6df4d54933d8176e687ac9dd11888e409f0d8c0b8a98ecd272 | 6d08a133140f08d4eb539affe113cb8da221716d6051d5ff3325131f2a771c36 | f996c82b16611440bf486a82a5bd37eb8ae59247e0ce53bb4b0b06ab20f66f8a |
cat-searcher/leandojo-benchmark-4-random | test | 3,893 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>em</a> (∃ x, f x = b) with (⟨x, rfl⟩ | hb') | case intro.intro.inr.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
h... | case intro.intro.inr.intro.intro.inl.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
g : Y →ᵇ ℝ
hgf : ⇑g ∘ e = ⇑f
xl : Y → X
hxl : ∀ (y : ... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rcases","sourceEnd":22278,"sourceStart":22272,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"em","semanticRole":"global","source":"em","sourceEnd":22281,"sourceStart":22279,"tag":"identifier"},{"children":[{"children":[{"sourc... | [] | [{"source":"em (∃ x, f x = b)","source_end":22298,"source_start":22279,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(⟨x, rfl⟩ | hb')","source_end":22324,"source_start":22304,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 97 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cc0039310f8d1de8e35b33d618ff171682643b053672f694f4f6cf6672d6163e | f996c82b16611440bf486a82a5bd37eb8ae59247e0ce53bb4b0b06ab20f66f8a | be0822203276eafa914d59581c3f5c98d80ef781c5dbe4ef1559cfe78ade91e1 | 3ff0e48fd7f12c519bda254d4c152f1ca0e1da91ae8cdbf1bb7d19881198339e |
cat-searcher/leandojo-benchmark-4-random | test | 3,894 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>exists_bounded_mem_Icc_of_closed_of_le</a> (he.isClosed_range.union <| isClosed_Iic.preimage g.continuous) (isClosed_singleton.preimage g.continuous) hd (<a>sub_nonneg</a>.2 hcb.le) with ⟨dg, dg0, dgb, dgmem⟩ | case intro.intro.inr.intro.intro.inr
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a... | case intro.intro.inr.intro.intro.inr.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rcases","sourceEnd":22713,"sourceStart":22707,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"exists_bounded_mem_Icc_of_closed_of_le","semanticRole":"global","source":"exists_bounded_mem_Icc_of_closed_of_le","sourceEnd":22752,"... | [] | [{"source":"exists_bounded_mem_Icc_of_closed_of_le\n (he.isClosed_range.union <| isClosed_Iic.preimage g.continuous)\n (isClosed_singleton.preimage g.continuous) hd (sub_nonneg.2 hcb.le)","source_end":22896,"source_start":22714,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨dg, dg0, dgb, dgmem⟩","source_en... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 120 | exact | true | 1 | 28 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0b779fe299f8ce17aa8a2df8a6489126740d0696614814b6dc643551629e2690 | d83431cd32c8a22d1ab99f3c17ac6cf6b79a133ee248303ea40f662604355245 | 20c3cfceea4b2f8b985bc1ace2789158bf6cd0eb6c2cc9549deacf9c5fc44a77 | e5786839ee753e5f5fbbdc745e9d5c888bf9d8da3e466af0a0a608e9431c21b9 |
cat-searcher/leandojo-benchmark-4-random | test | 3,895 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | replace hgf : ∀ x, (g - dg) (e x) = f x := by intro x simp [dg0 (<a>Or.inl</a> <| <a>Set.mem_range_self</a> _), ← hgf] | case intro.intro.inr.intro.intro.inr.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x... | case intro.intro.inr.intro.intro.inr.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"replace","sourceEnd":22941,"sourceStart":22934,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hgf","sourceEnd":22945,"sourceStart":22942,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hgf","sourceEnd":22945,"sourceStart":22942,"tag"... | [] | [{"source":"∀ x, (g - dg) (e x) = f x","source_end":22975,"source_start":22948,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"dg0 (Or.inl <| mem_range_self _)","source_end":23036,"source_start":23004,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hgf","source_end":23045,"source_start":23042,"syntax_kind":"ident"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 121 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8d2ed220dad0c28f72261668b9bc9d0e14d57ac042bdfdf5acd0c7c857a8dde1 | e5786839ee753e5f5fbbdc745e9d5c888bf9d8da3e466af0a0a608e9431c21b9 | 4691f1266caf987ab0d8c409673d14f7f3d022dffb37b8a74e997fa2d355de90 | ed33fc8feb1f47f44b657683419310b339b14dbfc5c4beb4ff5eb71b40670f76 |
cat-searcher/leandojo-benchmark-4-random | test | 3,896 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨g - dg, fun y => ?_, <a>funext</a> hgf⟩ | case intro.intro.inr.intro.intro.inr.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x... | case intro.intro.inr.intro.intro.inr.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":23055,"sourceStart":23049,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":23059,"sourceStart":23056,"tag":"atom"},{"children":[{"children":[{"contextIndex":22,"semanticRole":"local","source":"g","sourceEnd":23060,"sourceStart":23059,"tag":"identifier"},{"source":"-","sou... | [] | [{"source":"⟨g - dg, fun y => ?_, funext hgf⟩","source_end":23093,"source_start":23056,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 125 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 238d8e8b2f1821252c91066993705341631bf1c4d522b5f6815d4d0e1f3e4acd | ed33fc8feb1f47f44b657683419310b339b14dbfc5c4beb4ff5eb71b40670f76 | 183a5c4ecd6bacd754c9dfdf9c614152f0fcba118ac888c86445d662b6974fec | 6487d2b4b732d396def070b44387c900e202a8bca213b745a99dacd4396cb1fd |
cat-searcher/leandojo-benchmark-4-random | test | 3,897 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases hb.exists_between hyb with ⟨_, ⟨xu, rfl⟩, hyxu, _⟩ | case intro.intro.inr.intro.intro.inr.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x... | case intro.intro.inr.intro.intro.inr.intro.intro.intro.intro.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB ... | ((:c Exists) (:fv _uniq.144068) (:lambda x₁ (:fv _uniq.144068) ((:c Exists) (:fv _uniq.144068) (:lambda x₂ (:fv _uniq.144068) ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Rea... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x₁ :explicit (:fv FV0) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x₂ :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rcases","sourceEnd":23365,"sourceStart":23359,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"hb.exists_between","sourceEnd":23383,"sourceStart":23366,"tag":"identifier"},{"children":[{"contextIndex":34,"semanticRole":"local"... | [] | [{"source":"hb.exists_between hyb","source_end":23387,"source_start":23366,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨_, ⟨xu, rfl⟩, hyxu, _⟩","source_end":23424,"source_start":23393,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 140 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6ecc2b6e4d71d172bf1b5b9750177882efa7a93227bbb82875eb95e85725a541 | 4fa62b1fe5a3f82c096b40a242ab727ce0f383fec8d8221344e4b8827ec24149 | 4058d49601dd96b38b5698a4f0b0fff90d8590307a47a0edb665b7944cc26235 | 62ce7d00384aed5da82248ca32d6f7489ca34854453bba82cf48f322fa64a01f |
cat-searcher/leandojo-benchmark-4-random | test | 3,898 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases' <a>lt_or_le</a> c (g y) with hc hc | case intro.intro.inr.intro.intro.inr.intro.intro.intro.intro.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB ... | case intro.intro.inr.intro.intro.inr.intro.intro.intro.intro.intro.intro.intro.inl
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : Is... | ((:c Exists) (:fv _uniq.144068) (:lambda x₁ (:fv _uniq.144068) ((:c Exists) (:fv _uniq.144068) (:lambda x₂ (:fv _uniq.144068) ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Rea... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x₁ :explicit (:fv FV0) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x₂ :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"cases'","sourceEnd":23433,"sourceStart":23427,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"lt_or_le","semanticRole":"global","source":"lt_or_le","sourceEnd":23442,"sourceStart":23434,"tag":"identifier"},{"children":[{"contex... | [] | [{"source":"lt_or_le c (g y)","source_end":23450,"source_start":23434,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 141 | exact | true | 1 | 37 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d6c03d04491b4bfe676bb0ec21c63cc62d8ff6899a7ab10b0e965f742ccc29d8 | 62ce7d00384aed5da82248ca32d6f7489ca34854453bba82cf48f322fa64a01f | 9dc4f16e3b4116e6d36c9c5fbc94351ef848bfe9aedb93a1a5ca4d8bf358bd97 | a1df80d55d3196729c3cbc78f0d0612991476c03b6f866a70bdb18c790511b25 |
cat-searcher/leandojo-benchmark-4-random | test | 3,899 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : ∀ x, f x = a := by simpa using hmem | case intro.intro.inl
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
hb : IsLUB (range ⇑f) a
hmem : ∀ (x : X), f x ∈ Icc a a
hle : a ≤ a
⊢ ∃ g, ... | case intro.intro.inl
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
hb : IsLUB (range ⇑f) a
hmem : ∀ (x : X), f x ∈ Icc a a
hle : a ≤ a
this : ... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"have","sourceEnd":19364,"sourceStart":19360,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":19365,"sourceStart":19365,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":19365,"sourceStart":19365,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"∀ x, f x = a","source_end":19381,"source_start":19367,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"hmem","source_end":19404,"source_start":19400,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 14 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | abba96538a4ca9b1556220fe14a53e9b08243c128932199eee9a26a4ee267cb4 | 46cddbc95f625b0b3cacdfbbf5196e6c989c4514b282b5c6cfbae7ad8fff9a46 | 55d15668094ed8ae975e901194900544c481e979b3adb77f3b7737fb09618fac | 8b812ea6a1abe1e3f711fa3271a7386a8329f46fe2819becd57518e9a95563b9 |
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