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classes | raw_schema_version int64 4 4 | raw_extractor_version stringclasses 1
value | model_schema_version int64 2 2 | model_normalization stringclasses 1
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cat-searcher/leandojo-benchmark-4-random | test | 3,495 | FiniteDimensional.finrank_eq_zero_iff_isTorsion | Mathlib/LinearAlgebra/Dimension/Finite.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>rank_eq_zero_iff_isTorsion</a> (R := R), ← <a>finrank_eq_rank</a>] | R✝ : Type u
M M₁ : Type v
M' : Type v'
ι : Type w
inst✝¹⁵ : Ring R✝
inst✝¹⁴ : AddCommGroup M
inst✝¹³ : AddCommGroup M'
inst✝¹² : AddCommGroup M₁
inst✝¹¹ : Module R✝ M
inst✝¹⁰ : Module R✝ M'
inst✝⁹ : Module R✝ M₁
inst✝⁸ : Nontrivial R✝
inst✝⁷ : NoZeroSMulDivisors R✝ M
inst✝⁶ : StrongRankCondition R✝
inst✝⁵ : Module.Fini... | R✝ : Type u
M M₁ : Type v
M' : Type v'
ι : Type w
inst✝¹⁵ : Ring R✝
inst✝¹⁴ : AddCommGroup M
inst✝¹³ : AddCommGroup M'
inst✝¹² : AddCommGroup M₁
inst✝¹¹ : Module R✝ M
inst✝¹⁰ : Module R✝ M'
inst✝⁹ : Module R✝ M₁
inst✝⁸ : Nontrivial R✝
inst✝⁷ : NoZeroSMulDivisors R✝ M
inst✝⁶ : StrongRankCondition R✝
inst✝⁵ : Module.Fini... | ((:c Iff) ((:c Eq) (:c Nat) ((:c FiniteDimensional.finrank) (:fv _uniq.409090) (:fv _uniq.402950) ((:c CommSemiring.toSemiring) (:fv _uniq.409090) ((:c CommRing.toCommSemiring) (:fv _uniq.409090) (:fv _uniq.409091))) (:fv _uniq.402962) (:fv _uniq.409094)) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))... | [{"name":"R✝","sexp":"(:sort (+ u 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"M₁","sexp":"(:sort (+ v 1))"},{"name":"M'","sexp":"(:sort (+ v' 1))"},{"name":"ι","sexp":"(:sort (+ w 1))"},{"name":"inst✝¹⁵","sexp":"((:c Ring) (:fv _uniq.402948))"},{"name":"inst✝¹⁴","sexp":"((:c AddCommGroup) (:fv _uniq.402950))"}... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c FiniteDimensional.finrank) (:arg :explicit 0 (:fv FV17)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV17))))) (:arg :instance 3 (:instance-of (:app (:c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.402948","is_instance":false,"is_let":false,"name":"R✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.402950","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rw","sourceEnd":20758,"sourceStart":20756,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":20760,"sourceStart":20759,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":20763,"sourceSt... | [] | [{"source":"rank_eq_zero_iff_isTorsion (R := R)","source_end":20799,"source_start":20764,"syntax_kind":"Lean.Parser.Term.app"},{"source":"finrank_eq_rank","source_end":20820,"source_start":20805,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.402948","is_instance":false,"is_let":false,"user_name":"R✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.402950","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 112 | 4 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 068c33ede86db0e6ccff2d8740488a41fe653f9e2fe03ba48990fce2cb58d002 | cb48c9c53102fb5b63284c629e6a02dbd25a2c4d0b9635b402bec2e4eea07aaf | 24055fbff1ec047998f9e737a0c39570c06d680c2942f008b8d925fa1cfe71f4 | 225d67024d52da00d363a7dad8387bec9bf557eaca74a4b7fc70dd844dbdae53 |
cat-searcher/leandojo-benchmark-4-random | test | 3,496 | FiniteDimensional.finrank_eq_zero_iff_isTorsion | Mathlib/LinearAlgebra/Dimension/Finite.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_cast | R✝ : Type u
M M₁ : Type v
M' : Type v'
ι : Type w
inst✝¹⁵ : Ring R✝
inst✝¹⁴ : AddCommGroup M
inst✝¹³ : AddCommGroup M'
inst✝¹² : AddCommGroup M₁
inst✝¹¹ : Module R✝ M
inst✝¹⁰ : Module R✝ M'
inst✝⁹ : Module R✝ M₁
inst✝⁸ : Nontrivial R✝
inst✝⁷ : NoZeroSMulDivisors R✝ M
inst✝⁶ : StrongRankCondition R✝
inst✝⁵ : Module.Fini... | ((:c Iff) ((:c Eq) (:c Nat) ((:c FiniteDimensional.finrank) (:fv _uniq.409090) (:fv _uniq.402950) ((:c CommSemiring.toSemiring) (:fv _uniq.409090) ((:c CommRing.toCommSemiring) (:fv _uniq.409090) (:fv _uniq.409091))) (:fv _uniq.402962) (:fv _uniq.409094)) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))... | [{"name":"R✝","sexp":"(:sort (+ u 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"M₁","sexp":"(:sort (+ v 1))"},{"name":"M'","sexp":"(:sort (+ v' 1))"},{"name":"ι","sexp":"(:sort (+ w 1))"},{"name":"inst✝¹⁵","sexp":"((:c Ring) (:fv _uniq.402948))"},{"name":"inst✝¹⁴","sexp":"((:c AddCommGroup) (:fv _uniq.402950))"}... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c FiniteDimensional.finrank) (:arg :explicit 0 (:fv FV17)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV17))))) (:arg :instance 3 (:instance-of (:app (:c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.402948","is_instance":false,"is_let":false,"name":"R✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.402950","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"norm_cast","sourceEnd":20833,"sourceStart":20824,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.tacticNorm_cast_","source":"norm_cast","sourceEnd":20833,"sourceStart":20824,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.402948","is_instance":false,"is_let":false,"user_name":"R✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.402950","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 112 | 8 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0ad199e666ae81d62b07ac584dc66a1780de85949252347277709220c78e544c | 225d67024d52da00d363a7dad8387bec9bf557eaca74a4b7fc70dd844dbdae53 | 4526560ee387a60af0a3f42ddce7258b27dc8bd6782a63271dc2d5aa462e81b2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,497 | IsPGroup.powEquiv_symm_apply | Mathlib/GroupTheory/PGroup.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Nat.card_zpowers</a>] | p : ℕ
G : Type u_1
inst✝ : Group G
hG : IsPGroup p G
n : ℕ
hn : p.Coprime n
g : G
⊢ (hG.powEquiv hn).symm g = g ^ (orderOf g).gcdB n | p : ℕ
G : Type u_1
inst✝ : Group G
hG : IsPGroup p G
n : ℕ
hn : p.Coprime n
g : G
⊢ (hG.powEquiv hn).symm g = g ^ (Nat.card ↥(Subgroup.zpowers g)).gcdB n | ((:c Eq) (:fv _uniq.16779) ((:c DFunLike.coe) ((:c Equiv) (:fv _uniq.16779) (:fv _uniq.16779)) (:fv _uniq.16779) (:lambda _ (:fv _uniq.16779) (:fv _uniq.16779)) ((:c Equiv.instFunLike) (:fv _uniq.16779) (:fv _uniq.16779)) ((:c Equiv.symm) (:fv _uniq.16779) (:fv _uniq.16779) ((:c IsPGroup.powEquiv) (:fv _uniq.16776) (:f... | [{"name":"p","sexp":"(:c Nat)"},{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.16779))"},{"name":"hG","sexp":"((:c IsPGroup) (:fv _uniq.16776) (:fv _uniq.16779) (:fv _uniq.16782))"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c Nat.Coprime) (:fv _uniq.16776) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Equiv) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)))) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c FunLike) (:arg :explicit 0 (:app (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16776","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16779","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit"... | {"children":[{"source":"rw","sourceEnd":4973,"sourceStart":4971,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4975,"sourceStart":4974,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":4978,"sourceStart":... | [] | [{"source":"Nat.card_zpowers","source_end":4995,"source_start":4979,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16776","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16779","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 35 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a4db3bf97407fef2d55316beff74fc2ef68ba27dc1725e440d420dcf579884c9 | 36e9ca80e40ec42d27621d1fca382e36af73e1dc253dd563b8dbb7a3510e9e43 | 89516954b063fb48729a0ef30f548998bd3aa418b3bba0899b31aa3a761af364 | fd3637579c19ba060054e0e38f9fe916e58535fe0b2bdf344b9569419f3e57a1 |
cat-searcher/leandojo-benchmark-4-random | test | 3,498 | IsPGroup.powEquiv_symm_apply | Mathlib/GroupTheory/PGroup.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | p : ℕ
G : Type u_1
inst✝ : Group G
hG : IsPGroup p G
n : ℕ
hn : p.Coprime n
g : G
⊢ (hG.powEquiv hn).symm g = g ^ (Nat.card ↥(Subgroup.zpowers g)).gcdB n | ((:c Eq) (:fv _uniq.16779) ((:c DFunLike.coe) ((:c Equiv) (:fv _uniq.16779) (:fv _uniq.16779)) (:fv _uniq.16779) (:lambda _ (:fv _uniq.16779) (:fv _uniq.16779)) ((:c Equiv.instFunLike) (:fv _uniq.16779) (:fv _uniq.16779)) ((:c Equiv.symm) (:fv _uniq.16779) (:fv _uniq.16779) ((:c IsPGroup.powEquiv) (:fv _uniq.16776) (:f... | [{"name":"p","sexp":"(:c Nat)"},{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.16779))"},{"name":"hG","sexp":"((:c IsPGroup) (:fv _uniq.16776) (:fv _uniq.16779) (:fv _uniq.16782))"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c Nat.Coprime) (:fv _uniq.16776) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Equiv) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)))) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c FunLike) (:arg :explicit 0 (:app (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16776","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16779","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit"... | {"children":[{"source":"rfl","sourceEnd":5001,"sourceStart":4998,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":5001,"sourceStart":4998,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16776","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16779","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 35 | 8 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4b869cce7bb375fa85a96d45b30b165d8646a36a94d3aad9195903f0c6dbf83e | fd3637579c19ba060054e0e38f9fe916e58535fe0b2bdf344b9569419f3e57a1 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,499 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let A := <a>MeasureTheory.Measure.finiteSpanningSetsInOpen'</a> μ | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | ((:c Filter.Eventually) (:fv _uniq.280238) (:lambda x (:fv _uniq.280238) ((:c Filter.Tendsto) ((:c Set) (:fv _uniq.280238)) (:c ENNReal) (:lambda a ((:c Set) (:fv _uniq.280238)) ((:c HDiv.hDiv) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHDiv) (:c ENNReal) ((:c DivInvMonoid.toDiv) (:c ENNReal) (:c ENNReal.instDivIn... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:lambda a :explicit (:app (:c Set) (:arg :explicit 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"let","sourceEnd":47539,"sourceStart":47536,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"A","sourceEnd":47541,"sourceStart":47540,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{... | [] | [{"source":"MeasureTheory.Measure.finiteSpanningSetsInOpen' μ","source_end":47595,"source_start":47545,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 20ec595c4214337edf207c4bb34baf790207bc9ff205d6fc5631de16f039f213 | 56b2f7716fa6552bbaa07513906be92c761645d97621bd091d351656a83b353b | ae0393036848d1ec27336b8c973ba038a8455a32575104c97efb22ff506521bb | a4cb2fae092a6e3a40202ba3b4d11a2b7e39e001511f310dd0b68c921133db4f |
cat-searcher/leandojo-benchmark-4-random | test | 3,500 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases h'f.isSeparable_range with ⟨t, t_count, ht⟩ | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | case intro.intro
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
... | ((:c Filter.Eventually) (:fv _uniq.280238) (:lambda x (:fv _uniq.280238) ((:c Filter.Tendsto) ((:c Set) (:fv _uniq.280238)) (:c ENNReal) (:lambda a ((:c Set) (:fv _uniq.280238)) ((:c HDiv.hDiv) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHDiv) (:c ENNReal) ((:c DivInvMonoid.toDiv) (:c ENNReal) (:c ENNReal.instDivIn... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:lambda a :explicit (:app (:c Set) (:arg :explicit 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"rcases","sourceEnd":47604,"sourceStart":47598,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MeasureTheory.StronglyMeasurable.isSeparable_range","semanticRole":"global","source":"h'f.isSeparable_range","sourceEnd":47626,"sourceStart":47605... | [] | [{"source":"h'f.isSeparable_range","source_end":47626,"source_start":47605,"syntax_kind":"ident"},{"source":"⟨t, t_count, ht⟩","source_end":47652,"source_start":47632,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 5 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1faeba592778386d4bb10893b28b282a3c1a8db9d54ee44045652c044eb8ac7a | a4cb2fae092a6e3a40202ba3b4d11a2b7e39e001511f310dd0b68c921133db4f | 8c0d47f9ca04abc066c6e0f71625bcf74b5c27e78e5a974133fd5ea0f704b545 | 0b2ab48a2730de79c5948109faa4d63303e22906c0949389540f60a51150ff00 |
cat-searcher/leandojo-benchmark-4-random | test | 3,501 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards [main, v.ae_eventually_measure_pos] with x hx h'x | case intro.intro
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
... | case h
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : Stro... | ((:c Filter.Eventually) (:fv _uniq.280238) (:lambda x (:fv _uniq.280238) ((:c Filter.Tendsto) ((:c Set) (:fv _uniq.280238)) (:c ENNReal) (:lambda a ((:c Set) (:fv _uniq.280238)) ((:c HDiv.hDiv) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHDiv) (:c ENNReal) ((:c DivInvMonoid.toDiv) (:c ENNReal) (:c ENNReal.instDivIn... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:lambda a :explicit (:app (:c Set) (:arg :explicit 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"filter_upwards","sourceEnd":49124,"sourceStart":49110,"tag":"atom"},{"children":[{"source":"[","sourceEnd":49126,"sourceStart":49125,"tag":"atom"},{"children":[{"contextIndex":20,"semanticRole":"local","source":"main","sourceEnd":49130,"sourceStart":49126,"tag":"identifier"},{"source":",","sourc... | [] | [{"source":"v.ae_eventually_measure_pos","source_end":49159,"source_start":49132,"syntax_kind":"ident"},{"source":"main","source_end":49130,"source_start":49126,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 49 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b499abcaa53f3405a8372b7323b4a4bf32dd3beabed810addaf092c5268e5373 | cc5d04a840bd32ce9239eef9adab3dd3996c8d76a8ee7575d81d92ddea412dad | 1ab3f2c5689a0d72b2257f921e2f87b32d8a538b083a17523739dd21562a2700 | 988815bee1a063b361fcafe306e5341d5abb009baf29b60f6711b23eb01ada2c |
cat-searcher/leandojo-benchmark-4-random | test | 3,502 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have M : ∀ c ∈ t, <a>Filter.Tendsto</a> (fun a => (∫⁻ y in a, ‖f y - c‖₊ ∂μ) / μ a) (v.filterAt x) (𝓝 ‖f x - c‖₊) := by intro c hc obtain ⟨n, xn⟩ : ∃ n, x ∈ A.set n := by simpa [← A.spanning] using <a>Set.mem_univ</a> x specialize hx n c hc simp only [xn, <a>Set.indicator_of_mem</a>] at hx apply hx.congr' _ filter_upw... | case h
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : Stro... | case h
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : Stro... | ((:c Filter.Tendsto) ((:c Set) (:fv _uniq.280238)) (:c ENNReal) (:lambda a ((:c Set) (:fv _uniq.280238)) ((:c HDiv.hDiv) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHDiv) (:c ENNReal) ((:c DivInvMonoid.toDiv) (:c ENNReal) (:c ENNReal.instDivInvMonoid))) ((:c MeasureTheory.lintegral) (:fv _uniq.280238) (:fv _uniq.28... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:lambda a :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :im... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"have","sourceEnd":49181,"sourceStart":49177,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"M","sourceEnd":49183,"sourceStart":49182,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"M","sourceEnd":49183,"sourceStart":49182,"tag":"node"... | [] | [{"source":"∀ c ∈ t, Tendsto (fun a => (∫⁻ y in a, ‖f y - c‖₊ ∂μ) / μ a)\n (v.filterAt x) (𝓝 ‖f x - c‖₊)","source_end":49313,"source_start":49190,"syntax_kind":"Lean.«term∀__,_»"},{"source":"∃ n, x ∈ A.set n","source_end":49380,"source_start":49360,"syntax_kind":"«term∃_,_»"},{"source":"A.spanning","source_end":4... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 50 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8ed62f86563ad8783e1c680440a80900ce3767c842d8f1098ca9f51ceb3f952d | 988815bee1a063b361fcafe306e5341d5abb009baf29b60f6711b23eb01ada2c | c52c77fe11ed219f3f7c02a024ef72377844b002526a4ce9fb6829b3489f47ec | e86cb63604d64f5eba5a6328012c458905396429104e5929ee3db09bcc1db4f9 |
cat-searcher/leandojo-benchmark-4-random | test | 3,503 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>ENNReal.tendsto_nhds_zero</a>.2 fun ε εpos => ?_ | case h
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : Stro... | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | ((:c Filter.Tendsto) ((:c Set) (:fv _uniq.280238)) (:c ENNReal) (:lambda a ((:c Set) (:fv _uniq.280238)) ((:c HDiv.hDiv) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHDiv) (:c ENNReal) ((:c DivInvMonoid.toDiv) (:c ENNReal) (:c ENNReal.instDivInvMonoid))) ((:c MeasureTheory.lintegral) (:fv _uniq.280238) (:fv _uniq.28... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:lambda a :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :im... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"apply","sourceEnd":49801,"sourceStart":49796,"tag":"atom"},{"children":[{"children":[{"name":"ENNReal.tendsto_nhds_zero","semanticRole":"global","source":"ENNReal.tendsto_nhds_zero","sourceEnd":49827,"sourceStart":49802,"tag":"identifier"},{"source":".","sourceEnd":49828,"sourceStart":49827,"tag... | [] | [{"source":"ENNReal.tendsto_nhds_zero.2 fun ε εpos => ?_","source_end":49848,"source_start":49802,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 71 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d6cad3d242aa5a56bda2adfe5a72f792b24d9875a65d1e9d50fd347790a23339 | e86cb63604d64f5eba5a6328012c458905396429104e5929ee3db09bcc1db4f9 | 6da8e660e107a379d8faa9fd6bdbf90b61f086e4b49a4cea1ff3448027f3dd93 | 31474f157dca7cd1eb2020b24800f7e473b5158702958e41fc562871926f4fac |
cat-searcher/leandojo-benchmark-4-random | test | 3,504 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨c, ct, xc⟩ : ∃ c ∈ t, (‖f x - c‖₊ : ℝ≥0∞) < ε / 2 := by simp_rw [← <a>edist_eq_coe_nnnorm_sub</a>] have : f x ∈ <a>closure</a> t := ht (<a>Set.mem_range_self</a> _) exact <a>EMetric.mem_closure_iff</a>.1 this (ε / 2) (<a>ENNReal.half_pos</a> (<a>ne_of_gt</a> εpos)) | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | case intro.intro
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
... | ((:c Filter.Eventually) ((:c Set) (:fv _uniq.280238)) (:lambda x ((:c Set) (:fv _uniq.280238)) ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.toPartialOrder) (:c ENNReal) ((:c OrderedCommSemiring.toOrderedSemiring) (:c ENNReal) ((:c CanonicallyO... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda x :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"obtain","sourceEnd":49857,"sourceStart":49851,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":49861,"sourceStart":49858,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"c","sourceEn... | [] | [{"source":"∃ c ∈ t, (‖f x - c‖₊ : ℝ≥0∞) < ε / 2","source_end":49929,"source_start":49876,"syntax_kind":"Lean.«term∃__,_»"},{"source":"edist_eq_coe_nnnorm_sub","source_end":49976,"source_start":49953,"syntax_kind":"ident"},{"source":"f x ∈ closure t","source_end":50006,"source_start":49989,"syntax_kind":"«term_∈_»"},{"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 72 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e8ac2252a988b41104637f953f43fb9c6454883a71eac430ff66ba57ae2682a7 | 31474f157dca7cd1eb2020b24800f7e473b5158702958e41fc562871926f4fac | a62704b3a7a441cf5dcd98a2eb64fd054ac61ba9247047cb270d1a5308fae811 | 9019306b696d7743f15d0ccfa175e84759282c93907cb24c1f7304651dc4052b |
cat-searcher/leandojo-benchmark-4-random | test | 3,505 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards [(<a>tendsto_order</a>.1 (M c ct)).2 (ε / 2) xc, h'x, v.eventually_measure_lt_top x] with a ha h'a h''a | case intro.intro
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
... | case h
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : Stro... | ((:c Filter.Eventually) ((:c Set) (:fv _uniq.280238)) (:lambda x ((:c Set) (:fv _uniq.280238)) ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.toPartialOrder) (:c ENNReal) ((:c OrderedCommSemiring.toOrderedSemiring) (:c ENNReal) ((:c CanonicallyO... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda x :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"filter_upwards","sourceEnd":50134,"sourceStart":50120,"tag":"atom"},{"children":[{"source":"[","sourceEnd":50136,"sourceStart":50135,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"(","sourceEnd":50137,"sourceStart":50136,"tag":"atom"},{"children":[{"children":[{"nam... | [] | [{"source":"v.eventually_measure_lt_top x","source_end":50212,"source_start":50183,"syntax_kind":"Lean.Parser.Term.app"},{"source":"h'x","source_end":50181,"source_start":50178,"syntax_kind":"ident"},{"source":"(tendsto_order.1 (M c ct)).2 (ε / 2) xc","source_end":50176,"source_start":50136,"syntax_kind":"Lean.Parser.T... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 82 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1cdfb0825a60444d63a59f445ad7dce2e273c2e4dbca6c9bf8657992ab2c683a | 9019306b696d7743f15d0ccfa175e84759282c93907cb24c1f7304651dc4052b | 70aa67d2df50cb286dd402f6cf44f6c559a1ceaffb93d264d34bc85db9c53b5a | 6fc3f88879096112e17de17eb94f79b7d4320393c27b463f4aba9e49ec6e9893 |
cat-searcher/leandojo-benchmark-4-random | test | 3,506 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>ENNReal.div_le_of_le_mul</a> | case h
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : Stro... | case h.h
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : St... | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.toPartialOrder) (:c ENNReal) ((:c OrderedCommSemiring.toOrderedSemiring) (:c ENNReal) ((:c CanonicallyOrderedCommSemiring.toOrderedCommSemiring) (:c ENNReal) (:c ENNReal.instCanonicallyOrderedCommSe... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"apply","sourceEnd":50244,"sourceStart":50239,"tag":"atom"},{"name":"ENNReal.div_le_of_le_mul","semanticRole":"global","source":"ENNReal.div_le_of_le_mul","sourceEnd":50269,"sourceStart":50245,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply ENNReal.div_le_of_le_mul","source... | [] | [{"source":"ENNReal.div_le_of_le_mul","source_end":50269,"source_start":50245,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 83 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ef3d94f1e19e18858ad44f0854304611f2dad758cbc44c8b8f4dbff091de3850 | 6fc3f88879096112e17de17eb94f79b7d4320393c27b463f4aba9e49ec6e9893 | 95a55d54138a5eff65ca358b240d13399c37226370dc00912104fc2113a4912f | 7a0abc64d0b6b8922f5dc52e35b57a06c2bbf21c2ef1ee129d9ee4eba12bca6e |
cat-searcher/leandojo-benchmark-4-random | test | 3,507 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>MeasureTheory.ae_all_iff</a>] | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | ((:c Filter.Eventually) (:fv _uniq.280238) (:lambda x (:fv _uniq.280238) (:forall n (:c Nat) (:forall c (:fv _uniq.280317) (:forall _ ((:c Membership.mem) (:fv _uniq.280317) ((:c Set) (:fv _uniq.280317)) ((:c Set.instMembership) (:fv _uniq.280317)) 0 (:fv _uniq.283066)) ((:c Filter.Tendsto) ((:c Set) (:fv _uniq.280238)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:forall n :explicit (:c Nat) (:forall c :explicit (:fv FV5) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV5))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"simp_rw","sourceEnd":48055,"sourceStart":48048,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":48057,"sourceStart":48056,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MeasureTheo... | [] | [{"source":"ae_all_iff","source_end":48067,"source_start":48057,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 9 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cd359c10eb730611ce6c4a9a0d353da64f1889cb38f52804bc843960bd4f8dcb | 3df903c0889bbf1c731d284ac7e93431f73bfafccffc0eb372372eecdf86dfcc | 257d2cb5254e8a4166bee472085b74f145c30ee9ed390967d81afccce5bb1ab9 | 72cfc8cff7bf77e85feb2f6cea8832b434d996d666bec0eaad2663cff6b79089 |
cat-searcher/leandojo-benchmark-4-random | test | 3,508 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro x | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | (:forall i (:c Nat) ((:c Filter.Eventually) (:fv _uniq.280238) (:lambda a (:fv _uniq.280238) (:forall c (:fv _uniq.280317) (:forall _ ((:c Membership.mem) (:fv _uniq.280317) ((:c Set) (:fv _uniq.280317)) ((:c Set.instMembership) (:fv _uniq.280317)) 0 (:fv _uniq.283066)) ((:c Filter.Tendsto) ((:c Set) (:fv _uniq.280238)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:forall i :explicit (:c Nat) (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda a :explicit (:fv FV0) (:forall c :explicit (:fv FV5) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV5))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"intro","sourceEnd":48078,"sourceStart":48073,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":48080,"sourceStart":48079,"tag":"identifier"}],"kind":"null","source":"x","sourceEnd":48080,"sourceStart":48079,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"x","source_end":48080,"source_start":48079,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 12 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c74720bd010b5fe72e162bc5077deaaffd321379b3db4b5f90ba6ffdb34c4724 | 72cfc8cff7bf77e85feb2f6cea8832b434d996d666bec0eaad2663cff6b79089 | 727852cc0e84019aeee0e605b3833ee9bcd4d2abc203673e529dba747f5c5a0d | e42029bf155d1d190adc1d4622f021645f0cea3522f09d5a28e8d580e4f60b73 |
cat-searcher/leandojo-benchmark-4-random | test | 3,509 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.ae_ball_iff</a> t_count] | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | ((:c Filter.Eventually) (:fv _uniq.280238) (:lambda a (:fv _uniq.280238) (:forall c (:fv _uniq.280317) (:forall _ ((:c Membership.mem) (:fv _uniq.280317) ((:c Set) (:fv _uniq.280317)) ((:c Set.instMembership) (:fv _uniq.280317)) 0 (:fv _uniq.283066)) ((:c Filter.Tendsto) ((:c Set) (:fv _uniq.280238)) (:c ENNReal) (:lam... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda a :explicit (:fv FV0) (:forall c :explicit (:fv FV5) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :instance 2 (:instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"rw","sourceEnd":48084,"sourceStart":48082,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":48086,"sourceStart":48085,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Mea... | [] | [{"source":"ae_ball_iff t_count","source_end":48105,"source_start":48086,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 14 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 235ed6bc4b60ea2383609b58105b4190e3e050b403e13091dc6224f5a373da56 | e42029bf155d1d190adc1d4622f021645f0cea3522f09d5a28e8d580e4f60b73 | c1bd3eb831d3e36b0c8449376cd24de3d4c6ce2612fc51c83de68fb51daf6e27 | d1038bcfe33b2e39ba4feff04e95a55ac5570b3092a217493e89015181dc6a5e |
cat-searcher/leandojo-benchmark-4-random | test | 3,510 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | revert x | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | (:forall i (:fv _uniq.280317) (:forall hi ((:c Membership.mem) (:fv _uniq.280317) ((:c Set) (:fv _uniq.280317)) ((:c Set.instMembership) (:fv _uniq.280317)) 0 (:fv _uniq.283066)) ((:c Filter.Eventually) (:fv _uniq.280238) (:lambda x (:fv _uniq.280238) ((:c Filter.Tendsto) ((:c Set) (:fv _uniq.280238)) (:c ENNReal) (:la... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:forall i :explicit (:fv FV5) (:forall hi :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"revert","sourceEnd":48114,"sourceStart":48108,"tag":"atom"},{"children":[{"contextIndex":20,"semanticRole":"local","source":"x","sourceEnd":48116,"sourceStart":48115,"tag":"identifier"}],"kind":"null","source":"x","sourceEnd":48116,"sourceStart":48115,"tag":"node"}],"kind":"Lean.Parser.Tactic.re... | [] | [{"source":"x","source_end":48116,"source_start":48115,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 18 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eef59e983db1210e95a4a1cc6cc207ce13ce5eb4a2b963f9c305062292499df8 | d1038bcfe33b2e39ba4feff04e95a55ac5570b3092a217493e89015181dc6a5e | 0dda27fc5d89b467314f9ce033a63894e7fa64b810dcf3a502e0d3785a378cd0 | bcaa7a54ed988090cae0e3ba2816221560fc3777134e37d8cd7ef5d9e57dab9f |
cat-searcher/leandojo-benchmark-4-random | test | 3,511 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro n c _ | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | (:forall x (:c Nat) (:forall i (:fv _uniq.280317) (:forall hi ((:c Membership.mem) (:fv _uniq.280317) ((:c Set) (:fv _uniq.280317)) ((:c Set.instMembership) (:fv _uniq.280317)) 0 (:fv _uniq.283066)) ((:c Filter.Eventually) (:fv _uniq.280238) (:lambda x (:fv _uniq.280238) ((:c Filter.Tendsto) ((:c Set) (:fv _uniq.280238... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:forall x :explicit (:c Nat) (:forall i :explicit (:fv FV5) (:forall hi :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"intro","sourceEnd":48126,"sourceStart":48121,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"n","sourceEnd":48128,"sourceStart":48127,"tag":"identifier"},{"semanticRole":"scoped_local","source":"c","sourceEnd":48130,"sourceStart":48129,"tag":"identifier"},{"children":[{"sourc... | [{"role":"fresh_name","source":"n","source_end":48128,"source_start":48127,"syntax_kind":"ident"},{"role":"fresh_name","source":"c","source_end":48130,"source_start":48129,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 19 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dd6dbc1329831f72c0dacda5a328928c563f2ff6caa4c21c25f9ee36d48934a8 | bcaa7a54ed988090cae0e3ba2816221560fc3777134e37d8cd7ef5d9e57dab9f | c3e9175823cda7b012a68fd46c343240fe553194adcda0f78b500b072b3ad6ef | 28f5daff2ee7fea7aeb1c30ed6a01d6df5f23b85fa73e3f6df2d49b28d9f4ca2 |
cat-searcher/leandojo-benchmark-4-random | test | 3,512 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>VitaliFamily.ae_tendsto_lintegral_div'</a> | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | case hf
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : Str... | ((:c Filter.Eventually) (:fv _uniq.280238) (:lambda x (:fv _uniq.280238) ((:c Filter.Tendsto) ((:c Set) (:fv _uniq.280238)) (:c ENNReal) (:lambda a ((:c Set) (:fv _uniq.280238)) ((:c HDiv.hDiv) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHDiv) (:c ENNReal) ((:c DivInvMonoid.toDiv) (:c ENNReal) (:c ENNReal.instDivIn... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:lambda a :explicit (:app (:c Set) (:arg :explicit 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"apply","sourceEnd":48142,"sourceStart":48137,"tag":"atom"},{"name":"VitaliFamily.ae_tendsto_lintegral_div'","semanticRole":"global","source":"ae_tendsto_lintegral_div'","sourceEnd":48168,"sourceStart":48143,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply ae_tendsto_lintegr... | [] | [{"source":"ae_tendsto_lintegral_div'","source_end":48168,"source_start":48143,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 20 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d6d8f60b1ba1ffef6828d5bf901982f410301d5c6c09c9f96ca0607180edf72c | 28f5daff2ee7fea7aeb1c30ed6a01d6df5f23b85fa73e3f6df2d49b28d9f4ca2 | 770ba2b4a7ac61918b459c3a5e00a10b35a9aee0e7c998020d805c84c25cc22c | 216b2c4cf053da0fbcaf60a218f520104f9a39c3cb63adba648a3b2976bf847b |
cat-searcher/leandojo-benchmark-4-random | test | 3,513 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (h'f.sub ?_).<a>MeasureTheory.StronglyMeasurable.ennnorm</a> | case hf
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : Str... | case hf
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : Str... | ((:c Measurable) (:fv _uniq.280238) (:c ENNReal) (:fv _uniq.280244) (:c ENNReal.measurableSpace) (:lambda y (:fv _uniq.280238) ((:c ENNReal.ofNNReal) ((:c NNNorm.nnnorm) (:fv _uniq.280317) ((:c SeminormedAddGroup.toNNNorm) (:fv _uniq.280317) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) (:fv _uniq.280317) ((:c Norm... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Measurable) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 4 (:lambda y :explicit (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"refine","sourceEnd":48182,"sourceStart":48176,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":48184,"sourceStart":48183,"tag":"atom"},{"children":[{"source":"h'f.sub","sourceEnd":48191,"sourceStart":48184,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":4... | [] | [{"source":"(h'f.sub ?_).ennnorm","source_end":48203,"source_start":48183,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 25 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1569a00f0f7a4d0789b298fac465952afc601b668e1a3b7d3e612091d2d10bf9 | e292806f56006ed01ecfce7fe0f936f60ad3fbe5cda230eebdf706b19d84d6e7 | c84a866b840cfa04889973e02cb314cce17a9d8853941240c6e21b446a203f87 | df6ee25e777a7bf3e33b295faa2d0f012806d1d812e331e08366a5667021d161 |
cat-searcher/leandojo-benchmark-4-random | test | 3,514 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact stronglyMeasurable_const.indicator (<a>IsOpen.measurableSet</a> (A.set_mem n)) | case hf
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : Str... | ((:c MeasureTheory.StronglyMeasurable) (:fv _uniq.280238) (:fv _uniq.280317) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.280317) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.280317) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:fv _uniq.280317) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c MeasureTheory.StronglyMeasurable) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV5)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 3 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 4 (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"exact","sourceEnd":48215,"sourceStart":48210,"tag":"atom"},{"children":[{"source":"stronglyMeasurable_const.indicator","sourceEnd":48250,"sourceStart":48216,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":48252,"sourceStart":48251,"tag":"atom"},{"children":[{"name":"IsOpe... | [] | [{"source":"stronglyMeasurable_const.indicator (IsOpen.measurableSet (A.set_mem n))","source_end":48287,"source_start":48216,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 26 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c48daa6e886465aa5bd127901b3bf38c1961aac11ba056f7c1e4ad515eecfcfc | df6ee25e777a7bf3e33b295faa2d0f012806d1d812e331e08366a5667021d161 | 2da17d054b5f0a7cf2db4a255f621a616faf31e11272029670f7f17082c7dfb4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,515 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>ne_of_lt</a> | case h'f
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : St... | case h'f.h
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : ... | ((:c Ne) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.280238) (:fv _uniq.280244) (:fv _uniq.280253) (:lambda y (:fv _uniq.280238) ((:c ENNReal.ofNNReal) ((:c NNNorm.nnnorm) (:fv _uniq.280317) ((:c SeminormedAddGroup.toNNNorm) (:fv _uniq.280317) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) (:fv _uniq.28031... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Ne) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:lambda y :explicit (:fv FV0) (:app (:c ENNReal.ofNNReal) (:arg :explicit 0 (:app (:c NNNorm.nnnorm) (:arg :implici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"apply","sourceEnd":48300,"sourceStart":48295,"tag":"atom"},{"name":"ne_of_lt","semanticRole":"global","source":"ne_of_lt","sourceEnd":48309,"sourceStart":48301,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply ne_of_lt","sourceEnd":48309,"sourceStart":48295,"tag":"node"} | [] | [{"source":"ne_of_lt","source_end":48309,"source_start":48301,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 31 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cb3589866145946a5db78142fb9c6bc12c8ac536da077b8bfbbf0ac855d2b8fa | 3d251e3f825c5265439f6657b2d67c8315aa40d3d5eebbd669308d8b01819086 | ff746657b76581816553add00d0109442af37a62bc89d9c7031212fb3dc982ef | a0e14067e1ea5eefbe3dad095945b4b5e0da108322803bc30bedd031f6a8fac9 |
cat-searcher/leandojo-benchmark-4-random | test | 3,516 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | calc (∫⁻ y, ↑‖f y - (A.set n).<a>Set.indicator</a> (fun _ : α => c) y‖₊ ∂μ) ≤ ∫⁻ y, ‖f y‖₊ + ‖(A.set n).<a>Set.indicator</a> (fun _ : α => c) y‖₊ ∂μ := by apply <a>MeasureTheory.lintegral_mono</a> intro x dsimp rw [← <a>ENNReal.coe_add</a>] exact <a>ENNReal.coe_le_coe</a>.2 (<a>nnnorm_sub_le</a> _ _) _ = (∫⁻ y, ‖f y‖₊ ... | case h'f.h
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : ... | ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:lambda y :explicit (:fv FV0) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"calc","sourceEnd":48320,"sourceStart":48316,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"(","sourceEnd":48330,"sourceStart":48329,"tag":"atom"},{"children":[{"source":"∫⁻","sourceEnd":48336,"sourceStart":48330,"tag":"atom"},{"children":[{"children":[{"children":[{... | [] | [{"source":"(∫⁻ y, ↑‖f y - (A.set n).indicator (fun _ : α => c) y‖₊ ∂μ) ≤\n ∫⁻ y, ‖f y‖₊ + ‖(A.set n).indicator (fun _ : α => c) y‖₊ ∂μ","source_end":48500,"source_start":48329,"syntax_kind":"«term_≤_»"},{"source":"lintegral_mono","source_end":48537,"source_start":48523,"syntax_kind":"ident"},{"source":"ENNR... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 32 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d5ddb674112ef45066d4847022ebcf7fa1793c1f5b39c24583feec9efc89b493 | a0e14067e1ea5eefbe3dad095945b4b5e0da108322803bc30bedd031f6a8fac9 | 88e01e11cce9211bef8b45aa8a45174cf7431cb58a83900864c4eedfa64808f9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,517 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>MeasureTheory.lintegral_mono</a> | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | case hfg
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : St... | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:lambda y :explicit (:fv FV0) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"apply","sourceEnd":48522,"sourceStart":48517,"tag":"atom"},{"name":"MeasureTheory.lintegral_mono","semanticRole":"global","source":"lintegral_mono","sourceEnd":48537,"sourceStart":48523,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply lintegral_mono","sourceEnd":48537,"sour... | [] | [{"source":"lintegral_mono","source_end":48537,"source_start":48523,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 37 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 35f9078c3464dec6eebcbf734be463c31258f1e21271d56f11f9908422fa5856 | f40f3e0870bd679b8fdfa8943eaed0f95d26174001d323990fc275ecec602a23 | 0ee5eb6e9de773ba71f6da0ce1ea7a200b12198f45ff8c685881d59e08c7309b | 2cb0c51709c066ddfd5fae89e96203b15f87be36eac07b55d17654e2ff6cbe4e |
cat-searcher/leandojo-benchmark-4-random | test | 3,518 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro x | case hfg
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : St... | case hfg
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : St... | ((:c LE.le) (:forall _ (:fv _uniq.280238) (:c ENNReal)) ((:c Pi.hasLe) (:fv _uniq.280238) (:lambda _ (:fv _uniq.280238) (:c ENNReal)) (:lambda i (:fv _uniq.280238) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:c ENNReal))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:forall i :explicit (:fv FV0) (:c ENNReal)))))) (:arg :explicit 2 (:lambda a :explicit (:fv FV0) (:app (:c ENNReal.ofNNReal) (:arg :explicit 0 (:app (:c NNNorm.nnnorm) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"intro","sourceEnd":48553,"sourceStart":48548,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":48555,"sourceStart":48554,"tag":"identifier"}],"kind":"null","source":"x","sourceEnd":48555,"sourceStart":48554,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"x","source_end":48555,"source_start":48554,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 38 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ab4a2cbba0f4adf97fa09fba6a52e403472cdb7a609a3088422158df00bc9feb | 2cb0c51709c066ddfd5fae89e96203b15f87be36eac07b55d17654e2ff6cbe4e | 727852cc0e84019aeee0e605b3833ee9bcd4d2abc203673e529dba747f5c5a0d | a7751511f4eaf58134b131fec10d3004773e9d30437dccf52a649b803cb58fba |
cat-searcher/leandojo-benchmark-4-random | test | 3,519 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp | case hfg
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : St... | case hfg
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : St... | ((:c LE.le) ((:lambda _ (:fv _uniq.280238) (:c ENNReal)) (:fv _uniq.291096)) ((:lambda i (:fv _uniq.280238) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c Comple... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:lambda _ :explicit (:fv FV0) (:c ENNReal)) (:arg :explicit 0 (:fv FV23)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:lambda a :explicit (:fv FV0) (:app (:c ENNReal.ofNNReal) (:arg :explicit 0 (:app (:c NNNor... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"dsimp","sourceEnd":48571,"sourceStart":48566,"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":[],"k... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 39 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9edce14b889a919e40c77141404f337aa7b1f430eaee29da9a0c439bbd441414 | a7751511f4eaf58134b131fec10d3004773e9d30437dccf52a649b803cb58fba | 7854eab90b5d1f0eed9d2f7f6b885100cc44bc732b41c876b3af083c01260845 | a80bc04a11ed954a718d50c7e14e1a7f78c347b503a4ae21abf10f9613ea6716 |
cat-searcher/leandojo-benchmark-4-random | test | 3,520 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>ENNReal.coe_add</a>] | case hfg
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : St... | case hfg
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : St... | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c ENNReal.ofNNReal) (:arg :explicit 0 (:app (:c NNNorm.nnnorm) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c NNNorm) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"rw","sourceEnd":48584,"sourceStart":48582,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":48586,"sourceStart":48585,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":48589,"sourceSt... | [] | [{"source":"ENNReal.coe_add","source_end":48605,"source_start":48590,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 40 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5bc8f6c08c70a6738a4ff31aae5dc5125ed26900e38ac78d5347d76c111b3632 | a80bc04a11ed954a718d50c7e14e1a7f78c347b503a4ae21abf10f9613ea6716 | 53b90bc35452773e70fb13edf7788b5ee1f121e96d584474807dc8a63b02c24c | 620b2d6dd9f20f8e15e75c6d1d2afa508b65f55b9698990a0c9793420cd3fdc2 |
cat-searcher/leandojo-benchmark-4-random | test | 3,521 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>ENNReal.coe_le_coe</a>.2 (<a>nnnorm_sub_le</a> _ _) | case hfg
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : St... | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c ENNReal.ofNNReal) (:arg :explicit 0 (:app (:c NNNorm.nnnorm) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c NNNorm) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"exact","sourceEnd":48622,"sourceStart":48617,"tag":"atom"},{"children":[{"children":[{"name":"ENNReal.coe_le_coe","semanticRole":"global","source":"ENNReal.coe_le_coe","sourceEnd":48641,"sourceStart":48623,"tag":"identifier"},{"source":".","sourceEnd":48642,"sourceStart":48641,"tag":"atom"},{"ch... | [] | [{"source":"ENNReal.coe_le_coe.2 (nnnorm_sub_le _ _)","source_end":48663,"source_start":48623,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 43 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8a1f107796c55bc2d595e8231b5103611b8b2473e8e6989418c9d28126f9cdfc | 620b2d6dd9f20f8e15e75c6d1d2afa508b65f55b9698990a0c9793420cd3fdc2 | 79508677b203134a781c84c03ef5198fc2b546a55c40a894b92cf0844f5f031f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,522 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>MeasureTheory.integrable_indicator_iff</a> (<a>IsOpen.measurableSet</a> (A.set_mem n)), <a>MeasureTheory.integrableOn_const</a>, A.finite n, <a>or_true_iff</a>] | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | ((:c MeasureTheory.Integrable) (:fv _uniq.280317) (:fv _uniq.280320) (:fv _uniq.280238) (:fv _uniq.280244) ((:c Set.indicator) (:fv _uniq.280238) (:fv _uniq.280317) ((:c NegZeroClass.toZero) (:fv _uniq.280317) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.280317) ((:c SubtractionMonoid.toSubNegZeroMonoid) (:fv _uniq... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c MeasureTheory.Integrable) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :implicit-type 2 (:fv FV0)) (:arg :implicit 3) (:arg :explicit 4 (:app (:c Set.indicator) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":48941,"sourceStart":48937,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":48946,"sourceStart":48942,"tag":"atom"}],"kind"... | [] | [{"source":"integrable_indicator_iff (IsOpen.measurableSet (A.set_mem n))","source_end":49009,"source_start":48948,"syntax_kind":"Lean.Parser.Term.app"},{"source":"integrableOn_const","source_end":49043,"source_start":49025,"syntax_kind":"ident"},{"source":"A.finite n","source_end":49055,"source_start":49045,"syntax_ki... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 46 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0e4d47e2c6b43a7559f356d0f0fe43b771b4b5788268b0bd0a3c4d765f5ab0ec | b3cb5009a0a38285824ccd23d20816e2e53e14bc380d1d6e4bf929b9df41570c | 6343b4987216557201362ea32c8a1b52e277c524d46546120e39b85e098036e9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,523 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro c hc | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | (:forall c (:fv _uniq.280317) (:forall _ ((:c Membership.mem) (:fv _uniq.280317) ((:c Set) (:fv _uniq.280317)) ((:c Set.instMembership) (:fv _uniq.280317)) 0 (:fv _uniq.283066)) ((:c Filter.Tendsto) ((:c Set) (:fv _uniq.280238)) (:c ENNReal) (:lambda a ((:c Set) (:fv _uniq.280238)) ((:c HDiv.hDiv) (:c ENNReal) (:c ENNR... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:forall c :explicit (:fv FV5) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"intro","sourceEnd":49329,"sourceStart":49324,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"c","sourceEnd":49331,"sourceStart":49330,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hc","sourceEnd":49334,"sourceStart":49332,"tag":"identifier"}],"kind":"null","sou... | [{"role":"fresh_name","source":"c","source_end":49331,"source_start":49330,"syntax_kind":"ident"},{"role":"fresh_name","source":"hc","source_end":49334,"source_start":49332,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 52 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fbfef9c0247742cccdb1424690dc6a4f82a7901371119cd72255885f9aa57287 | 75952aec5d7a4beaba42c1af9973258578abf2ef2591b3127819e54d2d5af93b | 3888a74e960ab3d4324ca5f0d5961b2b4deb2fecd8b94c89d5640d4e9a2eb8db | 83c7c461ad561881b12e64287047cba8c182842b974ea67767d42d59531e6e5a |
cat-searcher/leandojo-benchmark-4-random | test | 3,524 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨n, xn⟩ : ∃ n, x ∈ A.set n := by simpa [← A.spanning] using <a>Set.mem_univ</a> x | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | case intro
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : ... | ((:c Filter.Tendsto) ((:c Set) (:fv _uniq.280238)) (:c ENNReal) (:lambda a ((:c Set) (:fv _uniq.280238)) ((:c HDiv.hDiv) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHDiv) (:c ENNReal) ((:c DivInvMonoid.toDiv) (:c ENNReal) (:c ENNReal.instDivInvMonoid))) ((:c MeasureTheory.lintegral) (:fv _uniq.280238) (:fv _uniq.28... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:lambda a :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :im... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"obtain","sourceEnd":49345,"sourceStart":49339,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":49349,"sourceStart":49346,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"n","sourceEn... | [] | [{"source":"∃ n, x ∈ A.set n","source_end":49380,"source_start":49360,"syntax_kind":"«term∃_,_»"},{"source":"A.spanning","source_end":49408,"source_start":49398,"syntax_kind":"ident"},{"source":"mem_univ x","source_end":49426,"source_start":49416,"syntax_kind":"Lean.Parser.Term.app"},{"source":"obtain","source_end":493... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 53 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bee9a61b942625057b51376ed6dc047063a332498e8303f6858a889eab66a9ce | 83c7c461ad561881b12e64287047cba8c182842b974ea67767d42d59531e6e5a | ab29dd4889069a068b97587fe936a3e99fd1bb4ac5c9f2b0ab1eaf0be7a307a3 | 14407c4b91e1233f5656470c2d2e6503cffa64217249ce56d3167005b4dca0ec |
cat-searcher/leandojo-benchmark-4-random | test | 3,525 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | specialize hx n c hc | case intro
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : ... | case intro
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : ... | ((:c Filter.Tendsto) ((:c Set) (:fv _uniq.280238)) (:c ENNReal) (:lambda a ((:c Set) (:fv _uniq.280238)) ((:c HDiv.hDiv) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHDiv) (:c ENNReal) ((:c DivInvMonoid.toDiv) (:c ENNReal) (:c ENNReal.instDivInvMonoid))) ((:c MeasureTheory.lintegral) (:fv _uniq.280238) (:fv _uniq.28... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:lambda a :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :im... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"specialize","sourceEnd":49441,"sourceStart":49431,"tag":"atom"},{"children":[{"contextIndex":22,"semanticRole":"local","source":"hx","sourceEnd":49444,"sourceStart":49442,"tag":"identifier"},{"children":[{"contextIndex":26,"semanticRole":"local","source":"n","sourceEnd":49446,"sourceStart":49445... | [] | [{"source":"hx n c hc","source_end":49451,"source_start":49442,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 59 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 19a2d6c13bafc88c54dc5aff7883097274848e833666fb5541184663d60466ac | 14407c4b91e1233f5656470c2d2e6503cffa64217249ce56d3167005b4dca0ec | 681bd17708eb1bfb03eb649e4740561c66535994ec02df7930e9ab36a0be8272 | 60722ad08cd950d0705c9a04c85ecb20478884de98ad9b8fe84650c9cbb14d72 |
cat-searcher/leandojo-benchmark-4-random | test | 3,526 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [xn, <a>Set.indicator_of_mem</a>] at hx | case intro
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : ... | case intro
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : ... | ((:c Filter.Tendsto) ((:c Set) (:fv _uniq.280238)) (:c ENNReal) (:lambda a ((:c Set) (:fv _uniq.280238)) ((:c HDiv.hDiv) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHDiv) (:c ENNReal) ((:c DivInvMonoid.toDiv) (:c ENNReal) (:c ENNReal.instDivInvMonoid))) ((:c MeasureTheory.lintegral) (:fv _uniq.280238) (:fv _uniq.28... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:lambda a :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :im... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"simp","sourceEnd":49460,"sourceStart":49456,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":49465,"sourceStart":49461,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":494... | [] | [{"source":"xn","source_end":49469,"source_start":49467,"syntax_kind":"ident"},{"source":"indicator_of_mem","source_end":49487,"source_start":49471,"syntax_kind":"ident"},{"source":"hx","source_end":49494,"source_start":49492,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 60 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 898ceee99fabf0c5fe67a6f34f82be53db154b6bdc0f9c7b0bce9b8726fef2a3 | 60722ad08cd950d0705c9a04c85ecb20478884de98ad9b8fe84650c9cbb14d72 | 62e5e401d6bee9ce7b46660e73149ddede56d304ddd74e62e15d6ec87b16a725 | 1f485df0a0d91f9a17b7fe2416570bfed56d08f33e82eb66c8d31b5bfb4a6280 |
cat-searcher/leandojo-benchmark-4-random | test | 3,527 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply hx.congr' _ | case intro
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : ... | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | ((:c Filter.Tendsto) ((:c Set) (:fv _uniq.280238)) (:c ENNReal) (:lambda a ((:c Set) (:fv _uniq.280238)) ((:c HDiv.hDiv) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHDiv) (:c ENNReal) ((:c DivInvMonoid.toDiv) (:c ENNReal) (:c ENNReal.instDivInvMonoid))) ((:c MeasureTheory.lintegral) (:fv _uniq.280238) (:fv _uniq.28... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:lambda a :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :im... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"apply","sourceEnd":49504,"sourceStart":49499,"tag":"atom"},{"children":[{"source":"hx.congr'","sourceEnd":49514,"sourceStart":49505,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":49516,"sourceStart":49515,"tag":"atom"}],"kind":"Lean.Parser.Term.hole","source":"_","source... | [] | [{"source":"hx.congr' _","source_end":49516,"source_start":49505,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 61 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ab7f6751c4c8673c67e21b59b5880586c84d6baf71a47a54fcced8dfbd30593c | 1f485df0a0d91f9a17b7fe2416570bfed56d08f33e82eb66c8d31b5bfb4a6280 | dc2b3f4214408ec702c94a0aeac2865d3c2dfede0a7c00a6939de2a60e9f505f | 7a6d1427b2bc55ecd4b236890242722587e55af14273cdf1063b6514747fe6f5 |
cat-searcher/leandojo-benchmark-4-random | test | 3,528 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards [v.eventually_filterAt_subset_of_nhds (<a>IsOpen.mem_nhds</a> (A.set_mem n) xn), v.eventually_filterAt_measurableSet x] with a ha h'a | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | case h
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : Stro... | ((:c Filter.EventuallyEq) ((:c Set) (:fv _uniq.280238)) (:c ENNReal) ((:c VitaliFamily.filterAt) (:fv _uniq.280238) (:fv _uniq.280241) (:fv _uniq.280244) (:fv _uniq.280253) (:fv _uniq.280314) (:fv _uniq.292403)) (:lambda a ((:c Set) (:fv _uniq.280238)) ((:c HDiv.hDiv) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHDi... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:app (:c VitaliFamily.filterAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MetricSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :impl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"filter_upwards","sourceEnd":49535,"sourceStart":49521,"tag":"atom"},{"children":[{"source":"[","sourceEnd":49537,"sourceStart":49536,"tag":"atom"},{"children":[{"children":[{"source":"v.eventually_filterAt_subset_of_nhds","sourceEnd":49573,"sourceStart":49537,"tag":"identifier"},{"children":[{"c... | [] | [{"source":"v.eventually_filterAt_measurableSet x","source_end":49653,"source_start":49616,"syntax_kind":"Lean.Parser.Term.app"},{"source":"v.eventually_filterAt_subset_of_nhds (IsOpen.mem_nhds (A.set_mem n) xn)","source_end":49608,"source_start":49537,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 62 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 886aa296c9dce3bbf65ea6c5263aa54154db0c17bf2a1e9aae79e181ed1e36f3 | 7a6d1427b2bc55ecd4b236890242722587e55af14273cdf1063b6514747fe6f5 | 34f77baa6612df1da8ba10904c707999e24775bd16efbdcca48fc2c35cecd4f0 | fb6d0e9dacf924f280e70258f887a5358adc410c580c7c9c8ac3343823beea5c |
cat-searcher/leandojo-benchmark-4-random | test | 3,529 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr 1 | case h
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : Stro... | case h.e_a
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : ... | ((:c Eq) (:c ENNReal) ((:c HDiv.hDiv) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHDiv) (:c ENNReal) ((:c DivInvMonoid.toDiv) (:c ENNReal) (:c ENNReal.instDivInvMonoid))) ((:c MeasureTheory.lintegral) (:fv _uniq.280238) (:fv _uniq.280244) ((:c MeasureTheory.Measure.restrict) (:fv _uniq.280238) (:fv _uniq.280244) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:c ENNReal)) (:arg :explicit 1 (:c ENNReal)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"congr","sourceEnd":49678,"sourceStart":49673,"tag":"atom"},{"children":[{"children":[{"source":"1","sourceEnd":49680,"sourceStart":49679,"tag":"atom"}],"kind":"num","source":"1","sourceEnd":49680,"sourceStart":49679,"tag":"node"}],"kind":"null","source":"1","sourceEnd":49680,"sourceStart":49679,... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 63 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 962195d0c3588798e2eb231aa99b31dd3d2440f553b547ef457b991ba1641f6a | fb6d0e9dacf924f280e70258f887a5358adc410c580c7c9c8ac3343823beea5c | 8f6f3e102b5370312cdd673cdfe3acc12b0ae98d6a7b45eb025d5bd0bb778a5b | eff7eb9462f78e286c2641681f51f902af4433d4bfdfd5c442e58ba4bff1d230 |
cat-searcher/leandojo-benchmark-4-random | test | 3,530 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>MeasureTheory.setLIntegral_congr_fun</a> h'a | case h.e_a
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : ... | case h.e_a
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : ... | ((:c Eq) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.280238) (:fv _uniq.280244) ((:c MeasureTheory.Measure.restrict) (:fv _uniq.280238) (:fv _uniq.280244) (:fv _uniq.280253) (:fv _uniq.295526)) (:lambda y (:fv _uniq.280238) ((:c ENNReal.ofNNReal) ((:c NNNorm.nnnorm) (:fv _uniq.280317) ((:c SeminormedAddGroup.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure.restrict) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"apply","sourceEnd":49690,"sourceStart":49685,"tag":"atom"},{"children":[{"name":"MeasureTheory.setLIntegral_congr_fun","semanticRole":"global","source":"setLIntegral_congr_fun","sourceEnd":49713,"sourceStart":49691,"tag":"identifier"},{"children":[{"contextIndex":30,"semanticRole":"local","sourc... | [] | [{"source":"setLIntegral_congr_fun h'a","source_end":49717,"source_start":49691,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 64 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2beb21484a2ee551b55c3712b64e14fe4bb6e697bd4f04c9d063024466833287 | eff7eb9462f78e286c2641681f51f902af4433d4bfdfd5c442e58ba4bff1d230 | 8253ba6a8b02b12d8fe102ec9da153d4743c46ec1146055b5e0b719f19838288 | a07c3934327b47e0a1f14636896ae864f47e70e605ba290bfd201d3883895f8d |
cat-searcher/leandojo-benchmark-4-random | test | 3,531 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards with y hy using (by simp only [ha hy, <a>Set.indicator_of_mem</a>]) | case h.e_a
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : ... | ((:c Filter.Eventually) (:fv _uniq.280238) (:lambda x (:fv _uniq.280238) (:forall _ ((:c Membership.mem) (:fv _uniq.280238) ((:c Set) (:fv _uniq.280238)) ((:c Set.instMembership) (:fv _uniq.280238)) 0 (:fv _uniq.295526)) ((:c Eq) (:c ENNReal) ((:c ENNReal.ofNNReal) ((:c NNNorm.nnnorm) (:fv _uniq.280317) ((:c Seminormed... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"filter_upwards","sourceEnd":49736,"sourceStart":49722,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"with","sourceEnd":49741,"sourceStart":49737,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":49743,"sourceStart":49... | [] | [{"source":"ha hy","source_end":49773,"source_start":49768,"syntax_kind":"Lean.Parser.Term.app"},{"source":"indicator_of_mem","source_end":49791,"source_start":49775,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 65 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3a50cc38d18acb3f5883bec26a784dc2c39d5996afbb368bb7d964f70d549b9e | a07c3934327b47e0a1f14636896ae864f47e70e605ba290bfd201d3883895f8d | 3d5855bdc637cfebe7c77d157c048d933ab546cff771ecc5684a2c839b0068b4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,532 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [← A.spanning] using <a>Set.mem_univ</a> x | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | ((:c Exists) (:c Nat) (:lambda n (:c Nat) ((:c Membership.mem) (:fv _uniq.280238) ((:c Set) (:fv _uniq.280238)) ((:c Set.instMembership) (:fv _uniq.280238)) (:fv _uniq.292403) ((:c MeasureTheory.Measure.FiniteSpanningSetsIn.set) (:fv _uniq.280238) (:fv _uniq.280244) (:fv _uniq.280253) ((:c setOf) ((:c Set) (:fv _uniq.2... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":49392,"sourceStart":49387,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"A.spanning","source_end":49408,"source_start":49398,"syntax_kind":"ident"},{"source":"mem_univ x","source_end":49426,"source_start":49416,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 56 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7bc91b7784732d23edfa85ecd2f7217402296639c6695d422e608ae7466c0be0 | f0002351cacf4e2bc3cc9511a448db6c7798eb92b86fe07d00380d91af150c60 | b5dbef45fc393bab2fac51b94962a6548bb0d7a9c95050c79c7a12984e70a1fb | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,533 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [ha hy, <a>Set.indicator_of_mem</a>] | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | ((:c Eq) (:c ENNReal) ((:c ENNReal.ofNNReal) ((:c NNNorm.nnnorm) (:fv _uniq.280317) ((:c SeminormedAddGroup.toNNNorm) (:fv _uniq.280317) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) (:fv _uniq.280317) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.280317) (:fv _uniq.280320)))) ((:c HSub.hSub) (:fv _u... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c ENNReal.ofNNReal) (:arg :explicit 0 (:app (:c NNNorm.nnnorm) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c NNNorm) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":49761,"sourceStart":49757,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":49766,"sourceStart":49762,"tag":"atom"}],"kind"... | [] | [{"source":"ha hy","source_end":49773,"source_start":49768,"syntax_kind":"Lean.Parser.Term.app"},{"source":"indicator_of_mem","source_end":49791,"source_start":49775,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 68 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 29b90523429ae65170eda562660b195e6415eddbb5d52201037428c3aa19ae95 | 3fc4942b1a4388509cfe6f898f643ac77b53a96a7c98896ae081bac242ecc0a9 | a8356bfa0fc9d2b289cf46b0255486b8c1efc5fa9b1648db5dc1db9856c5e80e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,534 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [← <a>edist_eq_coe_nnnorm_sub</a>] | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | ((:c Exists) (:fv _uniq.280317) (:lambda c (:fv _uniq.280317) ((:c And) ((:c Membership.mem) (:fv _uniq.280317) ((:c Set) (:fv _uniq.280317)) ((:c Set.instMembership) (:fv _uniq.280317)) 0 (:fv _uniq.283066)) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c Omega... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:lambda c :explicit (:fv FV5) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"simp_rw","sourceEnd":49947,"sourceStart":49940,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":49949,"sourceStart":49948,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":49952,"sou... | [] | [{"source":"edist_eq_coe_nnnorm_sub","source_end":49976,"source_start":49953,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 77 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d330a9e210d013cb6f50905c88bb60996ce7b1380988dfb55c97fb7f96a520a0 | 5e5b88d43712bc858be6b10b6b22c8594fc05067ffdd095f113a2703f9b6b93d | c3f51eb0e0025bd570d1318cfd0dd4418c113174bd40d499e5b15be831bfdd90 | 36821a2c40f0f2d8420365cb482d3712f7886f31329a74a69889de25467e6951 |
cat-searcher/leandojo-benchmark-4-random | test | 3,535 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : f x ∈ <a>closure</a> t := ht (<a>Set.mem_range_self</a> _) | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | ((:c Exists) (:fv _uniq.280317) (:lambda c (:fv _uniq.280317) ((:c And) ((:c Membership.mem) (:fv _uniq.280317) ((:c Set) (:fv _uniq.280317)) ((:c Set.instMembership) (:fv _uniq.280317)) 0 (:fv _uniq.283066)) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c Omega... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:lambda c :explicit (:fv FV5) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"have","sourceEnd":49986,"sourceStart":49982,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":49987,"sourceStart":49987,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":49987,"sourceStart":49987,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"f x ∈ closure t","source_end":50006,"source_start":49989,"syntax_kind":"«term_∈_»"},{"source":"ht (mem_range_self _)","source_end":50031,"source_start":50010,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 80 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e1986d8b6f08e9bef728b5c7bee3e129c7499e30d317d03e7d926b437b223506 | 36821a2c40f0f2d8420365cb482d3712f7886f31329a74a69889de25467e6951 | db97b7331ba9042a6c2bc5a233aa73fa70986c9f50cbff4315ef3baeeff75665 | c7470a1d002db18c2ec564d302dea095467e318214b93e1945486db3e828d238 |
cat-searcher/leandojo-benchmark-4-random | test | 3,536 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>EMetric.mem_closure_iff</a>.1 this (ε / 2) (<a>ENNReal.half_pos</a> (<a>ne_of_gt</a> εpos)) | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | ((:c Exists) (:fv _uniq.280317) (:lambda c (:fv _uniq.280317) ((:c And) ((:c Membership.mem) (:fv _uniq.280317) ((:c Set) (:fv _uniq.280317)) ((:c Set.instMembership) (:fv _uniq.280317)) 0 (:fv _uniq.283066)) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c Omega... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:lambda c :explicit (:fv FV5) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"exact","sourceEnd":50041,"sourceStart":50036,"tag":"atom"},{"children":[{"children":[{"name":"EMetric.mem_closure_iff","semanticRole":"global","source":"EMetric.mem_closure_iff","sourceEnd":50065,"sourceStart":50042,"tag":"identifier"},{"source":".","sourceEnd":50066,"sourceStart":50065,"tag":"a... | [] | [{"source":"EMetric.mem_closure_iff.1 this (ε / 2) (ENNReal.half_pos (ne_of_gt εpos))","source_end":50117,"source_start":50042,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 81 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 02c49482c986bdb80ce0ba259c037f1dccdc82bacb4cf8ff79b77af91aadd859 | c7470a1d002db18c2ec564d302dea095467e318214b93e1945486db3e828d238 | f39c2b15dee74940198cb793a25d9267a66fbae7ea7358167cf6d123335eee7e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,537 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>MeasureTheory.lintegral_mono</a> fun x => ?_ | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure.restrict) (:arg :implicit-typ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"apply","sourceEnd":50401,"sourceStart":50396,"tag":"atom"},{"children":[{"name":"MeasureTheory.lintegral_mono","semanticRole":"global","source":"lintegral_mono","sourceEnd":50416,"sourceStart":50402,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":50420,"sourceStart":504... | [] | [{"source":"lintegral_mono fun x => ?_","source_end":50428,"source_start":50402,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 89 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 61fa2ece9a250bca6a8dc32e4cb4193fd27ff7366281dbdb8c509ddea7289c4b | bfb72f7f9dde4dff933e0223e767a6a08f0c5090298a343bebef25833968f996 | c8f03e52f0814ab73bfdee03a1e6631947f8277bedc9e1e9bfa75211ca5d50d7 | 9fb74f9836dffac4ddded74d06df1d9e614e3748607f6bb03fdd8da92e5ea0a9 |
cat-searcher/leandojo-benchmark-4-random | test | 3,538 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [← <a>edist_eq_coe_nnnorm_sub</a>] using <a>edist_triangle_right</a> _ _ _ | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | ((:c LE.le) ((:lambda _ (:fv _uniq.280238) (:c ENNReal)) (:fv _uniq.303369)) ((:lambda i (:fv _uniq.280238) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c Comple... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:lambda _ :explicit (:fv FV0) (:c ENNReal)) (:arg :explicit 0 (:fv FV34)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c ENNReal.ofNNReal) (:arg :explicit 0 (:app (:c NNNorm.nnnorm) (:arg :implicit-type 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"simpa","sourceEnd":50440,"sourceStart":50435,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"ch... | [] | [{"source":"edist_eq_coe_nnnorm_sub","source_end":50474,"source_start":50451,"syntax_kind":"ident"},{"source":"edist_triangle_right _ _ _","source_end":50508,"source_start":50482,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 90 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 12311c7105459a2e6aa6c4266a08225672443eef72348f51009249b809b9b6bc | 9fb74f9836dffac4ddded74d06df1d9e614e3748607f6bb03fdd8da92e5ea0a9 | 487eec665baae401fadf7def267f2cd6f88645785a147ec4211b735207c5365f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,539 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | case h₁
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : Str... | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"gcongr","sourceEnd":50705,"sourceStart":50699,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":50705,"sourceStart":50699,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 95 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5cd36a8f958624a8cf9ca05b4c02c98b850004e6bad4f8c44467438faf6a26c0 | b01cc090078250c653acd287b80999672646781359de19462dbf890b2c39062d | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | 93234c45259ec9dcf177ca74f0f78f55ccf26969d5f8d7f745b4fb3781af73a5 |
cat-searcher/leandojo-benchmark-4-random | test | 3,540 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>ENNReal.div_lt_iff</a> (<a>Or.inl</a> h'a.ne') (<a>Or.inl</a> h''a.ne)] at ha | case h₁
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : Str... | case h₁
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : Str... | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure.restrict) (:arg :implicit-typ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"rw","sourceEnd":50717,"sourceStart":50715,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":50719,"sourceStart":50718,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"ENN... | [] | [{"source":"ha","source_end":50778,"source_start":50776,"syntax_kind":"ident"},{"source":"ENNReal.div_lt_iff (Or.inl h'a.ne') (Or.inl h''a.ne)","source_end":50771,"source_start":50719,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 100 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 178b11f61b82b058446243c9fc88428d87fb63cdc12a8e139f750b12cddc0210 | a57c0e756d516382e48d9daa6af620134b6f4b5935d108ee508ad3608fecd64f | 4effca8edc83c4a1f8170a0d61a793a626a5d3c46b42e86ad367bd2d822d3f13 | 01c2ed861697cf9b8d62ea9cc5f8408b4c85274d1b97ea5d0745f673f44ce172 |
cat-searcher/leandojo-benchmark-4-random | test | 3,541 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ha.le | case h₁
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : Str... | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure.restrict) (:arg :implicit-typ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"exact","sourceEnd":50792,"sourceStart":50787,"tag":"atom"},{"name":"LT.lt.le","semanticRole":"global","source":"ha.le","sourceEnd":50798,"sourceStart":50793,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact ha.le","sourceEnd":50798,"sourceStart":50787,"tag":"node"} | [] | [{"source":"ha.le","source_end":50798,"source_start":50793,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 103 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cf9fe08d9d2f7aeec6124cfb7fee795c25924ab84eed61df8e721a17999b4250 | 01c2ed861697cf9b8d62ea9cc5f8408b4c85274d1b97ea5d0745f673f44ce172 | 8d948d2fdf9a43962f70f6ff583f3c9d363b1dbee4ef81ce358b60b3e8303ab2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,542 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>MeasureTheory.lintegral_const</a>, <a>MeasureTheory.Measure.restrict_apply</a>, <a>MeasurableSet.univ</a>, <a>Set.univ_inter</a>] | case h₂
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : Str... | case h₂
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : Str... | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure.restrict) (:arg :implicit-typ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"simp","sourceEnd":50812,"sourceStart":50808,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":50817,"sourceStart":50813,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":508... | [] | [{"source":"lintegral_const","source_end":50834,"source_start":50819,"syntax_kind":"ident"},{"source":"Measure.restrict_apply","source_end":50858,"source_start":50836,"syntax_kind":"ident"},{"source":"MeasurableSet.univ","source_end":50878,"source_start":50860,"syntax_kind":"ident"},{"source":"univ_inter","source_end":... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 108 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c530c299b275e13d35ab27bfc332e7fd383d4bd38d15c11947fa59ecd0a96bfc | 49e6af45d2ebe6642132a67c42907435ac1d8f0455de160c788e2fb114e57e3b | d74b532df451f1779d4627c2b7db396eb613b3685dea5b5793a4c72fecfc0657 | 78bbbeb6b7f4c616f4005f753374f5d72e55b981853665ecc97a02462cab52c2 |
cat-searcher/leandojo-benchmark-4-random | test | 3,543 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | case h₂
α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : Str... | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"source":"gcongr","sourceEnd":50906,"sourceStart":50900,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":50906,"sourceStart":50900,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 109 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 13c2326a343062420db70343b83655974a7f66103f08dcad72b31cb92a35d489 | 78bbbeb6b7f4c616f4005f753374f5d72e55b981853665ecc97a02462cab52c2 | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,544 | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div'_of_integrable | Mathlib/MeasureTheory/Covering/Differentiation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>add_mul</a>, <a>ENNReal.add_halves</a>] | α : Type u_1
inst✝⁵ : MetricSpace α
m0 : MeasurableSpace α
μ : Measure α
v : VitaliFamily μ
E : Type u_2
inst✝⁴ : NormedAddCommGroup E
inst✝³ : SecondCountableTopology α
inst✝² : BorelSpace α
inst✝¹ : IsLocallyFiniteMeasure μ
ρ : Measure α
inst✝ : IsLocallyFiniteMeasure ρ
f : α → E
hf : Integrable f μ
h'f : StronglyMea... | ((:c Eq) (:c ENNReal) ((:c HAdd.hAdd) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHAdd) (:c ENNReal) ((:c Distrib.toAdd) (:c ENNReal) ((:c NonUnitalNonAssocSemiring.toDistrib) (:c ENNReal) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:c ENNReal) ((:c Semiring.toNonAssocSemiring) (:c ENNReal) ((:c OrderedSemi... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c MetricSpace) (:fv _uniq.280238))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.280238))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.280238) (:fv _uniq.280244))"},{"name":"v","sexp":"((:c VitaliFamily) (:fv _uniq.280238) (:... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c ENNReal)) (:arg :explicit 1 (:c ENNReal)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c MetricSpace) (:arg :e... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":50933,"sourceStart":50931,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":50935,"sourceStart":50934,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"add_mul","source_end":50946,"source_start":50939,"syntax_kind":"ident"},{"source":"ENNReal.add_halves","source_end":50966,"source_start":50948,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280238","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.280241","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 66 | 112 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f02203a45580ea7b3085c06742005e9a52083aaa4462893b9206bf301d9ccd62 | df2bf393aac0af1eb8e4b3794af6edd73cff5d561e155aff7f209a29d2a79ac4 | a44a5b3b8c0f2310f750eac0ced9ed8f98e989beb04202bea8cc7c61d51e17a5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,545 | Units.mul_right_eq_zero | Mathlib/Algebra/GroupWithZero/Units/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using <a>mul_eq_zero_of_right</a> (↑u⁻¹) h | α : Type u_1
M₀ : Type u_2
G₀ : Type u_3
M₀' : Type u_4
G₀' : Type u_5
F : Type u_6
F' : Type u_7
inst✝ : MonoidWithZero M₀
u : M₀ˣ
a : M₀
h : ↑u * a = 0
⊢ a = 0 | ((:c Eq) (:fv _uniq.1411) (:fv _uniq.1755) ((:c OfNat.ofNat) (:fv _uniq.1411) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.1411) ((:c MonoidWithZero.toZero) (:fv _uniq.1411) (:fv _uniq.1429))))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"M₀","sexp":"(:sort (+ u_2 1))"},{"name":"G₀","sexp":"(:sort (+ u_3 1))"},{"name":"M₀'","sexp":"(:sort (+ u_4 1))"},{"name":"G₀'","sexp":"(:sort (+ u_5 1))"},{"name":"F","sexp":"(:sort (+ u_6 1))"},{"name":"F'","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝","sexp":"((:c Mon... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV10)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:lit 0)))))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1408","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1411","is_instance":false,"is_let":false,"name":"M₀","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":1677,"sourceStart":1672,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"mul_eq_zero_of_right (↑u⁻¹) h","source_end":1718,"source_start":1684,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1408","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1411","is_instance":false,"is_let":false,"user_name":"M₀"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 11 | 2 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e38276fcdb5f58f7d869c272ccbd4cfbdf840051ced6cc4fc021b08c6d243713 | 995bcc5374c589a26fa66851d52ed0eaaad655dd3bb77af9948658aafdb92262 | 3fbd8bfea13c804a2a22f4283f27e750e473071520ddfafd945ffc8e567150a6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,546 | Seminorm.finset_sup_le_sum | Mathlib/Analysis/Seminorm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | classical refine Finset.sup_le_iff.mpr ?_ intro i hi rw [<a>Finset.sum_eq_sum_diff_singleton_add</a> hi, <a>le_add_iff_nonneg_left</a>] exact <a>bot_le</a> | R : Type u_1
R' : Type u_2
𝕜 : Type u_3
𝕜₂ : Type u_4
𝕜₃ : Type u_5
𝕝 : Type u_6
E : Type u_7
E₂ : Type u_8
E₃ : Type u_9
F : Type u_10
G : Type u_11
ι : Type u_12
inst✝¹⁸ : SeminormedRing 𝕜
inst✝¹⁷ : SeminormedRing 𝕜₂
inst✝¹⁶ : SeminormedRing 𝕜₃
σ₁₂ : 𝕜 →+* 𝕜₂
inst✝¹⁵ : RingHomIsometric σ₁₂
σ₂₃ : 𝕜₂ →+* 𝕜₃
... | ((:c LE.le) ((:c Seminorm) (:fv _uniq.330814) (:fv _uniq.330826) (:fv _uniq.330844) ((:c AddCommGroup.toAddGroup) (:fv _uniq.330826) (:fv _uniq.334210)) ((:c SMulZeroClass.toSMul) (:fv _uniq.330814) (:fv _uniq.330826) ((:c NegZeroClass.toZero) (:fv _uniq.330826) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.330826) ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R'","sexp":"(:sort (+ u_2 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜₂","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜₃","sexp":"(:sort (+ u_5 1))"},{"name":"𝕝","sexp":"(:sort (+ u_6 1))"},{"name":"E","sexp":"(:sort (+ u_7 1))"},{"name":"E₂","sexp":"(:sort (+ u... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Seminorm) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV6)) (:arg :instance 2 (:instance-of (:app (:c SeminormedRing) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 3 (:instance-of (:app (:c AddGroup) (:arg :explicit 0 (:fv FV6))))) (:arg :instance 4 (:instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.330808","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.330811","is_instance":false,"is_let":false,"name":"R'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"children":[{"children":[{"children":[{"source":"classical","sourceEnd":15895,"sourceStart":15886,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"refine","sourceEnd":15904,"sourceStart":15898,"tag":"atom"},{"children":[{"source":"Finset.sup_le_iff.mpr","sourceEnd":15926,"sourc... | [] | [{"source":"Finset.sup_le_iff.mpr ?_","source_end":15929,"source_start":15905,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Finset.sum_eq_sum_diff_singleton_add hi","source_end":15988,"source_start":15949,"syntax_kind":"Lean.Parser.Term.app"},{"source":"le_add_iff_nonneg_left","source_end":16012,"source_start":15990... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.330808","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.330811","is_instance":false,"is_let":false,"user_name":"R'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 123 | 2 | exact | true | 1 | 36 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 92fcd0252f83f0e61392e2aa0150451206ed8de2780c605d08a76177524baa87 | 7a1f2eccf49ac8fcec8e6edef078a884ffe77609c6ed597de661d23d2506d0a8 | 491d50db25f3f584893db6d37cde926352367282a2114a5f1521e7aa714f4f88 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,547 | Seminorm.finset_sup_le_sum | Mathlib/Analysis/Seminorm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine Finset.sup_le_iff.mpr ?_ | R : Type u_1
R' : Type u_2
𝕜 : Type u_3
𝕜₂ : Type u_4
𝕜₃ : Type u_5
𝕝 : Type u_6
E : Type u_7
E₂ : Type u_8
E₃ : Type u_9
F : Type u_10
G : Type u_11
ι : Type u_12
inst✝¹⁸ : SeminormedRing 𝕜
inst✝¹⁷ : SeminormedRing 𝕜₂
inst✝¹⁶ : SeminormedRing 𝕜₃
σ₁₂ : 𝕜 →+* 𝕜₂
inst✝¹⁵ : RingHomIsometric σ₁₂
σ₂₃ : 𝕜₂ →+* 𝕜₃
... | R : Type u_1
R' : Type u_2
𝕜 : Type u_3
𝕜₂ : Type u_4
𝕜₃ : Type u_5
𝕝 : Type u_6
E : Type u_7
E₂ : Type u_8
E₃ : Type u_9
F : Type u_10
G : Type u_11
ι : Type u_12
inst✝¹⁸ : SeminormedRing 𝕜
inst✝¹⁷ : SeminormedRing 𝕜₂
inst✝¹⁶ : SeminormedRing 𝕜₃
σ₁₂ : 𝕜 →+* 𝕜₂
inst✝¹⁵ : RingHomIsometric σ₁₂
σ₂₃ : 𝕜₂ →+* 𝕜₃
... | ((:c LE.le) ((:c Seminorm) (:fv _uniq.330814) (:fv _uniq.330826) (:fv _uniq.330844) ((:c AddCommGroup.toAddGroup) (:fv _uniq.330826) (:fv _uniq.334210)) ((:c SMulZeroClass.toSMul) (:fv _uniq.330814) (:fv _uniq.330826) ((:c NegZeroClass.toZero) (:fv _uniq.330826) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.330826) ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R'","sexp":"(:sort (+ u_2 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜₂","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜₃","sexp":"(:sort (+ u_5 1))"},{"name":"𝕝","sexp":"(:sort (+ u_6 1))"},{"name":"E","sexp":"(:sort (+ u_7 1))"},{"name":"E₂","sexp":"(:sort (+ u... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Seminorm) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV6)) (:arg :instance 2 (:instance-of (:app (:c SeminormedRing) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 3 (:instance-of (:app (:c AddGroup) (:arg :explicit 0 (:fv FV6))))) (:arg :instance 4 (:instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.330808","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.330811","is_instance":false,"is_let":false,"name":"R'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"refine","sourceEnd":15904,"sourceStart":15898,"tag":"atom"},{"children":[{"source":"Finset.sup_le_iff.mpr","sourceEnd":15926,"sourceStart":15905,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":15928,"sourceStart":15927,"tag":"atom"},{"children":[{"source":"_","sourceEnd":... | [] | [{"source":"Finset.sup_le_iff.mpr ?_","source_end":15929,"source_start":15905,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.330808","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.330811","is_instance":false,"is_let":false,"user_name":"R'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 123 | 7 | exact | true | 1 | 36 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c6b29a233094a1715f46a360424b590fab1b86a8bebc12141ac36a8a528a1b2c | 7a1f2eccf49ac8fcec8e6edef078a884ffe77609c6ed597de661d23d2506d0a8 | afedafc6848678f2e6ee19375b55835e9bb0a591446164424a9068a024c9bfeb | f1a811a5591a19558090011227c049aec7995def916e9a66826fdd0cba971add |
cat-searcher/leandojo-benchmark-4-random | test | 3,548 | Seminorm.finset_sup_le_sum | Mathlib/Analysis/Seminorm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro i hi | R : Type u_1
R' : Type u_2
𝕜 : Type u_3
𝕜₂ : Type u_4
𝕜₃ : Type u_5
𝕝 : Type u_6
E : Type u_7
E₂ : Type u_8
E₃ : Type u_9
F : Type u_10
G : Type u_11
ι : Type u_12
inst✝¹⁸ : SeminormedRing 𝕜
inst✝¹⁷ : SeminormedRing 𝕜₂
inst✝¹⁶ : SeminormedRing 𝕜₃
σ₁₂ : 𝕜 →+* 𝕜₂
inst✝¹⁵ : RingHomIsometric σ₁₂
σ₂₃ : 𝕜₂ →+* 𝕜₃
... | R : Type u_1
R' : Type u_2
𝕜 : Type u_3
𝕜₂ : Type u_4
𝕜₃ : Type u_5
𝕝 : Type u_6
E : Type u_7
E₂ : Type u_8
E₃ : Type u_9
F : Type u_10
G : Type u_11
ι : Type u_12
inst✝¹⁸ : SeminormedRing 𝕜
inst✝¹⁷ : SeminormedRing 𝕜₂
inst✝¹⁶ : SeminormedRing 𝕜₃
σ₁₂ : 𝕜 →+* 𝕜₂
inst✝¹⁵ : RingHomIsometric σ₁₂
σ₂₃ : 𝕜₂ →+* 𝕜₃
... | (:forall b (:fv _uniq.330841) (:forall _ ((:c Membership.mem) (:fv _uniq.330841) ((:c Finset) (:fv _uniq.330841)) ((:c Finset.instMembership) (:fv _uniq.330841)) 0 (:fv _uniq.339962)) ((:c LE.le) ((:c Seminorm) (:fv _uniq.330814) (:fv _uniq.330826) (:fv _uniq.330844) ((:c AddCommGroup.toAddGroup) (:fv _uniq.330826) (:f... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R'","sexp":"(:sort (+ u_2 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜₂","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜₃","sexp":"(:sort (+ u_5 1))"},{"name":"𝕝","sexp":"(:sort (+ u_6 1))"},{"name":"E","sexp":"(:sort (+ u_7 1))"},{"name":"E₂","sexp":"(:sort (+ u... | (:forall b :explicit (:fv FV11) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV11)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV11)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV11)) (:arg :explicit 1 (:app (:c Finset) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.330808","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.330811","is_instance":false,"is_let":false,"name":"R'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"intro","sourceEnd":15937,"sourceStart":15932,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"i","sourceEnd":15939,"sourceStart":15938,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hi","sourceEnd":15942,"sourceStart":15940,"tag":"identifier"}],"kind":"null","sou... | [{"role":"fresh_name","source":"i","source_end":15939,"source_start":15938,"syntax_kind":"ident"},{"role":"fresh_name","source":"hi","source_end":15942,"source_start":15940,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.330808","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.330811","is_instance":false,"is_let":false,"user_name":"R'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 123 | 8 | exact | true | 1 | 36 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 64827748220cb0d39882037beb3b2b36298c164aaea1c52ad82beb56edfeca99 | f1a811a5591a19558090011227c049aec7995def916e9a66826fdd0cba971add | f8dc8efe385c2627ebbcb0000fbf509f2b0935edbac43a186e1157fab879513b | 6d2a9b5bdec9e4bfd18e219dbf6df08eaef0547d4f52cf6edddfbcc254789ae8 |
cat-searcher/leandojo-benchmark-4-random | test | 3,549 | Seminorm.finset_sup_le_sum | Mathlib/Analysis/Seminorm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.sum_eq_sum_diff_singleton_add</a> hi, <a>le_add_iff_nonneg_left</a>] | R : Type u_1
R' : Type u_2
𝕜 : Type u_3
𝕜₂ : Type u_4
𝕜₃ : Type u_5
𝕝 : Type u_6
E : Type u_7
E₂ : Type u_8
E₃ : Type u_9
F : Type u_10
G : Type u_11
ι : Type u_12
inst✝¹⁸ : SeminormedRing 𝕜
inst✝¹⁷ : SeminormedRing 𝕜₂
inst✝¹⁶ : SeminormedRing 𝕜₃
σ₁₂ : 𝕜 →+* 𝕜₂
inst✝¹⁵ : RingHomIsometric σ₁₂
σ₂₃ : 𝕜₂ →+* 𝕜₃
... | R : Type u_1
R' : Type u_2
𝕜 : Type u_3
𝕜₂ : Type u_4
𝕜₃ : Type u_5
𝕝 : Type u_6
E : Type u_7
E₂ : Type u_8
E₃ : Type u_9
F : Type u_10
G : Type u_11
ι : Type u_12
inst✝¹⁸ : SeminormedRing 𝕜
inst✝¹⁷ : SeminormedRing 𝕜₂
inst✝¹⁶ : SeminormedRing 𝕜₃
σ₁₂ : 𝕜 →+* 𝕜₂
inst✝¹⁵ : RingHomIsometric σ₁₂
σ₂₃ : 𝕜₂ →+* 𝕜₃
... | ((:c LE.le) ((:c Seminorm) (:fv _uniq.330814) (:fv _uniq.330826) (:fv _uniq.330844) ((:c AddCommGroup.toAddGroup) (:fv _uniq.330826) (:fv _uniq.334210)) ((:c SMulZeroClass.toSMul) (:fv _uniq.330814) (:fv _uniq.330826) ((:c NegZeroClass.toZero) (:fv _uniq.330826) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.330826) ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R'","sexp":"(:sort (+ u_2 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜₂","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜₃","sexp":"(:sort (+ u_5 1))"},{"name":"𝕝","sexp":"(:sort (+ u_6 1))"},{"name":"E","sexp":"(:sort (+ u_7 1))"},{"name":"E₂","sexp":"(:sort (+ u... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Seminorm) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV6)) (:arg :instance 2 (:instance-of (:app (:c SeminormedRing) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 3 (:instance-of (:app (:c AddGroup) (:arg :explicit 0 (:fv FV6))))) (:arg :instance 4 (:instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.330808","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.330811","is_instance":false,"is_let":false,"name":"R'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rw","sourceEnd":15947,"sourceStart":15945,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15949,"sourceStart":15948,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Fin... | [] | [{"source":"Finset.sum_eq_sum_diff_singleton_add hi","source_end":15988,"source_start":15949,"syntax_kind":"Lean.Parser.Term.app"},{"source":"le_add_iff_nonneg_left","source_end":16012,"source_start":15990,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.330808","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.330811","is_instance":false,"is_let":false,"user_name":"R'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 123 | 9 | exact | true | 1 | 38 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8f678ccc972c6d250e1c19b18b49ad12ddc9cfa2a5ab04e756fe31ffb48c0577 | 6d2a9b5bdec9e4bfd18e219dbf6df08eaef0547d4f52cf6edddfbcc254789ae8 | c05de4ea0b293de1ee7ff5bd47ebe4210b3a16115796ac6b540deda269713b95 | 381a24821306331314dde746b7a778b7585dd8b3d62a6e63ae7a269f079a070f |
cat-searcher/leandojo-benchmark-4-random | test | 3,550 | Seminorm.finset_sup_le_sum | Mathlib/Analysis/Seminorm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>bot_le</a> | R : Type u_1
R' : Type u_2
𝕜 : Type u_3
𝕜₂ : Type u_4
𝕜₃ : Type u_5
𝕝 : Type u_6
E : Type u_7
E₂ : Type u_8
E₃ : Type u_9
F : Type u_10
G : Type u_11
ι : Type u_12
inst✝¹⁸ : SeminormedRing 𝕜
inst✝¹⁷ : SeminormedRing 𝕜₂
inst✝¹⁶ : SeminormedRing 𝕜₃
σ₁₂ : 𝕜 →+* 𝕜₂
inst✝¹⁵ : RingHomIsometric σ₁₂
σ₂₃ : 𝕜₂ →+* 𝕜₃
... | ((:c LE.le) ((:c Seminorm) (:fv _uniq.330814) (:fv _uniq.330826) (:fv _uniq.330844) ((:c AddCommGroup.toAddGroup) (:fv _uniq.330826) (:fv _uniq.334210)) ((:c SMulZeroClass.toSMul) (:fv _uniq.330814) (:fv _uniq.330826) ((:c NegZeroClass.toZero) (:fv _uniq.330826) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.330826) ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R'","sexp":"(:sort (+ u_2 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜₂","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜₃","sexp":"(:sort (+ u_5 1))"},{"name":"𝕝","sexp":"(:sort (+ u_6 1))"},{"name":"E","sexp":"(:sort (+ u_7 1))"},{"name":"E₂","sexp":"(:sort (+ u... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Seminorm) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV6)) (:arg :instance 2 (:instance-of (:app (:c SeminormedRing) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 3 (:instance-of (:app (:c AddGroup) (:arg :explicit 0 (:fv FV6))))) (:arg :instance 4 (:instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.330808","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.330811","is_instance":false,"is_let":false,"name":"R'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"exact","sourceEnd":16021,"sourceStart":16016,"tag":"atom"},{"name":"bot_le","semanticRole":"global","source":"bot_le","sourceEnd":16028,"sourceStart":16022,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact bot_le","sourceEnd":16028,"sourceStart":16016,"tag":"node"} | [] | [{"source":"bot_le","source_end":16028,"source_start":16022,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.330808","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.330811","is_instance":false,"is_let":false,"user_name":"R'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 123 | 13 | exact | true | 1 | 38 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3898cec75c125ba39fe41a494cf572906d508de1a7f5b0cea5039a0cd0b7f1c3 | 381a24821306331314dde746b7a778b7585dd8b3d62a6e63ae7a269f079a070f | 0b84778eb43634774572cc5fdcd2eee145b1bb6cda062d060a8a38d314f85295 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,551 | LinearMap.trace_tensorProduct | Mathlib/LinearAlgebra/Trace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply (<a>LinearMap.compl₁₂_inj</a> (show <a>Function.Surjective</a> (<a>dualTensorHom</a> R M M) from (<a>dualTensorHomEquiv</a> R M M).<a>LinearEquiv.surjective</a>) (show <a>Function.Surjective</a> (<a>dualTensorHom</a> R N N) from (<a>dualTensorHomEquiv</a> R N N).<a>LinearEquiv.surjective</a>)).1 | R : Type u_1
inst✝¹² : CommRing R
M : Type u_2
inst✝¹¹ : AddCommGroup M
inst✝¹⁰ : Module R M
N : Type u_3
P : Type u_4
inst✝⁹ : AddCommGroup N
inst✝⁸ : Module R N
inst✝⁷ : AddCommGroup P
inst✝⁶ : Module R P
ι : Type u_5
inst✝⁵ : Module.Free R M
inst✝⁴ : Module.Finite R M
inst✝³ : Module.Free R N
inst✝² : Module.Finite ... | R : Type u_1
inst✝¹² : CommRing R
M : Type u_2
inst✝¹¹ : AddCommGroup M
inst✝¹⁰ : Module R M
N : Type u_3
P : Type u_4
inst✝⁹ : AddCommGroup N
inst✝⁸ : Module R N
inst✝⁷ : AddCommGroup P
inst✝⁶ : Module R P
ι : Type u_5
inst✝⁵ : Module.Free R M
inst✝⁴ : Module.Finite R M
inst✝³ : Module.Free R N
inst✝² : Module.Finite ... | ((:c Eq) ((:c LinearMap) (:fv _uniq.219472) (:fv _uniq.219472) ((:c CommSemiring.toSemiring) (:fv _uniq.219472) ((:c CommRing.toCommSemiring) (:fv _uniq.219472) (:fv _uniq.219475))) ((:c CommSemiring.toSemiring) (:fv _uniq.219472) ((:c CommRing.toCommSemiring) (:fv _uniq.219472) (:fv _uniq.219475))) ((:c RingHom.id) (:... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹²","sexp":"((:c CommRing) (:fv _uniq.219472))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c AddCommGroup) (:fv _uniq.219478))"},{"name":"inst✝¹⁰","sexp":"((:c Module) (:fv _uniq.219472) (:fv _uniq.219478) ((:c CommSemiring.toSemiring) (:... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 4 (:app (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.219472","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.219475","is_instance":true,"is_let":false,"name":"inst✝¹²","sexp":"(:app (:c CommRing) (:arg :exp... | {"children":[{"source":"apply","sourceEnd":10038,"sourceStart":10033,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":10044,"sourceStart":10043,"tag":"atom"},{"children":[{"name":"LinearMap.compl₁₂_inj","semanticRole":"global","source":"compl₁₂_inj","sourceEnd":10059,"sourceStart":10044,"tag":"identifi... | [] | [{"source":"(compl₁₂_inj (show Surjective (dualTensorHom R M M) from (dualTensorHomEquiv R M M).surjective)\n (show Surjective (dualTensorHom R N N) from (dualTensorHomEquiv R N N).surjective)).1","source_end":10236,"source_start":10043,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.219472","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.219475","is_instance":true,"is_let":false,"user_name":"inst✝¹²"},{"binder_role":":explicit","context_index":2,"int... | 65 | 4 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fe3d849becc85e64ffd0420677a8e661e636bb191fe3c5c994430d1cc09f5823 | 35dbbc29e18055d44d67d9744e7dc8dd9e3870a6cece57310f4bc17d63381d97 | 199a23f0f1caf0534cd15f01bdf74d7a76527e3cd61811ff74d766ad7351cef2 | b42a96dc22ed9d565aebeee7bbd303dec839915cfc24e35ade367b169a7d1fd3 |
cat-searcher/leandojo-benchmark-4-random | test | 3,552 | LinearMap.trace_tensorProduct | Mathlib/LinearAlgebra/Trace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext f m g n | R : Type u_1
inst✝¹² : CommRing R
M : Type u_2
inst✝¹¹ : AddCommGroup M
inst✝¹⁰ : Module R M
N : Type u_3
P : Type u_4
inst✝⁹ : AddCommGroup N
inst✝⁸ : Module R N
inst✝⁷ : AddCommGroup P
inst✝⁶ : Module R P
ι : Type u_5
inst✝⁵ : Module.Free R M
inst✝⁴ : Module.Finite R M
inst✝³ : Module.Free R N
inst✝² : Module.Finite ... | case a.h.h.a.h.h
R : Type u_1
inst✝¹² : CommRing R
M : Type u_2
inst✝¹¹ : AddCommGroup M
inst✝¹⁰ : Module R M
N : Type u_3
P : Type u_4
inst✝⁹ : AddCommGroup N
inst✝⁸ : Module R N
inst✝⁷ : AddCommGroup P
inst✝⁶ : Module R P
ι : Type u_5
inst✝⁵ : Module.Free R M
inst✝⁴ : Module.Finite R M
inst✝³ : Module.Free R N
inst✝²... | ((:c Eq) ((:c LinearMap) (:fv _uniq.219472) (:fv _uniq.219472) ((:c CommSemiring.toSemiring) (:fv _uniq.219472) ((:c CommRing.toCommSemiring) (:fv _uniq.219472) (:fv _uniq.219475))) ((:c CommSemiring.toSemiring) (:fv _uniq.219472) ((:c CommRing.toCommSemiring) (:fv _uniq.219472) (:fv _uniq.219475))) ((:c RingHom.id) (:... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹²","sexp":"((:c CommRing) (:fv _uniq.219472))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c AddCommGroup) (:fv _uniq.219478))"},{"name":"inst✝¹⁰","sexp":"((:c Module) (:fv _uniq.219472) (:fv _uniq.219478) ((:c CommSemiring.toSemiring) (:... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 4 (:app (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.219472","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.219475","is_instance":true,"is_let":false,"name":"inst✝¹²","sexp":"(:app (:c CommRing) (:arg :exp... | {"children":[{"source":"ext","sourceEnd":10242,"sourceStart":10239,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"f","sourceEnd":10244,"sourceStart":10243,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"f","sourceEnd":10244,"sourceStart":10243,"tag... | [{"role":"fresh_name","source":"f","source_end":10244,"source_start":10243,"syntax_kind":"ident"},{"role":"fresh_name","source":"m","source_end":10246,"source_start":10245,"syntax_kind":"ident"},{"role":"fresh_name","source":"g","source_end":10248,"source_start":10247,"syntax_kind":"ident"},{"role":"fresh_name","source... | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.219472","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.219475","is_instance":true,"is_let":false,"user_name":"inst✝¹²"},{"binder_role":":explicit","context_index":2,"int... | 65 | 5 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2f4edd635b0e8af710c3600f1802386eb07304e45d85212ba9c84f0f13f6bf71 | b42a96dc22ed9d565aebeee7bbd303dec839915cfc24e35ade367b169a7d1fd3 | 3e4ed8c0481ef3b1ae14eb966c321d134ad2c4e0a53dc00320e31238b38ce086 | 4156413008a73bb193ef863f307da42fd0cebaecca3a28b1098a1197449158bb |
cat-searcher/leandojo-benchmark-4-random | test | 3,553 | LinearMap.trace_tensorProduct | Mathlib/LinearAlgebra/Trace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>TensorProduct.AlgebraTensorModule.curry_apply</a>, <a>LinearMap.toFun_eq_coe</a>, <a>TensorProduct.curry_apply</a>, <a>LinearMap.coe_restrictScalars</a>, <a>LinearMap.compl₁₂_apply</a>, <a>LinearMap.compr₂_apply</a>, <a>TensorProduct.mapBilinear_apply</a>, <a>LinearMap.trace_eq_contract_apply</a>, <a>cont... | case a.h.h.a.h.h
R : Type u_1
inst✝¹² : CommRing R
M : Type u_2
inst✝¹¹ : AddCommGroup M
inst✝¹⁰ : Module R M
N : Type u_3
P : Type u_4
inst✝⁹ : AddCommGroup N
inst✝⁸ : Module R N
inst✝⁷ : AddCommGroup P
inst✝⁶ : Module R P
ι : Type u_5
inst✝⁵ : Module.Free R M
inst✝⁴ : Module.Finite R M
inst✝³ : Module.Free R N
inst✝²... | ((:c Eq) (:fv _uniq.219472) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.219472) (:fv _uniq.219472) ((:c CommSemiring.toSemiring) (:fv _uniq.219472) ((:c CommRing.toCommSemiring) (:fv _uniq.219472) (:fv _uniq.219475))) ((:c CommSemiring.toSemiring) (:fv _uniq.219472) ((:c CommRing.toCommSemiring) (:fv _uniq.219472) (:... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹²","sexp":"((:c CommRing) (:fv _uniq.219472))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c AddCommGroup) (:fv _uniq.219478))"},{"name":"inst✝¹⁰","sexp":"((:c Module) (:fv _uniq.219472) (:fv _uniq.219478) ((:c CommSemiring.toSemiring) (:... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.219472","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.219475","is_instance":true,"is_let":false,"name":"inst✝¹²","sexp":"(:app (:c CommRing) (:arg :exp... | {"children":[{"source":"simp","sourceEnd":10257,"sourceStart":10253,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":10262,"sourceStart":10258,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":102... | [] | [{"source":"AlgebraTensorModule.curry_apply","source_end":10295,"source_start":10264,"syntax_kind":"ident"},{"source":"toFun_eq_coe","source_end":10309,"source_start":10297,"syntax_kind":"ident"},{"source":"TensorProduct.curry_apply","source_end":10336,"source_start":10311,"syntax_kind":"ident"},{"source":"coe_restrict... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.219472","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.219475","is_instance":true,"is_let":false,"user_name":"inst✝¹²"},{"binder_role":":explicit","context_index":2,"int... | 65 | 6 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b1eece669f498a29cedffddcb563c9e4f85ec3e4aa475dddd3ef4bfc02c7acba | 4156413008a73bb193ef863f307da42fd0cebaecca3a28b1098a1197449158bb | 41757bd468a1b25179655730d56ae0cbd10a967099d99e58ac82e78c8afa0fe4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,554 | Finset.sum_pow' | Mathlib/Algebra/BigOperators/Ring.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert @<a>Finset.prod_univ_sum</a> (<a>Fin</a> n) _ _ _ _ _ (fun _i ↦ s) fun _i d ↦ f d | ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
κ : ι → Type u_5
s✝ s₁ s₂ : Finset ι
i : ι
a : α
f✝ g : ι → α
inst✝¹ : CommSemiring α
inst✝ : DecidableEq ι
s : Finset ι
f : ι → α
n : ℕ
⊢ (∑ a ∈ s, f a) ^ n = ∑ p ∈ piFinset fun _i => s, ∏ i : Fin n, f (p i) | case h.e'_2
ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
κ : ι → Type u_5
s✝ s₁ s₂ : Finset ι
i : ι
a : α
f✝ g : ι → α
inst✝¹ : CommSemiring α
inst✝ : DecidableEq ι
s : Finset ι
f : ι → α
n : ℕ
⊢ (∑ a ∈ s, f a) ^ n = ∏ i : Fin n, ∑ j ∈ s, f j | ((:c Eq) (:fv _uniq.29082) ((:c HPow.hPow) (:fv _uniq.29082) (:c Nat) (:fv _uniq.29082) ((:c instHPow) (:fv _uniq.29082) (:c Nat) ((:c Monoid.toNatPow) (:fv _uniq.29082) ((:c MonoidWithZero.toMonoid) (:fv _uniq.29082) ((:c Semiring.toMonoidWithZero) (:fv _uniq.29082) ((:c CommSemiring.toSemiring) (:fv _uniq.29082) (:fv... | [{"name":"ι","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":"κ","sexp":"(:forall _ (:fv _uniq.29079) (:sort (+ u_5 1)))"},{"name":"s✝","sexp":"((:c Finset) (:fv _uniq.29079))"},{"name":"s₁","sexp":"((:c Finset) ... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:fv FV1)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29079","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29082","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"convert","sourceEnd":7672,"sourceStart":7665,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":"@","sourceEnd":7674,"sourceStart":7673,"tag":"atom"},{"name":"Finset.prod_univ_sum","seman... | [] | [{"source":"@prod_univ_sum (Fin n) _ _ _ _ _ (fun _i ↦ s) fun _i d ↦ f d","source_end":7737,"source_start":7673,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29079","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29082","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 61 | 4 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d2a0f89d20079cf36b22686bec95227bdcc464bf851395b884888a9988b7510d | d17e0c7529a27de4200ea0f270a117ae44186eec2196e2b6bb65a088ae46e542 | bd2fefb64dcee6a8d028a8fc4e3076491a624f68e7d2cf9d7955df8f824cdbf3 | f5d2a5737f548ac1e29862deb448fa8cef0bc06a989a7fe50325e3416a1b1e46 |
cat-searcher/leandojo-benchmark-4-random | test | 3,555 | Finset.sum_pow' | Mathlib/Algebra/BigOperators/Ring.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case h.e'_2
ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
κ : ι → Type u_5
s✝ s₁ s₂ : Finset ι
i : ι
a : α
f✝ g : ι → α
inst✝¹ : CommSemiring α
inst✝ : DecidableEq ι
s : Finset ι
f : ι → α
n : ℕ
⊢ (∑ a ∈ s, f a) ^ n = ∏ i : Fin n, ∑ j ∈ s, f j | ((:c Eq) (:fv _uniq.29082) ((:c HPow.hPow) (:fv _uniq.29082) (:c Nat) (:fv _uniq.29082) ((:c instHPow) (:fv _uniq.29082) (:c Nat) ((:c Monoid.toNatPow) (:fv _uniq.29082) ((:c MonoidWithZero.toMonoid) (:fv _uniq.29082) ((:c Semiring.toMonoidWithZero) (:fv _uniq.29082) ((:c CommSemiring.toSemiring) (:fv _uniq.29082) (:fv... | [{"name":"ι","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":"κ","sexp":"(:forall _ (:fv _uniq.29079) (:sort (+ u_5 1)))"},{"name":"s✝","sexp":"((:c Finset) (:fv _uniq.29079))"},{"name":"s₁","sexp":"((:c Finset) ... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:fv FV1)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29079","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29082","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":7743,"sourceStart":7739,"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.29079","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29082","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 61 | 6 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f52eb69844c46c1ee53eed0b5eea45d199be133c9d3654b66f452d2dbb39a1d9 | f5d2a5737f548ac1e29862deb448fa8cef0bc06a989a7fe50325e3416a1b1e46 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,556 | Finset.surj_on_of_inj_on_of_card_le | Mathlib/Data/Finset/Card.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | classical have h : (s.attach.image fun a : { a // a ∈ s } => f a a.prop).<a>Finset.card</a> = s.card := by rw [← @<a>Finset.card_attach</a> _ s, <a>Finset.card_image_of_injective</a>] intro ⟨_, _⟩ ⟨_, _⟩ h exact <a>Subtype.eq</a> <| hinj _ _ _ _ h obtain rfl : <a>Finset.image</a> (fun a : { a // a ∈ s } => f a a.prop) ... | α : Type u_1
β : Type u_2
R : Type u_3
s t✝ u : Finset α
f✝ : α → β
n : ℕ
t : Finset β
f : (a : α) → a ∈ s → β
hf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t
hinj : ∀ (a₁ a₂ : α) (ha₁ : a₁ ∈ s) (ha₂ : a₂ ∈ s), f a₁ ha₁ = f a₂ ha₂ → a₁ = a₂
hst : t.card ≤ s.card
⊢ ∀ b ∈ t, ∃ a, ∃ (ha : a ∈ s), b = f a ha | (:forall b (:fv _uniq.32929) (:forall _ ((:c Membership.mem) (:fv _uniq.32929) ((:c Finset) (:fv _uniq.32929)) ((:c Finset.instMembership) (:fv _uniq.32929)) 0 (:fv _uniq.32950)) ((:c Exists) (:fv _uniq.32926) (:lambda a (:fv _uniq.32926) ((:c Exists) ((:c Membership.mem) (:fv _uniq.32926) ((:c Finset) (:fv _uniq.32926... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"t✝","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"u","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"f✝","sexp":"(:forall _ (:fv... | (:forall b :explicit (:fv FV1) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"classical","sourceEnd":19336,"sourceStart":19327,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"have","sourceEnd":19343,"sourceStart":19339,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","so... | [] | [{"source":"(s.attach.image fun a : { a // a ∈ s } => f a a.prop).card = s.card","source_end":19417,"source_start":19348,"syntax_kind":"«term_=_»"},{"source":"@card_attach _ s","source_end":19452,"source_start":19436,"syntax_kind":"Lean.Parser.Term.app"},{"source":"card_image_of_injective","source_end":19477,"source_st... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 151 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 809638426b0d668226e9eefb3c3f460eee21f9f699414b342933622aa9129cb7 | 721e4fdbfd6467ab1bb9765424d8e958b01a3af18f1428a8b079b76c22a1d631 | 0cadfd88bc6af16b33d6811cce4095f9fab4e67f5707998d51870905beea3af5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,557 | Finset.surj_on_of_inj_on_of_card_le | Mathlib/Data/Finset/Card.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h : (s.attach.image fun a : { a // a ∈ s } => f a a.prop).<a>Finset.card</a> = s.card := by rw [← @<a>Finset.card_attach</a> _ s, <a>Finset.card_image_of_injective</a>] intro ⟨_, _⟩ ⟨_, _⟩ h exact <a>Subtype.eq</a> <| hinj _ _ _ _ h | α : Type u_1
β : Type u_2
R : Type u_3
s t✝ u : Finset α
f✝ : α → β
n : ℕ
t : Finset β
f : (a : α) → a ∈ s → β
hf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t
hinj : ∀ (a₁ a₂ : α) (ha₁ : a₁ ∈ s) (ha₂ : a₂ ∈ s), f a₁ ha₁ = f a₂ ha₂ → a₁ = a₂
hst : t.card ≤ s.card
⊢ ∀ b ∈ t, ∃ a, ∃ (ha : a ∈ s), b = f a ha | α : Type u_1
β : Type u_2
R : Type u_3
s t✝ u : Finset α
f✝ : α → β
n : ℕ
t : Finset β
f : (a : α) → a ∈ s → β
hf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t
hinj : ∀ (a₁ a₂ : α) (ha₁ : a₁ ∈ s) (ha₂ : a₂ ∈ s), f a₁ ha₁ = f a₂ ha₂ → a₁ = a₂
hst : t.card ≤ s.card
h : (image (fun a => f ↑a ⋯) s.attach).card = s.card
⊢ ∀ b ∈ t, ∃... | (:forall b (:fv _uniq.32929) (:forall _ ((:c Membership.mem) (:fv _uniq.32929) ((:c Finset) (:fv _uniq.32929)) ((:c Finset.instMembership) (:fv _uniq.32929)) 0 (:fv _uniq.32950)) ((:c Exists) (:fv _uniq.32926) (:lambda a (:fv _uniq.32926) ((:c Exists) ((:c Membership.mem) (:fv _uniq.32926) ((:c Finset) (:fv _uniq.32926... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"t✝","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"u","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"f✝","sexp":"(:forall _ (:fv... | (:forall b :explicit (:fv FV1) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":19343,"sourceStart":19339,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":19345,"sourceStart":19344,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":19345,"sourceStart":19344,"tag":"node"... | [] | [{"source":"(s.attach.image fun a : { a // a ∈ s } => f a a.prop).card = s.card","source_end":19417,"source_start":19348,"syntax_kind":"«term_=_»"},{"source":"@card_attach _ s","source_end":19452,"source_start":19436,"syntax_kind":"Lean.Parser.Term.app"},{"source":"card_image_of_injective","source_end":19477,"source_st... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 151 | 7 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8c6433270f1561be889c83b929a5e6f3d2457c862443527f71e86911ac3ca6a4 | 721e4fdbfd6467ab1bb9765424d8e958b01a3af18f1428a8b079b76c22a1d631 | 99cc5176538ead400491f43bc7d6aa91ea66fda7632e95fa2d200202374e7f74 | d4c6687350f38ca76d93ffbbb5b78251361e95e1a632e868c48ae1ef84bf7482 |
cat-searcher/leandojo-benchmark-4-random | test | 3,558 | Finset.surj_on_of_inj_on_of_card_le | Mathlib/Data/Finset/Card.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain rfl : <a>Finset.image</a> (fun a : { a // a ∈ s } => f a a.prop) s.attach = t := <a>Finset.eq_of_subset_of_card_le</a> (<a>Finset.image_subset_iff</a>.2 $ by simpa) (by simp [hst, h]) | α : Type u_1
β : Type u_2
R : Type u_3
s t✝ u : Finset α
f✝ : α → β
n : ℕ
t : Finset β
f : (a : α) → a ∈ s → β
hf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t
hinj : ∀ (a₁ a₂ : α) (ha₁ : a₁ ∈ s) (ha₂ : a₂ ∈ s), f a₁ ha₁ = f a₂ ha₂ → a₁ = a₂
hst : t.card ≤ s.card
h : (image (fun a => f ↑a ⋯) s.attach).card = s.card
⊢ ∀ b ∈ t, ∃... | α : Type u_1
β : Type u_2
R : Type u_3
s t u : Finset α
f✝ : α → β
n : ℕ
f : (a : α) → a ∈ s → β
hinj : ∀ (a₁ a₂ : α) (ha₁ : a₁ ∈ s) (ha₂ : a₂ ∈ s), f a₁ ha₁ = f a₂ ha₂ → a₁ = a₂
h : (image (fun a => f ↑a ⋯) s.attach).card = s.card
hf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ image (fun a => f ↑a ⋯) s.attach
hst : (image (fun... | (:forall b (:fv _uniq.32929) (:forall _ ((:c Membership.mem) (:fv _uniq.32929) ((:c Finset) (:fv _uniq.32929)) ((:c Finset.instMembership) (:fv _uniq.32929)) 0 (:fv _uniq.32950)) ((:c Exists) (:fv _uniq.32926) (:lambda a (:fv _uniq.32926) ((:c Exists) ((:c Membership.mem) (:fv _uniq.32926) ((:c Finset) (:fv _uniq.32926... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"t✝","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"u","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"f✝","sexp":"(:forall _ (:fv... | (:forall b :explicit (:fv FV1) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"obtain","sourceEnd":19560,"sourceStart":19554,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":19564,"sourceStart":19561,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl","sourceEnd":19564,"sou... | [] | [{"source":"image (fun a : { a // a ∈ s } => f a a.prop) s.attach = t","source_end":19626,"source_start":19567,"syntax_kind":"«term_=_»"},{"source":"eq_of_subset_of_card_le (image_subset_iff.2 $ by simpa) (by simp [hst, h])","source_end":19708,"source_start":19634,"syntax_kind":"Lean.Parser.Term.app"},{"source":"obtain... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 151 | 15 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 30ba259882d3e32b7ccafe892cb3c16311b93c969e2a70d5e2deb6dbbfae7d0b | d4c6687350f38ca76d93ffbbb5b78251361e95e1a632e868c48ae1ef84bf7482 | fa3ef3a08f153213d3188688993f1b5fea097e45ed70af55a84b0b7bbca1d7fe | 1cc6c738b8c7607b223e2a6f4835796a3556593209e8c3fd896a9281d623ae85 |
cat-searcher/leandojo-benchmark-4-random | test | 3,559 | Finset.surj_on_of_inj_on_of_card_le | Mathlib/Data/Finset/Card.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Finset.mem_image</a>, <a>Finset.mem_attach</a>, <a>true_and</a>, <a>Subtype.exists</a>, <a>forall_exists_index</a>] | α : Type u_1
β : Type u_2
R : Type u_3
s t u : Finset α
f✝ : α → β
n : ℕ
f : (a : α) → a ∈ s → β
hinj : ∀ (a₁ a₂ : α) (ha₁ : a₁ ∈ s) (ha₂ : a₂ ∈ s), f a₁ ha₁ = f a₂ ha₂ → a₁ = a₂
h : (image (fun a => f ↑a ⋯) s.attach).card = s.card
hf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ image (fun a => f ↑a ⋯) s.attach
hst : (image (fun... | α : Type u_1
β : Type u_2
R : Type u_3
s t u : Finset α
f✝ : α → β
n : ℕ
f : (a : α) → a ∈ s → β
hinj : ∀ (a₁ a₂ : α) (ha₁ : a₁ ∈ s) (ha₂ : a₂ ∈ s), f a₁ ha₁ = f a₂ ha₂ → a₁ = a₂
h : (image (fun a => f ↑a ⋯) s.attach).card = s.card
hf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ image (fun a => f ↑a ⋯) s.attach
hst : (image (fun... | (:forall b (:fv _uniq.32929) (:forall _ ((:c Membership.mem) (:fv _uniq.32929) ((:c Finset) (:fv _uniq.32929)) ((:c Finset.instMembership) (:fv _uniq.32929)) 0 ((:c Finset.image) ((:c Subtype) (:fv _uniq.32926) (:lambda a (:fv _uniq.32926) ((:c Membership.mem) (:fv _uniq.32926) ((:c Finset) (:fv _uniq.32926)) ((:c Fins... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"u","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"f✝","sexp":"(:forall _ (:fv ... | (:forall b :explicit (:fv FV1) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":19715,"sourceStart":19711,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":19720,"sourceStart":19716,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":197... | [] | [{"source":"mem_image","source_end":19731,"source_start":19722,"syntax_kind":"ident"},{"source":"mem_attach","source_end":19743,"source_start":19733,"syntax_kind":"ident"},{"source":"true_and","source_end":19753,"source_start":19745,"syntax_kind":"ident"},{"source":"Subtype.exists","source_end":19769,"source_start":197... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 151 | 26 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7dbfec071f3efc6a2384dd08fc861dd4f177c336e9afe5c8fc514aa5f4ecd520 | 1cc6c738b8c7607b223e2a6f4835796a3556593209e8c3fd896a9281d623ae85 | 291e3e4fe9c3c8dc7cd0601842c03deeba271076fefab9801d3b52ebeb5aced3 | 23133fdb3c9c03ecedf522ff85019a82b9e09ae834f5a712f98bd5c4e245d20d |
cat-searcher/leandojo-benchmark-4-random | test | 3,560 | Finset.surj_on_of_inj_on_of_card_le | Mathlib/Data/Finset/Card.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun b a ha hb ↦ ⟨a, ha, hb.symm⟩ | α : Type u_1
β : Type u_2
R : Type u_3
s t u : Finset α
f✝ : α → β
n : ℕ
f : (a : α) → a ∈ s → β
hinj : ∀ (a₁ a₂ : α) (ha₁ : a₁ ∈ s) (ha₂ : a₂ ∈ s), f a₁ ha₁ = f a₂ ha₂ → a₁ = a₂
h : (image (fun a => f ↑a ⋯) s.attach).card = s.card
hf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ image (fun a => f ↑a ⋯) s.attach
hst : (image (fun... | (:forall b (:fv _uniq.32929) (:forall x (:fv _uniq.32926) (:forall x ((:c Membership.mem) (:fv _uniq.32926) ((:c Finset) (:fv _uniq.32926)) ((:c Finset.instMembership) (:fv _uniq.32926)) 0 (:fv _uniq.32935)) (:forall h ((:c Eq) (:fv _uniq.32929) ((:fv _uniq.33112) 1 ((:c Subtype.prop) (:fv _uniq.32926) (:lambda a (:fv ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"u","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"f✝","sexp":"(:forall _ (:fv ... | (:forall b :explicit (:fv FV1) (:forall x :explicit (:fv FV0) (:forall x :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":19799,"sourceStart":19794,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":19803,"sourceStart":19800,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"b","sourceEnd":19805,"sourceStart":19804,"tag":"identifier"},{"semanticRole":"scoped_loca... | [] | [{"source":"fun b a ha hb ↦ ⟨a, ha, hb.symm⟩","source_end":19838,"source_start":19800,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 151 | 27 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 70788f93a0dfca558d090239780d48ae545b33e9d66b71e5ce14fd81b7fca24f | 23133fdb3c9c03ecedf522ff85019a82b9e09ae834f5a712f98bd5c4e245d20d | 7342be00448d482631769e560a1a2177211a7f5732be7e54315561c5fca417bf | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,561 | Finset.surj_on_of_inj_on_of_card_le | Mathlib/Data/Finset/Card.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← @<a>Finset.card_attach</a> _ s, <a>Finset.card_image_of_injective</a>] | α : Type u_1
β : Type u_2
R : Type u_3
s t✝ u : Finset α
f✝ : α → β
n : ℕ
t : Finset β
f : (a : α) → a ∈ s → β
hf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t
hinj : ∀ (a₁ a₂ : α) (ha₁ : a₁ ∈ s) (ha₂ : a₂ ∈ s), f a₁ ha₁ = f a₂ ha₂ → a₁ = a₂
hst : t.card ≤ s.card
⊢ (image (fun a => f ↑a ⋯) s.attach).card = s.card | case H
α : Type u_1
β : Type u_2
R : Type u_3
s t✝ u : Finset α
f✝ : α → β
n : ℕ
t : Finset β
f : (a : α) → a ∈ s → β
hf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t
hinj : ∀ (a₁ a₂ : α) (ha₁ : a₁ ∈ s) (ha₂ : a₂ ∈ s), f a₁ ha₁ = f a₂ ha₂ → a₁ = a₂
hst : t.card ≤ s.card
⊢ Injective fun a => f ↑a ⋯ | ((:c Eq) (:c Nat) ((:c Finset.card) (:fv _uniq.32929) ((:c Finset.image) ((:c Subtype) (:fv _uniq.32926) (:lambda a (:fv _uniq.32926) ((:c Membership.mem) (:fv _uniq.32926) ((:c Finset) (:fv _uniq.32926)) ((:c Finset.instMembership) (:fv _uniq.32926)) 0 (:fv _uniq.32935)))) (:fv _uniq.32929) (:lambda a (:fv _uniq.32929... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"t✝","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"u","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"f✝","sexp":"(:forall _ (:fv... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Finset.card) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Finset.image) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda a :explicit (:fv FV0) (:app (:c Membership.mem) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":19430,"sourceStart":19428,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":19432,"sourceStart":19431,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":19435,"sourceSt... | [] | [{"source":"@card_attach _ s","source_end":19452,"source_start":19436,"syntax_kind":"Lean.Parser.Term.app"},{"source":"card_image_of_injective","source_end":19477,"source_start":19454,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 151 | 9 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1dc8d3588ecac0868e5cea5a99caf0c83b626325db5e13bfb4315337d522d0c0 | c2e1196a4a2bc7ca82144dfdc0b2da8250ae9f3cdbd1a46678c0e56671fe9314 | 0216adca762bc5b1d9b1d458bc65835f4a857b9b93b6764eaec7ddc21727893a | 473b0d30c37f776e7ba09a96c049d2a79efff0efa6ad98064c437943568f93c7 |
cat-searcher/leandojo-benchmark-4-random | test | 3,562 | Finset.surj_on_of_inj_on_of_card_le | Mathlib/Data/Finset/Card.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro ⟨_, _⟩ ⟨_, _⟩ h | case H
α : Type u_1
β : Type u_2
R : Type u_3
s t✝ u : Finset α
f✝ : α → β
n : ℕ
t : Finset β
f : (a : α) → a ∈ s → β
hf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t
hinj : ∀ (a₁ a₂ : α) (ha₁ : a₁ ∈ s) (ha₂ : a₂ ∈ s), f a₁ ha₁ = f a₂ ha₂ → a₁ = a₂
hst : t.card ≤ s.card
⊢ Injective fun a => f ↑a ⋯ | case H
α : Type u_1
β : Type u_2
R : Type u_3
s t✝ u : Finset α
f✝ : α → β
n : ℕ
t : Finset β
f : (a : α) → a ∈ s → β
hf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t
hinj : ∀ (a₁ a₂ : α) (ha₁ : a₁ ∈ s) (ha₂ : a₂ ∈ s), f a₁ ha₁ = f a₂ ha₂ → a₁ = a₂
hst : t.card ≤ s.card
val✝¹ : α
property✝¹ : val✝¹ ∈ s
val✝ : α
property✝ : val✝... | ((:c Function.Injective) ((:c Subtype) (:fv _uniq.32926) (:lambda a (:fv _uniq.32926) ((:c Membership.mem) (:fv _uniq.32926) ((:c Finset) (:fv _uniq.32926)) ((:c Finset.instMembership) (:fv _uniq.32926)) 0 (:fv _uniq.32935)))) (:fv _uniq.32929) (:lambda a ((:c Subtype) (:fv _uniq.32926) (:lambda a (:fv _uniq.32926) ((:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"t✝","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"u","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"f✝","sexp":"(:forall _ (:fv... | (:app (:c Function.Injective) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda a :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"intro","sourceEnd":19488,"sourceStart":19483,"tag":"atom"},{"children":[{"children":[{"source":"⟨","sourceEnd":19492,"sourceStart":19489,"tag":"atom"},{"children":[{"children":[{"source":"_","sourceEnd":19493,"sourceStart":19492,"tag":"atom"}],"kind":"Lean.Parser.Term.hole","source":"_","sourceE... | [{"role":"fresh_name","source":"h","source_end":19512,"source_start":19511,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 151 | 13 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d650599ddb0e0a6b979a5b295b80b25228291cb86cfe210d2464b8154089918c | 473b0d30c37f776e7ba09a96c049d2a79efff0efa6ad98064c437943568f93c7 | 1391368d4e9379d6e9fd63145bc281adcf1ac3f34bc9ae0f43a3b03f2d74ef68 | b84730e74fa097e5ceb45e1509d7474bb671dceb615230d705748bb45295279e |
cat-searcher/leandojo-benchmark-4-random | test | 3,563 | Finset.surj_on_of_inj_on_of_card_le | Mathlib/Data/Finset/Card.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Subtype.eq</a> <| hinj _ _ _ _ h | case H
α : Type u_1
β : Type u_2
R : Type u_3
s t✝ u : Finset α
f✝ : α → β
n : ℕ
t : Finset β
f : (a : α) → a ∈ s → β
hf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t
hinj : ∀ (a₁ a₂ : α) (ha₁ : a₁ ∈ s) (ha₂ : a₂ ∈ s), f a₁ ha₁ = f a₂ ha₂ → a₁ = a₂
hst : t.card ≤ s.card
val✝¹ : α
property✝¹ : val✝¹ ∈ s
val✝ : α
property✝ : val✝... | ((:c Eq) ((:c Subtype) (:fv _uniq.32926) (:lambda a (:fv _uniq.32926) ((:c Membership.mem) (:fv _uniq.32926) ((:c Finset) (:fv _uniq.32926)) ((:c Finset.instMembership) (:fv _uniq.32926)) 0 (:fv _uniq.32935)))) ((:c Subtype.mk) (:fv _uniq.32926) (:lambda a (:fv _uniq.32926) ((:c Membership.mem) (:fv _uniq.32926) ((:c F... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"t✝","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"u","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"f✝","sexp":"(:forall _ (:fv... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda a :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Members... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":19522,"sourceStart":19517,"tag":"atom"},{"children":[{"name":"Subtype.eq","semanticRole":"global","source":"Subtype.eq","sourceEnd":19533,"sourceStart":19523,"tag":"identifier"},{"source":"<|","sourceEnd":19536,"sourceStart":19534,"tag":"atom"},{"children":[{"contextIndex":12,... | [] | [{"source":"Subtype.eq <| hinj _ _ _ _ h","source_end":19551,"source_start":19523,"syntax_kind":"«term_<|_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 151 | 14 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5d7dd11e68db85505cdd3cffe7731f6954410e1f7e978a37a7488fc0a37fa07e | b84730e74fa097e5ceb45e1509d7474bb671dceb615230d705748bb45295279e | b0df905383ab316666b05f861f2e12f1afb478bdf09646a8bf12af366af8ab36 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,564 | Finset.surj_on_of_inj_on_of_card_le | Mathlib/Data/Finset/Card.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa | α : Type u_1
β : Type u_2
R : Type u_3
s t✝ u : Finset α
f✝ : α → β
n : ℕ
t : Finset β
f : (a : α) → a ∈ s → β
hf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t
hinj : ∀ (a₁ a₂ : α) (ha₁ : a₁ ∈ s) (ha₂ : a₂ ∈ s), f a₁ ha₁ = f a₂ ha₂ → a₁ = a₂
hst : t.card ≤ s.card
h : (image (fun a => f ↑a ⋯) s.attach).card = s.card
⊢ ∀ x ∈ s.at... | (:forall x ((:c Subtype) (:fv _uniq.32926) (:lambda a (:fv _uniq.32926) ((:c Membership.mem) (:fv _uniq.32926) ((:c Finset) (:fv _uniq.32926)) ((:c Finset.instMembership) (:fv _uniq.32926)) 0 (:fv _uniq.32935)))) (:forall _ ((:c Membership.mem) ((:c Subtype) (:fv _uniq.32926) (:lambda a (:fv _uniq.32926) ((:c Membershi... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"t✝","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"u","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"f✝","sexp":"(:forall _ (:fv... | (:forall x :explicit (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda a :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":19688,"sourceStart":19683,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 151 | 18 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1f0f908b9f980bc3357edf01bdbf4175d70537587d2f65710c9ed2b0c27b0deb | 50b20ecf3fc704bbe1c0e7e68e531d36ca3cd1364cd153f8073e51a23d54c030 | edfd421d35afd10931f43b505e9dca6d13b79f4a744024949fbf865064271c32 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,565 | Finset.surj_on_of_inj_on_of_card_le | Mathlib/Data/Finset/Card.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [hst, h] | α : Type u_1
β : Type u_2
R : Type u_3
s t✝ u : Finset α
f✝ : α → β
n : ℕ
t : Finset β
f : (a : α) → a ∈ s → β
hf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t
hinj : ∀ (a₁ a₂ : α) (ha₁ : a₁ ∈ s) (ha₂ : a₂ ∈ s), f a₁ ha₁ = f a₂ ha₂ → a₁ = a₂
hst : t.card ≤ s.card
h : (image (fun a => f ↑a ⋯) s.attach).card = s.card
⊢ t.card ≤ (... | ((:c LE.le) (:c Nat) (:c instLENat) ((:c Finset.card) (:fv _uniq.32929) (:fv _uniq.32950)) ((:c Finset.card) (:fv _uniq.32929) ((:c Finset.image) ((:c Subtype) (:fv _uniq.32926) (:lambda a (:fv _uniq.32926) ((:c Membership.mem) (:fv _uniq.32926) ((:c Finset) (:fv _uniq.32926)) ((:c Finset.instMembership) (:fv _uniq.329... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"t✝","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"u","sexp":"((:c Finset) (:fv _uniq.32926))"},{"name":"f✝","sexp":"(:forall _ (:fv... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Finset.card) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV8)))) (:arg :explicit 3 (:app (:c Finset.card) (:arg :implicit-type 0 (:fv FV1)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":19698,"sourceStart":19694,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"hst","source_end":19703,"source_start":19700,"syntax_kind":"ident"},{"source":"h","source_end":19706,"source_start":19705,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32926","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32929","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 151 | 23 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8d7b2f904f8c71729f376b89248732510d49c84467518e68162aba9535b86397 | b428721ee0b507710c596044670a0b94442182e7ee2a74cbbeb324111991aca0 | 2b787ad1fe4d56f5464d4c4746c0eb036e68ec4f861282f7fa5e815cce9043ee | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,566 | Finsupp.neLocus_self_sub_right | Mathlib/Data/Finsupp/NeLocus.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>sub_eq_add_neg</a>, <a>Finsupp.neLocus_self_add_right</a>, <a>Finsupp.support_neg</a>] | α : Type u_1
M : Type u_2
N : Type u_3
P : Type u_4
inst✝² : DecidableEq α
inst✝¹ : DecidableEq N
inst✝ : AddGroup N
f f₁ f₂ g g₁ g₂ : α →₀ N
⊢ f.neLocus (f - g) = g.support | ((:c Eq) ((:c Finset) (:fv _uniq.20549)) ((:c Finsupp.neLocus) (:fv _uniq.20549) (:fv _uniq.20555) (:fv _uniq.20565) (:fv _uniq.20574) ((:c NegZeroClass.toZero) (:fv _uniq.20555) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.20555) ((:c SubtractionMonoid.toSubNegZeroMonoid) (:fv _uniq.20555) ((:c AddGroup.toSubtract... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"N","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.20549))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.20555))"},{"name":"inst✝","sexp":"((:c Ad... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Finsupp.neLocus) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c DecidableEq) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20549","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20552","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":6606,"sourceStart":6604,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6608,"sourceStart":6607,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"sub_eq_add_neg","source_end":6622,"source_start":6608,"syntax_kind":"ident"},{"source":"neLocus_self_add_right","source_end":6646,"source_start":6624,"syntax_kind":"ident"},{"source":"support_neg","source_end":6659,"source_start":6648,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20549","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20552","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 57 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 28277ac13c08f8df9399e1c39b3315cb084bcfe9125cfa9d93cc969befbcc899 | 03006525deb83dacbeb4fd7c209c252b7d00b5847950d889b5f937d3a3446422 | 741e79d1e2b7e75342dffe0613295ce8714f96686c42089eec90b0ba4d695d35 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,567 | UpperHalfPlane.center_zero | Mathlib/Analysis/Complex/UpperHalfPlane/Metric.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>UpperHalfPlane.center_im</a>, <a>Real.cosh_zero</a>, <a>mul_one</a>] | z✝ w : ℍ
r R : ℝ
z : ℍ
⊢ (z.center 0).im = z.im | ((:c Eq) (:c Real) ((:c UpperHalfPlane.im) ((:c UpperHalfPlane.center) (:fv _uniq.52955) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))) ((:c UpperHalfPlane.im) (:fv _uniq.52955))) | [{"name":"z✝","sexp":"(:c UpperHalfPlane)"},{"name":"w","sexp":"(:c UpperHalfPlane)"},{"name":"r","sexp":"(:c Real)"},{"name":"R","sexp":"(:c Real)"},{"name":"z","sexp":"(:c UpperHalfPlane)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c UpperHalfPlane.im) (:arg :explicit 0 (:app (:c UpperHalfPlane.center) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52916","is_instance":false,"is_let":false,"name":"z✝","sexp":"(:c UpperHalfPlane)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52918","is_instance":false,"is_let":false,"name":"w","sexp":"(:c UpperHalfPlane)"},{"binder_role":"... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":7302,"sourceStart":7300,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7304,"sourceStart":7303,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"center_im","source_end":7313,"source_start":7304,"syntax_kind":"ident"},{"source":"Real.cosh_zero","source_end":7329,"source_start":7315,"syntax_kind":"ident"},{"source":"mul_one","source_end":7338,"source_start":7331,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52916","is_instance":false,"is_let":false,"user_name":"z✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.52918","is_instance":false,"is_let":false,"user_name":"w"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 45 | 2 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a68149ae3257ac17e051e82ba7548d40e200562294d8b5372d587f16b04a6db5 | 2a11fd57fbe0a28fd5fec966aef325d16e18190d4c2c631656d2f6d9ff1c29cb | 93db34a6b7ca988a1a8b0bf795bf9bdc9857b4720708b79d80fddff6bc2067a1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,568 | ContinuousLinearMap.prod_ext_iff | Mathlib/Topology/Algebra/Module/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [← <a>ContinuousLinearMap.coe_inj</a>, <a>LinearMap.prod_ext_iff</a>] | R : Type u_1
R₂ : Type u_2
R₃ : Type u_3
S : Type u_4
S₃ : Type u_5
inst✝²⁹ : Semiring R
inst✝²⁸ : Semiring R₂
inst✝²⁷ : Semiring R₃
inst✝²⁶ : Semiring S
inst✝²⁵ : Semiring S₃
M : Type u_6
inst✝²⁴ : TopologicalSpace M
inst✝²³ : AddCommMonoid M
inst✝²² : Module R M
M₂ : Type u_7
inst✝²¹ : TopologicalSpace M₂
inst✝²⁰ : A... | R : Type u_1
R₂ : Type u_2
R₃ : Type u_3
S : Type u_4
S₃ : Type u_5
inst✝²⁹ : Semiring R
inst✝²⁸ : Semiring R₂
inst✝²⁷ : Semiring R₃
inst✝²⁶ : Semiring S
inst✝²⁵ : Semiring S₃
M : Type u_6
inst✝²⁴ : TopologicalSpace M
inst✝²³ : AddCommMonoid M
inst✝²² : Module R M
M₂ : Type u_7
inst✝²¹ : TopologicalSpace M₂
inst✝²⁰ : A... | ((:c Iff) ((:c Eq) ((:c ContinuousLinearMap) (:fv _uniq.1025215) (:fv _uniq.1025215) (:fv _uniq.1025230) (:fv _uniq.1025230) ((:c RingHom.id) (:fv _uniq.1025215) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.1025215) (:fv _uniq.1025230))) ((:c Prod) (:fv _uniq.1025245) (:fv _uniq.1025344)) ((:c instTopologicalSpaceProd)... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₂","sexp":"(:sort (+ u_2 1))"},{"name":"R₃","sexp":"(:sort (+ u_3 1))"},{"name":"S","sexp":"(:sort (+ u_4 1))"},{"name":"S₃","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝²⁹","sexp":"((:c Semiring) (:fv _uniq.1025215))"},{"name":"inst✝²⁸","sexp":"((:c Semiring) (:fv _uniq.... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1025215","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1025218","is_instance":false,"is_let":false,"name":"R₂","sexp":"(:sort Type)"},{"binder_role":":implicit"... | {"children":[{"source":"simp","sourceEnd":76503,"sourceStart":76499,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":76508,"sourceStart":76504,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":765... | [] | [{"source":"coe_inj","source_end":76521,"source_start":76514,"syntax_kind":"ident"},{"source":"LinearMap.prod_ext_iff","source_end":76545,"source_start":76523,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1025215","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1025218","is_instance":false,"is_let":false,"user_name":"R₂"},{"binder_role":":implicit","context_index":2,"internal_name"... | 536 | 4 | exact | true | 1 | 52 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b4e1d3471ba240ba6c3e998209bd1ca0b4fc29709b44e5cc24d63f61c8e85244 | 36cbc07860cad520c6ce138726860fafb947b3ec0f86c4a9208781c03df348d3 | 14fb4335119bc9dba6eb55f681531fac336fda827e08078b9d831c904018a9de | 46f29af7e9a738e3a3fa416d6e701fd5fcf5939564d0d8c146586efc31f4af53 |
cat-searcher/leandojo-benchmark-4-random | test | 3,569 | ContinuousLinearMap.prod_ext_iff | Mathlib/Topology/Algebra/Module/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | R : Type u_1
R₂ : Type u_2
R₃ : Type u_3
S : Type u_4
S₃ : Type u_5
inst✝²⁹ : Semiring R
inst✝²⁸ : Semiring R₂
inst✝²⁷ : Semiring R₃
inst✝²⁶ : Semiring S
inst✝²⁵ : Semiring S₃
M : Type u_6
inst✝²⁴ : TopologicalSpace M
inst✝²³ : AddCommMonoid M
inst✝²² : Module R M
M₂ : Type u_7
inst✝²¹ : TopologicalSpace M₂
inst✝²⁰ : A... | ((:c Iff) ((:c And) ((:c Eq) ((:c LinearMap) (:fv _uniq.1025215) (:fv _uniq.1025215) (:fv _uniq.1025230) (:fv _uniq.1025230) ((:c RingHom.id) (:fv _uniq.1025215) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.1025215) (:fv _uniq.1025230))) (:fv _uniq.1025245) (:fv _uniq.1025375) (:fv _uniq.1025251) (:fv _uniq.1025381) (:... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₂","sexp":"(:sort (+ u_2 1))"},{"name":"R₃","sexp":"(:sort (+ u_3 1))"},{"name":"S","sexp":"(:sort (+ u_4 1))"},{"name":"S₃","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝²⁹","sexp":"((:c Semiring) (:fv _uniq.1025215))"},{"name":"inst✝²⁸","sexp":"((:c Semiring) (:fv _uniq.... | (:app (:c Iff) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Se... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1025215","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1025218","is_instance":false,"is_let":false,"name":"R₂","sexp":"(:sort Type)"},{"binder_role":":implicit"... | {"children":[{"source":"rfl","sourceEnd":76552,"sourceStart":76549,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":76552,"sourceStart":76549,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1025215","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1025218","is_instance":false,"is_let":false,"user_name":"R₂"},{"binder_role":":implicit","context_index":2,"internal_name"... | 536 | 5 | exact | true | 1 | 52 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6011ca58883bdd230d874246774f55a992c6bd2246da5af16e706c406ab41be3 | 46f29af7e9a738e3a3fa416d6e701fd5fcf5939564d0d8c146586efc31f4af53 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,570 | Polynomial.eval₂_neg | Mathlib/Algebra/Polynomial/Eval.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>eq_neg_iff_add_eq_zero</a>, ← <a>Polynomial.eval₂_add</a>, <a>add_left_neg</a>, <a>Polynomial.eval₂_zero</a>] | R : Type u
S✝ : Type v
T : Type w
ι : Type y
a b : R
m n : ℕ
inst✝¹ : Ring R
p q r : R[X]
S : Type u_1
inst✝ : Ring S
f : R →+* S
x : S
⊢ eval₂ f x (-p) = -eval₂ f x p | ((:c Eq) (:fv _uniq.293624) ((:c Polynomial.eval₂) (:fv _uniq.292639) (:fv _uniq.293624) ((:c Ring.toSemiring) (:fv _uniq.292639) (:fv _uniq.292656)) ((:c Ring.toSemiring) (:fv _uniq.293624) (:fv _uniq.293625)) (:fv _uniq.293626) (:fv _uniq.293627) ((:c Neg.neg) ((:c Polynomial) (:fv _uniq.292639) ((:c Ring.toSemiring)... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S✝","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"a","sexp":"(:fv _uniq.292639)"},{"name":"b","sexp":"(:fv _uniq.292639)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV13)) (:arg :explicit 1 (:app (:c Polynomial.eval₂) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV13)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.292639","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.292641","is_instance":false,"is_let":false,"name":"S✝","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":49382,"sourceStart":49380,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":49384,"sourceStart":49383,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"eq_neg_iff_add_eq_zero","source_end":49406,"source_start":49384,"syntax_kind":"ident"},{"source":"eval₂_add","source_end":49423,"source_start":49412,"syntax_kind":"ident"},{"source":"add_left_neg","source_end":49437,"source_start":49425,"syntax_kind":"ident"},{"source":"eval₂_zero","source_end":49451,"sourc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.292639","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.292641","is_instance":false,"is_let":false,"user_name":"S✝"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 449 | 2 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 259cc2f1bd8f1ce1c746aa568cde1221a650b0803bf5bb3b4c6a582751aa79c7 | 37a1efcecadf3e3a0ad26735a067e04127e5694f65f3d977e2c1852d0148ee24 | c8a6561db6a9ffea5889de165eb09eb46aee68cc1db0888905b6f3d35a09405b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,571 | eq_of_vsub_eq_zero | Mathlib/Algebra/AddTorsor.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>vsub_vadd</a> p₁ p₂, h, <a>zero_vadd</a>] | G : Type u_1
P : Type u_2
inst✝ : AddGroup G
T : AddTorsor G P
p₁ p₂ : P
h : p₁ -ᵥ p₂ = 0
⊢ p₁ = p₂ | ((:c Eq) (:fv _uniq.7015) (:fv _uniq.7480) (:fv _uniq.7481)) | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c AddGroup) (:fv _uniq.7012))"},{"name":"T","sexp":"((:c AddTorsor) (:fv _uniq.7012) (:fv _uniq.7015) (:fv _uniq.7018))"},{"name":"p₁","sexp":"(:fv _uniq.7015)"},{"name":"p₂","sexp":"(:fv _uniq.7015)"},{"name":"h... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV5)) (:arg :explicit 2 (:fv FV6))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7012","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7015","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":4947,"sourceStart":4945,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4949,"sourceStart":4948,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"sour... | [] | [{"source":"vsub_vadd p₁ p₂","source_end":4972,"source_start":4953,"syntax_kind":"Lean.Parser.Term.app"},{"source":"h","source_end":4975,"source_start":4974,"syntax_kind":"ident"},{"source":"zero_vadd","source_end":4986,"source_start":4977,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7012","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7015","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 25 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 74263e769adb3e44ffa04f231199a163cecfd0831a0e72eb5063ea9bcdc422f3 | 751f9d3ee784a47333896bd6b1c9eb6d22f6145739e0fbe370fb4657e3e2fe40 | 581e7a731ce38bc0b55e06cf81a4dc8c1f6463582805b723252f5ff6698284a9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,572 | Complex.Gammaℝ_ne_zero_of_re_pos | Mathlib/Analysis/SpecialFunctions/Gamma/Deligne.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>mul_ne_zero</a> | s : ℂ
hs : 0 < s.re
⊢ s.Gammaℝ ≠ 0 | ((:c Ne) (:c Complex) ((:c Complex.Gammaℝ) (:fv _uniq.20959)) ((:c OfNat.ofNat) (:c Complex) (:lit 0) ((:c Zero.toOfNat0) (:c Complex) (:c Complex.instZero)))) | [{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Complex.re) (:fv _uniq.20959)))"}] | (:app (:c Ne) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c Complex.Gammaℝ) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Complex)) (:arg :... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20959","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20960","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R... | {"children":[{"children":[{"children":[{"children":[{"source":"apply","sourceEnd":2635,"sourceStart":2630,"tag":"atom"},{"name":"mul_ne_zero","semanticRole":"global","source":"mul_ne_zero","sourceEnd":2647,"sourceStart":2636,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply mul_ne_zero","sourceEnd"... | [] | [{"source":"mul_ne_zero","source_end":2647,"source_start":2636,"syntax_kind":"ident"},{"source":"pi_ne_zero","source_end":2669,"source_start":2659,"syntax_kind":"ident"},{"source":"Gamma_ne_zero_of_re_pos","source_end":2705,"source_start":2682,"syntax_kind":"ident"},{"source":"div_ofNat_re","source_end":2726,"source_st... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20959","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20960","is_instance":false,"is_let":false,"user_name":"hs"}] | 10 | 2 | branch_opener | false | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 155898e8c4bb68855027f7631ba7e808a7776a4bc570d2ae1874e3185f66f93f | 0259ccadaac898ba53559d0e023114086156f1e4be2995ba41e536730f71d658 | 2bb26d72b3605cba4e551158d6fb2c3b44b8b97ffe6fb22ec840df50311ddf4a | 6f9ed6671e607c3a0addcc60b3ad19c2316d0c7af82ebe6137ac52e543c47701 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,573 | Complex.Gammaℝ_ne_zero_of_re_pos | Mathlib/Analysis/SpecialFunctions/Gamma/Deligne.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Real.pi_ne_zero</a>] | case ha
s : ℂ
hs : 0 < s.re
⊢ ↑π ^ (-s / 2) ≠ 0 | ((:c Ne) (:c Complex) ((:c HPow.hPow) (:c Complex) (:c Complex) (:c Complex) ((:c instHPow) (:c Complex) (:c Complex) (:c Complex.instPow)) ((:c Complex.ofReal') (:c Real.pi)) ((:c HDiv.hDiv) (:c Complex) (:c Complex) (:c Complex) ((:c instHDiv) (:c Complex) ((:c Field.toDiv) (:c Complex) (:c Complex.instField))) ((:c ... | [{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Complex.re) (:fv _uniq.20959)))"}] | (:app (:c Ne) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Complex)) (:arg :implicit-type 1 (:c Complex)) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c Complex)) (:arg :explicit 1 (:c Complex)) (:arg :... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20959","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20960","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":2657,"sourceStart":2653,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"pi_ne_zero","source_end":2669,"source_start":2659,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20959","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20960","is_instance":false,"is_let":false,"user_name":"hs"}] | 10 | 7 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a070743fc9df47aa74ecc1aba69ba783a177ecb14a459fa5e93175b2286b3ad1 | 69c2df6a143bc41525aa6ff166f4313fb0ee10420da540c1ffc9a63a9cbed22f | 306e745dfa1fcf4b487df796c526c87910898d854daedcfb7bd3828e5e64d8b5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,574 | Complex.Gammaℝ_ne_zero_of_re_pos | Mathlib/Analysis/SpecialFunctions/Gamma/Deligne.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Complex.Gamma_ne_zero_of_re_pos</a> | case hb
s : ℂ
hs : 0 < s.re
⊢ Gamma (s / 2) ≠ 0 | case hb.hs
s : ℂ
hs : 0 < s.re
⊢ 0 < (s / 2).re | ((:c Ne) (:c Complex) ((:c Complex.Gamma) ((:c HDiv.hDiv) (:c Complex) (:c Complex) (:c Complex) ((:c instHDiv) (:c Complex) ((:c Field.toDiv) (:c Complex) (:c Complex.instField))) (:fv _uniq.20959) ((:c OfNat.ofNat) (:c Complex) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Complex) (:lit 2) ((:c Semiring.toNatCast) (:c Comp... | [{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Complex.re) (:fv _uniq.20959)))"}] | (:app (:c Ne) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c Complex.Gamma) (:arg :explicit 0 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Complex)) (:arg :implicit-type 1 (:c Complex)) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:c Comple... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20959","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20960","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R... | {"children":[{"source":"apply","sourceEnd":2681,"sourceStart":2676,"tag":"atom"},{"name":"Complex.Gamma_ne_zero_of_re_pos","semanticRole":"global","source":"Gamma_ne_zero_of_re_pos","sourceEnd":2705,"sourceStart":2682,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Gamma_ne_zero_of_re_pos","sourc... | [] | [{"source":"Gamma_ne_zero_of_re_pos","source_end":2705,"source_start":2682,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20959","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20960","is_instance":false,"is_let":false,"user_name":"hs"}] | 10 | 14 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4835de2138c5eb372e69ff788698c53aa4b929bb9a6cebd61255c1a877547c7a | bb11a0fe0c23f93aa8cf3af02f897a9496971442cb52d49a6df1ce936c72c080 | 4e1b848b6ff2c11a262a4a87333852c90c480bf6ffd2d128f048392d61d64bee | 87b674bc647f233871b66541a8f79c9f787df8cab6590797648c459e092b91aa |
cat-searcher/leandojo-benchmark-4-random | test | 3,575 | Complex.Gammaℝ_ne_zero_of_re_pos | Mathlib/Analysis/SpecialFunctions/Gamma/Deligne.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Complex.div_ofNat_re</a>] | case hb.hs
s : ℂ
hs : 0 < s.re
⊢ 0 < (s / 2).re | case hb.hs
s : ℂ
hs : 0 < s.re
⊢ 0 < s.re / 2 | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Complex.re) ((:c HDiv.hDiv) (:c Complex) (:c Complex) (:c Complex) ((:c instHDiv) (:c Complex) ((:c Field.toDiv) (:c Complex) (:c Complex.instField))) (:fv _uniq.20959) ((:c OfNat.ofNat) (... | [{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Complex.re) (:fv _uniq.20959)))"}] | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20959","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20960","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R... | {"children":[{"source":"rw","sourceEnd":2712,"sourceStart":2710,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2714,"sourceStart":2713,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Complex.div_ofNat_re... | [] | [{"source":"div_ofNat_re","source_end":2726,"source_start":2714,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20959","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20960","is_instance":false,"is_let":false,"user_name":"hs"}] | 10 | 15 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f79cc06a190edc191f8cb7b246e8510c1b4a9c10b94827735653ebb8e8e4a0e0 | 87b674bc647f233871b66541a8f79c9f787df8cab6590797648c459e092b91aa | 34568d223c5cd67a38cdfd7b4c4e51346df3975f9de010e02e18c21e11a75e53 | e3cd43f3813f76ba1e236c5b3b6df721186f93f5d4b8802da2e911155e0e5a3c |
cat-searcher/leandojo-benchmark-4-random | test | 3,576 | Complex.Gammaℝ_ne_zero_of_re_pos | Mathlib/Analysis/SpecialFunctions/Gamma/Deligne.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>div_pos</a> hs <a>two_pos</a> | case hb.hs
s : ℂ
hs : 0 < s.re
⊢ 0 < s.re / 2 | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Complex.re) (:fv _uniq.20959)) ((:c OfNat... | [{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Complex.re) (:fv _uniq.20959)))"}] | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20959","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20960","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R... | {"children":[{"source":"exact","sourceEnd":2737,"sourceStart":2732,"tag":"atom"},{"children":[{"name":"div_pos","semanticRole":"global","source":"div_pos","sourceEnd":2745,"sourceStart":2738,"tag":"identifier"},{"children":[{"contextIndex":2,"semanticRole":"local","source":"hs","sourceEnd":2748,"sourceStart":2746,"tag"... | [] | [{"source":"div_pos hs two_pos","source_end":2756,"source_start":2738,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20959","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20960","is_instance":false,"is_let":false,"user_name":"hs"}] | 10 | 18 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6f0fa0b47958ccff518b04a6d10a93dc52ae84953655dd218800ed3c9fd1095b | e3cd43f3813f76ba1e236c5b3b6df721186f93f5d4b8802da2e911155e0e5a3c | ea8b2fed736d4f33477ea42e487d8de88e4df91836376474c3eea01202254941 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,577 | HasProd.mul | Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp only [<a>HasProd</a>] at hf hg ⊢ | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
inst✝² : CommMonoid α
inst✝¹ : TopologicalSpace α
f g : β → α
a b : α
s : Finset β
inst✝ : ContinuousMul α
hf : HasProd f a
hg : HasProd g b
⊢ HasProd (fun b => f b * g b) (a * b) | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
inst✝² : CommMonoid α
inst✝¹ : TopologicalSpace α
f g : β → α
a b : α
s : Finset β
inst✝ : ContinuousMul α
hf : Tendsto (fun s => ∏ b ∈ s, f b) atTop (𝓝 a)
hg : Tendsto (fun s => ∏ b ∈ s, g b) atTop (𝓝 b)
⊢ Tendsto (fun s => ∏ b ∈ s, f b * g b) atTop (𝓝 (a * b)) | ((:c HasProd) (:fv _uniq.44071) (:fv _uniq.44074) (:fv _uniq.44083) (:fv _uniq.44086) (:lambda b (:fv _uniq.44074) ((:c HMul.hMul) (:fv _uniq.44071) (:fv _uniq.44071) (:fv _uniq.44071) ((:c instHMul) (:fv _uniq.44071) ((:c MulOneClass.toMul) (:fv _uniq.44071) ((:c Monoid.toMulOneClass) (:fv _uniq.44071) ((:c CommMonoid... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝²","sexp":"((:c CommMonoid) (:fv _uniq.44071))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.44071))"},{"name":"f","sexp":"(:foral... | (:app (:c HasProd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommMonoid) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 4 (:lambda b :explicit (:fv FV1) (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44071","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44074","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"dsimp","sourceEnd":11867,"sourceStart":11862,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":11872,"sourceStart":11868,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":11... | [] | [{"source":"HasProd","source_end":11881,"source_start":11874,"syntax_kind":"ident"},{"source":"hf","source_end":11888,"source_start":11886,"syntax_kind":"ident"},{"source":"hg","source_end":11891,"source_start":11889,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44071","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44074","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 73 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e016ab296e3c7e82ccec6cc6c99fbba194ffeef95234ce6c4ff739895aabdc4e | 15c65b194d5d8d767944875dc6b87b4be8e1db752a3c1a6837a03cb0f9d39bcd | b5fe46ef849ac2864d4b79d48ca5335ea724555860f38c2de835d8605071a5d2 | 8210ed60868bf8dc57f481a8d619e9a9aab4719ba7a25098f7a7d230ea20de06 |
cat-searcher/leandojo-benchmark-4-random | test | 3,578 | HasProd.mul | Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>Finset.prod_mul_distrib</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
inst✝² : CommMonoid α
inst✝¹ : TopologicalSpace α
f g : β → α
a b : α
s : Finset β
inst✝ : ContinuousMul α
hf : Tendsto (fun s => ∏ b ∈ s, f b) atTop (𝓝 a)
hg : Tendsto (fun s => ∏ b ∈ s, g b) atTop (𝓝 b)
⊢ Tendsto (fun s => ∏ b ∈ s, f b * g b) atTop (𝓝 (a * b)) | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
inst✝² : CommMonoid α
inst✝¹ : TopologicalSpace α
f g : β → α
a b : α
s : Finset β
inst✝ : ContinuousMul α
hf : Tendsto (fun s => ∏ b ∈ s, f b) atTop (𝓝 a)
hg : Tendsto (fun s => ∏ b ∈ s, g b) atTop (𝓝 b)
⊢ Tendsto (fun s => (∏ x ∈ s, f x) * ∏ x ∈ s, g x) atTop (𝓝 ... | ((:c Filter.Tendsto) ((:c Finset) (:fv _uniq.44074)) (:fv _uniq.44071) (:lambda s ((:c Finset) (:fv _uniq.44074)) ((:c Finset.prod) (:fv _uniq.44074) (:fv _uniq.44071) (:fv _uniq.44083) 0 (:lambda b (:fv _uniq.44074) ((:c HMul.hMul) (:fv _uniq.44071) (:fv _uniq.44071) (:fv _uniq.44071) ((:c instHMul) (:fv _uniq.44071) ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝²","sexp":"((:c CommMonoid) (:fv _uniq.44071))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.44071))"},{"name":"f","sexp":"(:foral... | (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:lambda s :explicit (:app (:c Finset) (:arg :explicit 0 (:fv FV1))) (:app (:c Finset.prod) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV0)) (:arg :ins... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44071","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44074","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp_rw","sourceEnd":11905,"sourceStart":11898,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11907,"sourceStart":11906,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.prod... | [] | [{"source":"prod_mul_distrib","source_end":11923,"source_start":11907,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44071","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44074","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 73 | 5 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e0fd1b80389278aa75a98119ef01866853242d1eb5013f67b4305291dc3df371 | 8210ed60868bf8dc57f481a8d619e9a9aab4719ba7a25098f7a7d230ea20de06 | e26d677c2012df17971abe72feddf335c1f744e9c27969750b48c8cf44f5a23e | 30bc9861ec720985f4c32a282c684f5666c4960dea717e99bb4bf9717ed9ca87 |
cat-searcher/leandojo-benchmark-4-random | test | 3,579 | HasProd.mul | Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hf.mul hg | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
inst✝² : CommMonoid α
inst✝¹ : TopologicalSpace α
f g : β → α
a b : α
s : Finset β
inst✝ : ContinuousMul α
hf : Tendsto (fun s => ∏ b ∈ s, f b) atTop (𝓝 a)
hg : Tendsto (fun s => ∏ b ∈ s, g b) atTop (𝓝 b)
⊢ Tendsto (fun s => (∏ x ∈ s, f x) * ∏ x ∈ s, g x) atTop (𝓝 ... | ((:c Filter.Tendsto) ((:c Finset) (:fv _uniq.44074)) (:fv _uniq.44071) (:lambda s ((:c Finset) (:fv _uniq.44074)) ((:c HMul.hMul) (:fv _uniq.44071) (:fv _uniq.44071) (:fv _uniq.44071) ((:c instHMul) (:fv _uniq.44071) ((:c MulOneClass.toMul) (:fv _uniq.44071) ((:c Monoid.toMulOneClass) (:fv _uniq.44071) ((:c CommMonoid.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝²","sexp":"((:c CommMonoid) (:fv _uniq.44071))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.44071))"},{"name":"f","sexp":"(:foral... | (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:lambda s :explicit (:app (:c Finset) (:arg :explicit 0 (:fv FV1))) (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :impli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44071","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44074","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":11932,"sourceStart":11927,"tag":"atom"},{"children":[{"source":"hf.mul","sourceEnd":11939,"sourceStart":11933,"tag":"identifier"},{"children":[{"contextIndex":14,"semanticRole":"local","source":"hg","sourceEnd":11942,"sourceStart":11940,"tag":"identifier"}],"kind":"null","sour... | [] | [{"source":"hf.mul hg","source_end":11942,"source_start":11933,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44071","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44074","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 73 | 8 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 85b22c3112eca1c56644cf5d9ee55ee7a67e00376af84cbb6ab7c4fa3c6f993f | 30bc9861ec720985f4c32a282c684f5666c4960dea717e99bb4bf9717ed9ca87 | 771551c5744d41fbeaf402be7d7a6a6ef3462e60afadd3cb5bcba7a6f2ade7b7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,580 | Lagrange.degree_interpolate_lt | Mathlib/LinearAlgebra/Lagrange.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>Finset.eq_empty_or_nonempty</a> s with (rfl | h) | F : Type u_1
inst✝¹ : Field F
ι : Type u_2
inst✝ : DecidableEq ι
s t : Finset ι
i j : ι
v r r' : ι → F
hvs : Set.InjOn v ↑s
⊢ ((interpolate s v) r).degree < ↑s.card | case inl
F : Type u_1
inst✝¹ : Field F
ι : Type u_2
inst✝ : DecidableEq ι
t : Finset ι
i j : ι
v r r' : ι → F
hvs : Set.InjOn v ↑∅
⊢ ((interpolate ∅ v) r).degree < ↑∅.card
case inr
F : Type u_1
inst✝¹ : Field F
ι : Type u_2
inst✝ : DecidableEq ι
s t : Finset ι
i j : ι
v r r' : ι → F
hvs : Set.InjOn v ↑s
h : s.Nonempty
... | ((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.65443) ((:c DivisionSemiring.toSemiring) (:... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.65443))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.65449))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.65449))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.65449))"},{"name":"i... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65443","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.65446","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"rcases","sourceEnd":15821,"sourceStart":15815,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Finset.eq_empty_or_nonempty","semanticRole":"global","source":"eq_empty_or_nonempty","sourceEnd":15842,"sourceStart":15822,"tag":"ide... | [] | [{"source":"eq_empty_or_nonempty s","source_end":15844,"source_start":15822,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(rfl | h)","source_end":15859,"source_start":15850,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65443","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.65446","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 104 | 7 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f65d5e89662d0898093851f5be6af06301c6c91172d2e82b2ca9e8a09cd39fdd | 81f25e415c3d60415f30f6e0a2409ce56663209d46ed10591dd92d56f27dff4e | 76a59546b3eb920fb5b00a1908428733e00f997bc7ae8d52a6b691169ba8851a | 90505abd2e6a5969d37b1287762537f79df8f09c5a9d9b29513518ee96d6fed5 |
cat-searcher/leandojo-benchmark-4-random | test | 3,581 | Lagrange.degree_interpolate_lt | Mathlib/LinearAlgebra/Lagrange.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Lagrange.interpolate_empty</a>, <a>Polynomial.degree_zero</a>, <a>Finset.card_empty</a>] | case inl
F : Type u_1
inst✝¹ : Field F
ι : Type u_2
inst✝ : DecidableEq ι
t : Finset ι
i j : ι
v r r' : ι → F
hvs : Set.InjOn v ↑∅
⊢ ((interpolate ∅ v) r).degree < ↑∅.card | case inl
F : Type u_1
inst✝¹ : Field F
ι : Type u_2
inst✝ : DecidableEq ι
t : Finset ι
i j : ι
v r r' : ι → F
hvs : Set.InjOn v ↑∅
⊢ ⊥ < ↑0 | ((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.65443) ((:c DivisionSemiring.toSemiring) (:... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.65443))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.65449))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.65449))"},{"name":"i","sexp":"(:fv _uniq.65449)"},{"name":"j","sexp":"(:fv... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65443","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.65446","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"rw","sourceEnd":15867,"sourceStart":15865,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15869,"sourceStart":15868,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Lagrange.interpo... | [] | [{"source":"interpolate_empty","source_end":15886,"source_start":15869,"syntax_kind":"ident"},{"source":"degree_zero","source_end":15899,"source_start":15888,"syntax_kind":"ident"},{"source":"card_empty","source_end":15911,"source_start":15901,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65443","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.65446","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 104 | 12 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7c1eae72aad21746e8d71824712ca83771fdf7d1ab5e0002011fffd1cefa0b5f | f7d8493be76dcda76e8a4d7b1fa3f23353d5e01cc806828b6d2ec7fd3a981b2f | fceb346ba5a30afffed18f3ff064bb34f89e3c54b4d26d15d5b8c16964e360f1 | bb93f2b3cf2bc02155cecdf1fc0a9317f2c200bd35b130f719411ef6f6d4b178 |
cat-searcher/leandojo-benchmark-4-random | test | 3,582 | Lagrange.degree_interpolate_lt | Mathlib/LinearAlgebra/Lagrange.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>WithBot.bot_lt_coe</a> _ | case inl
F : Type u_1
inst✝¹ : Field F
ι : Type u_2
inst✝ : DecidableEq ι
t : Finset ι
i j : ι
v r r' : ι → F
hvs : Set.InjOn v ↑∅
⊢ ⊥ < ↑0 | ((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Bot.bot) ((:c WithBot) (:c Nat)) ((:c WithBot.bot) (:c Nat))) ((:c WithBo... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.65443))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.65449))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.65449))"},{"name":"i","sexp":"(:fv _uniq.65449)"},{"name":"j","sexp":"(:fv... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Bot.bot) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65443","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.65446","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"exact","sourceEnd":15922,"sourceStart":15917,"tag":"atom"},{"children":[{"name":"WithBot.bot_lt_coe","semanticRole":"global","source":"WithBot.bot_lt_coe","sourceEnd":15941,"sourceStart":15923,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":15943,"sourceStart":15942,"tag"... | [] | [{"source":"WithBot.bot_lt_coe _","source_end":15943,"source_start":15923,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65443","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.65446","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 104 | 17 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e0e5b761536701235844b1d19ee35328c8a32709336bf602e7cfdff0c5a55af2 | bb93f2b3cf2bc02155cecdf1fc0a9317f2c200bd35b130f719411ef6f6d4b178 | 0602bb4ae9c02fc6aa39802d16abfcb7c3a688e03612d8b34d5a855a77b04291 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,583 | Lagrange.degree_interpolate_lt | Mathlib/LinearAlgebra/Lagrange.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>lt_of_le_of_lt</a> (<a>Lagrange.degree_interpolate_le</a> _ hvs) ?_ | case inr
F : Type u_1
inst✝¹ : Field F
ι : Type u_2
inst✝ : DecidableEq ι
s t : Finset ι
i j : ι
v r r' : ι → F
hvs : Set.InjOn v ↑s
h : s.Nonempty
⊢ ((interpolate s v) r).degree < ↑s.card | case inr
F : Type u_1
inst✝¹ : Field F
ι : Type u_2
inst✝ : DecidableEq ι
s t : Finset ι
i j : ι
v r r' : ι → F
hvs : Set.InjOn v ↑s
h : s.Nonempty
⊢ ↑(s.card - 1) < ↑s.card | ((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.65443) ((:c DivisionSemiring.toSemiring) (:... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.65443))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.65449))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.65449))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.65449))"},{"name":"i... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65443","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.65446","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"refine","sourceEnd":15955,"sourceStart":15949,"tag":"atom"},{"children":[{"name":"lt_of_le_of_lt","semanticRole":"global","source":"lt_of_le_of_lt","sourceEnd":15970,"sourceStart":15956,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":15972,"sourceStart":15971,"tag":"atom"... | [] | [{"source":"lt_of_le_of_lt (degree_interpolate_le _ hvs) ?_","source_end":16003,"source_start":15956,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65443","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.65446","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 104 | 22 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d37bad022dc8199517e70277d432cc51c80a560f88e7b338a1545225226f1edc | dd874bc4367bc167a4c51c6358843aadf43c3983fd3d7724fe52840776d7c1a6 | 6680eef2332d3eca999ae6b11f6875a719dc46fbe2201b6e2fb747278cbe0fdf | 224dce308e60953828bccfcaa1c762bf7065ccdd416daa0955b8ea7b5f934322 |
cat-searcher/leandojo-benchmark-4-random | test | 3,584 | Lagrange.degree_interpolate_lt | Mathlib/LinearAlgebra/Lagrange.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Nat.cast_withBot</a>, <a>WithBot.coe_lt_coe</a>] | case inr
F : Type u_1
inst✝¹ : Field F
ι : Type u_2
inst✝ : DecidableEq ι
s t : Finset ι
i j : ι
v r r' : ι → F
hvs : Set.InjOn v ↑s
h : s.Nonempty
⊢ ↑(s.card - 1) < ↑s.card | case inr
F : Type u_1
inst✝¹ : Field F
ι : Type u_2
inst✝ : DecidableEq ι
s t : Finset ι
i j : ι
v r r' : ι → F
hvs : Set.InjOn v ↑s
h : s.Nonempty
⊢ s.card - 1 < s.card | ((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Nat.cast) ((:c WithBot) (:c Nat)) ((:c Semiring.toNatCast) ((:c WithBot) ... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.65443))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.65449))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.65449))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.65449))"},{"name":"i... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Nat.cast) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65443","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.65446","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"rw","sourceEnd":16010,"sourceStart":16008,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16012,"sourceStart":16011,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Nat.cast_withBot... | [] | [{"source":"Nat.cast_withBot","source_end":16028,"source_start":16012,"syntax_kind":"ident"},{"source":"WithBot.coe_lt_coe","source_end":16048,"source_start":16030,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65443","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.65446","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 104 | 23 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e7558ce147a106afe7a41f389a57a6883456839ff9ceb42d12eebd999fa27595 | 224dce308e60953828bccfcaa1c762bf7065ccdd416daa0955b8ea7b5f934322 | 4e156bb6c3a62bf1c3a86bcfbf91dfe843ab95334a6c3e2cc134e4716e504cd6 | 89f1427d187b9845b1534f0b46ef6b70dae51398ab8ad8fa5271164e48da9c39 |
cat-searcher/leandojo-benchmark-4-random | test | 3,585 | Lagrange.degree_interpolate_lt | Mathlib/LinearAlgebra/Lagrange.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Nat.sub_lt</a> (<a>Finset.Nonempty.card_pos</a> h) <a>zero_lt_one</a> | case inr
F : Type u_1
inst✝¹ : Field F
ι : Type u_2
inst✝ : DecidableEq ι
s t : Finset ι
i j : ι
v r r' : ι → F
hvs : Set.InjOn v ↑s
h : s.Nonempty
⊢ s.card - 1 < s.card | ((:c LT.lt) (:c Nat) ((:c Preorder.toLT) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring)))) ((:c HSub.hSub) (:c Nat) (:c Nat) (:c Nat) ((:c instHSub) (:c Nat) (:c instSubNat)) ((:c Finset.card) (:fv _uniq.65449) (:fv _uniq.65461)) ((... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.65443))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.65449))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.65449))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.65449))"},{"name":"i... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HSub) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65443","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.65446","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"exact","sourceEnd":16059,"sourceStart":16054,"tag":"atom"},{"children":[{"name":"Nat.sub_lt","semanticRole":"global","source":"Nat.sub_lt","sourceEnd":16070,"sourceStart":16060,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":16072,"sourceStart":16071,"tag":"atom"},{"child... | [] | [{"source":"Nat.sub_lt (Nonempty.card_pos h) zero_lt_one","source_end":16104,"source_start":16060,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65443","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.65446","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 104 | 27 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4cd7080718145966f94154f6defdd6d3d031e082086f12f8fd2638def6ca6243 | 89f1427d187b9845b1534f0b46ef6b70dae51398ab8ad8fa5271164e48da9c39 | fb52835a41897c4955dd9365f1a0ca659abfee209e8d19e289fb75cda9056331 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,586 | Projectivization.submodule_injective | Mathlib/LinearAlgebra/Projectivization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction' u using <a>Projectivization.ind</a> with u hu | K : Type u_1
V : Type u_2
inst✝² : DivisionRing K
inst✝¹ : AddCommGroup V
inst✝ : Module K V
u v : ℙ K V
h : u.submodule = v.submodule
⊢ u = v | case h
K : Type u_1
V : Type u_2
inst✝² : DivisionRing K
inst✝¹ : AddCommGroup V
inst✝ : Module K V
v : ℙ K V
u : V
hu : u ≠ 0
h : (mk K u hu).submodule = v.submodule
⊢ mk K u hu = v | ((:c Eq) ((:c Projectivization) (:fv _uniq.42537) (:fv _uniq.42540) (:fv _uniq.42543) (:fv _uniq.42546) (:fv _uniq.43129)) (:fv _uniq.43996) (:fv _uniq.43999)) | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c DivisionRing) (:fv _uniq.42537))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.42540))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.42537) (:fv _uniq.42540) ((:c DivisionSemiring.toSemiring) (:... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Projectivization) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c DivisionRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.42537","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42540","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"induction'","sourceEnd":5660,"sourceStart":5650,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":6,"semanticRole":"local","source":"u","sourceEnd":5662,"sourceStart":5661,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","s... | [] | [{"source":"u","source_end":5662,"source_start":5661,"syntax_kind":"ident"},{"source":"ind","source_end":5672,"source_start":5669,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.42537","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42540","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 45 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 280c1092e62088141230019df7f371689aa4f124e8eab8b9c64fec7b3083fa59 | 39128fad41542ad931ee6d25e5bd3b8dbd71c6ac625ee294c35d06a7497c4233 | 457b05658155e60bbc54dc21f136c01116bfc511ad94d48398eddce7d793dcbc | f73b37b8b11c265a8b0c5030421ec7c019b374816312d86cc0990315abf1970c |
cat-searcher/leandojo-benchmark-4-random | test | 3,587 | Projectivization.submodule_injective | Mathlib/LinearAlgebra/Projectivization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction' v using <a>Projectivization.ind</a> with v hv | case h
K : Type u_1
V : Type u_2
inst✝² : DivisionRing K
inst✝¹ : AddCommGroup V
inst✝ : Module K V
v : ℙ K V
u : V
hu : u ≠ 0
h : (mk K u hu).submodule = v.submodule
⊢ mk K u hu = v | case h.h
K : Type u_1
V : Type u_2
inst✝² : DivisionRing K
inst✝¹ : AddCommGroup V
inst✝ : Module K V
u : V
hu : u ≠ 0
v : V
hv : v ≠ 0
h : (mk K u hu).submodule = (mk K v hv).submodule
⊢ mk K u hu = mk K v hv | ((:c Eq) ((:c Projectivization) (:fv _uniq.42537) (:fv _uniq.42540) (:fv _uniq.42543) (:fv _uniq.42546) (:fv _uniq.43129)) ((:c Projectivization.mk) (:fv _uniq.42537) (:fv _uniq.42540) (:fv _uniq.42543) (:fv _uniq.42546) (:fv _uniq.43129) (:fv _uniq.44042) (:fv _uniq.44043)) (:fv _uniq.43999)) | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c DivisionRing) (:fv _uniq.42537))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.42540))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.42537) (:fv _uniq.42540) ((:c DivisionSemiring.toSemiring) (:... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Projectivization) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c DivisionRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.42537","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42540","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"induction'","sourceEnd":5695,"sourceStart":5685,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":6,"semanticRole":"local","source":"v","sourceEnd":5697,"sourceStart":5696,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","s... | [] | [{"source":"v","source_end":5697,"source_start":5696,"syntax_kind":"ident"},{"source":"ind","source_end":5707,"source_start":5704,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.42537","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42540","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 45 | 5 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | db684e0aaee3b692d7965d189acf4c5f39d8499edb179635b7abe914ac66c3c1 | f73b37b8b11c265a8b0c5030421ec7c019b374816312d86cc0990315abf1970c | c633e34b266585223fa465d98f165b9bbbc670331685e430fadb4548fd6b3419 | d9a65b912c7ecb37ab4071a6d64c288350bb7b160a8cec675125bfbf2f5be19f |
cat-searcher/leandojo-benchmark-4-random | test | 3,588 | Projectivization.submodule_injective | Mathlib/LinearAlgebra/Projectivization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Projectivization.submodule_mk</a>, <a>Projectivization.submodule_mk</a>, <a>Submodule.span_singleton_eq_span_singleton</a>] at h | case h.h
K : Type u_1
V : Type u_2
inst✝² : DivisionRing K
inst✝¹ : AddCommGroup V
inst✝ : Module K V
u : V
hu : u ≠ 0
v : V
hv : v ≠ 0
h : (mk K u hu).submodule = (mk K v hv).submodule
⊢ mk K u hu = mk K v hv | case h.h
K : Type u_1
V : Type u_2
inst✝² : DivisionRing K
inst✝¹ : AddCommGroup V
inst✝ : Module K V
u : V
hu : u ≠ 0
v : V
hv : v ≠ 0
h : ∃ z, z • u = v
⊢ mk K u hu = mk K v hv | ((:c Eq) ((:c Projectivization) (:fv _uniq.42537) (:fv _uniq.42540) (:fv _uniq.42543) (:fv _uniq.42546) (:fv _uniq.43129)) ((:c Projectivization.mk) (:fv _uniq.42537) (:fv _uniq.42540) (:fv _uniq.42543) (:fv _uniq.42546) (:fv _uniq.43129) (:fv _uniq.44042) (:fv _uniq.44043)) ((:c Projectivization.mk) (:fv _uniq.42537) ... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c DivisionRing) (:fv _uniq.42537))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.42540))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.42537) (:fv _uniq.42540) ((:c DivisionSemiring.toSemiring) (:... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Projectivization) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c DivisionRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.42537","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42540","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":5722,"sourceStart":5720,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5724,"sourceStart":5723,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Projectivization.sub... | [] | [{"source":"submodule_mk","source_end":5736,"source_start":5724,"syntax_kind":"ident"},{"source":"h","source_end":5800,"source_start":5799,"syntax_kind":"ident"},{"source":"submodule_mk","source_end":5750,"source_start":5738,"syntax_kind":"ident"},{"source":"Submodule.span_singleton_eq_span_singleton","source_end":5794... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.42537","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42540","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 45 | 6 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 567a2d9fcf0839f2764541b1e9a4787913a8c404607f16b4228c460cf1597332 | d9a65b912c7ecb37ab4071a6d64c288350bb7b160a8cec675125bfbf2f5be19f | c1d42ef840f727e6be27f1ea7365924ce248faae54d1e5c303e7dea860875cad | 5db3d2e787dcf4301dbbc89b4bfb2c1c8634c8152900b12323bbc6308b87db11 |
cat-searcher/leandojo-benchmark-4-random | test | 3,589 | Projectivization.submodule_injective | Mathlib/LinearAlgebra/Projectivization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ((<a>Projectivization.mk_eq_mk_iff</a> K v u hv hu).2 h).<a>Eq.symm</a> | case h.h
K : Type u_1
V : Type u_2
inst✝² : DivisionRing K
inst✝¹ : AddCommGroup V
inst✝ : Module K V
u : V
hu : u ≠ 0
v : V
hv : v ≠ 0
h : ∃ z, z • u = v
⊢ mk K u hu = mk K v hv | ((:c Eq) ((:c Projectivization) (:fv _uniq.42537) (:fv _uniq.42540) (:fv _uniq.42543) (:fv _uniq.42546) (:fv _uniq.43129)) ((:c Projectivization.mk) (:fv _uniq.42537) (:fv _uniq.42540) (:fv _uniq.42543) (:fv _uniq.42546) (:fv _uniq.43129) (:fv _uniq.44042) (:fv _uniq.44043)) ((:c Projectivization.mk) (:fv _uniq.42537) ... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c DivisionRing) (:fv _uniq.42537))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.42540))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.42537) (:fv _uniq.42540) ((:c DivisionSemiring.toSemiring) (:... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Projectivization) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c DivisionRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.42537","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42540","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":5808,"sourceStart":5803,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":5810,"sourceStart":5809,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":5811,"sourceStart":5810,"tag":"atom"},{"children":[{"name":"Projectivization.mk_eq_m... | [] | [{"source":"((mk_eq_mk_iff K v u hv hu).2 h).symm","source_end":5846,"source_start":5809,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.42537","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42540","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 45 | 11 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1ac9e8b7094b0269b4701db89dcae6ad81b9d669c76d92c0d712f15e665943a9 | 5db3d2e787dcf4301dbbc89b4bfb2c1c8634c8152900b12323bbc6308b87db11 | 64726a4c407bb365665d3945a4d706db4c61b27ac60c5d102dd0d6cecd836196 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,590 | Rel.mul_edgeDensity_le_edgeDensity | Mathlib/Combinatorics/SimpleGraph/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hst : (s₂.card : ℚ) * t₂.card ≠ 0 := by simp [hs₂.ne_empty, ht₂.ne_empty] | 𝕜 : Type u_1
ι : Type u_2
κ : Type u_3
α : Type u_4
β : Type u_5
inst✝¹ : LinearOrderedField 𝕜
r : α → β → Prop
inst✝ : (a : α) → DecidablePred (r a)
s s₁ s₂ : Finset α
t t₁ t₂ : Finset β
a : α
b : β
δ : 𝕜
hs : s₂ ⊆ s₁
ht : t₂ ⊆ t₁
hs₂ : s₂.Nonempty
ht₂ : t₂.Nonempty
⊢ ↑s₂.card / ↑s₁.card * (↑t₂.card / ↑t₁.card) * e... | 𝕜 : Type u_1
ι : Type u_2
κ : Type u_3
α : Type u_4
β : Type u_5
inst✝¹ : LinearOrderedField 𝕜
r : α → β → Prop
inst✝ : (a : α) → DecidablePred (r a)
s s₁ s₂ : Finset α
t t₁ t₂ : Finset β
a : α
b : β
δ : 𝕜
hs : s₂ ⊆ s₁
ht : t₂ ⊆ t₁
hs₂ : s₂.Nonempty
ht₂ : t₂.Nonempty
hst : ↑s₂.card * ↑t₂.card ≠ 0
⊢ ↑s₂.card / ↑s₁.ca... | ((:c LE.le) (:c Rat) (:c Rat.instLE) ((:c HMul.hMul) (:c Rat) (:c Rat) (:c Rat) ((:c instHMul) (:c Rat) (:c Rat.instMul)) ((:c HMul.hMul) (:c Rat) (:c Rat) (:c Rat) ((:c instHMul) (:c Rat) (:c Rat.instMul)) ((:c HDiv.hDiv) (:c Rat) (:c Rat) (:c Rat) ((:c instHDiv) (:c Rat) (:c Rat.instDiv)) ((:c Nat.cast) (:c Rat) (:c ... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"κ","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"β","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.30351))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.30360... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Rat)) (:arg :implicit-type 1 (:c Rat)) (:arg :implicit-type 2 (:c Rat)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30351","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30354","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"have","sourceEnd":8214,"sourceStart":8210,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hst","sourceEnd":8218,"sourceStart":8215,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hst","sourceEnd":8218,"sourceStart":8215,"tag":"node"},... | [] | [{"source":"(s₂.card : ℚ) * t₂.card ≠ 0","source_end":8256,"source_start":8221,"syntax_kind":"«term_≠_»"},{"source":"hs₂.ne_empty","source_end":8283,"source_start":8269,"syntax_kind":"ident"},{"source":"ht₂.ne_empty","source_end":8299,"source_start":8285,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30351","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30354","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 56 | 4 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 27c576e398ce11522ebcb179046ef500393847ed4011f11af467f3e5a1c1106d | ec0453d6b003219d4d0ffcceee59d2419d414b14a659835e63198cf33d300c85 | aecbc1271ec374b23ba7902c6c5c02e1d139db0516819e9be7621aaced5aa7bc | b8819a6628a0f0ff39837f2caca26cacddd89fbefadda480d50cbcf43d5c70f1 |
cat-searcher/leandojo-benchmark-4-random | test | 3,591 | Rel.mul_edgeDensity_le_edgeDensity | Mathlib/Combinatorics/SimpleGraph/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Rel.edgeDensity</a>, <a>Rel.edgeDensity</a>, <a>div_mul_div_comm</a>, <a>mul_comm</a>, <a>div_mul_div_cancel</a> _ hst] | 𝕜 : Type u_1
ι : Type u_2
κ : Type u_3
α : Type u_4
β : Type u_5
inst✝¹ : LinearOrderedField 𝕜
r : α → β → Prop
inst✝ : (a : α) → DecidablePred (r a)
s s₁ s₂ : Finset α
t t₁ t₂ : Finset β
a : α
b : β
δ : 𝕜
hs : s₂ ⊆ s₁
ht : t₂ ⊆ t₁
hs₂ : s₂.Nonempty
ht₂ : t₂.Nonempty
hst : ↑s₂.card * ↑t₂.card ≠ 0
⊢ ↑s₂.card / ↑s₁.ca... | 𝕜 : Type u_1
ι : Type u_2
κ : Type u_3
α : Type u_4
β : Type u_5
inst✝¹ : LinearOrderedField 𝕜
r : α → β → Prop
inst✝ : (a : α) → DecidablePred (r a)
s s₁ s₂ : Finset α
t t₁ t₂ : Finset β
a : α
b : β
δ : 𝕜
hs : s₂ ⊆ s₁
ht : t₂ ⊆ t₁
hs₂ : s₂.Nonempty
ht₂ : t₂.Nonempty
hst : ↑s₂.card * ↑t₂.card ≠ 0
⊢ ↑(interedges r s₂... | ((:c LE.le) (:c Rat) (:c Rat.instLE) ((:c HMul.hMul) (:c Rat) (:c Rat) (:c Rat) ((:c instHMul) (:c Rat) (:c Rat.instMul)) ((:c HMul.hMul) (:c Rat) (:c Rat) (:c Rat) ((:c instHMul) (:c Rat) (:c Rat.instMul)) ((:c HDiv.hDiv) (:c Rat) (:c Rat) (:c Rat) ((:c instHDiv) (:c Rat) (:c Rat.instDiv)) ((:c Nat.cast) (:c Rat) (:c ... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"κ","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"β","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.30351))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.30360... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Rat)) (:arg :implicit-type 1 (:c Rat)) (:arg :implicit-type 2 (:c Rat)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30351","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30354","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"rw","sourceEnd":8305,"sourceStart":8303,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8307,"sourceStart":8306,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Rel.edgeDensity","se... | [] | [{"source":"edgeDensity","source_end":8318,"source_start":8307,"syntax_kind":"ident"},{"source":"edgeDensity","source_end":8331,"source_start":8320,"syntax_kind":"ident"},{"source":"div_mul_div_comm","source_end":8349,"source_start":8333,"syntax_kind":"ident"},{"source":"mul_comm","source_end":8359,"source_start":8351,... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30351","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30354","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 56 | 7 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | abc6e9dbcc521ae5effce29878f424d7416eee244655ff8228a7d02a8df59174 | b8819a6628a0f0ff39837f2caca26cacddd89fbefadda480d50cbcf43d5c70f1 | 58aec101a570539ed423a2df775c2cb316c299d6c07b4ec052e03ee008742cb2 | 0bfc34723c9f54d58088f5d7b8ce76d56d7e66a38bafa6f1b37ee2595eaf3274 |
cat-searcher/leandojo-benchmark-4-random | test | 3,592 | Rel.mul_edgeDensity_le_edgeDensity | Mathlib/Combinatorics/SimpleGraph/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | 𝕜 : Type u_1
ι : Type u_2
κ : Type u_3
α : Type u_4
β : Type u_5
inst✝¹ : LinearOrderedField 𝕜
r : α → β → Prop
inst✝ : (a : α) → DecidablePred (r a)
s s₁ s₂ : Finset α
t t₁ t₂ : Finset β
a : α
b : β
δ : 𝕜
hs : s₂ ⊆ s₁
ht : t₂ ⊆ t₁
hs₂ : s₂.Nonempty
ht₂ : t₂.Nonempty
hst : ↑s₂.card * ↑t₂.card ≠ 0
⊢ ↑(interedges r s₂... | case hab.h.a
𝕜 : Type u_1
ι : Type u_2
κ : Type u_3
α : Type u_4
β : Type u_5
inst✝¹ : LinearOrderedField 𝕜
r : α → β → Prop
inst✝ : (a : α) → DecidablePred (r a)
s s₁ s₂ : Finset α
t t₁ t₂ : Finset β
a : α
b : β
δ : 𝕜
hs : s₂ ⊆ s₁
ht : t₂ ⊆ t₁
hs₂ : s₂.Nonempty
ht₂ : t₂.Nonempty
hst : ↑s₂.card * ↑t₂.card ≠ 0
⊢ inte... | ((:c LE.le) (:c Rat) (:c Rat.instLE) ((:c HDiv.hDiv) (:c Rat) (:c Rat) (:c Rat) ((:c instHDiv) (:c Rat) ((:c GroupWithZero.toDiv) (:c Rat) ((:c DivisionSemiring.toGroupWithZero) (:c Rat) ((:c Semifield.toDivisionSemiring) (:c Rat) ((:c LinearOrderedSemifield.toSemifield) (:c Rat) ((:c LinearOrderedField.toLinearOrdered... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"κ","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"β","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.30351))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.30360... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Rat)) (:arg :implicit-type 1 (:c Rat)) (:arg :implicit-type 2 (:c Rat)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30351","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30354","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"gcongr","sourceEnd":8395,"sourceStart":8389,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":8395,"sourceStart":8389,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30351","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30354","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 56 | 14 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b0ad4d62a882089cac808f845eddad19e3142c62d7a962efc96de329dab12c88 | 0bfc34723c9f54d58088f5d7b8ce76d56d7e66a38bafa6f1b37ee2595eaf3274 | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | 3e759d928451c2a1db9f21b9d83ba830ad74e3fbf53cd3504751a1245fffd09b |
cat-searcher/leandojo-benchmark-4-random | test | 3,593 | Rel.mul_edgeDensity_le_edgeDensity | Mathlib/Combinatorics/SimpleGraph/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Rel.interedges_mono</a> hs ht | case hab.h.a
𝕜 : Type u_1
ι : Type u_2
κ : Type u_3
α : Type u_4
β : Type u_5
inst✝¹ : LinearOrderedField 𝕜
r : α → β → Prop
inst✝ : (a : α) → DecidablePred (r a)
s s₁ s₂ : Finset α
t t₁ t₂ : Finset β
a : α
b : β
δ : 𝕜
hs : s₂ ⊆ s₁
ht : t₂ ⊆ t₁
hs₂ : s₂.Nonempty
ht₂ : t₂.Nonempty
hst : ↑s₂.card * ↑t₂.card ≠ 0
⊢ inte... | ((:c HasSubset.Subset) ((:c Finset) ((:c Prod) (:fv _uniq.30360) (:fv _uniq.30363))) ((:c Finset.instHasSubset) ((:c Prod) (:fv _uniq.30360) (:fv _uniq.30363))) ((:c Rel.interedges) (:fv _uniq.30360) (:fv _uniq.30363) (:fv _uniq.30372) (:fv _uniq.30389) (:fv _uniq.30400) (:fv _uniq.30409)) ((:c Rel.interedges) (:fv _un... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"κ","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"β","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.30351))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.30360... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:fv FV4)))))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Finset) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV3)) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30351","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30354","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"exact","sourceEnd":8403,"sourceStart":8398,"tag":"atom"},{"children":[{"name":"Rel.interedges_mono","semanticRole":"global","source":"interedges_mono","sourceEnd":8419,"sourceStart":8404,"tag":"identifier"},{"children":[{"contextIndex":18,"semanticRole":"local","source":"hs","sourceEnd":8422,"so... | [] | [{"source":"interedges_mono hs ht","source_end":8425,"source_start":8404,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30351","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30354","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 56 | 15 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 366e30fbaa275c99c35d4d02743acbf794cad599a0677d59cbfbda264a8aa3ec | 3e759d928451c2a1db9f21b9d83ba830ad74e3fbf53cd3504751a1245fffd09b | f81b036eba54bc1342f27e67388c62689e9a807244e975e03486093c42f4c3a1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,594 | Rel.mul_edgeDensity_le_edgeDensity | Mathlib/Combinatorics/SimpleGraph/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [hs₂.ne_empty, ht₂.ne_empty] | 𝕜 : Type u_1
ι : Type u_2
κ : Type u_3
α : Type u_4
β : Type u_5
inst✝¹ : LinearOrderedField 𝕜
r : α → β → Prop
inst✝ : (a : α) → DecidablePred (r a)
s s₁ s₂ : Finset α
t t₁ t₂ : Finset β
a : α
b : β
δ : 𝕜
hs : s₂ ⊆ s₁
ht : t₂ ⊆ t₁
hs₂ : s₂.Nonempty
ht₂ : t₂.Nonempty
⊢ ↑s₂.card * ↑t₂.card ≠ 0 | ((:c Ne) (:c Rat) ((:c HMul.hMul) (:c Rat) (:c Rat) (:c Rat) ((:c instHMul) (:c Rat) (:c Rat.instMul)) ((:c Nat.cast) (:c Rat) (:c Rat.instNatCast) ((:c Finset.card) (:fv _uniq.30360) (:fv _uniq.30400))) ((:c Nat.cast) (:c Rat) (:c Rat.instNatCast) ((:c Finset.card) (:fv _uniq.30363) (:fv _uniq.30409)))) ((:c OfNat.ofN... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"κ","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"β","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.30351))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.30360... | (:app (:c Ne) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Rat)) (:arg :implicit-type 1 (:c Rat)) (:arg :implicit-type 2 (:c Rat)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Rat)) (:arg :explicit 1 (:c Rat)) (:arg :explicit 2 (:c Rat))))) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30351","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30354","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"simp","sourceEnd":8267,"sourceStart":8263,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8269,"sourceStart":8268,"tag":"atom"... | [] | [{"source":"hs₂.ne_empty","source_end":8283,"source_start":8269,"syntax_kind":"ident"},{"source":"ht₂.ne_empty","source_end":8299,"source_start":8285,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30351","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30354","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 56 | 6 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 693b75b8e36f985e83991c3bddca30fd5fce3617c4d099a7c639390a78d1c261 | 2bf06b8717a758fca0b2dd51ae88d60596ed47d5801cb12efd34f4d5dc7bd942 | b1b98e1b57a793531ced7962223c476dc68d7a90078a18227148620a7ee0e032 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 |
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