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value | row_index int64 0 4.5k | theorem stringlengths 7 81 | file_path stringclasses 723
values | repo_url stringclasses 1
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value | tactic stringlengths 3 2.13k | text_state stringlengths 7 2.31k | text_target_state stringlengths 0 4.07k | raw_goal_sexp stringlengths 10 11.8M | raw_hyp_sexps stringlengths 2 15.6M | model_goal_sexp stringlengths 10 2.68M | model_hyp_sexps stringlengths 2 3.62M | source_syntax stringlengths 179 164k | syntax_args stringclasses 256
values | term_ranges stringlengths 2 6.01k | local_context stringlengths 2 10.3k | unit_index int64 3 1.26k | invocation_index int64 0 357 | alignment_kind stringclasses 2
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classes | pending_goal_count int64 1 1 | hypothesis_count int64 0 77 | hypothesis_names_match bool 2
classes | raw_schema_version int64 4 4 | raw_extractor_version stringclasses 1
value | model_schema_version int64 2 2 | model_normalization stringclasses 1
value | trace_schema_version int64 3 3 | trace_extractor_version stringclasses 1
value | pantograph_commit stringclasses 1
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value | raw_record_sha256 stringlengths 64 64 | state_sha256 stringlengths 64 64 | tactic_sha256 stringlengths 64 64 | target_state_sha256 stringlengths 64 64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
cat-searcher/leandojo-benchmark-4-random | test | 1,960 | CategoryTheory.Preadditive.mono_of_isZero_kernel' | Mathlib/CategoryTheory/Preadditive/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨a, ha⟩ := <a>CategoryTheory.Limits.KernelFork.IsLimit.lift'</a> hc _ hg | C : Type u
inst✝¹ : Category.{v, u} C
inst✝ : Preadditive C
P Q R : C
f✝ f' : P ⟶ Q
g✝ g' : Q ⟶ R
X Y : C
f : X ⟶ Y
c : KernelFork f
hc : IsLimit c
h : IsZero c.pt
P✝ : C
g : P✝ ⟶ X
hg : g ≫ f = 0
⊢ g = 0 | case mk
C : Type u
inst✝¹ : Category.{v, u} C
inst✝ : Preadditive C
P Q R : C
f✝ f' : P ⟶ Q
g✝ g' : Q ⟶ R
X Y : C
f : X ⟶ Y
c : KernelFork f
hc : IsLimit c
h : IsZero c.pt
P✝ : C
g : P✝ ⟶ X
hg : g ≫ f = 0
a : P✝ ⟶ c.pt
ha : a ≫ Fork.ι c = g
⊢ g = 0 | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.39912) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.39912) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.39912) (:fv _uniq.39915))) (:fv _uniq.41007) (:fv _uniq.40873)) (:fv _uniq.41010) ((:c OfNat.ofNat) ((:c Quiver.Hom) (:fv _uniq.39912) ((:c CategoryTheory.... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.39912))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Preadditive) (:fv _uniq.39912) (:fv _uniq.39915))"},{"name":"P","sexp":"(:fv _uniq.39912)"},{"name":"Q","sexp":"(:fv _uniq.39912)"},{"name":"R","sexp":"(:fv _uni... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV17)) (:arg :explicit 3 (:fv FV11)))) (:arg :explicit 1 (:fv FV18)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :impli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.39912","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.39915","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"obtain","sourceEnd":10191,"sourceStart":10185,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":10195,"sourceStart":10192,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEn... | [] | [{"source":"KernelFork.IsLimit.lift' hc _ hg","source_end":10239,"source_start":10207,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨a, ha⟩","source_end":10203,"source_start":10192,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.39912","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.39915","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 74 | 4 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 40cdbd114c4dd19d33a3717a8dc7397b708ac7e80781e1bf1390a4295a641d56 | bbc16b0bccccf614f82c31eb318d8d7c66fa93586789164ab2757e9a2328d1c8 | ec5fd883edf884517c6f5159c8c86fba1557ee0002fbaa59ed1d75a0d21a32e0 | d9cf2a57938f52e6b921582407f7a6987388d7d83d9b4fea1e5d2186052e31bd |
cat-searcher/leandojo-benchmark-4-random | test | 1,961 | CategoryTheory.Preadditive.mono_of_isZero_kernel' | Mathlib/CategoryTheory/Preadditive/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← ha, h.eq_of_tgt a 0, <a>CategoryTheory.Limits.zero_comp</a>] | case mk
C : Type u
inst✝¹ : Category.{v, u} C
inst✝ : Preadditive C
P Q R : C
f✝ f' : P ⟶ Q
g✝ g' : Q ⟶ R
X Y : C
f : X ⟶ Y
c : KernelFork f
hc : IsLimit c
h : IsZero c.pt
P✝ : C
g : P✝ ⟶ X
hg : g ≫ f = 0
a : P✝ ⟶ c.pt
ha : a ≫ Fork.ι c = g
⊢ g = 0 | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.39912) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.39912) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.39912) (:fv _uniq.39915))) (:fv _uniq.41007) (:fv _uniq.40873)) (:fv _uniq.41010) ((:c OfNat.ofNat) ((:c Quiver.Hom) (:fv _uniq.39912) ((:c CategoryTheory.... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.39912))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Preadditive) (:fv _uniq.39912) (:fv _uniq.39915))"},{"name":"P","sexp":"(:fv _uniq.39912)"},{"name":"Q","sexp":"(:fv _uniq.39912)"},{"name":"R","sexp":"(:fv _uni... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV17)) (:arg :explicit 3 (:fv FV11)))) (:arg :explicit 1 (:fv FV18)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :impli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.39912","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.39915","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"rw","sourceEnd":10244,"sourceStart":10242,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10246,"sourceStart":10245,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":10249,"sourceSt... | [] | [{"source":"ha","source_end":10252,"source_start":10250,"syntax_kind":"ident"},{"source":"h.eq_of_tgt a 0","source_end":10269,"source_start":10254,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Limits.zero_comp","source_end":10287,"source_start":10271,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.39912","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.39915","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 74 | 5 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 23bd4d3dbfaf78e1dfc1202be38ee9b76d037972241203cf081ff90411dc4be5 | d9cf2a57938f52e6b921582407f7a6987388d7d83d9b4fea1e5d2186052e31bd | 40199b6bb495024eb0349ddbe70c1ca28a17d4e02d9d324b364b0e24c9037bfe | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,962 | balancedCoreAux_subset | Mathlib/Analysis/LocallyConvex/BalancedCoreHull.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>one_smul</a>] using <a>mem_balancedCoreAux_iff</a>.1 hx 1 norm_one.ge | 𝕜 : Type u_1
E : Type u_2
ι : Type u_3
inst✝² : NormedField 𝕜
inst✝¹ : AddCommGroup E
inst✝ : Module 𝕜 E
s✝ t s : Set E
x : E
hx : x ∈ balancedCoreAux 𝕜 s
⊢ x ∈ s | ((:c Membership.mem) (:fv _uniq.45757) ((:c Set) (:fv _uniq.45757)) ((:c Set.instMembership) (:fv _uniq.45757)) (:fv _uniq.47942) (:fv _uniq.47939)) | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c NormedField) (:fv _uniq.45754))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.45757))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.45754) (:fv _uniq.457... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:fv FV10)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45754","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45757","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":6145,"sourceStart":6140,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"one_smul","source_end":6160,"source_start":6152,"syntax_kind":"ident"},{"source":"mem_balancedCoreAux_iff.1 hx 1 norm_one.ge","source_end":6210,"source_start":6168,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45754","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45757","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 53 | 2 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4769b31df3c77d8e0e644b831e027959ed34774f3c038374b94d48e2b2a90ce7 | fb6a7fc78b5bf4bada4193dbd795fa275bee98d55543fbebcd2772e31388f9a9 | f249f0880abdbfb36845fed5a3793941fd6eedf89b753d2095fb87a5e9286619 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,963 | Equiv.swap_smul_self_smul | Mathlib/GroupTheory/Perm/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>smul_smul</a>] | α : Type u
β : Type v
inst✝¹ : DecidableEq α
inst✝ : MulAction (Perm α) β
i j : α
x : β
⊢ swap i j • swap i j • x = x | ((:c Eq) (:fv _uniq.40993) ((:c HSMul.hSMul) ((:c Equiv.Perm) (:fv _uniq.40991)) (:fv _uniq.40993) (:fv _uniq.40993) ((:c instHSMul) ((:c Equiv.Perm) (:fv _uniq.40991)) (:fv _uniq.40993) ((:c MulAction.toSMul) ((:c Equiv.Perm) (:fv _uniq.40991)) (:fv _uniq.40993) ((:c DivInvMonoid.toMonoid) ((:c Equiv.Perm) (:fv _uniq.... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.40991))"},{"name":"inst✝","sexp":"((:c MulAction) ((:c Equiv.Perm) (:fv _uniq.40991)) (:fv _uniq.40993) ((:c DivInvMonoid.toMonoid) ((:c Equiv.Perm) (:fv _uniq.40991)) ((:c Group.toDivInvMo... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:app (:c Equiv.Perm) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HSMul) (:arg :explicit 0 (:app (:c Equiv.Perm... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40991","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40993","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":21795,"sourceStart":21791,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"smul_smul","source_end":21806,"source_start":21797,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40991","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40993","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 187 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 26ead38d4b386656eae875a5d89880c831f847b221a57948d5efbafe75e458c6 | 124f1499a36d3cbd15e893b119775e0a21f38a91a6185e4cc949ceed1a7464a6 | 5bffc9ada26e1fd56416e9c7ed2fe006e0852697473a061c264c408fb0697c64 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,964 | BddBelow.isBoundedUnder | Mathlib/Order/LiminfLimsup.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [<a>mem_lowerBounds</a>] using hb | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
ι' : Type u_5
r : α → α → Prop
f✝ g : Filter α
inst✝ : Preorder α
f : Filter β
u : β → α
b : α
hb : b ∈ lowerBounds (range u)
⊢ ∀ (x : β), u x ≥ b | (:forall x (:fv _uniq.14848) ((:c GE.ge) (:fv _uniq.14845) ((:c Preorder.toLE) (:fv _uniq.14845) (:fv _uniq.15046)) ((:fv _uniq.15048) 0) (:fv _uniq.15082))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"ι'","sexp":"(:sort (+ u_5 1))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.14845) (:forall _ (:fv _uniq.14845) (:sort 0)))"},{"name":"f✝","sexp":"((:c ... | (:forall x :explicit (:fv FV1) (:app (:c GE.ge) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:fv FV11) (:arg :explicit 0 0))) (:arg :explicit 3 (:fv FV12)))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14845","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14848","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":7052,"sourceStart":7047,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"mem_lowerBounds","source_end":7069,"source_start":7054,"syntax_kind":"ident"},{"source":"hb","source_end":7079,"source_start":7077,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14845","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14848","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 37 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | badbc54b827f1cb57cb135817fba2ff1b70e84e0c22f6952b60f88945e451d0c | 306ce146940c9ac9efef931e9f1b9510861ad01df7d8beb1eb0318a68896f784 | ea75d4cb457b5940cdee6452e8356e4f53d51116a8683fb252b4a5206a8eb015 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,965 | MeasureTheory.SimpleFunc.ennrealRatEmbed_encode | Mathlib/MeasureTheory/Function/SimpleFunc.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.SimpleFunc.ennrealRatEmbed</a>, <a>Encodable.encodek</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
inst✝ : MeasurableSpace α
K : Type u_5
q : ℚ
⊢ ennrealRatEmbed (Encodable.encode q) = ↑(↑q).toNNReal | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
inst✝ : MeasurableSpace α
K : Type u_5
q : ℚ
⊢ ENNReal.ofReal ↑((some q).getD 0) = ↑(↑q).toNNReal | ((:c Eq) (:c ENNReal) ((:c MeasureTheory.SimpleFunc.ennrealRatEmbed) ((:c Encodable.encode) (:c Rat) (:c Rat.instEncodable) (:fv _uniq.129347))) ((:c ENNReal.ofNNReal) ((:c Real.toNNReal) ((:c Rat.cast) (:c Real) (:c Real.instRatCast) (:fv _uniq.129347))))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c MeasurableSpace) (:fv _uniq.129115))"},{"name":"K","sexp":"(:sort (+ u_5 1))"},{"name":"q","sexp":"(:c Rat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.SimpleFunc.ennrealRatEmbed) (:arg :explicit 0 (:app (:c Encodable.encode) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c Encodable) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:fv FV7)))))) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129115","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129118","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":42755,"sourceStart":42753,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":42757,"sourceStart":42756,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MeasureTheory.Si... | [] | [{"source":"ennrealRatEmbed","source_end":42772,"source_start":42757,"syntax_kind":"ident"},{"source":"Encodable.encodek","source_end":42791,"source_start":42774,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129115","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129118","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 330 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8fc1edfb1b6d4e5768c1fd0c9d73923e4a24c3ee8281a2cb92d6272ed4e756d9 | 227d1de32358dee3d2f11490498e42787cc43de6f8ce8a33251346c13b2ad360 | 868cfb677ea3109f0fadcccff8821932c28378052570377259668be6d9e2e8d0 | 8f14dce93ff2346de8e01b7c9b0e282f21d695bd182bf1e2b2192312e7c374d0 |
cat-searcher/leandojo-benchmark-4-random | test | 1,966 | MeasureTheory.SimpleFunc.ennrealRatEmbed_encode | Mathlib/MeasureTheory/Function/SimpleFunc.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
inst✝ : MeasurableSpace α
K : Type u_5
q : ℚ
⊢ ENNReal.ofReal ↑((some q).getD 0) = ↑(↑q).toNNReal | ((:c Eq) (:c ENNReal) ((:c ENNReal.ofReal) ((:c Rat.cast) (:c Real) (:c Real.instRatCast) ((:c Option.getD) (:c Rat) ((:c Option.some) (:c Rat) (:fv _uniq.129347)) ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0)))))) ((:c ENNReal.ofNNReal) ((:c Real.toNNReal) ((:c Rat.cast) (:c Real) (:c Real.instRatCa... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c MeasurableSpace) (:fv _uniq.129115))"},{"name":"K","sexp":"(:sort (+ u_5 1))"},{"name":"q","sexp":"(:c Rat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c ENNReal.ofReal) (:arg :explicit 0 (:app (:c Rat.cast) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c RatCast) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Option.getD) (:arg :implicit-type 0 (:c Ra... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129115","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129118","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rfl","sourceEnd":42797,"sourceStart":42794,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":42797,"sourceStart":42794,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.129115","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.129118","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 330 | 9 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ef003eeceeb137a138c559299b15b07dbc8b896518de2cde08a2c9f06c7f56b9 | 8f14dce93ff2346de8e01b7c9b0e282f21d695bd182bf1e2b2192312e7c374d0 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,967 | Stream'.Seq.not_terminates_iff | Mathlib/Data/Seq/Seq.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Stream'.Seq.Terminates</a>, <a>Stream'.Seq.TerminatedAt</a>, ← Ne.eq_def, <a>Option.ne_none_iff_isSome</a>, <a>not_exists</a>, <a>iff_self</a>] | α : Type u
β : Type v
γ : Type w
s : Seq α
⊢ ¬s.Terminates ↔ ∀ (n : ℕ), (s.get? n).isSome = true | ((:c Iff) ((:c Not) ((:c Stream'.Seq.Terminates) (:fv _uniq.1990) (:fv _uniq.2031))) (:forall n (:c Nat) ((:c Eq) (:c Bool) ((:c Option.isSome) (:fv _uniq.1990) ((:c Stream'.Seq.get?) (:fv _uniq.1990) (:fv _uniq.2031) 0)) (:c Bool.true)))) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"s","sexp":"((:c Stream'.Seq) (:fv _uniq.1990))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Not) (:arg :explicit 0 (:app (:c Stream'.Seq.Terminates) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV4)))))) (:arg :explicit 1 (:forall n :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:c Bool)) (:arg :explicit 1 (:app (:c Option.isSome) (:arg :implici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1990","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1992","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":4350,"sourceStart":4346,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":4355,"sourceStart":4351,"tag":"atom"}],"kind":"nu... | [] | [{"source":"Terminates","source_end":4367,"source_start":4357,"syntax_kind":"ident"},{"source":"TerminatedAt","source_end":4381,"source_start":4369,"syntax_kind":"ident"},{"source":"Ne.eq_def","source_end":4396,"source_start":4387,"syntax_kind":"ident"},{"source":"Option.ne_none_iff_isSome","source_end":4423,"source_st... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1990","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1992","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 43 | 2 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4bcfc3ab6b6954b405317474c9b3d5ec482acffa3f2b8bc0220104dd795f8c14 | b0a0ea4e5d234ed381d44e41ed9a44a589d34c12b220abbc277c2ed67e583967 | 58f71ea831854bf2087cfd386cb2a7e7e352f32c2dbd5093637c82fcd91613b7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,968 | MulAction.card_orbit_mul_card_stabilizer_eq_card_group | Mathlib/GroupTheory/GroupAction/Quotient.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Fintype.card_prod</a>, <a>Fintype.card_congr</a> (<a>MulAction.orbitProdStabilizerEquivGroup</a> α b)] | α : Type u
β : Type v
γ : Type w
inst✝⁵ inst✝⁴ : Group α
inst✝³ : MulAction α β
x b : β
inst✝² : Fintype α
inst✝¹ : Fintype ↑(orbit α b)
inst✝ : Fintype ↥(stabilizer α b)
⊢ Fintype.card ↑(orbit α b) * Fintype.card ↥(stabilizer α b) = Fintype.card α | ((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) ((:c Fintype.card) ((:c Set.Elem) (:fv _uniq.59486) ((:c MulAction.orbit) (:fv _uniq.59484) ((:c DivInvMonoid.toMonoid) (:fv _uniq.59484) ((:c Group.toDivInvMonoid) (:fv _uniq.59484) (:fv _uniq.59494))) (:fv _uniq.5948... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"inst✝⁵","sexp":"((:c Group) (:fv _uniq.59484))"},{"name":"inst✝⁴","sexp":"((:c Group) (:fv _uniq.59484))"},{"name":"inst✝³","sexp":"((:c MulAction) (:fv _uniq.59484) (:fv _uniq.59486) ((:c DivInvM... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.59484","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.59486","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":10079,"sourceStart":10077,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10081,"sourceStart":10080,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"Fintype.card_prod","source_end":10102,"source_start":10085,"syntax_kind":"ident"},{"source":"Fintype.card_congr (orbitProdStabilizerEquivGroup α b)","source_end":10159,"source_start":10104,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.59484","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.59486","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 73 | 2 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c05968789800372b7f0e63fc6028ea7f6bb235d14140114d661768bcf27e5e40 | 1cf7182b30959b4452e6fc00485140e70533c6c58a11b5fed29477750c560f1e | bb8d2f90a018a34bcd950129036a384ae455509dc7d895ad4b9c0d4c54959efd | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,969 | MeasureTheory.Measure.addHaar_parallelepiped | Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>FiniteDimensional</a> ℝ G := <a>FiniteDimensional.of_fintype_basis</a> b | E : Type u_1
inst✝¹⁴ : NormedAddCommGroup E
inst✝¹³ : NormedSpace ℝ E
inst✝¹² : MeasurableSpace E
inst✝¹¹ : BorelSpace E
inst✝¹⁰ : FiniteDimensional ℝ E
μ : Measure E
inst✝⁹ : μ.IsAddHaarMeasure
F : Type u_2
inst✝⁸ : NormedAddCommGroup F
inst✝⁷ : NormedSpace ℝ F
inst✝⁶ : CompleteSpace F
s : Set E
ι : Type u_3
G : Type ... | E : Type u_1
inst✝¹⁴ : NormedAddCommGroup E
inst✝¹³ : NormedSpace ℝ E
inst✝¹² : MeasurableSpace E
inst✝¹¹ : BorelSpace E
inst✝¹⁰ : FiniteDimensional ℝ E
μ : Measure E
inst✝⁹ : μ.IsAddHaarMeasure
F : Type u_2
inst✝⁸ : NormedAddCommGroup F
inst✝⁷ : NormedSpace ℝ F
inst✝⁶ : CompleteSpace F
s : Set E
ι : Type u_3
G : Type ... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.342863) (:fv _uniq.342989)) ((:c Set) (:fv _uniq.342863)) (:lambda _ ((:c Set) (:fv _uniq.342863)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.342863) (:fv _uniq.342989)) ((:c Basis.addHaar) (:fv _uniq.342860) (:fv _uni... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.341775))"},{"name":"inst✝¹³","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.341775) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.341775) (:fv _uniq.341778)))"},{"name":"inst✝¹²","... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV14)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV14))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.341775","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.341778","is_instance":true,"is_let":false,"name":"inst✝¹⁴","sexp":"(:app (:c NormedAddCommGroup) ... | {"children":[{"source":"have","sourceEnd":32484,"sourceStart":32480,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":32485,"sourceStart":32485,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":32485,"sourceStart":32485,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"FiniteDimensional ℝ G","source_end":32510,"source_start":32487,"syntax_kind":"Lean.Parser.Term.app"},{"source":"FiniteDimensional.of_fintype_basis b","source_end":32550,"source_start":32514,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.341775","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.341778","is_instance":true,"is_let":false,"user_name":"inst✝¹⁴"},{"binder_role":":instance-implicit","context_inde... | 109 | 4 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d6fd55f8d8382fef0b1d465779524710e3b9028d57dc3d28d95a0b9f0eda2013 | 000e3fdc14ff8a5e235cff74a18caea225335bc8678c275e25539b542eeb59e8 | e561ec7a274dbdf83c60c9ed941fa6d26e1132450c1f0e35ebf6dce2bd15cc5a | 73adde2fa85c34a490027e299ecc302c891949b4cedcfedd0bf2a252840cd67a |
cat-searcher/leandojo-benchmark-4-random | test | 1,971 | MeasureTheory.Measure.addHaar_parallelepiped | Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [A, <a>MeasureTheory.Measure.addHaar_image_linearMap</a>, b.addHaar_self, <a>mul_one</a>, ← <a>LinearMap.det_toMatrix</a> b, ← <a>Basis.toMatrix_eq_toMatrix_constr</a>, <a>Basis.det_apply</a>] | E : Type u_1
inst✝¹⁴ : NormedAddCommGroup E
inst✝¹³ : NormedSpace ℝ E
inst✝¹² : MeasurableSpace E
inst✝¹¹ : BorelSpace E
inst✝¹⁰ : FiniteDimensional ℝ E
μ : Measure E
inst✝⁹ : μ.IsAddHaarMeasure
F : Type u_2
inst✝⁸ : NormedAddCommGroup F
inst✝⁷ : NormedSpace ℝ F
inst✝⁶ : CompleteSpace F
s : Set E
ι : Type u_3
G : Type ... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.342863) (:fv _uniq.342989)) ((:c Set) (:fv _uniq.342863)) (:lambda _ ((:c Set) (:fv _uniq.342863)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.342863) (:fv _uniq.342989)) ((:c Basis.addHaar) (:fv _uniq.342860) (:fv _uni... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.341775))"},{"name":"inst✝¹³","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.341775) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.341775) (:fv _uniq.341778)))"},{"name":"inst✝¹²","... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV14)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV14))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.341775","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.341778","is_instance":true,"is_let":false,"name":"inst✝¹⁴","sexp":"(:app (:c NormedAddCommGroup) ... | {"children":[{"source":"rw","sourceEnd":32823,"sourceStart":32821,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32825,"sourceStart":32824,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":25,"seman... | [] | [{"source":"A","source_end":32826,"source_start":32825,"syntax_kind":"ident"},{"source":"addHaar_image_linearMap","source_end":32851,"source_start":32828,"syntax_kind":"ident"},{"source":"b.addHaar_self","source_end":32867,"source_start":32853,"syntax_kind":"ident"},{"source":"mul_one","source_end":32876,"source_start"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.341775","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.341778","is_instance":true,"is_let":false,"user_name":"inst✝¹⁴"},{"binder_role":":instance-implicit","context_inde... | 109 | 12 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 005963f2833680a38d2ab7803c05ed892c526837a7841daa98a0f2b3c3327d90 | acb65bf09a6534f2eb27748d2e67823160ac9e9008b9aae95fa281b413cb9159 | 7471e8d1f6b4d2190c5122b2716afc63cf0ebba88fa325f6f985c25204440893 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,972 | MeasureTheory.Measure.addHaar_parallelepiped | Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>image_parallelepiped</a>] | E : Type u_1
inst✝¹⁴ : NormedAddCommGroup E
inst✝¹³ : NormedSpace ℝ E
inst✝¹² : MeasurableSpace E
inst✝¹¹ : BorelSpace E
inst✝¹⁰ : FiniteDimensional ℝ E
μ : Measure E
inst✝⁹ : μ.IsAddHaarMeasure
F : Type u_2
inst✝⁸ : NormedAddCommGroup F
inst✝⁷ : NormedSpace ℝ F
inst✝⁶ : CompleteSpace F
s : Set E
ι : Type u_3
G : Type ... | E : Type u_1
inst✝¹⁴ : NormedAddCommGroup E
inst✝¹³ : NormedSpace ℝ E
inst✝¹² : MeasurableSpace E
inst✝¹¹ : BorelSpace E
inst✝¹⁰ : FiniteDimensional ℝ E
μ : Measure E
inst✝⁹ : μ.IsAddHaarMeasure
F : Type u_2
inst✝⁸ : NormedAddCommGroup F
inst✝⁷ : NormedSpace ℝ F
inst✝⁶ : CompleteSpace F
s : Set E
ι : Type u_3
G : Type ... | ((:c Eq) ((:c Set) (:fv _uniq.342863)) ((:c parallelepiped) (:fv _uniq.342860) (:fv _uniq.342863) (:fv _uniq.342866) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.342863) (:fv _uniq.342878)) ((:c NormedSpace.toModule) (:c Real) (:fv _uniq.342863) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGro... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.341775))"},{"name":"inst✝¹³","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.341775) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.341775) (:fv _uniq.341778)))"},{"name":"inst✝¹²","... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV14)))) (:arg :explicit 1 (:app (:c parallelepiped) (:arg :implicit-type 0 (:fv FV13)) (:arg :implicit-type 1 (:fv FV14)) (:arg :instance 2 (:instance-of (:app (:c Fintype) (:arg :explicit 0 (:fv FV13))))) (:arg :instance 3 (:instance-of (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.341775","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.341778","is_instance":true,"is_let":false,"name":"inst✝¹⁴","sexp":"(:app (:c NormedAddCommGroup) ... | {"children":[{"source":"rw","sourceEnd":32628,"sourceStart":32626,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32630,"sourceStart":32629,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"image_parallelep... | [] | [{"source":"image_parallelepiped","source_end":32650,"source_start":32630,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.341775","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.341778","is_instance":true,"is_let":false,"user_name":"inst✝¹⁴"},{"binder_role":":instance-implicit","context_inde... | 109 | 7 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7c4813747c2338e8a5a06eeab4fa68f58883b56c1904cc04e2a24d90505b4a64 | d46ca26041d2d7dfdb627e5204c3176b4cfb3e1f5b29c07886c053eca3618639 | df311762751972e92fc4ae72b1ea390b495f58963e3bf5c4af6161ccf9751c88 | 0c9c1c38523c93a46335796425887dfc334823eb0a404ffc098ce8800cd36a26 |
cat-searcher/leandojo-benchmark-4-random | test | 1,973 | MeasureTheory.Measure.addHaar_parallelepiped | Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>congr_arg</a> _ <| <a>funext</a> fun i ↦ ?_ | E : Type u_1
inst✝¹⁴ : NormedAddCommGroup E
inst✝¹³ : NormedSpace ℝ E
inst✝¹² : MeasurableSpace E
inst✝¹¹ : BorelSpace E
inst✝¹⁰ : FiniteDimensional ℝ E
μ : Measure E
inst✝⁹ : μ.IsAddHaarMeasure
F : Type u_2
inst✝⁸ : NormedAddCommGroup F
inst✝⁷ : NormedSpace ℝ F
inst✝⁶ : CompleteSpace F
s : Set E
ι : Type u_3
G : Type ... | E : Type u_1
inst✝¹⁴ : NormedAddCommGroup E
inst✝¹³ : NormedSpace ℝ E
inst✝¹² : MeasurableSpace E
inst✝¹¹ : BorelSpace E
inst✝¹⁰ : FiniteDimensional ℝ E
μ : Measure E
inst✝⁹ : μ.IsAddHaarMeasure
F : Type u_2
inst✝⁸ : NormedAddCommGroup F
inst✝⁷ : NormedSpace ℝ F
inst✝⁶ : CompleteSpace F
s : Set E
ι : Type u_3
G : Type ... | ((:c Eq) ((:c Set) (:fv _uniq.342863)) ((:c parallelepiped) (:fv _uniq.342860) (:fv _uniq.342863) (:fv _uniq.342866) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.342863) (:fv _uniq.342878)) ((:c NormedSpace.toModule) (:c Real) (:fv _uniq.342863) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGro... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.341775))"},{"name":"inst✝¹³","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.341775) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.341775) (:fv _uniq.341778)))"},{"name":"inst✝¹²","... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV14)))) (:arg :explicit 1 (:app (:c parallelepiped) (:arg :implicit-type 0 (:fv FV13)) (:arg :implicit-type 1 (:fv FV14)) (:arg :instance 2 (:instance-of (:app (:c Fintype) (:arg :explicit 0 (:fv FV13))))) (:arg :instance 3 (:instance-of (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.341775","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.341778","is_instance":true,"is_let":false,"name":"inst✝¹⁴","sexp":"(:app (:c NormedAddCommGroup) ... | {"children":[{"source":"refine","sourceEnd":32743,"sourceStart":32737,"tag":"atom"},{"children":[{"children":[{"name":"congr_arg","semanticRole":"global","source":"congr_arg","sourceEnd":32753,"sourceStart":32744,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":32755,"sourceStart":32754,"tag":"at... | [] | [{"source":"congr_arg _ <| funext fun i ↦ ?_","source_end":32778,"source_start":32744,"syntax_kind":"«term_<|_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.341775","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.341778","is_instance":true,"is_let":false,"user_name":"inst✝¹⁴"},{"binder_role":":instance-implicit","context_inde... | 109 | 10 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 76ac8aa5da72924be80b0d82b902260aef72b48cc452ef7c4114d5bb6ddbb74c | 0c9c1c38523c93a46335796425887dfc334823eb0a404ffc098ce8800cd36a26 | ed29194ca5885b48d178e1626e71970980a70a65dcf5a6d74a714059d46c95ea | 6f2f1ca5cda04f6a28f5b56e1dbd07d87c35d0f45094a2754e07047c6fec35ed |
cat-searcher/leandojo-benchmark-4-random | test | 1,974 | MeasureTheory.Measure.addHaar_parallelepiped | Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (b.constr_basis ℕ v i).<a>Eq.symm</a> | E : Type u_1
inst✝¹⁴ : NormedAddCommGroup E
inst✝¹³ : NormedSpace ℝ E
inst✝¹² : MeasurableSpace E
inst✝¹¹ : BorelSpace E
inst✝¹⁰ : FiniteDimensional ℝ E
μ : Measure E
inst✝⁹ : μ.IsAddHaarMeasure
F : Type u_2
inst✝⁸ : NormedAddCommGroup F
inst✝⁷ : NormedSpace ℝ F
inst✝⁶ : CompleteSpace F
s : Set E
ι : Type u_3
G : Type ... | ((:c Eq) (:fv _uniq.342863) ((:fv _uniq.344783) (:fv _uniq.352926)) ((:c Function.comp) (:fv _uniq.342860) (:fv _uniq.342863) (:fv _uniq.342863) ((:c DFunLike.coe) ((:c LinearMap) (:c Real) (:c Real) (:c Real.semiring) (:c Real.semiring) ((:c RingHom.id) (:c Real) ((:c Semiring.toNonAssocSemiring) (:c Real) (:c Real.se... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.341775))"},{"name":"inst✝¹³","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.341775) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.341775) (:fv _uniq.341778)))"},{"name":"inst✝¹²","... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV14)) (:arg :explicit 1 (:app (:fv FV23) (:arg :explicit 0 (:fv FV25)))) (:arg :explicit 2 (:app (:c Function.comp) (:arg :implicit-type 0 (:fv FV13)) (:arg :implicit-type 1 (:fv FV14)) (:arg :implicit-type 2 (:fv FV14)) (:arg :explicit 3 (:app (:c DFunLike.coe) (:arg :implici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.341775","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.341778","is_instance":true,"is_let":false,"name":"inst✝¹⁴","sexp":"(:app (:c NormedAddCommGroup) ... | {"children":[{"source":"exact","sourceEnd":32788,"sourceStart":32783,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":32790,"sourceStart":32789,"tag":"atom"},{"children":[{"source":"b.constr_basis","sourceEnd":32804,"sourceStart":32790,"tag":"identifier"},{"children":[{"children":[{"source":"ℕ","source... | [] | [{"source":"(b.constr_basis ℕ v i).symm","source_end":32818,"source_start":32789,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.341775","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.341778","is_instance":true,"is_let":false,"user_name":"inst✝¹⁴"},{"binder_role":":instance-implicit","context_inde... | 109 | 11 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b0210d51230de8b87041d02fcbb4c11829b7729802a1ff1ed8cd5bf7485a804d | 6f2f1ca5cda04f6a28f5b56e1dbd07d87c35d0f45094a2754e07047c6fec35ed | d0707e01f193f2af6e57673768034650863f1b766eacbe5732d7576c86f6946e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,975 | ContMDiffWithinAt.prod_mk | Mathlib/Geometry/Manifold/ContMDiff/Product.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>contMDiffWithinAt_iff</a>] at * | 𝕜 : Type u_1
inst✝³⁷ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³⁶ : NormedAddCommGroup E
inst✝³⁵ : NormedSpace 𝕜 E
H : Type u_3
inst✝³⁴ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝³³ : TopologicalSpace M
inst✝³² : ChartedSpace H M
inst✝³¹ : SmoothManifoldWithCorners I M
E' : Type u_5
inst✝... | 𝕜 : Type u_1
inst✝³⁷ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³⁶ : NormedAddCommGroup E
inst✝³⁵ : NormedSpace 𝕜 E
H : Type u_3
inst✝³⁴ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝³³ : TopologicalSpace M
inst✝³² : ChartedSpace H M
inst✝³¹ : SmoothManifoldWithCorners I M
E' : Type u_5
inst✝... | ((:c ContMDiffWithinAt) (:fv _uniq.4257) (:fv _uniq.4260) (:fv _uniq.4263) (:fv _uniq.4266) (:fv _uniq.4379) (:fv _uniq.4382) (:fv _uniq.4385) (:fv _uniq.4417) (:fv _uniq.4420) (:fv _uniq.4423) (:fv _uniq.4435) ((:c Prod) (:fv _uniq.4629) (:fv _uniq.5521)) ((:c Prod.normedAddCommGroup) (:fv _uniq.4629) (:fv _uniq.5521)... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³⁷","sexp":"((:c NontriviallyNormedField) (:fv _uniq.4257))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³⁶","sexp":"((:c NormedAddCommGroup) (:fv _uniq.4263))"},{"name":"inst✝³⁵","sexp":"((:c NormedSpace) (:fv _uniq.4257) (:fv _uniq.4263) ((:c Nontrivi... | (:app (:c ContMDiffWithinAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4257","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4260","is_instance":true,"is_let":false,"name":"inst✝³⁷","sexp":"(:app (:c NontriviallyNormedField... | {"children":[{"source":"rw","sourceEnd":2900,"sourceStart":2898,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2902,"sourceStart":2901,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"contMDiffWithinAt_if... | [] | [{"source":"contMDiffWithinAt_iff","source_end":2923,"source_start":2902,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4257","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4260","is_instance":true,"is_let":false,"user_name":"inst✝³⁷"},{"binder_role":":implicit","context_index":2,"intern... | 6 | 4 | exact | true | 1 | 77 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 76bb6c469eeea6d8845a7c9610cb402012497c460d77c848d630a002b7463476 | 83a2e05d81f9d658039a5ad787643e5b0713b2ee86edb6d9d372a341cf796014 | bf7a689f7dd57cfddc1fdc37043073f20d31af5aac77418452539961870ab69e | 676d41defce29182166946a95f166d372f850b879ad408d30c7c58aff428e460 |
cat-searcher/leandojo-benchmark-4-random | test | 1,976 | ContMDiffWithinAt.prod_mk | Mathlib/Geometry/Manifold/ContMDiff/Product.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨hf.1.<a>ContinuousWithinAt.prod</a> hg.1, hf.2.<a>ContDiffWithinAt.prod</a> hg.2⟩ | 𝕜 : Type u_1
inst✝³⁷ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³⁶ : NormedAddCommGroup E
inst✝³⁵ : NormedSpace 𝕜 E
H : Type u_3
inst✝³⁴ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝³³ : TopologicalSpace M
inst✝³² : ChartedSpace H M
inst✝³¹ : SmoothManifoldWithCorners I M
E' : Type u_5
inst✝... | ((:c And) ((:c ContinuousWithinAt) (:fv _uniq.4420) ((:c Prod) (:fv _uniq.4781) (:fv _uniq.5673)) (:fv _uniq.4423) ((:c instTopologicalSpaceProd) (:fv _uniq.4781) (:fv _uniq.5673) (:fv _uniq.4784) (:fv _uniq.5676)) (:lambda x (:fv _uniq.4420) ((:c Prod.mk) (:fv _uniq.4781) (:fv _uniq.5673) ((:fv _uniq.7472) 0) ((:fv _u... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³⁷","sexp":"((:c NontriviallyNormedField) (:fv _uniq.4257))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³⁶","sexp":"((:c NormedAddCommGroup) (:fv _uniq.4263))"},{"name":"inst✝³⁵","sexp":"((:c NormedSpace) (:fv _uniq.4257) (:fv _uniq.4263) ((:c Nontrivi... | (:app (:c And) (:arg :explicit 0 (:app (:c ContinuousWithinAt) (:arg :implicit-type 0 (:fv FV8)) (:arg :implicit-type 1 (:app (:c Prod) (:arg :explicit 0 (:fv FV18)) (:arg :explicit 1 (:fv FV47)))) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV8))))) (:arg :instance 3 (:instance-o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4257","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4260","is_instance":true,"is_let":false,"name":"inst✝³⁷","sexp":"(:app (:c NontriviallyNormedField... | {"children":[{"source":"exact","sourceEnd":2937,"sourceStart":2932,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":2941,"sourceStart":2938,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"contextIndex":76,"semanticRole":"local","source":"hf","sourceEnd":2943,"sourceStart":2941,"tag":"identifier"... | [] | [{"source":"⟨hf.1.prod hg.1, hf.2.prod hg.2⟩","source_end":2974,"source_start":2938,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4257","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4260","is_instance":true,"is_let":false,"user_name":"inst✝³⁷"},{"binder_role":":implicit","context_index":2,"intern... | 6 | 7 | exact | true | 1 | 77 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bdae7a1c5c4ee5bdf85a54613012dc87b8c9948eb0b4b8d89aa2021604578279 | 676d41defce29182166946a95f166d372f850b879ad408d30c7c58aff428e460 | 50254c707df89a5ea6b28413d2a9621da33a442032b4ef06393c1edd7eef23b3 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,977 | Trivialization.coordChange_coordChange | Mathlib/Topology/FiberBundle/Trivialization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Trivialization.coordChange</a>, e₁.mk_coordChange _ h₁ h₂, ← e₂.coe_coe, e₂.left_inv, <a>Trivialization.coordChange</a>] | ι : Type u_1
B : Type u_2
F : Type u_3
E : B → Type u_4
Z : Type u_5
inst✝³ : TopologicalSpace B
inst✝² : TopologicalSpace F
proj : Z → B
inst✝¹ : TopologicalSpace Z
inst✝ : TopologicalSpace (TotalSpace F E)
e : Trivialization F proj
x✝ : Z
e' : Trivialization F TotalSpace.proj
x' : TotalSpace F E
b✝ : B
y : E b✝
e₁ e₂... | ι : Type u_1
B : Type u_2
F : Type u_3
E : B → Type u_4
Z : Type u_5
inst✝³ : TopologicalSpace B
inst✝² : TopologicalSpace F
proj : Z → B
inst✝¹ : TopologicalSpace Z
inst✝ : TopologicalSpace (TotalSpace F E)
e : Trivialization F proj
x✝ : Z
e' : Trivialization F TotalSpace.proj
x' : TotalSpace F E
b✝ : B
y : E b✝
e₁ e₂... | ((:c Eq) (:fv _uniq.54097) ((:c Trivialization.coordChange) (:fv _uniq.54094) (:fv _uniq.54097) (:fv _uniq.54105) (:fv _uniq.54108) (:fv _uniq.54111) (:fv _uniq.54115) (:fv _uniq.54118) (:fv _uniq.54419) (:fv _uniq.54420) (:fv _uniq.54421) ((:c Trivialization.coordChange) (:fv _uniq.54094) (:fv _uniq.54097) (:fv _uniq.... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"B","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.54094) (:sort (+ u_4 1)))"},{"name":"Z","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.54094))"},{"name":"inst✝²","se... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Trivialization.coordChange) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:fv FV4)) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:in... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54091","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54094","is_instance":false,"is_let":false,"name":"B","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":35000,"sourceStart":34998,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":35002,"sourceStart":35001,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Trivialization.c... | [] | [{"source":"coordChange","source_end":35013,"source_start":35002,"syntax_kind":"ident"},{"source":"e₁.mk_coordChange _ h₁ h₂","source_end":35046,"source_start":35015,"syntax_kind":"Lean.Parser.Term.app"},{"source":"e₂.coe_coe","source_end":35064,"source_start":35052,"syntax_kind":"ident"},{"source":"e₂.left_inv","sourc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54091","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54094","is_instance":false,"is_let":false,"user_name":"B"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 232 | 4 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4379a54befa1045f6db6f0f1caa84cc9ae1f28d2819226f7ed0d9348fc2d37a6 | 54fca63a139cb6432436a8c5b5ebabfa861affd3b1384fb7334aab0d24fcc442 | fe2c00df421a9b17b9a93dd4ba791f18d7c39d43947756cd1820ac6e4c1eaf92 | 3a9542b96a742bdb162707ccb1ca56fcbf79ce3af40eb4bbbfee14213faf83c2 |
cat-searcher/leandojo-benchmark-4-random | test | 1,978 | Trivialization.coordChange_coordChange | Mathlib/Topology/FiberBundle/Trivialization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [e₂.mem_source, e₁.proj_symm_apply' h₁] | ι : Type u_1
B : Type u_2
F : Type u_3
E : B → Type u_4
Z : Type u_5
inst✝³ : TopologicalSpace B
inst✝² : TopologicalSpace F
proj : Z → B
inst✝¹ : TopologicalSpace Z
inst✝ : TopologicalSpace (TotalSpace F E)
e : Trivialization F proj
x✝ : Z
e' : Trivialization F TotalSpace.proj
x' : TotalSpace F E
b✝ : B
y : E b✝
e₁ e₂... | ((:c Membership.mem) (:fv _uniq.54105) ((:c Set) (:fv _uniq.54105)) ((:c Set.instMembership) (:fv _uniq.54105)) ((:c PartialHomeomorph.toFun') ((:c Prod) (:fv _uniq.54094) (:fv _uniq.54097)) (:fv _uniq.54105) ((:c instTopologicalSpaceProd) (:fv _uniq.54094) (:fv _uniq.54097) (:fv _uniq.54108) (:fv _uniq.54111)) (:fv _u... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"B","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.54094) (:sort (+ u_4 1)))"},{"name":"Z","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.54094))"},{"name":"inst✝²","se... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV4)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV4)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV4))))))) (:arg :explicit 3 (:app (:c PartialHomeom... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54091","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54094","is_instance":false,"is_let":false,"name":"B","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rwa","sourceEnd":35099,"sourceStart":35096,"tag":"atom"},{"children":[{"source":"[","sourceEnd":35101,"sourceStart":35100,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Trivialization.mem_source","semanticRole":"global","source":"e₂.mem_so... | [] | [{"source":"e₂.mem_source","source_end":35116,"source_start":35101,"syntax_kind":"ident"},{"source":"e₁.proj_symm_apply' h₁","source_end":35144,"source_start":35118,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54091","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54094","is_instance":false,"is_let":false,"user_name":"B"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 232 | 11 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5b473ea89e81b6418dceb9a214557d02f16ae9906ebfd32fc2b09f0d00bce58f | 3a9542b96a742bdb162707ccb1ca56fcbf79ce3af40eb4bbbfee14213faf83c2 | 70ac9f4ccc3e2707a3239532ba141c84d2d8e36157b206f36fc53dac0d7a0cb8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,979 | TensorProduct.LieModule.lie_tmul_right | Mathlib/Algebra/Lie/TensorProduct.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>TensorProduct.LieModule.hasBracketAux</a>, <a>LinearMap.rTensor_tmul</a>, <a>LieModule.toEnd_apply_apply</a>, <a>LinearMap.add_apply</a>, <a>LinearMap.lTensor_tmul</a>] | R : Type u
inst✝¹⁸ : CommRing R
L : Type v
M : Type w
N : Type w₁
P : Type w₂
Q : Type w₃
inst✝¹⁷ : LieRing L
inst✝¹⁶ : LieAlgebra R L
inst✝¹⁵ : AddCommGroup M
inst✝¹⁴ : Module R M
inst✝¹³ : LieRingModule L M
inst✝¹² : LieModule R L M
inst✝¹¹ : AddCommGroup N
inst✝¹⁰ : Module R N
inst✝⁹ : LieRingModule L N
inst✝⁸ : Lie... | ((:c Eq) ((:c TensorProduct) (:fv _uniq.93704) ((:c CommRing.toCommSemiring) (:fv _uniq.93704) (:fv _uniq.93707)) (:fv _uniq.93711) (:fv _uniq.93713) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.93711) (:fv _uniq.93740)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.93713) (:fv _uniq.94428)) (:fv _uniq.94352) (:fv _un... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹⁸","sexp":"((:c CommRing) (:fv _uniq.93704))"},{"name":"L","sexp":"(:sort (+ v 1))"},{"name":"M","sexp":"(:sort (+ w 1))"},{"name":"N","sexp":"(:sort (+ w₁ 1))"},{"name":"P","sexp":"(:sort (+ w₂ 1))"},{"name":"Q","sexp":"(:sort (+ w₃ 1))"},{"name":"inst✝¹⁷","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:fv FV4)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV3... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.93704","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.93707","is_instance":true,"is_let":false,"name":"inst✝¹⁸","sexp":"(:app (:c CommRing) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":3241,"sourceStart":3237,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":3246,"sourceStart":3242,"tag":"atom"}],"kind":"nu... | [] | [{"source":"hasBracketAux","source_end":3261,"source_start":3248,"syntax_kind":"ident"},{"source":"LinearMap.rTensor_tmul","source_end":3285,"source_start":3263,"syntax_kind":"ident"},{"source":"toEnd_apply_apply","source_end":3304,"source_start":3287,"syntax_kind":"ident"},{"source":"LinearMap.add_apply","source_end":... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.93704","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.93707","is_instance":true,"is_let":false,"user_name":"inst✝¹⁸"},{"binder_role":":implicit","context_index":2,"inter... | 22 | 0 | exact | true | 1 | 28 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aa2dae7181f4be091efb26058ed3ddc5cd1d9a8537c3e5840a07c9b9f12787d4 | be51002927f6192ed67ccbdad27559e35ae70615737134e2a8da02e53bdd021e | 1e6c0f33889eace7c6853a60181f0e4702afe93e709f4b54e73e73eae214439b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,980 | LieModule.coe_linearMap_maxTrivLinearMapEquivLieModuleHom | Mathlib/Algebra/Lie/Abelian.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext | R : Type u
L : Type v
M : Type w
N : Type w₁
inst✝¹⁰ : CommRing R
inst✝⁹ : LieRing L
inst✝⁸ : LieAlgebra R L
inst✝⁷ : AddCommGroup M
inst✝⁶ : Module R M
inst✝⁵ : LieRingModule L M
inst✝⁴ : LieModule R L M
inst✝³ : AddCommGroup N
inst✝² : Module R N
inst✝¹ : LieRingModule L N
inst✝ : LieModule R L N
f : ↥(maxTrivSubmodu... | case h
R : Type u
L : Type v
M : Type w
N : Type w₁
inst✝¹⁰ : CommRing R
inst✝⁹ : LieRing L
inst✝⁸ : LieAlgebra R L
inst✝⁷ : AddCommGroup M
inst✝⁶ : Module R M
inst✝⁵ : LieRingModule L M
inst✝⁴ : LieModule R L M
inst✝³ : AddCommGroup N
inst✝² : Module R N
inst✝¹ : LieRingModule L N
inst✝ : LieModule R L N
f : ↥(maxTriv... | ((:c Eq) ((:c LinearMap) (:fv _uniq.145150) (:fv _uniq.145150) ((:c CommSemiring.toSemiring) (:fv _uniq.145150) ((:c CommRing.toCommSemiring) (:fv _uniq.145150) (:fv _uniq.145159))) ((:c CommSemiring.toSemiring) (:fv _uniq.145150) ((:c CommRing.toCommSemiring) (:fv _uniq.145150) (:fv _uniq.145159))) ((:c RingHom.id) (:... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"L","sexp":"(:sort (+ v 1))"},{"name":"M","sexp":"(:sort (+ w 1))"},{"name":"N","sexp":"(:sort (+ w₁ 1))"},{"name":"inst✝¹⁰","sexp":"((:c CommRing) (:fv _uniq.145150))"},{"name":"inst✝⁹","sexp":"((:c LieRing) (:fv _uniq.145152))"},{"name":"inst✝⁸","sexp":"((:c LieAlgebra) ... | (: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":":implicit","context_index":0,"internal_name":"_uniq.145150","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.145152","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"ext","sourceEnd":11236,"sourceStart":11233,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":11236,"sourceStart":11233,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.145150","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.145152","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 63 | 4 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3b96f5a097794a156abb6155129e34aaaf93e9c3073ead0e8dac56e01e17fa79 | 4ec7f012a98453a463e51545fd3efa7e75660bb6621c4bbe84e2c03a8122a0a9 | a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de | 5ad64f86d722b7273220e788f649e3eee6d09c1092b154b1236e2d2a051a9227 |
cat-searcher/leandojo-benchmark-4-random | test | 1,981 | LieModule.coe_linearMap_maxTrivLinearMapEquivLieModuleHom | Mathlib/Algebra/Lie/Abelian.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case h
R : Type u
L : Type v
M : Type w
N : Type w₁
inst✝¹⁰ : CommRing R
inst✝⁹ : LieRing L
inst✝⁸ : LieAlgebra R L
inst✝⁷ : AddCommGroup M
inst✝⁶ : Module R M
inst✝⁵ : LieRingModule L M
inst✝⁴ : LieModule R L M
inst✝³ : AddCommGroup N
inst✝² : Module R N
inst✝¹ : LieRingModule L N
inst✝ : LieModule R L N
f : ↥(maxTriv... | ((:c Eq) (:fv _uniq.145156) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.145150) (:fv _uniq.145150) ((:c CommSemiring.toSemiring) (:fv _uniq.145150) ((:c CommRing.toCommSemiring) (:fv _uniq.145150) (:fv _uniq.145159))) ((:c CommSemiring.toSemiring) (:fv _uniq.145150) ((:c CommRing.toCommSemiring) (:fv _uniq.145150) (:... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"L","sexp":"(:sort (+ v 1))"},{"name":"M","sexp":"(:sort (+ w 1))"},{"name":"N","sexp":"(:sort (+ w₁ 1))"},{"name":"inst✝¹⁰","sexp":"((:c CommRing) (:fv _uniq.145150))"},{"name":"inst✝⁹","sexp":"((:c LieRing) (:fv _uniq.145152))"},{"name":"inst✝⁸","sexp":"((:c LieAlgebra) ... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (: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":":implicit","context_index":0,"internal_name":"_uniq.145150","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.145152","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rfl","sourceEnd":11241,"sourceStart":11238,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":11241,"sourceStart":11238,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.145150","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.145152","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 63 | 6 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6d3bbb2bc6b164b116112fdad0a1e57f712559655993b00bad19a7eef249669d | 5ad64f86d722b7273220e788f649e3eee6d09c1092b154b1236e2d2a051a9227 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,982 | Ordinal.IsNormal.bsup_eq | Mathlib/SetTheory/Ordinal/Arithmetic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Ordinal.IsNormal.bsup</a>.{u, u, v} H (fun x _ => x) h.1, <a>Ordinal.bsup_id_limit</a> h.2] | α : Type u_1
β : Type u_2
γ : Type u_3
r : α → α → Prop
s : β → β → Prop
t : γ → γ → Prop
f : Ordinal.{u} → Ordinal.{max u v}
H : IsNormal f
o : Ordinal.{u}
h : o.IsLimit
⊢ (o.bsup fun x x_1 => f x) = f o | ((:c Eq) (:c Ordinal) ((:c Ordinal.bsup) (:fv _uniq.233965) (:lambda x (:c Ordinal) (:lambda _ ((:c LT.lt) (:c Ordinal) ((:c Preorder.toLT) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) 0 (:fv _uniq.233965)) ((:fv _uniq.233963) 1)))) ((:fv _uniq.233963) (:fv _uniq.233965))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.233906) (:forall _ (:fv _uniq.233906) (:sort 0)))"},{"name":"s","sexp":"(:forall _ (:fv _uniq.233909) (:forall _ (:fv _uniq.233909) (:sort 0)))"},{"name":"t"... | (:app (:c Eq) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:app (:c Ordinal.bsup) (:arg :explicit 0 (:fv FV9)) (:arg :explicit 1 (:lambda x :explicit (:c Ordinal) (:lambda _ :explicit (:app (:c LT.lt) (:arg :implicit-type 0 (:c Ordinal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Ord... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.233906","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.233909","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":86766,"sourceStart":86764,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":86768,"sourceStart":86767,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"IsNormal.bsup.{u, u, v} H (fun x _ => x) h.1","source_end":86816,"source_start":86772,"syntax_kind":"Lean.Parser.Term.app"},{"source":"bsup_id_limit h.2","source_end":86835,"source_start":86818,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.233906","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.233909","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 599 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7307f4b54bbe55d47abf20a25309b6a8d21af4f9d8073a71fbd2e3dbf70022df | d2200075c246ac57fb363f6a78aced2c779c690fdfe2e6a978bf9a8cd7456a9d | d0cd486987fded439598b3389abdd3385412ff91220bb38b9067912d77f2abe2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,983 | EReal.sign_mul | Mathlib/Data/Real/EReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction x, y using <a>EReal.induction₂_symm_neg</a> with | top_zero => simp only [<a>MulZeroClass.zero_mul</a>, <a>MulZeroClass.mul_zero</a>, <a>sign_zero</a>] | top_top => rfl | symm h => rwa [<a>mul_comm</a>, <a>EReal.mul_comm</a>] | coe_coe => simp only [← <a>EReal.coe_mul</a>, <a>EReal.sign_coe</a>, <a>sign_mul</... | x y : EReal
⊢ sign (x * y) = sign x * sign y | ((:c Eq) (:c SignType) ((:c DFunLike.coe) ((:c OrderHom) (:c EReal) (:c SignType) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder)) ((:c PartialOrder.toPreorder) (:c SignType) ((:c SemilatticeInf.toPartialOrder) (:c SignType) ((:c Lattice.toSemilatticeInf) (:c SignType) ((:c DistribLattice.toLattice)... | [{"name":"x","sexp":"(:c EReal)"},{"name":"y","sexp":"(:c EReal)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c OrderHom) (:arg :explicit 0 (:c EReal)) (:arg :explicit 1 (:c SignType)) (:arg :instance 2 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c EReal))))) (:arg :instance 3 (:instance-of (:a... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.156419","is_instance":false,"is_let":false,"name":"x","sexp":"(:c EReal)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.156420","is_instance":false,"is_let":false,"name":"y","sexp":"(:c EReal)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"induction","sourceEnd":51872,"sourceStart":51863,"tag":"atom"},{"children":[{"contextIndex":1,"semanticRole":"local","source":"x","sourceEnd":51874,"sourceStart":51873,"tag":"identifier"},{"source":",","sourceEnd":51875,"sourceStart":51874,"tag":"atom"},{"c... | [] | [{"source":"x","source_end":51874,"source_start":51873,"syntax_kind":"ident"},{"source":"y","source_end":51877,"source_start":51876,"syntax_kind":"ident"},{"source":"induction₂_symm_neg","source_end":51905,"source_start":51884,"syntax_kind":"ident"},{"source":"zero_mul","source_end":51946,"source_start":51938,"syntax_k... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.156419","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.156420","is_instance":false,"is_let":false,"user_name":"y"}] | 402 | 2 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 360486f2b6cef19382a898d067ebaf08a01f075cbd25cee11838d77465859332 | 86e5c86b50d4cde9262df143f62d610d2b53f9118332da825ef545f68525c323 | 7fc78c5c03a787b95492316ca3de0abd6b4342321ec7c735d339fa2e7c2a6d97 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,984 | EReal.sign_mul | Mathlib/Data/Real/EReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>MulZeroClass.zero_mul</a>, <a>MulZeroClass.mul_zero</a>, <a>sign_zero</a>] | case top_zero
⊢ sign (⊤ * 0) = sign ⊤ * sign 0 | ((:c Eq) (:c SignType) ((:c DFunLike.coe) ((:c OrderHom) (:c EReal) (:c SignType) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder)) ((:c PartialOrder.toPreorder) (:c SignType) ((:c SemilatticeInf.toPartialOrder) (:c SignType) ((:c Lattice.toSemilatticeInf) (:c SignType) ((:c DistribLattice.toLattice)... | [] | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c OrderHom) (:arg :explicit 0 (:c EReal)) (:arg :explicit 1 (:c SignType)) (:arg :instance 2 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c EReal))))) (:arg :instance 3 (:instance-of (:a... | [] | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":51931,"sourceStart":51927,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":51936,"sourceStart":51932,"tag":"atom"}],"kind"... | [] | [{"source":"zero_mul","source_end":51946,"source_start":51938,"syntax_kind":"ident"},{"source":"mul_zero","source_end":51956,"source_start":51948,"syntax_kind":"ident"},{"source":"sign_zero","source_end":51967,"source_start":51958,"syntax_kind":"ident"}] | [] | 402 | 7 | exact | true | 1 | 0 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1c1a61230d93628fa99ba2508adf9263215dc6f10358ff0d459e3d28952bb1bb | eddad73c3cbef2c73b2fa867045fe4b1bf6303bd8ece1317eb62ee171d60c43f | ccbaae6594b6c6d6a0d58e8ec1bf2085bc5ca4304a812795448bc80791a6aa59 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,985 | EReal.sign_mul | Mathlib/Data/Real/EReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case top_top
⊢ sign (⊤ * ⊤) = sign ⊤ * sign ⊤ | ((:c Eq) (:c SignType) ((:c DFunLike.coe) ((:c OrderHom) (:c EReal) (:c SignType) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder)) ((:c PartialOrder.toPreorder) (:c SignType) ((:c SemilatticeInf.toPartialOrder) (:c SignType) ((:c Lattice.toSemilatticeInf) (:c SignType) ((:c DistribLattice.toLattice)... | [] | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c OrderHom) (:arg :explicit 0 (:c EReal)) (:arg :explicit 1 (:c SignType)) (:arg :instance 2 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c EReal))))) (:arg :instance 3 (:instance-of (:a... | [] | {"children":[{"children":[{"children":[{"children":[{"source":"rfl","sourceEnd":51987,"sourceStart":51984,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":51987,"sourceStart":51984,"tag":"node"}],"kind":"null","source":"rfl","sourceEnd":51987,"sourceStart":51984,"tag":"node"}],"kind":"Lea... | [] | [] | [] | 402 | 11 | exact | true | 1 | 0 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8b9a484f11687fd9362538fd9def851bc2454e3cb69e3a70c7838168029ff5d4 | 8aee2d2750aa2ebc356ed793ef1106a548fa22d9d5f3fcb5434a2307306476ec | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,986 | EReal.sign_mul | Mathlib/Data/Real/EReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>mul_comm</a>, <a>EReal.mul_comm</a>] | case symm
x✝ y✝ : EReal
h : sign (x✝ * y✝) = sign x✝ * sign y✝
⊢ sign (y✝ * x✝) = sign y✝ * sign x✝ | ((:c Eq) (:c SignType) ((:c DFunLike.coe) ((:c OrderHom) (:c EReal) (:c SignType) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder)) ((:c PartialOrder.toPreorder) (:c SignType) ((:c SemilatticeInf.toPartialOrder) (:c SignType) ((:c Lattice.toSemilatticeInf) (:c SignType) ((:c DistribLattice.toLattice)... | [{"name":"x✝","sexp":"(:c EReal)"},{"name":"y✝","sexp":"(:c EReal)"},{"name":"h","sexp":"((:c Eq) (:c SignType) ((:c DFunLike.coe) ((:c OrderHom) (:c EReal) (:c SignType) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder)) ((:c PartialOrder.toPreorder) (:c SignType) ((:c SemilatticeInf.toPartialOrder) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c OrderHom) (:arg :explicit 0 (:c EReal)) (:arg :explicit 1 (:c SignType)) (:arg :instance 2 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c EReal))))) (:arg :instance 3 (:instance-of (:a... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.157244","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c EReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.157245","is_instance":false,"is_let":false,"name":"y✝","sexp":"(:c EReal)"},{"binder_role":":explicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":52005,"sourceStart":52002,"tag":"atom"},{"children":[{"source":"[","sourceEnd":52007,"sourceStart":52006,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"mul_comm","semanticRole":"globa... | [] | [{"source":"mul_comm","source_end":52015,"source_start":52007,"syntax_kind":"ident"},{"source":"EReal.mul_comm","source_end":52031,"source_start":52017,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.157244","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.157245","is_instance":false,"is_let":false,"user_name":"y✝"},{"binder_role":":explicit","context_index":3,"internal_name":... | 402 | 15 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5ec8fb5bfb219037656bef4fd2674b6d226d068fef6fe074fdb8550456781b94 | 2a49b0f7a6334703f438274215dafd43244222f6a93bce858f802c1436b95cdd | d0a13fb7b16cf3437e17de0d4e354b88226d50c492eaf324433a8c38579b799c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,987 | EReal.sign_mul | Mathlib/Data/Real/EReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [← <a>EReal.coe_mul</a>, <a>EReal.sign_coe</a>, <a>sign_mul</a>, <a>ENNReal.ofReal_mul</a> (<a>abs_nonneg</a> _)] | case coe_coe
x✝ y✝ : ℝ
⊢ sign (↑x✝ * ↑y✝) = sign ↑x✝ * sign ↑y✝ | ((:c Eq) (:c SignType) ((:c DFunLike.coe) ((:c OrderHom) (:c EReal) (:c SignType) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder)) ((:c PartialOrder.toPreorder) (:c SignType) ((:c SemilatticeInf.toPartialOrder) (:c SignType) ((:c Lattice.toSemilatticeInf) (:c SignType) ((:c DistribLattice.toLattice)... | [{"name":"x✝","sexp":"(:c Real)"},{"name":"y✝","sexp":"(:c Real)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c OrderHom) (:arg :explicit 0 (:c EReal)) (:arg :explicit 1 (:c SignType)) (:arg :instance 2 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c EReal))))) (:arg :instance 3 (:instance-of (:a... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.158200","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.158201","is_instance":false,"is_let":false,"name":"y✝","sexp":"(:c Real)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":52052,"sourceStart":52048,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":52057,"sourceStart":52053,"tag":"atom"}],"kind"... | [] | [{"source":"coe_mul","source_end":52070,"source_start":52063,"syntax_kind":"ident"},{"source":"sign_coe","source_end":52080,"source_start":52072,"syntax_kind":"ident"},{"source":"_root_.sign_mul","source_end":52097,"source_start":52082,"syntax_kind":"ident"},{"source":"ENNReal.ofReal_mul (abs_nonneg _)","source_end":52... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.158200","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.158201","is_instance":false,"is_let":false,"user_name":"y✝"}] | 402 | 22 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f3d2c9e12adee8bb213e06eee8905cce237dffe15ab73fb4818520c9a3d539d4 | e20bece76ab0fbd03b02130d614dc55a23e51a737c73cd3325af0a16ae0e3ef6 | a884cd68498675a2e3bd8bfa96d0f597cb04f3f16638cee2e9493aef90ede2a3 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,988 | EReal.sign_mul | Mathlib/Data/Real/EReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>EReal.top_mul_coe_of_pos</a> h, <a>EReal.sign_top</a>, <a>one_mul</a>, <a>sign_pos</a> (<a>EReal.coe_pos</a>.2 h)] | case top_pos
x✝ : ℝ
h : 0 < x✝
⊢ sign (⊤ * ↑x✝) = sign ⊤ * sign ↑x✝ | ((:c Eq) (:c SignType) ((:c DFunLike.coe) ((:c OrderHom) (:c EReal) (:c SignType) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder)) ((:c PartialOrder.toPreorder) (:c SignType) ((:c SemilatticeInf.toPartialOrder) (:c SignType) ((:c Lattice.toSemilatticeInf) (:c SignType) ((:c DistribLattice.toLattice)... | [{"name":"x✝","sexp":"(:c Real)"},{"name":"h","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.158730))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c OrderHom) (:arg :explicit 0 (:c EReal)) (:arg :explicit 1 (:c SignType)) (:arg :instance 2 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c EReal))))) (:arg :instance 3 (:instance-of (:a... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.158730","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.158731","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Re... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":52159,"sourceStart":52157,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":52161,"sourceStart":52160,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"top_mul_coe_of_pos h","source_end":52181,"source_start":52161,"syntax_kind":"Lean.Parser.Term.app"},{"source":"sign_top","source_end":52191,"source_start":52183,"syntax_kind":"ident"},{"source":"one_mul","source_end":52200,"source_start":52193,"syntax_kind":"ident"},{"source":"sign_pos (EReal.coe_pos.2 h)",... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.158730","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.158731","is_instance":false,"is_let":false,"user_name":"h"}] | 402 | 26 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 125e0f8cdbe47f9750737af3c91902672c402369e36f8069237f19ce956ce438 | 9dc22eb7924f0082e547607be6b4f41fca9d4015c1260b6d3075a5891e25f795 | 93b8dc30ecb9c5a926f9075dff99f0c3c177ce10076a0a1ff91959f7b0bd5390 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,989 | EReal.sign_mul | Mathlib/Data/Real/EReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>neg_mul</a>, <a>EReal.sign_neg</a>, <a>EReal.sign_neg</a>, h, <a>neg_mul</a>] | case neg_left
x✝ y✝ : EReal
h : sign (x✝ * y✝) = sign x✝ * sign y✝
⊢ sign (-x✝ * y✝) = sign (-x✝) * sign y✝ | ((:c Eq) (:c SignType) ((:c DFunLike.coe) ((:c OrderHom) (:c EReal) (:c SignType) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder)) ((:c PartialOrder.toPreorder) (:c SignType) ((:c SemilatticeInf.toPartialOrder) (:c SignType) ((:c Lattice.toSemilatticeInf) (:c SignType) ((:c DistribLattice.toLattice)... | [{"name":"x✝","sexp":"(:c EReal)"},{"name":"y✝","sexp":"(:c EReal)"},{"name":"h","sexp":"((:c Eq) (:c SignType) ((:c DFunLike.coe) ((:c OrderHom) (:c EReal) (:c SignType) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder)) ((:c PartialOrder.toPreorder) (:c SignType) ((:c SemilatticeInf.toPartialOrder) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c OrderHom) (:arg :explicit 0 (:c EReal)) (:arg :explicit 1 (:c SignType)) (:arg :instance 2 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c EReal))))) (:arg :instance 3 (:instance-of (:a... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.159230","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c EReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.159231","is_instance":false,"is_let":false,"name":"y✝","sexp":"(:c EReal)"},{"binder_role":":explicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":52252,"sourceStart":52250,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":52254,"sourceStart":52253,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"neg_mul","source_end":52261,"source_start":52254,"syntax_kind":"ident"},{"source":"sign_neg","source_end":52271,"source_start":52263,"syntax_kind":"ident"},{"source":"sign_neg","source_end":52281,"source_start":52273,"syntax_kind":"ident"},{"source":"h","source_end":52284,"source_start":52283,"syntax_kind":... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.159230","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.159231","is_instance":false,"is_let":false,"user_name":"y✝"},{"binder_role":":explicit","context_index":3,"internal_name":... | 402 | 35 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 963bf15288bacf40964b025dc9e8cbe353869b60629783ef6f76683d0ec8f86c | a0e3fbabd2d534266420a0fa4ba90b4355fadf1327981347da977be5d46ff3df | 47cd110f49b26efaa1f1e518a49f8561c6eaa1d97a3358dfc9af355ee87e85d0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,990 | TopCat.Presheaf.ext | Mathlib/Topology/Sheaves/Presheaf.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>CategoryTheory.NatTrans.ext</a> | C : Type u
inst✝ : Category.{v, u} C
X : TopCat
P Q : Presheaf C X
f g : P ⟶ Q
w : ∀ (U : Opens ↑X), f.app { unop := U } = g.app { unop := U }
⊢ f = g | case app
C : Type u
inst✝ : Category.{v, u} C
X : TopCat
P Q : Presheaf C X
f g : P ⟶ Q
w : ∀ (U : Opens ↑X), f.app { unop := U } = g.app { unop := U }
⊢ f.app = g.app | ((:c Eq) ((:c Quiver.Hom) ((:c TopCat.Presheaf) (:fv _uniq.1864) (:fv _uniq.1867) (:fv _uniq.2526)) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c TopCat.Presheaf) (:fv _uniq.1864) (:fv _uniq.1867) (:fv _uniq.2526)) ((:c CategoryTheory.Category.toCategoryStruct) ((:c TopCat.Presheaf) (:fv _uniq.1864) (:fv _uniq.1867... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1864))"},{"name":"X","sexp":"(:c TopCat)"},{"name":"P","sexp":"((:c TopCat.Presheaf) (:fv _uniq.1864) (:fv _uniq.1867) (:fv _uniq.2526))"},{"name":"Q","sexp":"((:c TopCat.Presheaf) (:fv _uniq.1864) (:fv _uniq.1867) (... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:app (:c TopCat.Presheaf) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV3)))) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1864","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1867","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Category) (... | {"children":[{"source":"apply","sourceEnd":2211,"sourceStart":2206,"tag":"atom"},{"name":"CategoryTheory.NatTrans.ext","semanticRole":"global","source":"NatTrans.ext","sourceEnd":2224,"sourceStart":2212,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply NatTrans.ext","sourceEnd":2224,"sourceStart":2... | [] | [{"source":"NatTrans.ext","source_end":2224,"source_start":2212,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1864","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1867","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"internal_... | 12 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8c7a46d8b6e700f0da87690ea2524af3e658b1cba5528f45067e17df6cbe1dab | 8598dfd4ef5bfac746ddef40fe3fb2c6c7d99c724e8fd001e5cffa7d1139e0a8 | 0245225a309971c8a89a8caa205a94da86d7701a3630cdb84299001b10b74d6b | 7ec8721d7753f54fddb7284796e2be16bc6b6caf950a5f00ccf8de92156ae901 |
cat-searcher/leandojo-benchmark-4-random | test | 1,991 | TopCat.Presheaf.ext | Mathlib/Topology/Sheaves/Presheaf.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext U | case app
C : Type u
inst✝ : Category.{v, u} C
X : TopCat
P Q : Presheaf C X
f g : P ⟶ Q
w : ∀ (U : Opens ↑X), f.app { unop := U } = g.app { unop := U }
⊢ f.app = g.app | case app.h
C : Type u
inst✝ : Category.{v, u} C
X : TopCat
P Q : Presheaf C X
f g : P ⟶ Q
w : ∀ (U : Opens ↑X), f.app { unop := U } = g.app { unop := U }
U : (Opens ↑X)ᵒᵖ
⊢ f.app U = g.app U | ((:c Eq) (:forall X ((:c Opposite) ((:c TopologicalSpace.Opens) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) (:fv _uniq.2526)) ((:c TopCat.topologicalSpace_coe) (:fv _uniq.2526)))) ((:c Quiver.Hom) (:fv _uniq.1864) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.1864) ((:c CategoryTheory.Category.toCate... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1864))"},{"name":"X","sexp":"(:c TopCat)"},{"name":"P","sexp":"((:c TopCat.Presheaf) (:fv _uniq.1864) (:fv _uniq.1867) (:fv _uniq.2526))"},{"name":"Q","sexp":"((:c TopCat.Presheaf) (:fv _uniq.1864) (:fv _uniq.1867) (... | (:app (:c Eq) (:arg :implicit-type 0 (:forall X :explicit (:app (:c Opposite) (:arg :explicit 0 (:app (:c TopologicalSpace.Opens) (:arg :explicit 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:fv FV3)))) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:app (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1864","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1867","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Category) (... | {"children":[{"source":"ext","sourceEnd":2230,"sourceStart":2227,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"U","sourceEnd":2232,"sourceStart":2231,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"U","sourceEnd":2232,"sourceStart":2231,"tag":"nod... | [{"role":"fresh_name","source":"U","source_end":2232,"source_start":2231,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1864","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1867","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"internal_... | 12 | 5 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a844b508ef40c706654d791343944704f761595cacb922f5e2edaae32e60336e | 7ec8721d7753f54fddb7284796e2be16bc6b6caf950a5f00ccf8de92156ae901 | 913d1f9646d1d32e36b2a11bda2572daa110e03851c3e1816f55f57175c514d2 | 09647c9426a744c0a3de240c5f9d7f4fcaf06423572fd51c1b8f1335a9ce386b |
cat-searcher/leandojo-benchmark-4-random | test | 1,992 | TopCat.Presheaf.ext | Mathlib/Topology/Sheaves/Presheaf.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction U with | _ U => ?_ | case app.h
C : Type u
inst✝ : Category.{v, u} C
X : TopCat
P Q : Presheaf C X
f g : P ⟶ Q
w : ∀ (U : Opens ↑X), f.app { unop := U } = g.app { unop := U }
U : (Opens ↑X)ᵒᵖ
⊢ f.app U = g.app U | case app.h.h
C : Type u
inst✝ : Category.{v, u} C
X : TopCat
P Q : Presheaf C X
f g : P ⟶ Q
w : ∀ (U : Opens ↑X), f.app { unop := U } = g.app { unop := U }
U : Opens ↑X
⊢ f.app { unop := U } = g.app { unop := U } | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.1864) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.1864) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.1864) (:fv _uniq.1867))) ((:c Prefunctor.obj) ((:c Opposite) ((:c TopologicalSpace.Opens) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) (:fv _uniq.252... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1864))"},{"name":"X","sexp":"(:c TopCat)"},{"name":"P","sexp":"((:c TopCat.Presheaf) (:fv _uniq.1864) (:fv _uniq.1867) (:fv _uniq.2526))"},{"name":"Q","sexp":"((:c TopCat.Presheaf) (:fv _uniq.1864) (:fv _uniq.1867) (... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c Opposite) (:arg :explicit 0 (:app (:c TopologicalSpace.Opens) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1864","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1867","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Category) (... | {"children":[{"source":"induction","sourceEnd":2244,"sourceStart":2235,"tag":"atom"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"U","sourceEnd":2246,"sourceStart":2245,"tag":"identifier"}],"kind":"null","source":"U","sourceEnd":2246,"sourceStart":2245,"tag":"node"},{"children":[],"kind":"null","sour... | [] | [{"source":"U","source_end":2246,"source_start":2245,"syntax_kind":"ident"},{"source":"?_","source_end":2263,"source_start":2261,"syntax_kind":"Lean.Parser.Term.syntheticHole"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1864","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1867","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"internal_... | 12 | 6 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8824dcceedca4c20467ab98ccc179de1c8695a928f9a586716974d15a94d3872 | 09647c9426a744c0a3de240c5f9d7f4fcaf06423572fd51c1b8f1335a9ce386b | 028bcea1d3f60974f76283968a6a7af828c1616070e4d5785a0b88ea46f76efa | e9e3c45239445a405289e70588b55181170f82e774e23a1e2670a92b8086077a |
cat-searcher/leandojo-benchmark-4-random | test | 1,993 | TopCat.Presheaf.ext | Mathlib/Topology/Sheaves/Presheaf.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply w | case app.h.h
C : Type u
inst✝ : Category.{v, u} C
X : TopCat
P Q : Presheaf C X
f g : P ⟶ Q
w : ∀ (U : Opens ↑X), f.app { unop := U } = g.app { unop := U }
U : Opens ↑X
⊢ f.app { unop := U } = g.app { unop := U } | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.1864) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.1864) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.1864) (:fv _uniq.1867))) ((:c Prefunctor.obj) ((:c Opposite) ((:c TopologicalSpace.Opens) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) (:fv _uniq.252... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1864))"},{"name":"X","sexp":"(:c TopCat)"},{"name":"P","sexp":"((:c TopCat.Presheaf) (:fv _uniq.1864) (:fv _uniq.1867) (:fv _uniq.2526))"},{"name":"Q","sexp":"((:c TopCat.Presheaf) (:fv _uniq.1864) (:fv _uniq.1867) (... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c Opposite) (:arg :explicit 0 (:app (:c TopologicalSpace.Opens) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1864","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1867","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Category) (... | {"children":[{"source":"apply","sourceEnd":2271,"sourceStart":2266,"tag":"atom"},{"contextIndex":8,"semanticRole":"local","source":"w","sourceEnd":2273,"sourceStart":2272,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply w","sourceEnd":2273,"sourceStart":2266,"tag":"node"} | [] | [{"source":"w","source_end":2273,"source_start":2272,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1864","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1867","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"internal_... | 12 | 9 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a96a2b28d1166997bc577b604e4a1f0e8cd06af726d928dba5ce879f9355c1c7 | e9e3c45239445a405289e70588b55181170f82e774e23a1e2670a92b8086077a | 192e6c920f741fefafc95fc4aa906105d6c268f37b03be85cec193bf40e962d7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,994 | Finset.isGLB_mem | Mathlib/Data/Finset/Lattice.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Finset.mem_coe</a>] | F : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
ι : Type u_5
κ : Type u_6
inst✝ : LinearOrder α
i : α
s : Finset α
his : IsGLB (↑s) i
hs : s.Nonempty
⊢ i ∈ s | F : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
ι : Type u_5
κ : Type u_6
inst✝ : LinearOrder α
i : α
s : Finset α
his : IsGLB (↑s) i
hs : s.Nonempty
⊢ i ∈ ↑s | ((:c Membership.mem) (:fv _uniq.414096) ((:c Finset) (:fv _uniq.414096)) ((:c Finset.instMembership) (:fv _uniq.414096)) (:fv _uniq.414528) (:fv _uniq.414529)) | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"κ","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.414096))"},{"name":"i","se... | (: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 (:fv FV1))))))) (:arg :explicit 3 (:fv FV8)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.414093","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.414096","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":82706,"sourceStart":82704,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":82708,"sourceStart":82707,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":82711,"sourceSt... | [] | [{"source":"mem_coe","source_end":82719,"source_start":82712,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.414093","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.414096","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 664 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f85efe653d4c8da93308efb7f79353d5456dcfcd247dff8f81e2da995dd9d3d6 | c693518f813986e79ecd66d447ff69d16a240b75f9d1265b035c0c1ab6d86279 | 1acd6cd4b5e12fa5acb15d7c188018131b796fefaa1f62e1d11a603075f5c3a6 | 07f632a7c4c615146fb58c9848dbc648813b02c18df84a829b6439b70bf4149b |
cat-searcher/leandojo-benchmark-4-random | test | 1,995 | Finset.isGLB_mem | Mathlib/Data/Finset/Lattice.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ((<a>Finset.isGLB_iff_isLeast</a> i s hs).<a>Iff.mp</a> his).1 | F : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
ι : Type u_5
κ : Type u_6
inst✝ : LinearOrder α
i : α
s : Finset α
his : IsGLB (↑s) i
hs : s.Nonempty
⊢ i ∈ ↑s | ((:c Membership.mem) (:fv _uniq.414096) ((:c Set) (:fv _uniq.414096)) ((:c Set.instMembership) (:fv _uniq.414096)) (:fv _uniq.414528) ((:c Finset.toSet) (:fv _uniq.414096) (:fv _uniq.414529))) | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"κ","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.414096))"},{"name":"i","se... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:fv FV8)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.414093","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.414096","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":82728,"sourceStart":82723,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":82730,"sourceStart":82729,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":82731,"sourceStart":82730,"tag":"atom"},{"children":[{"name":"Finset.isGLB_iff_i... | [] | [{"source":"((isGLB_iff_isLeast i s hs).mp his).1","source_end":82766,"source_start":82729,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.414093","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.414096","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 664 | 7 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6323582fccdb39daaac3e9697082256f2c32493da65ae4ef3b30106bbe9effc5 | 07f632a7c4c615146fb58c9848dbc648813b02c18df84a829b6439b70bf4149b | 8d864daa287cf3696a1a3e69610c92d52f23b0a73b5d57e481999623c04163f4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,996 | pow_eq_one_iff_cases | Mathlib/Algebra/Order/Ring/Abs.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [← <a>pow_eq_pow_iff_cases</a>] | α : Type u_1
R : Type u_2
inst✝ : LinearOrderedRing R
a b : R
n : ℕ
⊢ a ^ n = 1 ↔ n = 0 ∨ a = 1 ∨ a = -1 ∧ Even n | ((:c Iff) ((:c Eq) (:fv _uniq.47239) ((:c HPow.hPow) (:fv _uniq.47239) (:c Nat) (:fv _uniq.47239) ((:c instHPow) (:fv _uniq.47239) (:c Nat) ((:c Monoid.toNatPow) (:fv _uniq.47239) ((:c MonoidWithZero.toMonoid) (:fv _uniq.47239) ((:c Semiring.toMonoidWithZero) (:fv _uniq.47239) ((:c StrictOrderedSemiring.toSemiring) (:f... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedRing) (:fv _uniq.47239))"},{"name":"a","sexp":"(:fv _uniq.47239)"},{"name":"b","sexp":"(:fv _uniq.47239)"},{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Iff) (:arg :explicit 0 (: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 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.47236","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.47239","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":8764,"sourceStart":8760,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"pow_eq_pow_iff_cases","source_end":8790,"source_start":8770,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.47236","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.47239","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 98 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d989d45646d3054fc37ac3611f56fed79ccadf2d9ba9e7f87194f9dafc3b1115 | 59d88d5e11d2bfceb2005022e6cbc851768bdbaaa5a85972474f7d74d73805c0 | 916f55e8cad78623bbca32653bf867dd471eb5d5aeea620d6b8f76f3e44178e6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,997 | CoxeterSystem.simple_mul_simple_cancel_left | Mathlib/GroupTheory/Coxeter/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [← <a>mul_assoc</a>] | B : Type u_1
B' : Type u_2
e : B ≃ B'
W : Type u_3
H : Type u_4
inst✝¹ : Group W
inst✝ : Group H
M : CoxeterMatrix B
cs : CoxeterSystem M W
w : W
i : B
⊢ cs.simple i * (cs.simple i * w) = w | ((:c Eq) (:fv _uniq.32573) ((:c HMul.hMul) (:fv _uniq.32573) (:fv _uniq.32573) (:fv _uniq.32573) ((:c instHMul) (:fv _uniq.32573) ((:c MulOneClass.toMul) (:fv _uniq.32573) ((:c Monoid.toMulOneClass) (:fv _uniq.32573) ((:c DivInvMonoid.toMonoid) (:fv _uniq.32573) ((:c Group.toDivInvMonoid) (:fv _uniq.32573) (:fv _uniq.3... | [{"name":"B","sexp":"(:sort (+ u_1 1))"},{"name":"B'","sexp":"(:sort (+ u_2 1))"},{"name":"e","sexp":"((:c Equiv) (:fv _uniq.32563) (:fv _uniq.32566))"},{"name":"W","sexp":"(:sort (+ u_3 1))"},{"name":"H","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.32573))"},{"name":"inst✝","sexp":"((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32563","is_instance":false,"is_let":false,"name":"B","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32566","is_instance":false,"is_let":false,"name":"B'","sexp":"(:sort Type)"},{"binder_role":":explicit","co... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":8814,"sourceStart":8810,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"mul_assoc","source_end":8829,"source_start":8820,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32563","is_instance":false,"is_let":false,"user_name":"B"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32566","is_instance":false,"is_let":false,"user_name":"B'"},{"binder_role":":explicit","context_index":2,"internal_name":"_u... | 37 | 2 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 16fa9c9c23ca4d2394c7f1792b7c392519a54e3e4852953d999c9add7c1cfbb1 | c0e21e8380949536c32af5f6eb19a8cff214ce03e59611341a220ea77208af07 | a1fb2f4ec9831db131ee593c58888cf4412c59a1e37e6331992ff8cf758abe19 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,998 | Associates.factors_subsingleton | Mathlib/RingTheory/UniqueFactorizationDomain.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>Subsingleton</a> (<a>Associates</a> α) := <a>inferInstance</a> | α : Type u_1
inst✝² : CancelCommMonoidWithZero α
inst✝¹ : UniqueFactorizationMonoid α
inst✝ : Subsingleton α
a : Associates α
⊢ a.factors = ⊤ | α : Type u_1
inst✝² : CancelCommMonoidWithZero α
inst✝¹ : UniqueFactorizationMonoid α
inst✝ : Subsingleton α
a : Associates α
this : Subsingleton (Associates α)
⊢ a.factors = ⊤ | ((:c Eq) ((:c Associates.FactorSet) (:fv _uniq.349372) (:fv _uniq.349375)) ((:c Associates.factors) (:fv _uniq.349372) (:fv _uniq.349375) (:fv _uniq.349384) (:fv _uniq.349792)) ((:c Top.top) ((:c Associates.FactorSet) (:fv _uniq.349372) (:fv _uniq.349375)) ((:c WithTop.top) ((:c Multiset) ((:c Subtype) ((:c Associates)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CancelCommMonoidWithZero) (:fv _uniq.349372))"},{"name":"inst✝¹","sexp":"((:c UniqueFactorizationMonoid) (:fv _uniq.349372) (:fv _uniq.349375))"},{"name":"inst✝","sexp":"((:c Subsingleton) (:fv _uniq.349372))"},{"name":"a","sexp":"((:c Associates) (... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Associates.FactorSet) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CancelCommMonoidWithZero) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c Associates.factors) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.349372","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.349375","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CancelCommMonoidWithZ... | {"children":[{"source":"have","sourceEnd":72153,"sourceStart":72149,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":72154,"sourceStart":72154,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":72154,"sourceStart":72154,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"Subsingleton (Associates α)","source_end":72184,"source_start":72156,"syntax_kind":"Lean.Parser.Term.app"},{"source":"inferInstance","source_end":72201,"source_start":72188,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.349372","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.349375","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 304 | 4 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0d2c6b40379de94ef360cc60f8ec205177cce75a9e5f24b9d29af81c28074311 | cb515e510a4281affeb6e67f52ee644a1a3e6b16d94f302887cc512f552ce864 | 7cf1d3955a6c73dedabdd25ad543638a0316f74d7cc7946a5e4a4d49fe2ad6f6 | 1f30df8be7db52850f33934e7e47e473f0b47657ed01f8ceb9deea66a104d377 |
cat-searcher/leandojo-benchmark-4-random | test | 1,999 | Associates.factors_subsingleton | Mathlib/RingTheory/UniqueFactorizationDomain.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert <a>Associates.factors_zero</a> | α : Type u_1
inst✝² : CancelCommMonoidWithZero α
inst✝¹ : UniqueFactorizationMonoid α
inst✝ : Subsingleton α
a : Associates α
this : Subsingleton (Associates α)
⊢ a.factors = ⊤ | ((:c Eq) ((:c Associates.FactorSet) (:fv _uniq.349372) (:fv _uniq.349375)) ((:c Associates.factors) (:fv _uniq.349372) (:fv _uniq.349375) (:fv _uniq.349384) (:fv _uniq.349792)) ((:c Top.top) ((:c Associates.FactorSet) (:fv _uniq.349372) (:fv _uniq.349375)) ((:c WithTop.top) ((:c Multiset) ((:c Subtype) ((:c Associates)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CancelCommMonoidWithZero) (:fv _uniq.349372))"},{"name":"inst✝¹","sexp":"((:c UniqueFactorizationMonoid) (:fv _uniq.349372) (:fv _uniq.349375))"},{"name":"inst✝","sexp":"((:c Subsingleton) (:fv _uniq.349372))"},{"name":"a","sexp":"((:c Associates) (... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Associates.FactorSet) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CancelCommMonoidWithZero) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c Associates.factors) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.349372","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.349375","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CancelCommMonoidWithZ... | {"children":[{"source":"convert","sourceEnd":72211,"sourceStart":72204,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Associates.factors_zero","semanticRole":"global","source":"factors_zero","sourceEnd":72224,"sourceStart":72212,"tag"... | [] | [{"source":"factors_zero","source_end":72224,"source_start":72212,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.349372","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.349375","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 304 | 5 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 15cd4c9cc34f0414b54bf255370de2e24cea31dd371ed1d277eb49eed3bf98ba | 1f30df8be7db52850f33934e7e47e473f0b47657ed01f8ceb9deea66a104d377 | 030c2f541aa572d9f72390aefbb858e5fb3e37c6c4b277df4c45b2331e8e3c8a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,000 | Fintype.card_piFinset | Mathlib/Data/Fintype/BigOperators.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Fintype.piFinset</a>, <a>Finset.card_map</a>] | α✝ : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
κ : Type u_5
α : ι → Type u_6
inst✝³ : DecidableEq ι
inst✝² : DecidableEq κ
inst✝¹ : Fintype ι
inst✝ : (i : ι) → DecidableEq (α i)
s : (i : ι) → Finset (α i)
⊢ (piFinset s).card = ∏ i : ι, (s i).card | ((:c Eq) (:c Nat) ((:c Finset.card) (:forall a (:fv _uniq.6063) ((:fv _uniq.6071) 0)) ((:c Fintype.piFinset) (:fv _uniq.6063) (:fv _uniq.6078) (:fv _uniq.6092) (:fv _uniq.6071) (:fv _uniq.6359))) ((:c Finset.prod) (:fv _uniq.6063) (:c Nat) (:c Nat.instCommMonoid) ((:c Finset.univ) (:fv _uniq.6063) (:fv _uniq.6092)) (:l... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"κ","sexp":"(:sort (+ u_5 1))"},{"name":"α","sexp":"(:forall _ (:fv _uniq.6063) (:sort (+ u_6 1)))"},{"name":"inst✝³","sexp":"((:c DecidableEq) (:fv _... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Finset.card) (:arg :implicit-type 0 (:forall a :explicit (:fv FV3) (:app (:fv FV5) (:arg :explicit 0 0)))) (:arg :explicit 1 (:app (:c Fintype.piFinset) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c DecidableEq) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6054","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6057","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":4441,"sourceStart":4437,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"piFinset","source_end":4451,"source_start":4443,"syntax_kind":"ident"},{"source":"card_map","source_end":4461,"source_start":4453,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6054","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6057","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 50 | 2 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bb71afeefa227dc0d9aaf454844ddb61800314a029da8b2e1c85c0582bfd8c74 | bdde4b7c1d9863d8e4631c321f8973ca4023623b5b41d6cdd977a09b723bbca3 | 03df8d6f280ec9cb0f7594c0a663aff226b082b828550b5d81959c89b6921679 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,001 | Ordnode.BalancedSz.symm | Mathlib/Data/Ordmap/Ordset.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>add_comm</a>] | α : Type u_1
l r : ℕ
⊢ l + r ≤ 1 → r + l ≤ 1 | α : Type u_1
l r : ℕ
⊢ r + l ≤ 1 → r + l ≤ 1 | (:forall _ ((:c LE.le) (:c Nat) (:c instLENat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.7355) (:fv _uniq.7356)) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) ((:c LE.le) (:c Nat) (:c instLENat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c ins... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"l","sexp":"(:c Nat)"},{"name":"r","sexp":"(:c Nat)"}] | (:forall _ :explicit (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7343","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.7355","is_instance":false,"is_let":false,"name":"l","sexp":"(:c Nat)"},{"binder_role":":implicit","context_i... | {"children":[{"source":"rw","sourceEnd":7431,"sourceStart":7429,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7433,"sourceStart":7432,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"add_comm","semanticR... | [] | [{"source":"add_comm","source_end":7441,"source_start":7433,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7343","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.7355","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":3,"internal_name":"_uniq... | 44 | 4 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eaec8ce574eb989c896a88604fbb766aad5c2a9055823ad750318633e3927f78 | 9aa0fe5d0c08767f9df2812cec8bbaa3e6f8dbc390bc099cf51a421733354300 | 707f7395094bb37fad92bf71eb5cc4cfd5bf0547886ddb8474de13ffc18b39f4 | 83b4ce6e2124550ecc1dd54a424d0bfee5e632867d113832325ccae5cf835ad2 |
cat-searcher/leandojo-benchmark-4-random | test | 2,002 | Ordnode.BalancedSz.symm | Mathlib/Data/Ordmap/Ordset.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>id</a> | α : Type u_1
l r : ℕ
⊢ r + l ≤ 1 → r + l ≤ 1 | (:forall _ ((:c LE.le) (:c Nat) (:c instLENat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) ((:c AddCommMagma.toAdd) (:c Nat) ((:c AddCommSemigroup.toAddCommMagma) (:c Nat) (:c Nat.instAddCommSemigroup)))) (:fv _uniq.7356) (:fv _uniq.7355)) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"l","sexp":"(:c Nat)"},{"name":"r","sexp":"(:c Nat)"}] | (:forall _ :explicit (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7343","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.7355","is_instance":false,"is_let":false,"name":"l","sexp":"(:c Nat)"},{"binder_role":":implicit","context_i... | {"children":[{"source":"exact","sourceEnd":7449,"sourceStart":7444,"tag":"atom"},{"name":"id","semanticRole":"global","source":"id","sourceEnd":7452,"sourceStart":7450,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact id","sourceEnd":7452,"sourceStart":7444,"tag":"node"} | [] | [{"source":"id","source_end":7452,"source_start":7450,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7343","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.7355","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":3,"internal_name":"_uniq... | 44 | 8 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b12559402d4fa1721d06aec8c15f31446b266f4ae9d0028b84a0c6ffbaea708d | 83b4ce6e2124550ecc1dd54a424d0bfee5e632867d113832325ccae5cf835ad2 | a67b6d777e05e5f79b02c59383bbc70076be94fcc97ccd32644632f1b8846707 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,003 | Filter.map_inf | Mathlib/Order/Filter/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine map_inf_le.antisymm ?_ | α : Type u
β : Type v
γ : Type w
δ : Type u_1
ι : Sort x
l f g : Filter α
m : α → β
h : Injective m
⊢ map m (f ⊓ g) = map m f ⊓ map m g | α : Type u
β : Type v
γ : Type w
δ : Type u_1
ι : Sort x
l f g : Filter α
m : α → β
h : Injective m
⊢ map m f ⊓ map m g ≤ map m (f ⊓ g) | ((:c Eq) ((:c Filter) (:fv _uniq.201362)) ((:c Filter.map) (:fv _uniq.201360) (:fv _uniq.201362) (:fv _uniq.201470) ((:c Inf.inf) ((:c Filter) (:fv _uniq.201360)) ((:c Filter.instInf) (:fv _uniq.201360)) (:fv _uniq.201468) (:fv _uniq.201469))) ((:c Inf.inf) ((:c Filter) (:fv _uniq.201362)) ((:c Filter.instInf) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"δ","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort x)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.201360))"},{"name":"f","sexp":"((:c Filter) (:fv _uniq.201360))"},{"name":"g","sexp":"((:... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Filter.map) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV9)) (:arg :explicit 3 (:app (:c Inf.inf) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201360","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201362","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":122414,"sourceStart":122408,"tag":"atom"},{"children":[{"source":"map_inf_le.antisymm","sourceEnd":122434,"sourceStart":122415,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":122436,"sourceStart":122435,"tag":"atom"},{"children":[{"source":"_","sourceE... | [] | [{"source":"map_inf_le.antisymm ?_","source_end":122437,"source_start":122415,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201360","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201362","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 931 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ea0fafbf0ca7b1fdd671a510378aeee32a9ec8f677430e9bcae7917d29062be7 | 1f8510723049a4989062c657691f5405ec443c01b640661df6a4a3383965cf7d | 03dfe3b8d7b863fc50b3283e1ef09dd88dc7cac3f451092aacd81337099f6cd4 | 3dff6835783c3116ecea2e5b5d4efc4167c4cff545a3e627cfd04d6edba15192 |
cat-searcher/leandojo-benchmark-4-random | test | 2,004 | Filter.map_inf | Mathlib/Order/Filter/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro t ⟨s₁, hs₁, s₂, hs₂, ht : m ⁻¹' t = s₁ ∩ s₂⟩ | α : Type u
β : Type v
γ : Type w
δ : Type u_1
ι : Sort x
l f g : Filter α
m : α → β
h : Injective m
⊢ map m f ⊓ map m g ≤ map m (f ⊓ g) | case intro.intro.intro.intro
α : Type u
β : Type v
γ : Type w
δ : Type u_1
ι : Sort x
l f g : Filter α
m : α → β
h : Injective m
t : Set β
s₁ : Set α
hs₁ : s₁ ∈ f
s₂ : Set α
hs₂ : s₂ ∈ g
ht : m ⁻¹' t = s₁ ∩ s₂
⊢ t ∈ map m f ⊓ map m g | ((:c LE.le) ((:c Filter) (:fv _uniq.201362)) ((:c Preorder.toLE) ((:c Filter) (:fv _uniq.201362)) ((:c PartialOrder.toPreorder) ((:c Filter) (:fv _uniq.201362)) ((:c Filter.instPartialOrder) (:fv _uniq.201362)))) ((:c Inf.inf) ((:c Filter) (:fv _uniq.201362)) ((:c Filter.instInf) (:fv _uniq.201362)) ((:c Filter.map) (:... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"δ","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort x)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.201360))"},{"name":"f","sexp":"((:c Filter) (:fv _uniq.201360))"},{"name":"g","sexp":"((:... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 2 (:app (:c Inf.inf) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV1)))) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201360","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201362","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rintro","sourceEnd":122446,"sourceStart":122440,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"t","sourceEnd":122448,"sourceStart":122447,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"t","sourceEnd":122448,"sourceStart":12... | [{"role":"fresh_name","source":"t","source_end":122448,"source_start":122447,"syntax_kind":"ident"},{"role":"fresh_name","source":"s₁","source_end":122456,"source_start":122452,"syntax_kind":"ident"},{"role":"fresh_name","source":"hs₁","source_end":122463,"source_start":122458,"syntax_kind":"ident"},{"role":"fresh_name... | [{"source":"⟨s₁, hs₁, s₂, hs₂, ht : m ⁻¹' t = s₁ ∩ s₂⟩","source_end":122512,"source_start":122449,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201360","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201362","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 931 | 5 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9e73a17b29bb3bc2196d14f6abf09b8d1c5eb1d6c66f029b36299c91a4618d25 | 3dff6835783c3116ecea2e5b5d4efc4167c4cff545a3e627cfd04d6edba15192 | 98b0320e2ad968cd5c0cb4a3abf6883f520618374f15087b2a2412cccfcb166d | 6fc24b081eaf493310a6f8a20cb8ad377635b91eea97723355c519222d3cbb76 |
cat-searcher/leandojo-benchmark-4-random | test | 2,005 | Filter.map_inf | Mathlib/Order/Filter/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Filter.mem_inf_of_inter</a> (<a>Filter.image_mem_map</a> hs₁) (<a>Filter.image_mem_map</a> hs₂) ?_ | case intro.intro.intro.intro
α : Type u
β : Type v
γ : Type w
δ : Type u_1
ι : Sort x
l f g : Filter α
m : α → β
h : Injective m
t : Set β
s₁ : Set α
hs₁ : s₁ ∈ f
s₂ : Set α
hs₂ : s₂ ∈ g
ht : m ⁻¹' t = s₁ ∩ s₂
⊢ t ∈ map m f ⊓ map m g | case intro.intro.intro.intro
α : Type u
β : Type v
γ : Type w
δ : Type u_1
ι : Sort x
l f g : Filter α
m : α → β
h : Injective m
t : Set β
s₁ : Set α
hs₁ : s₁ ∈ f
s₂ : Set α
hs₂ : s₂ ∈ g
ht : m ⁻¹' t = s₁ ∩ s₂
⊢ m '' s₁ ∩ m '' s₂ ⊆ t | ((:c Membership.mem) ((:c Set) (:fv _uniq.201362)) ((:c Filter) (:fv _uniq.201362)) ((:c instMembershipSetFilter) (:fv _uniq.201362)) (:fv _uniq.201541) ((:c Inf.inf) ((:c Filter) (:fv _uniq.201362)) ((:c Filter.instInf) (:fv _uniq.201362)) ((:c Filter.map) (:fv _uniq.201360) (:fv _uniq.201362) (:fv _uniq.201470) (:fv ... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"δ","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort x)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.201360))"},{"name":"f","sexp":"((:c Filter) (:fv _uniq.201360))"},{"name":"g","sexp":"((:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:app (:c Filter) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Filter)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201360","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201362","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":122521,"sourceStart":122515,"tag":"atom"},{"children":[{"name":"Filter.mem_inf_of_inter","semanticRole":"global","source":"mem_inf_of_inter","sourceEnd":122538,"sourceStart":122522,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":122540,"sourceStart":12... | [] | [{"source":"mem_inf_of_inter (image_mem_map hs₁) (image_mem_map hs₂) ?_","source_end":122585,"source_start":122522,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201360","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201362","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 931 | 6 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73f300597f2c714b32346abfaf6b38b0595d18ae67824e5db1525e599b3e4c6b | 6fc24b081eaf493310a6f8a20cb8ad377635b91eea97723355c519222d3cbb76 | 8bb9d0cfa9d8616c021fb48ee4f77d1ad98c341b5623df55e8f1aa73fddd976d | b6d185bbc98764f8c28bed3a32b95d69747f78c8aa181d7ce72d47b05f287b72 |
cat-searcher/leandojo-benchmark-4-random | test | 2,006 | Filter.map_inf | Mathlib/Order/Filter/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Set.image_inter</a> h, <a>Set.image_subset_iff</a>, ht] | case intro.intro.intro.intro
α : Type u
β : Type v
γ : Type w
δ : Type u_1
ι : Sort x
l f g : Filter α
m : α → β
h : Injective m
t : Set β
s₁ : Set α
hs₁ : s₁ ∈ f
s₂ : Set α
hs₂ : s₂ ∈ g
ht : m ⁻¹' t = s₁ ∩ s₂
⊢ m '' s₁ ∩ m '' s₂ ⊆ t | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.201362)) ((:c Set.instHasSubset) (:fv _uniq.201362)) ((:c Inter.inter) ((:c Set) (:fv _uniq.201362)) ((:c Set.instInter) (:fv _uniq.201362)) ((:c Set.image) (:fv _uniq.201360) (:fv _uniq.201362) (:fv _uniq.201470) (:fv _uniq.201566)) ((:c Set.image) (:fv _uniq.201360) (:fv _u... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"δ","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort x)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.201360))"},{"name":"f","sexp":"((:c Filter) (:fv _uniq.201360))"},{"name":"g","sexp":"((:... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 2 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201360","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201362","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":122590,"sourceStart":122588,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":122592,"sourceStart":122591,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":122595,"sou... | [] | [{"source":"image_inter h","source_end":122609,"source_start":122596,"syntax_kind":"Lean.Parser.Term.app"},{"source":"image_subset_iff","source_end":122627,"source_start":122611,"syntax_kind":"ident"},{"source":"ht","source_end":122631,"source_start":122629,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201360","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201362","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 931 | 7 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 76aacd692f195f4416f8de8c099ddcd240db597f2ec73b0a4c5be06155e2a141 | b6d185bbc98764f8c28bed3a32b95d69747f78c8aa181d7ce72d47b05f287b72 | 206f795df92c5a46e4dc8d045a55b5074223778fe49d04f442802ad75e2b629f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,007 | Set.image2_iUnion_left | Mathlib/Data/Set/Lattice.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [← <a>Set.image_prod</a>, <a>Set.iUnion_prod_const</a>, <a>Set.image_iUnion</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
ι₂ : Sort u_6
κ : ι → Sort u_7
κ₁ : ι → Sort u_8
κ₂ : ι → Sort u_9
κ' : ι' → Sort u_10
f : α → β → γ
s✝ : Set α
t✝ : Set β
s : ι → Set α
t : Set β
⊢ image2 f (⋃ i, s i) t = ⋃ i, image2 f (s i) t | ((:c Eq) ((:c Set) (:fv _uniq.193313)) ((:c Set.image2) (:fv _uniq.193307) (:fv _uniq.193310) (:fv _uniq.193313) (:fv _uniq.193348) ((:c Set.iUnion) (:fv _uniq.193307) (:fv _uniq.193316) (:lambda i (:fv _uniq.193316) ((:fv _uniq.193427) 0))) (:fv _uniq.193428)) ((:c Set.iUnion) (:fv _uniq.193313) (:fv _uniq.193316) (:l... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort u_4)"},{"name":"ι'","sexp":"(:sort u_5)"},{"name":"ι₂","sexp":"(:sort u_6)"},{"name":"κ","sexp":"(:forall _ (:fv _uniq.193316) (:sort u_7))"},{"name":"κ₁","sexp":"(:forall ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:app (:c Set.image2) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV2)) (:arg :explicit 3 (:fv FV10)) (:arg :explicit 4 (:app (:c Set.iUnion) (:arg :implicit-type 0 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193307","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193310","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":82618,"sourceStart":82614,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":82623,"sourceStart":82619,"tag":"atom"}],"kind"... | [] | [{"source":"image_prod","source_end":82639,"source_start":82629,"syntax_kind":"ident"},{"source":"iUnion_prod_const","source_end":82658,"source_start":82641,"syntax_kind":"ident"},{"source":"image_iUnion","source_end":82672,"source_start":82660,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.193307","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193310","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 676 | 2 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 12f92d0c9f9bfdd96b5516ae5c575429ac885bd0d8f9c454b2871c76bdeea746 | e454c20e3265ee341a4d321f3f390d8fe22901ed4d5d7091cabe1a06240750f8 | 359853be8db8525ed29ea7f120c4f81d16fb71a905b5bc3d04a2d0b319798fcf | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,008 | Finset.sdiff_erase | Mathlib/Data/Finset/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Finset.sdiff_singleton_eq_erase</a>, <a>Finset.sdiff_sdiff_eq_sdiff_union</a> (<a>Finset.singleton_subset_iff</a>.2 h), <a>Finset.insert_eq</a>, <a>Finset.union_comm</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
inst✝ : DecidableEq α
s t u v : Finset α
a b : α
h : a ∈ s
⊢ s \ t.erase a = insert a (s \ t) | ((:c Eq) ((:c Finset) (:fv _uniq.166419)) ((:c SDiff.sdiff) ((:c Finset) (:fv _uniq.166419)) ((:c Finset.instSDiff) (:fv _uniq.166419) (:fv _uniq.166432)) (:fv _uniq.166437) ((:c Finset.erase) (:fv _uniq.166419) (:fv _uniq.166432) (:fv _uniq.166440) (:fv _uniq.166448))) ((:c Insert.insert) (:fv _uniq.166419) ((:c Finse... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.166419))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.166419))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.166419))"},{"name":"u","sexp":"((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c SDiff.sdiff) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c SDiff) (:arg :explicit 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0))))))) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.166419","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.166422","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":98261,"sourceStart":98259,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":98263,"sourceStart":98262,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"sdiff_singleton_eq_erase","source_end":98291,"source_start":98267,"syntax_kind":"ident"},{"source":"sdiff_sdiff_eq_sdiff_union (singleton_subset_iff.2 h)","source_end":98346,"source_start":98293,"syntax_kind":"Lean.Parser.Term.app"},{"source":"insert_eq","source_end":98357,"source_start":98348,"syntax_kind"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.166419","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.166422","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 931 | 2 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 62a2f19bb441b646f77735c993ca41647e3ede9247e09de12584ee8ba8594d22 | 0c0f2f2fcaca859c83e41ea05513f55cf0bcddea5ba9bb2057ef76674bc38ce0 | f88a04788c0070c14c55a6fbc8ed7feca82c88c3c7aa276f58ecbd465b5269db | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,009 | ZMod.valMinAbs_eq_zero | Mathlib/Data/ZMod/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases' n with n | n : ℕ
x : ZMod n
⊢ x.valMinAbs = 0 ↔ x = 0 | ((:c Iff) ((:c Eq) (:c Int) ((:c ZMod.valMinAbs) (:fv _uniq.153437) (:fv _uniq.153438)) ((:c OfNat.ofNat) (:c Int) (:lit 0) ((:c instOfNat) (:lit 0)))) ((:c Eq) ((:c ZMod) (:fv _uniq.153437)) (:fv _uniq.153438) ((:c OfNat.ofNat) ((:c ZMod) (:fv _uniq.153437)) (:lit 0) ((:c Zero.toOfNat0) ((:c ZMod) (:fv _uniq.153437)) ... | [{"name":"n","sexp":"(:c Nat)"},{"name":"x","sexp":"((:c ZMod) (:fv _uniq.153437))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c ZMod.valMinAbs) (:arg :implicit 0) (:arg :explicit 1 (:fv FV2)))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c Of... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.153437","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.153438","is_instance":false,"is_let":false,"name":"x","sexp":"(:app (:c ZMod) (:arg :explicit 0 (:fv FV1)))"}] | {"children":[{"children":[{"children":[{"children":[{"source":"cases'","sourceEnd":45139,"sourceStart":45133,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":1,"semanticRole":"local","source":"n","sourceEnd":45141,"sourceStart":45140,"tag":"identifier"}],"ki... | [] | [{"source":"n","source_end":45141,"source_start":45140,"syntax_kind":"ident"},{"source":"valMinAbs_zero n.succ","source_end":45190,"source_start":45169,"syntax_kind":"Lean.Parser.Term.app"},{"source":"injective_valMinAbs.eq_iff","source_end":45226,"source_start":45200,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.153437","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.153438","is_instance":false,"is_let":false,"user_name":"x"}] | 318 | 2 | branch_opener | false | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e66780d40f3a93c1311a4d4bd2e27abeb082615ab6b0f4b63479a4fde59053a6 | 98d2e3ec82f115f1c3f97c290c31258fa8cd0396d013b400c2234bb25286febd | c7832e8177f0f48d1a93433f6da916304dc6877192de4506d57a7af16e576bdd | 167091645bf8bd366bf3b7bcd5d93240dfcdfb67d2093b2947dad3a0b1ed2da6 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,010 | ZMod.valMinAbs_eq_zero | Mathlib/Data/ZMod/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>ZMod.valMinAbs_zero</a> n.succ] | case succ
n : ℕ
x : ZMod (n + 1)
⊢ x.valMinAbs = 0 ↔ x = 0 | case succ
n : ℕ
x : ZMod (n + 1)
⊢ x.valMinAbs = valMinAbs 0 ↔ x = 0 | ((:c Iff) ((:c Eq) (:c Int) ((:c ZMod.valMinAbs) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.153477) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) (:fv _uniq.153491)) ((:c OfNat.ofNat) (:c Int) (:lit 0) ((:c instOfNat) (:lit 0)))) ((:c Eq) ((:c ZMo... | [{"name":"n","sexp":"(:c Nat)"},{"name":"x","sexp":"((:c ZMod) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.153477) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c ZMod.valMinAbs) (:arg :implicit 0) (:arg :explicit 1 (:fv FV2)))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c Of... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.153477","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.153491","is_instance":false,"is_let":false,"name":"x","sexp":"(:app (:c ZMod) (:arg :explicit 0 (:app (:c HAdd... | {"children":[{"source":"rw","sourceEnd":45163,"sourceStart":45161,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":45165,"sourceStart":45164,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":45168,"sourceSt... | [] | [{"source":"valMinAbs_zero n.succ","source_end":45190,"source_start":45169,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.153477","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.153491","is_instance":false,"is_let":false,"user_name":"x"}] | 318 | 10 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8402bbbbe2f560316c6970743aca19ee271c6377cbad1f656f3063c18d3ced91 | 42e8d61e466e9c61993b69d464fa3d2f31ed6cf7be7ef871220b6d70436bea55 | fec4fad6a8540e18c4db997bd772789832e03b136fd54ac97465257d1ee8c1d1 | 9aab0399b0ac626c6c80836565b0562b6a47aea913f6549adad22e97788a1ce2 |
cat-searcher/leandojo-benchmark-4-random | test | 2,011 | ZMod.valMinAbs_eq_zero | Mathlib/Data/ZMod/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply injective_valMinAbs.eq_iff | case succ
n : ℕ
x : ZMod (n + 1)
⊢ x.valMinAbs = valMinAbs 0 ↔ x = 0 | ((:c Iff) ((:c Eq) (:c Int) ((:c ZMod.valMinAbs) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.153477) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) (:fv _uniq.153491)) ((:c ZMod.valMinAbs) ((:c Nat.succ) (:fv _uniq.153477)) ((:c OfNat.ofNat) ((:c ZM... | [{"name":"n","sexp":"(:c Nat)"},{"name":"x","sexp":"((:c ZMod) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.153477) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c ZMod.valMinAbs) (:arg :implicit 0) (:arg :explicit 1 (:fv FV2)))) (:arg :explicit 2 (:app (:c ZMod.valMinAbs) (:arg :implicit 0) (:arg :explicit 1 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:app (:c ZMod) (:a... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.153477","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.153491","is_instance":false,"is_let":false,"name":"x","sexp":"(:app (:c ZMod) (:arg :explicit 0 (:app (:c HAdd... | {"children":[{"source":"apply","sourceEnd":45199,"sourceStart":45194,"tag":"atom"},{"name":"Function.Injective.eq_iff","semanticRole":"global","source":"injective_valMinAbs.eq_iff","sourceEnd":45226,"sourceStart":45200,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply injective_valMinAbs.eq_iff","s... | [] | [{"source":"injective_valMinAbs.eq_iff","source_end":45226,"source_start":45200,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.153477","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.153491","is_instance":false,"is_let":false,"user_name":"x"}] | 318 | 13 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 923f43698487af8b61f1022598e96281305660f695f704d9c31fff3d6c65eda8 | 9aab0399b0ac626c6c80836565b0562b6a47aea913f6549adad22e97788a1ce2 | 19d5a9e69093570ce0aa4bf3fba33d194f1da873a7eb865215a00f54287bc59b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,012 | ZMod.valMinAbs_eq_zero | Mathlib/Data/ZMod/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case zero
x : ZMod 0
⊢ x.valMinAbs = 0 ↔ x = 0 | ((:c Iff) ((:c Eq) (:c Int) ((:c ZMod.valMinAbs) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))) (:fv _uniq.153474)) ((:c OfNat.ofNat) (:c Int) (:lit 0) ((:c instOfNat) (:lit 0)))) ((:c Eq) ((:c ZMod) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) (:fv _uniq.153474) ((:c OfNat.ofNa... | [{"name":"x","sexp":"((:c ZMod) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c ZMod.valMinAbs) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c Of... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.153474","is_instance":false,"is_let":false,"name":"x","sexp":"(:app (:c ZMod) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c ... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":45158,"sourceStart":45154,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","sour... | [] | [] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.153474","is_instance":false,"is_let":false,"user_name":"x"}] | 318 | 7 | exact | true | 1 | 1 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dc0d48269163d2c4f4894d04962a49cd354d34dce901eb2e6759575e97efa2a5 | f261e3c5784c7bffc8ed54a28eb0dadb8ae5188af162b24c8dd46da06a0b862d | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,013 | Fintype.prod_bool | Mathlib/Data/Fintype/BigOperators.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | α : Type u_1
β : Type u_2
γ : Type u_3
inst✝ : CommMonoid α
f : Bool → α
⊢ ∏ b : Bool, f b = f true * f false | ((:c Eq) (:fv _uniq.12) ((:c Finset.prod) (:c Bool) (:fv _uniq.12) (:fv _uniq.353) ((:c Finset.univ) (:c Bool) (:c Bool.fintype)) (:lambda b (:c Bool) ((:fv _uniq.354) 0))) ((:c HMul.hMul) (:fv _uniq.12) (:fv _uniq.12) (:fv _uniq.12) ((:c instHMul) (:fv _uniq.12) ((:c MulOneClass.toMul) (:fv _uniq.12) ((:c Monoid.toMul... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c CommMonoid) (:fv _uniq.12))"},{"name":"f","sexp":"(:forall _ (:c Bool) (:fv _uniq.12))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset.prod) (:arg :implicit-type 0 (:c Bool)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c CommMonoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 3 (:app (:c Finset.univ) (:arg :implicit-type 0 (:c Bool)) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","context_i... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":1152,"sourceStart":1148,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.18"... | 6 | 2 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c98488c0f766c51e3a8070951be9550d9a9fd0d905f3406d83ccab650a53fddf | c5fe8f7a018d08a4f7a0d58ca5a21c37067f6931d4f1c982f5ea74cba2faa65f | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,014 | Mathlib.Meta.NormNum.isRat_div | Mathlib/Tactic/NormNum/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [<a>div_eq_mul_inv</a>] using h | α : Type u_1
inst✝ : DivisionRing α
x✝³ x✝² : α
x✝¹ : ℤ
x✝ : ℕ
h : IsRat (x✝³ * x✝²⁻¹) x✝¹ x✝
⊢ IsRat (x✝³ / x✝²) x✝¹ x✝ | ((:c Mathlib.Meta.NormNum.IsRat) (:fv _uniq.67893) ((:c DivisionRing.toRing) (:fv _uniq.67893) (:fv _uniq.67894)) ((:c HDiv.hDiv) (:fv _uniq.67893) (:fv _uniq.67893) (:fv _uniq.67893) ((:c instHDiv) (:fv _uniq.67893) ((:c DivisionRing.toDiv) (:fv _uniq.67893) (:fv _uniq.67894))) (:fv _uniq.67951) (:fv _uniq.67952)) (:f... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c DivisionRing) (:fv _uniq.67893))"},{"name":"x✝³","sexp":"(:fv _uniq.67893)"},{"name":"x✝²","sexp":"(:fv _uniq.67893)"},{"name":"x✝¹","sexp":"(:c Int)"},{"name":"x✝","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c Mathlib.Meta.NormNum.IsRat) (:fv _uniq.67... | (:app (:c Mathlib.Meta.NormNum.IsRat) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instanc... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.67893","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.67894","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DivisionRing) (:arg :exp... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":20802,"sourceStart":20797,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"div_eq_mul_inv","source_end":20818,"source_start":20804,"syntax_kind":"ident"},{"source":"h","source_end":20827,"source_start":20826,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.67893","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.67894","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":3,"interna... | 48 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0ee6cce0cbd89ee5259c49e32501696e9eca664fe4bade118bf497a88d054653 | c61c568c2aab9963e26e8cf0b739ccc648311b1464fe89e217f873507092b1fa | 9058420721524e2e510ad448972f7b13e87ac79954cb6546ec1eac7bac0b1c92 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,015 | ENNReal.rpow_lt_top_iff_of_pos | Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>lt_top_iff_ne_top</a>, <a>Ne</a>, <a>ENNReal.rpow_eq_top_iff_of_pos</a> hy] | x : ℝ≥0∞
y : ℝ
hy : 0 < y
⊢ x ^ y < ⊤ ↔ x < ⊤ | ((:c Iff) ((: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 CompleteLinearOrd... | [{"name":"x","sexp":"(:c ENNReal)"},{"name":"y","sexp":"(:c Real)"},{"name":"hy","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.65341))"}] | (:app (:c Iff) (:arg :explicit 0 (: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 HPow.hPow) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c ENNReal)) (:arg... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65340","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.65341","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"},{"binder_role":":explicit","contex... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":21663,"sourceStart":21659,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":21668,"sourceStart":21664,"tag":"atom"}],"kind"... | [] | [{"source":"lt_top_iff_ne_top","source_end":21687,"source_start":21670,"syntax_kind":"ident"},{"source":"Ne","source_end":21691,"source_start":21689,"syntax_kind":"ident"},{"source":"rpow_eq_top_iff_of_pos hy","source_end":21718,"source_start":21693,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65340","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.65341","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 175 | 2 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b8e50b74ed39f165c7d891929c3e47f18313ba31c705fe0999da31c040f4a3ec | 65971772e4c7d7b76a7364e1d70a0695553ae838fbe7eb7c713aca1c1b897202 | f99f656be771c6c198eb31a59202eb10025cd0100e508a03a61bb6c7ffb047e3 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,016 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨c₁, _, c₂, _, h⟩ := hf (1/2) (by norm_num) | f : ℝ → ℝ
hf : GrowsPolynomially f
⊢ (∀ᶠ (x : ℝ) in atTop, 0 ≤ f x) ∨ ∀ᶠ (x : ℝ) in atTop, f x ≤ 0 | case intro.intro.intro.intro
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
⊢ (∀ᶠ (x : ℝ) in atTop, 0 ≤ f x) ∨ ∀ᶠ (x : ℝ) in atTop, f x ≤ 0 | ((:c Or) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:fv _uniq.34812) 0))) ((:c Filter.atTop) (:c Real) (:c Real.instPreorder))) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Re... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"}] | (:app (:c Or) (:arg :explicit 0 (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (:c Real) (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"obtain","sourceEnd":6820,"sourceStart":6814,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":6824,"sourceStart":6821,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"c₁","sourceEnd":... | [] | [{"source":"hf (1/2) (by norm_num)","source_end":6872,"source_start":6850,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨c₁, _, c₂, _, h⟩","source_end":6846,"source_start":6821,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"}] | 14 | 4 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7e5e0dc0f31c38a301966cfc403dcafe0b1d05fe9c6ff6d91c2738ceaa613bd2 | ecafb637484a2fa2c020ccd43f51beee6e741cb1d621b69437a640ca717075de | 564a84dab9436169effe975d7d4a94845a8e28c3e4d82091293cc25931ac8296 | c631370d1c0ab630526a10677c6dcf8b957171d00eb9b93e8ab684f4eef2f60b |
cat-searcher/leandojo-benchmark-4-random | test | 2,018 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_num | f : ℝ → ℝ
hf : GrowsPolynomially f
⊢ 1 / 2 ∈ Set.Ioo 0 1 | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne)))... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"}] | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 3 (:app (:c HDiv.hDiv) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"norm_num","sourceEnd":6871,"sourceStart":6863,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","so... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"}] | 14 | 7 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a8fd534f5c959bec3cfb7ce5ecf87fd6c38c6cb82b9dea4a06f66a6e52426e97 | 9cfb6aa327485980e6233912737c5f6237d4dce277e3cd7b4116a8d96ea40c30 | 7c64df8336d5a348b5f037e1d91facb19224fdef00e798d5c48c07a184602a59 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,019 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | left | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
⊢ (∀ᶠ (x : ℝ) in atTop, 0 ≤ f x) ∨ ∀ᶠ (x : ℝ) in atTop, f x ≤ 0 | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
⊢ ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x | ((:c Or) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:fv _uniq.34812) 0))) ((:c Filter.atTop) (:c Real) (:c Real.instPreorder))) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Re... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Or) (:arg :explicit 0 (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (:c Real) (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"left","sourceEnd":6949,"sourceStart":6945,"tag":"atom"}],"kind":"Lean.Parser.Tactic.left","source":"left","sourceEnd":6949,"sourceStart":6945,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 14 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 466f88f5507f47d15442c1a1898b387f49f97621f1cd9edf585ca4aa798331cb | 1fc0e223067a5bf5afb1a2af4e34cba54f0f734083774addf648dd0bdcb96926 | 360f84035942243c6a36537ae2f8673485e6c04455a0a85a0db19690f2541480 | 0af85287592bbef7ef106bba2b0f7ae1e671f6c48736770b43677d21bd80f2ee |
cat-searcher/leandojo-benchmark-4-random | test | 2,020 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards [h, <a>Filter.eventually_ge_atTop</a> 0] with x hx hx_nonneg | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
⊢ ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
⊢ 0 ≤ f x | ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:fv _uniq.34812) 0))) ((:c Filter.atTop) (:c Real) (:c Real.instPreorder))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (:c Real) (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"filter_upwards","sourceEnd":6968,"sourceStart":6954,"tag":"atom"},{"children":[{"source":"[","sourceEnd":6970,"sourceStart":6969,"tag":"atom"},{"children":[{"contextIndex":7,"semanticRole":"local","source":"h","sourceEnd":6971,"sourceStart":6970,"tag":"identifier"},{"source":",","sourceEnd":6972... | [] | [{"source":"eventually_ge_atTop 0","source_end":6994,"source_start":6973,"syntax_kind":"Lean.Parser.Term.app"},{"source":"h","source_end":6971,"source_start":6970,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 15 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9721dfe8424ec2344c2902c18e9e0fd500cb7bafe44fbba2c4b95af663741f4f | 0af85287592bbef7ef106bba2b0f7ae1e671f6c48736770b43677d21bd80f2ee | 45cca812da1bba9e020c4d2165e097c1f6f0c6515ddb2c22b29928eb06ee138d | f9a62735282384895535a7f744d6a318dd8be6f9de791531b1227020eb4df8d5 |
cat-searcher/leandojo-benchmark-4-random | test | 2,021 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h' : 3 / 4 * x ∈ <a>Set.Icc</a> (1 / 2 * x) x := by rw [<a>Set.mem_Icc</a>] exact ⟨by gcongr ?_ * x; norm_num, by linarith⟩ | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
⊢ 0 ≤ f x | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:fv _uniq.34812) (:fv _uniq.35962))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"have","sourceEnd":7024,"sourceStart":7020,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h'","sourceEnd":7027,"sourceStart":7025,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h'","sourceEnd":7027,"sourceStart":7025,"tag":"node"},{"... | [] | [{"source":"3 / 4 * x ∈ Set.Icc (1 / 2 * x) x","source_end":7065,"source_start":7030,"syntax_kind":"«term_∈_»"},{"source":"Set.mem_Icc","source_end":7093,"source_start":7082,"syntax_kind":"ident"},{"source":"⟨by gcongr ?_ * x; norm_num, by linarith⟩","source_end":7152,"source_start":7107,"syntax_kind":"Lean.Parser.Term... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 16 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3d7c141b463a8f7a1d18286573d65c562211deef312d355e51f159ccdbba6670 | f9a62735282384895535a7f744d6a318dd8be6f9de791531b1227020eb4df8d5 | 2f9e47d9e3e25b761eb1eb49bdf6149eb330e5af4dd10c5ef5d1f22fe791dd5e | cad5dc245751e0e26d3e7cc309c8459b5928b6fdb58b182ef75f204c10be3c2e |
cat-searcher/leandojo-benchmark-4-random | test | 2,022 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hu := hx (3/4 * x) h' | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:fv _uniq.34812) (:fv _uniq.35962))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"have","sourceEnd":7161,"sourceStart":7157,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hu","sourceEnd":7164,"sourceStart":7162,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hu","sourceEnd":7164,"sourceStart":7162,"tag":"node"},{"... | [] | [{"source":"hx (3/4 * x) h'","source_end":7183,"source_start":7168,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 34 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3b84f957dd7f4b239d1da0ad40842164ec43125d45e749d359b617c639e3ea1a | cad5dc245751e0e26d3e7cc309c8459b5928b6fdb58b182ef75f204c10be3c2e | 7ac7256ec18bdc669dd5c6c379ff7a2b7a4649c785ca36976b974879d92c4670 | 3dbb882f8301b5368ee4450a3520ead3a9eefda62b2d5259c3ef2ceb446cef01 |
cat-searcher/leandojo-benchmark-4-random | test | 2,023 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hu := <a>Set.nonempty_of_mem</a> hu | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:fv _uniq.34812) (:fv _uniq.35962))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"have","sourceEnd":7192,"sourceStart":7188,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hu","sourceEnd":7195,"sourceStart":7193,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hu","sourceEnd":7195,"sourceStart":7193,"tag":"node"},{"... | [] | [{"source":"Set.nonempty_of_mem hu","source_end":7221,"source_start":7199,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 35 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 09d06ae4c9aa909c25a53246354e732032b3430a3bdd7916060857cc158d3099 | 3dbb882f8301b5368ee4450a3520ead3a9eefda62b2d5259c3ef2ceb446cef01 | a0cd199986d8eb2ee7019cd6b6968e5e837321dc7a2796078d3360bd441db6f8 | 73fc4fe3345803295ba163475c9d5f760bc249ef5ef8f317183438ec09955c8d |
cat-searcher/leandojo-benchmark-4-random | test | 2,024 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.nonempty_Icc</a>] at hu | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:fv _uniq.34812) (:fv _uniq.35962))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"rw","sourceEnd":7228,"sourceStart":7226,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7230,"sourceStart":7229,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.nonempty_Icc","s... | [] | [{"source":"Set.nonempty_Icc","source_end":7246,"source_start":7230,"syntax_kind":"ident"},{"source":"hu","source_end":7253,"source_start":7251,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 36 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b2f2b4811852cb761dddf19bec032f984020ac941bc359b58d6212ae439bdd6b | 73fc4fe3345803295ba163475c9d5f760bc249ef5ef8f317183438ec09955c8d | 38a626d16a510d469b084b3858518371d454752eb7e689e646d1db1e1960f339 | 1e09d6c0d8955657a38778f8e4492a8acb695ab7fd23a91a7a45a1d65aee614f |
cat-searcher/leandojo-benchmark-4-random | test | 2,025 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hu' : 0 ≤ (c₂ - c₁) * f x := by linarith | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:fv _uniq.34812) (:fv _uniq.35962))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"have","sourceEnd":7262,"sourceStart":7258,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hu'","sourceEnd":7266,"sourceStart":7263,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hu'","sourceEnd":7266,"sourceStart":7263,"tag":"node"},... | [] | [{"source":"0 ≤ (c₂ - c₁) * f x","source_end":7294,"source_start":7269,"syntax_kind":"«term_≤_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 39 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1d79724b35e794a38303568a65dcbe183caed60b977fed7596a2501b7ae17661 | 1e09d6c0d8955657a38778f8e4492a8acb695ab7fd23a91a7a45a1d65aee614f | 4886d875d55b9689f46e38c2793202068ce3f7bd99e35e6fed33dec0351c9d01 | ebafc8bbfae84b6ccdbaeebda91981e265a4a80d55b31e812760b8fd31f77871 |
cat-searcher/leandojo-benchmark-4-random | test | 2,026 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>nonneg_of_mul_nonneg_right</a> hu' (by linarith) | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:fv _uniq.34812) (:fv _uniq.35962))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"exact","sourceEnd":7319,"sourceStart":7314,"tag":"atom"},{"children":[{"name":"nonneg_of_mul_nonneg_right","semanticRole":"global","source":"nonneg_of_mul_nonneg_right","sourceEnd":7346,"sourceStart":7320,"tag":"identifier"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"hu'","... | [] | [{"source":"nonneg_of_mul_nonneg_right hu' (by linarith)","source_end":7364,"source_start":7320,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 42 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d115bf22e332d19a76b1c7fe316a9297b42bf7cccbd7fb14069525c5840f072b | ebafc8bbfae84b6ccdbaeebda91981e265a4a80d55b31e812760b8fd31f77871 | 8bb7db0dbfd72ba95f6cf74f6283f413b425afed0b79043d8381a2935757665b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,027 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.mem_Icc</a>] | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
⊢ 3 / 4 * x ∈ Set.Icc (1 / 2 * x) x | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
⊢ 1 / 2 * x ≤ 3 / 4 * x ∧ 3 / 4 * x ≤ x | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedFiel... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 3 (:app (:c HMul.hMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"rw","sourceEnd":7080,"sourceStart":7078,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7082,"sourceStart":7081,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.mem_Icc","semant... | [] | [{"source":"Set.mem_Icc","source_end":7093,"source_start":7082,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 18 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 60a24576eda21f9079b5e3a3ff84378648d74d4f264c5d705c921bd86270203f | b1bbaa109bc6589f4c23f9bf1d4643005279a19aaf03bee7fd4e7aa02a2e9877 | 7860e98a80f38e7bc18c1fe77ce3f4ad43754d2b1aac472b17191699e19eba20 | 7267b8cf889f236055a89e07938f951d9c1656ad5269a21ebc5a9faabebcfd02 |
cat-searcher/leandojo-benchmark-4-random | test | 2,028 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨by gcongr ?_ * x; norm_num, by linarith⟩ | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
⊢ 1 / 2 * x ≤ 3 / 4 * x ∧ 3 / 4 * x ≤ x | ((:c And) ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField)... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c And) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"exact","sourceEnd":7106,"sourceStart":7101,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":7110,"sourceStart":7107,"tag":"atom"},{"children":[{"children":[{"source":"by","sourceEnd":7112,"sourceStart":7110,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"gcongr",... | [] | [{"source":"⟨by gcongr ?_ * x; norm_num, by linarith⟩","source_end":7152,"source_start":7107,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 21 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e150aea1332816e868eebabc42fe6be78c25e5357eac928eda0f7ca22e27b9f0 | 7267b8cf889f236055a89e07938f951d9c1656ad5269a21ebc5a9faabebcfd02 | 1b18a511adad709c74aab8326e1e8e7f58797f1a267a78c377d366b53718d94e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,029 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr ?_ * x | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
⊢ 1 / 2 * x ≤ 3 / 4 * x | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
⊢ 1 / 2 ≤ 3 / 4 | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Of... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"gcongr","sourceEnd":7119,"sourceStart":7113,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"?","sourceEnd":7121,"sourceStart":7120,"tag":"atom"},{"children":[{"source":"_","sourceEnd":7122,"sourceStart":7121,"tag":"atom"}],"kind":"Lean.Parser.Term.hole","source":"_","sourceEnd":7... | [] | [{"source":"?_ * x","source_end":7126,"source_start":7120,"syntax_kind":"«term_*_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 26 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a6732a8df9d8ca592693d685d72a771c24e0eabded39c706ad43793f686a302e | afcb789300380628a5f403ce40fdee8d4d0adfab969a0c6738a74060c2cf5db6 | f75d71a937d83d46b0ea0e84993170b6d4920bbb4e993754b38a133ad64629d9 | b32375e842a6de79d346396c6e4096d67b570f1644b5a23a9cd8b1731f0b92a7 |
cat-searcher/leandojo-benchmark-4-random | test | 2,030 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_num | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
⊢ 1 / 2 ≤ 3 / 4 | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c OfNat.... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"norm_num","sourceEnd":7136,"sourceStart":7128,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 28 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aa249b633d08aa0bdc404a9841602fb1b65e1c1e7d7ec3d14797c06288203cd0 | b32375e842a6de79d346396c6e4096d67b570f1644b5a23a9cd8b1731f0b92a7 | 7c64df8336d5a348b5f037e1d91facb19224fdef00e798d5c48c07a184602a59 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,031 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
⊢ 3 / 4 * x ≤ x | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Of... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"linarith","sourceEnd":7149,"sourceStart":7141,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kin... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 31 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f0514f3be8ea983ed2cd80e49391cbb528933bb107634d9468f8a52c535cf161 | 19354ed5f4b036b98da41cec96f1ed6ecc8c3f20c469317f7d6b807fdc08b0a1 | 2c587e2f140ae41533b8e0551e8c940d4f70fbd4b1f4245ea1c9efcde110c9af | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,032 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x) x
hu✝... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) (:fv _uniq.35... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"linarith","sourceEnd":7309,"sourceStart":7301,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"k... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 41 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c55a5b31f09fb2d86803088d093501bd38b8d6754bde24886b92aac0dc55656c | 0f1d4fceec9f3938052315c2c19049362a45aeba970a62e0e41506b949849df5 | 2c587e2f140ae41533b8e0551e8c940d4f70fbd4b1f4245ea1c9efcde110c9af | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,033 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hlt : c₁ < c₂
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x) x
hu✝... | ((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) (:c Real.instLinearOrderedSemiring))))) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) ((:c M... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"linarith","sourceEnd":7363,"sourceStart":7355,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kin... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 45 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f538bde683fb5b4fd0e1b98369cdf3b61a58575260a36291fefcde77bad8d0fe | 157e22ba980246efa27e44f1e919f4dc373557ebbd5efdc8e1ceffa2cec058bd | 2c587e2f140ae41533b8e0551e8c940d4f70fbd4b1f4245ea1c9efcde110c9af | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,034 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | right | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
⊢ (∀ᶠ (x : ℝ) in atTop, 0 ≤ f x) ∨ ∀ᶠ (x : ℝ) in atTop, f x ≤ 0 | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
⊢ ∀ᶠ (x : ℝ) in atTop, f x ≤ 0 | ((:c Or) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:fv _uniq.34812) 0))) ((:c Filter.atTop) (:c Real) (:c Real.instPreorder))) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Re... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Or) (:arg :explicit 0 (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (:c Real) (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"right","sourceEnd":7412,"sourceStart":7407,"tag":"atom"}],"kind":"Lean.Parser.Tactic.right","source":"right","sourceEnd":7412,"sourceStart":7407,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 51 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8cd42aeb63a6ce2bd1d9b28064ab3a1100380a10a8dcc3290db05fe543d6fac3 | ebf40d074365d735af2348253e2e5dc6c1ad1ed0cf7eb466bd4294152c2321f0 | 27042f4e6eca7d0b2a7ee4026df2ecfa51d3339e6d122aa099118ecd8563bad9 | fc63fa166c76f44b5141cb705e987edc2fbdcc8b4066edaef0847c0a7868bfb5 |
cat-searcher/leandojo-benchmark-4-random | test | 2,035 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards [h, <a>Filter.eventually_ge_atTop</a> 0] with x hx hx_nonneg | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
⊢ ∀ᶠ (x : ℝ) in atTop, f x ≤ 0 | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
⊢ f x ≤ 0 | ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) ((:c LE.le) (:c Real) (:c Real.instLE) ((:fv _uniq.34812) 0) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))) ((:c Filter.atTop) (:c Real) (:c Real.instPreorder))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (:c Real) (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:fv FV0) (:arg :explicit 0 0))) (:arg :explicit 3 (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"filter_upwards","sourceEnd":7431,"sourceStart":7417,"tag":"atom"},{"children":[{"source":"[","sourceEnd":7433,"sourceStart":7432,"tag":"atom"},{"children":[{"contextIndex":7,"semanticRole":"local","source":"h","sourceEnd":7434,"sourceStart":7433,"tag":"identifier"},{"source":",","sourceEnd":7435... | [] | [{"source":"eventually_ge_atTop 0","source_end":7457,"source_start":7436,"syntax_kind":"Lean.Parser.Term.app"},{"source":"h","source_end":7434,"source_start":7433,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 52 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fb729c0f2aa6349acf143c3c20006a2af672ff6daa8522750507b465b872fa8e | fc63fa166c76f44b5141cb705e987edc2fbdcc8b4066edaef0847c0a7868bfb5 | 45cca812da1bba9e020c4d2165e097c1f6f0c6515ddb2c22b29928eb06ee138d | 54b68da763dae9025cc8f7bf5dd48f3212c8c0fcb7e3f3114227864515c4d47a |
cat-searcher/leandojo-benchmark-4-random | test | 2,036 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h' : 3 / 4 * x ∈ <a>Set.Icc</a> (1 / 2 * x) x := by rw [<a>Set.mem_Icc</a>] exact ⟨by gcongr ?_ * x; norm_num, by linarith⟩ | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
⊢ f x ≤ 0 | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:fv _uniq.34812) (:fv _uniq.41416)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:fv FV0) (:arg :explicit 0 (:fv FV9)))) (:arg :explicit 3 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:ins... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"have","sourceEnd":7487,"sourceStart":7483,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h'","sourceEnd":7490,"sourceStart":7488,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h'","sourceEnd":7490,"sourceStart":7488,"tag":"node"},{"... | [] | [{"source":"3 / 4 * x ∈ Set.Icc (1 / 2 * x) x","source_end":7528,"source_start":7493,"syntax_kind":"«term_∈_»"},{"source":"Set.mem_Icc","source_end":7556,"source_start":7545,"syntax_kind":"ident"},{"source":"⟨by gcongr ?_ * x; norm_num, by linarith⟩","source_end":7615,"source_start":7570,"syntax_kind":"Lean.Parser.Term... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 53 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0372aabc3a8d923cf6895233f3af16f7803a51837d42ad23c1c7a19b56fa6348 | 54b68da763dae9025cc8f7bf5dd48f3212c8c0fcb7e3f3114227864515c4d47a | 2f9e47d9e3e25b761eb1eb49bdf6149eb330e5af4dd10c5ef5d1f22fe791dd5e | 8d0000504475f6ed960d620799827e0b2325fab4826840283d0f4eccad276516 |
cat-searcher/leandojo-benchmark-4-random | test | 2,037 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hu := hx (3/4 * x) h' | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:fv _uniq.34812) (:fv _uniq.41416)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:fv FV0) (:arg :explicit 0 (:fv FV9)))) (:arg :explicit 3 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:ins... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"have","sourceEnd":7624,"sourceStart":7620,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hu","sourceEnd":7627,"sourceStart":7625,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hu","sourceEnd":7627,"sourceStart":7625,"tag":"node"},{"... | [] | [{"source":"hx (3/4 * x) h'","source_end":7646,"source_start":7631,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 71 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 69ed2ba09b089b3143e255ef89028cd6d3961618a24444e9f1a78cc7db8ded43 | 8d0000504475f6ed960d620799827e0b2325fab4826840283d0f4eccad276516 | 7ac7256ec18bdc669dd5c6c379ff7a2b7a4649c785ca36976b974879d92c4670 | 8257c7c9263e8dda40553060a31f625a7b0b72b339d0af9564a3aea0004deef7 |
cat-searcher/leandojo-benchmark-4-random | test | 2,038 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hu := <a>Set.nonempty_of_mem</a> hu | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:fv _uniq.34812) (:fv _uniq.41416)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:fv FV0) (:arg :explicit 0 (:fv FV9)))) (:arg :explicit 3 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:ins... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"have","sourceEnd":7655,"sourceStart":7651,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hu","sourceEnd":7658,"sourceStart":7656,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hu","sourceEnd":7658,"sourceStart":7656,"tag":"node"},{"... | [] | [{"source":"Set.nonempty_of_mem hu","source_end":7684,"source_start":7662,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 72 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0ade5146c41cefbc917155050acf12a9190ff8c53df3f37c2dc08ab37a3c186c | 8257c7c9263e8dda40553060a31f625a7b0b72b339d0af9564a3aea0004deef7 | a0cd199986d8eb2ee7019cd6b6968e5e837321dc7a2796078d3360bd441db6f8 | 197cd85363e427cef7ae7de920e96586baa5d60a66775a5fd4c6039e01edb218 |
cat-searcher/leandojo-benchmark-4-random | test | 2,039 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.nonempty_Icc</a>] at hu | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:fv _uniq.34812) (:fv _uniq.41416)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:fv FV0) (:arg :explicit 0 (:fv FV9)))) (:arg :explicit 3 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:ins... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"rw","sourceEnd":7691,"sourceStart":7689,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7693,"sourceStart":7692,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.nonempty_Icc","s... | [] | [{"source":"Set.nonempty_Icc","source_end":7709,"source_start":7693,"syntax_kind":"ident"},{"source":"hu","source_end":7716,"source_start":7714,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 73 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dc180472cef13d7b150e488ad1a0558e1c16cb05abcf171db5eae125c3332094 | 197cd85363e427cef7ae7de920e96586baa5d60a66775a5fd4c6039e01edb218 | 38a626d16a510d469b084b3858518371d454752eb7e689e646d1db1e1960f339 | 99939826d601675eb316310300c7ef20afdd8a8f0aecd729d4229fdc7e3c80c2 |
cat-searcher/leandojo-benchmark-4-random | test | 2,040 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hu' : (c₁ - c₂) * f x ≤ 0 := by linarith | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:fv _uniq.34812) (:fv _uniq.41416)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:fv FV0) (:arg :explicit 0 (:fv FV9)))) (:arg :explicit 3 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:ins... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"have","sourceEnd":7725,"sourceStart":7721,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hu'","sourceEnd":7729,"sourceStart":7726,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hu'","sourceEnd":7729,"sourceStart":7726,"tag":"node"},... | [] | [{"source":"(c₁ - c₂) * f x ≤ 0","source_end":7757,"source_start":7732,"syntax_kind":"«term_≤_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 76 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 012a33a0cec878f94b04a4d4b5ebdcfb5fe3f41e8b643e0fd6b8244c5da89a43 | 99939826d601675eb316310300c7ef20afdd8a8f0aecd729d4229fdc7e3c80c2 | 892f55f08dd86ffa87ad376239b70ca0a3a9ebf52a3894b2ac7c9ebc2153a0b1 | d348cf2b065d44e1831c5c6e5a8bccbcb53b915199006a96a202738146792394 |
cat-searcher/leandojo-benchmark-4-random | test | 2,041 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>nonpos_of_mul_nonpos_right</a> hu' (by linarith) | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:fv _uniq.34812) (:fv _uniq.41416)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:fv FV0) (:arg :explicit 0 (:fv FV9)))) (:arg :explicit 3 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:ins... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"exact","sourceEnd":7782,"sourceStart":7777,"tag":"atom"},{"children":[{"name":"nonpos_of_mul_nonpos_right","semanticRole":"global","source":"nonpos_of_mul_nonpos_right","sourceEnd":7809,"sourceStart":7783,"tag":"identifier"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"hu'","... | [] | [{"source":"nonpos_of_mul_nonpos_right hu' (by linarith)","source_end":7827,"source_start":7783,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 79 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b526327b5f0c03263189136068905bd5f0fb4bc15ee5e07d26312aa0023b60ac | d348cf2b065d44e1831c5c6e5a8bccbcb53b915199006a96a202738146792394 | 4f22cf4c940f8982c110b7d5370c2bf68db2c0bf02471281bb7bd150dca11723 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,042 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.mem_Icc</a>] | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
⊢ 3 / 4 * x ∈ Set.Icc (1 / 2 * x) x | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
⊢ 1 / 2 * x ≤ 3 / 4 * x ∧ 3 / 4 * x ≤ x | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedFiel... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 3 (:app (:c HMul.hMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"rw","sourceEnd":7543,"sourceStart":7541,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7545,"sourceStart":7544,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.mem_Icc","semant... | [] | [{"source":"Set.mem_Icc","source_end":7556,"source_start":7545,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 55 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fccbc1761b9b75dadbfe7d984e0f349769ad3c17d78e0be33981906ff9402d40 | 00662f20f04b7941a5a9d1369393c271e1146aa28b22db7c5adb6300e4760fd9 | 7860e98a80f38e7bc18c1fe77ce3f4ad43754d2b1aac472b17191699e19eba20 | ce691903580cc091b850d429f5b0657c9fd1e142e7b4ff611925625b5e67d8a2 |
cat-searcher/leandojo-benchmark-4-random | test | 2,043 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨by gcongr ?_ * x; norm_num, by linarith⟩ | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
⊢ 1 / 2 * x ≤ 3 / 4 * x ∧ 3 / 4 * x ≤ x | ((:c And) ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField)... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c And) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"exact","sourceEnd":7569,"sourceStart":7564,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":7573,"sourceStart":7570,"tag":"atom"},{"children":[{"children":[{"source":"by","sourceEnd":7575,"sourceStart":7573,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"gcongr",... | [] | [{"source":"⟨by gcongr ?_ * x; norm_num, by linarith⟩","source_end":7615,"source_start":7570,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 58 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1c1c7781ca0b2786a8bd39f5328160c83748d095c704cbaae9d5b1ac818c1617 | ce691903580cc091b850d429f5b0657c9fd1e142e7b4ff611925625b5e67d8a2 | 1b18a511adad709c74aab8326e1e8e7f58797f1a267a78c377d366b53718d94e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,044 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr ?_ * x | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
⊢ 1 / 2 * x ≤ 3 / 4 * x | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
⊢ 1 / 2 ≤ 3 / 4 | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Of... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"gcongr","sourceEnd":7582,"sourceStart":7576,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"?","sourceEnd":7584,"sourceStart":7583,"tag":"atom"},{"children":[{"source":"_","sourceEnd":7585,"sourceStart":7584,"tag":"atom"}],"kind":"Lean.Parser.Term.hole","source":"_","sourceEnd":7... | [] | [{"source":"?_ * x","source_end":7589,"source_start":7583,"syntax_kind":"«term_*_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 63 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4be938644c0562d513562d3f11761c19530e872eebdd8bf0daf52cedecab8f02 | ea5210c55c399332d273ef0f578449a0582652ae044e5222da5f40f6c9b68021 | f75d71a937d83d46b0ea0e84993170b6d4920bbb4e993754b38a133ad64629d9 | c7196e3e50043d8c8b5ded7a5af374ec0149509bfccef8769750e9b77c4f1aca |
cat-searcher/leandojo-benchmark-4-random | test | 2,045 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_num | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
⊢ 1 / 2 ≤ 3 / 4 | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c OfNat.... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"norm_num","sourceEnd":7599,"sourceStart":7591,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 65 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 19a3b2c52d4c69f71cc2a92b6dc0f3d1135396de7c588bce81a67679f5bc6320 | c7196e3e50043d8c8b5ded7a5af374ec0149509bfccef8769750e9b77c4f1aca | 7c64df8336d5a348b5f037e1d91facb19224fdef00e798d5c48c07a184602a59 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,046 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
⊢ 3 / 4 * x ≤ x | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Of... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"linarith","sourceEnd":7612,"sourceStart":7604,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kin... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 68 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c609c6344dc83e886fd0438e9ba667e5828890047b923b194b84a4809804c014 | 6bca975ec679d1dde52c49cdd7a14ed6aff9b85239cde66d876b44ef6bf15ff0 | 2c587e2f140ae41533b8e0551e8c940d4f70fbd4b1f4245ea1c9efcde110c9af | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,047 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x) x
hu✝... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) (:fv _uniq.35475) (:fv _uniq.35515)) ((:fv _uniq.34812) (:fv _uniq.41416))) ((:c OfNat.ofNat) (:c Rea... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"linarith","sourceEnd":7772,"sourceStart":7764,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"k... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 78 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b2f60644910d62e754419fca361097a558f3b94fcac23837b419790ca7ed7b6c | 9b2d95e13435ae37c09001ed0b0e465320d16402c4d56f847177d8de4fe8c3af | 2c587e2f140ae41533b8e0551e8c940d4f70fbd4b1f4245ea1c9efcde110c9af | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,048 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hgt : c₂ < c₁
x : ℝ
hx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
hx_nonneg : 0 ≤ x
h' : 3 / 4 * x ∈ Set.Icc (1 / 2 * x) x
hu✝... | ((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) (:c Real.instLinearOrderedSemiring))))) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) ((:c M... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"linarith","sourceEnd":7826,"sourceStart":7818,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kin... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 82 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dd173f2c01774909ffdaa394f4070cd99b884259dc7a0782a95960ae0635350f | 19e4f02ff994505bfe7c5e8775a13dc423f200dcd92a32f3f0112ce959d75af6 | 2c587e2f140ae41533b8e0551e8c940d4f70fbd4b1f4245ea1c9efcde110c9af | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,049 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hmain : ∃ c, ∀ᶠ x in <a>Filter.atTop</a>, f x = c := by simp only [heq, <a>Set.Icc_self</a>, <a>Set.mem_singleton_iff</a>, <a>one_mul</a>] at h rw [<a>Filter.eventually_atTop</a>] at h obtain ⟨n₀, hn₀⟩ := h refine ⟨f (<a>Max.max</a> n₀ 2), ?_⟩ rw [<a>Filter.eventually_atTop</a>] refine ⟨<a>Max.max</a> n₀ 2, ?_⟩ re... | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
heq : c₁ = c₂
⊢ (∀ᶠ (x : ℝ) in atTop, 0 ≤ f x) ∨ ∀ᶠ (x : ℝ) in atTop, f x ≤ 0 | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
heq : c₁ = c₂
hmain : ∃ c, ∀ᶠ (x : ℝ) in atTop, f x = c
⊢ (∀ᶠ (x : ℝ) in atTop, 0 ≤ f x) ∨ ∀ᶠ (x : ℝ) in atTop, f x ≤ 0 | ((:c Or) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:fv _uniq.34812) 0))) ((:c Filter.atTop) (:c Real) (:c Real.instPreorder))) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Re... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Or) (:arg :explicit 0 (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (:c Real) (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"have","sourceEnd":7874,"sourceStart":7870,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hmain","sourceEnd":7880,"sourceStart":7875,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hmain","sourceEnd":7880,"sourceStart":7875,"tag":"nod... | [] | [{"source":"∃ c, ∀ᶠ x in atTop, f x = c","source_end":7916,"source_start":7883,"syntax_kind":"«term∃_,_»"},{"source":"heq","source_end":7943,"source_start":7940,"syntax_kind":"ident"},{"source":"Set.Icc_self","source_end":7957,"source_start":7945,"syntax_kind":"ident"},{"source":"Set.mem_singleton_iff","source_end":798... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 88 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6acc9fa345db34d5868844c874492227f9680124038e756e376f301ee51bbee1 | 18b1376cd2e9b6e58566893fd524e91af03d2699e94a9439e0e386f2e171cb08 | fbf899499792a20757296f95f0fa2169be3d0891b01f571334fbca7d6a332508 | 176c7f8c62c329a10b7b145baddaec02aff7f1fd99cd80a5f02b7c3bde044b89 |
cat-searcher/leandojo-benchmark-4-random | test | 2,050 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨c, hc⟩ := hmain | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
heq : c₁ = c₂
hmain : ∃ c, ∀ᶠ (x : ℝ) in atTop, f x = c
⊢ (∀ᶠ (x : ℝ) in atTop, 0 ≤ f x) ∨ ∀ᶠ (x : ℝ) in atTop, f x ≤ 0 | case intro
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
heq : c₁ = c₂
c : ℝ
hc : ∀ᶠ (x : ℝ) in atTop, f x = c
⊢ (∀ᶠ (x : ℝ) in atTop, 0 ≤ f x) ∨ ∀ᶠ (x : ℝ) in atTop, f x ≤ 0 | ((:c Or) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:fv _uniq.34812) 0))) ((:c Filter.atTop) (:c Real) (:c Real.instPreorder))) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Re... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Or) (:arg :explicit 0 (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (:c Real) (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"obtain","sourceEnd":10322,"sourceStart":10316,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":10326,"sourceStart":10323,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"c","sourceEn... | [] | [{"source":"hmain","source_end":10343,"source_start":10338,"syntax_kind":"ident"},{"source":"⟨c, hc⟩","source_end":10334,"source_start":10323,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 272 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9d97b2172c08c5e17c52a009d73b0ff40eb4f43046e722d0372ccd33d809ce9f | 176c7f8c62c329a10b7b145baddaec02aff7f1fd99cd80a5f02b7c3bde044b89 | c0fc793c5d2e7de1a7314193ca9cb69237b1e490e48bfa07acca88e7a9cd5556 | 34172aad891384be166fd87c217396fbd896ee591b2990ea38aacc030ff76551 |
cat-searcher/leandojo-benchmark-4-random | test | 2,051 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases <a>le_or_lt</a> 0 c with | <a>Or.inl</a> hpos => exact <a>Or.inl</a> <| by filter_upwards [hc] with _ hc; simpa only [hc] | <a>Or.inr</a> hneg => right filter_upwards [hc] with x hc exact <a>le_of_lt</a> <| by simpa only [hc] | case intro
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
heq : c₁ = c₂
c : ℝ
hc : ∀ᶠ (x : ℝ) in atTop, f x = c
⊢ (∀ᶠ (x : ℝ) in atTop, 0 ≤ f x) ∨ ∀ᶠ (x : ℝ) in atTop, f x ≤ 0 | ((:c Or) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:fv _uniq.34812) 0))) ((:c Filter.atTop) (:c Real) (:c Real.instPreorder))) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Re... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Or) (:arg :explicit 0 (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (:c Real) (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"cases","sourceEnd":10353,"sourceStart":10348,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"le_or_lt","semanticRole":"global","source":"le_or_lt","sourceEnd":10362,"sourceStart":10354,"tag":"identifier"},{"children":[{"childre... | [] | [{"source":"le_or_lt 0 c","source_end":10366,"source_start":10354,"syntax_kind":"Lean.Parser.Term.app"},{"source":"inl","source_end":10381,"source_start":10378,"syntax_kind":"ident"},{"source":"Or.inl <| by filter_upwards [hc] with _ hc; simpa only [hc]","source_end":10461,"source_start":10402,"syntax_kind":"«term_<|_»... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 273 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ddaed77f4622f678fc0cf521ee299fc0700996b7b5a5952de49bec6d4dc89349 | 34172aad891384be166fd87c217396fbd896ee591b2990ea38aacc030ff76551 | e7dc183f8092b97e998ad45e594bcf1ecdc71f3794c9fa1667e922595ab72c56 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,052 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [heq, <a>Set.Icc_self</a>, <a>Set.mem_singleton_iff</a>, <a>one_mul</a>] at h | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
heq : c₁ = c₂
⊢ ∃ c, ∀ᶠ (x : ℝ) in atTop, f x = c | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u = c₂ * f x
⊢ ∃ c, ∀ᶠ (x : ℝ) in atTop, f x = c | ((:c Exists) (:c Real) (:lambda c (:c Real) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) ((:c Eq) (:c Real) ((:fv _uniq.34812) 0) 1)) ((:c Filter.atTop) (:c Real) (:c Real.instPreorder))))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c :explicit (:c Real) (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (:c Real) (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV0) (:arg :explicit 0 0))) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"simp","sourceEnd":7933,"sourceStart":7929,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":7938,"sourceStart":7934,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":7938,"s... | [] | [{"source":"heq","source_end":7943,"source_start":7940,"syntax_kind":"ident"},{"source":"Set.Icc_self","source_end":7957,"source_start":7945,"syntax_kind":"ident"},{"source":"Set.mem_singleton_iff","source_end":7980,"source_start":7959,"syntax_kind":"ident"},{"source":"one_mul","source_end":7989,"source_start":7982,"sy... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 90 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 86e5b371d9b2fa0693e5d548a635417baa6920ba67172cb88fb4280f9f9d4550 | c13d61fac4e2424f52ab1fc3f9471f52179a41075101cbf88daa9fdf0bf9e47c | 32baa29232bcfad8f0fc67c4c03b181dbadedca0ccd31946fba8d4094759857e | c13a5ed1d0f736cda09ce5e66c9d8e17871440c547f4488280e4e0466c29075c |
cat-searcher/leandojo-benchmark-4-random | test | 2,053 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Filter.eventually_atTop</a>] at h | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u = c₂ * f x
⊢ ∃ c, ∀ᶠ (x : ℝ) in atTop, f x = c | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
h : ∃ a, ∀ b ≥ a, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
⊢ ∃ c, ∀ᶠ (x : ℝ) in atTop, f x = c | ((:c Exists) (:c Real) (:lambda c (:c Real) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) ((:c Eq) (:c Real) ((:fv _uniq.34812) 0) 1)) ((:c Filter.atTop) (:c Real) (:c Real.instPreorder))))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c :explicit (:c Real) (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (:c Real) (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV0) (:arg :explicit 0 0))) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"rw","sourceEnd":8004,"sourceStart":8002,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8006,"sourceStart":8005,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Filter.eventually_at... | [] | [{"source":"eventually_atTop","source_end":8022,"source_start":8006,"syntax_kind":"ident"},{"source":"h","source_end":8028,"source_start":8027,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 91 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 012618073a6e3a7bb8a00df67c50c5ab0583e9f060b09ca7a654e0c99b519e0d | c13a5ed1d0f736cda09ce5e66c9d8e17871440c547f4488280e4e0466c29075c | 50080ffe00226139f15de3b57490673bc85038c1c5fbcb8a559220b1ac2c6979 | 69f51fba65c6ab5e81e5102f90b3bf8f4472ca3ebd6205d9a1c2bde77b1c5c27 |
cat-searcher/leandojo-benchmark-4-random | test | 2,054 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨n₀, hn₀⟩ := h | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
h : ∃ a, ∀ b ≥ a, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
⊢ ∃ c, ∀ᶠ (x : ℝ) in atTop, f x = c | case intro
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
⊢ ∃ c, ∀ᶠ (x : ℝ) in atTop, f x = c | ((:c Exists) (:c Real) (:lambda c (:c Real) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) ((:c Eq) (:c Real) ((:fv _uniq.34812) 0) 1)) ((:c Filter.atTop) (:c Real) (:c Real.instPreorder))))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c :explicit (:c Real) (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (:c Real) (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV0) (:arg :explicit 0 0))) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"obtain","sourceEnd":8041,"sourceStart":8035,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":8045,"sourceStart":8042,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"n₀","sourceEnd":... | [] | [{"source":"h","source_end":8064,"source_start":8063,"syntax_kind":"ident"},{"source":"⟨n₀, hn₀⟩","source_end":8059,"source_start":8042,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 94 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0f0816b995da15d63673ef3f42f851cc6a67c69bd5b6ee3371fa9b8f0591ec34 | 69f51fba65c6ab5e81e5102f90b3bf8f4472ca3ebd6205d9a1c2bde77b1c5c27 | 8dfe96647f5fe2df67ffdde67b309e55d45c234cb9c7f95cc2d21096bac2610a | f07ad60e33c387da68436b2efd85be55dd2bb5cdcfd66f312b311a43e938da46 |
cat-searcher/leandojo-benchmark-4-random | test | 2,055 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨f (<a>Max.max</a> n₀ 2), ?_⟩ | case intro
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
⊢ ∃ c, ∀ᶠ (x : ℝ) in atTop, f x = c | case intro
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
⊢ ∀ᶠ (x : ℝ) in atTop, f x = f (max n₀ 2) | ((:c Exists) (:c Real) (:lambda c (:c Real) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) ((:c Eq) (:c Real) ((:fv _uniq.34812) 0) 1)) ((:c Filter.atTop) (:c Real) (:c Real.instPreorder))))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c :explicit (:c Real) (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (:c Real) (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV0) (:arg :explicit 0 0))) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"refine","sourceEnd":8077,"sourceStart":8071,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":8081,"sourceStart":8078,"tag":"atom"},{"children":[{"children":[{"contextIndex":0,"semanticRole":"local","source":"f","sourceEnd":8082,"sourceStart":8081,"tag":"identifier"},{"children":[{"children":... | [] | [{"source":"⟨f (max n₀ 2), ?_⟩","source_end":8102,"source_start":8078,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 95 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 42ac7db0f9da15df9914d1728f0aa65e0a67e771d4dbf20d33f19f9465e45ebb | f07ad60e33c387da68436b2efd85be55dd2bb5cdcfd66f312b311a43e938da46 | e438714cc5608eeaf365f6ca16e53cb712edb3ed7c1e1186c567ce05bda75741 | f395d2972046ae8c0656d061dfa268c5e1e29f8415c727180700aa0056cc83bb |
cat-searcher/leandojo-benchmark-4-random | test | 2,056 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Filter.eventually_atTop</a>] | case intro
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
⊢ ∀ᶠ (x : ℝ) in atTop, f x = f (max n₀ 2) | case intro
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
⊢ ∃ a, ∀ b ≥ a, f b = f (max n₀ 2) | ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) ((:c Eq) (:c Real) ((:fv _uniq.34812) 0) ((:fv _uniq.34812) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (:c Real) (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV0) (:arg :explicit 0 0))) (:arg :explicit 2 (:app (:fv FV0) (:arg :explicit 0 (:app (:c Max.max) (:arg :implicit-type 0 (:c Real)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"rw","sourceEnd":8111,"sourceStart":8109,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8113,"sourceStart":8112,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Filter.eventually_at... | [] | [{"source":"eventually_atTop","source_end":8129,"source_start":8113,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 96 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3790f3a81231b45f54151fe98c7ec4aa8475f769184f33056a33ee8b4f8cadc2 | f395d2972046ae8c0656d061dfa268c5e1e29f8415c727180700aa0056cc83bb | 473d0fc2af556b031d0841053d0432f3fc87c5b1b68717b93cb5f71733d40988 | 03338e519af4fe68e4b3af35096a552cb9b666673018f7665b40625bacd344fc |
cat-searcher/leandojo-benchmark-4-random | test | 2,057 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨<a>Max.max</a> n₀ 2, ?_⟩ | case intro
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
⊢ ∃ a, ∀ b ≥ a, f b = f (max n₀ 2) | case intro
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
⊢ ∀ b ≥ max n₀ 2, f b = f (max n₀ 2) | ((:c Exists) (:c Real) (:lambda a (:c Real) (:forall b (:c Real) (:forall _ ((:c GE.ge) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c SemilatticeSup.toPartialOrder) (:c Real) (:c Real.instSemilatticeSup)))) 0 1) ((:c Eq) (:c Real) ((:fv _uniq.34812) 1) ((:fv _uniq.34812) ((:c Max.... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda a :explicit (:c Real) (:forall b :explicit (:c Real) (:forall _ :explicit (:app (:c GE.ge) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 0) (:arg :explicit 3... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"refine","sourceEnd":8143,"sourceStart":8137,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":8147,"sourceStart":8144,"tag":"atom"},{"children":[{"children":[{"name":"Max.max","semanticRole":"global","source":"max","sourceEnd":8150,"sourceStart":8147,"tag":"identifier"},{"children":[{"context... | [] | [{"source":"⟨max n₀ 2, ?_⟩","source_end":8164,"source_start":8144,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 99 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6ec0179e2eb26a0d832a432d00b6d5d92301d794e59c5869324ee5d8a904488d | 03338e519af4fe68e4b3af35096a552cb9b666673018f7665b40625bacd344fc | 586e3c165a17f8524eed230b0b6702626da5f9524062bc1a8430cc1d84d51712 | 142c505a899c9296469459d6847ae21b92b00bc1e8601cb1a473b5f09e0680d5 |
cat-searcher/leandojo-benchmark-4-random | test | 2,058 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Real.induction_Ico_mul</a> _ 2 (by norm_num) (by positivity) ?base ?step | case intro
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
⊢ ∀ b ≥ max n₀ 2, f b = f (max n₀ 2) | case base
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
⊢ ∀ x ∈ Set.Ico (max n₀ 2) (2 * max n₀ 2), f x = f (max n₀ 2)
case step
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ >... | (:forall b (:c Real) (:forall _ ((:c GE.ge) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c SemilatticeSup.toPartialOrder) (:c Real) (:c Real.instSemilatticeSup)))) 0 ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) (... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:forall b :explicit (:c Real) (:forall _ :explicit (:app (:c GE.ge) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 0) (:arg :explicit 3 (:app (:c Max.max) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Max) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"refine","sourceEnd":8177,"sourceStart":8171,"tag":"atom"},{"children":[{"name":"Real.induction_Ico_mul","semanticRole":"global","source":"Real.induction_Ico_mul","sourceEnd":8200,"sourceStart":8178,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":8202,"sourceStart":8201,"t... | [] | [{"source":"Real.induction_Ico_mul _ 2 (by norm_num) (by positivity) ?base ?step","source_end":8246,"source_start":8178,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 100 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0ec8ea2cd68ab18363c75640ef33d7c67399d77058d52fa0548bd9bd4b013700 | 142c505a899c9296469459d6847ae21b92b00bc1e8601cb1a473b5f09e0680d5 | 39ae505dd36c2484ce97725f9193ffa1d2ea1cba67a87965f8ad9fdd910c269b | e70802dcce65f1213519216f0c8dc8e1c0b20df7ee273220d1f85af36729951c |
cat-searcher/leandojo-benchmark-4-random | test | 2,060 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | case step => intro n hn hyp_ind z hz have z_nonneg : 0 ≤ z := by calc (0:ℝ) ≤ (2:ℝ)^n * <a>Max.max</a> n₀ 2 := by exact <a>mul_nonneg</a> (<a>pow_nonneg</a> (by norm_num) _) (by norm_num) _ ≤ z := by exact_mod_cast hz.1 have le_2n : <a>Max.max</a> n₀ 2 ≤ (2:ℝ)^n * <a>Max.max</a> n₀ 2 := by nth_rewrite 1 [← <a>one_mul</... | case step
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
⊢ ∀ n ≥ 1,
(∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)) →
∀ z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2), f... | (:forall n (:c Nat) (:forall _ ((:c GE.ge) (:c Nat) (:c instLENat) 0 ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) (:forall _ (:forall z (:c Real) (:forall _ ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) 0 ((:c Set.Ico) (:c Real) (:c Real.instPreorder) ((:c... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:forall n :explicit (:c Nat) (:forall _ :explicit (:app (:c GE.ge) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 0) (:arg :explicit 3 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"case","sourceEnd":8658,"sourceStart":8654,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"step","sourceEnd":8663,"sourceStart":8659,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"step","sourceEnd":8663,"sourceStart":8659,"tag":"node"},{"children":[],"kind":"null","sourc... | [] | [{"source":"0 ≤ z","source_end":8730,"source_start":8723,"syntax_kind":"«term_≤_»"},{"source":"(0:ℝ) ≤ (2:ℝ)^n * max n₀ 2","source_end":8786,"source_start":8752,"syntax_kind":"«term_≤_»"},{"source":"mul_nonneg (pow_nonneg (by norm_num) _) (by norm_num)","source_end":8876,"source_start":8823,"syntax_kind":"Lean.Parser.T... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 149 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1c9db9d81bc88f724687ff84a359fd0cc02d9a88ae63409a61d798dbe12c72e1 | 38ba7076e439dedd63942bdb3503c9b3c4f9c386a13cc5d0cf83db5c01468a99 | b2397e62abde6cb916a383fe92642e6e714fef0f263f1e1f78e30fc24776df5f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,061 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_num | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
⊢ 1 < 2 | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))))... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"norm_num","sourceEnd":8217,"sourceStart":8209,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","so... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 103 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 370a255400617598f638d4d51c7158d834ac76e3c052d1f41a2cf266c56ce7cf | 80ac0f7016a54b93d2d25b3efc92b0754ae9685600feea3ff5888c3cbe66124d | 7c64df8336d5a348b5f037e1d91facb19224fdef00e798d5c48c07a184602a59 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,062 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
⊢ 0 < max n₀ 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 Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"positivity","sourceEnd":8233,"sourceStart":8223,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":8233,"sourceStart":8223,"tag":"node"}],"kind":"null","source":"positivity","sourceEnd":8233,"sourceStart":8223,"ta... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 108 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f40311c9f3556d7080b72a1af8c21c6632932adbbe775721a4336e0870a434da | 605d5a45ec5a610a8760660afb62e5482565474ec77a51fb97fc699b37beb23a | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 |
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