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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
values | target_state_matches_invocation bool 2
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 | 609 | MeasureTheory.lmarginal_update_of_mem | Mathlib/MeasureTheory/Integral/Marginal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : j ≠ i := by rintro rfl; exact hj hi | case h
δ : Type u_1
δ' : Type u_2
π : δ → Type u_3
inst✝² : (x : δ) → MeasurableSpace (π x)
μ : (i : δ) → Measure (π i)
inst✝¹ : ∀ (i : δ), SigmaFinite (μ i)
inst✝ : DecidableEq δ
s t : Finset δ
f✝ g : ((i : δ) → π i) → ℝ≥0∞
x✝ y✝ : (i : δ) → π i
i✝ i : δ
hi : i ∈ s
f : ((i : δ) → π i) → ℝ≥0∞
x : (i : δ) → π i
y : π i
... | case h
δ : Type u_1
δ' : Type u_2
π : δ → Type u_3
inst✝² : (x : δ) → MeasurableSpace (π x)
μ : (i : δ) → Measure (π i)
inst✝¹ : ∀ (i : δ), SigmaFinite (μ i)
inst✝ : DecidableEq δ
s t : Finset δ
f✝ g : ((i : δ) → π i) → ℝ≥0∞
x✝ y✝ : (i : δ) → π i
i✝ i : δ
hi : i ∈ s
f : ((i : δ) → π i) → ℝ≥0∞
x : (i : δ) → π i
y : π i
... | ((:c Eq) ((:fv _uniq.13510) (:fv _uniq.13940)) ((:c Function.update) (:fv _uniq.13502) (:fv _uniq.13510) (:fv _uniq.13554) (:fv _uniq.13857) (:fv _uniq.13854) (:fv _uniq.13858) (:fv _uniq.13940)) ((:fv _uniq.13857) (:fv _uniq.13940))) | [{"name":"δ","sexp":"(:sort (+ u_1 1))"},{"name":"δ'","sexp":"(:sort (+ u_2 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.13502) (:sort (+ u_3 1)))"},{"name":"inst✝²","sexp":"(:forall x (:fv _uniq.13502) ((:c MeasurableSpace) ((:fv _uniq.13510) 0)))"},{"name":"μ","sexp":"(:forall i (:fv _uniq.13502) ((:c MeasureTheor... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:fv FV2) (:arg :explicit 0 (:fv FV20)))) (:arg :explicit 1 (:app (:c Function.update) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :instance 2 (:instance-of (:app (:c DecidableEq) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 3 (:fv FV18)) (:arg :explicit 4 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13502","is_instance":false,"is_let":false,"name":"δ","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13505","is_instance":false,"is_let":false,"name":"δ'","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"have","sourceEnd":4999,"sourceStart":4995,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":5000,"sourceStart":5000,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":5000,"sourceStart":5000,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"j ≠ i","source_end":5009,"source_start":5002,"syntax_kind":"«term_≠_»"},{"source":"rfl","source_end":5026,"source_start":5023,"syntax_kind":"ident"},{"source":"hj hi","source_end":5039,"source_start":5034,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13502","is_instance":false,"is_let":false,"user_name":"δ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13505","is_instance":false,"is_let":false,"user_name":"δ'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 16 | 6 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 201a0a2158884d85348a90f84af9c197e0c3df411c705c42ee5419484777ee1d | eee3408b2e0e69a58fd19769846b45f4e33a4e1b8528abd01317d9267171fa7d | f3a964e2aa16d37a593f9147410b5adb9ebe5ba6d4e00f197e954201647f29df | e8fad76a324d41a982c489162b0dfa13e5397d55e905aa1ddbc92b89c4c36ea2 |
cat-searcher/leandojo-benchmark-4-random | test | 610 | MeasureTheory.lmarginal_update_of_mem | Mathlib/MeasureTheory/Integral/Marginal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Function.update_noteq</a> this | case h
δ : Type u_1
δ' : Type u_2
π : δ → Type u_3
inst✝² : (x : δ) → MeasurableSpace (π x)
μ : (i : δ) → Measure (π i)
inst✝¹ : ∀ (i : δ), SigmaFinite (μ i)
inst✝ : DecidableEq δ
s t : Finset δ
f✝ g : ((i : δ) → π i) → ℝ≥0∞
x✝ y✝ : (i : δ) → π i
i✝ i : δ
hi : i ∈ s
f : ((i : δ) → π i) → ℝ≥0∞
x : (i : δ) → π i
y : π i
... | ((:c Eq) ((:fv _uniq.13510) (:fv _uniq.13940)) ((:c Function.update) (:fv _uniq.13502) (:fv _uniq.13510) (:fv _uniq.13554) (:fv _uniq.13857) (:fv _uniq.13854) (:fv _uniq.13858) (:fv _uniq.13940)) ((:fv _uniq.13857) (:fv _uniq.13940))) | [{"name":"δ","sexp":"(:sort (+ u_1 1))"},{"name":"δ'","sexp":"(:sort (+ u_2 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.13502) (:sort (+ u_3 1)))"},{"name":"inst✝²","sexp":"(:forall x (:fv _uniq.13502) ((:c MeasurableSpace) ((:fv _uniq.13510) 0)))"},{"name":"μ","sexp":"(:forall i (:fv _uniq.13502) ((:c MeasureTheor... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:fv FV2) (:arg :explicit 0 (:fv FV20)))) (:arg :explicit 1 (:app (:c Function.update) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :instance 2 (:instance-of (:app (:c DecidableEq) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 3 (:fv FV18)) (:arg :explicit 4 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13502","is_instance":false,"is_let":false,"name":"δ","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13505","is_instance":false,"is_let":false,"name":"δ'","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"apply","sourceEnd":5047,"sourceStart":5042,"tag":"atom"},{"children":[{"name":"Function.update_noteq","semanticRole":"global","source":"update_noteq","sourceEnd":5060,"sourceStart":5048,"tag":"identifier"},{"children":[{"contextIndex":22,"semanticRole":"local","source":"this","sourceEnd":5065,"s... | [] | [{"source":"update_noteq this","source_end":5065,"source_start":5048,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13502","is_instance":false,"is_let":false,"user_name":"δ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13505","is_instance":false,"is_let":false,"user_name":"δ'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 16 | 11 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 737e3ced9ddd0c1a498056fd3a2eba4db4371cae72cf289a6e65f64d01ecef7e | e8fad76a324d41a982c489162b0dfa13e5397d55e905aa1ddbc92b89c4c36ea2 | 6f2b786d0c92abf62a1a02b268991adad19142a28a0108030f736bb7ca9acfa6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 611 | MeasureTheory.lmarginal_update_of_mem | Mathlib/MeasureTheory/Integral/Marginal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro rfl | δ : Type u_1
δ' : Type u_2
π : δ → Type u_3
inst✝² : (x : δ) → MeasurableSpace (π x)
μ : (i : δ) → Measure (π i)
inst✝¹ : ∀ (i : δ), SigmaFinite (μ i)
inst✝ : DecidableEq δ
s t : Finset δ
f✝ g : ((i : δ) → π i) → ℝ≥0∞
x✝ y✝ : (i : δ) → π i
i✝ i : δ
hi : i ∈ s
f : ((i : δ) → π i) → ℝ≥0∞
x : (i : δ) → π i
y : π i
j : δ
h... | δ : Type u_1
δ' : Type u_2
π : δ → Type u_3
inst✝² : (x : δ) → MeasurableSpace (π x)
μ : (i : δ) → Measure (π i)
inst✝¹ : ∀ (i : δ), SigmaFinite (μ i)
inst✝ : DecidableEq δ
s t : Finset δ
f✝ g : ((i : δ) → π i) → ℝ≥0∞
x✝ y✝ : (i : δ) → π i
i : δ
f : ((i : δ) → π i) → ℝ≥0∞
x : (i : δ) → π i
j : δ
hj : j ∉ s
hi : j ∈ s
y... | ((:c Ne) (:fv _uniq.13502) (:fv _uniq.13940) (:fv _uniq.13854)) | [{"name":"δ","sexp":"(:sort (+ u_1 1))"},{"name":"δ'","sexp":"(:sort (+ u_2 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.13502) (:sort (+ u_3 1)))"},{"name":"inst✝²","sexp":"(:forall x (:fv _uniq.13502) ((:c MeasurableSpace) ((:fv _uniq.13510) 0)))"},{"name":"μ","sexp":"(:forall i (:fv _uniq.13502) ((:c MeasureTheor... | (:app (:c Ne) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV20)) (:arg :explicit 2 (:fv FV15))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13502","is_instance":false,"is_let":false,"name":"δ","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13505","is_instance":false,"is_let":false,"name":"δ'","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"rintro","sourceEnd":5022,"sourceStart":5016,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":5026,"sourceStart":5023,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl","sourceEnd":5026,"sourceStart":5023,"ta... | [] | [{"source":"rfl","source_end":5026,"source_start":5023,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13502","is_instance":false,"is_let":false,"user_name":"δ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13505","is_instance":false,"is_let":false,"user_name":"δ'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 16 | 8 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 168e7456557f3bca8aabf54cadf7c390b24b6eb77c4c0f558a4de03caedeca77 | f2d7cab28020c64fd2f933de7e28a98fdcee4b9a22b24b820b3198ed215e57e1 | 09e128cd6787f35d3c063b643315aff1382388dafa4e55b6546fbf9dcecb02da | 2656883d4b4e67a7b51822c69a1d02d1ed41411fcd55b22d5792125873e61260 |
cat-searcher/leandojo-benchmark-4-random | test | 612 | MeasureTheory.lmarginal_update_of_mem | Mathlib/MeasureTheory/Integral/Marginal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hj hi | δ : Type u_1
δ' : Type u_2
π : δ → Type u_3
inst✝² : (x : δ) → MeasurableSpace (π x)
μ : (i : δ) → Measure (π i)
inst✝¹ : ∀ (i : δ), SigmaFinite (μ i)
inst✝ : DecidableEq δ
s t : Finset δ
f✝ g : ((i : δ) → π i) → ℝ≥0∞
x✝ y✝ : (i : δ) → π i
i : δ
f : ((i : δ) → π i) → ℝ≥0∞
x : (i : δ) → π i
j : δ
hj : j ∉ s
hi : j ∈ s
y... | (:c False) | [{"name":"δ","sexp":"(:sort (+ u_1 1))"},{"name":"δ'","sexp":"(:sort (+ u_2 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.13502) (:sort (+ u_3 1)))"},{"name":"inst✝²","sexp":"(:forall x (:fv _uniq.13502) ((:c MeasurableSpace) ((:fv _uniq.13510) 0)))"},{"name":"μ","sexp":"(:forall i (:fv _uniq.13502) ((:c MeasureTheor... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13502","is_instance":false,"is_let":false,"name":"δ","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13505","is_instance":false,"is_let":false,"name":"δ'","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"exact","sourceEnd":5033,"sourceStart":5028,"tag":"atom"},{"children":[{"contextIndex":18,"semanticRole":"local","source":"hj","sourceEnd":5036,"sourceStart":5034,"tag":"identifier"},{"children":[{"contextIndex":19,"semanticRole":"local","source":"hi","sourceEnd":5039,"sourceStart":5037,"tag":"id... | [] | [{"source":"hj hi","source_end":5039,"source_start":5034,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13502","is_instance":false,"is_let":false,"user_name":"δ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13505","is_instance":false,"is_let":false,"user_name":"δ'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 16 | 10 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eb5c84401562dea4681ee43ae0a85f894d9b6e7ca9661e4f7b434c612973c702 | 2656883d4b4e67a7b51822c69a1d02d1ed41411fcd55b22d5792125873e61260 | 023505ba2169738b37b30db408c8fa280c86ecd3e53702ecbc7adebcf7ad9fdc | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 613 | Set.Icc_eq_singleton_iff | Mathlib/Order/Interval/Set/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨fun h => ?_, ?_⟩ | α : Type u_1
β : Type u_2
inst✝ : PartialOrder α
a b c : α
⊢ Icc a b = {c} ↔ a = c ∧ b = c | ((:c Iff) ((:c Eq) ((:c Set) (:fv _uniq.29531)) ((:c Set.Icc) (:fv _uniq.29531) ((:c PartialOrder.toPreorder) (:fv _uniq.29531) (:fv _uniq.29537)) (:fv _uniq.29539) (:fv _uniq.29541)) ((:c Singleton.singleton) (:fv _uniq.29531) ((:c Set) (:fv _uniq.29531)) ((:c Set.instSingletonSet) (:fv _uniq.29531)) (:fv _uniq.29543)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c PartialOrder) (:fv _uniq.29531))"},{"name":"a","sexp":"(:fv _uniq.29531)"},{"name":"b","sexp":"(:fv _uniq.29531)"},{"name":"c","sexp":"(:fv _uniq.29531)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Set.Icc) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29531","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29534","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"refine","sourceEnd":27935,"sourceStart":27929,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":27939,"sourceStart":27936,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":27942,"sourceStart":27939,"tag":"atom"},{"children":[{"children"... | [] | [{"source":"⟨fun h => ?_, ?_⟩","source_end":27957,"source_start":27936,"syntax_kind":"Lean.Parser.Term.anonymousCtor"},{"source":"a ≤ b","source_end":27981,"source_start":27974,"syntax_kind":"«term_≤_»"},{"source":"nonempty_Icc.1 (h.symm.subst <| singleton_nonempty c)","source_end":28038,"source_start":27985,"syntax_ki... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29531","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29534","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 344 | 2 | branch_opener | false | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 208057f2848aa8734011c5cc44655afefc82634222cf746e8ae3f76f13a4385f | 94e4f3d5a5c1f418737c06f555fef2a14637d7a134b9a2e392293a9df8e92f2f | ba410109fc662ad4055d60f644e28ecf5fe3ec3f0a8388ce86f73659bbbf72a2 | 62c2ddc6aafec34726e19944cbbaacd953c597d1b9b4059963a4161adc99efe1 | |
cat-searcher/leandojo-benchmark-4-random | test | 614 | Set.Icc_eq_singleton_iff | Mathlib/Order/Interval/Set/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hab : a ≤ b := <a>Set.nonempty_Icc</a>.1 (h.symm.subst <| <a>Set.singleton_nonempty</a> c) | case refine_1
α : Type u_1
β : Type u_2
inst✝ : PartialOrder α
a b c : α
h : Icc a b = {c}
⊢ a = c ∧ b = c | case refine_1
α : Type u_1
β : Type u_2
inst✝ : PartialOrder α
a b c : α
h : Icc a b = {c}
hab : a ≤ b
⊢ a = c ∧ b = c | ((:c And) ((:c Eq) (:fv _uniq.29531) (:fv _uniq.29539) (:fv _uniq.29543)) ((:c Eq) (:fv _uniq.29531) (:fv _uniq.29541) (:fv _uniq.29543))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c PartialOrder) (:fv _uniq.29531))"},{"name":"a","sexp":"(:fv _uniq.29531)"},{"name":"b","sexp":"(:fv _uniq.29531)"},{"name":"c","sexp":"(:fv _uniq.29531)"},{"name":"h","sexp":"((:c Eq) ((:c Set) (:fv _uniq.29531... | (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV4)) (:arg :explicit 2 (:fv FV5))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29531","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29534","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"have","sourceEnd":27967,"sourceStart":27963,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hab","sourceEnd":27971,"sourceStart":27968,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hab","sourceEnd":27971,"sourceStart":27968,"tag":"n... | [] | [{"source":"a ≤ b","source_end":27981,"source_start":27974,"syntax_kind":"«term_≤_»"},{"source":"nonempty_Icc.1 (h.symm.subst <| singleton_nonempty c)","source_end":28038,"source_start":27985,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29531","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29534","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 344 | 9 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 417931275424770e33bcf3deb97236bcbcfeaa9c57784b0f41e89a005161ae85 | 9497dd9860ea5b74ddb2e8fa28b3e3f062f8c97a168e25f7a00a4189f10a8728 | 29df968fd4de6eff7ce9729cd959d930f7ec32093efe142121608d502f5f5ef9 | 478556ac46d04b75c810e8004d991a10224c56654247448f9e90ba62c90302eb |
cat-searcher/leandojo-benchmark-4-random | test | 615 | Set.Icc_eq_singleton_iff | Mathlib/Order/Interval/Set/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨<a>Set.eq_of_mem_singleton</a> <| h.subst <| <a>Set.left_mem_Icc</a>.2 hab, <a>Set.eq_of_mem_singleton</a> <| h.subst <| <a>Set.right_mem_Icc</a>.2 hab⟩ | case refine_1
α : Type u_1
β : Type u_2
inst✝ : PartialOrder α
a b c : α
h : Icc a b = {c}
hab : a ≤ b
⊢ a = c ∧ b = c | ((:c And) ((:c Eq) (:fv _uniq.29531) (:fv _uniq.29539) (:fv _uniq.29543)) ((:c Eq) (:fv _uniq.29531) (:fv _uniq.29541) (:fv _uniq.29543))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c PartialOrder) (:fv _uniq.29531))"},{"name":"a","sexp":"(:fv _uniq.29531)"},{"name":"b","sexp":"(:fv _uniq.29531)"},{"name":"c","sexp":"(:fv _uniq.29531)"},{"name":"h","sexp":"((:c Eq) ((:c Set) (:fv _uniq.29531... | (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV4)) (:arg :explicit 2 (:fv FV5))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29531","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29534","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":28048,"sourceStart":28043,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":28058,"sourceStart":28055,"tag":"atom"},{"children":[{"children":[{"name":"Set.eq_of_mem_singleton","semanticRole":"global","source":"eq_of_mem_singleton","sourceEnd":28077,"sourceStart":28058,"tag"... | [] | [{"source":"⟨eq_of_mem_singleton <| h.subst <| left_mem_Icc.2 hab,\n eq_of_mem_singleton <| h.subst <| right_mem_Icc.2 hab⟩","source_end":28176,"source_start":28055,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29531","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29534","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 344 | 10 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5619dbf295c42984f0634cf397ca45d588b1b21a718a3501aceb1fae015e46d9 | 478556ac46d04b75c810e8004d991a10224c56654247448f9e90ba62c90302eb | 5a832861a8e4ab11e0a3b5c0f33707b3dc1e036e0ff4c00ebc81a854913bc6e9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 616 | Set.Icc_eq_singleton_iff | Mathlib/Order/Interval/Set/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨rfl, rfl⟩ | case refine_2
α : Type u_1
β : Type u_2
inst✝ : PartialOrder α
a b c : α
⊢ a = c ∧ b = c → Icc a b = {c} | case refine_2.intro
α : Type u_1
β : Type u_2
inst✝ : PartialOrder α
b : α
⊢ Icc b b = {b} | (:forall _ ((:c And) ((:c Eq) (:fv _uniq.29531) (:fv _uniq.29539) (:fv _uniq.29543)) ((:c Eq) (:fv _uniq.29531) (:fv _uniq.29541) (:fv _uniq.29543))) ((:c Eq) ((:c Set) (:fv _uniq.29531)) ((:c Set.Icc) (:fv _uniq.29531) ((:c PartialOrder.toPreorder) (:fv _uniq.29531) (:fv _uniq.29537)) (:fv _uniq.29539) (:fv _uniq.2954... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c PartialOrder) (:fv _uniq.29531))"},{"name":"a","sexp":"(:fv _uniq.29531)"},{"name":"b","sexp":"(:fv _uniq.29531)"},{"name":"c","sexp":"(:fv _uniq.29531)"}] | (:forall _ :explicit (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV4)) (:arg :explicit 2 (:fv FV5))))) (:app (:c Eq) (:arg :implicit-t... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29531","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29534","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rintro","sourceEnd":28188,"sourceStart":28182,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":28192,"sourceStart":28189,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":28195,"s... | [] | [{"source":"⟨rfl, rfl⟩","source_end":28203,"source_start":28189,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29531","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29534","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 344 | 15 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 603950c87ca94880a9088259b9228954ca10d1c82a68a163f373d80e4ae09e22 | c9175701138d8edd1cac85c54d9c0b9060aa51e9731948a80045ec482b548ec2 | 5797bf712fa00c681a09dd8d6e5cb501fce4e1b897e959ce6535019a23a19976 | d19f5fbc4fbbfbfe3cc9e5ae223bd3c33adf0c745eee96d3c0e730ddcfa75599 |
cat-searcher/leandojo-benchmark-4-random | test | 617 | Set.Icc_eq_singleton_iff | Mathlib/Order/Interval/Set/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Set.Icc_self</a> _ | case refine_2.intro
α : Type u_1
β : Type u_2
inst✝ : PartialOrder α
b : α
⊢ Icc b b = {b} | ((:c Eq) ((:c Set) (:fv _uniq.29531)) ((:c Set.Icc) (:fv _uniq.29531) ((:c PartialOrder.toPreorder) (:fv _uniq.29531) (:fv _uniq.29537)) (:fv _uniq.29541) (:fv _uniq.29541)) ((:c Singleton.singleton) (:fv _uniq.29531) ((:c Set) (:fv _uniq.29531)) ((:c Set.instSingletonSet) (:fv _uniq.29531)) (:fv _uniq.29541))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c PartialOrder) (:fv _uniq.29531))"},{"name":"b","sexp":"(:fv _uniq.29531)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Set.Icc) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:fv FV3)))) (:arg :explicit 2 (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29531","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29534","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":28213,"sourceStart":28208,"tag":"atom"},{"children":[{"name":"Set.Icc_self","semanticRole":"global","source":"Icc_self","sourceEnd":28222,"sourceStart":28214,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":28224,"sourceStart":28223,"tag":"atom"}],"kind"... | [] | [{"source":"Icc_self _","source_end":28224,"source_start":28214,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29531","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29534","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 344 | 16 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f3ca28fda63c58ae292648212ba889686afe84a0e9531ef4efa5168c0b5ce89e | d19f5fbc4fbbfbfe3cc9e5ae223bd3c33adf0c745eee96d3c0e730ddcfa75599 | b547470cff59608bfb2b38e9c60d371e5ae3b752bf3af5d6c152b8cdbaa5ec47 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 618 | Sym.ofVector_cons | Mathlib/Data/Sym/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases v | α : Type u_1
β : Type u_2
n n' m : ℕ
s : Sym α n
a✝ b a : α
v : Vector α n
⊢ ofVector (a ::ᵥ v) = a ::ₛ ofVector v | case mk
α : Type u_1
β : Type u_2
n n' m : ℕ
s : Sym α n
a✝ b a : α
val✝ : List α
property✝ : val✝.length = n
⊢ ofVector (a ::ᵥ ⟨val✝, property✝⟩) = a ::ₛ ofVector ⟨val✝, property✝⟩ | ((:c Eq) ((:c Sym) (:fv _uniq.5017) ((:c Nat.succ) (:fv _uniq.5022))) ((:c Sym.ofVector) (:fv _uniq.5017) ((:c Nat.succ) (:fv _uniq.5022)) ((:c Vector.cons) (:fv _uniq.5017) (:fv _uniq.5022) (:fv _uniq.5214) (:fv _uniq.5215))) ((:c Sym.cons) (:fv _uniq.5017) (:fv _uniq.5022) (:fv _uniq.5214) ((:c Sym.ofVector) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:c Nat)"},{"name":"n'","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"s","sexp":"((:c Sym) (:fv _uniq.5017) (:fv _uniq.5022))"},{"name":"a✝","sexp":"(:fv _uniq.5017)"},{"name":"b","sexp":"(:fv _uniq.5017)"}... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Sym) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Nat.succ) (:arg :explicit 0 (:fv FV2)))))) (:arg :explicit 1 (:app (:c Sym.ofVector) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c Vector.cons) (:arg :implicit-type 0 (:fv FV0)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5017","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5020","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"cases","sourceEnd":4764,"sourceStart":4759,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":10,"semanticRole":"local","source":"v","sourceEnd":4766,"sourceStart":4765,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","sourc... | [] | [{"source":"v","source_end":4766,"source_start":4765,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5017","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5020","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 43 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6569e7ed199a18dd59d56e8909779e93253bb65aec94f075b50b575900897759 | dcf28ce31c34968e035af7d029a6aa7886c89854426d4b253c727e15c6ea7ebb | 8ce8c7b2c8d608a7b1f24f7b842e4aa77eef54a36e9e63bc28d4e5e7e0c32b50 | ee6e3b1c852371f54b41843edd058e78b1dbfb473f06b74a6cd3125542510187 |
cat-searcher/leandojo-benchmark-4-random | test | 619 | Sym.ofVector_cons | Mathlib/Data/Sym/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case mk
α : Type u_1
β : Type u_2
n n' m : ℕ
s : Sym α n
a✝ b a : α
val✝ : List α
property✝ : val✝.length = n
⊢ ofVector (a ::ᵥ ⟨val✝, property✝⟩) = a ::ₛ ofVector ⟨val✝, property✝⟩ | ((:c Eq) ((:c Sym) (:fv _uniq.5017) ((:c Nat.succ) (:fv _uniq.5022))) ((:c Sym.ofVector) (:fv _uniq.5017) ((:c Nat.succ) (:fv _uniq.5022)) ((:c Vector.cons) (:fv _uniq.5017) (:fv _uniq.5022) (:fv _uniq.5214) ((:c Subtype.mk) ((:c List) (:fv _uniq.5017)) (:lambda l ((:c List) (:fv _uniq.5017)) ((:c Eq) (:c Nat) ((:c Lis... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:c Nat)"},{"name":"n'","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"s","sexp":"((:c Sym) (:fv _uniq.5017) (:fv _uniq.5022))"},{"name":"a✝","sexp":"(:fv _uniq.5017)"},{"name":"b","sexp":"(:fv _uniq.5017)"}... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Sym) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Nat.succ) (:arg :explicit 0 (:fv FV2)))))) (:arg :explicit 1 (:app (:c Sym.ofVector) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c Vector.cons) (:arg :implicit-type 0 (:fv FV0)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5017","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5020","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"rfl","sourceEnd":4772,"sourceStart":4769,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":4772,"sourceStart":4769,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5017","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5020","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 43 | 5 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9288e017652bfeee02218c42622bcf7bb812f66830566092067385812eba0fa6 | ee6e3b1c852371f54b41843edd058e78b1dbfb473f06b74a6cd3125542510187 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 620 | List.le_findIdx_of_not | Mathlib/Data/List/Indexes.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_contra! f | α : Type u
β : Type v
p : α → Bool
xs : List α
i : ℕ
h : i < xs.length
h2 : ∀ (j : ℕ) (hji : j < i), ¬p (xs.get ⟨j, ⋯⟩) = true
⊢ i ≤ findIdx p xs | α : Type u
β : Type v
p : α → Bool
xs : List α
i : ℕ
h : i < xs.length
h2 : ∀ (j : ℕ) (hji : j < i), ¬p (xs.get ⟨j, ⋯⟩) = true
f : findIdx p xs < i
⊢ False | ((:c LE.le) (:c Nat) (:c instLENat) (:fv _uniq.25046) ((:c List.findIdx) (:fv _uniq.24759) (:fv _uniq.25044) (:fv _uniq.25045))) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.24759) (:c Bool))"},{"name":"xs","sexp":"((:c List) (:fv _uniq.24759))"},{"name":"i","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c LT.lt) (:c Nat) (:c instLTNat) (:fv _uniq.25046) ((:c List.length) (:fv ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:app (:c List.findIdx) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV4))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24759","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24761","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"by_contra!","sourceEnd":12893,"sourceStart":12883,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"f","sourceEnd":12895,"sourceStart":12894,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"f","sourceEnd":12895,"sourceStart":12894,"tag":"node"}],"kind":"nul... | [] | [{"source":"f","source_end":12895,"source_start":12894,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24759","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24761","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 55 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4c11ab15aee05cc54dd1806f4d915b91ad9e9a9fdd5eadd6db55babdb57d4e83 | 1258f5e2ee743c86525f3812dce60c4b8dac81856c2e03405ac393277bb371e5 | 9916c56a3fb6ac62a06bc76d61423bf30e5f80e259808531ad1e044629f8ed60 | fc537f693581b0198e44a6fc0f5e42e6fa650b0a9c9fdc6817a10093c1fcee95 |
cat-searcher/leandojo-benchmark-4-random | test | 621 | List.le_findIdx_of_not | Mathlib/Data/List/Indexes.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>absurd</a> (@<a>List.findIdx_get</a> _ p xs (f.trans h)) (h2 (xs.findIdx p) f) | α : Type u
β : Type v
p : α → Bool
xs : List α
i : ℕ
h : i < xs.length
h2 : ∀ (j : ℕ) (hji : j < i), ¬p (xs.get ⟨j, ⋯⟩) = true
f : findIdx p xs < i
⊢ False | (:c False) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.24759) (:c Bool))"},{"name":"xs","sexp":"((:c List) (:fv _uniq.24759))"},{"name":"i","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c LT.lt) (:c Nat) (:c instLTNat) (:fv _uniq.25046) ((:c List.length) (:fv ... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24759","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24761","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":12903,"sourceStart":12898,"tag":"atom"},{"children":[{"name":"absurd","semanticRole":"global","source":"absurd","sourceEnd":12910,"sourceStart":12904,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":12912,"sourceStart":12911,"tag":"atom"},{"children":[{"... | [] | [{"source":"absurd (@findIdx_get _ p xs (f.trans h)) (h2 (xs.findIdx p) f)","source_end":12966,"source_start":12904,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24759","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24761","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 55 | 5 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c1a5d0b1f81a76b6a436d4a9d247b72ae20d4252955ccc1bb3eba2bb91d69b72 | fc537f693581b0198e44a6fc0f5e42e6fa650b0a9c9fdc6817a10093c1fcee95 | e8c8148e6a434fd71c36ab6173649907bc8a64d485895efa1d069e7f46fa6695 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 622 | MeasureTheory.lintegral_zero | Mathlib/MeasureTheory/Integral/Lebesgue.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
m : MeasurableSpace α
μ ν : Measure α
⊢ ∫⁻ (x : α), 0 ∂μ = 0 | ((:c Eq) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.18355) (:fv _uniq.18367) (:fv _uniq.18375) (:lambda _ (:fv _uniq.18355) ((:c OfNat.ofNat) (:c ENNReal) (:lit 0) ((:c Zero.toOfNat0) (:c ENNReal) (:c instENNRealZero))))) ((:c OfNat.ofNat) (:c ENNReal) (:lit 0) ((:c Zero.toOfNat0) (:c ENNReal) (:c instENNRea... | [{"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":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.18355))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.18355) (:fv _uniq.18367))"},{"name":"... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:lambda _ :explicit (:fv FV0) (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:lit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18355","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18358","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":6517,"sourceStart":6513,"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.18355","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18358","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 42 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c7fadfba70d1c1a628552b3e3775faab55cc58b271d9fe76a4b3693afd97f99c | f202b60eb648307eabfd09e14aa546a7174097c85a8e1a6b4411810b18b64c39 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 624 | Finset.noncommProd_commute | Mathlib/Data/Finset/NoncommProd.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Multiset.noncommProd_commute</a> | F : Type u_1
ι : Type u_2
α : Type u_3
β : Type u_4
γ : Type u_5
f✝ : α → β → β
op : α → α → α
inst✝² : Monoid β
inst✝¹ : Monoid γ
inst✝ : FunLike F β γ
s : Finset α
f : α → β
comm : (↑s).Pairwise fun a b => Commute (f a) (f b)
y : β
h : ∀ x ∈ s, Commute y (f x)
⊢ Commute y (s.noncommProd f comm) | case h
F : Type u_1
ι : Type u_2
α : Type u_3
β : Type u_4
γ : Type u_5
f✝ : α → β → β
op : α → α → α
inst✝² : Monoid β
inst✝¹ : Monoid γ
inst✝ : FunLike F β γ
s : Finset α
f : α → β
comm : (↑s).Pairwise fun a b => Commute (f a) (f b)
y : β
h : ∀ x ∈ s, Commute y (f x)
⊢ ∀ x ∈ Multiset.map f s.val, Commute y x | ((:c Commute) (:fv _uniq.38730) ((:c MulOneClass.toMul) (:fv _uniq.38730) ((:c Monoid.toMulOneClass) (:fv _uniq.38730) (:fv _uniq.38748))) (:fv _uniq.38941) ((:c Finset.noncommProd) (:fv _uniq.38727) (:fv _uniq.38730) (:fv _uniq.38748) (:fv _uniq.38938) (:fv _uniq.38939) (:fv _uniq.38940))) | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.38727) (:forall _ (:fv _uniq.38730) (:fv _uniq.38730)))"},{"name":"op","sexp... | (:app (:c Commute) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Mul) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:fv FV14)) (:arg :explicit 3 (:app (:c Finset.noncommProd) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38721","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38724","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"apply","sourceEnd":16191,"sourceStart":16186,"tag":"atom"},{"name":"Multiset.noncommProd_commute","semanticRole":"global","source":"Multiset.noncommProd_commute","sourceEnd":16220,"sourceStart":16192,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Multiset.noncommProd_comm... | [] | [{"source":"Multiset.noncommProd_commute","source_end":16220,"source_start":16192,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38721","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38724","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 100 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a366f1c63dbe6e16f879af1a2b730a15d7cc4ed3506d4f431aec9995e2931f09 | 3d0fa7723c8ddd33bee518606d2bfb57051b199dbbfd815bcb3a57b39e295f57 | 49102c25e9c55440a625827e139c4569a3ba71fbc93ee6b760750eeae243fe87 | 1944055ec404b48c0f67580c9e6089a241bbe3ba7fed92c881cd5fc9653e91ae |
cat-searcher/leandojo-benchmark-4-random | test | 625 | Finset.noncommProd_commute | Mathlib/Data/Finset/NoncommProd.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro y | case h
F : Type u_1
ι : Type u_2
α : Type u_3
β : Type u_4
γ : Type u_5
f✝ : α → β → β
op : α → α → α
inst✝² : Monoid β
inst✝¹ : Monoid γ
inst✝ : FunLike F β γ
s : Finset α
f : α → β
comm : (↑s).Pairwise fun a b => Commute (f a) (f b)
y : β
h : ∀ x ∈ s, Commute y (f x)
⊢ ∀ x ∈ Multiset.map f s.val, Commute y x | case h
F : Type u_1
ι : Type u_2
α : Type u_3
β : Type u_4
γ : Type u_5
f✝ : α → β → β
op : α → α → α
inst✝² : Monoid β
inst✝¹ : Monoid γ
inst✝ : FunLike F β γ
s : Finset α
f : α → β
comm : (↑s).Pairwise fun a b => Commute (f a) (f b)
y✝ : β
h : ∀ x ∈ s, Commute y✝ (f x)
y : β
⊢ y ∈ Multiset.map f s.val → Commute y✝ y | (:forall x (:fv _uniq.38730) (:forall _ ((:c Membership.mem) (:fv _uniq.38730) ((:c Multiset) (:fv _uniq.38730)) ((:c Multiset.instMembership) (:fv _uniq.38730)) 0 ((:c Multiset.map) (:fv _uniq.38727) (:fv _uniq.38730) (:fv _uniq.38939) ((:c Finset.val) (:fv _uniq.38727) (:fv _uniq.38938)))) ((:c Commute) (:fv _uniq.38... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.38727) (:forall _ (:fv _uniq.38730) (:fv _uniq.38730)))"},{"name":"op","sexp... | (:forall x :explicit (:fv FV3) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c Multiset) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:app (:c Multiset) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38721","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38724","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"intro","sourceEnd":16228,"sourceStart":16223,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":16230,"sourceStart":16229,"tag":"identifier"}],"kind":"null","source":"y","sourceEnd":16230,"sourceStart":16229,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"y","source_end":16230,"source_start":16229,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38721","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38724","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 100 | 5 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6e8652814f8e2a46507b58b5b1a83850b29c6feb66c5dc656bb77ad3e59c2e06 | 1944055ec404b48c0f67580c9e6089a241bbe3ba7fed92c881cd5fc9653e91ae | 85390ac44bda3124c08903df1f981e2eead2a91d5d3d503fc936003a462be0d3 | 9de0dcb76b72707259af55d83d1a41ec0742e3aedde26d1d938612c8def9930f |
cat-searcher/leandojo-benchmark-4-random | test | 626 | Finset.noncommProd_commute | Mathlib/Data/Finset/NoncommProd.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Multiset.mem_map</a>] | case h
F : Type u_1
ι : Type u_2
α : Type u_3
β : Type u_4
γ : Type u_5
f✝ : α → β → β
op : α → α → α
inst✝² : Monoid β
inst✝¹ : Monoid γ
inst✝ : FunLike F β γ
s : Finset α
f : α → β
comm : (↑s).Pairwise fun a b => Commute (f a) (f b)
y✝ : β
h : ∀ x ∈ s, Commute y✝ (f x)
y : β
⊢ y ∈ Multiset.map f s.val → Commute y✝ y | case h
F : Type u_1
ι : Type u_2
α : Type u_3
β : Type u_4
γ : Type u_5
f✝ : α → β → β
op : α → α → α
inst✝² : Monoid β
inst✝¹ : Monoid γ
inst✝ : FunLike F β γ
s : Finset α
f : α → β
comm : (↑s).Pairwise fun a b => Commute (f a) (f b)
y✝ : β
h : ∀ x ∈ s, Commute y✝ (f x)
y : β
⊢ (∃ a ∈ s.val, f a = y) → Commute y✝ y | (:forall _ ((:c Membership.mem) (:fv _uniq.38730) ((:c Multiset) (:fv _uniq.38730)) ((:c Multiset.instMembership) (:fv _uniq.38730)) (:fv _uniq.38983) ((:c Multiset.map) (:fv _uniq.38727) (:fv _uniq.38730) (:fv _uniq.38939) ((:c Finset.val) (:fv _uniq.38727) (:fv _uniq.38938)))) ((:c Commute) (:fv _uniq.38730) ((:c Mul... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.38727) (:forall _ (:fv _uniq.38730) (:fv _uniq.38730)))"},{"name":"op","sexp... | (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c Multiset) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:app (:c Multiset) (:arg :explicit 0 (:fv FV3))))))) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38721","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38724","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":16235,"sourceStart":16233,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16237,"sourceStart":16236,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Multiset.mem_map... | [] | [{"source":"Multiset.mem_map","source_end":16253,"source_start":16237,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38721","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38724","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 100 | 6 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e556adab7ac4f3d04527cbb12117d73daf4f9dc6ff111c96331409a1f38742c3 | 9de0dcb76b72707259af55d83d1a41ec0742e3aedde26d1d938612c8def9930f | ba8a64df34b6c8336f722826b4de33956285840a2956d466cf4422f65a3d85a2 | 8d3a932f71319ba76940deef8bdb97ff3b0784802e3fc7cea17d17d55382a90a |
cat-searcher/leandojo-benchmark-4-random | test | 627 | Finset.noncommProd_commute | Mathlib/Data/Finset/NoncommProd.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨x, ⟨hx, rfl⟩⟩ | case h
F : Type u_1
ι : Type u_2
α : Type u_3
β : Type u_4
γ : Type u_5
f✝ : α → β → β
op : α → α → α
inst✝² : Monoid β
inst✝¹ : Monoid γ
inst✝ : FunLike F β γ
s : Finset α
f : α → β
comm : (↑s).Pairwise fun a b => Commute (f a) (f b)
y✝ : β
h : ∀ x ∈ s, Commute y✝ (f x)
y : β
⊢ (∃ a ∈ s.val, f a = y) → Commute y✝ y | case h.intro.intro
F : Type u_1
ι : Type u_2
α : Type u_3
β : Type u_4
γ : Type u_5
f✝ : α → β → β
op : α → α → α
inst✝² : Monoid β
inst✝¹ : Monoid γ
inst✝ : FunLike F β γ
s : Finset α
f : α → β
comm : (↑s).Pairwise fun a b => Commute (f a) (f b)
y : β
h : ∀ x ∈ s, Commute y (f x)
x : α
hx : x ∈ s.val
⊢ Commute y (f x) | (:forall _ ((:c Exists) (:fv _uniq.38727) (:lambda a (:fv _uniq.38727) ((:c And) ((:c Membership.mem) (:fv _uniq.38727) ((:c Multiset) (:fv _uniq.38727)) ((:c Multiset.instMembership) (:fv _uniq.38727)) 0 ((:c Finset.val) (:fv _uniq.38727) (:fv _uniq.38938))) ((:c Eq) (:fv _uniq.38730) ((:fv _uniq.38939) 0) (:fv _uniq.... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.38727) (:forall _ (:fv _uniq.38730) (:fv _uniq.38730)))"},{"name":"op","sexp... | (:forall _ :explicit (:app (:c Exists) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda a :explicit (:fv FV2) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Multiset) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38721","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38724","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rintro","sourceEnd":16263,"sourceStart":16257,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":16267,"sourceStart":16264,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":16268,"sou... | [{"role":"fresh_name","source":"x","source_end":16268,"source_start":16267,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":16275,"source_start":16273,"syntax_kind":"ident"}] | [{"source":"⟨x, ⟨hx, rfl⟩⟩","source_end":16286,"source_start":16264,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38721","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38724","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 100 | 9 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ebbce4e7e8a8b5bb99092d6b6718fda94e6294475640c0bdba4e8041eae77f86 | 8d3a932f71319ba76940deef8bdb97ff3b0784802e3fc7cea17d17d55382a90a | 6f2e0601130ae1fe74f766d465a735d9b03696a8f23cf9a327fd044147f0b8f3 | a7bf8cdfea47c70f2273f30fa23beab38383b9eb8a9973a958b98e69003fcbfe |
cat-searcher/leandojo-benchmark-4-random | test | 628 | Finset.noncommProd_commute | Mathlib/Data/Finset/NoncommProd.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact h x hx | case h.intro.intro
F : Type u_1
ι : Type u_2
α : Type u_3
β : Type u_4
γ : Type u_5
f✝ : α → β → β
op : α → α → α
inst✝² : Monoid β
inst✝¹ : Monoid γ
inst✝ : FunLike F β γ
s : Finset α
f : α → β
comm : (↑s).Pairwise fun a b => Commute (f a) (f b)
y : β
h : ∀ x ∈ s, Commute y (f x)
x : α
hx : x ∈ s.val
⊢ Commute y (f x) | ((:c Commute) (:fv _uniq.38730) ((:c MulOneClass.toMul) (:fv _uniq.38730) ((:c Monoid.toMulOneClass) (:fv _uniq.38730) (:fv _uniq.38748))) (:fv _uniq.38941) ((:fv _uniq.38939) (:fv _uniq.39043))) | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.38727) (:forall _ (:fv _uniq.38730) (:fv _uniq.38730)))"},{"name":"op","sexp... | (:app (:c Commute) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Mul) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:fv FV14)) (:arg :explicit 3 (:app (:fv FV12) (:arg :explicit 0 (:fv FV16))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38721","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38724","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":16294,"sourceStart":16289,"tag":"atom"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"h","sourceEnd":16296,"sourceStart":16295,"tag":"identifier"},{"children":[{"contextIndex":16,"semanticRole":"local","source":"x","sourceEnd":16298,"sourceStart":16297,"tag"... | [] | [{"source":"h x hx","source_end":16301,"source_start":16295,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38721","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38724","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 100 | 10 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b719af834107cd5764642ea8d4c1bb9afc5ab6e9dcecc4c186a548268096e221 | a7bf8cdfea47c70f2273f30fa23beab38383b9eb8a9973a958b98e69003fcbfe | 61e7fef52507a9de1181abe1f6e108ce4ecfff9b0fafc1172a8379535ceeb94d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 629 | Finset.Ioc_subset_Iic_self | Mathlib/Order/Interval/Finset/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [← <a>Finset.coe_subset</a>] using <a>Set.Ioc_subset_Iic_self</a> | ι : Type u_1
α : Type u_2
inst✝² : Preorder α
inst✝¹ : LocallyFiniteOrder α
a a₁ a₂ b b₁ b₂ c x : α
inst✝ : LocallyFiniteOrderBot α
⊢ Ioc a b ⊆ Iic b | ((:c HasSubset.Subset) ((:c Finset) (:fv _uniq.50723)) ((:c Finset.instHasSubset) (:fv _uniq.50723)) ((:c Finset.Ioc) (:fv _uniq.50723) (:fv _uniq.50726) (:fv _uniq.50734) (:fv _uniq.50736) (:fv _uniq.50742)) ((:c Finset.Iic) (:fv _uniq.50723) (:fv _uniq.50726) (:fv _uniq.50756) (:fv _uniq.50742))) | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Preorder) (:fv _uniq.50723))"},{"name":"inst✝¹","sexp":"((:c LocallyFiniteOrder) (:fv _uniq.50723) (:fv _uniq.50726))"},{"name":"a","sexp":"(:fv _uniq.50723)"},{"name":"a₁","sexp":"(:fv _uniq.50723)"},{"name":... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 2 (:app (:c Finset.Ioc) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:ins... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.50720","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.50723","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":17691,"sourceStart":17686,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"coe_subset","source_end":17707,"source_start":17697,"syntax_kind":"ident"},{"source":"Set.Ioc_subset_Iic_self","source_end":17738,"source_start":17715,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.50720","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.50723","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 174 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eb5ea731c5cce374f70c8b1eca408b4441f349873ac5e4d5d43634f1f4be2325 | 00d8f483f1c6424d92904d26d0d289f26c1f7ff1aa5d799646c4ef26314ea5dd | 7a190682c4f7e87250d392ea04373c530bb740246f2a9920f1855ac684e36517 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 630 | ExteriorAlgebra.ι_ne_one | Mathlib/LinearAlgebra/ExteriorAlgebra/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← (<a>algebraMap</a> R (<a>ExteriorAlgebra</a> R M)).<a>RingHom.map_one</a>, <a>Ne</a>, <a>ExteriorAlgebra.ι_eq_algebraMap_iff</a>] | R : Type u1
inst✝⁵ : CommRing R
M : Type u2
inst✝⁴ : AddCommGroup M
inst✝³ : Module R M
A : Type u_1
inst✝² : Semiring A
inst✝¹ : Algebra R A
inst✝ : Nontrivial R
x : M
⊢ (ι R) x ≠ 1 | R : Type u1
inst✝⁵ : CommRing R
M : Type u2
inst✝⁴ : AddCommGroup M
inst✝³ : Module R M
A : Type u_1
inst✝² : Semiring A
inst✝¹ : Algebra R A
inst✝ : Nontrivial R
x : M
⊢ ¬(x = 0 ∧ 1 = 0) | ((:c Ne) ((:c ExteriorAlgebra) (:fv _uniq.172748) (:fv _uniq.172751) (:fv _uniq.172753) (:fv _uniq.172756) (:fv _uniq.173369)) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.172748) (:fv _uniq.172748) ((:c CommSemiring.toSemiring) (:fv _uniq.172748) ((:c CommRing.toCommSemiring) (:fv _uniq.172748) (:fv _uniq.172751))) (... | [{"name":"R","sexp":"(:sort (+ u1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.172748))"},{"name":"M","sexp":"(:sort (+ u2 1))"},{"name":"inst✝⁴","sexp":"((:c AddCommGroup) (:fv _uniq.172753))"},{"name":"inst✝³","sexp":"((:c Module) (:fv _uniq.172748) (:fv _uniq.172753) ((:c CommSemiring.toSemiring) (:fv _u... | (:app (:c Ne) (:arg :implicit-type 0 (:app (:c ExteriorAlgebra) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instan... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.172748","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.172751","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :expl... | {"children":[{"source":"rw","sourceEnd":10420,"sourceStart":10418,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10422,"sourceStart":10421,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":10425,"sourceSt... | [] | [{"source":"(algebraMap R (ExteriorAlgebra R M)).map_one","source_end":10470,"source_start":10426,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"Ne","source_end":10474,"source_start":10472,"syntax_kind":"ident"},{"source":"ι_eq_algebraMap_iff","source_end":10496,"source_start":10476,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.172748","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.172751","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 70 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6d5a0b1baaf97050b263b0cc3d30a421cdc5ea0c720ef70958d1d6624d1e1a9d | b13dbb3eb17d0c2ffceea868afdd5cfdef96ce9b32d9a2174628911d96227178 | b5303529e9ddf4a3f43c75de176a17a08a9535ce9e6f63ddf7e31ebfefcb74ac | 975d9bc786292061036c06484dd144fa3d464d5e8db6acf08104e88a818769e6 |
cat-searcher/leandojo-benchmark-4-random | test | 631 | ExteriorAlgebra.ι_ne_one | Mathlib/LinearAlgebra/ExteriorAlgebra/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>one_ne_zero</a> ∘ <a>And.right</a> | R : Type u1
inst✝⁵ : CommRing R
M : Type u2
inst✝⁴ : AddCommGroup M
inst✝³ : Module R M
A : Type u_1
inst✝² : Semiring A
inst✝¹ : Algebra R A
inst✝ : Nontrivial R
x : M
⊢ ¬(x = 0 ∧ 1 = 0) | ((:c Not) ((:c And) ((:c Eq) (:fv _uniq.172753) (:fv _uniq.174925) ((:c OfNat.ofNat) (:fv _uniq.172753) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.172753) ((:c NegZeroClass.toZero) (:fv _uniq.172753) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.172753) ((:c SubtractionMonoid.toSubNegZeroMonoid) (:fv _uniq.172753) ((:c... | [{"name":"R","sexp":"(:sort (+ u1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.172748))"},{"name":"M","sexp":"(:sort (+ u2 1))"},{"name":"inst✝⁴","sexp":"((:c AddCommGroup) (:fv _uniq.172753))"},{"name":"inst✝³","sexp":"((:c Module) (:fv _uniq.172748) (:fv _uniq.172753) ((:c CommSemiring.toSemiring) (:fv _u... | (:app (:c Not) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:fv FV10)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.172748","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.172751","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :expl... | {"children":[{"source":"exact","sourceEnd":10505,"sourceStart":10500,"tag":"atom"},{"children":[{"name":"one_ne_zero","semanticRole":"global","source":"one_ne_zero","sourceEnd":10517,"sourceStart":10506,"tag":"identifier"},{"source":"∘","sourceEnd":10521,"sourceStart":10518,"tag":"atom"},{"name":"And.right","semanticRo... | [] | [{"source":"one_ne_zero ∘ And.right","source_end":10531,"source_start":10506,"syntax_kind":"«term_∘_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.172748","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.172751","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":implicit","context_index":2,"inte... | 70 | 9 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 06346252ce1680fc298d0e100886db0d61d3182649216001e54e637e06aef7c5 | 975d9bc786292061036c06484dd144fa3d464d5e8db6acf08104e88a818769e6 | d9f85623c75cb46b497aa21645166f87577c692e3c5bc018e749933d820f54db | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 632 | CategoryTheory.MorphismProperty.IsInvertedBy.unop | Mathlib/CategoryTheory/MorphismProperty/IsInvertedBy.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | haveI := h f.op hf | C : Type u
inst✝¹ : Category.{v, u} C
D : Type u'
inst✝ : Category.{v', u'} D
W : MorphismProperty C
L : Cᵒᵖ ⥤ Dᵒᵖ
h : W.op.IsInvertedBy L
X Y : C
f : X ⟶ Y
hf : W f
⊢ IsIso (L.unop.map f) | C : Type u
inst✝¹ : Category.{v, u} C
D : Type u'
inst✝ : Category.{v', u'} D
W : MorphismProperty C
L : Cᵒᵖ ⥤ Dᵒᵖ
h : W.op.IsInvertedBy L
X Y : C
f : X ⟶ Y
hf : W f
this : IsIso (L.map f.op)
⊢ IsIso (L.unop.map f) | ((:c CategoryTheory.IsIso) (:fv _uniq.2704) (:fv _uniq.2707) ((:c Prefunctor.obj) (:fv _uniq.2699) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.2699) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.2699) (:fv _uniq.2702))) (:fv _uniq.2704) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.270... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.2699))"},{"name":"D","sexp":"(:sort (+ u' 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.2704))"},{"name":"W","sexp":"((:c CategoryTheory.MorphismProperty) (:fv _uniq.2699) (:fv _uniq.2702))"... | (:app (:c CategoryTheory.IsIso) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV2))))) (:arg :implicit 2) (:arg :implicit 3) (:arg :explicit 4 (:app (:c Prefunctor.map) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2699","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2702","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category) ... | {"children":[{"source":"haveI","sourceEnd":2727,"sourceStart":2722,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":2728,"sourceStart":2728,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":2728,"sourceStart":2728,"tag":"node"}],"kind":"Lean.Parser.Term.haveId",... | [] | [{"source":"h f.op hf","source_end":2740,"source_start":2731,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2699","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2702","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 17 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 67233f8219ee60e6b5c463fc9967bd7e3e06c8ba0350af15097662639a52b232 | 2e435689fd71226013a6c32c4f1dd6d5fe303b5ff53774adf3b0ec36fad41ee6 | 7dd7fa6a30176e23a8b7deb68583889f0eb055a692944330cedf7a20dbd978a4 | caf42e8ed68397289a06110d74322466a470c22c9119cbf4c9e21ea8621e711e |
cat-searcher/leandojo-benchmark-4-random | test | 633 | CategoryTheory.MorphismProperty.IsInvertedBy.unop | Mathlib/CategoryTheory/MorphismProperty/IsInvertedBy.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp | C : Type u
inst✝¹ : Category.{v, u} C
D : Type u'
inst✝ : Category.{v', u'} D
W : MorphismProperty C
L : Cᵒᵖ ⥤ Dᵒᵖ
h : W.op.IsInvertedBy L
X Y : C
f : X ⟶ Y
hf : W f
this : IsIso (L.map f.op)
⊢ IsIso (L.unop.map f) | C : Type u
inst✝¹ : Category.{v, u} C
D : Type u'
inst✝ : Category.{v', u'} D
W : MorphismProperty C
L : Cᵒᵖ ⥤ Dᵒᵖ
h : W.op.IsInvertedBy L
X Y : C
f : X ⟶ Y
hf : W f
this : IsIso (L.map f.op)
⊢ IsIso (L.map f.op).unop | ((:c CategoryTheory.IsIso) (:fv _uniq.2704) (:fv _uniq.2707) ((:c Prefunctor.obj) (:fv _uniq.2699) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.2699) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.2699) (:fv _uniq.2702))) (:fv _uniq.2704) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.270... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.2699))"},{"name":"D","sexp":"(:sort (+ u' 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.2704))"},{"name":"W","sexp":"((:c CategoryTheory.MorphismProperty) (:fv _uniq.2699) (:fv _uniq.2702))"... | (:app (:c CategoryTheory.IsIso) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV2))))) (:arg :implicit 2) (:arg :implicit 3) (:arg :explicit 4 (:app (:c Prefunctor.map) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2699","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2702","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category) ... | {"children":[{"source":"dsimp","sourceEnd":2748,"sourceStart":2743,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kin... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2699","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2702","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 17 | 5 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0a6dbbaec3cef8c0042cb52e04a01433c61b5ca81762593bccce2ea7f550a9f7 | caf42e8ed68397289a06110d74322466a470c22c9119cbf4c9e21ea8621e711e | 7854eab90b5d1f0eed9d2f7f6b885100cc44bc732b41c876b3af083c01260845 | 2a9622d82855f5a7e73a7c88a19d640cfdc81d20d8850681c2ddfb5a48cc77a5 |
cat-searcher/leandojo-benchmark-4-random | test | 634 | CategoryTheory.MorphismProperty.IsInvertedBy.unop | Mathlib/CategoryTheory/MorphismProperty/IsInvertedBy.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | infer_instance | C : Type u
inst✝¹ : Category.{v, u} C
D : Type u'
inst✝ : Category.{v', u'} D
W : MorphismProperty C
L : Cᵒᵖ ⥤ Dᵒᵖ
h : W.op.IsInvertedBy L
X Y : C
f : X ⟶ Y
hf : W f
this : IsIso (L.map f.op)
⊢ IsIso (L.map f.op).unop | ((:c CategoryTheory.IsIso) (:fv _uniq.2704) (:fv _uniq.2707) ((:c Opposite.unop) (:fv _uniq.2704) ((:c Prefunctor.obj) ((:c Opposite) (:fv _uniq.2699)) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c Opposite) (:fv _uniq.2699)) ((:c CategoryTheory.Category.toCategoryStruct) ((:c Opposite) (:fv _uniq.2699)) ((:c Categ... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.2699))"},{"name":"D","sexp":"(:sort (+ u' 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.2704))"},{"name":"W","sexp":"((:c CategoryTheory.MorphismProperty) (:fv _uniq.2699) (:fv _uniq.2702))"... | (:app (:c CategoryTheory.IsIso) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV2))))) (:arg :implicit 2) (:arg :implicit 3) (:arg :explicit 4 (:app (:c Quiver.Hom.unop) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2699","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2702","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category) ... | {"children":[{"source":"infer_instance","sourceEnd":2765,"sourceStart":2751,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticInfer_instance","source":"infer_instance","sourceEnd":2765,"sourceStart":2751,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2699","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2702","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 17 | 6 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fed9f752e8d75f431698797f9ae407966e60205020abf5817c5a9f1d28ab4d8c | 2a9622d82855f5a7e73a7c88a19d640cfdc81d20d8850681c2ddfb5a48cc77a5 | 1be023dbb859162463cfcba2e9fc80f1c85bab9d31edeb816d1518206e2b70fa | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 635 | Metric.mem_ball_comm | Mathlib/Topology/MetricSpace/Pseudo/Defs.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Metric.mem_ball'</a>, <a>Metric.mem_ball</a>] | α : Type u
β : Type v
X : Type u_1
ι : Type u_2
inst✝ : PseudoMetricSpace α
x y z : α
δ ε ε₁ ε₂ : ℝ
s : Set α
⊢ x ∈ ball y ε ↔ y ∈ ball x ε | ((:c Iff) ((:c Membership.mem) (:fv _uniq.38639) ((:c Set) (:fv _uniq.38639)) ((:c Set.instMembership) (:fv _uniq.38639)) (:fv _uniq.38652) ((:c Metric.ball) (:fv _uniq.38639) (:fv _uniq.38650) (:fv _uniq.38654) (:fv _uniq.38660))) ((:c Membership.mem) (:fv _uniq.38639) ((:c Set) (:fv _uniq.38639)) ((:c Set.instMembers... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c PseudoMetricSpace) (:fv _uniq.38639))"},{"name":"x","sexp":"(:fv _uniq.38639)"},{"name":"y","sexp":"(:fv _uniq.38639)"},{"name":"z","s... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38639","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38641","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":25436,"sourceStart":25434,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":25438,"sourceStart":25437,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"mem_ball'","source_end":25447,"source_start":25438,"syntax_kind":"ident"},{"source":"mem_ball","source_end":25457,"source_start":25449,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38639","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38641","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 190 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bbcbfc1bd68f2fb268f5261187607805744c7cce16baab39aeffedd8c4cc3780 | 85a87e7f16ae0c1afb5cef4ea7d4871029d3978b5dc62c7b6e34bbcd3f31517f | 80da6a9e2ffe187b6bbd30ac5f5252e91a51d4b20eaa1af0713238bf2f7bf78e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 636 | lp.coeFn_sum | Mathlib/Analysis/NormedSpace/lpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | α : Type u_1
E : α → Type u_2
p q : ℝ≥0∞
inst✝ : (i : α) → NormedAddCommGroup (E i)
ι : Type u_3
f : ι → ↥(lp E p)
s : Finset ι
⊢ ↑(∑ i ∈ s, f i) = ∑ i ∈ s, ↑(f i) | ((:c Eq) (:forall i (:fv _uniq.116506) ((:fv _uniq.116511) 0)) ((:c Subtype.val) (:forall i (:fv _uniq.116506) ((:fv _uniq.116511) 0)) (:lambda x ((:c PreLp) (:fv _uniq.116506) (:fv _uniq.116511) (:fv _uniq.116523)) ((:c Membership.mem) ((:c PreLp) (:fv _uniq.116506) (:fv _uniq.116511) (:fv _uniq.116523)) ((:c AddSubgr... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.116506) (:sort (+ u_2 1)))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"q","sexp":"(:c ENNReal)"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.116506) ((:c NormedAddCommGroup) ((:fv _uniq.116511) 0)))"},{"name":"ι","sexp":"(:sort (+ u_... | (:app (:c Eq) (:arg :implicit-type 0 (:forall i :explicit (:fv FV0) (:app (:fv FV1) (:arg :explicit 0 0)))) (:arg :explicit 1 (:app (:c Subtype.val) (:arg :implicit-type 0 (:forall i :explicit (:fv FV0) (:app (:fv FV1) (:arg :explicit 0 0)))) (:arg :implicit 1) (:arg :explicit 2 (:app (:c Finset.sum) (:arg :implicit-ty... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.116506","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.116511","is_instance":false,"is_let":false,"name":"E","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":14841,"sourceStart":14837,"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":":implicit","context_index":0,"internal_name":"_uniq.116506","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.116511","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 84 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | da49dd838ec43d61735cc079b1665c3a1043608054cb47f149c244dcdcd96554 | 93d53c651cddaa0a68d78cacb26c31c999e5cc8a7c75fa6137b55602e371821c | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 637 | isLUB_iff_sSup_eq | Mathlib/Order/CompleteLattice.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro rfl | α : Type u_1
β : Type u_2
β₂ : Type u_3
γ : Type u_4
ι : Sort u_5
ι' : Sort u_6
κ : ι → Sort u_7
κ' : ι' → Sort u_8
inst✝ : CompleteSemilatticeSup α
s t : Set α
a b : α
⊢ sSup s = a → IsLUB s a | α : Type u_1
β : Type u_2
β₂ : Type u_3
γ : Type u_4
ι : Sort u_5
ι' : Sort u_6
κ : ι → Sort u_7
κ' : ι' → Sort u_8
inst✝ : CompleteSemilatticeSup α
s t : Set α
b : α
⊢ IsLUB s (sSup s) | (:forall _ ((:c Eq) (:fv _uniq.970) ((:c SupSet.sSup) (:fv _uniq.970) ((:c CompleteSemilatticeSup.toSupSet) (:fv _uniq.970) (:fv _uniq.998)) (:fv _uniq.1001)) (:fv _uniq.1006)) ((:c IsLUB) (:fv _uniq.970) ((:c PartialOrder.toPreorder) (:fv _uniq.970) ((:c CompleteSemilatticeSup.toPartialOrder) (:fv _uniq.970) (:fv _uni... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"β₂","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort u_5)"},{"name":"ι'","sexp":"(:sort u_6)"},{"name":"κ","sexp":"(:forall _ (:fv _uniq.982) (:sort u_7))"},{"name":"κ'","sexp":"(:fora... | (:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c SupSet.sSup) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c SupSet) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV9)))) (:arg :explicit 2 (:fv FV11))) (:app (:c IsLUB) (:arg :implicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","context... | {"children":[{"source":"rintro","sourceEnd":3110,"sourceStart":3104,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":3114,"sourceStart":3111,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl","sourceEnd":3114,"sourceStart":3111,"ta... | [] | [{"source":"rfl","source_end":3114,"source_start":3111,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.9... | 16 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0c9dea9716cd672714869bc0c70b52affb27e668f514a950af894c11fca792a8 | 74a5d27a9d1ff830a0678ae4a80bc06ac18f3f948628b2feda4fb41c81f6a512 | 09e128cd6787f35d3c063b643315aff1382388dafa4e55b6546fbf9dcecb02da | 38f930a4e641038bc0296f0ad2d95f2a2d255e55eef228432b4fa4a1bd4ac99d |
cat-searcher/leandojo-benchmark-4-random | test | 638 | isLUB_iff_sSup_eq | Mathlib/Order/CompleteLattice.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>isLUB_sSup</a> _ | α : Type u_1
β : Type u_2
β₂ : Type u_3
γ : Type u_4
ι : Sort u_5
ι' : Sort u_6
κ : ι → Sort u_7
κ' : ι' → Sort u_8
inst✝ : CompleteSemilatticeSup α
s t : Set α
b : α
⊢ IsLUB s (sSup s) | ((:c IsLUB) (:fv _uniq.970) ((:c PartialOrder.toPreorder) (:fv _uniq.970) ((:c CompleteSemilatticeSup.toPartialOrder) (:fv _uniq.970) (:fv _uniq.998))) (:fv _uniq.1001) ((:c SupSet.sSup) (:fv _uniq.970) ((:c CompleteSemilatticeSup.toSupSet) (:fv _uniq.970) (:fv _uniq.998)) (:fv _uniq.1001))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"β₂","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort u_5)"},{"name":"ι'","sexp":"(:sort u_6)"},{"name":"κ","sexp":"(:forall _ (:fv _uniq.982) (:sort u_7))"},{"name":"κ'","sexp":"(:fora... | (:app (:c IsLUB) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV9)) (:arg :explicit 3 (:app (:c SupSet.sSup) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c SupSet) (:arg :explicit 0 (:fv FV0)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","context... | {"children":[{"source":"exact","sourceEnd":3121,"sourceStart":3116,"tag":"atom"},{"children":[{"name":"isLUB_sSup","semanticRole":"global","source":"isLUB_sSup","sourceEnd":3132,"sourceStart":3122,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":3134,"sourceStart":3133,"tag":"atom"}],"kind":"Lean... | [] | [{"source":"isLUB_sSup _","source_end":3134,"source_start":3122,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.9... | 16 | 6 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1258a92415096ec388eded9750bd883f2137f63effc406e01eb174af02af655a | 38f930a4e641038bc0296f0ad2d95f2a2d255e55eef228432b4fa4a1bd4ac99d | 62c20d07271ae27545ecec5990c874892b03f324c9560db1bd59c38c37441ad1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 639 | denselyOrdered_orderDual | Mathlib/Order/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert @<a>OrderDual.denselyOrdered</a> αᵒᵈ _ | ι : Type u_1
α : Type u_2
β : Type u_3
π : ι → Type u_4
inst✝ : LT α
⊢ DenselyOrdered αᵒᵈ → DenselyOrdered α | (:forall _ ((:c DenselyOrdered) ((:c OrderDual) (:fv _uniq.71171)) ((:c OrderDual.instLT) (:fv _uniq.71171) (:fv _uniq.71202))) ((:c DenselyOrdered) (:fv _uniq.71171) (:fv _uniq.71202))) | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.71168) (:sort (+ u_4 1)))"},{"name":"inst✝","sexp":"((:c LT) (:fv _uniq.71171))"}] | (:forall _ :explicit (:app (:c DenselyOrdered) (:arg :explicit 0 (:app (:c OrderDual) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c OrderDual) (:arg :explicit 0 (:fv FV1)))))))) (:app (:c DenselyOrdered) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.71168","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.71171","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"convert","sourceEnd":52642,"sourceStart":52635,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":"@","sourceEnd":52644,"sourceStart":52643,"tag":"a... | [] | [{"source":"@OrderDual.denselyOrdered αᵒᵈ _","source_end":52679,"source_start":52643,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.71168","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.71171","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 477 | 2 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5fb4414ba24e27b51ad1feb3fe25387810c544def1336100fd21ad12d572b7d2 | 6d554127a5d8b1cca750f95e616e7fea5594fe3cc9d5a1f6e8a7bb3cae10ac5e | 8597295f72c530c9207eda431f46fdaaba8158211ffe4fcc5184709a0f1ab6fe | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 640 | range_two_mul | Mathlib/Algebra/Ring/Parity.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext x | F : Type u_1
α✝ : Type u_2
β : Type u_3
R : Type u_4
inst✝² : Semiring α✝
inst✝¹ : Semiring β
a b : α✝
m n : ℕ
α : Type u_5
inst✝ : Semiring α
⊢ (Set.range fun x => 2 * x) = {a | Even a} | case h
F : Type u_1
α✝ : Type u_2
β : Type u_3
R : Type u_4
inst✝² : Semiring α✝
inst✝¹ : Semiring β
a b : α✝
m n : ℕ
α : Type u_5
inst✝ : Semiring α
x : α
⊢ (x ∈ Set.range fun x => 2 * x) ↔ x ∈ {a | Even a} | ((:c Eq) ((:c Set) (:fv _uniq.10109)) ((:c Set.range) (:fv _uniq.10109) (:fv _uniq.10109) (:lambda x (:fv _uniq.10109) ((:c HMul.hMul) (:fv _uniq.10109) (:fv _uniq.10109) (:fv _uniq.10109) ((:c instHMul) (:fv _uniq.10109) ((:c NonUnitalNonAssocSemiring.toMul) (:fv _uniq.10109) ((:c NonAssocSemiring.toNonUnitalNonAssocS... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α✝","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.9699))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.9702))"},{"name":"a","sexp":"(:fv _uniq.9699)"}... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV11)))) (:arg :explicit 1 (:app (:c Set.range) (:arg :implicit-type 0 (:fv FV11)) (:arg :implicit-type 1 (:fv FV11)) (:arg :explicit 2 (:lambda x :explicit (:fv FV11) (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV11)) (:arg :implicit-type ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9696","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9699","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"source":"ext","sourceEnd":2796,"sourceStart":2793,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":2798,"sourceStart":2797,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":2798,"sourceStart":2797,"tag":"nod... | [{"role":"fresh_name","source":"x","source_end":2798,"source_start":2797,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9696","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9699","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 34 | 4 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bfe206491182f382a0f9ede01306788c5bd843b6f2bff476dcc2a767922daf31 | 2c763d664908533b6b03467764b6fc9f50d0105235cfcea74785d2d373c41f0c | ee522618587c4a8062e9541e92fad69d5c6e7dbdf5366e9d82c63ebe3c1e08c5 | b2757dfc6227cab036a24339c0c32e5aff27677317eb6339d6d67c8db8ac2222 |
cat-searcher/leandojo-benchmark-4-random | test | 641 | range_two_mul | Mathlib/Algebra/Ring/Parity.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>eq_comm</a>, <a>two_mul</a>, <a>Even</a>] | case h
F : Type u_1
α✝ : Type u_2
β : Type u_3
R : Type u_4
inst✝² : Semiring α✝
inst✝¹ : Semiring β
a b : α✝
m n : ℕ
α : Type u_5
inst✝ : Semiring α
x : α
⊢ (x ∈ Set.range fun x => 2 * x) ↔ x ∈ {a | Even a} | ((:c Iff) ((:c Membership.mem) (:fv _uniq.10109) ((:c Set) (:fv _uniq.10109)) ((:c Set.instMembership) (:fv _uniq.10109)) (:fv _uniq.10135) ((:c Set.range) (:fv _uniq.10109) (:fv _uniq.10109) (:lambda x (:fv _uniq.10109) ((:c HMul.hMul) (:fv _uniq.10109) (:fv _uniq.10109) (:fv _uniq.10109) ((:c instHMul) (:fv _uniq.101... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α✝","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.9699))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.9702))"},{"name":"a","sexp":"(:fv _uniq.9699)"}... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV11)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV11)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV11)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV11))))))) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9696","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9699","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"source":"simp","sourceEnd":2805,"sourceStart":2801,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2807,"sourceStart":2806,"tag":"atom"... | [] | [{"source":"eq_comm","source_end":2814,"source_start":2807,"syntax_kind":"ident"},{"source":"two_mul","source_end":2823,"source_start":2816,"syntax_kind":"ident"},{"source":"Even","source_end":2829,"source_start":2825,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9696","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9699","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 34 | 5 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ab6a60bd3798572c902bccd3143e92d6b160ffd9b48145458b4aad624bfeab4e | b2757dfc6227cab036a24339c0c32e5aff27677317eb6339d6d67c8db8ac2222 | 0e974611f77390735a06e41184beaf0eba08c8bd76dc22e11eab16a3f96fcb8c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 643 | PMF.pure_bind | Mathlib/Probability/ProbabilityMassFunction/Monad.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : ∀ b a', <a>ite</a> (a' = a) (f a' b) 0 = <a>ite</a> (a' = a) (f a b) 0 := fun b a' => by split_ifs with h <;> simp [h] | α : Type u_1
β : Type u_2
γ : Type u_3
p : PMF α
f✝ : α → PMF β
g : β → PMF γ
a : α
f : α → PMF β
⊢ (pure a).bind f = f a | α : Type u_1
β : Type u_2
γ : Type u_3
p : PMF α
f✝ : α → PMF β
g : β → PMF γ
a : α
f : α → PMF β
this : ∀ (b : β) (a' : α), (if a' = a then (f a') b else 0) = if a' = a then (f a) b else 0
⊢ (pure a).bind f = f a | ((:c Eq) ((:c PMF) (:fv _uniq.32687)) ((:c PMF.bind) (:fv _uniq.32684) (:fv _uniq.32687) ((:c PMF.pure) (:fv _uniq.32684) (:fv _uniq.32735)) (:fv _uniq.32736)) ((:fv _uniq.32736) (:fv _uniq.32735))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"p","sexp":"((:c PMF) (:fv _uniq.32684))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.32684) ((:c PMF) (:fv _uniq.32687)))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.32687) ((:c PMF) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c PMF) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c PMF.bind) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:app (:c PMF.pure) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV7)))) (:arg :explicit 3 (:fv FV8))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32684","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32687","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":4508,"sourceStart":4504,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":4509,"sourceStart":4509,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":4509,"sourceStart":4509,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"∀ b a', ite (a' = a) (f a' b) 0 = ite (a' = a) (f a b) 0","source_end":4569,"source_start":4511,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"fun b a' => by\n split_ifs with h <;> simp [h]","source_end":4621,"source_start":4573,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32684","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32687","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 46 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2815461b6f642a2283174ba37a55e79208e80f038809405a0246e6adceee55d2 | d2296ffe2dbec1034553110ebae50552b4ee3b6cc060d56f681b030a1b231397 | 9b35c938a976768efdac70cdcc2eafa89c23a2896c21fffd0747fd98a414d8fc | af019adce859043e4795e58e9cfebc26ca116d720ab94704bda4817b6778fd75 |
cat-searcher/leandojo-benchmark-4-random | test | 644 | PMF.pure_bind | Mathlib/Probability/ProbabilityMassFunction/Monad.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext b | α : Type u_1
β : Type u_2
γ : Type u_3
p : PMF α
f✝ : α → PMF β
g : β → PMF γ
a : α
f : α → PMF β
this : ∀ (b : β) (a' : α), (if a' = a then (f a') b else 0) = if a' = a then (f a) b else 0
⊢ (pure a).bind f = f a | case h
α : Type u_1
β : Type u_2
γ : Type u_3
p : PMF α
f✝ : α → PMF β
g : β → PMF γ
a : α
f : α → PMF β
this : ∀ (b : β) (a' : α), (if a' = a then (f a') b else 0) = if a' = a then (f a) b else 0
b : β
⊢ ((pure a).bind f) b = (f a) b | ((:c Eq) ((:c PMF) (:fv _uniq.32687)) ((:c PMF.bind) (:fv _uniq.32684) (:fv _uniq.32687) ((:c PMF.pure) (:fv _uniq.32684) (:fv _uniq.32735)) (:fv _uniq.32736)) ((:fv _uniq.32736) (:fv _uniq.32735))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"p","sexp":"((:c PMF) (:fv _uniq.32684))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.32684) ((:c PMF) (:fv _uniq.32687)))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.32687) ((:c PMF) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c PMF) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c PMF.bind) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:app (:c PMF.pure) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV7)))) (:arg :explicit 3 (:fv FV8))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32684","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32687","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"ext","sourceEnd":4627,"sourceStart":4624,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"b","sourceEnd":4629,"sourceStart":4628,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"b","sourceEnd":4629,"sourceStart":4628,"tag":"nod... | [{"role":"fresh_name","source":"b","source_end":4629,"source_start":4628,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32684","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32687","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 46 | 14 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f4dd89c2ddfb02bdc3887267d48a689ff7863f19d88aaa8a0ac1611f90ab769f | af019adce859043e4795e58e9cfebc26ca116d720ab94704bda4817b6778fd75 | 1acca098ecda75ed7773bdb24252cccd986cb6e6767a54331e92f5527c7be865 | 422b751abb599fce5758c67c0f91a0c8c3de7fb80ff35ed1435a2d8606da532e |
cat-searcher/leandojo-benchmark-4-random | test | 645 | PMF.pure_bind | Mathlib/Probability/ProbabilityMassFunction/Monad.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [this] | case h
α : Type u_1
β : Type u_2
γ : Type u_3
p : PMF α
f✝ : α → PMF β
g : β → PMF γ
a : α
f : α → PMF β
this : ∀ (b : β) (a' : α), (if a' = a then (f a') b else 0) = if a' = a then (f a) b else 0
b : β
⊢ ((pure a).bind f) b = (f a) b | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c PMF) (:fv _uniq.32687)) (:fv _uniq.32687) (:lambda _ (:fv _uniq.32687) (:c ENNReal)) ((:c PMF.instFunLike) (:fv _uniq.32687)) ((:c PMF.bind) (:fv _uniq.32684) (:fv _uniq.32687) ((:c PMF.pure) (:fv _uniq.32684) (:fv _uniq.32735)) (:fv _uniq.32736)) (:fv _uniq.34208)) ((:c DF... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"p","sexp":"((:c PMF) (:fv _uniq.32684))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.32684) ((:c PMF) (:fv _uniq.32687)))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.32687) ((:c PMF) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c PMF) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c FunLike) (:arg :explicit 0 (:app (:c PMF) (:arg :explicit 0 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32684","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32687","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":4636,"sourceStart":4632,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4638,"sourceStart":4637,"tag":"atom"... | [] | [{"source":"this","source_end":4642,"source_start":4638,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32684","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32687","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 46 | 15 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 106bc68fb6eab8beb896d3b9e037f8a7c6bf47eddd2c22a9fc7953fe05f25671 | 422b751abb599fce5758c67c0f91a0c8c3de7fb80ff35ed1435a2d8606da532e | 2739860bec7952c6457e85d62dcc82ff2a268ce0336906f3574a07be169573c0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 646 | PMF.pure_bind | Mathlib/Probability/ProbabilityMassFunction/Monad.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split_ifs with h <;> simp [h] | α : Type u_1
β : Type u_2
γ : Type u_3
p : PMF α
f✝ : α → PMF β
g : β → PMF γ
a : α
f : α → PMF β
b : β
a' : α
⊢ (if a' = a then (f a') b else 0) = if a' = a then (f a) b else 0 | ((:c Eq) (:c ENNReal) ((:c ite) (:c ENNReal) ((:c Eq) (:fv _uniq.32684) (:fv _uniq.33032) (:fv _uniq.32735)) ((:c Classical.propDecidable) ((:c Eq) (:fv _uniq.32684) (:fv _uniq.33032) (:fv _uniq.32735))) ((:c DFunLike.coe) ((:c PMF) (:fv _uniq.32687)) (:fv _uniq.32687) (:lambda _ (:fv _uniq.32687) (:c ENNReal)) ((:c PM... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"p","sexp":"((:c PMF) (:fv _uniq.32684))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.32684) ((:c PMF) (:fv _uniq.32687)))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.32687) ((:c PMF) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c ite) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV10)) (:arg :explicit 2 (:fv FV7)))) (:arg :instance 2 (:instance-of (:app (:c Decidable) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32684","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32687","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"split_ifs","sourceEnd":4601,"sourceStart":4592,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"with","sourceEnd":4606,"sourceStart":4602,"tag":"atom"},{"children":[{"children":[{"source":"h","sourceE... | [] | [{"source":"h","source_end":4620,"source_start":4619,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32684","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32687","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 46 | 7 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7dfbd5d19ab2d543ef23c5ac1ef9b8f413392bca451dcf4c2fe1d67242e6e6a7 | 2dfa86bd44fd40d7b743f2a2dd7a7b95eda83d1b4d4b860649c328befcc57c5c | 967de915a4bca2de7578bb7c1d71b707362e00ce57612b82ae6b17853f81e240 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 647 | MeasureTheory.Measure.rnDeriv_withDensity_left | Mathlib/MeasureTheory/Decomposition/RadonNikodym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let μ' := ν.withDensity (μ.rnDeriv ν) | α : Type u_1
β : Type u_2
m : MeasurableSpace α
μ✝¹ ν✝¹ μ✝ ν✝ : Measure α
f : α → ℝ≥0∞
μ ν : Measure α
inst✝¹ : SigmaFinite μ
inst✝ : SigmaFinite ν
hfμ : AEMeasurable f μ
hfν : AEMeasurable f ν
hf_ne_top : ∀ᵐ (x : α) ∂μ, f x ≠ ⊤
⊢ (μ.withDensity f).rnDeriv ν =ᶠ[ae ν] fun x => f x * μ.rnDeriv ν x | α : Type u_1
β : Type u_2
m : MeasurableSpace α
μ✝¹ ν✝¹ μ✝ ν✝ : Measure α
f : α → ℝ≥0∞
μ ν : Measure α
inst✝¹ : SigmaFinite μ
inst✝ : SigmaFinite ν
hfμ : AEMeasurable f μ
hfν : AEMeasurable f ν
hf_ne_top : ∀ᵐ (x : α) ∂μ, f x ≠ ⊤
μ' : Measure α := ν.withDensity (μ.rnDeriv ν)
⊢ (μ.withDensity f).rnDeriv ν =ᶠ[ae ν] fun x ... | ((:c Filter.EventuallyEq) (:fv _uniq.12892) (:c ENNReal) ((:c MeasureTheory.ae) (:fv _uniq.12892) ((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.12892) (:fv _uniq.12898)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.12892) (:fv _uniq.1... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.12892))"},{"name":"μ✝¹","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898))"},{"name":"ν✝¹","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898))"... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:app (:c MeasureTheory.ae) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableS... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12892","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12895","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"let","sourceEnd":7344,"sourceStart":7341,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"μ'","sourceEnd":7348,"sourceStart":7345,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"so... | [] | [{"source":"ν.withDensity (μ.rnDeriv ν)","source_end":7382,"source_start":7352,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12892","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12895","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 19 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b21f3bac1cac6a647c6b430075c1a4cbdf228be67b874f36c8b0b53879703c74 | 723c2a6b8e84fcb13f88798bf4b2cba0421cc05927e17e25f87e827f8b68cca1 | 4c71aa5d3927a80e5548b0c8c28bd629b9d1661e9c6f1290757104da44de439a | f4d7a7512017c7c95157da16cb1f1da72e3c45c8cd28eadc03093227b1569ec2 |
cat-searcher/leandojo-benchmark-4-random | test | 648 | MeasureTheory.Measure.rnDeriv_withDensity_left | Mathlib/MeasureTheory/Decomposition/RadonNikodym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hμ'ν : μ' ≪ ν := <a>MeasureTheory.withDensity_absolutelyContinuous</a> _ _ | α : Type u_1
β : Type u_2
m : MeasurableSpace α
μ✝¹ ν✝¹ μ✝ ν✝ : Measure α
f : α → ℝ≥0∞
μ ν : Measure α
inst✝¹ : SigmaFinite μ
inst✝ : SigmaFinite ν
hfμ : AEMeasurable f μ
hfν : AEMeasurable f ν
hf_ne_top : ∀ᵐ (x : α) ∂μ, f x ≠ ⊤
μ' : Measure α := ν.withDensity (μ.rnDeriv ν)
⊢ (μ.withDensity f).rnDeriv ν =ᶠ[ae ν] fun x ... | α : Type u_1
β : Type u_2
m : MeasurableSpace α
μ✝¹ ν✝¹ μ✝ ν✝ : Measure α
f : α → ℝ≥0∞
μ ν : Measure α
inst✝¹ : SigmaFinite μ
inst✝ : SigmaFinite ν
hfμ : AEMeasurable f μ
hfν : AEMeasurable f ν
hf_ne_top : ∀ᵐ (x : α) ∂μ, f x ≠ ⊤
μ' : Measure α := ν.withDensity (μ.rnDeriv ν)
hμ'ν : μ' ≪ ν
⊢ (μ.withDensity f).rnDeriv ν =... | ((:c Filter.EventuallyEq) (:fv _uniq.12892) (:c ENNReal) ((:c MeasureTheory.ae) (:fv _uniq.12892) ((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.12892) (:fv _uniq.12898)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.12892) (:fv _uniq.1... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.12892))"},{"name":"μ✝¹","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898))"},{"name":"ν✝¹","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898))"... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:app (:c MeasureTheory.ae) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableS... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12892","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12895","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":7389,"sourceStart":7385,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hμ'ν","sourceEnd":7396,"sourceStart":7390,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hμ'ν","sourceEnd":7396,"sourceStart":7390,"tag":"node"... | [] | [{"source":"μ' ≪ ν","source_end":7409,"source_start":7399,"syntax_kind":"MeasureTheory.«term_≪_»"},{"source":"withDensity_absolutelyContinuous _ _","source_end":7449,"source_start":7413,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12892","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12895","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 19 | 5 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 68e2b2e1dc369d6646050d67da7f4a6b01cecde2704acce81cc0597c558ede29 | f4d7a7512017c7c95157da16cb1f1da72e3c45c8cd28eadc03093227b1569ec2 | 0acc73753bd2adb5fd5a580018c845b22a2ee814a7b0972b73629b37fda190f7 | f9cd9702c35fba9147c6c6b19cc4d80c74fc2b41b4f64e57529a4b7d713db25e |
cat-searcher/leandojo-benchmark-4-random | test | 649 | MeasureTheory.Measure.rnDeriv_withDensity_left | Mathlib/MeasureTheory/Decomposition/RadonNikodym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h := <a>MeasureTheory.Measure.rnDeriv_withDensity_left_of_absolutelyContinuous</a> hμ'ν hfν | α : Type u_1
β : Type u_2
m : MeasurableSpace α
μ✝¹ ν✝¹ μ✝ ν✝ : Measure α
f : α → ℝ≥0∞
μ ν : Measure α
inst✝¹ : SigmaFinite μ
inst✝ : SigmaFinite ν
hfμ : AEMeasurable f μ
hfν : AEMeasurable f ν
hf_ne_top : ∀ᵐ (x : α) ∂μ, f x ≠ ⊤
μ' : Measure α := ν.withDensity (μ.rnDeriv ν)
hμ'ν : μ' ≪ ν
⊢ (μ.withDensity f).rnDeriv ν =... | α : Type u_1
β : Type u_2
m : MeasurableSpace α
μ✝¹ ν✝¹ μ✝ ν✝ : Measure α
f : α → ℝ≥0∞
μ ν : Measure α
inst✝¹ : SigmaFinite μ
inst✝ : SigmaFinite ν
hfμ : AEMeasurable f μ
hfν : AEMeasurable f ν
hf_ne_top : ∀ᵐ (x : α) ∂μ, f x ≠ ⊤
μ' : Measure α := ν.withDensity (μ.rnDeriv ν)
hμ'ν : μ' ≪ ν
h : (μ'.withDensity f).rnDeriv ... | ((:c Filter.EventuallyEq) (:fv _uniq.12892) (:c ENNReal) ((:c MeasureTheory.ae) (:fv _uniq.12892) ((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.12892) (:fv _uniq.12898)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.12892) (:fv _uniq.1... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.12892))"},{"name":"μ✝¹","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898))"},{"name":"ν✝¹","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898))"... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:app (:c MeasureTheory.ae) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableS... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12892","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12895","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":7456,"sourceStart":7452,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":7458,"sourceStart":7457,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":7458,"sourceStart":7457,"tag":"node"},{"ch... | [] | [{"source":"rnDeriv_withDensity_left_of_absolutelyContinuous hμ'ν hfν","source_end":7522,"source_start":7462,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12892","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12895","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 19 | 6 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73a16100bfd46ebf96ae3b9fd9425782f923664027fc241775aa212dc6cd7765 | f9cd9702c35fba9147c6c6b19cc4d80c74fc2b41b4f64e57529a4b7d713db25e | 7852c3e2a2356b2e994f4137f5150791d5af8c0eb7e372e61d8877dd1a3c1947 | 03033f263a91e71fb22bf3c3cb85aed4e207e4734dd311464c28ad7482fb9804 |
cat-searcher/leandojo-benchmark-4-random | test | 650 | MeasureTheory.Measure.rnDeriv_withDensity_left | Mathlib/MeasureTheory/Decomposition/RadonNikodym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h1 : μ'.rnDeriv ν =ᵐ[ν] μ.rnDeriv ν := <a>MeasureTheory.Measure.rnDeriv_withDensity</a> _ (<a>MeasureTheory.Measure.measurable_rnDeriv</a> _ _) | α : Type u_1
β : Type u_2
m : MeasurableSpace α
μ✝¹ ν✝¹ μ✝ ν✝ : Measure α
f : α → ℝ≥0∞
μ ν : Measure α
inst✝¹ : SigmaFinite μ
inst✝ : SigmaFinite ν
hfμ : AEMeasurable f μ
hfν : AEMeasurable f ν
hf_ne_top : ∀ᵐ (x : α) ∂μ, f x ≠ ⊤
μ' : Measure α := ν.withDensity (μ.rnDeriv ν)
hμ'ν : μ' ≪ ν
h : (μ'.withDensity f).rnDeriv ... | α : Type u_1
β : Type u_2
m : MeasurableSpace α
μ✝¹ ν✝¹ μ✝ ν✝ : Measure α
f : α → ℝ≥0∞
μ ν : Measure α
inst✝¹ : SigmaFinite μ
inst✝ : SigmaFinite ν
hfμ : AEMeasurable f μ
hfν : AEMeasurable f ν
hf_ne_top : ∀ᵐ (x : α) ∂μ, f x ≠ ⊤
μ' : Measure α := ν.withDensity (μ.rnDeriv ν)
hμ'ν : μ' ≪ ν
h : (μ'.withDensity f).rnDeriv ... | ((:c Filter.EventuallyEq) (:fv _uniq.12892) (:c ENNReal) ((:c MeasureTheory.ae) (:fv _uniq.12892) ((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.12892) (:fv _uniq.12898)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.12892) (:fv _uniq.1... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.12892))"},{"name":"μ✝¹","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898))"},{"name":"ν✝¹","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898))"... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:app (:c MeasureTheory.ae) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableS... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12892","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12895","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":7529,"sourceStart":7525,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h1","sourceEnd":7532,"sourceStart":7530,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h1","sourceEnd":7532,"sourceStart":7530,"tag":"node"},{"... | [] | [{"source":"μ'.rnDeriv ν =ᵐ[ν] μ.rnDeriv ν","source_end":7572,"source_start":7535,"syntax_kind":"MeasureTheory.«term_=ᵐ[_]_»"},{"source":"Measure.rnDeriv_withDensity _ (Measure.measurable_rnDeriv _ _)","source_end":7642,"source_start":7580,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12892","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12895","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 19 | 7 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0be612a806fdda208462c73781dead9715d8827ec991213e5a0bc1c4c08ad3dc | 03033f263a91e71fb22bf3c3cb85aed4e207e4734dd311464c28ad7482fb9804 | 694a4d69e80d2537a98acd142824fd8ff4b36b461ff3127c391ac6449705c031 | d78ef7af5bacd560575a7db85625cc2942a0fb70babd301cfe5824301c4d848e |
cat-searcher/leandojo-benchmark-4-random | test | 651 | MeasureTheory.Measure.rnDeriv_withDensity_left | Mathlib/MeasureTheory/Decomposition/RadonNikodym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h2 : (μ'.withDensity f).<a>MeasureTheory.Measure.rnDeriv</a> ν =ᵐ[ν] (μ.withDensity f).<a>MeasureTheory.Measure.rnDeriv</a> ν := by exact <a>MeasureTheory.Measure.rnDeriv_withDensity_withDensity_rnDeriv_left</a> μ ν hfμ hf_ne_top | α : Type u_1
β : Type u_2
m : MeasurableSpace α
μ✝¹ ν✝¹ μ✝ ν✝ : Measure α
f : α → ℝ≥0∞
μ ν : Measure α
inst✝¹ : SigmaFinite μ
inst✝ : SigmaFinite ν
hfμ : AEMeasurable f μ
hfν : AEMeasurable f ν
hf_ne_top : ∀ᵐ (x : α) ∂μ, f x ≠ ⊤
μ' : Measure α := ν.withDensity (μ.rnDeriv ν)
hμ'ν : μ' ≪ ν
h : (μ'.withDensity f).rnDeriv ... | α : Type u_1
β : Type u_2
m : MeasurableSpace α
μ✝¹ ν✝¹ μ✝ ν✝ : Measure α
f : α → ℝ≥0∞
μ ν : Measure α
inst✝¹ : SigmaFinite μ
inst✝ : SigmaFinite ν
hfμ : AEMeasurable f μ
hfν : AEMeasurable f ν
hf_ne_top : ∀ᵐ (x : α) ∂μ, f x ≠ ⊤
μ' : Measure α := ν.withDensity (μ.rnDeriv ν)
hμ'ν : μ' ≪ ν
h : (μ'.withDensity f).rnDeriv ... | ((:c Filter.EventuallyEq) (:fv _uniq.12892) (:c ENNReal) ((:c MeasureTheory.ae) (:fv _uniq.12892) ((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.12892) (:fv _uniq.12898)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.12892) (:fv _uniq.1... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.12892))"},{"name":"μ✝¹","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898))"},{"name":"ν✝¹","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898))"... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:app (:c MeasureTheory.ae) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableS... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12892","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12895","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":7649,"sourceStart":7645,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h2","sourceEnd":7652,"sourceStart":7650,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h2","sourceEnd":7652,"sourceStart":7650,"tag":"node"},{"... | [] | [{"source":"(μ'.withDensity f).rnDeriv ν =ᵐ[ν] (μ.withDensity f).rnDeriv ν","source_end":7724,"source_start":7655,"syntax_kind":"MeasureTheory.«term_=ᵐ[_]_»"},{"source":"rnDeriv_withDensity_withDensity_rnDeriv_left μ ν hfμ hf_ne_top","source_end":7806,"source_start":7741,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12892","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12895","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 19 | 8 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9ca12fa324f10d8375f85eff4f7968bedc117fa6cf94db85021011b216025eec | d78ef7af5bacd560575a7db85625cc2942a0fb70babd301cfe5824301c4d848e | c0301a779f831dc43fa2b51aa40fc74728712f787c46281112ab78a17518a430 | 2235dc8e1f06c5fc1129e5d0de5d53ca5736b1ccc6c8ad1fcd3a2b5457b6e758 |
cat-searcher/leandojo-benchmark-4-random | test | 652 | MeasureTheory.Measure.rnDeriv_withDensity_left | Mathlib/MeasureTheory/Decomposition/RadonNikodym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards [h, h1, h2] with x hx hx1 hx2 | α : Type u_1
β : Type u_2
m : MeasurableSpace α
μ✝¹ ν✝¹ μ✝ ν✝ : Measure α
f : α → ℝ≥0∞
μ ν : Measure α
inst✝¹ : SigmaFinite μ
inst✝ : SigmaFinite ν
hfμ : AEMeasurable f μ
hfν : AEMeasurable f ν
hf_ne_top : ∀ᵐ (x : α) ∂μ, f x ≠ ⊤
μ' : Measure α := ν.withDensity (μ.rnDeriv ν)
hμ'ν : μ' ≪ ν
h : (μ'.withDensity f).rnDeriv ... | case h
α : Type u_1
β : Type u_2
m : MeasurableSpace α
μ✝¹ ν✝¹ μ✝ ν✝ : Measure α
f : α → ℝ≥0∞
μ ν : Measure α
inst✝¹ : SigmaFinite μ
inst✝ : SigmaFinite ν
hfμ : AEMeasurable f μ
hfν : AEMeasurable f ν
hf_ne_top : ∀ᵐ (x : α) ∂μ, f x ≠ ⊤
μ' : Measure α := ν.withDensity (μ.rnDeriv ν)
hμ'ν : μ' ≪ ν
h : (μ'.withDensity f).r... | ((:c Filter.EventuallyEq) (:fv _uniq.12892) (:c ENNReal) ((:c MeasureTheory.ae) (:fv _uniq.12892) ((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.12892) (:fv _uniq.12898)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.12892) (:fv _uniq.1... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.12892))"},{"name":"μ✝¹","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898))"},{"name":"ν✝¹","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898))"... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:app (:c MeasureTheory.ae) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableS... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12892","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12895","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"filter_upwards","sourceEnd":7823,"sourceStart":7809,"tag":"atom"},{"children":[{"source":"[","sourceEnd":7825,"sourceStart":7824,"tag":"atom"},{"children":[{"contextIndex":18,"semanticRole":"local","source":"h","sourceEnd":7826,"sourceStart":7825,"tag":"identifier"},{"source":",","sourceEnd":782... | [] | [{"source":"h2","source_end":7834,"source_start":7832,"syntax_kind":"ident"},{"source":"h1","source_end":7830,"source_start":7828,"syntax_kind":"ident"},{"source":"h","source_end":7826,"source_start":7825,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12892","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12895","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 19 | 11 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 26a948121ebf63b7aa02b3e0afbda1cc4269b6c5e537349892c8f6299987951d | 2235dc8e1f06c5fc1129e5d0de5d53ca5736b1ccc6c8ad1fcd3a2b5457b6e758 | 513dfbde3ae87aa27ad23c8875c51f46d075df074bbe044bd3ada060389fb4db | bb2ab7ad3078b567c9f1764e7661dd4da93872e7eaa011f5b62b0ffcf79715f4 |
cat-searcher/leandojo-benchmark-4-random | test | 653 | MeasureTheory.Measure.rnDeriv_withDensity_left | Mathlib/MeasureTheory/Decomposition/RadonNikodym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hx2, hx, hx1] | case h
α : Type u_1
β : Type u_2
m : MeasurableSpace α
μ✝¹ ν✝¹ μ✝ ν✝ : Measure α
f : α → ℝ≥0∞
μ ν : Measure α
inst✝¹ : SigmaFinite μ
inst✝ : SigmaFinite ν
hfμ : AEMeasurable f μ
hfν : AEMeasurable f ν
hf_ne_top : ∀ᵐ (x : α) ∂μ, f x ≠ ⊤
μ' : Measure α := ν.withDensity (μ.rnDeriv ν)
hμ'ν : μ' ≪ ν
h : (μ'.withDensity f).r... | ((:c Eq) (:c ENNReal) ((:c MeasureTheory.Measure.rnDeriv) (:fv _uniq.12892) (:fv _uniq.12898) ((:c MeasureTheory.Measure.withDensity) (:fv _uniq.12892) (:fv _uniq.12898) (:fv _uniq.13751) (:fv _uniq.12923)) (:fv _uniq.13752) (:fv _uniq.14775)) ((:c HMul.hMul) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHMul) (:c EN... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.12892))"},{"name":"μ✝¹","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898))"},{"name":"ν✝¹","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898))"... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.Measure.rnDeriv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure.withDensity) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV9)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12892","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12895","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":7858,"sourceStart":7856,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7860,"sourceStart":7859,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":7863,"sourceStart":... | [] | [{"source":"hx2","source_end":7867,"source_start":7864,"syntax_kind":"ident"},{"source":"hx","source_end":7871,"source_start":7869,"syntax_kind":"ident"},{"source":"hx1","source_end":7876,"source_start":7873,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12892","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12895","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 19 | 12 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2a42bb62133010b962bdf1401458f1adc14998626f07223c62e9fa07915368ab | bb2ab7ad3078b567c9f1764e7661dd4da93872e7eaa011f5b62b0ffcf79715f4 | 92b3b262053a977ec239f5f35b1162b649265effb1813b37358d92ea0083df6f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 654 | MeasureTheory.Measure.rnDeriv_withDensity_left | Mathlib/MeasureTheory/Decomposition/RadonNikodym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>MeasureTheory.Measure.rnDeriv_withDensity_withDensity_rnDeriv_left</a> μ ν hfμ hf_ne_top | α : Type u_1
β : Type u_2
m : MeasurableSpace α
μ✝¹ ν✝¹ μ✝ ν✝ : Measure α
f : α → ℝ≥0∞
μ ν : Measure α
inst✝¹ : SigmaFinite μ
inst✝ : SigmaFinite ν
hfμ : AEMeasurable f μ
hfν : AEMeasurable f ν
hf_ne_top : ∀ᵐ (x : α) ∂μ, f x ≠ ⊤
μ' : Measure α := ν.withDensity (μ.rnDeriv ν)
hμ'ν : μ' ≪ ν
h : (μ'.withDensity f).rnDeriv ... | ((:c Filter.EventuallyEq) (:fv _uniq.12892) (:c ENNReal) ((:c MeasureTheory.ae) (:fv _uniq.12892) ((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.12892) (:fv _uniq.12898)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.12892) (:fv _uniq.1... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.12892))"},{"name":"μ✝¹","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898))"},{"name":"ν✝¹","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.12892) (:fv _uniq.12898))"... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:app (:c MeasureTheory.ae) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableS... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12892","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12895","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":7740,"sourceStart":7735,"tag":"atom"},{"children":[{"name":"MeasureTheory.Measure.rnDeriv_withDensity_withDensity_rnDeriv_left","semanticRole":"global","source":"rnDeriv_withDensity_withDensity_rnDeriv_left","sourceEnd":7785,"sourceStart":7741,"tag":"identifier"},{"children":[... | [] | [{"source":"rnDeriv_withDensity_withDensity_rnDeriv_left μ ν hfμ hf_ne_top","source_end":7806,"source_start":7741,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12892","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12895","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 19 | 10 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2aca4c7d2de9e19696835fd68cacc229d801fb11b887b52fae8c1e1fabd93fcc | 8e9a42789a098cbde5e3aed588d19ca1d87b221162c03f9e9bcc1c560a520251 | 6080ad6a15a7bdc0e8978d72d6fc0f868f6aac071bc6114bd0ac6ff8549244c2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 655 | lp.norm_apply_le_norm | Mathlib/Analysis/NormedSpace/lpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>eq_or_ne</a> p ∞ with (rfl | hp') | α : Type u_1
E : α → Type u_2
p q : ℝ≥0∞
inst✝ : (i : α) → NormedAddCommGroup (E i)
hp : p ≠ 0
f : ↥(lp E p)
i : α
⊢ ‖↑f i‖ ≤ ‖f‖ | case inl
α : Type u_1
E : α → Type u_2
q : ℝ≥0∞
inst✝ : (i : α) → NormedAddCommGroup (E i)
i : α
hp : ⊤ ≠ 0
f : ↥(lp E ⊤)
⊢ ‖↑f i‖ ≤ ‖f‖
case inr
α : Type u_1
E : α → Type u_2
p q : ℝ≥0∞
inst✝ : (i : α) → NormedAddCommGroup (E i)
hp : p ≠ 0
f : ↥(lp E p)
i : α
hp' : p ≠ ⊤
⊢ ‖↑f i‖ ≤ ‖f‖ | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) ((:fv _uniq.213678) (:fv _uniq.214012)) ((:c NormedAddCommGroup.toNorm) ((:fv _uniq.213678) (:fv _uniq.214012)) ((:fv _uniq.213690) (:fv _uniq.214012))) ((:c Subtype.val) (:forall i (:fv _uniq.213673) ((:fv _uniq.213678) 0)) (:lambda x ((:c PreLp) (:fv _uniq.213673... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.213673) (:sort (+ u_2 1)))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"q","sexp":"(:c ENNReal)"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.213673) ((:c NormedAddCommGroup) ((:fv _uniq.213678) 0)))"},{"name":"hp","sexp":"((:c Ne) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV8)))) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:app (:fv FV1) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.213673","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.213678","is_instance":false,"is_let":false,"name":"E","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))... | {"children":[{"source":"rcases","sourceEnd":22519,"sourceStart":22513,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"eq_or_ne","semanticRole":"global","source":"eq_or_ne","sourceEnd":22528,"sourceStart":22520,"tag":"identifier"},{"children":[{"contex... | [] | [{"source":"eq_or_ne p ∞","source_end":22534,"source_start":22520,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(rfl | hp')","source_end":22551,"source_start":22540,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.213673","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.213678","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 119 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b211323be8f76c0ccbfe51b92a4e85fd45653634b6d2de3086c1b663440352cb | 2e70604efad6c565387ca12dee3eae3bdf9c4eace1c01099d9f78c1cc9f6ce22 | f83ea471d980600068c905e468ff98ae534fd6431ba4b32481a870668d7d45b2 | 53a86657dbd7d584727f45215bc63e2ec3d84aace828ac27665b256691f7ddef |
cat-searcher/leandojo-benchmark-4-random | test | 656 | lp.norm_apply_le_norm | Mathlib/Analysis/NormedSpace/lpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hp'' : 0 < p.toReal := <a>ENNReal.toReal_pos</a> hp hp' | case inr
α : Type u_1
E : α → Type u_2
p q : ℝ≥0∞
inst✝ : (i : α) → NormedAddCommGroup (E i)
hp : p ≠ 0
f : ↥(lp E p)
i : α
hp' : p ≠ ⊤
⊢ ‖↑f i‖ ≤ ‖f‖ | case inr
α : Type u_1
E : α → Type u_2
p q : ℝ≥0∞
inst✝ : (i : α) → NormedAddCommGroup (E i)
hp : p ≠ 0
f : ↥(lp E p)
i : α
hp' : p ≠ ⊤
hp'' : 0 < p.toReal
⊢ ‖↑f i‖ ≤ ‖f‖ | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) ((:fv _uniq.213678) (:fv _uniq.214012)) ((:c NormedAddCommGroup.toNorm) ((:fv _uniq.213678) (:fv _uniq.214012)) ((:fv _uniq.213690) (:fv _uniq.214012))) ((:c Subtype.val) (:forall i (:fv _uniq.213673) ((:fv _uniq.213678) 0)) (:lambda x ((:c PreLp) (:fv _uniq.213673... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.213673) (:sort (+ u_2 1)))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"q","sexp":"(:c ENNReal)"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.213673) ((:c NormedAddCommGroup) ((:fv _uniq.213678) 0)))"},{"name":"hp","sexp":"((:c Ne) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV8)))) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:app (:fv FV1) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.213673","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.213678","is_instance":false,"is_let":false,"name":"E","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))... | {"children":[{"source":"have","sourceEnd":22634,"sourceStart":22630,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hp''","sourceEnd":22639,"sourceStart":22635,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hp''","sourceEnd":22639,"sourceStart":22635,"tag":... | [] | [{"source":"0 < p.toReal","source_end":22654,"source_start":22642,"syntax_kind":"«term_<_»"},{"source":"ENNReal.toReal_pos hp hp'","source_end":22683,"source_start":22658,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.213673","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.213678","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 119 | 11 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0b3ef2cd91e92fb55de36bb20076145e6da4c1804c2305685eecb92bdadbc25c | 07ae97bf0a9c403a8ff1507feaf6b2629039e934463a48a5e4f94a99e827bd06 | 82801bb2d3f026a61440dabb3b25123d2482e56f9be297f1832d05cee23f95aa | e618ca2d86998663ead0635ee2d136e66da161cf1bbc5622245416aae7593004 |
cat-searcher/leandojo-benchmark-4-random | test | 657 | lp.norm_apply_le_norm | Mathlib/Analysis/NormedSpace/lpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : ∀ i, 0 ≤ ‖f i‖ ^ p.toReal := fun i => <a>Real.rpow_nonneg</a> (<a>norm_nonneg</a> _) _ | case inr
α : Type u_1
E : α → Type u_2
p q : ℝ≥0∞
inst✝ : (i : α) → NormedAddCommGroup (E i)
hp : p ≠ 0
f : ↥(lp E p)
i : α
hp' : p ≠ ⊤
hp'' : 0 < p.toReal
⊢ ‖↑f i‖ ≤ ‖f‖ | case inr
α : Type u_1
E : α → Type u_2
p q : ℝ≥0∞
inst✝ : (i : α) → NormedAddCommGroup (E i)
hp : p ≠ 0
f : ↥(lp E p)
i : α
hp' : p ≠ ⊤
hp'' : 0 < p.toReal
this : ∀ (i : α), 0 ≤ ‖↑f i‖ ^ p.toReal
⊢ ‖↑f i‖ ≤ ‖f‖ | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) ((:fv _uniq.213678) (:fv _uniq.214012)) ((:c NormedAddCommGroup.toNorm) ((:fv _uniq.213678) (:fv _uniq.214012)) ((:fv _uniq.213690) (:fv _uniq.214012))) ((:c Subtype.val) (:forall i (:fv _uniq.213673) ((:fv _uniq.213678) 0)) (:lambda x ((:c PreLp) (:fv _uniq.213673... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.213673) (:sort (+ u_2 1)))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"q","sexp":"(:c ENNReal)"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.213673) ((:c NormedAddCommGroup) ((:fv _uniq.213678) 0)))"},{"name":"hp","sexp":"((:c Ne) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV8)))) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:app (:fv FV1) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.213673","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.213678","is_instance":false,"is_let":false,"name":"E","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))... | {"children":[{"source":"have","sourceEnd":22690,"sourceStart":22686,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":22691,"sourceStart":22691,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":22691,"sourceStart":22691,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"∀ i, 0 ≤ ‖f i‖ ^ p.toReal","source_end":22726,"source_start":22693,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"fun i => Real.rpow_nonneg (norm_nonneg _) _","source_end":22773,"source_start":22730,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.213673","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.213678","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 119 | 12 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 469292ae4244058e444fb9cb867984df3e4f45ea3c0a7b9aeab0a671fef38680 | e618ca2d86998663ead0635ee2d136e66da161cf1bbc5622245416aae7593004 | 48fa0a97dd5b33ee4505d82e9ede524a772512d81a4e762d548fd174966e3056 | c746416319730534e19fa3ffcbca39b8579344b378da86e9b7a2845b54518fe2 |
cat-searcher/leandojo-benchmark-4-random | test | 658 | lp.norm_apply_le_norm | Mathlib/Analysis/NormedSpace/lpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Real.rpow_le_rpow_iff</a> (<a>norm_nonneg</a> _) (<a>lp.norm_nonneg'</a> _) hp''] | case inr
α : Type u_1
E : α → Type u_2
p q : ℝ≥0∞
inst✝ : (i : α) → NormedAddCommGroup (E i)
hp : p ≠ 0
f : ↥(lp E p)
i : α
hp' : p ≠ ⊤
hp'' : 0 < p.toReal
this : ∀ (i : α), 0 ≤ ‖↑f i‖ ^ p.toReal
⊢ ‖↑f i‖ ≤ ‖f‖ | case inr
α : Type u_1
E : α → Type u_2
p q : ℝ≥0∞
inst✝ : (i : α) → NormedAddCommGroup (E i)
hp : p ≠ 0
f : ↥(lp E p)
i : α
hp' : p ≠ ⊤
hp'' : 0 < p.toReal
this : ∀ (i : α), 0 ≤ ‖↑f i‖ ^ p.toReal
⊢ ‖↑f i‖ ^ p.toReal ≤ ‖f‖ ^ p.toReal | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) ((:fv _uniq.213678) (:fv _uniq.214012)) ((:c NormedAddCommGroup.toNorm) ((:fv _uniq.213678) (:fv _uniq.214012)) ((:fv _uniq.213690) (:fv _uniq.214012))) ((:c Subtype.val) (:forall i (:fv _uniq.213673) ((:fv _uniq.213678) 0)) (:lambda x ((:c PreLp) (:fv _uniq.213673... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.213673) (:sort (+ u_2 1)))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"q","sexp":"(:c ENNReal)"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.213673) ((:c NormedAddCommGroup) ((:fv _uniq.213678) 0)))"},{"name":"hp","sexp":"((:c Ne) (:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV8)))) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:app (:fv FV1) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.213673","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.213678","is_instance":false,"is_let":false,"name":"E","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))... | {"children":[{"source":"rw","sourceEnd":22778,"sourceStart":22776,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":22780,"sourceStart":22779,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":22783,"sourceSt... | [] | [{"source":"Real.rpow_le_rpow_iff (norm_nonneg _) (norm_nonneg' _) hp''","source_end":22843,"source_start":22784,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.213673","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.213678","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 119 | 13 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f888d90611d46aec3b4b3ff806ea8bd09a186e7cf360e1edaf2929cea0bda362 | c746416319730534e19fa3ffcbca39b8579344b378da86e9b7a2845b54518fe2 | d44e1f3e155b5e7b0f79da038447f0de0b2a48fceb8d96f929eaaf3b83b43fe1 | f51455bf92c5619abe6258f2e359b98d8cb52a6875eab38ff3ceb1f031796575 |
cat-searcher/leandojo-benchmark-4-random | test | 659 | lp.norm_apply_le_norm | Mathlib/Analysis/NormedSpace/lpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert <a>le_hasSum</a> (<a>lp.hasSum_norm</a> hp'' f) i fun i _ => this i | case inr
α : Type u_1
E : α → Type u_2
p q : ℝ≥0∞
inst✝ : (i : α) → NormedAddCommGroup (E i)
hp : p ≠ 0
f : ↥(lp E p)
i : α
hp' : p ≠ ⊤
hp'' : 0 < p.toReal
this : ∀ (i : α), 0 ≤ ‖↑f i‖ ^ p.toReal
⊢ ‖↑f i‖ ^ p.toReal ≤ ‖f‖ ^ p.toReal | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) ((:c Norm.norm) ((:fv _uniq.213678) (:fv _uniq.214012)) ((:c SeminormedAddGroup.toNorm) ((:fv _uniq.213678) (:fv _uniq.214012)) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) ((:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.213673) (:sort (+ u_2 1)))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"q","sexp":"(:c ENNReal)"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.213673) ((:c NormedAddCommGroup) ((:fv _uniq.213678) 0)))"},{"name":"hp","sexp":"((:c Ne) (:... | (: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 HPow.hPow) (: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 HPow) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.213673","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.213678","is_instance":false,"is_let":false,"name":"E","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))... | {"children":[{"source":"convert","sourceEnd":22854,"sourceStart":22847,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"le_hasSum","semanticRole":"global","source":"le_hasSum","sourceEnd":22864,"sourceStart":22855,"tag":"id... | [] | [{"source":"le_hasSum (hasSum_norm hp'' f) i fun i _ => this i","source_end":22905,"source_start":22855,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.213673","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.213678","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 119 | 16 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 47d880a0601757f3544ec584d51411b6b71c2acd710519f4874d6a15f537aa94 | f51455bf92c5619abe6258f2e359b98d8cb52a6875eab38ff3ceb1f031796575 | f96b7757ec2c293d090bb99a0fc833ae0aab84c73856ecc7a86c2bb2d003b2e8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 660 | lp.norm_apply_le_norm | Mathlib/Analysis/NormedSpace/lpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | haveI : <a>Nonempty</a> α := ⟨i⟩ | case inl
α : Type u_1
E : α → Type u_2
q : ℝ≥0∞
inst✝ : (i : α) → NormedAddCommGroup (E i)
i : α
hp : ⊤ ≠ 0
f : ↥(lp E ⊤)
⊢ ‖↑f i‖ ≤ ‖f‖ | case inl
α : Type u_1
E : α → Type u_2
q : ℝ≥0∞
inst✝ : (i : α) → NormedAddCommGroup (E i)
i : α
hp : ⊤ ≠ 0
f : ↥(lp E ⊤)
this : Nonempty α
⊢ ‖↑f i‖ ≤ ‖f‖ | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) ((:fv _uniq.213678) (:fv _uniq.214012)) ((:c NormedAddCommGroup.toNorm) ((:fv _uniq.213678) (:fv _uniq.214012)) ((:fv _uniq.213690) (:fv _uniq.214012))) ((:c Subtype.val) (:forall i (:fv _uniq.213673) ((:fv _uniq.213678) 0)) (:lambda x ((:c PreLp) (:fv _uniq.213673... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.213673) (:sort (+ u_2 1)))"},{"name":"q","sexp":"(:c ENNReal)"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.213673) ((:c NormedAddCommGroup) ((:fv _uniq.213678) 0)))"},{"name":"i","sexp":"(:fv _uniq.213673)"},{"name":"hp","sexp":"((:c ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV4)))) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:app (:fv FV1) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.213673","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.213678","is_instance":false,"is_let":false,"name":"E","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))... | {"children":[{"source":"haveI","sourceEnd":22562,"sourceStart":22557,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":22563,"sourceStart":22563,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":22563,"sourceStart":22563,"tag":"node"}],"kind":"Lean.Parser.Term.ha... | [] | [{"source":"Nonempty α","source_end":22576,"source_start":22565,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨i⟩","source_end":22587,"source_start":22580,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.213673","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.213678","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 119 | 9 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ee7b0c0128b478a6c9efb975fa368faf3da84a3e6b9919393ebb085f091b497e | 03c6222f86116352a43a4169345a2ac324bc0ef1caf558268d1a454d5429fc1a | 3c972ca2d81e93c5dde258c1c74893df3b75053a3ea4a5f7b548f7b8ad40e523 | 409cc0bf3465e26a09914d1ff59eb5e6d5d027bcd427968cb647fbfa75fe7fa5 |
cat-searcher/leandojo-benchmark-4-random | test | 661 | lp.norm_apply_le_norm | Mathlib/Analysis/NormedSpace/lpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>lp.isLUB_norm</a> f).1 ⟨i, <a>rfl</a>⟩ | case inl
α : Type u_1
E : α → Type u_2
q : ℝ≥0∞
inst✝ : (i : α) → NormedAddCommGroup (E i)
i : α
hp : ⊤ ≠ 0
f : ↥(lp E ⊤)
this : Nonempty α
⊢ ‖↑f i‖ ≤ ‖f‖ | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) ((:fv _uniq.213678) (:fv _uniq.214012)) ((:c NormedAddCommGroup.toNorm) ((:fv _uniq.213678) (:fv _uniq.214012)) ((:fv _uniq.213690) (:fv _uniq.214012))) ((:c Subtype.val) (:forall i (:fv _uniq.213673) ((:fv _uniq.213678) 0)) (:lambda x ((:c PreLp) (:fv _uniq.213673... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.213673) (:sort (+ u_2 1)))"},{"name":"q","sexp":"(:c ENNReal)"},{"name":"inst✝","sexp":"(:forall i (:fv _uniq.213673) ((:c NormedAddCommGroup) ((:fv _uniq.213678) 0)))"},{"name":"i","sexp":"(:fv _uniq.213673)"},{"name":"hp","sexp":"((:c ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:fv FV1) (:arg :explicit 0 (:fv FV4)))) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:app (:fv FV1) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.213673","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.213678","is_instance":false,"is_let":false,"name":"E","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))... | {"children":[{"source":"exact","sourceEnd":22597,"sourceStart":22592,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":22599,"sourceStart":22598,"tag":"atom"},{"children":[{"name":"lp.isLUB_norm","semanticRole":"global","source":"isLUB_norm","sourceEnd":22609,"sourceStart":22599,"tag":"iden... | [] | [{"source":"(isLUB_norm f).1 ⟨i, rfl⟩","source_end":22627,"source_start":22598,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.213673","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.213678","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 119 | 10 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1fa71f7f4425509538ec8de70fe1ae46cc037f126a108246fb8c1507893c04c7 | 409cc0bf3465e26a09914d1ff59eb5e6d5d027bcd427968cb647fbfa75fe7fa5 | 20433cd8b9e2c73f8c191ef4bb91a2dcebf414968b6685c288ed98ad7b305878 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 662 | Concept.ext | Mathlib/Order/Concept.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨⟨s₁, t₁⟩, h₁, _⟩ := c | ι : Sort u_1
α : Type u_2
β : Type u_3
γ : Type u_4
κ : ι → Sort u_5
r : α → β → Prop
s s₁ s₂ : Set α
t t₁ t₂ : Set β
c d : Concept α β r
h : c.toProd.1 = d.toProd.1
⊢ c = d | case mk.mk
ι : Sort u_1
α : Type u_2
β : Type u_3
γ : Type u_4
κ : ι → Sort u_5
r : α → β → Prop
s s₁✝ s₂ : Set α
t t₁✝ t₂ : Set β
d : Concept α β r
s₁ : Set α
t₁ : Set β
h₁ : intentClosure r (s₁, t₁).1 = (s₁, t₁).2
closure_snd✝ : extentClosure r (s₁, t₁).2 = (s₁, t₁).1
h : { toProd := (s₁, t₁), closure_fst := h₁, clos... | ((:c Eq) ((:c Concept) (:fv _uniq.5460) (:fv _uniq.5463) (:fv _uniq.5477)) (:fv _uniq.5501) (:fv _uniq.5507)) | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"κ","sexp":"(:forall _ (:fv _uniq.5457) (:sort u_5))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.5460) (:forall _ (:fv _uniq.5463) (:sort 0)))"},{"name":"s",... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Concept) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:fv FV12)) (:arg :explicit 2 (:fv FV13))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5457","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5460","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"obtain","sourceEnd":6755,"sourceStart":6749,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":6759,"sourceStart":6756,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":6762,"sourceStart":6759,"tag":"... | [] | [{"source":"c","source_end":6792,"source_start":6791,"syntax_kind":"ident"},{"source":"⟨⟨s₁, t₁⟩, h₁, _⟩","source_end":6787,"source_start":6756,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5457","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5460","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 56 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8395e8ea0dd89de07a25974d9140e188413e8343521da6195108469f3cea1a9b | 3fc7117fd9345dc104dc14a3c2f8179bcf3a7c62f230a8a05c851f6cae9258b4 | 2e893e8c740639da1cd896441ad9ead80e7d8eaf5e5fea6e7fc7b6b93ddcde48 | 108d003f08968fa7dc1e7ab6e56af85bd46ebe047613a48a55a4a215986596db |
cat-searcher/leandojo-benchmark-4-random | test | 663 | Concept.ext | Mathlib/Order/Concept.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨⟨s₂, t₂⟩, h₂, _⟩ := d | case mk.mk
ι : Sort u_1
α : Type u_2
β : Type u_3
γ : Type u_4
κ : ι → Sort u_5
r : α → β → Prop
s s₁✝ s₂ : Set α
t t₁✝ t₂ : Set β
d : Concept α β r
s₁ : Set α
t₁ : Set β
h₁ : intentClosure r (s₁, t₁).1 = (s₁, t₁).2
closure_snd✝ : extentClosure r (s₁, t₁).2 = (s₁, t₁).1
h : { toProd := (s₁, t₁), closure_fst := h₁, clos... | case mk.mk.mk.mk
ι : Sort u_1
α : Type u_2
β : Type u_3
γ : Type u_4
κ : ι → Sort u_5
r : α → β → Prop
s s₁✝ s₂✝ : Set α
t t₁✝ t₂✝ : Set β
s₁ : Set α
t₁ : Set β
h₁ : intentClosure r (s₁, t₁).1 = (s₁, t₁).2
closure_snd✝¹ : extentClosure r (s₁, t₁).2 = (s₁, t₁).1
s₂ : Set α
t₂ : Set β
h₂ : intentClosure r (s₂, t₂).1 = (s... | ((:c Eq) ((:c Concept) (:fv _uniq.5460) (:fv _uniq.5463) (:fv _uniq.5477)) ((:c Concept.mk) (:fv _uniq.5460) (:fv _uniq.5463) (:fv _uniq.5477) ((:c Prod.mk) ((:c Set) (:fv _uniq.5460)) ((:c Set) (:fv _uniq.5463)) (:fv _uniq.5605) (:fv _uniq.5606)) (:fv _uniq.5609) (:fv _uniq.5610)) (:fv _uniq.5507)) | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"κ","sexp":"(:forall _ (:fv _uniq.5457) (:sort u_5))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.5460) (:forall _ (:fv _uniq.5463) (:sort 0)))"},{"name":"s",... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Concept) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:app (:c Concept.mk) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit 2) (:arg :explicit 3 (:app (:c Prod.mk) (:arg :impl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5457","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5460","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"obtain","sourceEnd":6801,"sourceStart":6795,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":6805,"sourceStart":6802,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":6808,"sourceStart":6805,"tag":"... | [] | [{"source":"d","source_end":6838,"source_start":6837,"syntax_kind":"ident"},{"source":"⟨⟨s₂, t₂⟩, h₂, _⟩","source_end":6833,"source_start":6802,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5457","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5460","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 56 | 5 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 672895f1e05cf85636172d633f7865df8f685404d88ec691c116fa1baebbe1e7 | 108d003f08968fa7dc1e7ab6e56af85bd46ebe047613a48a55a4a215986596db | ba2b0137178a991a20b2a8cd5460d925d968f231d4cbb166307060bc6198edaa | 696aa99f2607d671978dbe16e4512ada3d9cf577b4b6a98ff3b4c1eb5c62fcb4 |
cat-searcher/leandojo-benchmark-4-random | test | 664 | Concept.ext | Mathlib/Order/Concept.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp at h₁ h₂ h | case mk.mk.mk.mk
ι : Sort u_1
α : Type u_2
β : Type u_3
γ : Type u_4
κ : ι → Sort u_5
r : α → β → Prop
s s₁✝ s₂✝ : Set α
t t₁✝ t₂✝ : Set β
s₁ : Set α
t₁ : Set β
h₁ : intentClosure r (s₁, t₁).1 = (s₁, t₁).2
closure_snd✝¹ : extentClosure r (s₁, t₁).2 = (s₁, t₁).1
s₂ : Set α
t₂ : Set β
h₂ : intentClosure r (s₂, t₂).1 = (s... | case mk.mk.mk.mk
ι : Sort u_1
α : Type u_2
β : Type u_3
γ : Type u_4
κ : ι → Sort u_5
r : α → β → Prop
s s₁✝ s₂✝ : Set α
t t₁✝ t₂✝ : Set β
s₁ : Set α
t₁ : Set β
h₁ : intentClosure r s₁ = t₁
closure_snd✝¹ : extentClosure r (s₁, t₁).2 = (s₁, t₁).1
s₂ : Set α
t₂ : Set β
h₂ : intentClosure r s₂ = t₂
closure_snd✝ : extentCl... | ((:c Eq) ((:c Concept) (:fv _uniq.5460) (:fv _uniq.5463) (:fv _uniq.5477)) ((:c Concept.mk) (:fv _uniq.5460) (:fv _uniq.5463) (:fv _uniq.5477) ((:c Prod.mk) ((:c Set) (:fv _uniq.5460)) ((:c Set) (:fv _uniq.5463)) (:fv _uniq.5605) (:fv _uniq.5606)) (:fv _uniq.5609) (:fv _uniq.5610)) ((:c Concept.mk) (:fv _uniq.5460) (:f... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"κ","sexp":"(:forall _ (:fv _uniq.5457) (:sort u_5))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.5460) (:forall _ (:fv _uniq.5463) (:sort 0)))"},{"name":"s",... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Concept) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:app (:c Concept.mk) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit 2) (:arg :explicit 3 (:app (:c Prod.mk) (:arg :impl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5457","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5460","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"dsimp","sourceEnd":6846,"sourceStart":6841,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"chil... | [] | [{"source":"h₁","source_end":6854,"source_start":6850,"syntax_kind":"ident"},{"source":"h₂","source_end":6859,"source_start":6855,"syntax_kind":"ident"},{"source":"h","source_end":6861,"source_start":6860,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5457","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5460","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 56 | 6 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bee0bee6c93a1c6935d46fce4b3497e7e540af5fba15ced0e423ec413b914fe8 | 696aa99f2607d671978dbe16e4512ada3d9cf577b4b6a98ff3b4c1eb5c62fcb4 | b81427a502408774d14b2dc3fe185e7f8eb751cb05b62210559c07ac3351eb2c | c1b7bd800d1eca914646ac135c95ded2bbc063678e7c2f39b7d035f6d5ba6186 |
cat-searcher/leandojo-benchmark-4-random | test | 665 | Concept.ext | Mathlib/Order/Concept.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | substs h h₁ h₂ | case mk.mk.mk.mk
ι : Sort u_1
α : Type u_2
β : Type u_3
γ : Type u_4
κ : ι → Sort u_5
r : α → β → Prop
s s₁✝ s₂✝ : Set α
t t₁✝ t₂✝ : Set β
s₁ : Set α
t₁ : Set β
h₁ : intentClosure r s₁ = t₁
closure_snd✝¹ : extentClosure r (s₁, t₁).2 = (s₁, t₁).1
s₂ : Set α
t₂ : Set β
h₂ : intentClosure r s₂ = t₂
closure_snd✝ : extentCl... | case mk.mk.mk.mk
ι : Sort u_1
α : Type u_2
β : Type u_3
γ : Type u_4
κ : ι → Sort u_5
r : α → β → Prop
s s₁✝ s₂ : Set α
t t₁ t₂ : Set β
s₁ : Set α
closure_snd✝¹ closure_snd✝ : extentClosure r (s₁, intentClosure r s₁).2 = (s₁, intentClosure r s₁).1
⊢ { toProd := (s₁, intentClosure r s₁), closure_fst := ⋯, closure_snd :=... | ((:c Eq) ((:c Concept) (:fv _uniq.5460) (:fv _uniq.5463) (:fv _uniq.5477)) ((:c Concept.mk) (:fv _uniq.5460) (:fv _uniq.5463) (:fv _uniq.5477) ((:c Prod.mk) ((:c Set) (:fv _uniq.5460)) ((:c Set) (:fv _uniq.5463)) (:fv _uniq.5605) (:fv _uniq.5606)) (:fv _uniq.5609) (:fv _uniq.5610)) ((:c Concept.mk) (:fv _uniq.5460) (:f... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"κ","sexp":"(:forall _ (:fv _uniq.5457) (:sort u_5))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.5460) (:forall _ (:fv _uniq.5463) (:sort 0)))"},{"name":"s",... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Concept) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:app (:c Concept.mk) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit 2) (:arg :explicit 3 (:app (:c Prod.mk) (:arg :impl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5457","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5460","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"substs","sourceEnd":6870,"sourceStart":6864,"tag":"atom"},{"children":[{"contextIndex":20,"semanticRole":"local","source":"h","sourceEnd":6872,"sourceStart":6871,"tag":"identifier"},{"contextIndex":14,"semanticRole":"local","source":"h₁","sourceEnd":6877,"sourceStart":6873,"tag":"identifier"},{"... | [] | [{"source":"h","source_end":6872,"source_start":6871,"syntax_kind":"ident"},{"source":"h₁","source_end":6877,"source_start":6873,"syntax_kind":"ident"},{"source":"h₂","source_end":6882,"source_start":6878,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5457","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5460","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 56 | 7 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f610408ce1b7b4320562850c2be6cb1eeb3870c1df61ee5475a24ad317cd8b26 | c1b7bd800d1eca914646ac135c95ded2bbc063678e7c2f39b7d035f6d5ba6186 | 634b497d49f74657a7ef07f879d714ab8c5404796fcbbfcf845016f10a77c38d | 64cee397a6fbeb1f358ad3d052b2ded4650f7fa93d809e510e10c40107fd69ea |
cat-searcher/leandojo-benchmark-4-random | test | 666 | Concept.ext | Mathlib/Order/Concept.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case mk.mk.mk.mk
ι : Sort u_1
α : Type u_2
β : Type u_3
γ : Type u_4
κ : ι → Sort u_5
r : α → β → Prop
s s₁✝ s₂ : Set α
t t₁ t₂ : Set β
s₁ : Set α
closure_snd✝¹ closure_snd✝ : extentClosure r (s₁, intentClosure r s₁).2 = (s₁, intentClosure r s₁).1
⊢ { toProd := (s₁, intentClosure r s₁), closure_fst := ⋯, closure_snd :=... | ((:c Eq) ((:c Concept) (:fv _uniq.5460) (:fv _uniq.5463) (:fv _uniq.5477)) ((:c Concept.mk) (:fv _uniq.5460) (:fv _uniq.5463) (:fv _uniq.5477) ((:c Prod.mk) ((:c Set) (:fv _uniq.5460)) ((:c Set) (:fv _uniq.5463)) (:fv _uniq.5605) ((:c intentClosure) (:fv _uniq.5460) (:fv _uniq.5463) (:fv _uniq.5477) (:fv _uniq.5605))) ... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"κ","sexp":"(:forall _ (:fv _uniq.5457) (:sort u_5))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.5460) (:forall _ (:fv _uniq.5463) (:sort 0)))"},{"name":"s",... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Concept) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:app (:c Concept.mk) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit 2) (:arg :explicit 3 (:app (:c Prod.mk) (:arg :impl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5457","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5460","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"rfl","sourceEnd":6888,"sourceStart":6885,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":6888,"sourceStart":6885,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5457","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5460","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 56 | 8 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c39a556caea9a7260ec96eea1844ee37adae22a39b26cdae6c48e6b489d2d7e1 | 64cee397a6fbeb1f358ad3d052b2ded4650f7fa93d809e510e10c40107fd69ea | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 667 | SemidirectProduct.map_inr | Mathlib/GroupTheory/SemidirectProduct.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>SemidirectProduct.map</a>] | N : Type u_1
G : Type u_2
H : Type u_3
inst✝⁴ : Group N
inst✝³ : Group G
inst✝² : Group H
φ : G →* MulAut N
N₁ : Type u_4
G₁ : Type u_5
inst✝¹ : Group N₁
inst✝ : Group G₁
φ₁ : G₁ →* MulAut N₁
f₁ : N →* N₁
f₂ : G →* G₁
h : ∀ (g : G), f₁.comp (MulEquiv.toMonoidHom (φ g)) = (MulEquiv.toMonoidHom (φ₁ (f₂ g))).comp f₁
g : G... | ((:c Eq) ((:c SemidirectProduct) (:fv _uniq.84179) (:fv _uniq.84182) (:fv _uniq.84185) (:fv _uniq.84188) (:fv _uniq.84409)) ((:c DFunLike.coe) ((:c MonoidHom) ((:c SemidirectProduct) (:fv _uniq.83940) (:fv _uniq.83943) (:fv _uniq.83949) (:fv _uniq.83952) (:fv _uniq.84176)) ((:c SemidirectProduct) (:fv _uniq.84179) (:fv... | [{"name":"N","sexp":"(:sort (+ u_1 1))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"H","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁴","sexp":"((:c Group) (:fv _uniq.83940))"},{"name":"inst✝³","sexp":"((:c Group) (:fv _uniq.83943))"},{"name":"inst✝²","sexp":"((:c Group) (:fv _uniq.83946))"},{"name":"φ","sexp":"((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c SemidirectProduct) (:arg :explicit 0 (:fv FV7)) (:arg :explicit 1 (:fv FV8)) (:arg :instance 2 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV7))))) (:arg :instance 3 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV8))))) (:arg :explicit 4 (:fv FV11)))) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.83940","is_instance":false,"is_let":false,"name":"N","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.83943","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":12125,"sourceStart":12121,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"map","source_end":12130,"source_start":12127,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.83940","is_instance":false,"is_let":false,"user_name":"N"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.83943","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 105 | 2 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3f807850dbff5e74cbdd61a753aa23267a8a3c935be1266b029208c1056cd2da | 3ad2bb21a9df04f2cace2bc6372724c60b287f10af5343cc43c854f6ce2ee1a0 | 4c269c9b6e83e80d2751130ff5a4ed02c6fd473cd3a8bf9a1160c570bfc47d47 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 668 | convex_iff_ordConnected | Mathlib/Analysis/Convex/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>convex_iff_segment_subset</a>, <a>segment_eq_uIcc</a>, <a>Set.ordConnected_iff_uIcc_subset</a>] | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
β : Type u_4
inst✝ : LinearOrderedField 𝕜
s : Set 𝕜
⊢ Convex 𝕜 s ↔ s.OrdConnected | ((:c Iff) ((:c Convex) (:fv _uniq.302590) (:fv _uniq.302590) ((:c OrderedCommSemiring.toOrderedSemiring) (:fv _uniq.302590) ((:c StrictOrderedCommSemiring.toOrderedCommSemiring) (:fv _uniq.302590) ((:c LinearOrderedCommSemiring.toStrictOrderedCommSemiring) (:fv _uniq.302590) ((:c LinearOrderedSemifield.toLinearOrderedC... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedField) (:fv _uniq.302590))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.302590))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Convex) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c OrderedSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instan... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.302590","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.302593","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":26316,"sourceStart":26309,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":26318,"sourceStart":26317,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source... | [] | [{"source":"convex_iff_segment_subset","source_end":26343,"source_start":26318,"syntax_kind":"ident"},{"source":"segment_eq_uIcc","source_end":26360,"source_start":26345,"syntax_kind":"ident"},{"source":"ordConnected_iff_uIcc_subset","source_end":26390,"source_start":26362,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.302590","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.302593","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 238 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4e9c9dbe488ee658eb03ca17fc51ae0b594287355fa9e5b2724d4a77d51ff9cc | 5cbc59f3bd54d97081cb54832b04a63e2092c75735b707cfbba282617baf9fbb | 5c695753b7ea6faae5efc566234e4ce390b2b27009abb288a10a8651713e47d4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 669 | Basis.flag_le_ker_coord_iff | Mathlib/LinearAlgebra/Basis/Flag.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Basis.flag_le_iff</a>, <a>Finsupp.single_apply_eq_zero</a>, <a>imp_false</a>, <a>imp_not_comm</a>] | R : Type u_1
M : Type u_2
inst✝³ : CommRing R
inst✝² : AddCommGroup M
inst✝¹ : Module R M
n : ℕ
inst✝ : Nontrivial R
b : Basis (Fin n) R M
k : Fin (n + 1)
l : Fin n
⊢ b.flag k ≤ LinearMap.ker (b.coord l) ↔ k ≤ l.castSucc | ((:c Iff) ((:c LE.le) ((:c Submodule) (:fv _uniq.18666) (:fv _uniq.18669) ((:c CommSemiring.toSemiring) (:fv _uniq.18666) ((:c CommRing.toCommSemiring) (:fv _uniq.18666) (:fv _uniq.18672))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.18669) (:fv _uniq.18675)) (:fv _uniq.19288)) ((:c Preorder.toLE) ((:c Submodule) (:f... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.18666))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.18669))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.18666) (:fv _uniq.18669) ((:c CommSemiring.toSemiring) (:fv _uni... | (:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV1)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18666","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18669","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":2524,"sourceStart":2520,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"flag_le_iff","source_end":2537,"source_start":2526,"syntax_kind":"ident"},{"source":"Finsupp.single_apply_eq_zero","source_end":2567,"source_start":2539,"syntax_kind":"ident"},{"source":"imp_false","source_end":2578,"source_start":2569,"syntax_kind":"ident"},{"source":"imp_not_comm","source_end":2592,"sourc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18666","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18669","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 18 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4f4aa848dba17ba1c231cb074c1d1a0ec92b56c6708460411802f9448d6b373e | d186f553abfea368a012a01a36edf576f2c91e3286580f6e3d3f64276215d0d6 | 99add3a7855be89c24fbd685a6e288ef9cab5d8225ee7df8fcd582582287eff2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 670 | ConjAct.orbitRel_conjAct | Mathlib/GroupTheory/GroupAction/ConjAct.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MulAction.orbitRel_apply</a>, <a>ConjAct.mem_orbit_conjAct</a>] | α : Type u_1
M : Type u_2
G : Type u_3
G₀ : Type u_4
R : Type u_5
K : Type u_6
inst✝ : Group G
g h : G
⊢ (orbitRel (ConjAct G) G).Rel g h = IsConj g h | ((:c Eq) (:sort 0) ((:c Setoid.Rel) (:fv _uniq.60127) ((:c MulAction.orbitRel) ((:c ConjAct) (:fv _uniq.60127)) (:fv _uniq.60127) ((:c ConjAct.instGroup) (:fv _uniq.60127) (:fv _uniq.60139)) ((:c MulDistribMulAction.toMulAction) ((:c ConjAct) (:fv _uniq.60127)) (:fv _uniq.60127) ((:c DivInvMonoid.toMonoid) ((:c ConjAct... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"G","sexp":"(:sort (+ u_3 1))"},{"name":"G₀","sexp":"(:sort (+ u_4 1))"},{"name":"R","sexp":"(:sort (+ u_5 1))"},{"name":"K","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.60127))"},{"name":"g","sexp":"(... | (:app (:c Eq) (:arg :implicit-type 0 (:sort Prop)) (:arg :explicit 1 (:app (:c Setoid.Rel) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c MulAction.orbitRel) (:arg :explicit 0 (:app (:c ConjAct) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c Group) (... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.60121","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60124","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":11316,"sourceStart":11314,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11318,"sourceStart":11317,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"orbitRel_apply","source_end":11332,"source_start":11318,"syntax_kind":"ident"},{"source":"mem_orbit_conjAct","source_end":11351,"source_start":11334,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.60121","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.60124","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 99 | 2 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6e82b5c079de117312c4a40ba84260e910681c2615adcf1799649092bd2bb4aa | 19793e455c38df2b0d524050ac3ab13a4c4d5af37e2263947414924db9e8f012 | 3336efabb10c80bf98062b0c546545f871b283c43d56ad0040b348f1e12c60ab | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 671 | IsPreconnected.eq_or_eq_neg_of_sq_eq | Mathlib/Topology/Algebra/Field.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hsq : <a>Set.EqOn</a> ((f / g) ^ 2) 1 S := fun x hx => by simpa [<a>div_eq_one_iff_eq</a> (<a>pow_ne_zero</a> _ (hg_ne hx))] using hsq hx | K : Type u_1
inst✝⁷ : DivisionRing K
inst✝⁶ : TopologicalSpace K
α : Type u_2
𝕜 : Type u_3
f g : α → 𝕜
S : Set α
inst✝⁵ : TopologicalSpace α
inst✝⁴ : TopologicalSpace 𝕜
inst✝³ : T1Space 𝕜
inst✝² : Field 𝕜
inst✝¹ : HasContinuousInv₀ 𝕜
inst✝ : ContinuousMul 𝕜
hS : IsPreconnected S
hf : ContinuousOn f S
hg : Contin... | K : Type u_1
inst✝⁷ : DivisionRing K
inst✝⁶ : TopologicalSpace K
α : Type u_2
𝕜 : Type u_3
f g : α → 𝕜
S : Set α
inst✝⁵ : TopologicalSpace α
inst✝⁴ : TopologicalSpace 𝕜
inst✝³ : T1Space 𝕜
inst✝² : Field 𝕜
inst✝¹ : HasContinuousInv₀ 𝕜
inst✝ : ContinuousMul 𝕜
hS : IsPreconnected S
hf : ContinuousOn f S
hg : Contin... | ((:c Or) ((:c Set.EqOn) (:fv _uniq.20744) (:fv _uniq.20747) (:fv _uniq.20751) (:fv _uniq.20755) (:fv _uniq.20758)) ((:c Set.EqOn) (:fv _uniq.20744) (:fv _uniq.20747) (:fv _uniq.20751) ((:c Neg.neg) (:forall _ (:fv _uniq.20744) (:fv _uniq.20747)) ((:c Pi.instNeg) (:fv _uniq.20744) (:lambda _ (:fv _uniq.20744) (:fv _uniq... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁷","sexp":"((:c DivisionRing) (:fv _uniq.20735))"},{"name":"inst✝⁶","sexp":"((:c TopologicalSpace) (:fv _uniq.20735))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.20744) (:fv _uniq.2074... | (:app (:c Or) (:arg :explicit 0 (:app (:c Set.EqOn) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:fv FV4)) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:fv FV6)) (:arg :explicit 4 (:fv FV7)))) (:arg :explicit 1 (:app (:c Set.EqOn) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:fv FV4)) (:arg... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.20735","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20738","is_instance":true,"is_let":false,"name":"inst✝⁷","sexp":"(:app (:c DivisionRing) (:arg :ex... | {"children":[{"source":"have","sourceEnd":6004,"sourceStart":6000,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hsq","sourceEnd":6008,"sourceStart":6005,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hsq","sourceEnd":6008,"sourceStart":6005,"tag":"node"},... | [] | [{"source":"EqOn ((f / g) ^ 2) 1 S","source_end":6033,"source_start":6011,"syntax_kind":"Lean.Parser.Term.app"},{"source":"fun x hx => by\n simpa [div_eq_one_iff_eq (pow_ne_zero _ (hg_ne hx))] using hsq hx","source_end":6121,"source_start":6037,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.20735","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20738","is_instance":true,"is_let":false,"user_name":"inst✝⁷"},{"binder_role":":instance-implicit","context_index":... | 39 | 4 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7def0deb26e9903c356fa00eea45ef4a5e582ed81d467313ad0f0872a4a136eb | 09c044562ee84f08e23afba694c231d2268a1146a732a94575f35b66980f956a | 7fa5d074a1245a8205255368445c8fd57c180380142e7accc48d0dd4125f6fd4 | 82370e76ed19d51c1d19324f8d9089d1811a64a5a7a022a3ad8af237813d643e |
cat-searcher/leandojo-benchmark-4-random | test | 672 | IsPreconnected.eq_or_eq_neg_of_sq_eq | Mathlib/Topology/Algebra/Field.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa (config := { contextual := <a>Bool.true</a> }) [<a>Set.EqOn</a>, <a>div_eq_iff</a> (hg_ne _)] using hS.eq_one_or_eq_neg_one_of_sq_eq (hf.div hg fun z => hg_ne) hsq | K : Type u_1
inst✝⁷ : DivisionRing K
inst✝⁶ : TopologicalSpace K
α : Type u_2
𝕜 : Type u_3
f g : α → 𝕜
S : Set α
inst✝⁵ : TopologicalSpace α
inst✝⁴ : TopologicalSpace 𝕜
inst✝³ : T1Space 𝕜
inst✝² : Field 𝕜
inst✝¹ : HasContinuousInv₀ 𝕜
inst✝ : ContinuousMul 𝕜
hS : IsPreconnected S
hf : ContinuousOn f S
hg : Contin... | ((:c Or) ((:c Set.EqOn) (:fv _uniq.20744) (:fv _uniq.20747) (:fv _uniq.20751) (:fv _uniq.20755) (:fv _uniq.20758)) ((:c Set.EqOn) (:fv _uniq.20744) (:fv _uniq.20747) (:fv _uniq.20751) ((:c Neg.neg) (:forall _ (:fv _uniq.20744) (:fv _uniq.20747)) ((:c Pi.instNeg) (:fv _uniq.20744) (:lambda _ (:fv _uniq.20744) (:fv _uniq... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁷","sexp":"((:c DivisionRing) (:fv _uniq.20735))"},{"name":"inst✝⁶","sexp":"((:c TopologicalSpace) (:fv _uniq.20735))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.20744) (:fv _uniq.2074... | (:app (:c Or) (:arg :explicit 0 (:app (:c Set.EqOn) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:fv FV4)) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:fv FV6)) (:arg :explicit 4 (:fv FV7)))) (:arg :explicit 1 (:app (:c Set.EqOn) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:fv FV4)) (:arg... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.20735","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20738","is_instance":true,"is_let":false,"name":"inst✝⁷","sexp":"(:app (:c DivisionRing) (:arg :ex... | {"children":[{"source":"simpa","sourceEnd":6129,"sourceStart":6124,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":6131,"sourceStart":6130,"tag":"atom"},{"source":"config","source... | [] | [{"source":"{ contextual := true }","source_end":6163,"source_start":6141,"syntax_kind":"Lean.Parser.Term.structInst"},{"source":"EqOn","source_end":6170,"source_start":6166,"syntax_kind":"ident"},{"source":"div_eq_iff (hg_ne _)","source_end":6192,"source_start":6172,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hS.... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.20735","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20738","is_instance":true,"is_let":false,"user_name":"inst✝⁷"},{"binder_role":":instance-implicit","context_index":... | 39 | 10 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dd5e8a5bcc9bbe0d32da796e9de319431f44751c55f82e8d045ef26daf2e07fa | 82370e76ed19d51c1d19324f8d9089d1811a64a5a7a022a3ad8af237813d643e | 33ac81a25767aba114e5dd0fc29bf0c3060dc0dce7a86ea122b98af45ac8eead | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 673 | IsPreconnected.eq_or_eq_neg_of_sq_eq | Mathlib/Topology/Algebra/Field.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [<a>div_eq_one_iff_eq</a> (<a>pow_ne_zero</a> _ (hg_ne hx))] using hsq hx | K : Type u_1
inst✝⁷ : DivisionRing K
inst✝⁶ : TopologicalSpace K
α : Type u_2
𝕜 : Type u_3
f g : α → 𝕜
S : Set α
inst✝⁵ : TopologicalSpace α
inst✝⁴ : TopologicalSpace 𝕜
inst✝³ : T1Space 𝕜
inst✝² : Field 𝕜
inst✝¹ : HasContinuousInv₀ 𝕜
inst✝ : ContinuousMul 𝕜
hS : IsPreconnected S
hf : ContinuousOn f S
hg : Contin... | ((:c Eq) (:fv _uniq.20747) ((:c HPow.hPow) (:forall _ (:fv _uniq.20744) (:fv _uniq.20747)) (:c Nat) (:forall _ (:fv _uniq.20744) (:fv _uniq.20747)) ((:c instHPow) (:forall _ (:fv _uniq.20744) (:fv _uniq.20747)) (:c Nat) ((:c Monoid.toNatPow) (:forall _ (:fv _uniq.20744) (:fv _uniq.20747)) ((:c Pi.monoid) (:fv _uniq.207... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁷","sexp":"((:c DivisionRing) (:fv _uniq.20735))"},{"name":"inst✝⁶","sexp":"((:c TopologicalSpace) (:fv _uniq.20735))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.20744) (:fv _uniq.2074... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV3) (:fv FV4))) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:forall _ :explicit (:fv FV3) (:fv FV4))) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.20735","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20738","is_instance":true,"is_let":false,"name":"inst✝⁷","sexp":"(:app (:c DivisionRing) (:arg :ex... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":6061,"sourceStart":6056,"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_one_iff_eq (pow_ne_zero _ (hg_ne hx))","source_end":6107,"source_start":6063,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hsq hx","source_end":6121,"source_start":6115,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.20735","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.20738","is_instance":true,"is_let":false,"user_name":"inst✝⁷"},{"binder_role":":instance-implicit","context_index":... | 39 | 7 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 022c044f8babbf9f9aa3dd3a59dc72f18d142f8b8ed016cd0b07a34fa35cdb7c | 2c0438916958be346881e7ebbf917f000e79c9d4c620090011b85ea1aa343c1f | fd64fbdf8747e32951e1050ecb58a37e85a9d07b22c21d07027d2a7304b53e19 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 674 | Polynomial.not_irreducible_C | Mathlib/Algebra/Polynomial/FieldDivision.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases H : x = 0 | R : Type u
S : Type v
k : Type y
A : Type z
a b : R
n : ℕ
inst✝ : Field R
p q : R[X]
x : R
⊢ ¬Irreducible (C x) | case pos
R : Type u
S : Type v
k : Type y
A : Type z
a b : R
n : ℕ
inst✝ : Field R
p q : R[X]
x : R
H : x = 0
⊢ ¬Irreducible (C x)
case neg
R : Type u
S : Type v
k : Type y
A : Type z
a b : R
n : ℕ
inst✝ : Field R
p q : R[X]
x : R
H : ¬x = 0
⊢ ¬Irreducible (C x) | ((:c Not) ((:c Irreducible) ((:c Polynomial) (:fv _uniq.195083) ((:c DivisionSemiring.toSemiring) (:fv _uniq.195083) ((:c Semifield.toDivisionSemiring) (:fv _uniq.195083) ((:c Field.toSemifield) (:fv _uniq.195083) (:fv _uniq.195098))))) ((:c MonoidWithZero.toMonoid) ((:c Polynomial) (:fv _uniq.195083) ((:c DivisionSemi... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"k","sexp":"(:sort (+ y 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.195083)"},{"name":"b","sexp":"(:fv _uniq.195083)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c Field) (:fv _uniq.195083)... | (:app (:c Not) (:arg :explicit 0 (:app (:c Irreducible) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.195083","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.195085","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"by_cases","sourceEnd":27907,"sourceStart":27899,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"H","sourceEnd":27909,"sourceStart":27908,"tag":"identifier"},{"source":":","sourceEnd":27911,"sourceStart":27910,"tag":"atom"}],"kind":"null","source":"H :","sourceEnd":27911,"sour... | [] | [{"source":"x = 0","source_end":27917,"source_start":27912,"syntax_kind":"«term_=_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.195083","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.195085","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 157 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c6f044002e5e1389167daa6aad961fb994ffece7bdbac1c8ef0f6e1a14125195 | 51dff65def454810ada7f7a0a77a28fe7d246d5231028a0bae1fb284bc078d48 | 9695f28e28789c5e57014efdec6073824023354c71128967d725130f77512089 | 01dc3f044009b04ca8bc5ed9aefcd52e884daa6feb01adc49386376afb30642a |
cat-searcher/leandojo-benchmark-4-random | test | 675 | Polynomial.not_irreducible_C | Mathlib/Algebra/Polynomial/FieldDivision.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [H, <a>Polynomial.C_0</a>] | case pos
R : Type u
S : Type v
k : Type y
A : Type z
a b : R
n : ℕ
inst✝ : Field R
p q : R[X]
x : R
H : x = 0
⊢ ¬Irreducible (C x) | case pos
R : Type u
S : Type v
k : Type y
A : Type z
a b : R
n : ℕ
inst✝ : Field R
p q : R[X]
x : R
H : x = 0
⊢ ¬Irreducible 0 | ((:c Not) ((:c Irreducible) ((:c Polynomial) (:fv _uniq.195083) ((:c DivisionSemiring.toSemiring) (:fv _uniq.195083) ((:c Semifield.toDivisionSemiring) (:fv _uniq.195083) ((:c Field.toSemifield) (:fv _uniq.195083) (:fv _uniq.195098))))) ((:c MonoidWithZero.toMonoid) ((:c Polynomial) (:fv _uniq.195083) ((:c DivisionSemi... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"k","sexp":"(:sort (+ y 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.195083)"},{"name":"b","sexp":"(:fv _uniq.195083)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c Field) (:fv _uniq.195083)... | (:app (:c Not) (:arg :explicit 0 (:app (:c Irreducible) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.195083","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.195085","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":27925,"sourceStart":27923,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27927,"sourceStart":27926,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":12,"seman... | [] | [{"source":"H","source_end":27928,"source_start":27927,"syntax_kind":"ident"},{"source":"C_0","source_end":27933,"source_start":27930,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.195083","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.195085","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 157 | 9 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b54915f9837f0031298adaf970f94dc6cb2863f9e4d4bfae282f83bd9fbd9e09 | 31a319a2c746f1b72a894f882ea8438f040303448cda5f98c01413b040ec7eae | 99b697c7f8a6fa3282d33ffc0c8a14a79be40361145d92aa39cb940710a2a561 | 753805000a5227d142a79d60cab003488ba80339131d74a45578285b0e71ff39 |
cat-searcher/leandojo-benchmark-4-random | test | 676 | Polynomial.not_irreducible_C | Mathlib/Algebra/Polynomial/FieldDivision.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>not_irreducible_zero</a> | case pos
R : Type u
S : Type v
k : Type y
A : Type z
a b : R
n : ℕ
inst✝ : Field R
p q : R[X]
x : R
H : x = 0
⊢ ¬Irreducible 0 | ((:c Not) ((:c Irreducible) ((:c Polynomial) (:fv _uniq.195083) ((:c DivisionSemiring.toSemiring) (:fv _uniq.195083) ((:c Semifield.toDivisionSemiring) (:fv _uniq.195083) ((:c Field.toSemifield) (:fv _uniq.195083) (:fv _uniq.195098))))) ((:c MonoidWithZero.toMonoid) ((:c Polynomial) (:fv _uniq.195083) ((:c DivisionSemi... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"k","sexp":"(:sort (+ y 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.195083)"},{"name":"b","sexp":"(:fv _uniq.195083)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c Field) (:fv _uniq.195083)... | (:app (:c Not) (:arg :explicit 0 (:app (:c Irreducible) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.195083","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.195085","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":27944,"sourceStart":27939,"tag":"atom"},{"name":"not_irreducible_zero","semanticRole":"global","source":"not_irreducible_zero","sourceEnd":27965,"sourceStart":27945,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact not_irreducible_zero","sourceEnd":27965,"... | [] | [{"source":"not_irreducible_zero","source_end":27965,"source_start":27945,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.195083","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.195085","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 157 | 13 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 87dbb12d861702d399338378383b40993221da3260c8b2874a8171068b286bd1 | 753805000a5227d142a79d60cab003488ba80339131d74a45578285b0e71ff39 | 5b5e1e1c98dd26d499a36bda500e2ec784a8ad720320f6eb7f06c2b352c9db4b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 677 | Polynomial.not_irreducible_C | Mathlib/Algebra/Polynomial/FieldDivision.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun hx => <a>Irreducible.not_unit</a> hx <| <a>Polynomial.isUnit_C</a>.2 <| <a>isUnit_iff_ne_zero</a>.2 H | case neg
R : Type u
S : Type v
k : Type y
A : Type z
a b : R
n : ℕ
inst✝ : Field R
p q : R[X]
x : R
H : ¬x = 0
⊢ ¬Irreducible (C x) | ((:c Not) ((:c Irreducible) ((:c Polynomial) (:fv _uniq.195083) ((:c DivisionSemiring.toSemiring) (:fv _uniq.195083) ((:c Semifield.toDivisionSemiring) (:fv _uniq.195083) ((:c Field.toSemifield) (:fv _uniq.195083) (:fv _uniq.195098))))) ((:c MonoidWithZero.toMonoid) ((:c Polynomial) (:fv _uniq.195083) ((:c DivisionSemi... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"k","sexp":"(:sort (+ y 1))"},{"name":"A","sexp":"(:sort (+ z 1))"},{"name":"a","sexp":"(:fv _uniq.195083)"},{"name":"b","sexp":"(:fv _uniq.195083)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c Field) (:fv _uniq.195083)... | (:app (:c Not) (:arg :explicit 0 (:app (:c Irreducible) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.195083","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.195085","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":27976,"sourceStart":27971,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":27980,"sourceStart":27977,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"hx","sourceEnd":27983,"sourceStart":27981,"tag":"i... | [] | [{"source":"fun hx => Irreducible.not_unit hx <| isUnit_C.2 <| isUnit_iff_ne_zero.2 H","source_end":28050,"source_start":27977,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.195083","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.195085","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 157 | 16 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 69d8be51911a757e9d5689347f6411f69ab669fc7a4807d6ed69f98e26e2acc6 | 5275b81cba8d7c6dcd78808b93a8f5a856428a391bd97c302d6e3c89a3b8cbc4 | 1af8e6dbbc81c41076dda80cf79764ba01cead37ac07ffe508b553e6deab70ce | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 678 | EisensteinSeries.r1_eq | Mathlib/NumberTheory/ModularForms/EisensteinSeries/UniformConvergence.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>div_pow</a>, <a>div_add_one</a> (by positivity), <a>one_div_div</a>, <a>EisensteinSeries.r1</a>] | z : ℍ
⊢ r1 z = 1 / ((z.re / z.im) ^ 2 + 1) | ((:c Eq) (:c Real) ((:c EisensteinSeries.r1) (:fv _uniq.1924)) ((: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 HAdd.hAdd) (:c Real... | [{"name":"z","sexp":"(:c UpperHalfPlane)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c EisensteinSeries.r1) (:arg :explicit 0 (:fv FV0)))) (: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) (:a... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1924","is_instance":false,"is_let":false,"name":"z","sexp":"(:c UpperHalfPlane)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":1830,"sourceStart":1828,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1832,"sourceStart":1831,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"div_pow","source_end":1839,"source_start":1832,"syntax_kind":"ident"},{"source":"div_add_one (by positivity)","source_end":1868,"source_start":1841,"syntax_kind":"Lean.Parser.Term.app"},{"source":"one_div_div","source_end":1881,"source_start":1870,"syntax_kind":"ident"},{"source":"r1","source_end":1885,"sou... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1924","is_instance":false,"is_let":false,"user_name":"z"}] | 9 | 2 | exact | true | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1059bc0816ab0213aed4d796c3b7141bc0b347c7aad163b67b7ada96eaf4280c | 8d438d8acbfbdf8518713bb7814dae9769696c3c30edaa29268c37c99fde1d5f | f6d93da188f2f0fcdb0a9d8076467680aac5d13e110416ff18f78ddfa0c75e4f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 679 | EisensteinSeries.r1_eq | Mathlib/NumberTheory/ModularForms/EisensteinSeries/UniformConvergence.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | z : ℍ
⊢ z.im ^ 2 ≠ 0 | ((:c Ne) (:c Real) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNatPow) (:c Real) ((:c DivInvMonoid.toMonoid) (:c Real) ((:c DivisionMonoid.toDivInvMonoid) (:c Real) ((:c DivisionCommMonoid.toDivisionMonoid) (:c Real) ((:c CommGroupWithZero.toDivisionCommMonoid) (:c Real)... | [{"name":"z","sexp":"(:c UpperHalfPlane)"}] | (:app (:c Ne) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Real)... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1924","is_instance":false,"is_let":false,"name":"z","sexp":"(:c UpperHalfPlane)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"positivity","sourceEnd":1867,"sourceStart":1857,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":1867,"sourceStart":1857,"tag":"node"}],"kind":"null","source":"positivity","sourceEnd":1867,"sourceStart":1857,"ta... | [] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1924","is_instance":false,"is_let":false,"user_name":"z"}] | 9 | 9 | exact | true | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b0d46bb6063243c2e800f6434a3a60012027c77bfbb68816fc8d813c6859c63c | 5978d899e0bc594b7897d1e18d83d2839fd576c25054b92244db7683681ee658 | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 680 | Metric.glueDist_swap | Mathlib/Topology/MetricSpace/Gluing.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Metric.glueDist</a>, <a>Sum.swap_inl</a>, <a>Sum.swap_inr</a>, <a>dist_comm</a>, <a>add_comm</a>] | X : Type u
Y : Type v
Z : Type w
inst✝¹ : MetricSpace X
inst✝ : MetricSpace Y
Φ✝ : Z → X
Ψ✝ : Z → Y
ε✝ : ℝ
Φ : Z → X
Ψ : Z → Y
ε : ℝ
val✝¹ : X
val✝ : Y
⊢ glueDist Ψ Φ ε (Sum.inl val✝¹).swap (Sum.inr val✝).swap = glueDist Φ Ψ ε (Sum.inl val✝¹) (Sum.inr val✝) | ((:c Eq) (:c Real) ((:c Metric.glueDist) (:fv _uniq.2697) (:fv _uniq.2695) (:fv _uniq.2699) (:fv _uniq.2705) (:fv _uniq.2702) (:fv _uniq.2792) (:fv _uniq.2791) (:fv _uniq.2793) ((:c Sum.swap) (:fv _uniq.2695) (:fv _uniq.2697) ((:c Sum.inl) (:fv _uniq.2695) (:fv _uniq.2697) (:fv _uniq.2967))) ((:c Sum.swap) (:fv _uniq.2... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"Z","sexp":"(:sort (+ w 1))"},{"name":"inst✝¹","sexp":"((:c MetricSpace) (:fv _uniq.2695))"},{"name":"inst✝","sexp":"((:c MetricSpace) (:fv _uniq.2697))"},{"name":"Φ✝","sexp":"(:forall _ (:fv _uniq.2699) (:fv _uniq.2695))"},{"name":"Ψ✝... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Metric.glueDist) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c MetricSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2695","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2697","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":3952,"sourceStart":3948,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":3957,"sourceStart":3953,"tag":"atom"}],"kind":"nu... | [] | [{"source":"glueDist","source_end":3967,"source_start":3959,"syntax_kind":"ident"},{"source":"Sum.swap_inl","source_end":3981,"source_start":3969,"syntax_kind":"ident"},{"source":"Sum.swap_inr","source_end":3995,"source_start":3983,"syntax_kind":"ident"},{"source":"dist_comm","source_end":4006,"source_start":3997,"synt... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2695","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2697","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 15 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bbf8990cebf1a9b9be5bbd14985571dc59e65641b0d0780af562575b0d12fdcb | 2cd7cf83fac7fba750c2c0a3f28ce553dd5ef0ca027c94a43eed8098ef9e0ea1 | 0f5f4883a84e6da8769f96b3ae7cb436227178491da9eccb83a856682e4873a1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 681 | Metric.glueDist_swap | Mathlib/Topology/MetricSpace/Gluing.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Metric.glueDist</a>, <a>Sum.swap_inl</a>, <a>Sum.swap_inr</a>, <a>dist_comm</a>, <a>add_comm</a>] | X : Type u
Y : Type v
Z : Type w
inst✝¹ : MetricSpace X
inst✝ : MetricSpace Y
Φ✝ : Z → X
Ψ✝ : Z → Y
ε✝ : ℝ
Φ : Z → X
Ψ : Z → Y
ε : ℝ
val✝¹ : Y
val✝ : X
⊢ glueDist Ψ Φ ε (Sum.inr val✝¹).swap (Sum.inl val✝).swap = glueDist Φ Ψ ε (Sum.inr val✝¹) (Sum.inl val✝) | ((:c Eq) (:c Real) ((:c Metric.glueDist) (:fv _uniq.2697) (:fv _uniq.2695) (:fv _uniq.2699) (:fv _uniq.2705) (:fv _uniq.2702) (:fv _uniq.2792) (:fv _uniq.2791) (:fv _uniq.2793) ((:c Sum.swap) (:fv _uniq.2695) (:fv _uniq.2697) ((:c Sum.inr) (:fv _uniq.2695) (:fv _uniq.2697) (:fv _uniq.2997))) ((:c Sum.swap) (:fv _uniq.2... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"Z","sexp":"(:sort (+ w 1))"},{"name":"inst✝¹","sexp":"((:c MetricSpace) (:fv _uniq.2695))"},{"name":"inst✝","sexp":"((:c MetricSpace) (:fv _uniq.2697))"},{"name":"Φ✝","sexp":"(:forall _ (:fv _uniq.2699) (:fv _uniq.2695))"},{"name":"Ψ✝... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Metric.glueDist) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c MetricSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2695","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2697","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":4047,"sourceStart":4043,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":4052,"sourceStart":4048,"tag":"atom"}],"kind":"nu... | [] | [{"source":"glueDist","source_end":4062,"source_start":4054,"syntax_kind":"ident"},{"source":"Sum.swap_inl","source_end":4076,"source_start":4064,"syntax_kind":"ident"},{"source":"Sum.swap_inr","source_end":4090,"source_start":4078,"syntax_kind":"ident"},{"source":"dist_comm","source_end":4101,"source_start":4092,"synt... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2695","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2697","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 15 | 7 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3ee8d96772fcd714d50bdf228b462ed4a398ebe9e13406f55d7f6c8fe3a8704c | c9f055c0ef2056d50f88e2230ad5b715136319e2d531b20966ec108f102ea019 | 0f5f4883a84e6da8769f96b3ae7cb436227178491da9eccb83a856682e4873a1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 682 | Real.isConjExponent_iff_eq_conjExponent | Mathlib/Data/Real/ConjExponents.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | field_simp [h] | a b p q : ℝ
h✝ : p.IsConjExponent q
hp : 1 < p
h : q = p / (p - 1)
⊢ p⁻¹ + q⁻¹ = 1 | ((:c Eq) (:c Real) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) ((:c Inv.inv) (:c Real) (:c Real.instInv) (:fv _uniq.15451)) ((:c Inv.inv) (:c Real) (:c Real.instInv) (:fv _uniq.15453))) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne)))) | [{"name":"a","sexp":"(:c Real)"},{"name":"b","sexp":"(:c Real)"},{"name":"p","sexp":"(:c Real)"},{"name":"q","sexp":"(:c Real)"},{"name":"h✝","sexp":"((:c Real.IsConjExponent) (:fv _uniq.15451) (:fv _uniq.15453))"},{"name":"hp","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (: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 HAdd) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15447","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15449","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Real)"},{"binder_role":":implicit","context_i... | {"children":[{"children":[{"children":[{"children":[{"source":"field_simp","sourceEnd":5732,"sourceStart":5722,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"so... | [] | [{"source":"h","source_end":5735,"source_start":5734,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15447","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15449","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 50 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aab076498b57cb8bb767fff818e808c762c510fcf110620c89015a026a723499 | 4578c55f0d4158564a8feb32132ec8c5eee0e7eb6d8881703211abbe4d2d9786 | 1542942a29d020ed3ff46fdc8824efeda9f08708fe68d0ac7cc090eb14482174 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 683 | NNReal.tendsto_sum_nat_add | Mathlib/Topology/Instances/ENNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>NNReal.tendsto_coe</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
f : ℕ → ℝ≥0
⊢ Tendsto (fun i => ∑' (k : ℕ), f (k + i)) atTop (𝓝 0) | α : Type u_1
β : Type u_2
γ : Type u_3
f : ℕ → ℝ≥0
⊢ Tendsto (fun a => ↑(∑' (k : ℕ), f (k + a))) atTop (𝓝 ↑0) | ((:c Filter.Tendsto) (:c Nat) (:c NNReal) (:lambda i (:c Nat) ((:c tsum) (:c NNReal) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:c NNReal) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:c NNReal) ((:c Semiring.toNonAssocSemiring) (:c NNReal) (:c instNNRealSemiring)))) (:c NNReal.instTopologicalSpace) (:c Na... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:c NNReal))"}] | (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c NNReal)) (:arg :explicit 2 (:lambda i :explicit (:c Nat) (:app (:c tsum) (:arg :implicit-type 0 (:c NNReal)) (:arg :instance 1 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c NNReal))))) (:arg :instance 2 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.289291","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.289294","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":63910,"sourceStart":63908,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":63912,"sourceStart":63911,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":63915,"sourceSt... | [] | [{"source":"tendsto_coe","source_end":63927,"source_start":63916,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.289291","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.289294","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 379 | 4 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3ca90a66d596a7cb918385116c79961f45b5abd44e77601db621ff0c110ecfd1 | 464995490049152cb6da794b1a5ee48cedb902548ce3e040aee6bea824e96d3d | b3b7900657a1d06ee97f85d4e8c0cd6fa56629d57def1a09065917f59358101f | c04326d334c232d1157b0fe3b3c73e60f2235fdf217a9bb83bdd07e2c4d35347 |
cat-searcher/leandojo-benchmark-4-random | test | 684 | NNReal.tendsto_sum_nat_add | Mathlib/Topology/Instances/ENNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert <a>tendsto_sum_nat_add</a> fun i => (f i : ℝ) | α : Type u_1
β : Type u_2
γ : Type u_3
f : ℕ → ℝ≥0
⊢ Tendsto (fun a => ↑(∑' (k : ℕ), f (k + a))) atTop (𝓝 ↑0) | case h.e'_3.h
α : Type u_1
β : Type u_2
γ : Type u_3
f : ℕ → ℝ≥0
x✝ : ℕ
⊢ ↑(∑' (k : ℕ), f (k + x✝)) = ∑' (k : ℕ), ↑(f (k + x✝)) | ((:c Filter.Tendsto) (:c Nat) (:c Real) (:lambda a (:c Nat) ((:c NNReal.toReal) ((:c tsum) (:c NNReal) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:c NNReal) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:c NNReal) ((:c Semiring.toNonAssocSemiring) (:c NNReal) (:c instNNRealSemiring)))) (:c NNReal.instTopolo... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:c NNReal))"}] | (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Real)) (:arg :explicit 2 (:lambda a :explicit (:c Nat) (:app (:c NNReal.toReal) (:arg :explicit 0 (:app (:c tsum) (:arg :implicit-type 0 (:c NNReal)) (:arg :instance 1 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c NNRea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.289291","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.289294","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"convert","sourceEnd":63938,"sourceStart":63931,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"tendsto_sum_nat_add","semanticRole":"global","source":"_root_.tendsto_sum_nat_add","sourceEnd":63965,"s... | [] | [{"source":"_root_.tendsto_sum_nat_add fun i => (f i : ℝ)","source_end":63986,"source_start":63939,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.289291","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.289294","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 379 | 7 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 11e30ecc88c1c201c9c1094b92ad666606359e24846b2e46bca1c7dc0c0d149e | c04326d334c232d1157b0fe3b3c73e60f2235fdf217a9bb83bdd07e2c4d35347 | 5e11fe7d6effceaed698c162cbb24c9cb01e8ede0f271e4c0670fe54171c4dc3 | 1e179fc5f1d13e2c8e4bdc311145d49580730913f460faf007ba1ae4d40651fd |
cat-searcher/leandojo-benchmark-4-random | test | 685 | NNReal.tendsto_sum_nat_add | Mathlib/Topology/Instances/ENNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_cast | case h.e'_3.h
α : Type u_1
β : Type u_2
γ : Type u_3
f : ℕ → ℝ≥0
x✝ : ℕ
⊢ ↑(∑' (k : ℕ), f (k + x✝)) = ∑' (k : ℕ), ↑(f (k + x✝)) | ((:c Eq) (:c Real) ((:c NNReal.toReal) ((:c tsum) (:c NNReal) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:c NNReal) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:c NNReal) ((:c Semiring.toNonAssocSemiring) (:c NNReal) (:c instNNRealSemiring)))) (:c NNReal.instTopologicalSpace) (:c Nat) (:lambda k (:c Nat) ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:c NNReal))"},{"name":"x✝","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c NNReal.toReal) (:arg :explicit 0 (:app (:c tsum) (:arg :implicit-type 0 (:c NNReal)) (:arg :instance 1 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c NNReal))))) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.289291","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.289294","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"norm_cast","sourceEnd":63998,"sourceStart":63989,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.tacticNorm_cast_","source":"norm_cast","sourceEnd":63998,"sourceStart":63989,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.289291","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.289294","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 379 | 8 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 918bf1bad1e9d46ab0c193d8c235092a9206c718a8468b92d9bd67527c9b7d0b | 1e179fc5f1d13e2c8e4bdc311145d49580730913f460faf007ba1ae4d40651fd | 4526560ee387a60af0a3f42ddce7258b27dc8bd6782a63271dc2d5aa462e81b2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 686 | List.formPerm_apply_get_length | Mathlib/GroupTheory/Perm/List.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | α : Type u_1
β : Type u_2
inst✝ : DecidableEq α
l : List α
x✝ x : α
xs : List α
⊢ xs.length < (x :: xs).length | ((:c LT.lt) (:c Nat) (:c instLTNat) ((:c List.length) (:fv _uniq.23466) (:fv _uniq.23488)) ((:c List.length) (:fv _uniq.23466) ((:c List.cons) (:fv _uniq.23466) (:fv _uniq.23485) (:fv _uniq.23488)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.23466))"},{"name":"l","sexp":"((:c List) (:fv _uniq.23466))"},{"name":"x✝","sexp":"(:fv _uniq.23466)"},{"name":"x","sexp":"(:fv _uniq.23466)"},{"name":"xs","sexp":"((:c List) (:fv _uniq.... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c List.length) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV6)))) (:arg :explicit 3 (:app (:c List.length) (:arg :implicit-type 0 (:fv FV0)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23466","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23469","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":6358,"sourceStart":6354,"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.23466","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23469","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 42 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 77c4bb0a33cec1013d0f92ebd2796558f64f152b5ef84f109bcca1e8669ac29e | 921f178e48cd84a1f19db1f070125eca81bd6292b1afa0fb49793009460b6b00 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 687 | List.formPerm_apply_get_length | Mathlib/GroupTheory/Perm/List.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>List.formPerm_apply_getElem_length</a>] | α : Type u_1
β : Type u_2
inst✝ : DecidableEq α
l : List α
x✝ x : α
xs : List α
⊢ (x :: xs).formPerm ((x :: xs).get ⟨xs.length, ⋯⟩) = x | ((:c Eq) (:fv _uniq.23466) ((:c DFunLike.coe) ((:c Equiv.Perm) (:fv _uniq.23466)) (:fv _uniq.23466) (:lambda _ (:fv _uniq.23466) (:fv _uniq.23466)) ((:c Equiv.instFunLike) (:fv _uniq.23466) (:fv _uniq.23466)) ((:c List.formPerm) (:fv _uniq.23466) (:fv _uniq.23476) ((:c List.cons) (:fv _uniq.23466) (:fv _uniq.24034) (:f... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.23466))"},{"name":"l","sexp":"((:c List) (:fv _uniq.23466))"},{"name":"x✝","sexp":"(:fv _uniq.23466)"},{"name":"x","sexp":"(:fv _uniq.23466)"},{"name":"xs","sexp":"((:c List) (:fv _uniq.... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Equiv.Perm) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c FunLike) (:arg :explicit 0 (:app (:c Equiv) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23466","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23469","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":6378,"sourceStart":6374,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"formPerm_apply_getElem_length","source_end":6409,"source_start":6380,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23466","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23469","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 42 | 7 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 035271694cb312ca8c3e43d6ff803c8c5ffa901acc5c1db7be1193d39c44371f | 74f609b4310b368826936de6c2b7111cff458fce4eecbc73b77cea42fc181faa | eabdfecdb926331a5d06c4c3cc0c949e0e92217842830a1333e1ff179ae16d9e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 688 | Polynomial.natDegree_C_add | Mathlib/Algebra/Polynomial/Degree/Definitions.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>add_comm</a> _ p] | R : Type u
S : Type v
a✝ b c d : R
n m : ℕ
inst✝ : Semiring R
p✝ p q : R[X]
ι : Type u_1
a : R
⊢ (C a + p).natDegree = p.natDegree | ((:c Eq) (:c Nat) ((:c Polynomial.natDegree) (:fv _uniq.131029) (:fv _uniq.131046) ((:c HAdd.hAdd) ((:c Polynomial) (:fv _uniq.131029) (:fv _uniq.131046)) ((:c Polynomial) (:fv _uniq.131029) (:fv _uniq.131046)) ((:c Polynomial) (:fv _uniq.131029) (:fv _uniq.131046)) ((:c instHAdd) ((:c Polynomial) (:fv _uniq.131029) (:... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a✝","sexp":"(:fv _uniq.131029)"},{"name":"b","sexp":"(:fv _uniq.131029)"},{"name":"c","sexp":"(:fv _uniq.131029)"},{"name":"d","sexp":"(:fv _uniq.131029)"},{"name":"n","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"inst✝",... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Polynomial.natDegree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.131029","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.131031","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":33213,"sourceStart":33209,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"add_comm _ p","source_end":33227,"source_start":33215,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.131029","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.131031","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 277 | 2 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0cf2ccfa5d916f9494a1488b20be3d4f64b00e876c5a920e865a0ee7fd37a299 | 0342b1d11a17de10e8d2c72517dbb0c34f657fc825368f74df8f0bca21965ea7 | f318db183a5c6bf7701b97c486957d55e0b2aedc46bddee7ef89909194e5ec19 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 689 | AffineSubspace.wOppSide_iff_exists_left | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y p₁ : P
h : p₁ ∈ s
⊢ s.WOppSide x y ↔ x ∈ s ∨ ∃ p₂ ∈ s, Same... | case mp
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y p₁ : P
h : p₁ ∈ s
⊢ s.WOppSide x y → x ∈ s ∨ ∃ p₂ ∈... | ((:c Iff) ((:c AffineSubspace.WOppSide) (:fv _uniq.264906) (:fv _uniq.264909) (:fv _uniq.264915) ((:c LinearOrderedCommRing.toStrictOrderedCommRing) (:fv _uniq.264906) ((:c LinearOrderedField.toLinearOrderedCommRing) (:fv _uniq.264906) (:fv _uniq.264921))) (:fv _uniq.264924) (:fv _uniq.265505) (:fv _uniq.265700) (:fv _... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c LinearOrderedField) (:fv _uniq.264906))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup) (... | (:app (:c Iff) (:arg :explicit 0 (:app (:c AffineSubspace.WOppSide) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c StrictOrderedCommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c AddCommGrou... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"constructor","sourceEnd":23859,"sourceStart":23848,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":23859,"sourceStart":23848,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 152 | 4 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3751ecbcc23324522587ff340682adf3e75bf74d5ebaf4b56524bdb73ba51b83 | d04b322ad26614470cc14951b4aa5368a458c7c2a1efc95e165f5dbbf128be07 | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | fd1ccfd564cb78271ad9a6a9a0c04f948dd1ea5823afa95d45a7890954c360b7 |
cat-searcher/leandojo-benchmark-4-random | test | 690 | AffineSubspace.wOppSide_iff_exists_left | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨p₁', hp₁', p₂', hp₂', h0 | h0 | ⟨r₁, r₂, hr₁, hr₂, hr⟩⟩ | case mp
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y p₁ : P
h : p₁ ∈ s
⊢ s.WOppSide x y → x ∈ s ∨ ∃ p₂ ∈... | case mp.intro.intro.intro.intro.inl
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y p₁ : P
h : p₁ ∈ s
p₁' :... | (:forall _ ((:c AffineSubspace.WOppSide) (:fv _uniq.264906) (:fv _uniq.264909) (:fv _uniq.264915) ((:c LinearOrderedCommRing.toStrictOrderedCommRing) (:fv _uniq.264906) ((:c LinearOrderedField.toLinearOrderedCommRing) (:fv _uniq.264906) (:fv _uniq.264921))) (:fv _uniq.264924) (:fv _uniq.265505) (:fv _uniq.265700) (:fv ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c LinearOrderedField) (:fv _uniq.264906))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup) (... | (:forall _ :explicit (:app (:c AffineSubspace.WOppSide) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c StrictOrderedCommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c AddCommGroup) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rintro","sourceEnd":23871,"sourceStart":23865,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":23875,"sourceStart":23872,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"p₁'","sourceEnd":23880,"s... | [{"role":"fresh_name","source":"p₁'","source_end":23880,"source_start":23875,"syntax_kind":"ident"},{"role":"fresh_name","source":"hp₁'","source_end":23888,"source_start":23882,"syntax_kind":"ident"},{"role":"fresh_name","source":"p₂'","source_end":23895,"source_start":23890,"syntax_kind":"ident"},{"role":"fresh_name",... | [{"source":"⟨p₁', hp₁', p₂', hp₂', h0 | h0 | ⟨r₁, r₂, hr₁, hr₂, hr⟩⟩","source_end":23952,"source_start":23872,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 152 | 9 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 136ddddc19b07b37dea1e4d597a6b4e5d007eab85de58a183b267e97d54441c3 | 2478740c7dd36ae06c7a003903d3294edd054fbf8b9724b9137eb5c42b66c294 | 9932c7b58075129c2c2f105c0c1dcc451a37d5fb6a027990fccd726c0a4aae2d | 347199c67983bf8676b26f65fcee117a0c88af60cdcee4c264cec0d75f38d3c0 |
cat-searcher/leandojo-benchmark-4-random | test | 691 | AffineSubspace.wOppSide_iff_exists_left | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>vsub_eq_zero_iff_eq</a>] at h0 | case mp.intro.intro.intro.intro.inl
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y p₁ : P
h : p₁ ∈ s
p₁' :... | case mp.intro.intro.intro.intro.inl
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y p₁ : P
h : p₁ ∈ s
p₁' :... | ((:c Or) ((:c Membership.mem) (:fv _uniq.264915) ((:c AffineSubspace) (:fv _uniq.264906) (:fv _uniq.264909) (:fv _uniq.264915) ((:c StrictOrderedRing.toRing) (:fv _uniq.264906) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.264906) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.264906) ((:c LinearOr... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c LinearOrderedField) (:fv _uniq.264906))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup) (... | (:app (:c Or) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c AffineSubspace) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV0))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":23962,"sourceStart":23960,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":23964,"sourceStart":23963,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"vsub_eq_zero_iff... | [] | [{"source":"vsub_eq_zero_iff_eq","source_end":23983,"source_start":23964,"syntax_kind":"ident"},{"source":"h0","source_end":23990,"source_start":23988,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 152 | 14 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 80fa86a7eed53d2b0fb1852d8ba859b298cae63ec94edfe83acc391819b39fd8 | ec2022a3715b2c2406c7dac2e12c284061716143400d75d599207b93eb051418 | 3f726fc8a420e3daaea59293002c150dd8739d85874630bec079b9424e54d6db | cd7491daf087584e4c73df5051dff7aead43a56f0fc07f9aa02d48702cbb3bef |
cat-searcher/leandojo-benchmark-4-random | test | 692 | AffineSubspace.wOppSide_iff_exists_left | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [h0] | case mp.intro.intro.intro.intro.inl
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y p₁ : P
h : p₁ ∈ s
p₁' :... | case mp.intro.intro.intro.intro.inl
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y p₁ : P
h : p₁ ∈ s
p₁' :... | ((:c Or) ((:c Membership.mem) (:fv _uniq.264915) ((:c AffineSubspace) (:fv _uniq.264906) (:fv _uniq.264909) (:fv _uniq.264915) ((:c StrictOrderedRing.toRing) (:fv _uniq.264906) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.264906) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.264906) ((:c LinearOr... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c LinearOrderedField) (:fv _uniq.264906))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup) (... | (:app (:c Or) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c AffineSubspace) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV0))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":23999,"sourceStart":23997,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":24001,"sourceStart":24000,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":22,"seman... | [] | [{"source":"h0","source_end":24003,"source_start":24001,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 152 | 17 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a933643d9e36b727f5b147dc7ec2fed0cda1b998bc7f6d61d5968651bd1a52f9 | cd7491daf087584e4c73df5051dff7aead43a56f0fc07f9aa02d48702cbb3bef | 15331275b3704972b10951d5910c82461e1cf03a07f26c77af2f7dab1011cc9c | fa6da686c626e843bf64f4e007a34fc4df90883f52425a731a668249adf1a420 |
cat-searcher/leandojo-benchmark-4-random | test | 693 | AffineSubspace.wOppSide_iff_exists_left | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Or.inl</a> hp₁' | case mp.intro.intro.intro.intro.inl
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y p₁ : P
h : p₁ ∈ s
p₁' :... | ((:c Or) ((:c Membership.mem) (:fv _uniq.264915) ((:c AffineSubspace) (:fv _uniq.264906) (:fv _uniq.264909) (:fv _uniq.264915) ((:c StrictOrderedRing.toRing) (:fv _uniq.264906) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.264906) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.264906) ((:c LinearOr... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c LinearOrderedField) (:fv _uniq.264906))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup) (... | (:app (:c Or) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c AffineSubspace) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV0))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":24016,"sourceStart":24011,"tag":"atom"},{"children":[{"name":"Or.inl","semanticRole":"constructor","source":"Or.inl","sourceEnd":24023,"sourceStart":24017,"tag":"identifier"},{"children":[{"contextIndex":19,"semanticRole":"local","source":"hp₁'","sourceEnd":24030,"sourceStart"... | [] | [{"source":"Or.inl hp₁'","source_end":24030,"source_start":24017,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 152 | 20 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 346882dd3472742ee31ba15cf26ee73e87cdee6ba7590340773cb1fcee25f515 | fa6da686c626e843bf64f4e007a34fc4df90883f52425a731a668249adf1a420 | ad4349d95bce9aa35f798f605b7bef84625c5bb2ad92cb283e9c20ba9b30b18d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 694 | AffineSubspace.wOppSide_iff_exists_left | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Or.inr</a> ⟨p₂', hp₂', ?_⟩ | case mp.intro.intro.intro.intro.inr.inl
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y p₁ : P
h : p₁ ∈ s
p... | case mp.intro.intro.intro.intro.inr.inl
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y p₁ : P
h : p₁ ∈ s
p... | ((:c Or) ((:c Membership.mem) (:fv _uniq.264915) ((:c AffineSubspace) (:fv _uniq.264906) (:fv _uniq.264909) (:fv _uniq.264915) ((:c StrictOrderedRing.toRing) (:fv _uniq.264906) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.264906) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.264906) ((:c LinearOr... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c LinearOrderedField) (:fv _uniq.264906))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup) (... | (:app (:c Or) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c AffineSubspace) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV0))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":24044,"sourceStart":24038,"tag":"atom"},{"children":[{"name":"Or.inr","semanticRole":"constructor","source":"Or.inr","sourceEnd":24051,"sourceStart":24045,"tag":"identifier"},{"children":[{"children":[{"source":"⟨","sourceEnd":24055,"sourceStart":24052,"tag":"atom"},{"childre... | [] | [{"source":"Or.inr ⟨p₂', hp₂', ?_⟩","source_end":24075,"source_start":24045,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 152 | 25 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5254854bd33e6d6106ac968e9f6212ddee8c15890d973a203b54114e9726ba17 | 3a30bfff1c6dc3e4c2d1355500572f929a58b390f470770ee375d24a97a7f29b | 5b7c93aded80f17b75a97e1b132faee43d66d62a40219f5afae8d34b650fc6a8 | 7232fc2cf890b2664058a692ef8b1ad3fb45026ec15f43aac8cdcc19dce2be88 |
cat-searcher/leandojo-benchmark-4-random | test | 695 | AffineSubspace.wOppSide_iff_exists_left | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [h0] | case mp.intro.intro.intro.intro.inr.inl
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y p₁ : P
h : p₁ ∈ s
p... | case mp.intro.intro.intro.intro.inr.inl
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y p₁ : P
h : p₁ ∈ s
p... | ((:c SameRay) (:fv _uniq.264906) ((:c LinearOrderedCommSemiring.toStrictOrderedCommSemiring) (:fv _uniq.264906) ((:c LinearOrderedSemifield.toLinearOrderedCommSemiring) (:fv _uniq.264906) ((:c LinearOrderedField.toLinearOrderedSemifield) (:fv _uniq.264906) (:fv _uniq.264921)))) (:fv _uniq.264909) ((:c AddCommGroup.toAd... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c LinearOrderedField) (:fv _uniq.264906))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup) (... | (:app (:c SameRay) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c StrictOrderedCommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:app (:c Module... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":24084,"sourceStart":24082,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":24086,"sourceStart":24085,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":22,"seman... | [] | [{"source":"h0","source_end":24088,"source_start":24086,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 152 | 26 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0b9674d07006b557f37fa1751031ecd2454b754285d1879ef2e02e5e6aafe336 | 7232fc2cf890b2664058a692ef8b1ad3fb45026ec15f43aac8cdcc19dce2be88 | 15331275b3704972b10951d5910c82461e1cf03a07f26c77af2f7dab1011cc9c | ede9ba75de7d926b166bf94b0d8b9dbc3b39942fbf4f15f22be2de5f2a1caae7 |
cat-searcher/leandojo-benchmark-4-random | test | 696 | AffineSubspace.wOppSide_iff_exists_left | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>SameRay.zero_right</a> _ | case mp.intro.intro.intro.intro.inr.inl
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y p₁ : P
h : p₁ ∈ s
p... | ((:c SameRay) (:fv _uniq.264906) ((:c LinearOrderedCommSemiring.toStrictOrderedCommSemiring) (:fv _uniq.264906) ((:c LinearOrderedSemifield.toLinearOrderedCommSemiring) (:fv _uniq.264906) ((:c LinearOrderedField.toLinearOrderedSemifield) (:fv _uniq.264906) (:fv _uniq.264921)))) (:fv _uniq.264909) ((:c AddCommGroup.toAd... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c LinearOrderedField) (:fv _uniq.264906))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup) (... | (:app (:c SameRay) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c StrictOrderedCommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:app (:c Module... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":24101,"sourceStart":24096,"tag":"atom"},{"children":[{"name":"SameRay.zero_right","semanticRole":"global","source":"SameRay.zero_right","sourceEnd":24120,"sourceStart":24102,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":24122,"sourceStart":24121,"tag"... | [] | [{"source":"SameRay.zero_right _","source_end":24122,"source_start":24102,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 152 | 29 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d96630c1879aa6302c993900169de6604e64348c63517ca17526b73d49f55f17 | ede9ba75de7d926b166bf94b0d8b9dbc3b39942fbf4f15f22be2de5f2a1caae7 | 1533293dc06ad109262436592a71545c5df90d256967145b18557d8d161e2b84 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 697 | AffineSubspace.wOppSide_iff_exists_left | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Or.inr</a> ⟨(-r₁ / r₂) • (p₁ -ᵥ p₁') +ᵥ p₂', s.smul_vsub_vadd_mem _ h hp₁' hp₂', <a>Or.inr</a> (<a>Or.inr</a> ⟨r₁, r₂, hr₁, hr₂, ?_⟩)⟩ | case mp.intro.intro.intro.intro.inr.inr.intro.intro.intro.intro
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P... | case mp.intro.intro.intro.intro.inr.inr.intro.intro.intro.intro
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P... | ((:c Or) ((:c Membership.mem) (:fv _uniq.264915) ((:c AffineSubspace) (:fv _uniq.264906) (:fv _uniq.264909) (:fv _uniq.264915) ((:c StrictOrderedRing.toRing) (:fv _uniq.264906) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.264906) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.264906) ((:c LinearOr... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c LinearOrderedField) (:fv _uniq.264906))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup) (... | (:app (:c Or) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c AffineSubspace) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV0))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":24136,"sourceStart":24130,"tag":"atom"},{"children":[{"name":"Or.inr","semanticRole":"constructor","source":"Or.inr","sourceEnd":24143,"sourceStart":24137,"tag":"identifier"},{"children":[{"children":[{"source":"⟨","sourceEnd":24147,"sourceStart":24144,"tag":"atom"},{"childre... | [] | [{"source":"Or.inr ⟨(-r₁ / r₂) • (p₁ -ᵥ p₁') +ᵥ p₂', s.smul_vsub_vadd_mem _ h hp₁' hp₂',\n Or.inr (Or.inr ⟨r₁, r₂, hr₁, hr₂, ?_⟩)⟩","source_end":24297,"source_start":24137,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 152 | 34 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | af1f6de8a98946670de988eebe5e72cefad56d942404166b88908d9c5c2c7d47 | f3ea68f394f35b8d35af5939ab8814b69b2c836b0ffaed4e4a0bd5062230d0a2 | be45a9f53e6c2e36f11d5cdb7148817ceee7b21526454bab570bdba75897b1cf | 9a83f94379415e09a07f91fba6138c80c67b64067d068d9af384420c814c1268 |
cat-searcher/leandojo-benchmark-4-random | test | 698 | AffineSubspace.wOppSide_iff_exists_left | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>vadd_vsub_assoc</a>, <a>smul_add</a>, ← hr, <a>smul_smul</a>, <a>neg_div</a>, <a>mul_neg</a>, <a>mul_div_cancel₀</a> _ hr₂.ne.symm, <a>neg_smul</a>, <a>neg_add_eq_sub</a>, ← <a>smul_sub</a>, <a>vsub_sub_vsub_cancel_right</a>] | case mp.intro.intro.intro.intro.inr.inr.intro.intro.intro.intro
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P... | ((:c Eq) (:fv _uniq.264909) ((:c HSMul.hSMul) (:fv _uniq.264906) (:fv _uniq.264909) (:fv _uniq.264909) ((:c instHSMul) (:fv _uniq.264906) (:fv _uniq.264909) ((:c SMulZeroClass.toSMul) (:fv _uniq.264906) (:fv _uniq.264909) ((:c AddMonoid.toZero) (:fv _uniq.264909) ((:c AddCommMonoid.toAddMonoid) (:fv _uniq.264909) ((:c ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c LinearOrderedField) (:fv _uniq.264906))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup) (... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 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 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":24306,"sourceStart":24304,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":24308,"sourceStart":24307,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"vadd_vsub_assoc"... | [] | [{"source":"vadd_vsub_assoc","source_end":24323,"source_start":24308,"syntax_kind":"ident"},{"source":"smul_add","source_end":24333,"source_start":24325,"syntax_kind":"ident"},{"source":"hr","source_end":24341,"source_start":24339,"syntax_kind":"ident"},{"source":"smul_smul","source_end":24352,"source_start":24343,"syn... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 152 | 35 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7cf1d05d689c29f1dfb60e512a7d7f0301e74de265676f42df60401fbfe75f9a | 9a83f94379415e09a07f91fba6138c80c67b64067d068d9af384420c814c1268 | 03a47dd56483d51d5e8c626e00212a049ae058c665b42b5a94ef6f0082958f17 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 699 | AffineSubspace.wOppSide_iff_exists_left | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro (h' | ⟨h₁, h₂, h₃⟩) | case mpr
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y p₁ : P
h : p₁ ∈ s
⊢ (x ∈ s ∨ ∃ p₂ ∈ s, SameRay R (... | case mpr.inl
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y p₁ : P
h : p₁ ∈ s
h' : x ∈ s
⊢ s.WOppSide x y
... | (:forall _ ((:c Or) ((:c Membership.mem) (:fv _uniq.264915) ((:c AffineSubspace) (:fv _uniq.264906) (:fv _uniq.264909) (:fv _uniq.264915) ((:c StrictOrderedRing.toRing) (:fv _uniq.264906) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.264906) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.264906) ((... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c LinearOrderedField) (:fv _uniq.264906))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup) (... | (:forall _ :explicit (:app (:c Or) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c AffineSubspace) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rintro","sourceEnd":24502,"sourceStart":24496,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":24504,"sourceStart":24503,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h'","sourceEnd":24506,"sourceStart":24... | [{"role":"fresh_name","source":"h'","source_end":24506,"source_start":24504,"syntax_kind":"ident"},{"role":"fresh_name","source":"h₁","source_end":24516,"source_start":24512,"syntax_kind":"ident"},{"role":"fresh_name","source":"h₂","source_end":24522,"source_start":24518,"syntax_kind":"ident"},{"role":"fresh_name","sou... | [{"source":"(h' | ⟨h₁, h₂, h₃⟩)","source_end":24532,"source_start":24503,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 152 | 52 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2947a505971bf42a65b1e54272cb9ce89f44b39c1c78ddd2139e474793fd129a | e5b9c9822e4c43feb885e727dd98b3b621827c1a4cadb4972a836412389c8c49 | 87aff4b1277d52e69d0e8e18873b78f42da5182bfdd8c168ca67e25998dba056 | fadc2fdb67761f723f11dcb529a87f8d88c8b0f1e57b7a2667e8ddd732c1143d |
cat-searcher/leandojo-benchmark-4-random | test | 700 | AffineSubspace.wOppSide_iff_exists_left | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>AffineSubspace.wOppSide_of_left_mem</a> y h' | case mpr.inl
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y p₁ : P
h : p₁ ∈ s
h' : x ∈ s
⊢ s.WOppSide x y | ((:c AffineSubspace.WOppSide) (:fv _uniq.264906) (:fv _uniq.264909) (:fv _uniq.264915) ((:c LinearOrderedCommRing.toStrictOrderedCommRing) (:fv _uniq.264906) ((:c LinearOrderedField.toLinearOrderedCommRing) (:fv _uniq.264906) (:fv _uniq.264921))) (:fv _uniq.264924) (:fv _uniq.265505) (:fv _uniq.265700) (:fv _uniq.26766... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c LinearOrderedField) (:fv _uniq.264906))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup) (... | (:app (:c AffineSubspace.WOppSide) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c StrictOrderedCommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV1))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":24545,"sourceStart":24540,"tag":"atom"},{"children":[{"name":"AffineSubspace.wOppSide_of_left_mem","semanticRole":"global","source":"wOppSide_of_left_mem","sourceEnd":24566,"sourceStart":24546,"tag":"identifier"},{"children":[{"contextInd... | [] | [{"source":"wOppSide_of_left_mem y h'","source_end":24571,"source_start":24546,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 152 | 55 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ff58f7b29a85e81b40a5ccbc8a9a696318f2086ace8279a200cabaa62ea52c04 | 8b74271ea674d7a6a3c18b30eb4403bc96aced6af2d8a5454e091a77ca57c2f2 | 5969c6b0d6b6058264b9f90146d8d4223d03d0794fe9e939f8090839df219ee4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 701 | AffineSubspace.wOppSide_iff_exists_left | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨p₁, h, h₁, h₂, h₃⟩ | case mpr.inr.intro.intro
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : LinearOrderedField R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y p₁ : P
h : p₁ ∈ s
h₁ : P
h₂ : h₁ ∈... | ((:c AffineSubspace.WOppSide) (:fv _uniq.264906) (:fv _uniq.264909) (:fv _uniq.264915) ((:c LinearOrderedCommRing.toStrictOrderedCommRing) (:fv _uniq.264906) ((:c LinearOrderedField.toLinearOrderedCommRing) (:fv _uniq.264906) (:fv _uniq.264921))) (:fv _uniq.264924) (:fv _uniq.265505) (:fv _uniq.265700) (:fv _uniq.26766... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c LinearOrderedField) (:fv _uniq.264906))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup) (... | (:app (:c AffineSubspace.WOppSide) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c StrictOrderedCommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV1))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":24584,"sourceStart":24579,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":24588,"sourceStart":24585,"tag":"atom"},{"children":[{"contextIndex":16,"semanticRole":"local","source":"p₁","sourceEnd":24592,"sourceStart":24588,"tag":"ident... | [] | [{"source":"⟨p₁, h, h₁, h₂, h₃⟩","source_end":24616,"source_start":24585,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.264906","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.264909","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 152 | 60 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 66341d79438025d2312ab0dd624e7f7ed89ddcc9ea34684e85779cb88d86ac3c | b270eec4ebe973497e2d1b5928b54e5332df3d9242a6d13a371e89d7549a4802 | c7a5b60382b6bd296f2aa9e585c34f424d8a6cdf6cee2159ec078ca3f2f95b19 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 702 | Int.neg_pred | Mathlib/Data/Int/Defs.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← Int.neg_eq_comm.mp (<a>Int.neg_succ</a> (-a)), <a>Int.neg_neg</a>] | a✝ b c d m n a : ℤ
⊢ -a.pred = (-a).succ | ((:c Eq) (:c Int) ((:c Neg.neg) (:c Int) (:c Int.instNegInt) ((:c Int.pred) (:fv _uniq.6453))) ((:c Int.succ) ((:c Neg.neg) (:c Int) (:c Int.instNegInt) (:fv _uniq.6453)))) | [{"name":"a✝","sexp":"(:c Int)"},{"name":"b","sexp":"(:c Int)"},{"name":"c","sexp":"(:c Int)"},{"name":"d","sexp":"(:c Int)"},{"name":"m","sexp":"(:c Int)"},{"name":"n","sexp":"(:c Int)"},{"name":"a","sexp":"(:c Int)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:app (:c Int.pred) (:arg :explicit 0 (:fv FV7)))))) (:arg :explicit 2 (:app (:c Int.succ) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6428","is_instance":false,"is_let":false,"name":"a✝","sexp":"(:c Int)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6430","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Int)"},{"binder_role":":implicit","context_inde... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":8201,"sourceStart":8199,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8203,"sourceStart":8202,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"sour... | [] | [{"source":"Int.neg_eq_comm.mp (neg_succ (-a))","source_end":8241,"source_start":8207,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Int.neg_neg","source_end":8254,"source_start":8243,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6428","is_instance":false,"is_let":false,"user_name":"a✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6430","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 113 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7b5adf34b79489bcd4cb235149f0f1dc644610063995e0a18d869ed816f19399 | 1812637edb99609f5613c96c0b44edad390de4c596876f1a806a8184414c957f | e1077185b7dd17a2080daacc59fa020a406ce57ad64fe0502fdb903d15bba041 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 703 | FractionalIdeal.coe_spanSingleton | Mathlib/RingTheory/FractionalIdeal/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>FractionalIdeal.spanSingleton</a>] | R : Type u_1
inst✝⁶ : CommRing R
S : Submonoid R
P : Type u_2
inst✝⁵ : CommRing P
inst✝⁴ : Algebra R P
loc : IsLocalization S P
R₁ : Type u_3
inst✝³ : CommRing R₁
K : Type u_4
inst✝² : Field K
inst✝¹ : Algebra R₁ K
inst✝ : IsFractionRing R₁ K
x : P
⊢ ↑(spanSingleton S x) = span R {x} | R : Type u_1
inst✝⁶ : CommRing R
S : Submonoid R
P : Type u_2
inst✝⁵ : CommRing P
inst✝⁴ : Algebra R P
loc : IsLocalization S P
R₁ : Type u_3
inst✝³ : CommRing R₁
K : Type u_4
inst✝² : Field K
inst✝¹ : Algebra R₁ K
inst✝ : IsFractionRing R₁ K
x : P
⊢ ↑⟨span R {x}, ⋯⟩ = span R {x} | ((:c Eq) ((:c Submodule) (:fv _uniq.392581) (:fv _uniq.392796) ((:c CommSemiring.toSemiring) (:fv _uniq.392581) ((:c CommRing.toCommSemiring) (:fv _uniq.392581) (:fv _uniq.392584))) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.392796) ((:c NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring) (:fv _u... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁶","sexp":"((:c CommRing) (:fv _uniq.392581))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.392581) ((:c MulZeroOneClass.toMulOneClass) (:fv _uniq.392581) ((:c NonAssocSemiring.toMulZeroOneClass) (:fv _uniq.392581) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.39... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV3))))) (:arg :instance 4 (:instance-of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.392581","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.392584","is_instance":true,"is_let":false,"name":"inst✝⁶","sexp":"(:app (:c CommRing) (:arg :expl... | {"children":[{"source":"rw","sourceEnd":26323,"sourceStart":26321,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":26325,"sourceStart":26324,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"FractionalIdeal.... | [] | [{"source":"spanSingleton","source_end":26338,"source_start":26325,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.392581","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.392584","is_instance":true,"is_let":false,"user_name":"inst✝⁶"},{"binder_role":":explicit","context_index":2,"inte... | 180 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3846ed443d8e28174ec022af77cc2233a8cad240519559a03309704449474134 | e5e377083abb07e8fb4048c6929a332b68b267bb53681e4983dc1a7e181e240d | 4c1068a9b7781702824c5fac415e02b07a3553e65bd27bca376030470830c279 | 7f52b601a9e1998e53e5ec5589b39d7c6bedbde57e1d8854413fb91b90599aa5 |
cat-searcher/leandojo-benchmark-4-random | test | 704 | FractionalIdeal.coe_spanSingleton | Mathlib/RingTheory/FractionalIdeal/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | R : Type u_1
inst✝⁶ : CommRing R
S : Submonoid R
P : Type u_2
inst✝⁵ : CommRing P
inst✝⁴ : Algebra R P
loc : IsLocalization S P
R₁ : Type u_3
inst✝³ : CommRing R₁
K : Type u_4
inst✝² : Field K
inst✝¹ : Algebra R₁ K
inst✝ : IsFractionRing R₁ K
x : P
⊢ ↑⟨span R {x}, ⋯⟩ = span R {x} | ((:c Eq) ((:c Submodule) (:fv _uniq.392581) (:fv _uniq.392796) ((:c CommSemiring.toSemiring) (:fv _uniq.392581) ((:c CommRing.toCommSemiring) (:fv _uniq.392581) (:fv _uniq.392584))) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.392796) ((:c NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring) (:fv _u... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁶","sexp":"((:c CommRing) (:fv _uniq.392581))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.392581) ((:c MulZeroOneClass.toMulOneClass) (:fv _uniq.392581) ((:c NonAssocSemiring.toMulZeroOneClass) (:fv _uniq.392581) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.39... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV3))))) (:arg :instance 4 (:instance-of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.392581","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.392584","is_instance":true,"is_let":false,"name":"inst✝⁶","sexp":"(:app (:c CommRing) (:arg :expl... | {"children":[{"source":"rfl","sourceEnd":26345,"sourceStart":26342,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":26345,"sourceStart":26342,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.392581","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.392584","is_instance":true,"is_let":false,"user_name":"inst✝⁶"},{"binder_role":":explicit","context_index":2,"inte... | 180 | 7 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | db9e5e0d2ae1ad0b0c0064c8531ab5be0f07d4c7717f44cc16dc18a2a5ff9451 | 7f52b601a9e1998e53e5ec5589b39d7c6bedbde57e1d8854413fb91b90599aa5 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 705 | MeasureTheory.setLIntegral_tilted | Mathlib/MeasureTheory/Measure/Tilted.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases hf : <a>AEMeasurable</a> f μ | α : Type u_1
mα : MeasurableSpace α
μ : Measure α
f✝ : α → ℝ
inst✝ : SFinite μ
f : α → ℝ
g : α → ℝ≥0∞
s : Set α
⊢ ∫⁻ (x : α) in s, g x ∂μ.tilted f = ∫⁻ (x : α) in s, ENNReal.ofReal (rexp (f x) / ∫ (x : α), rexp (f x) ∂μ) * g x ∂μ | case pos
α : Type u_1
mα : MeasurableSpace α
μ : Measure α
f✝ : α → ℝ
inst✝ : SFinite μ
f : α → ℝ
g : α → ℝ≥0∞
s : Set α
hf : AEMeasurable f μ
⊢ ∫⁻ (x : α) in s, g x ∂μ.tilted f = ∫⁻ (x : α) in s, ENNReal.ofReal (rexp (f x) / ∫ (x : α), rexp (f x) ∂μ) * g x ∂μ
case neg
α : Type u_1
mα : MeasurableSpace α
μ : Measure α
... | ((:c Eq) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.40119) (:fv _uniq.40122) ((:c MeasureTheory.Measure.restrict) (:fv _uniq.40119) (:fv _uniq.40122) ((:c MeasureTheory.Measure.tilted) (:fv _uniq.40119) (:fv _uniq.40122) (:fv _uniq.40131) (:fv _uniq.40494)) (:fv _uniq.40496)) (:lambda x (:fv _uniq.40119) ((:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.40119))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.40119) (:fv _uniq.40122))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.40119) (:c Real))"},{"name":"inst✝","sexp":"((:c MeasureTheory.SFinite) (:fv _uniq.40... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure.restrict) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure.... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"name":"mα","sexp":"(:app (:c MeasurableSpace) (:arg :explicit 0 ... | {"children":[{"source":"by_cases","sourceEnd":7330,"sourceStart":7322,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hf","sourceEnd":7333,"sourceStart":7331,"tag":"identifier"},{"source":":","sourceEnd":7335,"sourceStart":7334,"tag":"atom"}],"kind":"null","source":"hf :","sourceEnd":7335,"sourceSta... | [] | [{"source":"AEMeasurable f μ","source_end":7353,"source_start":7336,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"user_name":"mα"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 24 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6f0e37388609c7ca8e88d0d4fc68e63580fc9aeca0443329b5e46a072fa2a510 | 7900b00b278b1f4f354d540f29f253c543b035488fefba3dda23eed17a48c6ae | 1990c89bffd1f0f11e1fc1453f62147a12a4f91ba29c153fbf93b2605ec48aa3 | dfce0891911bc92c8b6d661eebefca8bec82d0b42af071ed3c1fcc55beb9b8b9 |
cat-searcher/leandojo-benchmark-4-random | test | 706 | MeasureTheory.setLIntegral_tilted | Mathlib/MeasureTheory/Measure/Tilted.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.Measure.tilted</a>, <a>MeasureTheory.setLIntegral_withDensity_eq_setLIntegral_mul_non_measurable₀'</a>] | case pos
α : Type u_1
mα : MeasurableSpace α
μ : Measure α
f✝ : α → ℝ
inst✝ : SFinite μ
f : α → ℝ
g : α → ℝ≥0∞
s : Set α
hf : AEMeasurable f μ
⊢ ∫⁻ (x : α) in s, g x ∂μ.tilted f = ∫⁻ (x : α) in s, ENNReal.ofReal (rexp (f x) / ∫ (x : α), rexp (f x) ∂μ) * g x ∂μ | case pos
α : Type u_1
mα : MeasurableSpace α
μ : Measure α
f✝ : α → ℝ
inst✝ : SFinite μ
f : α → ℝ
g : α → ℝ≥0∞
s : Set α
hf : AEMeasurable f μ
⊢ ∫⁻ (a : α) in s, ((fun x => ENNReal.ofReal (rexp (f x) / ∫ (x : α), rexp (f x) ∂μ)) * g) a ∂μ =
∫⁻ (x : α) in s, ENNReal.ofReal (rexp (f x) / ∫ (x : α), rexp (f x) ∂μ) * g... | ((:c Eq) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.40119) (:fv _uniq.40122) ((:c MeasureTheory.Measure.restrict) (:fv _uniq.40119) (:fv _uniq.40122) ((:c MeasureTheory.Measure.tilted) (:fv _uniq.40119) (:fv _uniq.40122) (:fv _uniq.40131) (:fv _uniq.40494)) (:fv _uniq.40496)) (:lambda x (:fv _uniq.40119) ((:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.40119))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.40119) (:fv _uniq.40122))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.40119) (:c Real))"},{"name":"inst✝","sexp":"((:c MeasureTheory.SFinite) (:fv _uniq.40... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure.restrict) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure.... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"name":"mα","sexp":"(:app (:c MeasurableSpace) (:arg :explicit 0 ... | {"children":[{"source":"rw","sourceEnd":7361,"sourceStart":7359,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7363,"sourceStart":7362,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MeasureTheory.Measur... | [] | [{"source":"Measure.tilted","source_end":7377,"source_start":7363,"syntax_kind":"ident"},{"source":"setLIntegral_withDensity_eq_setLIntegral_mul_non_measurable₀'","source_end":7442,"source_start":7379,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"user_name":"mα"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 24 | 9 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b235aef8f2eeb290c8f1e301af7f5eadd76c210fbb55d48a9e36859db1475bda | 4c3414921b6add36593a51bafdb572368519c5ce8e2bd7bd1ab6c1c79cf92fb9 | 9c1cc5c9d12aed22ed0a43540d541265bd2bb6bf2d145b7acd5b1b46de703f60 | 7159274117ad510649d031dd678294812e2110d7a51c51c4263527f159ae5705 |
cat-searcher/leandojo-benchmark-4-random | test | 707 | MeasureTheory.setLIntegral_tilted | Mathlib/MeasureTheory/Measure/Tilted.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Pi.mul_apply</a>] | case pos
α : Type u_1
mα : MeasurableSpace α
μ : Measure α
f✝ : α → ℝ
inst✝ : SFinite μ
f : α → ℝ
g : α → ℝ≥0∞
s : Set α
hf : AEMeasurable f μ
⊢ ∫⁻ (a : α) in s, ((fun x => ENNReal.ofReal (rexp (f x) / ∫ (x : α), rexp (f x) ∂μ)) * g) a ∂μ =
∫⁻ (x : α) in s, ENNReal.ofReal (rexp (f x) / ∫ (x : α), rexp (f x) ∂μ) * g... | ((:c Eq) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.40119) (:fv _uniq.40122) ((:c MeasureTheory.Measure.restrict) (:fv _uniq.40119) (:fv _uniq.40122) (:fv _uniq.40131) (:fv _uniq.40496)) (:lambda a (:fv _uniq.40119) ((:c HMul.hMul) (:forall _ (:fv _uniq.40119) (:c ENNReal)) (:forall _ (:fv _uniq.40119) (:c E... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.40119))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.40119) (:fv _uniq.40122))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.40119) (:c Real))"},{"name":"inst✝","sexp":"((:c MeasureTheory.SFinite) (:fv _uniq.40... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure.restrict) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"name":"mα","sexp":"(:app (:c MeasurableSpace) (:arg :explicit 0 ... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":7455,"sourceStart":7451,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":7460,"sourceStart":7456,"tag":"atom"}],"kind":"nu... | [] | [{"source":"Pi.mul_apply","source_end":7474,"source_start":7462,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"user_name":"mα"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 24 | 15 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 71206527b0afb864867a544ce3396c6f07e36e44cce4191ce24bc87a914501ee | b6a50613a58da013c2b7e30a978c68de92ce11a3f1332a7a60b35b9d8397e22b | 763bad5b1c675904f16ca5533042ee01cecd97599dcd6576b21dc67c8b57b095 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 708 | MeasureTheory.setLIntegral_tilted | Mathlib/MeasureTheory/Measure/Tilted.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>AEMeasurable.restrict</a> ?_ | case pos.hf
α : Type u_1
mα : MeasurableSpace α
μ : Measure α
f✝ : α → ℝ
inst✝ : SFinite μ
f : α → ℝ
g : α → ℝ≥0∞
s : Set α
hf : AEMeasurable f μ
⊢ AEMeasurable (fun x => ENNReal.ofReal (rexp (f x) / ∫ (x : α), rexp (f x) ∂μ)) (μ.restrict s) | case pos.hf
α : Type u_1
mα : MeasurableSpace α
μ : Measure α
f✝ : α → ℝ
inst✝ : SFinite μ
f : α → ℝ
g : α → ℝ≥0∞
s : Set α
hf : AEMeasurable f μ
⊢ AEMeasurable (fun x => ENNReal.ofReal (rexp (f x) / ∫ (x : α), rexp (f x) ∂μ)) μ | ((:c AEMeasurable) (:fv _uniq.40119) (:c ENNReal) (:c ENNReal.measurableSpace) (:fv _uniq.40122) (:lambda x (:fv _uniq.40119) ((:c ENNReal.ofReal) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Real.exp) ((:fv _uniq... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.40119))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.40119) (:fv _uniq.40122))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.40119) (:c Real))"},{"name":"inst✝","sexp":"((:c MeasureTheory.SFinite) (:fv _uniq.40... | (:app (:c AEMeasurable) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c ENNReal))))) (:arg :implicit 3) (:arg :explicit 4 (:lambda x :explicit (:fv FV0) (:app (:c ENNReal.ofReal) (:arg :explicit 0 (:app (:c HDiv.hDiv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"name":"mα","sexp":"(:app (:c MeasurableSpace) (:arg :explicit 0 ... | {"children":[{"source":"refine","sourceEnd":7489,"sourceStart":7483,"tag":"atom"},{"children":[{"name":"AEMeasurable.restrict","semanticRole":"global","source":"AEMeasurable.restrict","sourceEnd":7511,"sourceStart":7490,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":7513,"sourceStart":7512,"tag... | [] | [{"source":"AEMeasurable.restrict ?_","source_end":7514,"source_start":7490,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"user_name":"mα"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 24 | 22 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 81d3e37a36d2b7573528f618bf7cea02fe7090380060196861e96a5c2e3b7cec | 4ab571840a5a09b23ee415b710f3adab7cf5841f26bff217671112dd0e50792b | 8c728cc72abe9f4e750a8e1c3083d2063f0a0d9b0410a3d76869e1b4eadaef79 | 433e3a68706cf16bfa731a065a6e374ba83a6bddec42e3dcec265ba34797cb6f |
cat-searcher/leandojo-benchmark-4-random | test | 709 | MeasureTheory.setLIntegral_tilted | Mathlib/MeasureTheory/Measure/Tilted.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ((measurable_exp.comp_aemeasurable hf).<a>AEMeasurable.div_const</a> _).<a>AEMeasurable.ennreal_ofReal</a> | case pos.hf
α : Type u_1
mα : MeasurableSpace α
μ : Measure α
f✝ : α → ℝ
inst✝ : SFinite μ
f : α → ℝ
g : α → ℝ≥0∞
s : Set α
hf : AEMeasurable f μ
⊢ AEMeasurable (fun x => ENNReal.ofReal (rexp (f x) / ∫ (x : α), rexp (f x) ∂μ)) μ | ((:c AEMeasurable) (:fv _uniq.40119) (:c ENNReal) (:c ENNReal.measurableSpace) (:fv _uniq.40122) (:lambda x (:fv _uniq.40119) ((:c ENNReal.ofReal) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Real.exp) ((:fv _uniq... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.40119))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.40119) (:fv _uniq.40122))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.40119) (:c Real))"},{"name":"inst✝","sexp":"((:c MeasureTheory.SFinite) (:fv _uniq.40... | (:app (:c AEMeasurable) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c ENNReal))))) (:arg :implicit 3) (:arg :explicit 4 (:lambda x :explicit (:fv FV0) (:app (:c ENNReal.ofReal) (:arg :explicit 0 (:app (:c HDiv.hDiv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"name":"mα","sexp":"(:app (:c MeasurableSpace) (:arg :explicit 0 ... | {"children":[{"source":"exact","sourceEnd":7526,"sourceStart":7521,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":7528,"sourceStart":7527,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":7529,"sourceStart":7528,"tag":"atom"},{"children":[{"source":"measurable_exp.comp_ae... | [] | [{"source":"((measurable_exp.comp_aemeasurable hf).div_const _).ennreal_ofReal","source_end":7593,"source_start":7527,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"user_name":"mα"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 24 | 23 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 766ea8feb8c19c9ee5a917d9b8a9cfc57fa0352dcb70b0555a820f6164e941c0 | 433e3a68706cf16bfa731a065a6e374ba83a6bddec42e3dcec265ba34797cb6f | b9a30a14fe41186e850e90b66608b133475933f844448a353b638c1feae4a062 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 710 | MeasureTheory.setLIntegral_tilted | Mathlib/MeasureTheory/Measure/Tilted.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards | case pos.h'f
α : Type u_1
mα : MeasurableSpace α
μ : Measure α
f✝ : α → ℝ
inst✝ : SFinite μ
f : α → ℝ
g : α → ℝ≥0∞
s : Set α
hf : AEMeasurable f μ
⊢ ∀ᵐ (x : α) ∂μ.restrict s, ENNReal.ofReal (rexp (f x) / ∫ (x : α), rexp (f x) ∂μ) < ⊤ | case pos.h'f.h
α : Type u_1
mα : MeasurableSpace α
μ : Measure α
f✝ : α → ℝ
inst✝ : SFinite μ
f : α → ℝ
g : α → ℝ≥0∞
s : Set α
hf : AEMeasurable f μ
⊢ ∀ (a : α), ENNReal.ofReal (rexp (f a) / ∫ (x : α), rexp (f x) ∂μ) < ⊤ | ((:c Filter.Eventually) (:fv _uniq.40119) (:lambda x (:fv _uniq.40119) ((: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 CompletelyDistribL... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.40119))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.40119) (:fv _uniq.40122))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.40119) (:c Real))"},{"name":"inst✝","sexp":"((:c MeasureTheory.SFinite) (:fv _uniq.40... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (: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 ENNReal.ofReal) (:arg :explicit 0 (:app (:c H... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"name":"mα","sexp":"(:app (:c MeasurableSpace) (:arg :explicit 0 ... | {"children":[{"source":"filter_upwards","sourceEnd":7615,"sourceStart":7601,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.filterUpwards","source":"filter_upwards",... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40119","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40122","is_instance":false,"is_let":false,"user_name":"mα"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 24 | 28 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2cd48d5ead40e77ca8b51745c270ce0758b3adb301d963530a753803032e58ff | d4532e986008c6765dd24e19aa6e9bcdb7b47150d51d276a5a8de9c4f4747fa0 | 33333af2b5c573cd08e7dd2ae3b8b65fda16c82fd02aa8fbee4b0d4327295033 | 8e2fd4636e4bb4bf41f279bf534d7e4ae8596da3e114ce474b102efc3f12aa3a |
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