dataset stringclasses 1
value | split stringclasses 1
value | row_index int64 0 4.5k | theorem stringlengths 7 81 | file_path stringclasses 723
values | repo_url stringclasses 1
value | repo_commit stringclasses 1
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
value | model_pantograph_commit stringclasses 1
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 | 4,312 | MeasureTheory.AEStronglyMeasurable.ae_integrable_condKernel_iff | Mathlib/Probability/Kernel/Disintegration/Integral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.Measure.integrable_compProd_iff</a> hf] | α : Type u_1
Ω : Type u_2
E : Type u_3
F : Type u_4
mα : MeasurableSpace α
inst✝⁶ : MeasurableSpace Ω
inst✝⁵ : StandardBorelSpace Ω
inst✝⁴ : Nonempty Ω
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace ℝ E
inst✝¹ : NormedAddCommGroup F
ρ : Measure (α × Ω)
inst✝ : IsFiniteMeasure ρ
f : α × Ω → F
hf : AEStronglyMeasurab... | ((:c Iff) ((:c And) ((:c Filter.Eventually) (:fv _uniq.56916) (:lambda a (:fv _uniq.56916) ((:c MeasureTheory.Integrable) (:fv _uniq.56925) (:fv _uniq.57060) (:fv _uniq.56919) (:fv _uniq.56931) (:lambda ω (:fv _uniq.56919) ((:fv _uniq.58381) ((:c Prod.mk) (:fv _uniq.56916) (:fv _uniq.56919) 1 0))) ((:c DFunLike.coe) ((... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"Ω","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"F","sexp":"(:sort (+ u_4 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.56916))"},{"name":"inst✝⁶","sexp":"((:c MeasurableSpace) (:fv _uniq.56919))"},{"name":"inst✝⁵","sexp":"((... | (:app (:c Iff) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda a :explicit (:fv FV0) (:app (:c MeasureTheory.Integrable) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.56916","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.56919","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":13412,"sourceStart":13410,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13414,"sourceStart":13413,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Mea... | [] | [{"source":"Measure.integrable_compProd_iff hf","source_end":13448,"source_start":13414,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.56916","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.56919","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 72 | 12 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 02974b4ad1669b2cef47d072f0b079627cf3376f9bc1368abb033a5da51dcf12 | 565d78ff9744394427e3142ae8e8437cfaa554d2aa6e2ffff88eba0fb048288e | 5bd86d356652cc6ecb26cd3a5c587b8f03dee6aeddf12dc6d05b4e3f5afee64d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,313 | smul_inv_smul | Mathlib/GroupTheory/GroupAction/Group.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>smul_smul</a>, <a>mul_right_inv</a>, <a>one_smul</a>] | α : Type u
β : Type v
γ : Type w
inst✝¹ : Group α
inst✝ : MulAction α β
c : α
x : β
⊢ c • c⁻¹ • x = x | ((:c Eq) (:fv _uniq.1243) ((:c HSMul.hSMul) (:fv _uniq.1241) (:fv _uniq.1243) (:fv _uniq.1243) ((:c instHSMul) (:fv _uniq.1241) (:fv _uniq.1243) ((:c MulAction.toSMul) (:fv _uniq.1241) (:fv _uniq.1243) ((:c DivInvMonoid.toMonoid) (:fv _uniq.1241) ((:c Group.toDivInvMonoid) (:fv _uniq.1241) (:fv _uniq.1248))) (:fv _uniq... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.1241))"},{"name":"inst✝","sexp":"((:c MulAction) (:fv _uniq.1241) (:fv _uniq.1243) ((:c DivInvMonoid.toMonoid) (:fv _uniq.1241) ((:c Group.toDivInvMonoid) (:... | (: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.1241","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1243","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":1038,"sourceStart":1036,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1040,"sourceStart":1039,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"smul_smul","source_end":1049,"source_start":1040,"syntax_kind":"ident"},{"source":"mul_right_inv","source_end":1064,"source_start":1051,"syntax_kind":"ident"},{"source":"one_smul","source_end":1074,"source_start":1066,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1241","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1243","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 10 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f55906fd92471ee289c03cddce873e3783c9ab677f5aa8f8547ac9a1d4f90804 | 3475aae6071091a10c616fa548f80c8e5ceee5f70235db5b511052ee52b15373 | 6a1d0d52d1b87c224d52fa12f2fb6bc0f6ad566ed88046b6f2f2d881a06804f0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,314 | RingHom.pNilradical_le_ker_of_perfectRing | Mathlib/FieldTheory/IsPerfectClosure.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨n, h⟩ := <a>mem_pNilradical</a>.1 h | K : Type u_1
L : Type u_2
M : Type u_3
N : Type u_4
inst✝⁶ : CommSemiring K
inst✝⁵ : CommSemiring L
inst✝⁴ : CommSemiring M
i : K →+* L
j : K →+* M
f : L →+* M
p : ℕ
inst✝³ : ExpChar K p
inst✝² : ExpChar L p
inst✝¹ : ExpChar M p
inst✝ : PerfectRing L p
x : K
h : x ∈ pNilradical K p
⊢ x ∈ ker i | case intro
K : Type u_1
L : Type u_2
M : Type u_3
N : Type u_4
inst✝⁶ : CommSemiring K
inst✝⁵ : CommSemiring L
inst✝⁴ : CommSemiring M
i : K →+* L
j : K →+* M
f : L →+* M
p : ℕ
inst✝³ : ExpChar K p
inst✝² : ExpChar L p
inst✝¹ : ExpChar M p
inst✝ : PerfectRing L p
x : K
h✝ : x ∈ pNilradical K p
n : ℕ
h : x ^ p ^ n = 0
⊢... | ((:c Membership.mem) (:fv _uniq.40038) ((:c Submodule) (:fv _uniq.40038) (:fv _uniq.40038) ((:c CommSemiring.toSemiring) (:fv _uniq.40038) (:fv _uniq.40050)) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.40038) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.40038) ((:c Semiring.toNonAssocSem... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"N","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁶","sexp":"((:c CommSemiring) (:fv _uniq.40038))"},{"name":"inst✝⁵","sexp":"((:c CommSemiring) (:fv _uniq.40041))"},{"name":"inst✝⁴","sexp":"((:c... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40038","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40041","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"obtain","sourceEnd":9022,"sourceStart":9016,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":9026,"sourceStart":9023,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"n","sourceEnd":9... | [] | [{"source":"mem_pNilradical.1 h","source_end":9056,"source_start":9037,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨n, h⟩","source_end":9033,"source_start":9023,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40038","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40041","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 27 | 4 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5326a9663f014410efd394bc4b926614acdc905d0b730fe588a395fb30e39cf2 | bfe598e364d74a6fc58a6387230b001fd3c4b979c73bcd4af16a9639bcde3ab3 | 1cf82a6d340ba0a7d0b78189bfdd8d055d7f7de11d6b090d3c01829658f57caf | b5fc8a8c42d64cf4d8fca61c96ac9b46734e3e4daf5839da5a9b9eb7c7a4b7e9 |
cat-searcher/leandojo-benchmark-4-random | test | 4,315 | RingHom.pNilradical_le_ker_of_perfectRing | Mathlib/FieldTheory/IsPerfectClosure.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | replace h := congr((<a>iterateFrobeniusEquiv</a> L p n).<a>RingEquiv.symm</a> (i $h)) | case intro
K : Type u_1
L : Type u_2
M : Type u_3
N : Type u_4
inst✝⁶ : CommSemiring K
inst✝⁵ : CommSemiring L
inst✝⁴ : CommSemiring M
i : K →+* L
j : K →+* M
f : L →+* M
p : ℕ
inst✝³ : ExpChar K p
inst✝² : ExpChar L p
inst✝¹ : ExpChar M p
inst✝ : PerfectRing L p
x : K
h✝ : x ∈ pNilradical K p
n : ℕ
h : x ^ p ^ n = 0
⊢... | case intro
K : Type u_1
L : Type u_2
M : Type u_3
N : Type u_4
inst✝⁶ : CommSemiring K
inst✝⁵ : CommSemiring L
inst✝⁴ : CommSemiring M
i : K →+* L
j : K →+* M
f : L →+* M
p : ℕ
inst✝³ : ExpChar K p
inst✝² : ExpChar L p
inst✝¹ : ExpChar M p
inst✝ : PerfectRing L p
x : K
h✝ : x ∈ pNilradical K p
n : ℕ
h : (iterateFrobeni... | ((:c Membership.mem) (:fv _uniq.40038) ((:c Submodule) (:fv _uniq.40038) (:fv _uniq.40038) ((:c CommSemiring.toSemiring) (:fv _uniq.40038) (:fv _uniq.40050)) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.40038) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.40038) ((:c Semiring.toNonAssocSem... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"N","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁶","sexp":"((:c CommSemiring) (:fv _uniq.40038))"},{"name":"inst✝⁵","sexp":"((:c CommSemiring) (:fv _uniq.40041))"},{"name":"inst✝⁴","sexp":"((:c... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40038","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40041","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"replace","sourceEnd":9066,"sourceStart":9059,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":9068,"sourceStart":9067,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":9068,"sourceStart":9067,"tag":"node"},{... | [] | [{"source":"congr((iterateFrobeniusEquiv L p n).symm (i $h))","source_end":9120,"source_start":9072,"syntax_kind":"Mathlib.Tactic.TermCongr.termCongr"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40038","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40041","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 27 | 5 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d6f48c9e11a213a87c04efe68a87f4c8810d17c4d9641991a609ae0a0a2650e7 | b5fc8a8c42d64cf4d8fca61c96ac9b46734e3e4daf5839da5a9b9eb7c7a4b7e9 | 4eb0309b8f8680479b30cccc1db488fd11a9d19f6974e5d399b68bc7f2770aff | b242f1c92579703457fec84691d9bc6e78712caee9b18b830de08d38cd40a4e5 |
cat-searcher/leandojo-benchmark-4-random | test | 4,316 | RingHom.pNilradical_le_ker_of_perfectRing | Mathlib/FieldTheory/IsPerfectClosure.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>map_pow</a>, ← <a>iterateFrobenius_def</a>, ← <a>iterateFrobeniusEquiv_apply</a>, <a>RingEquiv.symm_apply_apply</a>, <a>map_zero</a>, <a>map_zero</a>] at h | case intro
K : Type u_1
L : Type u_2
M : Type u_3
N : Type u_4
inst✝⁶ : CommSemiring K
inst✝⁵ : CommSemiring L
inst✝⁴ : CommSemiring M
i : K →+* L
j : K →+* M
f : L →+* M
p : ℕ
inst✝³ : ExpChar K p
inst✝² : ExpChar L p
inst✝¹ : ExpChar M p
inst✝ : PerfectRing L p
x : K
h✝ : x ∈ pNilradical K p
n : ℕ
h : (iterateFrobeni... | ((:c Membership.mem) (:fv _uniq.40038) ((:c Submodule) (:fv _uniq.40038) (:fv _uniq.40038) ((:c CommSemiring.toSemiring) (:fv _uniq.40038) (:fv _uniq.40050)) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.40038) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.40038) ((:c Semiring.toNonAssocSem... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"N","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁶","sexp":"((:c CommSemiring) (:fv _uniq.40038))"},{"name":"inst✝⁵","sexp":"((:c CommSemiring) (:fv _uniq.40041))"},{"name":"inst✝⁴","sexp":"((:c... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40038","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40041","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rwa","sourceEnd":9126,"sourceStart":9123,"tag":"atom"},{"children":[{"source":"[","sourceEnd":9128,"sourceStart":9127,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"map_pow","semanticRole":"global","source":"map_pow","sourceEnd":9135,"sour... | [] | [{"source":"map_pow","source_end":9135,"source_start":9128,"syntax_kind":"ident"},{"source":"h","source_end":9252,"source_start":9251,"syntax_kind":"ident"},{"source":"iterateFrobenius_def","source_end":9161,"source_start":9141,"syntax_kind":"ident"},{"source":"iterateFrobeniusEquiv_apply","source_end":9194,"source_sta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40038","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.40041","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 27 | 6 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ab82657c5718c99d0f358d33fb7fdf3fa4bfcddbe99310c262f722d874716fea | b242f1c92579703457fec84691d9bc6e78712caee9b18b830de08d38cd40a4e5 | bfdec8937b3cb10db2b0548d0c7a47db209dcb9b8ad5b1de28c448d045a6a82f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,317 | infPrime_iff_infIrred | Mathlib/Order/Irreducible.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [← <a>sup_eq_left</a>, <a>sup_inf_left</a>] | ι : Type u_1
α : Type u_2
inst✝ : DistribLattice α
a b✝ c✝ : α
h : ∀ ⦃b c : α⦄, b ⊓ c = a → b = a ∨ c = a
b c : α
⊢ b ⊓ c ≤ a → b ≤ a ∨ c ≤ a | ι : Type u_1
α : Type u_2
inst✝ : DistribLattice α
a b✝ c✝ : α
h : ∀ ⦃b c : α⦄, b ⊓ c = a → b = a ∨ c = a
b c : α
⊢ (a ⊔ b) ⊓ (a ⊔ c) = a → a ⊔ b = a ∨ a ⊔ c = a | (:forall _ ((:c LE.le) (:fv _uniq.31466) ((:c Preorder.toLE) (:fv _uniq.31466) ((:c PartialOrder.toPreorder) (:fv _uniq.31466) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.31466) ((:c Lattice.toSemilatticeInf) (:fv _uniq.31466) ((:c DistribLattice.toLattice) (:fv _uniq.31466) (:fv _uniq.31469)))))) ((:c Inf.inf) (:fv... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DistribLattice) (:fv _uniq.31466))"},{"name":"a","sexp":"(:fv _uniq.31466)"},{"name":"b✝","sexp":"(:fv _uniq.31466)"},{"name":"c✝","sexp":"(:fv _uniq.31466)"},{"name":"h","sexp":"(:forall b (:fv _uniq.31466) (:... | (:forall _ :explicit (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Inf.inf) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Inf) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31463","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31466","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"simp_rw","sourceEnd":10906,"sourceStart":10899,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10908,"sourceStart":10907,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":10911,"sou... | [] | [{"source":"sup_eq_left","source_end":10923,"source_start":10912,"syntax_kind":"ident"},{"source":"sup_inf_left","source_end":10937,"source_start":10925,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31463","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31466","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 121 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 96aae9ca202ed30c519fa0c167654d26da80ecc61a337bb1134f85fc4128bdbe | 65abf74b48200f8ef26c1242274039f300e54c283b1adea47931bb2a7b21a7ab | 65f615e47274f7bfff0deb7090244fe078f9c1604f1c6da3ee28bffa2a7e4c38 | 5a58a8ad0ad31d9dd5fd2dc14064af33c8a16d364f7930f52343ddaaa03f9bdd |
cat-searcher/leandojo-benchmark-4-random | test | 4,318 | infPrime_iff_infIrred | Mathlib/Order/Irreducible.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact @h _ _ | ι : Type u_1
α : Type u_2
inst✝ : DistribLattice α
a b✝ c✝ : α
h : ∀ ⦃b c : α⦄, b ⊓ c = a → b = a ∨ c = a
b c : α
⊢ (a ⊔ b) ⊓ (a ⊔ c) = a → a ⊔ b = a ∨ a ⊔ c = a | (:forall _ ((:c Eq) (:fv _uniq.31466) ((:c Inf.inf) (:fv _uniq.31466) ((:c Lattice.toInf) (:fv _uniq.31466) ((:c DistribLattice.toLattice) (:fv _uniq.31466) (:fv _uniq.31469))) ((:c Sup.sup) (:fv _uniq.31466) ((:c SemilatticeSup.toSup) (:fv _uniq.31466) ((:c Lattice.toSemilatticeSup) (:fv _uniq.31466) ((:c DistribLatti... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DistribLattice) (:fv _uniq.31466))"},{"name":"a","sexp":"(:fv _uniq.31466)"},{"name":"b✝","sexp":"(:fv _uniq.31466)"},{"name":"c✝","sexp":"(:fv _uniq.31466)"},{"name":"h","sexp":"(:forall b (:fv _uniq.31466) (:... | (:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Inf.inf) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Inf) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Sup.sup) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31463","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31466","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":10945,"sourceStart":10940,"tag":"atom"},{"children":[{"children":[{"source":"@","sourceEnd":10947,"sourceStart":10946,"tag":"atom"},{"contextIndex":7,"semanticRole":"local","source":"h","sourceEnd":10948,"sourceStart":10947,"tag":"identifier"}],"kind":"Lean.Parser.Term.explici... | [] | [{"source":"@h _ _","source_end":10952,"source_start":10946,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31463","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31466","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 121 | 9 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3a0a72efbc90bf036610b15a90d8b0c77f72f59816185f9e7ea530e0d91e3e78 | 5a58a8ad0ad31d9dd5fd2dc14064af33c8a16d364f7930f52343ddaaa03f9bdd | fa25e7d2af4a4ca57060750ea43492296bc0eac9cd16a6cbd8ca8c70c07254fb | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,319 | Nat.count_one | Mathlib/Data/Nat/Count.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Nat.count_succ</a>] | p : ℕ → Prop
inst✝ : DecidablePred p
⊢ count p 1 = if p 0 then 1 else 0 | ((:c Eq) (:c Nat) ((:c Nat.count) (:fv _uniq.7430) (:fv _uniq.7439) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) ((:c ite) (:c Nat) ((:fv _uniq.7430) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) ((:fv _uniq.7439) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)... | [{"name":"p","sexp":"(:forall _ (:c Nat) (:sort 0))"},{"name":"inst✝","sexp":"((:c DecidablePred) (:c Nat) (:fv _uniq.7430))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.count) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c DecidablePred) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV0))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :ex... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.7430","is_instance":false,"is_let":false,"name":"p","sexp":"(:forall _ :explicit (:c Nat) (:sort Prop))"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.7439","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":3238,"sourceStart":3234,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"count_succ","source_end":3250,"source_start":3240,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.7430","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.7439","is_instance":true,"is_let":false,"user_name":"inst✝"}] | 27 | 2 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4ebe30f3f1d8c4b7026a9afc891a3f1011763b083951df7036d40b56378bdb96 | 2799800f5d39270cfa3cbc7c473e961928d83b135a0bfdda78c3ae63c957bbe4 | 19f915410030168dfb076ffe3aa4defb9cca08d921aa1cd1e025a97e6c560d2f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,320 | TensorProduct.liftAux.smul | Mathlib/LinearAlgebra/TensorProduct/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [← <a>TensorProduct.tmul_smul</a>, <a>TensorProduct.liftAux_tmul</a>, (f p).<a>LinearMap.map_smul</a>] | R : Type u_1
inst✝¹⁶ : CommSemiring R
R' : Type u_2
inst✝¹⁵ : Monoid R'
R'' : Type u_3
inst✝¹⁴ : Semiring R''
M : Type u_4
N : Type u_5
P : Type u_6
Q : Type u_7
S : Type u_8
T : Type u_9
inst✝¹³ : AddCommMonoid M
inst✝¹² : AddCommMonoid N
inst✝¹¹ : AddCommMonoid P
inst✝¹⁰ : AddCommMonoid Q
inst✝⁹ : AddCommMonoid S
ins... | ((:c Eq) (:fv _uniq.508986) ((:c DFunLike.coe) ((:c AddMonoidHom) ((:c TensorProduct) (:fv _uniq.508962) (:fv _uniq.508965) (:fv _uniq.508980) (:fv _uniq.508983) (:fv _uniq.508998) (:fv _uniq.509001) (:fv _uniq.509156) (:fv _uniq.509266)) (:fv _uniq.508986) ((:c TensorProduct.addZeroClass) (:fv _uniq.508962) (:fv _uniq... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁶","sexp":"((:c CommSemiring) (:fv _uniq.508962))"},{"name":"R'","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁵","sexp":"((:c Monoid) (:fv _uniq.508968))"},{"name":"R''","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹⁴","sexp":"((:c Semiring) (:fv _uniq.508974))"},{"nam... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV8)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AddMonoidHom) (:arg :explicit 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.508962","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.508965","is_instance":true,"is_let":false,"name":"inst✝¹⁶","sexp":"(:app (:c CommSemiring) (:arg ... | {"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":22576,"sourceStart":22569,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":22578,"sourceStart":22577,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children... | [] | [{"source":"tmul_smul","source_end":22591,"source_start":22582,"syntax_kind":"ident"},{"source":"liftAux_tmul","source_end":22605,"source_start":22593,"syntax_kind":"ident"},{"source":"(f p).map_smul","source_end":22621,"source_start":22607,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.508962","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.508965","is_instance":true,"is_let":false,"user_name":"inst✝¹⁶"},{"binder_role":":implicit","context_index":2,"int... | 147 | 2 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9e0f81a8bc6d2bd067ddacf3fb58650fbd3ab37a1710272faa1c4b21d9bc91dc | 11af66be065e1f8902cb1727c7c08a9c66eca513ab538b3b0f8426be12a95ba6 | b018bfbed832e0ccc3b806c4f3c85815a2e19980f0c88a5c98f17de7af9166e7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,321 | TensorProduct.liftAux.smul | Mathlib/LinearAlgebra/TensorProduct/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>smul_add</a>, (<a>TensorProduct.liftAux</a> f).<a>AddMonoidHom.map_add</a>, ih1, ih2, <a>smul_add</a>] | R : Type u_1
inst✝¹⁶ : CommSemiring R
R' : Type u_2
inst✝¹⁵ : Monoid R'
R'' : Type u_3
inst✝¹⁴ : Semiring R''
M : Type u_4
N : Type u_5
P : Type u_6
Q : Type u_7
S : Type u_8
T : Type u_9
inst✝¹³ : AddCommMonoid M
inst✝¹² : AddCommMonoid N
inst✝¹¹ : AddCommMonoid P
inst✝¹⁰ : AddCommMonoid Q
inst✝⁹ : AddCommMonoid S
ins... | ((:c Eq) (:fv _uniq.508986) ((:c DFunLike.coe) ((:c AddMonoidHom) ((:c TensorProduct) (:fv _uniq.508962) (:fv _uniq.508965) (:fv _uniq.508980) (:fv _uniq.508983) (:fv _uniq.508998) (:fv _uniq.509001) (:fv _uniq.509156) (:fv _uniq.509266)) (:fv _uniq.508986) ((:c TensorProduct.addZeroClass) (:fv _uniq.508962) (:fv _uniq... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁶","sexp":"((:c CommSemiring) (:fv _uniq.508962))"},{"name":"R'","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁵","sexp":"((:c Monoid) (:fv _uniq.508968))"},{"name":"R''","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹⁴","sexp":"((:c Semiring) (:fv _uniq.508974))"},{"nam... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV8)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AddMonoidHom) (:arg :explicit 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.508962","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.508965","is_instance":true,"is_let":false,"name":"inst✝¹⁶","sexp":"(:app (:c CommSemiring) (:arg ... | {"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":22657,"sourceStart":22650,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":22659,"sourceStart":22658,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source... | [] | [{"source":"smul_add","source_end":22667,"source_start":22659,"syntax_kind":"ident"},{"source":"(liftAux f).map_add","source_end":22688,"source_start":22669,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"ih1","source_end":22693,"source_start":22690,"syntax_kind":"ident"},{"source":"ih2","source_end":22698,"source_st... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.508962","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.508965","is_instance":true,"is_let":false,"user_name":"inst✝¹⁶"},{"binder_role":":implicit","context_index":2,"int... | 147 | 11 | exact | true | 1 | 33 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fa9ee385b9aac501e200db990ec166cd0209de340f421a3609006c5ef024ed95 | 7eac4113f52567d7682461359a282b65aefbea107c9a3444b8fb0c233da16396 | 4ce1b86d0b74521dff4a6b66cd33179f783e0dd59371e686988c737631b3395f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,322 | NumberField.mem_span_integralBasis | Mathlib/NumberTheory/NumberField/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>NumberField.integralBasis</a>, <a>Basis.localizationLocalization_span</a>, <a>LinearMap.mem_range</a>, <a>IsScalarTower.coe_toAlgHom'</a>, <a>RingHom.mem_range</a>] | K : Type u_1
L : Type u_2
inst✝¹ : Field K
inst✝ : Field L
nf : NumberField K
x : K
⊢ x ∈ Submodule.span ℤ (Set.range ⇑(integralBasis K)) ↔ x ∈ (algebraMap (𝓞 K) K).range | ((:c Iff) ((:c Membership.mem) (:fv _uniq.108635) ((:c Submodule) (:c Int) (:fv _uniq.108635) (:c Int.instSemiring) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.108635) ((:c NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.108635) ((:c NonUnitalNonAssocCommRing.toNonUnitalNonAssocComm... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.108635))"},{"name":"inst✝","sexp":"((:c Field) (:fv _uniq.108638))"},{"name":"nf","sexp":"((:c NumberField) (:fv _uniq.108635) (:fv _uniq.108641))"},{"name":"x","sexp":"(:fv _uniq.108635)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:c Int)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Int))))) (:arg :instance 3 (:instance-of (:app (:c A... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.108635","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.108638","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":11484,"sourceStart":11482,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11486,"sourceStart":11485,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"integralBasis","source_end":11499,"source_start":11486,"syntax_kind":"ident"},{"source":"Basis.localizationLocalization_span","source_end":11536,"source_start":11501,"syntax_kind":"ident"},{"source":"LinearMap.mem_range","source_end":11557,"source_start":11538,"syntax_kind":"ident"},{"source":"IsScalarTower... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.108635","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.108638","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal... | 82 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4c9d372bb9442c0311f6bada01ee36ee33fb63bde2119cdf515e66cda3fc5ab7 | f8ac5bd73363464ad50d24c6751115ea351aa0b7d223cc46dc8220a847d3817b | 5f8f35769dd9db99e41c342fe59ea1fa01f1be03d2c6766507470987e562b925 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,323 | MvPolynomial.weightedHomogeneousComponent_eq_zero | Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | classical rw [<a>MvPolynomial.weightedHomogeneousComponent_apply</a>, <a>Finset.sum_eq_zero</a>] intro d hd rw [<a>Finset.mem_filter</a>] at hd exfalso apply <a>lt_irrefl</a> n nth_rw 1 [← hd.2] exact <a>lt_of_le_of_lt</a> (<a>MvPolynomial.le_weightedTotalDegree</a> w hd.1) h | R : Type u_1
M : Type u_2
inst✝³ : CommSemiring R
σ : Type u_3
inst✝² : AddCommMonoid M
w : σ → M
n : M
φ ψ : MvPolynomial σ R
inst✝¹ : SemilatticeSup M
inst✝ : OrderBot M
h : weightedTotalDegree w φ < n
⊢ (weightedHomogeneousComponent w n) φ = 0 | ((:c Eq) ((:c MvPolynomial) (:fv _uniq.81554) (:fv _uniq.81545) (:fv _uniq.81551)) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.81545) (:fv _uniq.81545) ((:c CommSemiring.toSemiring) (:fv _uniq.81545) (:fv _uniq.81551)) ((:c CommSemiring.toSemiring) (:fv _uniq.81545) (:fv _uniq.81551)) ((:c RingHom.id) (:fv _uniq.8154... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommSemiring) (:fv _uniq.81545))"},{"name":"σ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c AddCommMonoid) (:fv _uniq.81548))"},{"name":"w","sexp":"(:forall _ (:fv _uniq.81554) (:fv _uniq.81548))"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81545","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81548","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"classical","sourceEnd":18595,"sourceStart":18586,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":18600,"sourceStart":18598,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"sourc... | [] | [{"source":"weightedHomogeneousComponent_apply","source_end":18636,"source_start":18602,"syntax_kind":"ident"},{"source":"sum_eq_zero","source_end":18649,"source_start":18638,"syntax_kind":"ident"},{"source":"Finset.mem_filter","source_end":18687,"source_start":18670,"syntax_kind":"ident"},{"source":"hd","source_end":1... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81545","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81548","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 94 | 2 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8a4b6a0805f19d21fad88189504fe4471c7d81e98656e9dcd8b4415a1704702c | 25c8fe94dd2b97d0b1d7af92f7aac38f2d69dfc7b6a87a3b460ff9d5c7804194 | 3345c17776b32650f6d33ec240dc8c50de54b3865416b015a730d72c361f52ea | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,324 | MvPolynomial.weightedHomogeneousComponent_eq_zero | Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MvPolynomial.weightedHomogeneousComponent_apply</a>, <a>Finset.sum_eq_zero</a>] | R : Type u_1
M : Type u_2
inst✝³ : CommSemiring R
σ : Type u_3
inst✝² : AddCommMonoid M
w : σ → M
n : M
φ ψ : MvPolynomial σ R
inst✝¹ : SemilatticeSup M
inst✝ : OrderBot M
h : weightedTotalDegree w φ < n
⊢ (weightedHomogeneousComponent w n) φ = 0 | R : Type u_1
M : Type u_2
inst✝³ : CommSemiring R
σ : Type u_3
inst✝² : AddCommMonoid M
w : σ → M
n : M
φ ψ : MvPolynomial σ R
inst✝¹ : SemilatticeSup M
inst✝ : OrderBot M
h : weightedTotalDegree w φ < n
⊢ ∀ x ∈ Finset.filter (fun d => (weightedDegree w) d = n) φ.support, (monomial x) (coeff x φ) = 0 | ((:c Eq) ((:c MvPolynomial) (:fv _uniq.81554) (:fv _uniq.81545) (:fv _uniq.81551)) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.81545) (:fv _uniq.81545) ((:c CommSemiring.toSemiring) (:fv _uniq.81545) (:fv _uniq.81551)) ((:c CommSemiring.toSemiring) (:fv _uniq.81545) (:fv _uniq.81551)) ((:c RingHom.id) (:fv _uniq.8154... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommSemiring) (:fv _uniq.81545))"},{"name":"σ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c AddCommMonoid) (:fv _uniq.81548))"},{"name":"w","sexp":"(:forall _ (:fv _uniq.81554) (:fv _uniq.81548))"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81545","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81548","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":18600,"sourceStart":18598,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":18602,"sourceStart":18601,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MvPolynomial.wei... | [] | [{"source":"weightedHomogeneousComponent_apply","source_end":18636,"source_start":18602,"syntax_kind":"ident"},{"source":"sum_eq_zero","source_end":18649,"source_start":18638,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81545","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81548","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 94 | 7 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eeb8afcb02272553dc94fa7cdf00aa44b82ffa79aac6ae2706e910940039779f | 25c8fe94dd2b97d0b1d7af92f7aac38f2d69dfc7b6a87a3b460ff9d5c7804194 | 9c8fbfa1bbcf1651cf67147824d4842230d07e110843bb97480b6e5e23c7e45e | a7a190fd1f2d66ade812697d500afbb57e271eebd0eed5ef11a96d45ae765241 |
cat-searcher/leandojo-benchmark-4-random | test | 4,325 | MvPolynomial.weightedHomogeneousComponent_eq_zero | Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro d hd | R : Type u_1
M : Type u_2
inst✝³ : CommSemiring R
σ : Type u_3
inst✝² : AddCommMonoid M
w : σ → M
n : M
φ ψ : MvPolynomial σ R
inst✝¹ : SemilatticeSup M
inst✝ : OrderBot M
h : weightedTotalDegree w φ < n
⊢ ∀ x ∈ Finset.filter (fun d => (weightedDegree w) d = n) φ.support, (monomial x) (coeff x φ) = 0 | R : Type u_1
M : Type u_2
inst✝³ : CommSemiring R
σ : Type u_3
inst✝² : AddCommMonoid M
w : σ → M
n : M
φ ψ : MvPolynomial σ R
inst✝¹ : SemilatticeSup M
inst✝ : OrderBot M
h : weightedTotalDegree w φ < n
d : σ →₀ ℕ
hd : d ∈ Finset.filter (fun d => (weightedDegree w) d = n) φ.support
⊢ (monomial d) (coeff d φ) = 0 | (:forall x ((:c Finsupp) (:fv _uniq.81554) (:c Nat) ((:c LinearOrderedCommMonoidWithZero.toZero) (:c Nat) (:c Nat.instLinearOrderedCommMonoidWithZero))) (:forall _ ((:c Membership.mem) ((:c Finsupp) (:fv _uniq.81554) (:c Nat) ((:c LinearOrderedCommMonoidWithZero.toZero) (:c Nat) (:c Nat.instLinearOrderedCommMonoidWithZ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommSemiring) (:fv _uniq.81545))"},{"name":"σ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c AddCommMonoid) (:fv _uniq.81548))"},{"name":"w","sexp":"(:forall _ (:fv _uniq.81554) (:fv _uniq.81548))"... | (:forall x :explicit (:app (:c Finsupp) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:c Nat)))))) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Finsupp) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:c Nat... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81545","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81548","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"intro","sourceEnd":18658,"sourceStart":18653,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"d","sourceEnd":18660,"sourceStart":18659,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hd","sourceEnd":18663,"sourceStart":18661,"tag":"identifier"}],"kind":"null","sou... | [{"role":"fresh_name","source":"d","source_end":18660,"source_start":18659,"syntax_kind":"ident"},{"role":"fresh_name","source":"hd","source_end":18663,"source_start":18661,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81545","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81548","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 94 | 11 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 25fb8545cdf1142eaf16e88a7d5a80ca6bbe25a6f8cbdb4cdd3f365120ac0b1e | a7a190fd1f2d66ade812697d500afbb57e271eebd0eed5ef11a96d45ae765241 | 73ef711d637e1cd5819247a7e580b05ffe46a64508d66c881b4559b277b50af0 | 6b6d5f02e26ac487cccfbc9cff3c05bf7ee5f611cb676b4787942cebfde78171 |
cat-searcher/leandojo-benchmark-4-random | test | 4,326 | MvPolynomial.weightedHomogeneousComponent_eq_zero | Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.mem_filter</a>] at hd | R : Type u_1
M : Type u_2
inst✝³ : CommSemiring R
σ : Type u_3
inst✝² : AddCommMonoid M
w : σ → M
n : M
φ ψ : MvPolynomial σ R
inst✝¹ : SemilatticeSup M
inst✝ : OrderBot M
h : weightedTotalDegree w φ < n
d : σ →₀ ℕ
hd : d ∈ Finset.filter (fun d => (weightedDegree w) d = n) φ.support
⊢ (monomial d) (coeff d φ) = 0 | R : Type u_1
M : Type u_2
inst✝³ : CommSemiring R
σ : Type u_3
inst✝² : AddCommMonoid M
w : σ → M
n : M
φ ψ : MvPolynomial σ R
inst✝¹ : SemilatticeSup M
inst✝ : OrderBot M
h : weightedTotalDegree w φ < n
d : σ →₀ ℕ
hd : d ∈ φ.support ∧ (weightedDegree w) d = n
⊢ (monomial d) (coeff d φ) = 0 | ((:c Eq) ((:c MvPolynomial) (:fv _uniq.81554) (:fv _uniq.81545) (:fv _uniq.81551)) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.81545) (:fv _uniq.81545) ((:c CommSemiring.toSemiring) (:fv _uniq.81545) (:fv _uniq.81551)) ((:c CommSemiring.toSemiring) (:fv _uniq.81545) (:fv _uniq.81551)) ((:c RingHom.id) (:fv _uniq.8154... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommSemiring) (:fv _uniq.81545))"},{"name":"σ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c AddCommMonoid) (:fv _uniq.81548))"},{"name":"w","sexp":"(:forall _ (:fv _uniq.81554) (:fv _uniq.81548))"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81545","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81548","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":18668,"sourceStart":18666,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":18670,"sourceStart":18669,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.mem_filte... | [] | [{"source":"Finset.mem_filter","source_end":18687,"source_start":18670,"syntax_kind":"ident"},{"source":"hd","source_end":18694,"source_start":18692,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81545","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81548","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 94 | 12 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4a48546a31d1595214c96ea231d5a0afee5cd70ef61cdd169dd9d1e7d4e1abf8 | 6b6d5f02e26ac487cccfbc9cff3c05bf7ee5f611cb676b4787942cebfde78171 | 709ad8c1034b009d778de6056a9e5a057e105027d6d8d2d096a1ef40e3c356ae | 3cf2e338ec4f5e3e67b48bd31c37e03c1e9dc14292701d3bd01ec0d0d16dfd7b |
cat-searcher/leandojo-benchmark-4-random | test | 4,327 | MvPolynomial.weightedHomogeneousComponent_eq_zero | Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exfalso | R : Type u_1
M : Type u_2
inst✝³ : CommSemiring R
σ : Type u_3
inst✝² : AddCommMonoid M
w : σ → M
n : M
φ ψ : MvPolynomial σ R
inst✝¹ : SemilatticeSup M
inst✝ : OrderBot M
h : weightedTotalDegree w φ < n
d : σ →₀ ℕ
hd : d ∈ φ.support ∧ (weightedDegree w) d = n
⊢ (monomial d) (coeff d φ) = 0 | R : Type u_1
M : Type u_2
inst✝³ : CommSemiring R
σ : Type u_3
inst✝² : AddCommMonoid M
w : σ → M
n : M
φ ψ : MvPolynomial σ R
inst✝¹ : SemilatticeSup M
inst✝ : OrderBot M
h : weightedTotalDegree w φ < n
d : σ →₀ ℕ
hd : d ∈ φ.support ∧ (weightedDegree w) d = n
⊢ False | ((:c Eq) ((:c MvPolynomial) (:fv _uniq.81554) (:fv _uniq.81545) (:fv _uniq.81551)) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.81545) (:fv _uniq.81545) ((:c CommSemiring.toSemiring) (:fv _uniq.81545) (:fv _uniq.81551)) ((:c CommSemiring.toSemiring) (:fv _uniq.81545) (:fv _uniq.81551)) ((:c RingHom.id) (:fv _uniq.8154... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommSemiring) (:fv _uniq.81545))"},{"name":"σ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c AddCommMonoid) (:fv _uniq.81548))"},{"name":"w","sexp":"(:forall _ (:fv _uniq.81554) (:fv _uniq.81548))"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81545","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81548","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exfalso","sourceEnd":18704,"sourceStart":18697,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticExfalso","source":"exfalso","sourceEnd":18704,"sourceStart":18697,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81545","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81548","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 94 | 15 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 846c626f661d6f998b560cbcb0f9d61aff55a25cb5dc34550a436f4fdcf794f4 | 3cf2e338ec4f5e3e67b48bd31c37e03c1e9dc14292701d3bd01ec0d0d16dfd7b | c68edda11cdb69125c1486c6356b60cedaec50aa8c4d3442e85a91513f01648d | d51795b87cc80ff6750dc3571f3a51cdfe961bc645d1da260dcded2b270897ab |
cat-searcher/leandojo-benchmark-4-random | test | 4,328 | MvPolynomial.weightedHomogeneousComponent_eq_zero | Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>lt_irrefl</a> n | R : Type u_1
M : Type u_2
inst✝³ : CommSemiring R
σ : Type u_3
inst✝² : AddCommMonoid M
w : σ → M
n : M
φ ψ : MvPolynomial σ R
inst✝¹ : SemilatticeSup M
inst✝ : OrderBot M
h : weightedTotalDegree w φ < n
d : σ →₀ ℕ
hd : d ∈ φ.support ∧ (weightedDegree w) d = n
⊢ False | R : Type u_1
M : Type u_2
inst✝³ : CommSemiring R
σ : Type u_3
inst✝² : AddCommMonoid M
w : σ → M
n : M
φ ψ : MvPolynomial σ R
inst✝¹ : SemilatticeSup M
inst✝ : OrderBot M
h : weightedTotalDegree w φ < n
d : σ →₀ ℕ
hd : d ∈ φ.support ∧ (weightedDegree w) d = n
⊢ n < n | (:c False) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommSemiring) (:fv _uniq.81545))"},{"name":"σ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c AddCommMonoid) (:fv _uniq.81548))"},{"name":"w","sexp":"(:forall _ (:fv _uniq.81554) (:fv _uniq.81548))"... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81545","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81548","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"apply","sourceEnd":18712,"sourceStart":18707,"tag":"atom"},{"children":[{"name":"lt_irrefl","semanticRole":"global","source":"lt_irrefl","sourceEnd":18722,"sourceStart":18713,"tag":"identifier"},{"children":[{"contextIndex":6,"semanticRole":"local","source":"n","sourceEnd":18724,"sourceStart":18... | [] | [{"source":"lt_irrefl n","source_end":18724,"source_start":18713,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81545","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81548","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 94 | 16 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6d938318c0f2b8a2c35de2e0ec576319a0055cca0f79681dbaab0832989e9988 | d51795b87cc80ff6750dc3571f3a51cdfe961bc645d1da260dcded2b270897ab | 51c7f613f696a37513d209e9dbc8ede0094802eab7ec4d88f587f9c0aa75b375 | 038f09b54a770274c82ebf5433051f49aea0208af7b87229a4d01048c992dc7f |
cat-searcher/leandojo-benchmark-4-random | test | 4,329 | MvPolynomial.weightedHomogeneousComponent_eq_zero | Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | nth_rw 1 [← hd.2] | R : Type u_1
M : Type u_2
inst✝³ : CommSemiring R
σ : Type u_3
inst✝² : AddCommMonoid M
w : σ → M
n : M
φ ψ : MvPolynomial σ R
inst✝¹ : SemilatticeSup M
inst✝ : OrderBot M
h : weightedTotalDegree w φ < n
d : σ →₀ ℕ
hd : d ∈ φ.support ∧ (weightedDegree w) d = n
⊢ n < n | R : Type u_1
M : Type u_2
inst✝³ : CommSemiring R
σ : Type u_3
inst✝² : AddCommMonoid M
w : σ → M
n : M
φ ψ : MvPolynomial σ R
inst✝¹ : SemilatticeSup M
inst✝ : OrderBot M
h : weightedTotalDegree w φ < n
d : σ →₀ ℕ
hd : d ∈ φ.support ∧ (weightedDegree w) d = n
⊢ (weightedDegree w) d < n | ((:c LT.lt) (:fv _uniq.81548) ((:c Preorder.toLT) (:fv _uniq.81548) ((:c PartialOrder.toPreorder) (:fv _uniq.81548) ((:c SemilatticeSup.toPartialOrder) (:fv _uniq.81548) (:fv _uniq.83801)))) (:fv _uniq.81563) (:fv _uniq.81563)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommSemiring) (:fv _uniq.81545))"},{"name":"σ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c AddCommMonoid) (:fv _uniq.81548))"},{"name":"w","sexp":"(:forall _ (:fv _uniq.81554) (:fv _uniq.81548))"... | (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV6)) (:arg :explicit 3 (:fv FV6))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81545","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81548","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"nth_rw","sourceEnd":18733,"sourceStart":18727,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"source":"1","sourceEnd":18735,"sourceStart":18734,"tag":"atom"}],"kind":"num","source":"1","sourceEnd":18735,"... | [] | [{"source":"hd.2","source_end":18745,"source_start":18741,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81545","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81548","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 94 | 17 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8a652d6d80374180ee68e8050cf03461e0cbdd153496a05454f94108c24f2202 | 038f09b54a770274c82ebf5433051f49aea0208af7b87229a4d01048c992dc7f | c25dd5e6ce364bdb33861adc6803e280a60ba76f02d056775fc72f70c199a1f0 | c5e7875f4573b5ab572db3312447d3ea53b4f28f3c089e3b34fe11384af1ad8b |
cat-searcher/leandojo-benchmark-4-random | test | 4,330 | MvPolynomial.weightedHomogeneousComponent_eq_zero | Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>lt_of_le_of_lt</a> (<a>MvPolynomial.le_weightedTotalDegree</a> w hd.1) h | R : Type u_1
M : Type u_2
inst✝³ : CommSemiring R
σ : Type u_3
inst✝² : AddCommMonoid M
w : σ → M
n : M
φ ψ : MvPolynomial σ R
inst✝¹ : SemilatticeSup M
inst✝ : OrderBot M
h : weightedTotalDegree w φ < n
d : σ →₀ ℕ
hd : d ∈ φ.support ∧ (weightedDegree w) d = n
⊢ (weightedDegree w) d < n | ((:c LT.lt) (:fv _uniq.81548) ((:c Preorder.toLT) (:fv _uniq.81548) ((:c PartialOrder.toPreorder) (:fv _uniq.81548) ((:c SemilatticeSup.toPartialOrder) (:fv _uniq.81548) (:fv _uniq.83801)))) ((:c DFunLike.coe) ((:c AddMonoidHom) ((:c Finsupp) (:fv _uniq.81554) (:c Nat) ((:c LinearOrderedCommMonoidWithZero.toZero) (:c N... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommSemiring) (:fv _uniq.81545))"},{"name":"σ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c AddCommMonoid) (:fv _uniq.81548))"},{"name":"w","sexp":"(:forall _ (:fv _uniq.81554) (:fv _uniq.81548))"... | (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AddMonoidHom) (:arg :explicit 0 (:app (:c Finsupp) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:c Nat)) (:arg :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81545","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81548","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":18754,"sourceStart":18749,"tag":"atom"},{"children":[{"name":"lt_of_le_of_lt","semanticRole":"global","source":"lt_of_le_of_lt","sourceEnd":18769,"sourceStart":18755,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":18771,"sourceStart":18770,"tag":"atom"}... | [] | [{"source":"lt_of_le_of_lt (le_weightedTotalDegree w hd.1) h","source_end":18803,"source_start":18755,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.81545","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81548","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 94 | 20 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 215d4dabae5ea040153fb27d9d177debefff7265700fd192bc1ba236d1d29d2c | c5e7875f4573b5ab572db3312447d3ea53b4f28f3c089e3b34fe11384af1ad8b | 97f7e3495d4a39371fd7b42d8569a2ada9a7fcb00be1c61d5fed16d0e70b5686 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,331 | IsPurelyInseparable.tower_bot | Mathlib/FieldTheory/PurelyInseparable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨⟨fun x ↦ (<a>IsPurelyInseparable.isIntegral'</a> F (<a>algebraMap</a> E K x)).<a>IsIntegral.tower_bot_of_field</a>⟩, fun x h ↦ ?_⟩ | F : Type u
E : Type v
inst✝⁷ : Field F
inst✝⁶ : Field E
inst✝⁵ : Algebra F E
K : Type w
inst✝⁴ : Field K
inst✝³ : Algebra F K
inst✝² : Algebra E K
inst✝¹ : IsScalarTower F E K
inst✝ : IsPurelyInseparable F K
⊢ IsPurelyInseparable F E | F : Type u
E : Type v
inst✝⁷ : Field F
inst✝⁶ : Field E
inst✝⁵ : Algebra F E
K : Type w
inst✝⁴ : Field K
inst✝³ : Algebra F K
inst✝² : Algebra E K
inst✝¹ : IsScalarTower F E K
inst✝ : IsPurelyInseparable F K
x : E
h : (minpoly F x).Separable
⊢ x ∈ (algebraMap F E).range | ((:c IsPurelyInseparable) (:fv _uniq.57135) (:fv _uniq.57137) (:fv _uniq.57140) (:fv _uniq.57143) (:fv _uniq.57230)) | [{"name":"F","sexp":"(:sort (+ u 1))"},{"name":"E","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.57135))"},{"name":"inst✝⁶","sexp":"((:c Field) (:fv _uniq.57137))"},{"name":"inst✝⁵","sexp":"((:c Algebra) (:fv _uniq.57135) (:fv _uniq.57137) ((:c Semifield.toCommSemiring) (:fv _uniq.57135) ((:... | (:app (:c IsPurelyInseparable) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:app (:c Algebra) (:arg :explicit 0 ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.57135","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.57137","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"refine","sourceEnd":20396,"sourceStart":20390,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":20400,"sourceStart":20397,"tag":"atom"},{"children":[{"children":[{"source":"⟨","sourceEnd":20403,"sourceStart":20400,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":20406,"sour... | [] | [{"source":"⟨⟨fun x ↦ (isIntegral' F (algebraMap E K x)).tower_bot_of_field⟩, fun x h ↦ ?_⟩","source_end":20488,"source_start":20397,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.57135","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.57137","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 56 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7b068bdb87b95e952cac1b93e4b8103fcf543f671a464020f375371d9bf81b26 | 498bf0eb48d162bb7dd397c4f171fe907198f6e45027719806803d56e185a005 | e129cac27c3f5073a7daf3796e9c7f2fca762627bd71b96e657e911523a6fc4c | b267c2c279568840d17ad5371576b0c2bbf4e3c814c3bb144e631f3ec08da362 |
cat-searcher/leandojo-benchmark-4-random | test | 4,332 | IsPurelyInseparable.tower_bot | Mathlib/FieldTheory/PurelyInseparable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>minpoly.algebraMap_eq</a> (<a>algebraMap</a> E K).<a>RingHom.injective</a>] at h | F : Type u
E : Type v
inst✝⁷ : Field F
inst✝⁶ : Field E
inst✝⁵ : Algebra F E
K : Type w
inst✝⁴ : Field K
inst✝³ : Algebra F K
inst✝² : Algebra E K
inst✝¹ : IsScalarTower F E K
inst✝ : IsPurelyInseparable F K
x : E
h : (minpoly F x).Separable
⊢ x ∈ (algebraMap F E).range | F : Type u
E : Type v
inst✝⁷ : Field F
inst✝⁶ : Field E
inst✝⁵ : Algebra F E
K : Type w
inst✝⁴ : Field K
inst✝³ : Algebra F K
inst✝² : Algebra E K
inst✝¹ : IsScalarTower F E K
inst✝ : IsPurelyInseparable F K
x : E
h : (minpoly F ((algebraMap E K) x)).Separable
⊢ x ∈ (algebraMap F E).range | ((:c Membership.mem) (:fv _uniq.57137) ((:c Subring) (:fv _uniq.57137) ((:c DivisionRing.toRing) (:fv _uniq.57137) ((:c Field.toDivisionRing) (:fv _uniq.57137) (:fv _uniq.57143)))) ((:c SetLike.instMembership) ((:c Subring) (:fv _uniq.57137) ((:c DivisionRing.toRing) (:fv _uniq.57137) ((:c Field.toDivisionRing) (:fv _u... | [{"name":"F","sexp":"(:sort (+ u 1))"},{"name":"E","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.57135))"},{"name":"inst✝⁶","sexp":"((:c Field) (:fv _uniq.57137))"},{"name":"inst✝⁵","sexp":"((:c Algebra) (:fv _uniq.57135) (:fv _uniq.57137) ((:c Semifield.toCommSemiring) (:fv _uniq.57135) ((:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Subring) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV1))))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.57135","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.57137","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":20493,"sourceStart":20491,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":20495,"sourceStart":20494,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":20498,"sourceSt... | [] | [{"source":"h","source_end":20553,"source_start":20552,"syntax_kind":"ident"},{"source":"minpoly.algebraMap_eq (algebraMap E K).injective","source_end":20547,"source_start":20499,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.57135","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.57137","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 56 | 5 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5f0724e7c8c57cc96a8f2b83b44186128560d0934357650fae3d3e609ec1d6ba | b267c2c279568840d17ad5371576b0c2bbf4e3c814c3bb144e631f3ec08da362 | f952f5637d86bfdd6821a1834303e39b35fba5db14b3109399e0681b0e710a1e | 76c42d2b9996606583a9a292055715220268a093ffb4b27f8601f725aab47b1c |
cat-searcher/leandojo-benchmark-4-random | test | 4,333 | IsPurelyInseparable.tower_bot | Mathlib/FieldTheory/PurelyInseparable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨y, h⟩ := <a>IsPurelyInseparable.inseparable</a> F _ h | F : Type u
E : Type v
inst✝⁷ : Field F
inst✝⁶ : Field E
inst✝⁵ : Algebra F E
K : Type w
inst✝⁴ : Field K
inst✝³ : Algebra F K
inst✝² : Algebra E K
inst✝¹ : IsScalarTower F E K
inst✝ : IsPurelyInseparable F K
x : E
h : (minpoly F ((algebraMap E K) x)).Separable
⊢ x ∈ (algebraMap F E).range | case intro
F : Type u
E : Type v
inst✝⁷ : Field F
inst✝⁶ : Field E
inst✝⁵ : Algebra F E
K : Type w
inst✝⁴ : Field K
inst✝³ : Algebra F K
inst✝² : Algebra E K
inst✝¹ : IsScalarTower F E K
inst✝ : IsPurelyInseparable F K
x : E
h✝ : (minpoly F ((algebraMap E K) x)).Separable
y : F
h : (algebraMap F K) y = (algebraMap E K)... | ((:c Membership.mem) (:fv _uniq.57137) ((:c Subring) (:fv _uniq.57137) ((:c DivisionRing.toRing) (:fv _uniq.57137) ((:c Field.toDivisionRing) (:fv _uniq.57137) (:fv _uniq.57143)))) ((:c SetLike.instMembership) ((:c Subring) (:fv _uniq.57137) ((:c DivisionRing.toRing) (:fv _uniq.57137) ((:c Field.toDivisionRing) (:fv _u... | [{"name":"F","sexp":"(:sort (+ u 1))"},{"name":"E","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.57135))"},{"name":"inst✝⁶","sexp":"((:c Field) (:fv _uniq.57137))"},{"name":"inst✝⁵","sexp":"((:c Algebra) (:fv _uniq.57135) (:fv _uniq.57137) ((:c Semifield.toCommSemiring) (:fv _uniq.57135) ((:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Subring) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV1))))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.57135","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.57137","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"obtain","sourceEnd":20562,"sourceStart":20556,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":20566,"sourceStart":20563,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"y","sourceEn... | [] | [{"source":"inseparable F _ h","source_end":20594,"source_start":20577,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨y, h⟩","source_end":20573,"source_start":20563,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.57135","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.57137","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 56 | 8 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c39c92bf0c7794a03d28564e1fd4b7e8bd53b280850cfa71b0a2100e6bf13f80 | 76c42d2b9996606583a9a292055715220268a093ffb4b27f8601f725aab47b1c | 54faa9a867f5e56e4eddf280a7a415434895b4aee6ef56cd1791f853e0958676 | be3889f7acdaaabe160fb0cb48590be38f614f1ee9b2039b22d90c23ac6a7979 |
cat-searcher/leandojo-benchmark-4-random | test | 4,334 | IsPurelyInseparable.tower_bot | Mathlib/FieldTheory/PurelyInseparable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨y, (<a>algebraMap</a> E K).<a>RingHom.injective</a> (h.symm ▸ (<a>IsScalarTower.algebraMap_apply</a> F E K y).<a>Eq.symm</a>)⟩ | case intro
F : Type u
E : Type v
inst✝⁷ : Field F
inst✝⁶ : Field E
inst✝⁵ : Algebra F E
K : Type w
inst✝⁴ : Field K
inst✝³ : Algebra F K
inst✝² : Algebra E K
inst✝¹ : IsScalarTower F E K
inst✝ : IsPurelyInseparable F K
x : E
h✝ : (minpoly F ((algebraMap E K) x)).Separable
y : F
h : (algebraMap F K) y = (algebraMap E K)... | ((:c Membership.mem) (:fv _uniq.57137) ((:c Subring) (:fv _uniq.57137) ((:c DivisionRing.toRing) (:fv _uniq.57137) ((:c Field.toDivisionRing) (:fv _uniq.57137) (:fv _uniq.57143)))) ((:c SetLike.instMembership) ((:c Subring) (:fv _uniq.57137) ((:c DivisionRing.toRing) (:fv _uniq.57137) ((:c Field.toDivisionRing) (:fv _u... | [{"name":"F","sexp":"(:sort (+ u 1))"},{"name":"E","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.57135))"},{"name":"inst✝⁶","sexp":"((:c Field) (:fv _uniq.57137))"},{"name":"inst✝⁵","sexp":"((:c Algebra) (:fv _uniq.57135) (:fv _uniq.57137) ((:c Semifield.toCommSemiring) (:fv _uniq.57135) ((:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Subring) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV1))))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.57135","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.57137","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":20602,"sourceStart":20597,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":20606,"sourceStart":20603,"tag":"atom"},{"children":[{"contextIndex":14,"semanticRole":"local","source":"y","sourceEnd":20607,"sourceStart":20606,"tag":"identifier"},{"source":",","sourceEnd":20608,... | [] | [{"source":"⟨y, (algebraMap E K).injective (h.symm ▸ (IsScalarTower.algebraMap_apply F E K y).symm)⟩","source_end":20697,"source_start":20603,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.57135","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.57137","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 56 | 9 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 60f289204054abda28e3401d9b791df0491192db05e1276146f0ee2a8733029b | be3889f7acdaaabe160fb0cb48590be38f614f1ee9b2039b22d90c23ac6a7979 | de014216152e48ca24d98d5f9d01ceeb0c0e455080a2a616dffc0c38ba2d282c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,335 | Finset.card_union_eq_card_add_card | Mathlib/Data/Finset/Card.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Finset.card_union_add_card_inter</a>] | α : Type u_1
β : Type u_2
R : Type u_3
s t u : Finset α
f : α → β
n : ℕ
inst✝ : DecidableEq α
⊢ (s ∪ t).card = s.card + t.card ↔ _root_.Disjoint s t | α : Type u_1
β : Type u_2
R : Type u_3
s t u : Finset α
f : α → β
n : ℕ
inst✝ : DecidableEq α
⊢ (s ∪ t).card = (s ∪ t).card + (s ∩ t).card ↔ _root_.Disjoint s t | ((:c Iff) ((:c Eq) (:c Nat) ((:c Finset.card) (:fv _uniq.43242) ((:c Union.union) ((:c Finset) (:fv _uniq.43242)) ((:c Finset.instUnion) (:fv _uniq.43242) (:fv _uniq.43270)) (:fv _uniq.43251) (:fv _uniq.43254))) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c Finset.card) (:fv _... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.43242))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.43242))"},{"name":"u","sexp":"((:c Finset) (:fv _uniq.43242))"},{"name":"f","sexp":"(:forall _ (:fv _... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Finset.card) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Union.union) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c Union) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43242","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.43245","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":22558,"sourceStart":22556,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":22560,"sourceStart":22559,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":22563,"sourceSt... | [] | [{"source":"card_union_add_card_inter","source_end":22589,"source_start":22564,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43242","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.43245","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 169 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5053d004d9fb58dae87e3df9b3f195c71c653f956834c6f318580f0587bd7e63 | ef2ab42d7b261ca6e5692a34bf4e56e109eb5ac4c9d8938bae1f5309222ae0d0 | c8035967c859b21977fd916b3961b71490c87510ed3102fff1e6a3e705b1ed86 | ec031a361b5e444fc1e27489e6fa3c008dac69600273dd493ed4acce92249b8e |
cat-searcher/leandojo-benchmark-4-random | test | 4,336 | Finset.card_union_eq_card_add_card | Mathlib/Data/Finset/Card.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Finset.disjoint_iff_inter_eq_empty</a>] | α : Type u_1
β : Type u_2
R : Type u_3
s t u : Finset α
f : α → β
n : ℕ
inst✝ : DecidableEq α
⊢ (s ∪ t).card = (s ∪ t).card + (s ∩ t).card ↔ _root_.Disjoint s t | ((:c Iff) ((:c Eq) (:c Nat) ((:c Finset.card) (:fv _uniq.43242) ((:c Union.union) ((:c Finset) (:fv _uniq.43242)) ((:c Finset.instUnion) (:fv _uniq.43242) (:fv _uniq.43270)) (:fv _uniq.43251) (:fv _uniq.43254))) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c Finset.card) (:fv _... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.43242))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.43242))"},{"name":"u","sexp":"((:c Finset) (:fv _uniq.43242))"},{"name":"f","sexp":"(:forall _ (:fv _... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Finset.card) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Union.union) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c Union) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43242","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.43245","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":22596,"sourceStart":22592,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":22598,"sourceStart":22597,"tag":"a... | [] | [{"source":"disjoint_iff_inter_eq_empty","source_end":22625,"source_start":22598,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43242","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.43245","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 169 | 8 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 14fcd1d24336a1b4e371e708e71bc5769a2edbe48d30bb200c3fa6040c1cf267 | ec031a361b5e444fc1e27489e6fa3c008dac69600273dd493ed4acce92249b8e | bc11e6836af7a85d964ff5d194061c5f44090502d7e7838388658bcc135bf47d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,337 | sdiff_lt | Mathlib/Order/BooleanAlgebra.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine sdiff_le.lt_of_ne fun h => hy ?_ | α : Type u
β : Type u_1
w x y z : α
inst✝ : GeneralizedBooleanAlgebra α
hx : y ≤ x
hy : y ≠ ⊥
⊢ x \ y < x | α : Type u
β : Type u_1
w x y z : α
inst✝ : GeneralizedBooleanAlgebra α
hx : y ≤ x
hy : y ≠ ⊥
h : x \ y = x
⊢ y = ⊥ | ((:c LT.lt) (:fv _uniq.23622) ((:c Preorder.toLT) (:fv _uniq.23622) ((:c PartialOrder.toPreorder) (:fv _uniq.23622) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.23622) ((:c Lattice.toSemilatticeInf) (:fv _uniq.23622) ((:c GeneralizedCoheytingAlgebra.toLattice) (:fv _uniq.23622) ((:c GeneralizedBooleanAlgebra.toGenera... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u_1 1))"},{"name":"w","sexp":"(:fv _uniq.23622)"},{"name":"x","sexp":"(:fv _uniq.23622)"},{"name":"y","sexp":"(:fv _uniq.23622)"},{"name":"z","sexp":"(:fv _uniq.23622)"},{"name":"inst✝","sexp":"((:c GeneralizedBooleanAlgebra) (:fv _uniq.23622))"},{"na... | (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c SDiff.sdiff) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c SDiff) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV3)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23622","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23625","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":13779,"sourceStart":13773,"tag":"atom"},{"children":[{"source":"sdiff_le.lt_of_ne","sourceEnd":13797,"sourceStart":13780,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":13801,"sourceStart":13798,"tag":"atom"},{"children":[{"children":[{"semanticRole"... | [] | [{"source":"sdiff_le.lt_of_ne fun h => hy ?_","source_end":13812,"source_start":13780,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23622","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23625","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 64 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 255fa897d6029a0424fc55eef45a5efdfdb3f33108e153afbda68b523639edb9 | 30f83319f76d84a1c06ec9fea098e9da8194518d1533886f0abedc9afba1ce07 | 0b09fb3090c314960b2be9e8bc21d1c895f2a8ba0eadc70f75ddd6c0f64bf5d8 | 34060b44a19b86e88351b8ec0f1eee88ff98573762b347d01f61a75f215bafda |
cat-searcher/leandojo-benchmark-4-random | test | 4,338 | sdiff_lt | Mathlib/Order/BooleanAlgebra.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>sdiff_eq_self_iff_disjoint'</a>, <a>disjoint_iff</a>] at h | α : Type u
β : Type u_1
w x y z : α
inst✝ : GeneralizedBooleanAlgebra α
hx : y ≤ x
hy : y ≠ ⊥
h : x \ y = x
⊢ y = ⊥ | α : Type u
β : Type u_1
w x y z : α
inst✝ : GeneralizedBooleanAlgebra α
hx : y ≤ x
hy : y ≠ ⊥
h : x ⊓ y = ⊥
⊢ y = ⊥ | ((:c Eq) (:fv _uniq.23622) (:fv _uniq.23631) ((:c Bot.bot) (:fv _uniq.23622) ((:c GeneralizedBooleanAlgebra.toBot) (:fv _uniq.23622) (:fv _uniq.23636)))) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u_1 1))"},{"name":"w","sexp":"(:fv _uniq.23622)"},{"name":"x","sexp":"(:fv _uniq.23622)"},{"name":"y","sexp":"(:fv _uniq.23622)"},{"name":"z","sexp":"(:fv _uniq.23622)"},{"name":"inst✝","sexp":"((:c GeneralizedBooleanAlgebra) (:fv _uniq.23622))"},{"na... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV4)) (:arg :explicit 2 (:app (:c Bot.bot) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Bot) (:arg :explicit 0 (:fv FV0)))))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23622","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23625","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":13817,"sourceStart":13815,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13819,"sourceStart":13818,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"sdiff_eq_self_if... | [] | [{"source":"sdiff_eq_self_iff_disjoint'","source_end":13846,"source_start":13819,"syntax_kind":"ident"},{"source":"h","source_end":13866,"source_start":13865,"syntax_kind":"ident"},{"source":"disjoint_iff","source_end":13860,"source_start":13848,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23622","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23625","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 64 | 5 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8326a38d28ad62e952496b31eed21a02b9c94034257cc60211713ac2b82c9965 | 34060b44a19b86e88351b8ec0f1eee88ff98573762b347d01f61a75f215bafda | 192693f53e07e7f38bb299df87f463d50d6651e7fee52aaa64d509855d4d12e0 | 1124d942fdffee293df18374a5fd5d054b31fb7a4b910880256e794590240189 |
cat-searcher/leandojo-benchmark-4-random | test | 4,339 | sdiff_lt | Mathlib/Order/BooleanAlgebra.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← h, inf_eq_right.mpr hx] | α : Type u
β : Type u_1
w x y z : α
inst✝ : GeneralizedBooleanAlgebra α
hx : y ≤ x
hy : y ≠ ⊥
h : x ⊓ y = ⊥
⊢ y = ⊥ | ((:c Eq) (:fv _uniq.23622) (:fv _uniq.23631) ((:c Bot.bot) (:fv _uniq.23622) ((:c GeneralizedBooleanAlgebra.toBot) (:fv _uniq.23622) (:fv _uniq.23636)))) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u_1 1))"},{"name":"w","sexp":"(:fv _uniq.23622)"},{"name":"x","sexp":"(:fv _uniq.23622)"},{"name":"y","sexp":"(:fv _uniq.23622)"},{"name":"z","sexp":"(:fv _uniq.23622)"},{"name":"inst✝","sexp":"((:c GeneralizedBooleanAlgebra) (:fv _uniq.23622))"},{"na... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV4)) (:arg :explicit 2 (:app (:c Bot.bot) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Bot) (:arg :explicit 0 (:fv FV0)))))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23622","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23625","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":13871,"sourceStart":13869,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13873,"sourceStart":13872,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":13876,"sourceSt... | [] | [{"source":"h","source_end":13878,"source_start":13877,"syntax_kind":"ident"},{"source":"inf_eq_right.mpr hx","source_end":13899,"source_start":13880,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23622","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23625","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 64 | 9 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 614082d871b0fb9d5819b5ce3249b50481fff050c580eb7f07294387c05ac56f | 1124d942fdffee293df18374a5fd5d054b31fb7a4b910880256e794590240189 | 7c9abf2e2ba0d7c8f49e6317143dbc330e35c12e090ade78448655b666ef534c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,340 | nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts | Mathlib/Analysis/NormedSpace/Star/ContinuousFunctionalCalculus/Instances.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨fun ha ↦ ⟨.of_nonneg ha, .nnreal_of_nonneg ha⟩, ?_⟩ | A : Type u_1
inst✝¹⁰ : NonUnitalRing A
inst✝⁹ : PartialOrder A
inst✝⁸ : StarRing A
inst✝⁷ : StarOrderedRing A
inst✝⁶ : TopologicalSpace A
inst✝⁵ : Module ℝ A
inst✝⁴ : IsScalarTower ℝ A A
inst✝³ : SMulCommClass ℝ A A
inst✝² : NonUnitalContinuousFunctionalCalculus ℝ IsSelfAdjoint
inst✝¹ : NonnegSpectrumClass ℝ A
inst✝ : ... | A : Type u_1
inst✝¹⁰ : NonUnitalRing A
inst✝⁹ : PartialOrder A
inst✝⁸ : StarRing A
inst✝⁷ : StarOrderedRing A
inst✝⁶ : TopologicalSpace A
inst✝⁵ : Module ℝ A
inst✝⁴ : IsScalarTower ℝ A A
inst✝³ : SMulCommClass ℝ A A
inst✝² : NonUnitalContinuousFunctionalCalculus ℝ IsSelfAdjoint
inst✝¹ : NonnegSpectrumClass ℝ A
inst✝ : ... | ((:c Iff) ((:c LE.le) (:fv _uniq.542559) ((:c Preorder.toLE) (:fv _uniq.542559) ((:c PartialOrder.toPreorder) (:fv _uniq.542559) (:fv _uniq.542565))) ((:c OfNat.ofNat) (:fv _uniq.542559) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.542559) ((:c SemigroupWithZero.toZero) (:fv _uniq.542559) ((:c NonUnitalSemiring.toSemigroupW... | [{"name":"A","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NonUnitalRing) (:fv _uniq.542559))"},{"name":"inst✝⁹","sexp":"((:c PartialOrder) (:fv _uniq.542559))"},{"name":"inst✝⁸","sexp":"((:c StarRing) (:fv _uniq.542559) ((:c NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring) (:fv _uniq.542559) ((:c NonUni... | (:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.542559","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.542562","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NonUnitalRing) (:arg... | {"children":[{"source":"refine","sourceEnd":15658,"sourceStart":15652,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":15662,"sourceStart":15659,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":15665,"sourceStart":15662,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","sourc... | [] | [{"source":"⟨fun ha ↦ ⟨.of_nonneg ha, .nnreal_of_nonneg ha⟩, ?_⟩","source_end":15721,"source_start":15659,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.542559","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.542562","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":instance-implicit","context_inde... | 49 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a4a14cde1ecd66e389f68f3919f79a2ad4c2848663eb365625e983b3e18f3dc6 | 70ac01ce5cbfbb866111d4d9db8f111c703c7149bcc85a3ac3b8a4cec1c1d979 | b9eb64eea85447eb9d39e7f0292e9d1c5f500c316e0414fd4dbbe565158c0c3e | fc49b1b90c13bf41f105b38c1f89407f0eb6e8cd11c46f2210e2ca950827cd28 |
cat-searcher/leandojo-benchmark-4-random | test | 4,341 | nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts | Mathlib/Analysis/NormedSpace/Star/ContinuousFunctionalCalculus/Instances.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨ha₁, ha₂⟩ | A : Type u_1
inst✝¹⁰ : NonUnitalRing A
inst✝⁹ : PartialOrder A
inst✝⁸ : StarRing A
inst✝⁷ : StarOrderedRing A
inst✝⁶ : TopologicalSpace A
inst✝⁵ : Module ℝ A
inst✝⁴ : IsScalarTower ℝ A A
inst✝³ : SMulCommClass ℝ A A
inst✝² : NonUnitalContinuousFunctionalCalculus ℝ IsSelfAdjoint
inst✝¹ : NonnegSpectrumClass ℝ A
inst✝ : ... | case intro
A : Type u_1
inst✝¹⁰ : NonUnitalRing A
inst✝⁹ : PartialOrder A
inst✝⁸ : StarRing A
inst✝⁷ : StarOrderedRing A
inst✝⁶ : TopologicalSpace A
inst✝⁵ : Module ℝ A
inst✝⁴ : IsScalarTower ℝ A A
inst✝³ : SMulCommClass ℝ A A
inst✝² : NonUnitalContinuousFunctionalCalculus ℝ IsSelfAdjoint
inst✝¹ : NonnegSpectrumClass ℝ... | (:forall _ ((:c And) ((:c IsSelfAdjoint) (:fv _uniq.542559) ((:c InvolutiveStar.toStar) (:fv _uniq.542559) ((:c StarAddMonoid.toInvolutiveStar) (:fv _uniq.542559) ((:c SubNegMonoid.toAddMonoid) (:fv _uniq.542559) ((:c AddGroup.toSubNegMonoid) (:fv _uniq.542559) ((:c AddCommGroup.toAddGroup) (:fv _uniq.542559) ((:c Orde... | [{"name":"A","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NonUnitalRing) (:fv _uniq.542559))"},{"name":"inst✝⁹","sexp":"((:c PartialOrder) (:fv _uniq.542559))"},{"name":"inst✝⁸","sexp":"((:c StarRing) (:fv _uniq.542559) ((:c NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring) (:fv _uniq.542559) ((:c NonUni... | (:forall _ :explicit (:app (:c And) (:arg :explicit 0 (:app (:c IsSelfAdjoint) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Star) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV13)))) (:arg :explicit 1 (:app (:c QuasispectrumRestricts) (:arg :implicit-type 0 (:c NNReal)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.542559","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.542562","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NonUnitalRing) (:arg... | {"children":[{"source":"rintro","sourceEnd":15730,"sourceStart":15724,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":15734,"sourceStart":15731,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"ha₁","sourceEnd":15739,"s... | [{"role":"fresh_name","source":"ha₁","source_end":15739,"source_start":15734,"syntax_kind":"ident"},{"role":"fresh_name","source":"ha₂","source_end":15746,"source_start":15741,"syntax_kind":"ident"}] | [{"source":"⟨ha₁, ha₂⟩","source_end":15749,"source_start":15731,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.542559","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.542562","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":instance-implicit","context_inde... | 49 | 5 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d17ecf8be6b3aff3190876da32977f7abb38c6f76e0b43c42606c5ed6a6f0433 | fc49b1b90c13bf41f105b38c1f89407f0eb6e8cd11c46f2210e2ca950827cd28 | b43eb656357ac7016fda963ca68d515ab7661f3dc2f71cb45b9d4164ef2117d8 | 905b13a89a7af7e7dca4cb9ade2d3e0677eeed988fae8b23965d11d151f25190 |
cat-searcher/leandojo-benchmark-4-random | test | 4,342 | nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts | Mathlib/Analysis/NormedSpace/Star/ContinuousFunctionalCalculus/Instances.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨x, hx, -, rfl⟩ := <a>CFC.exists_sqrt_of_isSelfAdjoint_of_quasispectrumRestricts</a> ha₁ ha₂ | case intro
A : Type u_1
inst✝¹⁰ : NonUnitalRing A
inst✝⁹ : PartialOrder A
inst✝⁸ : StarRing A
inst✝⁷ : StarOrderedRing A
inst✝⁶ : TopologicalSpace A
inst✝⁵ : Module ℝ A
inst✝⁴ : IsScalarTower ℝ A A
inst✝³ : SMulCommClass ℝ A A
inst✝² : NonUnitalContinuousFunctionalCalculus ℝ IsSelfAdjoint
inst✝¹ : NonnegSpectrumClass ℝ... | case intro.intro.intro.intro
A : Type u_1
inst✝¹⁰ : NonUnitalRing A
inst✝⁹ : PartialOrder A
inst✝⁸ : StarRing A
inst✝⁷ : StarOrderedRing A
inst✝⁶ : TopologicalSpace A
inst✝⁵ : Module ℝ A
inst✝⁴ : IsScalarTower ℝ A A
inst✝³ : SMulCommClass ℝ A A
inst✝² : NonUnitalContinuousFunctionalCalculus ℝ IsSelfAdjoint
inst✝¹ : Non... | ((:c LE.le) (:fv _uniq.542559) ((:c Preorder.toLE) (:fv _uniq.542559) ((:c PartialOrder.toPreorder) (:fv _uniq.542559) (:fv _uniq.542565))) ((:c OfNat.ofNat) (:fv _uniq.542559) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.542559) ((:c SemigroupWithZero.toZero) (:fv _uniq.542559) ((:c NonUnitalSemiring.toSemigroupWithZero) (... | [{"name":"A","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NonUnitalRing) (:fv _uniq.542559))"},{"name":"inst✝⁹","sexp":"((:c PartialOrder) (:fv _uniq.542559))"},{"name":"inst✝⁸","sexp":"((:c StarRing) (:fv _uniq.542559) ((:c NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring) (:fv _uniq.542559) ((:c NonUni... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV0)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.542559","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.542562","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NonUnitalRing) (:arg... | {"children":[{"source":"obtain","sourceEnd":15758,"sourceStart":15752,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":15762,"sourceStart":15759,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEn... | [] | [{"source":"CFC.exists_sqrt_of_isSelfAdjoint_of_quasispectrumRestricts ha₁ ha₂","source_end":15852,"source_start":15782,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨x, hx, -, rfl⟩","source_end":15778,"source_start":15759,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.542559","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.542562","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":instance-implicit","context_inde... | 49 | 6 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a4e01fdae6f83afd428aafc0f127ef881e884d905a26ea628e60b6f00cf5c4ce | 905b13a89a7af7e7dca4cb9ade2d3e0677eeed988fae8b23965d11d151f25190 | e4282f3ff8281141f39c33a8f07379131001a086e13ebfd4f3c6da1360311916 | 32c5d0e1ca8b9fd6d478592f789a7160d1f7d65bedaff46713cc3306cf76c2e2 |
cat-searcher/leandojo-benchmark-4-random | test | 4,343 | nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts | Mathlib/Analysis/NormedSpace/Star/ContinuousFunctionalCalculus/Instances.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [<a>sq</a>, hx.star_eq] using <a>star_mul_self_nonneg</a> x | case intro.intro.intro.intro
A : Type u_1
inst✝¹⁰ : NonUnitalRing A
inst✝⁹ : PartialOrder A
inst✝⁸ : StarRing A
inst✝⁷ : StarOrderedRing A
inst✝⁶ : TopologicalSpace A
inst✝⁵ : Module ℝ A
inst✝⁴ : IsScalarTower ℝ A A
inst✝³ : SMulCommClass ℝ A A
inst✝² : NonUnitalContinuousFunctionalCalculus ℝ IsSelfAdjoint
inst✝¹ : Non... | ((:c LE.le) (:fv _uniq.542559) ((:c Preorder.toLE) (:fv _uniq.542559) ((:c PartialOrder.toPreorder) (:fv _uniq.542559) (:fv _uniq.542565))) ((:c OfNat.ofNat) (:fv _uniq.542559) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.542559) ((:c SemigroupWithZero.toZero) (:fv _uniq.542559) ((:c NonUnitalSemiring.toSemigroupWithZero) (... | [{"name":"A","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NonUnitalRing) (:fv _uniq.542559))"},{"name":"inst✝⁹","sexp":"((:c PartialOrder) (:fv _uniq.542559))"},{"name":"inst✝⁸","sexp":"((:c StarRing) (:fv _uniq.542559) ((:c NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring) (:fv _uniq.542559) ((:c NonUni... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV0)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.542559","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.542562","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NonUnitalRing) (:arg... | {"children":[{"source":"simpa","sourceEnd":15860,"sourceStart":15855,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"ch... | [] | [{"source":"sq","source_end":15864,"source_start":15862,"syntax_kind":"ident"},{"source":"hx.star_eq","source_end":15876,"source_start":15866,"syntax_kind":"ident"},{"source":"star_mul_self_nonneg x","source_end":15906,"source_start":15884,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.542559","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.542562","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":instance-implicit","context_inde... | 49 | 7 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 767e8304c99384d1dc08968fed6cb438aa2f7dea8e3d5231f7ed0f76acaac1e9 | 32c5d0e1ca8b9fd6d478592f789a7160d1f7d65bedaff46713cc3306cf76c2e2 | 52d11ab56aa88c42327846c9537b55ff11b39c3f64deb64ec8683119c1564f34 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,344 | MeasureTheory.Lp.norm_const | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have := <a>NeZero.ne</a> μ | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝⁴ : NormedAddCommGroup E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedAddCommGroup G
inst✝¹ : IsFiniteMeasure μ
c : E
inst✝ : NeZero μ
hp_zero : p ≠ 0
⊢ ‖(Lp.const p μ) c‖ = ‖c‖ * (μ Set.univ).toReal ^ (1 / ... | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝⁴ : NormedAddCommGroup E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedAddCommGroup G
inst✝¹ : IsFiniteMeasure μ
c : E
inst✝ : NeZero μ
hp_zero : p ≠ 0
this : μ ≠ 0
⊢ ‖(Lp.const p μ) c‖ = ‖c‖ * (μ Set.univ).t... | ((:c Eq) (:c Real) ((:c Norm.norm) ((:c Subtype) ((:c MeasureTheory.AEEqFun) (:fv _uniq.377049) (:fv _uniq.377052) (:fv _uniq.377064) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.377052) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.377052) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:fv _uniq.377052) ((:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.377049))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.377049))"},{"name":"p","sexp":"(:c ENNRea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c MeasureTheory.AEEqFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.377049","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.377052","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":44268,"sourceStart":44264,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":44269,"sourceStart":44269,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":44269,"sourceStart":44269,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"NeZero.ne μ","source_end":44284,"source_start":44272,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.377049","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.377052","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 260 | 4 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 107c1dacb373ba27ca34e4bc49322f95a154ff7d88ab45de013225243d3a15fb | c53423afbf1391c7c94cb94539a45d69dc6c810e071a6d536f65284e317d2e41 | 78e394cf01f662a5af04a440b4ad05c6364f32837b43ea67185b6a5dc6d673e8 | bb45ff3a8c5cf9e7e006c7becc7499f2718d2b20eeb2d3f59a7057951f51c05d |
cat-searcher/leandojo-benchmark-4-random | test | 4,345 | MeasureTheory.Lp.norm_const | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>MeasureTheory.Memℒp.toLp_const</a>, <a>MeasureTheory.Lp.norm_toLp</a>, <a>MeasureTheory.snorm_const</a>] <;> try assumption | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝⁴ : NormedAddCommGroup E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedAddCommGroup G
inst✝¹ : IsFiniteMeasure μ
c : E
inst✝ : NeZero μ
hp_zero : p ≠ 0
this : μ ≠ 0
⊢ ‖(Lp.const p μ) c‖ = ‖c‖ * (μ Set.univ).t... | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝⁴ : NormedAddCommGroup E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedAddCommGroup G
inst✝¹ : IsFiniteMeasure μ
c : E
inst✝ : NeZero μ
hp_zero : p ≠ 0
this : μ ≠ 0
⊢ (↑‖c‖₊ * μ Set.univ ^ (1 / p.toReal)).toR... | ((:c Eq) (:c Real) ((:c Norm.norm) ((:c Subtype) ((:c MeasureTheory.AEEqFun) (:fv _uniq.377049) (:fv _uniq.377052) (:fv _uniq.377064) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.377052) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.377052) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:fv _uniq.377052) ((:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.377049))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.377049))"},{"name":"p","sexp":"(:c ENNRea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c MeasureTheory.AEEqFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.377049","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.377052","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"source":"rw","sourceEnd":44289,"sourceStart":44287,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":44291,"sourceStart":44290,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":44... | [] | [{"source":"Memℒp.toLp_const","source_end":44313,"source_start":44295,"syntax_kind":"ident"},{"source":"Lp.norm_toLp","source_end":44327,"source_start":44315,"syntax_kind":"ident"},{"source":"snorm_const","source_end":44340,"source_start":44329,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.377049","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.377052","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 260 | 5 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cf7dbf1e69fbd213de03999f6d8e47e542f793c84d834ffa5ee5e00a7f626a9c | bb45ff3a8c5cf9e7e006c7becc7499f2718d2b20eeb2d3f59a7057951f51c05d | bbf26a7f55babcbd60290f7263ef8b5b7bb4202fd46c49227535e25d9eabfa84 | b146b4e982aa3b7044d4d7bc26437c6fee3875e294a91f060a2324673a5aee89 |
cat-searcher/leandojo-benchmark-4-random | test | 4,346 | MeasureTheory.Lp.norm_const | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>ENNReal.toReal_mul</a>, <a>ENNReal.coe_toReal</a>, ← <a>ENNReal.toReal_rpow</a>, <a>coe_nnnorm</a>] | α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝⁴ : NormedAddCommGroup E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedAddCommGroup G
inst✝¹ : IsFiniteMeasure μ
c : E
inst✝ : NeZero μ
hp_zero : p ≠ 0
this : μ ≠ 0
⊢ (↑‖c‖₊ * μ Set.univ ^ (1 / p.toReal)).toR... | ((:c Eq) (:c Real) ((:c ENNReal.toReal) ((:c HMul.hMul) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHMul) (:c ENNReal) ((:c CanonicallyOrderedCommSemiring.toMul) (:c ENNReal) (:c ENNReal.instCanonicallyOrderedCommSemiring))) ((:c ENNReal.ofNNReal) ((:c NNNorm.nnnorm) (:fv _uniq.377052) ((:c SeminormedAddGroup.toNNN... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.377049))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.377049))"},{"name":"p","sexp":"(:c ENNRea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c ENNReal.toReal) (:arg :explicit 0 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c ENNReal)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.377049","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.377052","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":44365,"sourceStart":44363,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":44367,"sourceStart":44366,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"ENNReal.toReal_m... | [] | [{"source":"ENNReal.toReal_mul","source_end":44385,"source_start":44367,"syntax_kind":"ident"},{"source":"ENNReal.coe_toReal","source_end":44405,"source_start":44387,"syntax_kind":"ident"},{"source":"ENNReal.toReal_rpow","source_end":44430,"source_start":44411,"syntax_kind":"ident"},{"source":"coe_nnnorm","source_end":... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.377049","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.377052","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 260 | 24 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 904041302b13ed53361a68bee80c1fabc60c9e897217b69062421dc1979560eb | b146b4e982aa3b7044d4d7bc26437c6fee3875e294a91f060a2324673a5aee89 | aa4a4bb2490853739a3170fd220c3df490309c6ca9df3231de9c3b16e9a9f02b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,347 | MeasureTheory.Lp.norm_const | Mathlib/MeasureTheory/Function/LpSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | assumption | case hμ
α : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
m m0 : MeasurableSpace α
p : ℝ≥0∞
q : ℝ
μ ν : Measure α
inst✝⁴ : NormedAddCommGroup E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedAddCommGroup G
inst✝¹ : IsFiniteMeasure μ
c : E
inst✝ : NeZero μ
hp_zero : p ≠ 0
this : μ ≠ 0
⊢ μ ≠ 0 | ((:c Ne) ((:c MeasureTheory.Measure) (:fv _uniq.377049) (:fv _uniq.377064)) (:fv _uniq.377077) ((:c OfNat.ofNat) ((:c MeasureTheory.Measure) (:fv _uniq.377049) (:fv _uniq.377064)) (:lit 0) ((:c Zero.toOfNat0) ((:c MeasureTheory.Measure) (:fv _uniq.377049) (:fv _uniq.377064)) ((:c MeasureTheory.Measure.instZero) (:fv _u... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.377049))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.377049))"},{"name":"p","sexp":"(:c ENNRea... | (:app (:c Ne) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:fv FV8)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.377049","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.377052","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"assumption","sourceEnd":44360,"sourceStart":44350,"tag":"atom"}],"kind":"Lean.Parser.Tactic.assumption","source":"assumption","sourceEnd":44360,"sourceStart":44350,"tag":"node"}],"kind":"null","source":"assumption","sourceEnd":44360,"sourceStart":44350,"tag... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.377049","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.377052","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 260 | 21 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 760be51bd56f58bb460b1b0a00b1f7f3a35244f76aea71fa09d766ec4850272e | 92f3621ac2d39b6845cc9df384875c965010ed5db32afee5c64ad7f15ee61d39 | c081dd376ba93a530dd044cffc81e70953e86d86f7d0796dc26bc1597302573d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,348 | MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendsto | Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>tendsto_nhds_unique</a> (<a>MeasureTheory.intervalIntegral_tendsto_integral_Ioi</a> a f'int <a>Filter.tendsto_id</a>) ?_ | E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont✝ : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
hcont : ContinuousOn f (Ici a)
⊢ ∫ ... | E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont✝ : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
hcont : ContinuousOn f (Ici a)
⊢ Te... | ((:c Eq) (:fv _uniq.179672) ((:c MeasureTheory.integral) (:c Real) (:fv _uniq.179672) (:fv _uniq.179699) (:fv _uniq.179809) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)) ((:c MeasureTheory.Measure.restrict) (:c Real) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"f'","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g'","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:c Real)"},{"name":"b"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c MeasureTheory.integral) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c NormedSpace) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:fv FV0))"},... | {"children":[{"source":"refine","sourceEnd":45058,"sourceStart":45052,"tag":"atom"},{"children":[{"name":"tendsto_nhds_unique","semanticRole":"global","source":"tendsto_nhds_unique","sourceEnd":45078,"sourceStart":45059,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":45080,"sourceStart":45079,"t... | [] | [{"source":"tendsto_nhds_unique (intervalIntegral_tendsto_integral_Ioi a f'int tendsto_id) ?_","source_end":45140,"source_start":45059,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 188 | 18 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5e6653d71f21cbf5ecb55b2cedbd2f8a17b701f092a6779b1d040ea68ceb4fb4 | 41299e0cd4572ce2694c7b0a8beed62cfd1a5b6242cf929a0e97023f136dd8c4 | 8c42b84a59eabe04748fd365ca52bfe81ee5caee941b9ced7794016c4fd64490 | 69cb81e1de5beb3a57444580212a4b2ec938838bfa3f672da49d115548f6eb74 |
cat-searcher/leandojo-benchmark-4-random | test | 4,349 | MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendsto | Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Filter.Tendsto.congr'</a> _ (hf.sub_const _) | E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont✝ : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
hcont : ContinuousOn f (Ici a)
⊢ Te... | E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont✝ : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
hcont : ContinuousOn f (Ici a)
⊢ (f... | ((:c Filter.Tendsto) (:c Real) (:fv _uniq.179672) (:lambda i (:c Real) ((:c intervalIntegral) (:fv _uniq.179672) (:fv _uniq.179699) (:fv _uniq.179809) (:lambda x (:c Real) ((:fv _uniq.179680) 0)) (:fv _uniq.179690) ((:c id) (:c Real) 0) ((:c MeasureTheory.MeasureSpace.volume) (:c Real) (:c Real.measureSpace)))) ((:c Fi... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"f'","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g'","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:c Real)"},{"name":"b"... | (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:lambda i :explicit (:c Real) (:app (:c intervalIntegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:fv FV0))"},... | {"children":[{"source":"apply","sourceEnd":45148,"sourceStart":45143,"tag":"atom"},{"children":[{"name":"Filter.Tendsto.congr'","semanticRole":"global","source":"Tendsto.congr'","sourceEnd":45163,"sourceStart":45149,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":45165,"sourceStart":45164,"tag":... | [] | [{"source":"Tendsto.congr' _ (hf.sub_const _)","source_end":45182,"source_start":45149,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 188 | 19 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fe6252f5011f222b0676e1ab878ea9a3236bca447a58aeb778d462c986f35382 | 69cb81e1de5beb3a57444580212a4b2ec938838bfa3f672da49d115548f6eb74 | b0d1ce7aa6516d68b16b1f968c7c60909e70960ea19d8c43691c96661c2c5e71 | d61caeb582e5d92bdad86052fa0b7953f521355ed0895ccc7210227b6e54cf5b |
cat-searcher/leandojo-benchmark-4-random | test | 4,350 | MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendsto | Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards [<a>Filter.Ioi_mem_atTop</a> a] with x hx | E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont✝ : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
hcont : ContinuousOn f (Ici a)
⊢ (f... | case h
E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont✝ : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
hcont : ContinuousOn f (Ici ... | ((:c Filter.EventuallyEq) (:c Real) (:fv _uniq.179672) ((:c Filter.atTop) (:c Real) (:c Real.instPreorder)) (:lambda _ (:c Real) ((:c HSub.hSub) (:fv _uniq.179672) (:fv _uniq.179672) (:fv _uniq.179672) ((:c instHSub) (:fv _uniq.179672) ((:c SubNegMonoid.toSub) (:fv _uniq.179672) ((:c AddGroup.toSubNegMonoid) (:fv _uniq... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"f'","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g'","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:c Real)"},{"name":"b"... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:app (:c Filter.atTop) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 3 (:lambda _ :explicit (:c Real) (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:fv FV0))"},... | {"children":[{"source":"filter_upwards","sourceEnd":45199,"sourceStart":45185,"tag":"atom"},{"children":[{"source":"[","sourceEnd":45201,"sourceStart":45200,"tag":"atom"},{"children":[{"children":[{"name":"Filter.Ioi_mem_atTop","semanticRole":"global","source":"Ioi_mem_atTop","sourceEnd":45214,"sourceStart":45201,"tag"... | [] | [{"source":"Ioi_mem_atTop a","source_end":45216,"source_start":45201,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 188 | 20 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 605962fb1a67f3704988733d99323ceb0d795f2944840b3188bfff6fc4baeffe | d61caeb582e5d92bdad86052fa0b7953f521355ed0895ccc7210227b6e54cf5b | b471f36f8d62040b01a10acd3deb644ee52b3c1827487f8df47e87558c2202f3 | fe35596aec12603f508c9990ab1053a13fbcddf3f9b3b9669c564a4e6e3485b3 |
cat-searcher/leandojo-benchmark-4-random | test | 4,351 | MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendsto | Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h'x : a ≤ <a>id</a> x := <a>le_of_lt</a> hx | case h
E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont✝ : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
hcont : ContinuousOn f (Ici ... | case h
E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont✝ : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
hcont : ContinuousOn f (Ici ... | ((:c Eq) (:fv _uniq.179672) ((:c HSub.hSub) (:fv _uniq.179672) (:fv _uniq.179672) (:fv _uniq.179672) ((:c instHSub) (:fv _uniq.179672) ((:c SubNegMonoid.toSub) (:fv _uniq.179672) ((:c AddGroup.toSubNegMonoid) (:fv _uniq.179672) ((:c NormedAddGroup.toAddGroup) (:fv _uniq.179672) ((:c NormedAddCommGroup.toNormedAddGroup)... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"f'","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g'","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:c Real)"},{"name":"b"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HSub) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:fv FV0))"},... | {"children":[{"source":"have","sourceEnd":45234,"sourceStart":45230,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h'x","sourceEnd":45238,"sourceStart":45235,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h'x","sourceEnd":45238,"sourceStart":45235,"tag":"n... | [] | [{"source":"a ≤ id x","source_end":45251,"source_start":45241,"syntax_kind":"«term_≤_»"},{"source":"le_of_lt hx","source_end":45266,"source_start":45255,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 188 | 21 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aecd101a472b1105714d90354d3ad286cb108edec226ffb19ea59083ba86f54d | fe35596aec12603f508c9990ab1053a13fbcddf3f9b3b9669c564a4e6e3485b3 | de9fd36c711d656d6122931954599a4c373793965726d55e5ac01653d56d8d9f | 5de325ab20dc34c4be4a60cc5586fa13ece8df5828c5ff951675726f2eb69b8e |
cat-searcher/leandojo-benchmark-4-random | test | 4,352 | MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendsto | Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | symm | case h
E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont✝ : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
hcont : ContinuousOn f (Ici ... | case h
E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont✝ : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
hcont : ContinuousOn f (Ici ... | ((:c Eq) (:fv _uniq.179672) ((:c HSub.hSub) (:fv _uniq.179672) (:fv _uniq.179672) (:fv _uniq.179672) ((:c instHSub) (:fv _uniq.179672) ((:c SubNegMonoid.toSub) (:fv _uniq.179672) ((:c AddGroup.toSubNegMonoid) (:fv _uniq.179672) ((:c NormedAddGroup.toAddGroup) (:fv _uniq.179672) ((:c NormedAddCommGroup.toNormedAddGroup)... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"f'","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g'","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:c Real)"},{"name":"b"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HSub) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:fv FV0))"},... | {"children":[{"source":"symm","sourceEnd":45273,"sourceStart":45269,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.symm","source":"symm","sourceEnd":45273,"sourceStart":45269,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 188 | 22 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5ecb538ca9949bc4c6c08cc1d7157776e06ae1f8913d96139fad33d1c16739c0 | 5de325ab20dc34c4be4a60cc5586fa13ece8df5828c5ff951675726f2eb69b8e | f97373c83b943be1711d624ac8176e49b7c19e0f5ce55ad3a0ad56d8d1aae1fa | c454da2241c578bb5b29f60a20469fbbce3ee22a1fce24cbeaa8d7b318b252a1 |
cat-searcher/leandojo-benchmark-4-random | test | 4,353 | MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendsto | Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>intervalIntegral.integral_eq_sub_of_hasDerivAt_of_le</a> h'x (hcont.mono <a>Set.Icc_subset_Ici_self</a>) fun y hy => hderiv y hy.1 | case h
E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont✝ : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
hcont : ContinuousOn f (Ici ... | case h
E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont✝ : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
hcont : ContinuousOn f (Ici ... | ((:c Eq) (:fv _uniq.179672) ((:c intervalIntegral) (:fv _uniq.179672) (:fv _uniq.179699) (:fv _uniq.179809) (:lambda x (:c Real) ((:fv _uniq.179680) 0)) (:fv _uniq.179690) ((:c id) (:c Real) (:fv _uniq.185348)) ((:c MeasureTheory.MeasureSpace.volume) (:c Real) (:c Real.measureSpace))) ((:c HSub.hSub) (:fv _uniq.179672)... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"f'","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g'","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:c Real)"},{"name":"b"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c intervalIntegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c NormedSpace) (:arg :explicit 0 (:c Real)) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:fv FV0))"},... | {"children":[{"source":"apply","sourceEnd":45281,"sourceStart":45276,"tag":"atom"},{"children":[{"name":"intervalIntegral.integral_eq_sub_of_hasDerivAt_of_le","semanticRole":"global","source":"intervalIntegral.integral_eq_sub_of_hasDerivAt_of_le","sourceEnd":45338,"sourceStart":45286,"tag":"identifier"},{"children":[{"... | [] | [{"source":"intervalIntegral.integral_eq_sub_of_hasDerivAt_of_le h'x (hcont.mono Icc_subset_Ici_self)\n fun y hy => hderiv y hy.1","source_end":45407,"source_start":45286,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 188 | 23 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c9c33cfbe3c45bb7ec71c1d539c85870ee8b49598c32a7ae68d7fd5a8ddb8c98 | c454da2241c578bb5b29f60a20469fbbce3ee22a1fce24cbeaa8d7b318b252a1 | d940a752aeddcceaaded3d00830d681937422885a00b423c7d87bfc3d8d5aed9 | 64e6a37891645a4003c09f6955a4721c2e84880233827c1acc58ecea00481ae1 |
cat-searcher/leandojo-benchmark-4-random | test | 4,354 | MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendsto | Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>intervalIntegrable_iff_integrableOn_Ioc_of_le</a> h'x] | case h
E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont✝ : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
hcont : ContinuousOn f (Ici ... | case h
E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont✝ : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
hcont : ContinuousOn f (Ici ... | ((:c IntervalIntegrable) (:fv _uniq.179672) (:fv _uniq.179699) (:fv _uniq.179680) ((:c MeasureTheory.MeasureSpace.volume) (:c Real) (:c Real.measureSpace)) (:fv _uniq.179690) ((:c id) (:c Real) (:fv _uniq.185348))) | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"f'","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g'","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:c Real)"},{"name":"b"... | (:app (:c IntervalIntegrable) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:app (:c MeasureTheory.MeasureSpace.volume) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:fv FV0))"},... | {"children":[{"source":"rw","sourceEnd":45412,"sourceStart":45410,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":45414,"sourceStart":45413,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"int... | [] | [{"source":"intervalIntegrable_iff_integrableOn_Ioc_of_le h'x","source_end":45463,"source_start":45414,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 188 | 24 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 57e1fe84ea5777a07e6a038ee7a61c9de28533a23b5b65917411fa5ba53847b6 | 64e6a37891645a4003c09f6955a4721c2e84880233827c1acc58ecea00481ae1 | 42cb67672990f86343f86eb6b015ef9246006078f86fa9dc1122ca0003419b7b | 43a44d248ad3f9da1d69634c5f279a2ae97a183a3d566769f7173bd8a376b012 |
cat-searcher/leandojo-benchmark-4-random | test | 4,355 | MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendsto | Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact f'int.mono (fun y hy => hy.1) <a>le_rfl</a> | case h
E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont✝ : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
hcont : ContinuousOn f (Ici ... | ((:c MeasureTheory.IntegrableOn) (:c Real) (:fv _uniq.179672) (:c Real.measurableSpace) (:fv _uniq.179699) (:fv _uniq.179680) ((:c Set.Ioc) (:c Real) (:c Real.instPreorder) (:fv _uniq.179690) ((:c id) (:c Real) (:fv _uniq.185348))) ((:c MeasureTheory.MeasureSpace.volume) (:c Real) (:c Real.measureSpace))) | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"f'","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g'","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:c Real)"},{"name":"b"... | (:app (:c MeasureTheory.IntegrableOn) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 4 (:fv FV2)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:fv FV0))"},... | {"children":[{"source":"exact","sourceEnd":45472,"sourceStart":45467,"tag":"atom"},{"children":[{"source":"f'int.mono","sourceEnd":45483,"sourceStart":45473,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":45485,"sourceStart":45484,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":45488,"sou... | [] | [{"source":"f'int.mono (fun y hy => hy.1) le_rfl","source_end":45509,"source_start":45473,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 188 | 27 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | db342c140afb093e2055f51e48f2a0c4020ee352bcccb6272a091701789a3f12 | 43a44d248ad3f9da1d69634c5f279a2ae97a183a3d566769f7173bd8a376b012 | fb255fd4ea05c841ff1831dc0f44b58bfc9b792491b1a105711d8c285921c37f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,356 | MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendsto | Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro x hx | E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
⊢ ContinuousOn f (Ici a) | E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
x : ℝ
hx : x ∈ Ici a
⊢ ContinuousWit... | ((:c ContinuousOn) (:c Real) (:fv _uniq.179672) ((:c UniformSpace.toTopologicalSpace) (:c Real) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.pseudoMetricSpace))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.179672) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.179672) ((:c SeminormedAddCommGroup.to... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"f'","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g'","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:c Real)"},{"name":"b"... | (:app (:c ContinuousOn) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 4 (:fv FV1)) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:fv FV0))"},... | {"children":[{"source":"intro","sourceEnd":44927,"sourceStart":44922,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":44929,"sourceStart":44928,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hx","sourceEnd":44932,"sourceStart":44930,"tag":"identifier"}],"kind":"null","sou... | [{"role":"fresh_name","source":"x","source_end":44929,"source_start":44928,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":44932,"source_start":44930,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 188 | 6 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c1443d48d3e621ec69ab1fe01c0a0bcb24ebcae5f6b658c60a8d13e13d476eeb | 1f6f37f59e536edcdaa422ced494403f6b257f906ca498236759deb01e1e0e8c | 65777af1f444837568ec00c3040db2bdc96178d91d8bf83037116b747be939ac | aee0f130e07030a6bb9d26b74b5cab07170c07f26e8bfc83cb4933be1ca2e2e4 |
cat-searcher/leandojo-benchmark-4-random | test | 4,357 | MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendsto | Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases hx.out.eq_or_lt with rfl|hx | E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
x : ℝ
hx : x ∈ Ici a
⊢ ContinuousWit... | case inl
E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
hx : a ∈ Ici a
⊢ Continuous... | ((:c ContinuousWithinAt) (:c Real) (:fv _uniq.179672) ((:c UniformSpace.toTopologicalSpace) (:c Real) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.pseudoMetricSpace))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.179672) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.179672) ((:c SeminormedAddCommGr... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"f'","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g'","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:c Real)"},{"name":"b"... | (:app (:c ContinuousWithinAt) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 4 (:fv FV1)) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:fv FV0))"},... | {"children":[{"source":"rcases","sourceEnd":44943,"sourceStart":44937,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"LE.le.eq_or_lt","semanticRole":"global","source":"hx.out.eq_or_lt","sourceEnd":44959,"sourceStart":44944,"tag":"identifier"}],"kind":"Lean.Parser.... | [] | [{"source":"hx.out.eq_or_lt","source_end":44959,"source_start":44944,"syntax_kind":"ident"},{"source":"rfl|hx","source_end":44971,"source_start":44965,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 188 | 7 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1b41a42b5c365a8537afb6346f646c96dee354e3c41a96b84ee0bca6db5760fe | aee0f130e07030a6bb9d26b74b5cab07170c07f26e8bfc83cb4933be1ca2e2e4 | df8c34612610b9e36213d0baeada7f9e9c62e439934e1705a38a1d16640dc964 | 05fb71a88127cfded2cf67bd50e7934d894c8b07ecd9e5c260cd55ba6b978b81 |
cat-searcher/leandojo-benchmark-4-random | test | 4,358 | MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendsto | Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hcont | case inl
E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
hx : a ∈ Ici a
⊢ Continuous... | ((:c ContinuousWithinAt) (:c Real) (:fv _uniq.179672) ((:c UniformSpace.toTopologicalSpace) (:c Real) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.pseudoMetricSpace))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.179672) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.179672) ((:c SeminormedAddCommGr... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"f'","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g'","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:c Real)"},{"name":"b"... | (:app (:c ContinuousWithinAt) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 4 (:fv FV1)) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:fv FV0))"},... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":44984,"sourceStart":44979,"tag":"atom"},{"contextIndex":13,"semanticRole":"local","source":"hcont","sourceEnd":44990,"sourceStart":44985,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact hcont","sourceEnd":44990,"sour... | [] | [{"source":"hcont","source_end":44990,"source_start":44985,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 188 | 10 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cfe51b5fe9d18a3c51a10cce5b243cf4cc45a575cefb078bc3174c7f9057b5fe | d2173e70ca0e205af5884d49f7014f46d789877a4668b549fb375424e14375cb | a7de200bdb9f8e3c90417e78790663c2e93d971bf5256e905a3fa7d10d622ce0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,359 | MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendsto | Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (hderiv x hx).continuousAt.continuousWithinAt | case inr
E : Type u_1
f f' : ℝ → E
g g' : ℝ → ℝ
a b l : ℝ
m : E
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
hcont : ContinuousWithinAt f (Ici a) a
hderiv : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x
f'int : IntegrableOn f' (Ioi a) volume
hf : Tendsto f atTop (𝓝 m)
x : ℝ
hx✝ : x ∈ Ici a
hx : ... | ((:c ContinuousWithinAt) (:c Real) (:fv _uniq.179672) ((:c UniformSpace.toTopologicalSpace) (:c Real) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.pseudoMetricSpace))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.179672) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.179672) ((:c SeminormedAddCommGr... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"f'","sexp":"(:forall _ (:c Real) (:fv _uniq.179672))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g'","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:c Real)"},{"name":"b"... | (:app (:c ContinuousWithinAt) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 4 (:fv FV1)) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:fv FV0))"},... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":45003,"sourceStart":44998,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":45005,"sourceStart":45004,"tag":"atom"},{"children":[{"contextIndex":14,"semanticRole":"local","source":"hderiv","sourceEnd":45011,"sourceStart":4... | [] | [{"source":"(hderiv x hx).continuousAt.continuousWithinAt","source_end":45049,"source_start":45004,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179672","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179676","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 188 | 15 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ccd7dbe057a0633f6d81a0ede0d08d0b748209b1b3a1211c1e0f01715d12941c | 2643e73ebace4ed2276d2c7e2362c7afb9062c058fed947c2ce4c97f34c127de | ca62c653a44a205f17e91970d7e3af06a91fbb3707f1643cbc8b938b99da0965 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,360 | BoxIntegral.Box.measurableSet_coe | Mathlib/Analysis/BoxIntegral/Partition/Measure.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>BoxIntegral.Box.coe_eq_pi</a>] | ι : Type u_1
I : Box ι
inst✝ : Countable ι
⊢ MeasurableSet ↑I | ι : Type u_1
I : Box ι
inst✝ : Countable ι
⊢ MeasurableSet (univ.pi fun i => Ioc (I.lower i) (I.upper i)) | ((:c MeasurableSet) (:forall _ (:fv _uniq.7809) (:c Real)) ((:c MeasurableSpace.pi) (:fv _uniq.7809) (:lambda _ (:fv _uniq.7809) (:c Real)) (:lambda a (:fv _uniq.7809) (:c Real.measurableSpace))) ((:c BoxIntegral.Box.toSet) (:fv _uniq.7809) (:fv _uniq.7812))) | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"I","sexp":"((:c BoxIntegral.Box) (:fv _uniq.7809))"},{"name":"inst✝","sexp":"((:c Countable) (:fv _uniq.7809))"}] | (:app (:c MeasurableSet) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:c Real))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:forall a :explicit (:fv FV0) (:c Real)))))) (:arg :explicit 2 (:app (:c BoxIntegral.Box.toSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7809","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.7812","is_instance":false,"is_let":false,"name":"I","sexp":"(:app (:c BoxIntegral.Box) (:arg :explicit 0 (:f... | {"children":[{"source":"rw","sourceEnd":1805,"sourceStart":1803,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1807,"sourceStart":1806,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"BoxIntegral.Box.coe_... | [] | [{"source":"coe_eq_pi","source_end":1816,"source_start":1807,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7809","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.7812","is_instance":false,"is_let":false,"user_name":"I"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 16 | 4 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e5c384d58dc0e756e3c806575b8b75a805167916a03dd45af072ffe5b43d4b35 | c826fcf87b57b0bac855e5f1d381345f814a788a082d1c7f569ad34f0ba2c06b | 018e46a174caee5824b597dc0303514f37dd9ab666957274058f00988296ff44 | bc02fbb28856621db5293104867538926d03d3779bb3c000371eebbc221bafeb |
cat-searcher/leandojo-benchmark-4-random | test | 4,361 | BoxIntegral.Box.measurableSet_coe | Mathlib/Analysis/BoxIntegral/Partition/Measure.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>MeasurableSet.univ_pi</a> fun i => <a>measurableSet_Ioc</a> | ι : Type u_1
I : Box ι
inst✝ : Countable ι
⊢ MeasurableSet (univ.pi fun i => Ioc (I.lower i) (I.upper i)) | ((:c MeasurableSet) (:forall _ (:fv _uniq.7809) (:c Real)) ((:c MeasurableSpace.pi) (:fv _uniq.7809) (:lambda _ (:fv _uniq.7809) (:c Real)) (:lambda a (:fv _uniq.7809) (:c Real.measurableSpace))) ((:c Set.pi) (:fv _uniq.7809) (:lambda i (:fv _uniq.7809) (:c Real)) ((:c Set.univ) (:fv _uniq.7809)) (:lambda i (:fv _uniq.... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"I","sexp":"((:c BoxIntegral.Box) (:fv _uniq.7809))"},{"name":"inst✝","sexp":"((:c Countable) (:fv _uniq.7809))"}] | (:app (:c MeasurableSet) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:c Real))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:forall a :explicit (:fv FV0) (:c Real)))))) (:arg :explicit 2 (:app (:c Set.pi) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7809","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.7812","is_instance":false,"is_let":false,"name":"I","sexp":"(:app (:c BoxIntegral.Box) (:arg :explicit 0 (:f... | {"children":[{"source":"exact","sourceEnd":1825,"sourceStart":1820,"tag":"atom"},{"children":[{"name":"MeasurableSet.univ_pi","semanticRole":"global","source":"MeasurableSet.univ_pi","sourceEnd":1847,"sourceStart":1826,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":1851,"sourceStart":1848,"ta... | [] | [{"source":"MeasurableSet.univ_pi fun i => measurableSet_Ioc","source_end":1874,"source_start":1826,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7809","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.7812","is_instance":false,"is_let":false,"user_name":"I"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 16 | 7 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 96b8a036200fed65557a3db04d6bacb1abc735d4930b879a7c6dcfdce108aa34 | bc02fbb28856621db5293104867538926d03d3779bb3c000371eebbc221bafeb | b452e8c871eda58f01ebd481927965ec84235808f35dba1299c10ac02ca0c92d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,362 | Sum.lex_acc_inr | .lake/packages/batteries/Batteries/Data/Sum/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction acb with | <a>Acc.intro</a> _ _ IH => constructor intro y h cases h with | <a>Sum.Lex.inr</a> h' => exact IH _ h' | <a>Sum.Lex.sep</a> => exact aca _ | α✝ : Type u_1
r : α✝ → α✝ → Prop
β✝ : Type u_2
s : β✝ → β✝ → Prop
aca : ∀ (a : α✝), Acc (Lex r s) (inl a)
b : β✝
acb : Acc s b
⊢ Acc (Lex r s) (inr b) | ((:c Acc) ((:c Sum) (:fv _uniq.16722) (:fv _uniq.16724)) ((:c Sum.Lex) (:fv _uniq.16722) (:fv _uniq.16724) (:fv _uniq.16723) (:fv _uniq.16725)) ((:c Sum.inr) (:fv _uniq.16722) (:fv _uniq.16724) (:fv _uniq.16727))) | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.16722) (:forall _ (:fv _uniq.16722) (:sort 0)))"},{"name":"β✝","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"(:forall _ (:fv _uniq.16724) (:forall _ (:fv _uniq.16724) (:sort 0)))"},{"name":"aca","sexp":"(:forall a (:fv _uniq.16722) ((... | (:app (:c Acc) (:arg :implicit-type 0 (:app (:c Sum) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV3)))) (:arg :explicit 1 (:app (:c Sum.Lex) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV3)) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV4)))) (:arg :explicit 2 (:app (:c Sum.inr) (:arg... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16722","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.16723","is_instance":false,"is_let":false,"name":"r","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :ex... | {"children":[{"children":[{"children":[{"children":[{"source":"induction","sourceEnd":8500,"sourceStart":8491,"tag":"atom"},{"children":[{"contextIndex":7,"semanticRole":"local","source":"acb","sourceEnd":8504,"sourceStart":8501,"tag":"identifier"}],"kind":"null","source":"acb","sourceEnd":8504,"sourceStart":8501,"tag"... | [] | [{"source":"acb","source_end":8504,"source_start":8501,"syntax_kind":"ident"},{"source":"intro","source_end":8519,"source_start":8514,"syntax_kind":"ident"},{"source":"h","source_end":8571,"source_start":8570,"syntax_kind":"ident"},{"source":"inr","source_end":8586,"source_start":8583,"syntax_kind":"ident"},{"source":"... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16722","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.16723","is_instance":false,"is_let":false,"user_name":"r"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 68 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 88018f87ccebb29dfe33aaf5ec1ddef79de26cdb7321b0688fe3d169abbfb07a | 8ece53ae73049d21d09959318c3557567435b003c10839ca94847f01efec524a | 8c705ec2ad1a693d19714e0769f87d4514a6182c786a367137881e1b32b3da2c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,363 | Sum.lex_acc_inr | .lake/packages/batteries/Batteries/Data/Sum/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | case intro
α✝ : Type u_1
r : α✝ → α✝ → Prop
β✝ : Type u_2
s : β✝ → β✝ → Prop
aca : ∀ (a : α✝), Acc (Lex r s) (inl a)
b x✝ : β✝
h✝ : ∀ (y : β✝), s y x✝ → Acc s y
IH : ∀ (y : β✝), s y x✝ → Acc (Lex r s) (inr y)
⊢ Acc (Lex r s) (inr x✝) | case intro.h
α✝ : Type u_1
r : α✝ → α✝ → Prop
β✝ : Type u_2
s : β✝ → β✝ → Prop
aca : ∀ (a : α✝), Acc (Lex r s) (inl a)
b x✝ : β✝
h✝ : ∀ (y : β✝), s y x✝ → Acc s y
IH : ∀ (y : β✝), s y x✝ → Acc (Lex r s) (inr y)
⊢ ∀ (y : α✝ ⊕ β✝), Lex r s y (inr x✝) → Acc (Lex r s) y | ((:c Acc) ((:c Sum) (:fv _uniq.16722) (:fv _uniq.16724)) ((:c Sum.Lex) (:fv _uniq.16722) (:fv _uniq.16724) (:fv _uniq.16723) (:fv _uniq.16725)) ((:c Sum.inr) (:fv _uniq.16722) (:fv _uniq.16724) (:fv _uniq.16770))) | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.16722) (:forall _ (:fv _uniq.16722) (:sort 0)))"},{"name":"β✝","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"(:forall _ (:fv _uniq.16724) (:forall _ (:fv _uniq.16724) (:sort 0)))"},{"name":"aca","sexp":"(:forall a (:fv _uniq.16722) ((... | (:app (:c Acc) (:arg :implicit-type 0 (:app (:c Sum) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV3)))) (:arg :explicit 1 (:app (:c Sum.Lex) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV3)) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV4)))) (:arg :explicit 2 (:app (:c Sum.inr) (:arg... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16722","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.16723","is_instance":false,"is_let":false,"name":"r","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :ex... | {"children":[{"source":"constructor","sourceEnd":8545,"sourceStart":8534,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":8545,"sourceStart":8534,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16722","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.16723","is_instance":false,"is_let":false,"user_name":"r"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 68 | 9 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5c7b4da14e9de50139a9988e5cf54984613e8fc60543cea8557548b9c2a27caf | dc95c5f1726159fe37a0585dcb441183bd8ffc91bbe47783c2fe07e81f6d25e5 | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | 48064ef8ab21e06519d6639131548dec6b9e6c9db49d45b904190133dbf21d54 |
cat-searcher/leandojo-benchmark-4-random | test | 4,364 | Sum.lex_acc_inr | .lake/packages/batteries/Batteries/Data/Sum/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro y h | case intro.h
α✝ : Type u_1
r : α✝ → α✝ → Prop
β✝ : Type u_2
s : β✝ → β✝ → Prop
aca : ∀ (a : α✝), Acc (Lex r s) (inl a)
b x✝ : β✝
h✝ : ∀ (y : β✝), s y x✝ → Acc s y
IH : ∀ (y : β✝), s y x✝ → Acc (Lex r s) (inr y)
⊢ ∀ (y : α✝ ⊕ β✝), Lex r s y (inr x✝) → Acc (Lex r s) y | case intro.h
α✝ : Type u_1
r : α✝ → α✝ → Prop
β✝ : Type u_2
s : β✝ → β✝ → Prop
aca : ∀ (a : α✝), Acc (Lex r s) (inl a)
b x✝ : β✝
h✝ : ∀ (y : β✝), s y x✝ → Acc s y
IH : ∀ (y : β✝), s y x✝ → Acc (Lex r s) (inr y)
y : α✝ ⊕ β✝
h : Lex r s y (inr x✝)
⊢ Acc (Lex r s) y | (:forall y ((:c Sum) (:fv _uniq.16722) (:fv _uniq.16724)) (:forall _ ((:c Sum.Lex) (:fv _uniq.16722) (:fv _uniq.16724) (:fv _uniq.16723) (:fv _uniq.16725) 0 ((:c Sum.inr) (:fv _uniq.16722) (:fv _uniq.16724) (:fv _uniq.16770))) ((:c Acc) ((:c Sum) (:fv _uniq.16722) (:fv _uniq.16724)) ((:c Sum.Lex) (:fv _uniq.16722) (:fv... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.16722) (:forall _ (:fv _uniq.16722) (:sort 0)))"},{"name":"β✝","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"(:forall _ (:fv _uniq.16724) (:forall _ (:fv _uniq.16724) (:sort 0)))"},{"name":"aca","sexp":"(:forall a (:fv _uniq.16722) ((... | (:forall y :explicit (:app (:c Sum) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV3))) (:forall _ :explicit (:app (:c Sum.Lex) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV3)) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV4)) (:arg :explicit 4 0) (:arg :explicit 5 (:app (:c Sum.inr) (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16722","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.16723","is_instance":false,"is_let":false,"name":"r","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :ex... | {"children":[{"source":"intro","sourceEnd":8555,"sourceStart":8550,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":8557,"sourceStart":8556,"tag":"identifier"},{"semanticRole":"scoped_local","source":"h","sourceEnd":8559,"sourceStart":8558,"tag":"identifier"}],"kind":"null","source":"y... | [{"role":"fresh_name","source":"y","source_end":8557,"source_start":8556,"syntax_kind":"ident"},{"role":"fresh_name","source":"h","source_end":8559,"source_start":8558,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16722","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.16723","is_instance":false,"is_let":false,"user_name":"r"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 68 | 10 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e6a00a8413330d6542bb868facac28e11eb9dd4a62889d8d14eae0296f898de7 | 48064ef8ab21e06519d6639131548dec6b9e6c9db49d45b904190133dbf21d54 | 1eb1fed223eb3a4422e1cfe3040fd5ac0eb08422faa3d95493839a43d43e0077 | 685197b81b12643121ad9d14d15274b5879a9b249da13286a550f0675988391b |
cat-searcher/leandojo-benchmark-4-random | test | 4,365 | Sum.lex_acc_inr | .lake/packages/batteries/Batteries/Data/Sum/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases h with | <a>Sum.Lex.inr</a> h' => exact IH _ h' | <a>Sum.Lex.sep</a> => exact aca _ | case intro.h
α✝ : Type u_1
r : α✝ → α✝ → Prop
β✝ : Type u_2
s : β✝ → β✝ → Prop
aca : ∀ (a : α✝), Acc (Lex r s) (inl a)
b x✝ : β✝
h✝ : ∀ (y : β✝), s y x✝ → Acc s y
IH : ∀ (y : β✝), s y x✝ → Acc (Lex r s) (inr y)
y : α✝ ⊕ β✝
h : Lex r s y (inr x✝)
⊢ Acc (Lex r s) y | ((:c Acc) ((:c Sum) (:fv _uniq.16722) (:fv _uniq.16724)) ((:c Sum.Lex) (:fv _uniq.16722) (:fv _uniq.16724) (:fv _uniq.16723) (:fv _uniq.16725)) (:fv _uniq.16793)) | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.16722) (:forall _ (:fv _uniq.16722) (:sort 0)))"},{"name":"β✝","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"(:forall _ (:fv _uniq.16724) (:forall _ (:fv _uniq.16724) (:sort 0)))"},{"name":"aca","sexp":"(:forall a (:fv _uniq.16722) ((... | (:app (:c Acc) (:arg :implicit-type 0 (:app (:c Sum) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV3)))) (:arg :explicit 1 (:app (:c Sum.Lex) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV3)) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV4)))) (:arg :explicit 2 (:fv FV10))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16722","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.16723","is_instance":false,"is_let":false,"name":"r","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :ex... | {"children":[{"source":"cases","sourceEnd":8569,"sourceStart":8564,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":11,"semanticRole":"local","source":"h","sourceEnd":8571,"sourceStart":8570,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","sourc... | [] | [{"source":"h","source_end":8571,"source_start":8570,"syntax_kind":"ident"},{"source":"inr","source_end":8586,"source_start":8583,"syntax_kind":"ident"},{"source":"IH _ h'","source_end":8606,"source_start":8599,"syntax_kind":"Lean.Parser.Term.app"},{"source":"sep","source_end":8616,"source_start":8613,"syntax_kind":"id... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16722","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.16723","is_instance":false,"is_let":false,"user_name":"r"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 68 | 11 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3476894bd4ee9c38de45d4c28f69f143c3688e680e999c275c161675ca0c7157 | 685197b81b12643121ad9d14d15274b5879a9b249da13286a550f0675988391b | 3dc6fca160813cd469ae85047ef657ffc4f6e6ecfec860488bc903bdc7c4db51 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,366 | Sum.lex_acc_inr | .lake/packages/batteries/Batteries/Data/Sum/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact IH _ h' | case intro.h.inr
α✝ : Type u_1
r : α✝ → α✝ → Prop
β✝ : Type u_2
s : β✝ → β✝ → Prop
aca : ∀ (a : α✝), Acc (Lex r s) (inl a)
b x✝ : β✝
h✝ : ∀ (y : β✝), s y x✝ → Acc s y
IH : ∀ (y : β✝), s y x✝ → Acc (Lex r s) (inr y)
b₁✝ : β✝
h' : s b₁✝ x✝
⊢ Acc (Lex r s) (inr b₁✝) | ((:c Acc) ((:c Sum) (:fv _uniq.16722) (:fv _uniq.16724)) ((:c Sum.Lex) (:fv _uniq.16722) (:fv _uniq.16724) (:fv _uniq.16723) (:fv _uniq.16725)) ((:c Sum.inr) (:fv _uniq.16722) (:fv _uniq.16724) (:fv _uniq.16887))) | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.16722) (:forall _ (:fv _uniq.16722) (:sort 0)))"},{"name":"β✝","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"(:forall _ (:fv _uniq.16724) (:forall _ (:fv _uniq.16724) (:sort 0)))"},{"name":"aca","sexp":"(:forall a (:fv _uniq.16722) ((... | (:app (:c Acc) (:arg :implicit-type 0 (:app (:c Sum) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV3)))) (:arg :explicit 1 (:app (:c Sum.Lex) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV3)) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV4)))) (:arg :explicit 2 (:app (:c Sum.inr) (:arg... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16722","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.16723","is_instance":false,"is_let":false,"name":"r","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :ex... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":8598,"sourceStart":8593,"tag":"atom"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"IH","sourceEnd":8601,"sourceStart":8599,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":8603,"sourceStart":8602,... | [] | [{"source":"IH _ h'","source_end":8606,"source_start":8599,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16722","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.16723","is_instance":false,"is_let":false,"user_name":"r"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 68 | 14 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 68000975d626707e69448264892967f76a46efe377f72744c871882401315fc1 | c87c74eff20f8c5cf95b31d23189592ed97959c29aa351caf209e5fb8492855f | 1077cde50a9175174ac9d486be36deefbd931c009a99ffe281982c6660323a9a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,367 | Sum.lex_acc_inr | .lake/packages/batteries/Batteries/Data/Sum/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact aca _ | case intro.h.sep
α✝ : Type u_1
r : α✝ → α✝ → Prop
β✝ : Type u_2
s : β✝ → β✝ → Prop
aca : ∀ (a : α✝), Acc (Lex r s) (inl a)
b x✝ : β✝
h✝ : ∀ (y : β✝), s y x✝ → Acc s y
IH : ∀ (y : β✝), s y x✝ → Acc (Lex r s) (inr y)
a✝ : α✝
⊢ Acc (Lex r s) (inl a✝) | ((:c Acc) ((:c Sum) (:fv _uniq.16722) (:fv _uniq.16724)) ((:c Sum.Lex) (:fv _uniq.16722) (:fv _uniq.16724) (:fv _uniq.16723) (:fv _uniq.16725)) ((:c Sum.inl) (:fv _uniq.16722) (:fv _uniq.16724) (:fv _uniq.16959))) | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.16722) (:forall _ (:fv _uniq.16722) (:sort 0)))"},{"name":"β✝","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"(:forall _ (:fv _uniq.16724) (:forall _ (:fv _uniq.16724) (:sort 0)))"},{"name":"aca","sexp":"(:forall a (:fv _uniq.16722) ((... | (:app (:c Acc) (:arg :implicit-type 0 (:app (:c Sum) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV3)))) (:arg :explicit 1 (:app (:c Sum.Lex) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV3)) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV4)))) (:arg :explicit 2 (:app (:c Sum.inl) (:arg... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16722","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.16723","is_instance":false,"is_let":false,"name":"r","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :ex... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":8625,"sourceStart":8620,"tag":"atom"},{"children":[{"contextIndex":5,"semanticRole":"local","source":"aca","sourceEnd":8629,"sourceStart":8626,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":8631,"sourceStart":8630... | [] | [{"source":"aca _","source_end":8631,"source_start":8626,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16722","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.16723","is_instance":false,"is_let":false,"user_name":"r"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 68 | 18 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a62d0cd11fb43c470e70f4b53e7390b71a8affc4522f518421fb60378a76a946 | 974121984a48a96133f51a49bac9f494cfe2b6c503ab6c0716f5c082788bb4ad | 5075f7a4ff34bb391ef43d6166978a9b708e246f23d129b4b9d043c3b9ff95a7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,368 | Nat.bit0_val | Mathlib/Data/Nat/Bits.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Nat.zero_add</a>] | m n✝ n : ℕ
⊢ n + n = 0 + n + n | ((:c Eq) (:c Nat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.5901) (:fv _uniq.5901)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c OfNat.ofNa... | [{"name":"m","sexp":"(:c Nat)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5823","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5825","is_instance":false,"is_let":false,"name":"n✝","sexp":"(:c Nat)"},{"binder_role":":explicit","context_inde... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":4655,"sourceStart":4653,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4657,"sourceStart":4656,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"Nat.zero_add","source_end":4669,"source_start":4657,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5823","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5825","is_instance":false,"is_let":false,"user_name":"n✝"},{"binder_role":":explicit","context_index":3,"internal_name":"_uni... | 42 | 2 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1c69895e41db70898e89bf0ae97cdc711a42b48713ce24bd30d3c268461c9666 | 35bf059353246ea8b137da4a16a630180c9a7d69509e64ac0a7c7c737335febf | 327c266eb4ef6c19085249c1f1ac847909a7195dbd2835b422e88e03e8bc35ac | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,369 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.ae_iff</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
⊢ ∀ᵐ (x : γ) ∂(fst κ) a, densityProcess κ (fst κ) n a x univ = 1 | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
⊢ ((fst κ) a) {a_1 | ¬densityProcess κ (fst κ) n a a_1 univ = 1} = 0 | ((:c Filter.Eventually) (:fv _uniq.249503) (:lambda x (:fv _uniq.249503) ((:c Eq) (:c Real) ((:c ProbabilityTheory.kernel.densityProcess) (:fv _uniq.249497) (:fv _uniq.249500) (:fv _uniq.249503) (:fv _uniq.249506) (:fv _uniq.249509) (:fv _uniq.249512) (:fv _uniq.249522) (:fv _uniq.250305) ((:c ProbabilityTheory.kernel.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda x :explicit (:fv FV2) (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c ProbabilityTheory.kernel.densityProcess) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":37929,"sourceStart":37927,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":37931,"sourceStart":37930,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MeasureTheory.ae... | [] | [{"source":"ae_iff","source_end":37937,"source_start":37931,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 47edd3336a7d7334f9d9ea6452c9448865b7e5d91234c1f93bb1e62f20ebda67 | fa8180a6e509e66562ce1ef2d738823300e5167972a918f206d73c1e53afc195 | bd1260b0f07e5f2386aae80f0ae8176026f53863514455f85e82bef3d0e5ef85 | 31a024b737b8c2f2e5853249bdf80a30dd98d2c7bece25bf518f6bbf02d24d88 |
cat-searcher/leandojo-benchmark-4-random | test | 4,370 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : {x | ¬ <a>ProbabilityTheory.kernel.densityProcess</a> κ (<a>ProbabilityTheory.kernel.fst</a> κ) n a x <a>Set.univ</a> = 1} ⊆ {x | <a>ProbabilityTheory.kernel.fst</a> κ a (<a>MeasurableSpace.countablePartitionSet</a> n x) = 0} := by intro x hx simp only [<a>Set.mem_setOf_eq</a>] at hx ⊢ rw [<a>ProbabilityTheory.k... | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
⊢ ((fst κ) a) {a_1 | ¬densityProcess κ (fst κ) n a a_1 univ = 1} = 0 | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ) a) (coun... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c Set) (:fv _uniq.249503)) (:lambda _ ((:c Set) (:fv _uniq.249503)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV2))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":37945,"sourceStart":37941,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":37946,"sourceStart":37946,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":37946,"sourceStart":37946,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"{x | ¬ densityProcess κ (fst κ) n a x univ = 1}\n ⊆ {x | fst κ a (countablePartitionSet n x) = 0}","source_end":38055,"source_start":37948,"syntax_kind":"«term_⊆_»"},{"source":"mem_setOf_eq","source_end":38104,"source_start":38092,"syntax_kind":"ident"},{"source":"hx","source_end":38111,"source_start":... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 7 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b015c6b4aa6c498f381e77bb2a2d596e7d741a378ee27632dc30afa19de34009 | 31a024b737b8c2f2e5853249bdf80a30dd98d2c7bece25bf518f6bbf02d24d88 | 4a76df588870f876701624ef82cde4e5af2d230d36540cfa02b47c5974aa5a6b | adf4f448745e2df520977583f4d7f7a48ea7e5bc3057ca62dd961b65ebde940f |
cat-searcher/leandojo-benchmark-4-random | test | 4,371 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>MeasureTheory.measure_mono_null</a> this ?_ | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ) a) (coun... | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ) a) (coun... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c Set) (:fv _uniq.249503)) (:lambda _ ((:c Set) (:fv _uniq.249503)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV2))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":38182,"sourceStart":38176,"tag":"atom"},{"children":[{"name":"MeasureTheory.measure_mono_null","semanticRole":"global","source":"measure_mono_null","sourceEnd":38200,"sourceStart":38183,"tag":"identifier"},{"children":[{"contextIndex":14,"semanticRole":"local","source":"this"... | [] | [{"source":"measure_mono_null this ?_","source_end":38208,"source_start":38183,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 15 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 779ac52c2d48918ad1d1e562830f4e76ad86ce07ae08258aa96e33128f2e2be5 | adf4f448745e2df520977583f4d7f7a48ea7e5bc3057ca62dd961b65ebde940f | 84998d47910772c4559fa4a87d8cf9e96bb8ee9ec4c54d95ac49625406de054f | 7ba45d00614fde8123ab5f5ebdb7a305e665ac8be715a396b342e9be3666ccc8 |
cat-searcher/leandojo-benchmark-4-random | test | 4,372 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : {x | <a>ProbabilityTheory.kernel.fst</a> κ a (<a>MeasurableSpace.countablePartitionSet</a> n x) = 0} ⊆ ⋃ (u) (_ : u ∈ <a>MeasurableSpace.countablePartition</a> γ n) (_ : <a>ProbabilityTheory.kernel.fst</a> κ a u = 0), u := by intro t ht simp only [<a>Set.mem_setOf_eq</a>, <a>Set.mem_iUnion</a>, <a>exists_prop</a... | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ) a) (coun... | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this✝ : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ) a) (cou... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c Set) (:fv _uniq.249503)) (:lambda _ ((:c Set) (:fv _uniq.249503)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV2))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":38215,"sourceStart":38211,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":38216,"sourceStart":38216,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":38216,"sourceStart":38216,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"{x | fst κ a (countablePartitionSet n x) = 0}\n ⊆ ⋃ (u) (_ : u ∈ countablePartition γ n) (_ : fst κ a u = 0), u","source_end":38342,"source_start":38218,"syntax_kind":"«term_⊆_»"},{"source":"mem_setOf_eq","source_end":38391,"source_start":38379,"syntax_kind":"ident"},{"source":"mem_iUnion","source_end"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 16 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 25e38d9150b13accf84d8a3d97397d6a01790f8c48f2e4c15543ed5ee56b13b2 | 7ba45d00614fde8123ab5f5ebdb7a305e665ac8be715a396b342e9be3666ccc8 | fb2bc8c83007742c908cef92e8b2b0d6500566860520c1b22b551a0d38fddab7 | 051cb8cb954db95292ee237a8b5e03afa0d7e67798f8149de76951537ee5a687 |
cat-searcher/leandojo-benchmark-4-random | test | 4,373 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>MeasureTheory.measure_mono_null</a> this ?_ | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this✝ : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ) a) (cou... | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this✝ : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ) a) (cou... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c Set) (:fv _uniq.249503)) (:lambda _ ((:c Set) (:fv _uniq.249503)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV2))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":38550,"sourceStart":38544,"tag":"atom"},{"children":[{"name":"MeasureTheory.measure_mono_null","semanticRole":"global","source":"measure_mono_null","sourceEnd":38568,"sourceStart":38551,"tag":"identifier"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"this"... | [] | [{"source":"measure_mono_null this ?_","source_end":38576,"source_start":38551,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 21 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6488b4019200f765cbfa75d9f895d9a1a79530146e58b5fd548715ad2efd11b1 | 051cb8cb954db95292ee237a8b5e03afa0d7e67798f8149de76951537ee5a687 | 84998d47910772c4559fa4a87d8cf9e96bb8ee9ec4c54d95ac49625406de054f | 4b6acc8fcfed77d49c14559de323c631b4cc082b637ca26831ce3f8b1a8c1173 |
cat-searcher/leandojo-benchmark-4-random | test | 4,374 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.measure_biUnion</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this✝ : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ) a) (cou... | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this✝ : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ) a) (cou... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c Set) (:fv _uniq.249503)) (:lambda _ ((:c Set) (:fv _uniq.249503)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV2))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":38581,"sourceStart":38579,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":38583,"sourceStart":38582,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MeasureTheory.me... | [] | [{"source":"measure_biUnion","source_end":38598,"source_start":38583,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 22 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8918fa67b8ba9310176ea2f87b5af859f1b02f9373a9007f86c0ce6fa8de2345 | 4b6acc8fcfed77d49c14559de323c631b4cc082b637ca26831ce3f8b1a8c1173 | 8c6035998e3f181b6e3a4548e7e573f576ffacd275349e8c40ff3fbe194a40b1 | 2bdeb6084926eee4579331fc8a90e77f855bea82e8bae195538e62e20553a6df |
cat-searcher/leandojo-benchmark-4-random | test | 4,375 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro x hx | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
⊢ {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ) a) (countable... | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
x : γ
hx : x ∈ {x | ¬densityProcess κ (fst κ) n a x univ = 1}
⊢ x ∈ {x | ((fst... | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.249503)) ((:c Set.instHasSubset) (:fv _uniq.249503)) ((:c setOf) (:fv _uniq.249503) (:lambda x (:fv _uniq.249503) ((:c Not) ((:c Eq) (:c Real) ((:c ProbabilityTheory.kernel.densityProcess) (:fv _uniq.249497) (:fv _uniq.249500) (:fv _uniq.249503) (:fv _uniq.249506) (:fv _uniq.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 2 (:app (:c setOf) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda x :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"intro","sourceEnd":38071,"sourceStart":38066,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":38073,"sourceStart":38072,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hx","sourceEnd":38076,"sourceStart":38074,"tag":"identifier"}],"kind":"null","sou... | [{"role":"fresh_name","source":"x","source_end":38073,"source_start":38072,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":38076,"source_start":38074,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 9 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1454be0c2482f0a3703e1102e7aa53562ea0bd153efc6aaf5fbb6e4fa572cf0f | 68bde58e6b7aa7ec38240e28ad6efc2ee44984f606e99551f82ab6dba00dd431 | 65777af1f444837568ec00c3040db2bdc96178d91d8bf83037116b747be939ac | 28b2dc9ecca7a45e8e327f58d9540da0c758b4c655cd44e2cb389e0fc09f1d7a |
cat-searcher/leandojo-benchmark-4-random | test | 4,376 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.mem_setOf_eq</a>] at hx ⊢ | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
x : γ
hx : x ∈ {x | ¬densityProcess κ (fst κ) n a x univ = 1}
⊢ x ∈ {x | ((fst... | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
x : γ
hx : ¬densityProcess κ (fst κ) n a x univ = 1
⊢ ((fst κ) a) (countablePa... | ((:c Membership.mem) (:fv _uniq.249503) ((:c Set) (:fv _uniq.249503)) ((:c Set.instMembership) (:fv _uniq.249503)) (:fv _uniq.251169) ((:c setOf) (:fv _uniq.249503) (:lambda x (:fv _uniq.249503) ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c Set) (:fv _u... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 3 (:fv FV14)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":38085,"sourceStart":38081,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":38090,"sourceStart":38086,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":380... | [] | [{"source":"mem_setOf_eq","source_end":38104,"source_start":38092,"syntax_kind":"ident"},{"source":"hx","source_end":38111,"source_start":38109,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 10 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 34c440c5b3ebf801147064796c08f5b5596e3e8beda1d107c62d8dd6b82be814 | 28b2dc9ecca7a45e8e327f58d9540da0c758b4c655cd44e2cb389e0fc09f1d7a | 3a612571935a790d35cc1764160c28c2f57d3d6ece9c8ee541e929ebdb243e88 | 1d97a20ac6af1235aac30990c9294e6ed6b1a1f1bad89ba5930362964c2f9206 |
cat-searcher/leandojo-benchmark-4-random | test | 4,377 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>ProbabilityTheory.kernel.densityProcess_fst_univ</a>] at hx | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
x : γ
hx : ¬densityProcess κ (fst κ) n a x univ = 1
⊢ ((fst κ) a) (countablePa... | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
x : γ
hx : ¬(if ((fst κ) a) (countablePartitionSet n x) = 0 then 0 else 1) = 1... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c Set) (:fv _uniq.249503)) (:lambda _ ((:c Set) (:fv _uniq.249503)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV2))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":38122,"sourceStart":38120,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":38124,"sourceStart":38123,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"ProbabilityTheor... | [] | [{"source":"densityProcess_fst_univ","source_end":38147,"source_start":38124,"syntax_kind":"ident"},{"source":"hx","source_end":38154,"source_start":38152,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 11 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7220f09943b0604ffa096ad6aa401be6a4a555686fe4ea474c9dc48ce07223b4 | 1d97a20ac6af1235aac30990c9294e6ed6b1a1f1bad89ba5930362964c2f9206 | ad445f6fc164f77339c0b02c47a853504437eeed4a8aea748adc2e05cf0fb8f0 | 562f7e904e48a2fd2c4f1dcf56363ba67db90b63ca6dd689a67cc4d3977750af |
cat-searcher/leandojo-benchmark-4-random | test | 4,378 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using hx | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
x : γ
hx : ¬(if ((fst κ) a) (countablePartitionSet n x) = 0 then 0 else 1) = 1... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c Set) (:fv _uniq.249503)) (:lambda _ ((:c Set) (:fv _uniq.249503)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV2))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simpa","sourceEnd":38164,"sourceStart":38159,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"ch... | [] | [{"source":"hx","source_end":38173,"source_start":38171,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 14 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c5a76060b90e2f4a11e3043bbc193d00f098e3b7003e373cfbdf782bcb8e5771 | 562f7e904e48a2fd2c4f1dcf56363ba67db90b63ca6dd689a67cc4d3977750af | 1974ce2fe37f145b393fc7f91fbc4c8c354a914949a5a54eb847e3c50da7bcb5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,379 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro t ht | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ) a) (coun... | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ) a) (coun... | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.249503)) ((:c Set.instHasSubset) (:fv _uniq.249503)) ((:c setOf) (:fv _uniq.249503) (:lambda x (:fv _uniq.249503) ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c Set) (:fv _uniq.249503)) (:lambda _ ((:c Set) (:f... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 2 (:app (:c setOf) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda x :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"intro","sourceEnd":38358,"sourceStart":38353,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"t","sourceEnd":38360,"sourceStart":38359,"tag":"identifier"},{"semanticRole":"scoped_local","source":"ht","sourceEnd":38363,"sourceStart":38361,"tag":"identifier"}],"kind":"null","sou... | [{"role":"fresh_name","source":"t","source_end":38360,"source_start":38359,"syntax_kind":"ident"},{"role":"fresh_name","source":"ht","source_end":38363,"source_start":38361,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 18 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 01a89145ea8a1252cf22174e6cea1f137c0fd858d45304d1167f069acd8bc855 | c89fb736898563e00d053b7560467a7ef5d2e4d737c45bf974d9a4b34820b601 | 0739bfdcdc031efb63257ff4b2cf0a312c689994658859969f8eae6b2c78c652 | 16bced11d2a6ff48017bc0592f7983d8848c66d4b97f00bdc9eba2c40cd467f1 |
cat-searcher/leandojo-benchmark-4-random | test | 4,380 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.mem_setOf_eq</a>, <a>Set.mem_iUnion</a>, <a>exists_prop</a>] at ht ⊢ | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ) a) (coun... | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ) a) (coun... | ((:c Membership.mem) (:fv _uniq.249503) ((:c Set) (:fv _uniq.249503)) ((:c Set.instMembership) (:fv _uniq.249503)) (:fv _uniq.257570) ((:c Set.iUnion) (:fv _uniq.249503) ((:c Set) (:fv _uniq.249503)) (:lambda u ((:c Set) (:fv _uniq.249503)) ((:c Set.iUnion) (:fv _uniq.249503) ((:c Membership.mem) ((:c Set) (:fv _uniq.2... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 3 (:fv FV15)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":38372,"sourceStart":38368,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":38377,"sourceStart":38373,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":383... | [] | [{"source":"mem_setOf_eq","source_end":38391,"source_start":38379,"syntax_kind":"ident"},{"source":"mem_iUnion","source_end":38403,"source_start":38393,"syntax_kind":"ident"},{"source":"exists_prop","source_end":38416,"source_start":38405,"syntax_kind":"ident"},{"source":"ht","source_end":38423,"source_start":38421,"sy... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 19 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 143b1c0cc18cfe7a19cb242d7273b3b25ec17f2d34c708b1aa56a77b6cd4f9aa | 16bced11d2a6ff48017bc0592f7983d8848c66d4b97f00bdc9eba2c40cd467f1 | a9802d87f5e664ed4e351957f7836316e1f8bc6cb4f2484c00cbb8cb37e6bd04 | 08e56490d319665f0adefafe32f60a4a37e3062730044c31b66872d33afdab0b |
cat-searcher/leandojo-benchmark-4-random | test | 4,381 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨<a>MeasurableSpace.countablePartitionSet</a> n t, <a>MeasurableSpace.countablePartitionSet_mem</a> _ _, ht, <a>MeasurableSpace.mem_countablePartitionSet</a> _ _⟩ | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ) a) (coun... | ((:c Exists) ((:c Set) (:fv _uniq.249503)) (:lambda i ((:c Set) (:fv _uniq.249503)) ((:c And) ((:c Membership.mem) ((:c Set) (:fv _uniq.249503)) ((:c Set) ((:c Set) (:fv _uniq.249503))) ((:c Set.instMembership) ((:c Set) (:fv _uniq.249503))) 0 ((:c MeasurableSpace.countablePartition) (:fv _uniq.249503) (:fv _uniq.24951... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:lambda i :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV2))) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :implicit-type ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":38437,"sourceStart":38432,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":38441,"sourceStart":38438,"tag":"atom"},{"children":[{"children":[{"name":"MeasurableSpace.countablePartitionSet","semanticRole":"global","source":"countablePartitionSet","sourceEnd":38462,"sourceSt... | [] | [{"source":"⟨countablePartitionSet n t, countablePartitionSet_mem _ _, ht,\n mem_countablePartitionSet _ _⟩","source_end":38541,"source_start":38438,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 20 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 71b13db67eb635adedbf6eff76bdf8363f2a2e43c3ea7bc6a83c28ebb325cfc5 | 08e56490d319665f0adefafe32f60a4a37e3062730044c31b66872d33afdab0b | e38b1f6d0893cd88bd8842f4eae7dae439c16e85ecbe79adbf900df061c5f92f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,382 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this✝ : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ) a) (cou... | ((:c Eq) (:c ENNReal) ((:c tsum) (:c ENNReal) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:c ENNReal) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:c ENNReal) ((:c Semiring.toNonAssocSemiring) (:c ENNReal) ((:c OrderedSemiring.toSemiring) (:c ENNReal) ((:c OrderedCommSemiring.toOrderedSemiring) (:c ENNReal)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c tsum) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c ENNReal))))) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c ENNReal))))) (:arg :impl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":38609,"sourceStart":38605,"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.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 27 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 687150906c7bc71a65f2c36db677924856c375d18a0ffbe62c27f00825c6b159 | 4591753d8e347a5c3ec6b8709e4888a3825ad979f011df764560d4961a99e363 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,383 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>MeasurableSpace.finite_countablePartition</a> _ _).<a>Set.Finite.countable</a> | case hs
α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this✝ : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ)... | ((:c Set.Countable) ((:c Set) (:fv _uniq.249503)) ((:c MeasurableSpace.countablePartition) (:fv _uniq.249503) (:fv _uniq.249512) (:fv _uniq.249522) (:fv _uniq.250307))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c Set.Countable) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:app (:c MeasurableSpace.countablePartition) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 2 (:instance-of (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":38620,"sourceStart":38615,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":38622,"sourceStart":38621,"tag":"atom"},{"children":[{"name":"MeasurableSpace.finite_countablePartition","semanticRole":"global","source":"finite_... | [] | [{"source":"(finite_countablePartition _ _).countable","source_end":38662,"source_start":38621,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 32 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 472ad337c5df251d426d7a39fdaf9873d411e7565bbf5197ab7b7f8729edcddc | 6beb6add4ac9771abe54fb884f38cc475ee2fbd05b38c73bed1301116311859a | 91f422bda1dca122f6a4bfc9feb1ff1eb2d72c38c2e57f2ef964d8fa18b754d1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,384 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro s hs t ht hst | case hd
α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this✝ : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ)... | case hd
α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this✝ : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ)... | ((:c Set.PairwiseDisjoint) ((:c Set) (:fv _uniq.249503)) ((:c Set) (:fv _uniq.249503)) ((:c OmegaCompletePartialOrder.toPartialOrder) ((:c Set) (:fv _uniq.249503)) ((:c CompleteLattice.instOmegaCompletePartialOrder) ((:c Set) (:fv _uniq.249503)) ((:c CompletelyDistribLattice.toCompleteLattice) ((:c Set) (:fv _uniq.2495... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c Set.PairwiseDisjoint) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :instance 3 (:instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"intro","sourceEnd":38673,"sourceStart":38668,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"s","sourceEnd":38675,"sourceStart":38674,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hs","sourceEnd":38678,"sourceStart":38676,"tag":"identifier"},{"semanticRole":"sc... | [{"role":"fresh_name","source":"s","source_end":38675,"source_start":38674,"syntax_kind":"ident"},{"role":"fresh_name","source":"hs","source_end":38678,"source_start":38676,"syntax_kind":"ident"},{"role":"fresh_name","source":"t","source_end":38680,"source_start":38679,"syntax_kind":"ident"},{"role":"fresh_name","sourc... | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 39 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b704f46e074762c68452e5f7c70d73ea588a58e1842f184065abdb7303276ddd | 66c2d3f45cfa00d63eb797bfb497bdc952be592d464dba12ad0d60feedbb3079 | 824664a92c65ae345093fffecf33b838e163cc55f22391992f4360cb9817dc35 | 4604eba36a0a04652ef1d51cbb48b5c4a7c70cf732ad5f7b44996d4146671b83 |
cat-searcher/leandojo-benchmark-4-random | test | 4,385 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.disjoint_iUnion_right</a>, <a>Set.disjoint_iUnion_left</a>] | case hd
α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this✝ : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ)... | case hd
α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this✝ : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ)... | ((:c Function.onFun) ((:c Set) (:fv _uniq.249503)) ((:c Set) (:fv _uniq.249503)) (:sort 0) ((:c Disjoint) ((:c Set) (:fv _uniq.249503)) ((:c OmegaCompletePartialOrder.toPartialOrder) ((:c Set) (:fv _uniq.249503)) ((:c CompleteLattice.instOmegaCompletePartialOrder) ((:c Set) (:fv _uniq.249503)) ((:c CompletelyDistribLat... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c Function.onFun) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :implicit-type 2 (:sort Prop)) (:arg :explicit 3 (:app (:c Disjoint) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :insta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":38696,"sourceStart":38692,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":38701,"sourceStart":38697,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":387... | [] | [{"source":"disjoint_iUnion_right","source_end":38724,"source_start":38703,"syntax_kind":"ident"},{"source":"disjoint_iUnion_left","source_end":38746,"source_start":38726,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 40 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 51f0f88bee57ea40db8949b90a7457d51749b0d52b920197c4a95b7dca83fbd6 | 4604eba36a0a04652ef1d51cbb48b5c4a7c70cf732ad5f7b44996d4146671b83 | 9b0ed26618484e23051fb778db1ec3fb1ae7e9a976dac8fc274c4ff7adf4bc4c | 72d49fe0d43191aeb9075d417ba44d254d3100d9f5778c745f5291c59470b49c |
cat-searcher/leandojo-benchmark-4-random | test | 4,386 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun _ _ ↦ <a>MeasurableSpace.disjoint_countablePartition</a> hs ht hst | case hd
α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this✝ : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ)... | (:forall i ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c Set) (:fv _uniq.249503)) (:lambda _ ((:c Set) (:fv _uniq.249503)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c DFunLike.coe) ((:c Subtype) (:fo... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:forall i :explicit (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV2))))))) (:arg :implicit-type 1 (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":38757,"sourceStart":38752,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":38761,"sourceStart":38758,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"_","sourceEnd":38763,"sourceStart":38762,"tag":"atom"}],"kind":"Lean.Parser.Term.hole","source":"_","sourc... | [] | [{"source":"fun _ _ ↦ disjoint_countablePartition hs ht hst","source_end":38807,"source_start":38758,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 41 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ec6a326c598562c10b7a4340e072d420ac54ebce976e590ad2d3f5302776d41a | 72d49fe0d43191aeb9075d417ba44d254d3100d9f5778c745f5291c59470b49c | 8a337a4c97e053fee394f87cacd9dc7baf4e6f7870a1fa375c5d06878f22f328 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,387 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro s hs | case h
α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this✝ : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ) ... | case h
α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this✝ : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ) ... | (:forall b ((:c Set) (:fv _uniq.249503)) (:forall _ ((:c Membership.mem) ((:c Set) (:fv _uniq.249503)) ((:c Set) ((:c Set) (:fv _uniq.249503))) ((:c Set.instMembership) ((:c Set) (:fv _uniq.249503))) 0 ((:c MeasurableSpace.countablePartition) (:fv _uniq.249503) (:fv _uniq.249512) (:fv _uniq.249522) (:fv _uniq.250307)))... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:forall b :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV2))) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))))) (:arg :instance 2 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"intro","sourceEnd":38818,"sourceStart":38813,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"s","sourceEnd":38820,"sourceStart":38819,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hs","sourceEnd":38823,"sourceStart":38821,"tag":"identifier"}],"kind":"null","sou... | [{"role":"fresh_name","source":"s","source_end":38820,"source_start":38819,"syntax_kind":"ident"},{"role":"fresh_name","source":"hs","source_end":38823,"source_start":38821,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 46 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 691626347af5623cc0bf7e8cb60f637d1ecd64fbc5268a09283463b0046215b2 | 186bc5041641dade087b016ea9b9da94c356e0edec678b2bca332d165d4cde74 | 7efa99c53f9cbe8bb490675f144d09b2569a79e2d9902d691b34e36ba60dcc9b | 72c558543035a216887aae6ae51716538c6e3a213712491d5c12dc862692911a |
cat-searcher/leandojo-benchmark-4-random | test | 4,388 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases h : <a>ProbabilityTheory.kernel.fst</a> κ a s = 0 | case h
α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this✝ : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ) ... | case pos
α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this✝ : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ... | ((:c MeasurableSet) (:fv _uniq.249503) (:fv _uniq.249512) ((:c Set.iUnion) (:fv _uniq.249503) ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c Set) (:fv _uniq.249503)) (:lambda _ ((:c Set) (:fv _uniq.249503)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFu... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c MeasurableSet) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 (:app (:c Set.iUnion) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"by_cases","sourceEnd":38836,"sourceStart":38828,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":38838,"sourceStart":38837,"tag":"identifier"},{"source":":","sourceEnd":38840,"sourceStart":38839,"tag":"atom"}],"kind":"null","source":"h :","sourceEnd":38840,"sour... | [] | [{"source":"fst κ a s = 0","source_end":38855,"source_start":38841,"syntax_kind":"«term_=_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 47 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8591bdf63e90f78a55bea4a9e89e06e724850d895425787c26d3fe16bc08ecc1 | 72c558543035a216887aae6ae51716538c6e3a213712491d5c12dc862692911a | ac2643444e943f215de6b976c5b440e7c20fe9179fb867ae8e827a08cb9ed830 | 3182e6af1f797252c72ecb07a3f28c25d7d935977ad32b6d9794ccae03e45d7f |
cat-searcher/leandojo-benchmark-4-random | test | 4,389 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [h, <a>MeasurableSpace.measurableSet_countablePartition</a> n hs] | case pos
α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this✝ : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ... | ((:c MeasurableSet) (:fv _uniq.249503) (:fv _uniq.249512) ((:c Set.iUnion) (:fv _uniq.249503) ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c Set) (:fv _uniq.249503)) (:lambda _ ((:c Set) (:fv _uniq.249503)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFu... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c MeasurableSet) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 (:app (:c Set.iUnion) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":38867,"sourceStart":38863,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"h","source_end":38870,"source_start":38869,"syntax_kind":"ident"},{"source":"measurableSet_countablePartition n hs","source_end":38909,"source_start":38872,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 50 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | da2efd5512b0665b117ea9d0e3457719f5d6ed7062b76e15b00a4afd40f1da9b | 319b98513c199e9eac5805a7cab6eae4c251aaddaffcaa96b09667ae2ea32cbe | 2578e8e7812cfd0ea5dd18dff796a904e9ddd91e33944731077451da7c3fece7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,390 | ProbabilityTheory.kernel.densityProcess_fst_univ_ae | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [h] | case neg
α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝¹ : CountablyGenerated γ
κ✝ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
κ : ↥(kernel α (γ × β))
inst✝ : IsFiniteKernel κ
n : ℕ
a : α
this✝ : {x | ¬densityProcess κ (fst κ) n a x univ = 1} ⊆ {x | ((fst κ... | ((:c MeasurableSet) (:fv _uniq.249503) (:fv _uniq.249512) ((:c Set.iUnion) (:fv _uniq.249503) ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.249503) (:fv _uniq.249512)) ((:c Set) (:fv _uniq.249503)) (:lambda _ ((:c Set) (:fv _uniq.249503)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFu... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.249497))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.249500))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.249503))"},{"na... | (:app (:c MeasurableSet) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 (:app (:c Set.iUnion) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":38922,"sourceStart":38918,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"h","source_end":38925,"source_start":38924,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249497","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249500","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 71 | 55 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c0aa2e8d34a6099ceaaae9f115cc19f2cb5da23592940bb3a6d8ca6abcc58aee | 8d356a9c8211422052a7bbbcea3d103ebed29f7ac022348b31f74246b089267b | 80b5426f4cd8afb2daab5c530b5abbdb5bd333c6b56653091017c22104b3e089 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,391 | TensorProduct.LieModule.liftLie_apply | Mathlib/Algebra/Lie/TensorProduct.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>TensorProduct.LieModule.coe_liftLie_eq_lift_coe</a>, <a>LieModuleHom.coe_toLinearMap</a>, <a>TensorProduct.LieModule.lift_apply</a>] | R : Type u
inst✝¹⁸ : CommRing R
L : Type v
M : Type w
N : Type w₁
P : Type w₂
Q : Type w₃
inst✝¹⁷ : LieRing L
inst✝¹⁶ : LieAlgebra R L
inst✝¹⁵ : AddCommGroup M
inst✝¹⁴ : Module R M
inst✝¹³ : LieRingModule L M
inst✝¹² : LieModule R L M
inst✝¹¹ : AddCommGroup N
inst✝¹⁰ : Module R N
inst✝⁹ : LieRingModule L N
inst✝⁸ : Lie... | ((:c Eq) (:fv _uniq.168672) ((:c DFunLike.coe) ((:c LieModuleHom) (:fv _uniq.168661) (:fv _uniq.168666) ((:c TensorProduct) (:fv _uniq.168661) ((:c CommRing.toCommSemiring) (:fv _uniq.168661) (:fv _uniq.168664)) (:fv _uniq.168668) (:fv _uniq.168670) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.168668) (:fv _uniq.16869... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹⁸","sexp":"((:c CommRing) (:fv _uniq.168661))"},{"name":"L","sexp":"(:sort (+ v 1))"},{"name":"M","sexp":"(:sort (+ w 1))"},{"name":"N","sexp":"(:sort (+ w₁ 1))"},{"name":"P","sexp":"(:sort (+ w₂ 1))"},{"name":"Q","sexp":"(:sort (+ w₃ 1))"},{"name":"inst✝¹⁷","sexp":... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LieModuleHom) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemirin... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.168661","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.168664","is_instance":true,"is_let":false,"name":"inst✝¹⁸","sexp":"(:app (:c CommRing) (:arg :exp... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":5684,"sourceStart":5680,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":5689,"sourceStart":5685,"tag":"atom"}],"kind":"nu... | [] | [{"source":"coe_liftLie_eq_lift_coe","source_end":5714,"source_start":5691,"syntax_kind":"ident"},{"source":"LieModuleHom.coe_toLinearMap","source_end":5744,"source_start":5716,"syntax_kind":"ident"},{"source":"lift_apply","source_end":5756,"source_start":5746,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.168661","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.168664","is_instance":true,"is_let":false,"user_name":"inst✝¹⁸"},{"binder_role":":explicit","context_index":2,"int... | 33 | 2 | exact | true | 1 | 28 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d4bcc5d7d1b10fa3d7f2c1304a0cb40459c0c2f2c5b3a47861d5810e1b65c5a9 | b3bebf124d6bfa52389eb8af285a1b38789d06bc80be41fe5e635d5e37f06ec1 | 0824a8a6dbcb87dbd12fb22c947c47892aa79ee5ee47915d304b8c2d96f86c9b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,392 | Rat.divInt_nonneg | Mathlib/Algebra/Order/Ring/Rat.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain rfl | hb := hb.eq_or_lt | a✝ b✝ c p q : ℚ
a b : ℤ
ha : 0 ≤ a
hb : 0 ≤ b
⊢ 0 ≤ a /. b | ((:c LE.le) (:c Rat) (:c Rat.instLE) ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0))) ((:c Rat.divInt) (:fv _uniq.764) (:fv _uniq.765))) | [{"name":"a✝","sexp":"(:c Rat)"},{"name":"b✝","sexp":"(:c Rat)"},{"name":"c","sexp":"(:c Rat)"},{"name":"p","sexp":"(:c Rat)"},{"name":"q","sexp":"(:c Rat)"},{"name":"a","sexp":"(:c Int)"},{"name":"b","sexp":"(:c Int)"},{"name":"ha","sexp":"((:c LE.le) (:c Int) (:c Int.instLEInt) ((:c OfNat.ofNat) (:c Int) (:lit 0) ((:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Rat)) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.652","is_instance":false,"is_let":false,"name":"a✝","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.654","is_instance":false,"is_let":false,"name":"b✝","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index... | {"children":[{"children":[{"children":[{"children":[{"source":"obtain","sourceEnd":1463,"sourceStart":1457,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":1467,"sourceStart":1464,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","s... | [] | [{"source":"hb.eq_or_lt","source_end":1487,"source_start":1476,"syntax_kind":"ident"},{"source":"rfl | hb","source_end":1472,"source_start":1464,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"},{"source":"divInt_nonneg_iff_of_pos_right hb","source_end":1546,"source_start":1513,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.652","is_instance":false,"is_let":false,"user_name":"a✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.654","is_instance":false,"is_let":false,"user_name":"b✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 10 | 2 | branch_opener | false | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bb1d570204d4a5f1cb74de92c870fa0c2512ab24ead77609c5f611dffd6c6d28 | c5e666bb3f8a0b736f7fd76397bb4fbe29d823a8671127cc7f0ab516f2227b7a | c533a5bfbe1ad49ecd3b2f77b9e17517e2db0ac716adb69399486f1c8a17330a | 5e072e5bb735e42399d14ec981a653a5d447064eaa72aa52fab1030f74406b3c | |
cat-searcher/leandojo-benchmark-4-random | test | 4,393 | Rat.divInt_nonneg | Mathlib/Algebra/Order/Ring/Rat.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>Rat.divInt_nonneg_iff_of_pos_right</a> hb] | case inr
a✝ b✝ c p q : ℚ
a b : ℤ
ha : 0 ≤ a
hb✝ : 0 ≤ b
hb : 0 < b
⊢ 0 ≤ a /. b | ((:c LE.le) (:c Rat) (:c Rat.instLE) ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0))) ((:c Rat.divInt) (:fv _uniq.764) (:fv _uniq.765))) | [{"name":"a✝","sexp":"(:c Rat)"},{"name":"b✝","sexp":"(:c Rat)"},{"name":"c","sexp":"(:c Rat)"},{"name":"p","sexp":"(:c Rat)"},{"name":"q","sexp":"(:c Rat)"},{"name":"a","sexp":"(:c Int)"},{"name":"b","sexp":"(:c Int)"},{"name":"ha","sexp":"((:c LE.le) (:c Int) (:c Int.instLEInt) ((:c OfNat.ofNat) (:c Int) (:lit 0) ((:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Rat)) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.652","is_instance":false,"is_let":false,"name":"a✝","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.654","is_instance":false,"is_let":false,"name":"b✝","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index... | {"children":[{"source":"rwa","sourceEnd":1511,"sourceStart":1508,"tag":"atom"},{"children":[{"source":"[","sourceEnd":1513,"sourceStart":1512,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Rat.divInt_nonneg_iff_of_pos_right","semanticRole":"global","... | [] | [{"source":"divInt_nonneg_iff_of_pos_right hb","source_end":1546,"source_start":1513,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.652","is_instance":false,"is_let":false,"user_name":"a✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.654","is_instance":false,"is_let":false,"user_name":"b✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 10 | 11 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 32c41ebb89631ce549631557ba1d17774a0095a273bef3b2e4bea62f1d1074d7 | 0610c3868c3985d217c29778bd5ee75e708bc81f3f963a4d7511e136c18505a6 | 36bce23501a94318ca6171dec5c0b038f108066fab8b658a13aef18a179ec521 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,394 | Rat.divInt_nonneg | Mathlib/Algebra/Order/Ring/Rat.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case inl
a✝ b c p q : ℚ
a : ℤ
ha : 0 ≤ a
hb : 0 ≤ 0
⊢ 0 ≤ a /. 0 | case inl
a✝ b c p q : ℚ
a : ℤ
ha : 0 ≤ a
hb : 0 ≤ 0
⊢ 0 ≤ 0 | ((:c LE.le) (:c Rat) (:c Rat.instLE) ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0))) ((:c Rat.divInt) (:fv _uniq.764) ((:c OfNat.ofNat) (:c Int) (:lit 0) ((:c instOfNat) (:lit 0))))) | [{"name":"a✝","sexp":"(:c Rat)"},{"name":"b","sexp":"(:c Rat)"},{"name":"c","sexp":"(:c Rat)"},{"name":"p","sexp":"(:c Rat)"},{"name":"q","sexp":"(:c Rat)"},{"name":"a","sexp":"(:c Int)"},{"name":"ha","sexp":"((:c LE.le) (:c Int) (:c Int.instLEInt) ((:c OfNat.ofNat) (:c Int) (:lit 0) ((:c instOfNat) (:lit 0))) (:fv _un... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Rat)) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.652","is_instance":false,"is_let":false,"name":"a✝","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.654","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index"... | {"children":[{"source":"simp","sourceEnd":1497,"sourceStart":1493,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.652","is_instance":false,"is_let":false,"user_name":"a✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.654","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.... | 10 | 9 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e780c5f2f00b526903dbf635a48e5152d0695045186208d8be03712d52f94a82 | aab8a85ed2204dbea8c6e892f68cfdf6a3736ca14d80f09104ea5398b22c9d88 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | 4003553ee356b9a8d751fda91bd7f1feb1678037f3adb18d0e3edef53bd3c6e9 |
cat-searcher/leandojo-benchmark-4-random | test | 4,395 | Rat.divInt_nonneg | Mathlib/Algebra/Order/Ring/Rat.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case inl
a✝ b c p q : ℚ
a : ℤ
ha : 0 ≤ a
hb : 0 ≤ 0
⊢ 0 ≤ 0 | ((:c LE.le) (:c Rat) (:c Rat.instLE) ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0))) ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0)))) | [{"name":"a✝","sexp":"(:c Rat)"},{"name":"b","sexp":"(:c Rat)"},{"name":"c","sexp":"(:c Rat)"},{"name":"p","sexp":"(:c Rat)"},{"name":"q","sexp":"(:c Rat)"},{"name":"a","sexp":"(:c Int)"},{"name":"ha","sexp":"((:c LE.le) (:c Int) (:c Int.instLEInt) ((:c OfNat.ofNat) (:c Int) (:lit 0) ((:c instOfNat) (:lit 0))) (:fv _un... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Rat)) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.652","is_instance":false,"is_let":false,"name":"a✝","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.654","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index"... | {"children":[{"source":"rfl","sourceEnd":1505,"sourceStart":1502,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":1505,"sourceStart":1502,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.652","is_instance":false,"is_let":false,"user_name":"a✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.654","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.... | 10 | 10 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 34b60926b68ad5bdcf86eebb8ecab29d89c260d1ec75058a1c0022eb637f75af | 4003553ee356b9a8d751fda91bd7f1feb1678037f3adb18d0e3edef53bd3c6e9 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,396 | TotallyBounded.isSeparable | Mathlib/Topology/Metrizable/Uniformity.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | letI := (<a>UniformSpace.pseudoMetricSpace</a> (X := X)).<a>PseudoMetricSpace.toPseudoEMetricSpace</a> | X : Type u_1
inst✝ : UniformSpace X
i : (𝓤 X).IsCountablyGenerated
s : Set X
h : TotallyBounded s
⊢ TopologicalSpace.IsSeparable s | X : Type u_1
inst✝ : UniformSpace X
i : (𝓤 X).IsCountablyGenerated
s : Set X
h : TotallyBounded s
this : PseudoEMetricSpace X := PseudoMetricSpace.toPseudoEMetricSpace
⊢ TopologicalSpace.IsSeparable s | ((:c TopologicalSpace.IsSeparable) (:fv _uniq.40719) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.40719) (:fv _uniq.40823)) (:fv _uniq.40825)) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c UniformSpace) (:fv _uniq.40719))"},{"name":"i","sexp":"((:c Filter.IsCountablyGenerated) ((:c Prod) (:fv _uniq.40719) (:fv _uniq.40719)) ((:c uniformity) (:fv _uniq.40719) (:fv _uniq.40823)))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.40719))"},{"nam... | (:app (:c TopologicalSpace.IsSeparable) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV4))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c UniformSpace) (:arg :exp... | {"children":[{"source":"letI","sourceEnd":15860,"sourceStart":15856,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":15861,"sourceStart":15861,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":15861,"sourceStart":15861,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"(UniformSpace.pseudoMetricSpace (X := X)).toPseudoEMetricSpace","source_end":15926,"source_start":15864,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":instance-implicit","context_index":3... | 25 | 4 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d8fbb20c350d4b9a319de6d3a6da63bde8f2d0982c7fd0c6acbe76178eb51109 | ed11b1e5bf3fed237d9b367700a4126bfc7d107fbaeb3a67f3312951575c42d6 | 25c27aacc4e5f3e866a5d7f269ad3bd32829ceeeca4827142f7cffd009c7c517 | af159a50756d30b6d7e9b60922525d480b2929a0dd116ce666393acc5608f4ba |
cat-searcher/leandojo-benchmark-4-random | test | 4,397 | TotallyBounded.isSeparable | Mathlib/Topology/Metrizable/Uniformity.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>EMetric.totallyBounded_iff</a>] at h | X : Type u_1
inst✝ : UniformSpace X
i : (𝓤 X).IsCountablyGenerated
s : Set X
h : TotallyBounded s
this : PseudoEMetricSpace X := PseudoMetricSpace.toPseudoEMetricSpace
⊢ TopologicalSpace.IsSeparable s | X : Type u_1
inst✝ : UniformSpace X
i : (𝓤 X).IsCountablyGenerated
s : Set X
this : PseudoEMetricSpace X := PseudoMetricSpace.toPseudoEMetricSpace
h : ∀ ε > 0, ∃ t, t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
⊢ TopologicalSpace.IsSeparable s | ((:c TopologicalSpace.IsSeparable) (:fv _uniq.40719) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.40719) (:fv _uniq.40823)) (:fv _uniq.40825)) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c UniformSpace) (:fv _uniq.40719))"},{"name":"i","sexp":"((:c Filter.IsCountablyGenerated) ((:c Prod) (:fv _uniq.40719) (:fv _uniq.40719)) ((:c uniformity) (:fv _uniq.40719) (:fv _uniq.40823)))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.40719))"},{"nam... | (:app (:c TopologicalSpace.IsSeparable) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV4))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c UniformSpace) (:arg :exp... | {"children":[{"source":"rw","sourceEnd":15931,"sourceStart":15929,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15933,"sourceStart":15932,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"EMetric.totallyB... | [] | [{"source":"EMetric.totallyBounded_iff","source_end":15959,"source_start":15933,"syntax_kind":"ident"},{"source":"h","source_end":15965,"source_start":15964,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":instance-implicit","context_index":3... | 25 | 5 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7804b3443b93968f652a1a43ff7d1b55c6e9f0324ac70cf470b9245b9cba31d2 | af159a50756d30b6d7e9b60922525d480b2929a0dd116ce666393acc5608f4ba | b67dd342cd4584ffba73fc1099b122b216c4bc91bb6e6608f2e796ef9cb04001 | 124c057e5b55fd67d3b634f4f699ef5aa8606d797f27e46eaa6cc794c08cf83f |
cat-searcher/leandojo-benchmark-4-random | test | 4,398 | TotallyBounded.isSeparable | Mathlib/Topology/Metrizable/Uniformity.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h' : ∀ ε > 0, ∃ t, <a>Set.Countable</a> t ∧ s ⊆ ⋃ y ∈ t, <a>EMetric.closedBall</a> y ε := by intro ε hε obtain ⟨t, ht⟩ := h ε hε refine ⟨t, ht.1.<a>Set.Finite.countable</a>, <a>subset_trans</a> ht.2 ?_⟩ gcongr exact <a>EMetric.ball_subset_closedBall</a> | X : Type u_1
inst✝ : UniformSpace X
i : (𝓤 X).IsCountablyGenerated
s : Set X
this : PseudoEMetricSpace X := PseudoMetricSpace.toPseudoEMetricSpace
h : ∀ ε > 0, ∃ t, t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
⊢ TopologicalSpace.IsSeparable s | X : Type u_1
inst✝ : UniformSpace X
i : (𝓤 X).IsCountablyGenerated
s : Set X
this : PseudoEMetricSpace X := PseudoMetricSpace.toPseudoEMetricSpace
h : ∀ ε > 0, ∃ t, t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
h' : ∀ ε > 0, ∃ t, t.Countable ∧ s ⊆ ⋃ y ∈ t, EMetric.closedBall y ε
⊢ TopologicalSpace.IsSeparable s | ((:c TopologicalSpace.IsSeparable) (:fv _uniq.40719) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.40719) (:fv _uniq.40823)) (:fv _uniq.40825)) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c UniformSpace) (:fv _uniq.40719))"},{"name":"i","sexp":"((:c Filter.IsCountablyGenerated) ((:c Prod) (:fv _uniq.40719) (:fv _uniq.40719)) ((:c uniformity) (:fv _uniq.40719) (:fv _uniq.40823)))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.40719))"},{"nam... | (:app (:c TopologicalSpace.IsSeparable) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV4))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c UniformSpace) (:arg :exp... | {"children":[{"source":"have","sourceEnd":15972,"sourceStart":15968,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h'","sourceEnd":15975,"sourceStart":15973,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h'","sourceEnd":15975,"sourceStart":15973,"tag":"nod... | [] | [{"source":"∀ ε > 0, ∃ t, Set.Countable t ∧ s ⊆ ⋃ y ∈ t, EMetric.closedBall y ε","source_end":16059,"source_start":15978,"syntax_kind":"Lean.«term∀__,_»"},{"source":"h ε hε","source_end":16117,"source_start":16109,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨t, ht⟩","source_end":16105,"source_start":16094,"syntax_... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":instance-implicit","context_index":3... | 25 | 8 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0bf16b8d0c2d868c6e1b59950b25337e485eb97a56fc6a2b90eb81ecdfaca051 | 124c057e5b55fd67d3b634f4f699ef5aa8606d797f27e46eaa6cc794c08cf83f | 7d071f78b05a21172eb17c8b692931638c679b2a8a4112b18f2b50b60b5fddca | db80c420208806edc01e6145b037a3d1bbe14c2c6985535fbe6aa3fd583f1c89 |
cat-searcher/leandojo-benchmark-4-random | test | 4,399 | TotallyBounded.isSeparable | Mathlib/Topology/Metrizable/Uniformity.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨t, _, htc, hts⟩ := <a>EMetric.subset_countable_closure_of_almost_dense_set</a> s h' | X : Type u_1
inst✝ : UniformSpace X
i : (𝓤 X).IsCountablyGenerated
s : Set X
this : PseudoEMetricSpace X := PseudoMetricSpace.toPseudoEMetricSpace
h : ∀ ε > 0, ∃ t, t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
h' : ∀ ε > 0, ∃ t, t.Countable ∧ s ⊆ ⋃ y ∈ t, EMetric.closedBall y ε
⊢ TopologicalSpace.IsSeparable s | case intro.intro.intro
X : Type u_1
inst✝ : UniformSpace X
i : (𝓤 X).IsCountablyGenerated
s : Set X
this : PseudoEMetricSpace X := PseudoMetricSpace.toPseudoEMetricSpace
h : ∀ ε > 0, ∃ t, t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
h' : ∀ ε > 0, ∃ t, t.Countable ∧ s ⊆ ⋃ y ∈ t, EMetric.closedBall y ε
t : Set X
left✝ : t ⊆... | ((:c TopologicalSpace.IsSeparable) (:fv _uniq.40719) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.40719) (:fv _uniq.40823)) (:fv _uniq.40825)) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c UniformSpace) (:fv _uniq.40719))"},{"name":"i","sexp":"((:c Filter.IsCountablyGenerated) ((:c Prod) (:fv _uniq.40719) (:fv _uniq.40719)) ((:c uniformity) (:fv _uniq.40719) (:fv _uniq.40823)))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.40719))"},{"nam... | (:app (:c TopologicalSpace.IsSeparable) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV4))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c UniformSpace) (:arg :exp... | {"children":[{"source":"obtain","sourceEnd":16235,"sourceStart":16229,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":16239,"sourceStart":16236,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"t","sourceEn... | [] | [{"source":"EMetric.subset_countable_closure_of_almost_dense_set s h'","source_end":16317,"source_start":16260,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨t, _, htc, hts⟩","source_end":16256,"source_start":16236,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":instance-implicit","context_index":3... | 25 | 15 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 17deba68989e3a1addc90e0674930ae40e8f70f8be1e4d6ec8e40abe5c672f10 | db80c420208806edc01e6145b037a3d1bbe14c2c6985535fbe6aa3fd583f1c89 | b57d66e56d7f61fb601e76d36f0c1ed0ce4a14b023d0c05e1b5511dd18a07f1d | 7a03ba4e80e2499d6ab0f966267e0c3efa3d0733717bcde67cd5dc00986e4a37 |
cat-searcher/leandojo-benchmark-4-random | test | 4,400 | TotallyBounded.isSeparable | Mathlib/Topology/Metrizable/Uniformity.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨t, htc, hts⟩ | case intro.intro.intro
X : Type u_1
inst✝ : UniformSpace X
i : (𝓤 X).IsCountablyGenerated
s : Set X
this : PseudoEMetricSpace X := PseudoMetricSpace.toPseudoEMetricSpace
h : ∀ ε > 0, ∃ t, t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
h' : ∀ ε > 0, ∃ t, t.Countable ∧ s ⊆ ⋃ y ∈ t, EMetric.closedBall y ε
t : Set X
left✝ : t ⊆... | ((:c TopologicalSpace.IsSeparable) (:fv _uniq.40719) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.40719) (:fv _uniq.40823)) (:fv _uniq.40825)) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c UniformSpace) (:fv _uniq.40719))"},{"name":"i","sexp":"((:c Filter.IsCountablyGenerated) ((:c Prod) (:fv _uniq.40719) (:fv _uniq.40719)) ((:c uniformity) (:fv _uniq.40719) (:fv _uniq.40823)))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.40719))"},{"nam... | (:app (:c TopologicalSpace.IsSeparable) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV4))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c UniformSpace) (:arg :exp... | {"children":[{"source":"exact","sourceEnd":16325,"sourceStart":16320,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":16329,"sourceStart":16326,"tag":"atom"},{"children":[{"contextIndex":8,"semanticRole":"local","source":"t","sourceEnd":16330,"sourceStart":16329,"tag":"identifier"},{"source":",","sourceEnd":16331,"... | [] | [{"source":"⟨t, htc, hts⟩","source_end":16343,"source_start":16326,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":instance-implicit","context_index":3... | 25 | 16 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9a8ea7616791134051d26f2c1a1e957488938e840a87b0d07d2c3234021563bc | 7a03ba4e80e2499d6ab0f966267e0c3efa3d0733717bcde67cd5dc00986e4a37 | 2c893e27679671a68ffff6ba69f831f6965b3de8dabef8c762ad3dbda6e0eaf3 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,401 | TotallyBounded.isSeparable | Mathlib/Topology/Metrizable/Uniformity.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro ε hε | X : Type u_1
inst✝ : UniformSpace X
i : (𝓤 X).IsCountablyGenerated
s : Set X
this : PseudoEMetricSpace X := PseudoMetricSpace.toPseudoEMetricSpace
h : ∀ ε > 0, ∃ t, t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
⊢ ∀ ε > 0, ∃ t, t.Countable ∧ s ⊆ ⋃ y ∈ t, EMetric.closedBall y ε | X : Type u_1
inst✝ : UniformSpace X
i : (𝓤 X).IsCountablyGenerated
s : Set X
this : PseudoEMetricSpace X := PseudoMetricSpace.toPseudoEMetricSpace
h : ∀ ε > 0, ∃ t, t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
ε : ENNReal
hε : ε > 0
⊢ ∃ t, t.Countable ∧ s ⊆ ⋃ y ∈ t, EMetric.closedBall y ε | (:forall ε (:c ENNReal) (:forall _ ((:c GT.gt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c CompleteSemilatticeInf.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.toCompleteSemilatticeInf) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c ... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c UniformSpace) (:fv _uniq.40719))"},{"name":"i","sexp":"((:c Filter.IsCountablyGenerated) ((:c Prod) (:fv _uniq.40719) (:fv _uniq.40719)) ((:c uniformity) (:fv _uniq.40719) (:fv _uniq.40823)))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.40719))"},{"nam... | (:forall ε :explicit (:c ENNReal) (:forall _ :explicit (:app (:c GT.gt) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 0) (:arg :explicit 3 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:lit 0)) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c UniformSpace) (:arg :exp... | {"children":[{"source":"intro","sourceEnd":16075,"sourceStart":16070,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"ε","sourceEnd":16078,"sourceStart":16076,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hε","sourceEnd":16082,"sourceStart":16079,"tag":"identifier"}],"kind":"null","sou... | [{"role":"fresh_name","source":"ε","source_end":16078,"source_start":16076,"syntax_kind":"ident"},{"role":"fresh_name","source":"hε","source_end":16082,"source_start":16079,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":instance-implicit","context_index":3... | 25 | 10 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 963123a358a5564532c38972395a47c676fbc42fc527b141fad6ce0c29b99644 | 552a76dacbd2c92a770113529a97b5e0d72c17043da10f9e1cd0d26b041d1ce2 | ab19f3bd4984459704398ec0941ae3cc8fe5fd3ddc60b4162c8b8b2db0723828 | 0a247e175e22c91adb9d626104780a8eddc04a726309b4555f58e369bab8bc1a |
cat-searcher/leandojo-benchmark-4-random | test | 4,402 | TotallyBounded.isSeparable | Mathlib/Topology/Metrizable/Uniformity.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨t, ht⟩ := h ε hε | X : Type u_1
inst✝ : UniformSpace X
i : (𝓤 X).IsCountablyGenerated
s : Set X
this : PseudoEMetricSpace X := PseudoMetricSpace.toPseudoEMetricSpace
h : ∀ ε > 0, ∃ t, t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
ε : ENNReal
hε : ε > 0
⊢ ∃ t, t.Countable ∧ s ⊆ ⋃ y ∈ t, EMetric.closedBall y ε | case intro
X : Type u_1
inst✝ : UniformSpace X
i : (𝓤 X).IsCountablyGenerated
s : Set X
this : PseudoEMetricSpace X := PseudoMetricSpace.toPseudoEMetricSpace
h : ∀ ε > 0, ∃ t, t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
ε : ENNReal
hε : ε > 0
t : Set X
ht : t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
⊢ ∃ t, t.Countable ∧ s ... | ((:c Exists) ((:c Set) (:fv _uniq.40719)) (:lambda t ((:c Set) (:fv _uniq.40719)) ((:c And) ((:c Set.Countable) (:fv _uniq.40719) 0) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.40719)) ((:c Set.instHasSubset) (:fv _uniq.40719)) (:fv _uniq.40825) ((:c Set.iUnion) (:fv _uniq.40719) (:fv _uniq.40719) (:lambda y (:fv _uniq... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c UniformSpace) (:fv _uniq.40719))"},{"name":"i","sexp":"((:c Filter.IsCountablyGenerated) ((:c Prod) (:fv _uniq.40719) (:fv _uniq.40719)) ((:c uniformity) (:fv _uniq.40719) (:fv _uniq.40823)))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.40719))"},{"nam... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c Set.Countable) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 0))) (:arg :explicit 1 (:app (:c HasSub... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c UniformSpace) (:arg :exp... | {"children":[{"source":"obtain","sourceEnd":16093,"sourceStart":16087,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":16097,"sourceStart":16094,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"t","sourceEn... | [] | [{"source":"h ε hε","source_end":16117,"source_start":16109,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨t, ht⟩","source_end":16105,"source_start":16094,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":instance-implicit","context_index":3... | 25 | 11 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0dfac78692dea5232c7fa9bac9c77aca2b1b59a9adee0c8a5510fea6eb630392 | 0a247e175e22c91adb9d626104780a8eddc04a726309b4555f58e369bab8bc1a | 2e8a93faf83aa121805138fb2f93e7e386823518ec58c1a7f0fe511ceed5038a | 563c44d4bf152e195937995028051e79f2fdbb3eff5fbfbdbef3e82d72cbb7fe |
cat-searcher/leandojo-benchmark-4-random | test | 4,403 | TotallyBounded.isSeparable | Mathlib/Topology/Metrizable/Uniformity.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨t, ht.1.<a>Set.Finite.countable</a>, <a>subset_trans</a> ht.2 ?_⟩ | case intro
X : Type u_1
inst✝ : UniformSpace X
i : (𝓤 X).IsCountablyGenerated
s : Set X
this : PseudoEMetricSpace X := PseudoMetricSpace.toPseudoEMetricSpace
h : ∀ ε > 0, ∃ t, t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
ε : ENNReal
hε : ε > 0
t : Set X
ht : t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
⊢ ∃ t, t.Countable ∧ s ... | case intro
X : Type u_1
inst✝ : UniformSpace X
i : (𝓤 X).IsCountablyGenerated
s : Set X
this : PseudoEMetricSpace X := PseudoMetricSpace.toPseudoEMetricSpace
h : ∀ ε > 0, ∃ t, t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
ε : ENNReal
hε : ε > 0
t : Set X
ht : t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
⊢ ⋃ y ∈ t, EMetric.ball... | ((:c Exists) ((:c Set) (:fv _uniq.40719)) (:lambda t ((:c Set) (:fv _uniq.40719)) ((:c And) ((:c Set.Countable) (:fv _uniq.40719) 0) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.40719)) ((:c Set.instHasSubset) (:fv _uniq.40719)) (:fv _uniq.40825) ((:c Set.iUnion) (:fv _uniq.40719) (:fv _uniq.40719) (:lambda y (:fv _uniq... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c UniformSpace) (:fv _uniq.40719))"},{"name":"i","sexp":"((:c Filter.IsCountablyGenerated) ((:c Prod) (:fv _uniq.40719) (:fv _uniq.40719)) ((:c uniformity) (:fv _uniq.40719) (:fv _uniq.40823)))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.40719))"},{"nam... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c Set.Countable) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 0))) (:arg :explicit 1 (:app (:c HasSub... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c UniformSpace) (:arg :exp... | {"children":[{"source":"refine","sourceEnd":16128,"sourceStart":16122,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":16132,"sourceStart":16129,"tag":"atom"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"t","sourceEnd":16133,"sourceStart":16132,"tag":"identifier"},{"source":",","sourceEnd":16134,... | [] | [{"source":"⟨t, ht.1.countable, subset_trans ht.2 ?_⟩","source_end":16174,"source_start":16129,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":instance-implicit","context_index":3... | 25 | 12 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6345637d8c7af2eb62f45e986c119f7c72cef53b169e862a8c6dd58e54964867 | 563c44d4bf152e195937995028051e79f2fdbb3eff5fbfbdbef3e82d72cbb7fe | b7b3da462d5817cd701dd951d178781fd89706a6430041ec5f4bebdad12d2b56 | f197ed8ae0fa340b10dc8ee3d1ccdccd373ee929b77ccfd57f27d73a2ec5687e |
cat-searcher/leandojo-benchmark-4-random | test | 4,404 | TotallyBounded.isSeparable | Mathlib/Topology/Metrizable/Uniformity.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | case intro
X : Type u_1
inst✝ : UniformSpace X
i : (𝓤 X).IsCountablyGenerated
s : Set X
this : PseudoEMetricSpace X := PseudoMetricSpace.toPseudoEMetricSpace
h : ∀ ε > 0, ∃ t, t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
ε : ENNReal
hε : ε > 0
t : Set X
ht : t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
⊢ ⋃ y ∈ t, EMetric.ball... | case intro.h.h
X : Type u_1
inst✝ : UniformSpace X
i : (𝓤 X).IsCountablyGenerated
s : Set X
this : PseudoEMetricSpace X := PseudoMetricSpace.toPseudoEMetricSpace
h : ∀ ε > 0, ∃ t, t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
ε : ENNReal
hε : ε > 0
t : Set X
ht : t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
i✝¹ : X
i✝ : i✝¹ ∈ ... | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.40719)) ((:c Set.instHasSubset) (:fv _uniq.40719)) ((:c Set.iUnion) (:fv _uniq.40719) (:fv _uniq.40719) (:lambda y (:fv _uniq.40719) ((:c Set.iUnion) (:fv _uniq.40719) ((:c Membership.mem) (:fv _uniq.40719) ((:c Set) (:fv _uniq.40719)) ((:c Set.instMembership) (:fv _uniq.4071... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c UniformSpace) (:fv _uniq.40719))"},{"name":"i","sexp":"((:c Filter.IsCountablyGenerated) ((:c Prod) (:fv _uniq.40719) (:fv _uniq.40719)) ((:c uniformity) (:fv _uniq.40719) (:fv _uniq.40823)))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.40719))"},{"nam... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:c Set.iUnion) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c UniformSpace) (:arg :exp... | {"children":[{"source":"gcongr","sourceEnd":16185,"sourceStart":16179,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":16185,"sourceStart":16179,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":instance-implicit","context_index":3... | 25 | 13 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0b05b05b46c51b4b8357b8a619cfdfbae16f9f26b486babe5b7a11a077a30b56 | f197ed8ae0fa340b10dc8ee3d1ccdccd373ee929b77ccfd57f27d73a2ec5687e | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | cfb9b00beea7f56bad6cb4d67b5fbcb32783eb4caf438e2f8d6db4b2fbd16f20 |
cat-searcher/leandojo-benchmark-4-random | test | 4,405 | TotallyBounded.isSeparable | Mathlib/Topology/Metrizable/Uniformity.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>EMetric.ball_subset_closedBall</a> | case intro.h.h
X : Type u_1
inst✝ : UniformSpace X
i : (𝓤 X).IsCountablyGenerated
s : Set X
this : PseudoEMetricSpace X := PseudoMetricSpace.toPseudoEMetricSpace
h : ∀ ε > 0, ∃ t, t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
ε : ENNReal
hε : ε > 0
t : Set X
ht : t.Finite ∧ s ⊆ ⋃ y ∈ t, EMetric.ball y ε
i✝¹ : X
i✝ : i✝¹ ∈ ... | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.40719)) ((:c Set.instHasSubset) (:fv _uniq.40719)) ((:c EMetric.ball) (:fv _uniq.40719) (:fv _uniq.40846) (:fv _uniq.42195) (:fv _uniq.41205)) ((:c EMetric.closedBall) (:fv _uniq.40719) (:fv _uniq.40846) (:fv _uniq.42195) (:fv _uniq.41205))) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c UniformSpace) (:fv _uniq.40719))"},{"name":"i","sexp":"((:c Filter.IsCountablyGenerated) ((:c Prod) (:fv _uniq.40719) (:fv _uniq.40719)) ((:c uniformity) (:fv _uniq.40719) (:fv _uniq.40823)))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.40719))"},{"nam... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:c EMetric.ball) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c UniformSpace) (:arg :exp... | {"children":[{"source":"exact","sourceEnd":16195,"sourceStart":16190,"tag":"atom"},{"name":"EMetric.ball_subset_closedBall","semanticRole":"global","source":"EMetric.ball_subset_closedBall","sourceEnd":16226,"sourceStart":16196,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact EMetric.ball_subset_c... | [] | [{"source":"EMetric.ball_subset_closedBall","source_end":16226,"source_start":16196,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.40719","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.40823","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":instance-implicit","context_index":3... | 25 | 14 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f2141249e7ce8a4cec074679c821e4949dea73c66bfc6cab54a83b8cf5853f56 | cfb9b00beea7f56bad6cb4d67b5fbcb32783eb4caf438e2f8d6db4b2fbd16f20 | 8c4920fbcd234b21561b785e9e44e67826fd1f4a760f7d71f1e66b74e244cffb | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,406 | FractionalIdeal.dual_inv | Mathlib/RingTheory/DedekindDomain/Different.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>FractionalIdeal.dual_eq_mul_inv</a>, <a>inv_inv</a>] | A : Type u_1
K : Type u_2
L : Type u
B : Type u_3
inst✝¹⁹ : CommRing A
inst✝¹⁸ : Field K
inst✝¹⁷ : CommRing B
inst✝¹⁶ : Field L
inst✝¹⁵ : Algebra A K
inst✝¹⁴ : Algebra B L
inst✝¹³ : Algebra A B
inst✝¹² : Algebra K L
inst✝¹¹ : Algebra A L
inst✝¹⁰ : IsScalarTower A K L
inst✝⁹ : IsScalarTower A B L
inst✝⁸ : IsDomain A
ins... | ((:c Eq) ((:c FractionalIdeal) (:fv _uniq.431232) (:fv _uniq.431241) ((:c nonZeroDivisors) (:fv _uniq.431232) ((:c Semiring.toMonoidWithZero) (:fv _uniq.431232) ((:c CommSemiring.toSemiring) (:fv _uniq.431232) ((:c CommRing.toCommSemiring) (:fv _uniq.431232) (:fv _uniq.431241))))) (:fv _uniq.431229) ((:c EuclideanDomai... | [{"name":"A","sexp":"(:sort (+ u_1 1))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹⁹","sexp":"((:c CommRing) (:fv _uniq.431224))"},{"name":"inst✝¹⁸","sexp":"((:c Field) (:fv _uniq.431227))"},{"name":"inst✝¹⁷","sexp":"((:c CommRin... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c FractionalIdeal) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c nonZeroDivisors) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c MonoidWithZero) (:arg ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.431224","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.431227","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":12353,"sourceStart":12351,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12355,"sourceStart":12354,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"dual_eq_mul_inv","source_end":12370,"source_start":12355,"syntax_kind":"ident"},{"source":"inv_inv","source_end":12379,"source_start":12372,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.431224","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.431227","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 58 | 2 | exact | true | 1 | 28 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e44840412ee7fc2b655e351e92a9b9c8573edd42350b3ad611f2c5fe14f2a333 | 7b1566c332a14a28cf0e6a068ce810b2bdabc70d93a3956b01a6f03334d9df29 | 921e7b978668698fe97c09977318d301e250ac912e9ee75382d6d2ccedff1a89 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,407 | normEDS_three | Mathlib/NumberTheory/EllipticDivisibilitySequence.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | erw [<a>normEDS_ofNat</a>, <a>preNormEDS'_three</a>, <a>if_neg</a> <| by decide, <a>mul_one</a>] | R : Type u
S : Type v
inst✝¹ : CommRing R
inst✝ : CommRing S
W : ℤ → R
f : R →+* S
b c d : R
⊢ normEDS b c d 3 = c | ((:c Eq) (:fv _uniq.114189) ((:c normEDS) (:fv _uniq.114189) (:fv _uniq.114194) (:fv _uniq.114565) (:fv _uniq.114567) (:fv _uniq.114569) ((:c OfNat.ofNat) (:c Int) (:lit 3) ((:c instOfNat) (:lit 3)))) (:fv _uniq.114567)) | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.114189))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.114191))"},{"name":"W","sexp":"(:forall _ (:c Int) (:fv _uniq.114189))"},{"name":"f","sexp":"((:c RingHom) (:fv _uniq.114189) (:fv ... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c normEDS) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV6)) (:arg :explicit 3 (:fv FV7)) (:arg :explicit 4 (:fv FV8)) (:arg :explicit 5 (:app (:c Of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.114189","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.114191","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"erw","sourceEnd":9400,"sourceStart":9397,"tag":"atom"},{"children":[{"source":"[","sourceEnd":9402,"sourceStart":9401,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"normEDS_ofNat","semanticRole":"glob... | [] | [{"source":"normEDS_ofNat","source_end":9415,"source_start":9402,"syntax_kind":"ident"},{"source":"preNormEDS'_three","source_end":9434,"source_start":9417,"syntax_kind":"ident"},{"source":"if_neg <| by decide","source_end":9455,"source_start":9436,"syntax_kind":"«term_<|_»"},{"source":"mul_one","source_end":9464,"sour... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.114189","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.114191","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal... | 37 | 2 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 660e36724295ff5ac1d48e407b03d1df9226aef086e6b2570e679149aa6f1d8e | b7076e5950bc034cac9dda7b59aa3264abe876c65f4aec07057a8665a0df20e5 | 030c883b5fc549c4f503dadade077a41c5607e59ad8ea72c47aae1574e585d1a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,408 | normEDS_three | Mathlib/NumberTheory/EllipticDivisibilitySequence.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | decide | R : Type u
S : Type v
inst✝¹ : CommRing R
inst✝ : CommRing S
W : ℤ → R
f : R →+* S
b c d : R
⊢ ¬Even 3 | ((:c Not) ((:c Even) (:c Nat) (:c instAddNat) (:lit 3))) | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.114189))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.114191))"},{"name":"W","sexp":"(:forall _ (:c Int) (:fv _uniq.114189))"},{"name":"f","sexp":"((:c RingHom) (:fv _uniq.114189) (:fv ... | (:app (:c Not) (:arg :explicit 0 (:app (:c Even) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c Add) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:lit 3))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.114189","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.114191","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"decide","sourceEnd":9455,"sourceStart":9449,"tag":"atom"}],"kind":"Lean.Parser.Tactic.decide","source":"decide","sourceEnd":9455,"sourceStart":9449,"tag":"node"}],"kind":"null","source":"decide","sourceEnd":9455,"sourceStart":9449,"tag":"node"}],"kind":"Lea... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.114189","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.114191","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal... | 37 | 10 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 78d05d6982857a9e29d97d3daa2d370b7ed78c35e1dcc8715fa836259b9948e8 | e61bfbb046289cc4dbbf50adc0ab68c253975a7e0b4a33f3ad2c3b4b52a046d9 | 5589aa5863c2d85622d06d651add002416e5513afdbb455666cdde01bb3e257d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,409 | CategoryTheory.monoidalOfHasFiniteProducts.associator_hom_fst | Mathlib/CategoryTheory/Monoidal/OfHasFiniteProducts.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>CategoryTheory.monoidalOfHasFiniteProducts.associator_hom</a>] | C : Type u
inst✝² : Category.{v, u} C
X✝ Y✝ : C
inst✝¹ : HasTerminal C
inst✝ : HasBinaryProducts C
X Y Z : C
⊢ (α_ X Y Z).hom ≫ prod.fst = prod.fst ≫ prod.fst | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.84438) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.84438) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.84438) (:fv _uniq.84441))) ((:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:fv _uniq.84438) (:fv _uniq.84441) ((:c CategoryTheory.MonoidalCategory.t... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.84438))"},{"name":"X✝","sexp":"(:fv _uniq.84438)"},{"name":"Y✝","sexp":"(:fv _uniq.84438)"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Limits.HasTerminal) (:fv _uniq.84438) (:fv _uniq.84441))"},{"name":"inst✝","se... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.84438","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.84441","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":5335,"sourceStart":5331,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"associator_hom","source_end":5351,"source_start":5337,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.84438","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.84441","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern... | 35 | 2 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f2d3d128eae4cb8c2e3e4951c9ce7ed31880e1162889297b9a126ceb426058c8 | 6cbed2faa020aa11a277be97c9b2fff468e93bc006e6d40f0632e01742f963ce | 14521de5a5eed5873fbc3a98627977a44841b50b82f8626d23c8e45fd51fe5f7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,410 | Cardinal.cantor | Mathlib/SetTheory/Cardinal/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction' a using <a>Cardinal.inductionOn</a> with α | α β : Type u
a : Cardinal.{u}
⊢ a < 2 ^ a | case h
α✝ β α : Type u
⊢ #α < 2 ^ #α | ((:c LT.lt) (:c Cardinal) ((:c Preorder.toLT) (:c Cardinal) ((:c PartialOrder.toPreorder) (:c Cardinal) (:c Cardinal.partialOrder))) (:fv _uniq.39389) ((:c HPow.hPow) (:c Cardinal) (:c Cardinal) (:c Cardinal) ((:c instHPow) (:c Cardinal) (:c Cardinal) (:c Cardinal.instPowCardinal)) ((:c OfNat.ofNat) (:c Cardinal) (:lit... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u 1))"},{"name":"a","sexp":"(:c Cardinal)"}] | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Cardinal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Cardinal))))) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Cardinal)) (:arg :implicit-type 1 (:c Cardinal)) (:arg :implicit-type 2 (:c Cardinal)) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.39281","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.39283","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":explicit","con... | {"children":[{"source":"induction'","sourceEnd":29609,"sourceStart":29599,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":3,"semanticRole":"local","source":"a","sourceEnd":29611,"sourceStart":29610,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget... | [] | [{"source":"a","source_end":29611,"source_start":29610,"syntax_kind":"ident"},{"source":"Cardinal.inductionOn","source_end":29638,"source_start":29618,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.39281","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.39283","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 225 | 4 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 74774ff1190545c0a3b257a45a3c967ea64610025c107a3b778080189d896222 | 7cd99261f1136746c4c59c409030e1b81a1638584e135c876ce3c9c60ae82022 | bba3b8d43e5697e276858ba809e9073eede876dd16f9c3d6bbd7a8d4b5370fe9 | 90f1d76ec37ee196b5ad137ea98efea57b68c4fe1fa5b008193f9f0971ec1622 |
cat-searcher/leandojo-benchmark-4-random | test | 4,411 | Cardinal.cantor | Mathlib/SetTheory/Cardinal/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Cardinal.mk_set</a>] | case h
α✝ β α : Type u
⊢ #α < 2 ^ #α | case h
α✝ β α : Type u
⊢ #α < #(Set α) | ((:c LT.lt) (:c Cardinal) ((:c Preorder.toLT) (:c Cardinal) ((:c PartialOrder.toPreorder) (:c Cardinal) (:c Cardinal.partialOrder))) ((:c Cardinal.mk) (:fv _uniq.39402)) ((:c HPow.hPow) (:c Cardinal) (:c Cardinal) (:c Cardinal) ((:c instHPow) (:c Cardinal) (:c Cardinal) (:c Cardinal.instPowCardinal)) ((:c OfNat.ofNat) ... | [{"name":"α✝","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u 1))"},{"name":"α","sexp":"(:sort (+ u 1))"}] | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Cardinal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Cardinal))))) (:arg :explicit 2 (:app (:c Cardinal.mk) (:arg :explicit 0 (:fv FV3)))) (:arg :explicit 3 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Cardinal)) (:arg :implicit-type 1 (:c Cardina... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.39281","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.39283","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":explicit","co... | {"children":[{"source":"rw","sourceEnd":29651,"sourceStart":29649,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":29653,"sourceStart":29652,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":29656,"sourceSt... | [] | [{"source":"mk_set","source_end":29663,"source_start":29657,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.39281","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.39283","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 225 | 5 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b979188c41123f8f61400370ffc9329865b381f4b539d48d2628bb944d4468e0 | 90f1d76ec37ee196b5ad137ea98efea57b68c4fe1fa5b008193f9f0971ec1622 | cc8293f092a611ebc389de5bc1b792b57954e51dcfd04b620a55746598f0a03e | be90314891384b9144804246516464305452ad36e3d47005cd5272039df94cd5 |
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