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 | 4,104 | List.takeD_eq_takeDTR | .lake/packages/batteries/Batteries/Data/List/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>List.takeDTR</a>, <a>List.takeDTR_go_eq</a>] | case h.h.h.h
α : Type u_1
f : Nat
n : List α
l : α
⊢ takeD f n l = takeDTR f n l | ((:c Eq) ((:c List) (:fv _uniq.30141)) ((:c List.takeD) (:fv _uniq.30141) (:fv _uniq.30166) (:fv _uniq.30190) (:fv _uniq.30213)) ((:c List.takeDTR) (:fv _uniq.30141) (:fv _uniq.30166) (:fv _uniq.30190) (:fv _uniq.30213))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:c Nat)"},{"name":"n","sexp":"((:c List) (:fv _uniq.30141))"},{"name":"l","sexp":"(:fv _uniq.30141)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c List.takeD) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:fv FV4)))) (:arg :explicit 2 (:app (:c List.takeDTR) (:arg :implicit-type 0 (:fv FV1... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.30141","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.30166","is_instance":false,"is_let":false,"name":"f","sexp":"(:c Nat)"},{"binder_role":":explicit","context... | {"children":[{"source":"simp","sourceEnd":13802,"sourceStart":13798,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13804,"sourceStart":13803,"tag":"a... | [] | [{"source":"takeDTR","source_end":13811,"source_start":13804,"syntax_kind":"ident"},{"source":"takeDTR_go_eq","source_end":13826,"source_start":13813,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.30141","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.30166","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 56 | 6 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bba76bfe48a183a9b5aea5c1e2a40040c7ad73383b7595eceba11fb130e991dc | 226761daaff29b0170cd63c7f389ae98ec3c8ba45b41bf7e6093b8a01b08e181 | 5c57c8b9d2da370f900683bc5632a41df86c3de8eecf7b48f9f6d02966a42620 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,105 | unitInterval.mem_iff_one_sub_mem | Mathlib/Topology/UnitInterval.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.mem_Icc</a>, <a>Set.mem_Icc</a>] | t : ℝ
⊢ t ∈ I ↔ 1 - t ∈ I | t : ℝ
⊢ 0 ≤ t ∧ t ≤ 1 ↔ 0 ≤ 1 - t ∧ 1 - t ≤ 1 | ((:c Iff) ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) (:fv _uniq.3305) (:c unitInterval)) ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c OfN... | [{"name":"t","sexp":"(:c Real)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :e... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3305","is_instance":false,"is_let":false,"name":"t","sexp":"(:c Real)"}] | {"children":[{"source":"rw","sourceEnd":1874,"sourceStart":1872,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1876,"sourceStart":1875,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.mem_Icc","semant... | [] | [{"source":"mem_Icc","source_end":1883,"source_start":1876,"syntax_kind":"ident"},{"source":"mem_Icc","source_end":1892,"source_start":1885,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3305","is_instance":false,"is_let":false,"user_name":"t"}] | 21 | 4 | exact | true | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1f803393344ad7bb40b0654f8dba60649bdc74e79b75e7cd88cd4e1edb73d8ec | 6a25303f096a528e5c471739e92c1721a83e24ae94a67113c67c21d87215783a | 58ba6d46eb546b38cb77f0cca2ae395225969d7a3268af34e2132381921f58fd | 38c4e4790a62e5338cd2a3c3f250c066889fbd215f5d2a7e773c94e0bb6de695 |
cat-searcher/leandojo-benchmark-4-random | test | 4,106 | unitInterval.mem_iff_one_sub_mem | Mathlib/Topology/UnitInterval.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor <;> intro <;> constructor <;> linarith | t : ℝ
⊢ 0 ≤ t ∧ t ≤ 1 ↔ 0 ≤ 1 - t ∧ 1 - t ≤ 1 | ((:c Iff) ((:c And) ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.3305)) ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) (:fv _uniq.3305) ((:c OfNat.ofNat) (:c Rea... | [{"name":"t","sexp":"(:c Real)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:in... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3305","is_instance":false,"is_let":false,"name":"t","sexp":"(:c Real)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"constructor","sourceEnd":1907,"sourceStart":1896,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":1907,"sourceStart":1896,"tag":"node"},{"source":"<;>","sourceEnd":1911,"sourceStart":1908,"tag":"atom"},{"children":[{... | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3305","is_instance":false,"is_let":false,"user_name":"t"}] | 21 | 8 | exact | true | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7f5b78124a08b08abba921e0265f250bbca874f90140de5d20608bbd38564665 | 38c4e4790a62e5338cd2a3c3f250c066889fbd215f5d2a7e773c94e0bb6de695 | f4f7550e304befd59231c55ebca99233b2c00cb5e25f3994d17374043229305b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,107 | Set.encard_tsub_one_le_encard_diff_singleton | Mathlib/Data/Set/Card.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Set.encard_singleton</a> x] | α : Type u_1
β : Type u_2
s✝ t : Set α
a b : α
s : Set α
x : α
⊢ s.encard - 1 ≤ (s \ {x}).encard | α : Type u_1
β : Type u_2
s✝ t : Set α
a b : α
s : Set α
x : α
⊢ s.encard - {x}.encard ≤ (s \ {x}).encard | ((:c LE.le) (:c ENat) ((:c Preorder.toLE) (:c ENat) ((:c PartialOrder.toPreorder) (:c ENat) ((:c CompleteSemilatticeInf.toPartialOrder) (:c ENat) ((:c CompleteLattice.toCompleteSemilatticeInf) (:c ENat) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENat) ((:c CompleteLinearOrder.toCompletelyDistribLattice) (:c E... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.31651))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.31651))"},{"name":"a","sexp":"(:fv _uniq.31651)"},{"name":"b","sexp":"(:fv _uniq.31651)"},{"name":"s","sexp":"((:c Set) (:fv _uniq.31651))"},{"nam... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENat))))) (:arg :explicit 2 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:c ENat)) (:arg :implicit-type 1 (:c ENat)) (:arg :implicit-type 2 (:c ENat)) (:arg :instance 3 (:instance-of (:app (:c HSub) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31651","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31654","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":12577,"sourceStart":12575,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12579,"sourceStart":12578,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":12582,"sourceSt... | [] | [{"source":"encard_singleton x","source_end":12601,"source_start":12583,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31651","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31654","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 57 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 43dd2d11a37887c524bc47373d938448e56252a2a946324c980c86fd9a001b06 | 1d60d02a7607399e304433c95ea531b2a78e70d6085bd42537524a57362d4e8f | fd78df9a581a404b75e164e6f5af453078a6fe04e2a7721c1b44cf9638d4526a | 4e9bdbe9fdde93f8981f557c8f7850b557ec0a2da9892bb7f89859bab89aba3a |
cat-searcher/leandojo-benchmark-4-random | test | 4,108 | Set.encard_tsub_one_le_encard_diff_singleton | Mathlib/Data/Set/Card.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Set.tsub_encard_le_encard_diff</a> | α : Type u_1
β : Type u_2
s✝ t : Set α
a b : α
s : Set α
x : α
⊢ s.encard - {x}.encard ≤ (s \ {x}).encard | ((:c LE.le) (:c ENat) ((:c Preorder.toLE) (:c ENat) ((:c PartialOrder.toPreorder) (:c ENat) ((:c CompleteSemilatticeInf.toPartialOrder) (:c ENat) ((:c CompleteLattice.toCompleteSemilatticeInf) (:c ENat) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENat) ((:c CompleteLinearOrder.toCompletelyDistribLattice) (:c E... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.31651))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.31651))"},{"name":"a","sexp":"(:fv _uniq.31651)"},{"name":"b","sexp":"(:fv _uniq.31651)"},{"name":"s","sexp":"((:c Set) (:fv _uniq.31651))"},{"nam... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENat))))) (:arg :explicit 2 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:c ENat)) (:arg :implicit-type 1 (:c ENat)) (:arg :implicit-type 2 (:c ENat)) (:arg :instance 3 (:instance-of (:app (:c HSub) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31651","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31654","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"apply","sourceEnd":12609,"sourceStart":12604,"tag":"atom"},{"name":"Set.tsub_encard_le_encard_diff","semanticRole":"global","source":"tsub_encard_le_encard_diff","sourceEnd":12636,"sourceStart":12610,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply tsub_encard_le_encard_dif... | [] | [{"source":"tsub_encard_le_encard_diff","source_end":12636,"source_start":12610,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31651","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31654","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 57 | 8 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 466a91d42b886b761cc61dd60ebf981d8e55480cd5ddd1c9b7c953f5cf4c1869 | 4e9bdbe9fdde93f8981f557c8f7850b557ec0a2da9892bb7f89859bab89aba3a | da33bcd59767cb1f009bfab7b5fbba4dbbc5e7b3323cafc6c6be9a11074c6a1d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,109 | Ideal.IsPrime.mul_mem_pow | Mathlib/RingTheory/DedekindDomain/Ideal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases n | R : Type u_1
A : Type u_2
K : Type u_3
inst✝³ : CommRing R
inst✝² : CommRing A
inst✝¹ : Field K
inst✝ : IsDedekindDomain R
I : Ideal R
hI : I.IsPrime
a b : R
n : ℕ
h : a * b ∈ I ^ n
⊢ a ∈ I ∨ b ∈ I ^ n | case zero
R : Type u_1
A : Type u_2
K : Type u_3
inst✝³ : CommRing R
inst✝² : CommRing A
inst✝¹ : Field K
inst✝ : IsDedekindDomain R
I : Ideal R
hI : I.IsPrime
a b : R
h : a * b ∈ I ^ 0
⊢ a ∈ I ∨ b ∈ I ^ 0
case succ
R : Type u_1
A : Type u_2
K : Type u_3
inst✝³ : CommRing R
inst✝² : CommRing A
inst✝¹ : Field K
inst✝ : ... | ((:c Or) ((:c Membership.mem) (:fv _uniq.437350) ((:c Ideal) (:fv _uniq.437350) ((:c CommSemiring.toSemiring) (:fv _uniq.437350) ((:c CommRing.toCommSemiring) (:fv _uniq.437350) (:fv _uniq.437359)))) ((:c SetLike.instMembership) ((:c Ideal) (:fv _uniq.437350) ((:c CommSemiring.toSemiring) (:fv _uniq.437350) ((:c CommRi... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"K","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.437350))"},{"name":"inst✝²","sexp":"((:c CommRing) (:fv _uniq.437353))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.437356))"},{"name":"inst✝",... | (:app (:c Or) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437350","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.437353","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":explicit","c... | {"children":[{"source":"cases","sourceEnd":61037,"sourceStart":61032,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":12,"semanticRole":"local","source":"n","sourceEnd":61039,"sourceStart":61038,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","s... | [] | [{"source":"n","source_end":61039,"source_start":61038,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437350","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.437353","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":explicit","context_index":2,"internal_name":"_... | 276 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bca1845f0b476bc76af82bd51579caf9b3c5292ad3e1528636f67fc060709695 | 15e47230bb12e7aad0def7ae9405b9f9a610442a32ff8234c23cdb41619e22db | 587af0ace40623dade91be1b78e831facc5de085c3c720b59185b89ff09878a4 | 9a28cdf9d05b0bd6fd8487b946fbffe04bb9e6d6a8558e9eb3897ca73b363e10 |
cat-searcher/leandojo-benchmark-4-random | test | 4,110 | Ideal.IsPrime.mul_mem_pow | Mathlib/RingTheory/DedekindDomain/Ideal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases hI0 : I = ⊥ | case succ
R : Type u_1
A : Type u_2
K : Type u_3
inst✝³ : CommRing R
inst✝² : CommRing A
inst✝¹ : Field K
inst✝ : IsDedekindDomain R
I : Ideal R
hI : I.IsPrime
a b : R
n✝ : ℕ
h : a * b ∈ I ^ (n✝ + 1)
⊢ a ∈ I ∨ b ∈ I ^ (n✝ + 1) | case pos
R : Type u_1
A : Type u_2
K : Type u_3
inst✝³ : CommRing R
inst✝² : CommRing A
inst✝¹ : Field K
inst✝ : IsDedekindDomain R
I : Ideal R
hI : I.IsPrime
a b : R
n✝ : ℕ
h : a * b ∈ I ^ (n✝ + 1)
hI0 : I = ⊥
⊢ a ∈ I ∨ b ∈ I ^ (n✝ + 1)
case neg
R : Type u_1
A : Type u_2
K : Type u_3
inst✝³ : CommRing R
inst✝² : CommR... | ((:c Or) ((:c Membership.mem) (:fv _uniq.437350) ((:c Ideal) (:fv _uniq.437350) ((:c CommSemiring.toSemiring) (:fv _uniq.437350) ((:c CommRing.toCommSemiring) (:fv _uniq.437350) (:fv _uniq.437359)))) ((:c SetLike.instMembership) ((:c Ideal) (:fv _uniq.437350) ((:c CommSemiring.toSemiring) (:fv _uniq.437350) ((:c CommRi... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"K","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.437350))"},{"name":"inst✝²","sexp":"((:c CommRing) (:fv _uniq.437353))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.437356))"},{"name":"inst✝",... | (:app (:c Or) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437350","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.437353","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":explicit","c... | {"children":[{"source":"by_cases","sourceEnd":61059,"sourceStart":61051,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hI0","sourceEnd":61063,"sourceStart":61060,"tag":"identifier"},{"source":":","sourceEnd":61065,"sourceStart":61064,"tag":"atom"}],"kind":"null","source":"hI0 :","sourceEnd":61065,"... | [] | [{"source":"I = ⊥","source_end":61073,"source_start":61066,"syntax_kind":"«term_=_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437350","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.437353","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":explicit","context_index":2,"internal_name":"_... | 276 | 11 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2d44566347546ca53fa63cc3cbefca079853105dbdfd0002f4a320779d89bc39 | 75a30c956fcf045cafbe960c75c325069fd959d47f1f914c278e307fad4933e1 | 53365914a601f33f1fae265c9bb3f3dedaea168288f22c7528d70900cc11c8ac | 3e2efee77dc14efbec961f2a717d986b28a21863a68706b14ded4a9c4835e9b0 |
cat-searcher/leandojo-benchmark-4-random | test | 4,111 | Ideal.IsPrime.mul_mem_pow | Mathlib/RingTheory/DedekindDomain/Ideal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [← <a>Submodule.span_singleton_le_iff_mem</a>, <a>Ideal.submodule_span_eq</a>, ← <a>Ideal.dvd_iff_le</a>, ← <a>Ideal.span_singleton_mul_span_singleton</a>] at h ⊢ | case neg
R : Type u_1
A : Type u_2
K : Type u_3
inst✝³ : CommRing R
inst✝² : CommRing A
inst✝¹ : Field K
inst✝ : IsDedekindDomain R
I : Ideal R
hI : I.IsPrime
a b : R
n✝ : ℕ
h : a * b ∈ I ^ (n✝ + 1)
hI0 : ¬I = ⊥
⊢ a ∈ I ∨ b ∈ I ^ (n✝ + 1) | case neg
R : Type u_1
A : Type u_2
K : Type u_3
inst✝³ : CommRing R
inst✝² : CommRing A
inst✝¹ : Field K
inst✝ : IsDedekindDomain R
I : Ideal R
hI : I.IsPrime
a b : R
n✝ : ℕ
hI0 : ¬I = ⊥
h : I ^ (n✝ + 1) ∣ span {a} * span {b}
⊢ I ∣ span {a} ∨ I ^ (n✝ + 1) ∣ span {b} | ((:c Or) ((:c Membership.mem) (:fv _uniq.437350) ((:c Ideal) (:fv _uniq.437350) ((:c CommSemiring.toSemiring) (:fv _uniq.437350) ((:c CommRing.toCommSemiring) (:fv _uniq.437350) (:fv _uniq.437359)))) ((:c SetLike.instMembership) ((:c Ideal) (:fv _uniq.437350) ((:c CommSemiring.toSemiring) (:fv _uniq.437350) ((:c CommRi... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"K","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.437350))"},{"name":"inst✝²","sexp":"((:c CommRing) (:fv _uniq.437353))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.437356))"},{"name":"inst✝",... | (:app (:c Or) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437350","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.437353","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":explicit","c... | {"children":[{"source":"simp","sourceEnd":61114,"sourceStart":61110,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":61119,"sourceStart":61115,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":611... | [] | [{"source":"Submodule.span_singleton_le_iff_mem","source_end":61160,"source_start":61125,"syntax_kind":"ident"},{"source":"Ideal.submodule_span_eq","source_end":61185,"source_start":61162,"syntax_kind":"ident"},{"source":"Ideal.dvd_iff_le","source_end":61207,"source_start":61191,"syntax_kind":"ident"},{"source":"Ideal.... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437350","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.437353","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":explicit","context_index":2,"internal_name":"_... | 276 | 18 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 396a5c20c7bbc88b0ad3dec9e8ef8a229deb3ae5f66ba6461fef2ebdda2d75d5 | 1dccebf571aa32086506e15e6182aeca96dea5113b22bdb02ac51bd2e2e681a5 | 9d5aac5c628bef581de4b5a13686ae2ee337d2fe16bc39bc859e4e3bfd9aac99 | 74c957c0bbf886862177f4451e732b7210b147ceec931fb7c53308da84dcd90e |
cat-searcher/leandojo-benchmark-4-random | test | 4,112 | Ideal.IsPrime.mul_mem_pow | Mathlib/RingTheory/DedekindDomain/Ideal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases ha : I ∣ <a>Ideal.span</a> {a} | case neg
R : Type u_1
A : Type u_2
K : Type u_3
inst✝³ : CommRing R
inst✝² : CommRing A
inst✝¹ : Field K
inst✝ : IsDedekindDomain R
I : Ideal R
hI : I.IsPrime
a b : R
n✝ : ℕ
hI0 : ¬I = ⊥
h : I ^ (n✝ + 1) ∣ span {a} * span {b}
⊢ I ∣ span {a} ∨ I ^ (n✝ + 1) ∣ span {b} | case pos
R : Type u_1
A : Type u_2
K : Type u_3
inst✝³ : CommRing R
inst✝² : CommRing A
inst✝¹ : Field K
inst✝ : IsDedekindDomain R
I : Ideal R
hI : I.IsPrime
a b : R
n✝ : ℕ
hI0 : ¬I = ⊥
h : I ^ (n✝ + 1) ∣ span {a} * span {b}
ha : I ∣ span {a}
⊢ I ∣ span {a} ∨ I ^ (n✝ + 1) ∣ span {b}
case neg
R : Type u_1
A : Type u_2
... | ((:c Or) ((:c Dvd.dvd) ((:c Ideal) (:fv _uniq.437350) ((:c CommSemiring.toSemiring) (:fv _uniq.437350) ((:c CommRing.toCommSemiring) (:fv _uniq.437350) (:fv _uniq.437359)))) ((:c semigroupDvd) ((:c Ideal) (:fv _uniq.437350) ((:c CommSemiring.toSemiring) (:fv _uniq.437350) ((:c CommRing.toCommSemiring) (:fv _uniq.437350... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"K","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.437350))"},{"name":"inst✝²","sexp":"((:c CommRing) (:fv _uniq.437353))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.437356))"},{"name":"inst✝",... | (:app (:c Or) (:arg :explicit 0 (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437350","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.437353","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":explicit","c... | {"children":[{"source":"by_cases","sourceEnd":61277,"sourceStart":61269,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"ha","sourceEnd":61280,"sourceStart":61278,"tag":"identifier"},{"source":":","sourceEnd":61282,"sourceStart":61281,"tag":"atom"}],"kind":"null","source":"ha :","sourceEnd":61282,"so... | [] | [{"source":"I ∣ span {a}","source_end":61297,"source_start":61283,"syntax_kind":"«term_∣_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437350","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.437353","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":explicit","context_index":2,"internal_name":"_... | 276 | 19 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3c994dc456e1022441c50af79666e293c031859965d615be4080bf12da3e6aab | 74c957c0bbf886862177f4451e732b7210b147ceec931fb7c53308da84dcd90e | bdd61482def409c842d151a4955b38f2062dc839c6356620d9020c904f556510 | 50a8e2bf9c1efc48e3f5bafde84b6959672b3475d11a081c5a1104aeebe7b48d |
cat-searcher/leandojo-benchmark-4-random | test | 4,113 | Ideal.IsPrime.mul_mem_pow | Mathlib/RingTheory/DedekindDomain/Ideal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>mul_comm</a>] at h | case neg
R : Type u_1
A : Type u_2
K : Type u_3
inst✝³ : CommRing R
inst✝² : CommRing A
inst✝¹ : Field K
inst✝ : IsDedekindDomain R
I : Ideal R
hI : I.IsPrime
a b : R
n✝ : ℕ
hI0 : ¬I = ⊥
h : I ^ (n✝ + 1) ∣ span {a} * span {b}
ha : ¬I ∣ span {a}
⊢ I ∣ span {a} ∨ I ^ (n✝ + 1) ∣ span {b} | case neg
R : Type u_1
A : Type u_2
K : Type u_3
inst✝³ : CommRing R
inst✝² : CommRing A
inst✝¹ : Field K
inst✝ : IsDedekindDomain R
I : Ideal R
hI : I.IsPrime
a b : R
n✝ : ℕ
hI0 : ¬I = ⊥
h : I ^ (n✝ + 1) ∣ span {b} * span {a}
ha : ¬I ∣ span {a}
⊢ I ∣ span {a} ∨ I ^ (n✝ + 1) ∣ span {b} | ((:c Or) ((:c Dvd.dvd) ((:c Ideal) (:fv _uniq.437350) ((:c CommSemiring.toSemiring) (:fv _uniq.437350) ((:c CommRing.toCommSemiring) (:fv _uniq.437350) (:fv _uniq.437359)))) ((:c semigroupDvd) ((:c Ideal) (:fv _uniq.437350) ((:c CommSemiring.toSemiring) (:fv _uniq.437350) ((:c CommRing.toCommSemiring) (:fv _uniq.437350... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"K","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.437350))"},{"name":"inst✝²","sexp":"((:c CommRing) (:fv _uniq.437353))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.437356))"},{"name":"inst✝",... | (:app (:c Or) (:arg :explicit 0 (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437350","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.437353","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":explicit","c... | {"children":[{"source":"rw","sourceEnd":61323,"sourceStart":61321,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":61325,"sourceStart":61324,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"mul_comm","seman... | [] | [{"source":"mul_comm","source_end":61333,"source_start":61325,"syntax_kind":"ident"},{"source":"h","source_end":61339,"source_start":61338,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437350","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.437353","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":explicit","context_index":2,"internal_name":"_... | 276 | 25 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 80b5301e109a827050d28030a3ed4edb7a45775dc45ccb2cca56d32a45a905db | 402b048a3f6485fdf720942df83be8a767ec96704ff6c044b1aac6e0d46f0c27 | 8aef77e9d68a5f117b52cc7cd19d9aa3f9ea1d07e3846230cc4d5d766898788c | 8184262983615da30f6aacc50926141d6116e1a00323b33c2a2ec47bbf2024f3 |
cat-searcher/leandojo-benchmark-4-random | test | 4,114 | Ideal.IsPrime.mul_mem_pow | Mathlib/RingTheory/DedekindDomain/Ideal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Or.inr</a> (<a>Prime.pow_dvd_of_dvd_mul_right</a> ((<a>Ideal.prime_iff_isPrime</a> hI0).<a>Iff.mpr</a> hI) _ ha h) | case neg
R : Type u_1
A : Type u_2
K : Type u_3
inst✝³ : CommRing R
inst✝² : CommRing A
inst✝¹ : Field K
inst✝ : IsDedekindDomain R
I : Ideal R
hI : I.IsPrime
a b : R
n✝ : ℕ
hI0 : ¬I = ⊥
h : I ^ (n✝ + 1) ∣ span {b} * span {a}
ha : ¬I ∣ span {a}
⊢ I ∣ span {a} ∨ I ^ (n✝ + 1) ∣ span {b} | ((:c Or) ((:c Dvd.dvd) ((:c Ideal) (:fv _uniq.437350) ((:c CommSemiring.toSemiring) (:fv _uniq.437350) ((:c CommRing.toCommSemiring) (:fv _uniq.437350) (:fv _uniq.437359)))) ((:c semigroupDvd) ((:c Ideal) (:fv _uniq.437350) ((:c CommSemiring.toSemiring) (:fv _uniq.437350) ((:c CommRing.toCommSemiring) (:fv _uniq.437350... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"K","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.437350))"},{"name":"inst✝²","sexp":"((:c CommRing) (:fv _uniq.437353))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.437356))"},{"name":"inst✝",... | (:app (:c Or) (:arg :explicit 0 (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437350","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.437353","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":explicit","c... | {"children":[{"source":"exact","sourceEnd":61347,"sourceStart":61342,"tag":"atom"},{"children":[{"name":"Or.inr","semanticRole":"constructor","source":"Or.inr","sourceEnd":61354,"sourceStart":61348,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":61356,"sourceStart":61355,"tag":"atom"},{"children... | [] | [{"source":"Or.inr (Prime.pow_dvd_of_dvd_mul_right ((Ideal.prime_iff_isPrime hI0).mpr hI) _ ha h)","source_end":61433,"source_start":61348,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437350","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.437353","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":explicit","context_index":2,"internal_name":"_... | 276 | 28 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b7887a7607be2101351684f00eab647250339019c9f66e93bd378cd77b04ab29 | 8184262983615da30f6aacc50926141d6116e1a00323b33c2a2ec47bbf2024f3 | fe5be98b0960a32222b5073a90b163ada177958d191ce00aa99b66959a8f613c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,115 | Ideal.IsPrime.mul_mem_pow | Mathlib/RingTheory/DedekindDomain/Ideal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case zero
R : Type u_1
A : Type u_2
K : Type u_3
inst✝³ : CommRing R
inst✝² : CommRing A
inst✝¹ : Field K
inst✝ : IsDedekindDomain R
I : Ideal R
hI : I.IsPrime
a b : R
h : a * b ∈ I ^ 0
⊢ a ∈ I ∨ b ∈ I ^ 0 | ((:c Or) ((:c Membership.mem) (:fv _uniq.437350) ((:c Ideal) (:fv _uniq.437350) ((:c CommSemiring.toSemiring) (:fv _uniq.437350) ((:c CommRing.toCommSemiring) (:fv _uniq.437350) (:fv _uniq.437359)))) ((:c SetLike.instMembership) ((:c Ideal) (:fv _uniq.437350) ((:c CommSemiring.toSemiring) (:fv _uniq.437350) ((:c CommRi... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"K","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.437350))"},{"name":"inst✝²","sexp":"((:c CommRing) (:fv _uniq.437353))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.437356))"},{"name":"inst✝",... | (:app (:c Or) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437350","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.437353","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":explicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":61048,"sourceStart":61044,"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.437350","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.437353","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":explicit","context_index":2,"internal_name":"_... | 276 | 8 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c17908e0e580fc4de8cb982313d49acb80a9b651b90d75737f61be4b21c098b8 | 0663a54681e929cbe893fd737d7dcfb70e1639e510100e5feb54db100e753b6f | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,116 | Ideal.IsPrime.mul_mem_pow | Mathlib/RingTheory/DedekindDomain/Ideal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [<a>pow_succ</a>, hI0] using h | case pos
R : Type u_1
A : Type u_2
K : Type u_3
inst✝³ : CommRing R
inst✝² : CommRing A
inst✝¹ : Field K
inst✝ : IsDedekindDomain R
I : Ideal R
hI : I.IsPrime
a b : R
n✝ : ℕ
h : a * b ∈ I ^ (n✝ + 1)
hI0 : I = ⊥
⊢ a ∈ I ∨ b ∈ I ^ (n✝ + 1) | ((:c Or) ((:c Membership.mem) (:fv _uniq.437350) ((:c Ideal) (:fv _uniq.437350) ((:c CommSemiring.toSemiring) (:fv _uniq.437350) ((:c CommRing.toCommSemiring) (:fv _uniq.437350) (:fv _uniq.437359)))) ((:c SetLike.instMembership) ((:c Ideal) (:fv _uniq.437350) ((:c CommSemiring.toSemiring) (:fv _uniq.437350) ((:c CommRi... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"K","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.437350))"},{"name":"inst✝²","sexp":"((:c CommRing) (:fv _uniq.437353))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.437356))"},{"name":"inst✝",... | (:app (:c Or) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437350","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.437353","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":explicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":61083,"sourceStart":61078,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"pow_succ","source_end":61093,"source_start":61085,"syntax_kind":"ident"},{"source":"hI0","source_end":61098,"source_start":61095,"syntax_kind":"ident"},{"source":"h","source_end":61107,"source_start":61106,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437350","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.437353","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":explicit","context_index":2,"internal_name":"_... | 276 | 15 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 342ae2bad6ef417ced91f9e289a49289600430dbd0bdd003d0b02e2318687a87 | c74b7812655b62e57638d09cc816ae239485dc4dd7d8a3f053c76bc21ab924a6 | 92a1f0e3959dba01db93419de50f5ebfa4feb999e1a6ebe7a7b6e798cd174d8c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,117 | Ideal.IsPrime.mul_mem_pow | Mathlib/RingTheory/DedekindDomain/Ideal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Or.inl</a> ha | case pos
R : Type u_1
A : Type u_2
K : Type u_3
inst✝³ : CommRing R
inst✝² : CommRing A
inst✝¹ : Field K
inst✝ : IsDedekindDomain R
I : Ideal R
hI : I.IsPrime
a b : R
n✝ : ℕ
hI0 : ¬I = ⊥
h : I ^ (n✝ + 1) ∣ span {a} * span {b}
ha : I ∣ span {a}
⊢ I ∣ span {a} ∨ I ^ (n✝ + 1) ∣ span {b} | ((:c Or) ((:c Dvd.dvd) ((:c Ideal) (:fv _uniq.437350) ((:c CommSemiring.toSemiring) (:fv _uniq.437350) ((:c CommRing.toCommSemiring) (:fv _uniq.437350) (:fv _uniq.437359)))) ((:c semigroupDvd) ((:c Ideal) (:fv _uniq.437350) ((:c CommSemiring.toSemiring) (:fv _uniq.437350) ((:c CommRing.toCommSemiring) (:fv _uniq.437350... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"K","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.437350))"},{"name":"inst✝²","sexp":"((:c CommRing) (:fv _uniq.437353))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.437356))"},{"name":"inst✝",... | (:app (:c Or) (:arg :explicit 0 (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437350","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.437353","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":explicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":61308,"sourceStart":61303,"tag":"atom"},{"children":[{"name":"Or.inl","semanticRole":"constructor","source":"Or.inl","sourceEnd":61315,"sourceStart":61309,"tag":"identifier"},{"children":[{"contextIndex":15,"semanticRole":"local","source"... | [] | [{"source":"Or.inl ha","source_end":61318,"source_start":61309,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437350","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.437353","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":explicit","context_index":2,"internal_name":"_... | 276 | 22 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7ced0e54c6b61b7d09f1697549df9be30e1ec24eb4888ea571149f78caaf01de | 9a1375fc6b9450c837cf9a74ddb9bebc2e047faf7bd1ed2be1f2221a1cffa7d8 | 94d371efc08218fa9b0c9ae5c4eaf18511162fd1cb948c6a97e2da45e93f4e17 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,118 | MeasureTheory.memℒp_zero_iff_aestronglyMeasurable | Mathlib/MeasureTheory/Function/LpSeminorm/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>MeasureTheory.Memℒp</a>, <a>MeasureTheory.snorm_exponent_zero</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✝² : NormedAddCommGroup E
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedAddCommGroup G
f : α → E
⊢ Memℒp f 0 μ ↔ AEStronglyMeasurable f μ | ((:c Iff) ((:c MeasureTheory.Memℒp) (:fv _uniq.19660) (:fv _uniq.19692) (:fv _uniq.19657) (:fv _uniq.19672) (:fv _uniq.19881) ((:c OfNat.ofNat) (:c ENNReal) (:lit 0) ((:c Zero.toOfNat0) (:c ENNReal) (:c instENNRealZero))) (:fv _uniq.19685)) ((:c MeasureTheory.AEStronglyMeasurable) (:fv _uniq.19657) (:fv _uniq.19660) ((... | [{"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.19657))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.19657))"},{"name":"p","sexp":"(:c ENNReal)... | (:app (:c Iff) (:arg :explicit 0 (:app (:c MeasureTheory.Memℒp) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:fv FV0)) (:arg :implicit 3) (:arg :explicit 4 (:fv FV14)) (:arg :explicit 5 (:app (:c OfNat.ofNat) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.19657","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.19660","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":8874,"sourceStart":8870,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"Memℒp","source_end":8883,"source_start":8876,"syntax_kind":"ident"},{"source":"snorm_exponent_zero","source_end":8904,"source_start":8885,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.19657","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.19660","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 52 | 2 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a520514412d8cdaed235eccff6cc990e7f805e94f3f07b0213124c673c7a0c6e | 938ff31a30229bb58a3be4a811474ee903454847e9c155c51c4cfd11f7b6159d | 2ee16657212bace75ab30b99038767a6e822f0a60d5f1bf12f372321bf2ee4a9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,119 | Ring.DirectLimit.congr_symm_apply_of | Mathlib/Algebra/DirectLimit.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Ring.DirectLimit.congr</a>, <a>RingEquiv.ofHomInv_symm_apply</a>, <a>Ring.DirectLimit.map_apply_of</a>, <a>RingHom.coe_coe</a>] | R : Type u
inst✝⁷ : Ring R
ι : Type v
inst✝⁶ : Preorder ι
G : ι → Type w
inst✝⁵ : (i : ι) → CommRing (G i)
f✝ : (i j : ι) → i ≤ j → G i → G j
f'✝ : (i j : ι) → i ≤ j → G i →+* G j
P : Type u₁
inst✝⁴ : CommRing P
g✝ : (i : ι) → G i →+* P
Hg : ∀ (i j : ι) (hij : i ≤ j) (x : G i), (g✝ j) (f✝ i j hij x) = (g✝ i) x
f : (i j... | ((:c Eq) ((:c Ring.DirectLimit) (:fv _uniq.768069) (:fv _uniq.768072) (:fv _uniq.768076) (:fv _uniq.768084) (:lambda _ (:fv _uniq.768069) (:lambda _ (:fv _uniq.768069) (:lambda h ((:c LE.le) (:fv _uniq.768069) ((:c Preorder.toLE) (:fv _uniq.768069) (:fv _uniq.768072)) 1 0) ((:c DFunLike.coe) ((:c RingHom) ((:fv _uniq.7... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝⁷","sexp":"((:c Ring) (:fv _uniq.768064))"},{"name":"ι","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁶","sexp":"((:c Preorder) (:fv _uniq.768069))"},{"name":"G","sexp":"(:forall _ (:fv _uniq.768069) (:sort (+ w 1)))"},{"name":"inst✝⁵","sexp":"(:forall i (:fv _uniq.768069)... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Ring.DirectLimit) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 (:fv FV4)) (:arg :instance 3 (:instance-of (:forall i :explicit (:fv FV2) (:app (:c CommRing) (:arg :explicit 0 (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.768064","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.768067","is_instance":true,"is_let":false,"name":"inst✝⁷","sexp":"(:app (:c Ring) (:arg :explicit... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":42020,"sourceStart":42016,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":42025,"sourceStart":42021,"tag":"atom"}],"kind"... | [] | [{"source":"congr","source_end":42032,"source_start":42027,"syntax_kind":"ident"},{"source":"RingEquiv.ofHomInv_symm_apply","source_end":42063,"source_start":42034,"syntax_kind":"ident"},{"source":"map_apply_of","source_end":42077,"source_start":42065,"syntax_kind":"ident"},{"source":"RingHom.coe_coe","source_end":4209... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.768064","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.768067","is_instance":true,"is_let":false,"user_name":"inst✝⁷"},{"binder_role":":implicit","context_index":2,"inte... | 205 | 2 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5e47f7c73fd2d388891346ff2d4efc905cdfed238997831ed166f31a36e1e502 | 45c112557f78beaa4cc409c0f0b126d58e5cc525694ada5a313e154770ce1405 | bf923b2fb59e2f6e305848bbe5c1fee88b7fd184c1a80201c9ae0196843d3dd3 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,120 | eq_one_div_of_mul_eq_one_left | Mathlib/Algebra/Group/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>eq_inv_of_mul_eq_one_left</a> h, <a>one_div</a>] | α : Type u_1
β : Type u_2
G : Type u_3
M : Type u_4
inst✝ : DivisionMonoid α
a b c d : α
h : b * a = 1
⊢ b = 1 / a | ((:c Eq) (:fv _uniq.32598) (:fv _uniq.32614) ((:c HDiv.hDiv) (:fv _uniq.32598) (:fv _uniq.32598) (:fv _uniq.32598) ((:c instHDiv) (:fv _uniq.32598) ((:c DivInvMonoid.toDiv) (:fv _uniq.32598) ((:c DivisionMonoid.toDivInvMonoid) (:fv _uniq.32598) (:fv _uniq.32610)))) ((:c OfNat.ofNat) (:fv _uniq.32598) (:lit 1) ((:c One.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"G","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c DivisionMonoid) (:fv _uniq.32598))"},{"name":"a","sexp":"(:fv _uniq.32598)"},{"name":"b","sexp":"(:fv _uniq.32598)"},{"name":"c","... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV6)) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32598","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32601","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":16304,"sourceStart":16302,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16306,"sourceStart":16305,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"eq_inv_of_mul_eq_one_left h","source_end":16333,"source_start":16306,"syntax_kind":"Lean.Parser.Term.app"},{"source":"one_div","source_end":16342,"source_start":16335,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32598","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32601","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 239 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3b53472c28499cf981fc2b764f2ba95d940f1e50e933270c9de34d38dc2f8229 | 83047c4ffd66429e3314c4fd8fd847c8bd76517c1b8da884fc9ab8c1e549ad6d | 3ba828ed8b032bcf6213ae0453a99d22166d086df4d3643e61d94f3e4b224ecd | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,121 | ProbabilityTheory.kernel.compProdFun_tsum_left | Mathlib/Probability/Kernel/Composition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>ProbabilityTheory.kernel.compProdFun</a>, (<a>ProbabilityTheory.kernel.measure_sum_seq</a> κ _).<a>Eq.symm</a>, <a>MeasureTheory.lintegral_sum_measure</a>] | α : Type u_1
β : Type u_2
ι : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
γ : Type u_4
mγ : MeasurableSpace γ
s✝ : Set (β × γ)
κ : ↥(kernel α β)
η : ↥(kernel (α × β) γ)
inst✝ : IsSFiniteKernel κ
a : α
s : Set (β × γ)
⊢ compProdFun κ η a s = ∑' (n : ℕ), compProdFun (seq κ n) η a s | ((:c Eq) (:c ENNReal) ((:c ProbabilityTheory.kernel.compProdFun) (:fv _uniq.9852) (:fv _uniq.9855) (:fv _uniq.9861) (:fv _uniq.9864) (:fv _uniq.9867) (:fv _uniq.9870) (:fv _uniq.10503) (:fv _uniq.10504) (:fv _uniq.10506) (:fv _uniq.10507)) ((:c tsum) (:c ENNReal) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:c ENNR... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.9852))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.9855))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"mγ","sexp":"((:c Measura... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c ProbabilityTheory.kernel.compProdFun) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :implicit 3) (:arg :implicit-type 4 (:fv FV5)) (:arg :implicit 5) (:arg :explicit 6 (:fv FV9)) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9852","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9855","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":7056,"sourceStart":7049,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7058,"sourceStart":7057,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":""... | [] | [{"source":"compProdFun","source_end":7069,"source_start":7058,"syntax_kind":"ident"},{"source":"(measure_sum_seq κ _).symm","source_end":7098,"source_start":7071,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"lintegral_sum_measure","source_end":7121,"source_start":7100,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9852","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9855","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 18 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 758b79fffe2e3d377a39a25a459e8425dd61873a77b8397efb6fca4f1c30dbcd | a4864a4a56aca18307e5a371b9b63c83f3939919baa20902ef485caf6977d7bc | 8e4a225326f0cb34780e2b758fefc2115e163564aff2f17d1fd3907ab4003356 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,122 | MulAction.Supports.smul | Mathlib/GroupTheory/GroupAction/Support.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro g' hg' | G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
inst✝⁶ : Group H
inst✝⁵ : SMul G α
inst✝⁴ : SMul G β
inst✝³ : MulAction H α
inst✝² : SMul H β
inst✝¹ : SMulCommClass G H β
inst✝ : SMulCommClass G H α
s t : Set α
b : β
g : H
h : Supports G s b
⊢ Supports G (g • s) (g • b) | G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
inst✝⁶ : Group H
inst✝⁵ : SMul G α
inst✝⁴ : SMul G β
inst✝³ : MulAction H α
inst✝² : SMul H β
inst✝¹ : SMulCommClass G H β
inst✝ : SMulCommClass G H α
s t : Set α
b : β
g : H
h : Supports G s b
g' : G
hg' : ∀ ⦃a : α⦄, a ∈ g • s → g' • a = a
⊢ g' • g • b = g • b | ((:c MulAction.Supports) (:fv _uniq.1759) (:fv _uniq.1765) (:fv _uniq.1768) (:fv _uniq.1775) (:fv _uniq.1779) ((:c HSMul.hSMul) (:fv _uniq.1762) ((:c Set) (:fv _uniq.1765)) ((:c Set) (:fv _uniq.1765)) ((:c instHSMul) (:fv _uniq.1762) ((:c Set) (:fv _uniq.1765)) ((:c Set.smulSet) (:fv _uniq.1762) (:fv _uniq.1765) ((:c M... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁶","sexp":"((:c Group) (:fv _uniq.1762))"},{"name":"inst✝⁵","sexp":"((:c SMul) (:fv _uniq.1759) (:fv _uniq.1765))"},{"name":"inst✝⁴","sexp":"((:c... | (:app (:c MulAction.Supports) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c SMul) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2))))) (:arg :instance 4 (:instance-of (:app (:c SMul) (:arg :explicit 0 (:fv FV0)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1759","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1762","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"rintro","sourceEnd":1933,"sourceStart":1927,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"g'","sourceEnd":1936,"sourceStart":1934,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"g'","sourceEnd":1936,"sourceStart":1934,"tag"... | [{"role":"fresh_name","source":"g'","source_end":1936,"source_start":1934,"syntax_kind":"ident"},{"role":"fresh_name","source":"hg'","source_end":1940,"source_start":1937,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1759","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1762","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 20 | 4 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 107b2ae317133ccdc6e1ce44d6385f02782954e7c83fffa8b705bf9d498c5a5c | 9babcd324aa584ec262fb152ca0a7dd9e2670186ce9f4c12a419274f85ace263 | 928f2e877fce4c281c2f2a3c510f70e19c4ae39180eaf068330214b67eeda382 | ddd291b55e2c28d8e7a45c8803dd678b225624c7faaec21ab30e4a7d2d0c2b84 |
cat-searcher/leandojo-benchmark-4-random | test | 4,123 | MulAction.Supports.smul | Mathlib/GroupTheory/GroupAction/Support.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>SMulCommClass.smul_comm</a>, h] | G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
inst✝⁶ : Group H
inst✝⁵ : SMul G α
inst✝⁴ : SMul G β
inst✝³ : MulAction H α
inst✝² : SMul H β
inst✝¹ : SMulCommClass G H β
inst✝ : SMulCommClass G H α
s t : Set α
b : β
g : H
h : Supports G s b
g' : G
hg' : ∀ ⦃a : α⦄, a ∈ g • s → g' • a = a
⊢ g' • g • b = g • b | case a
G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
inst✝⁶ : Group H
inst✝⁵ : SMul G α
inst✝⁴ : SMul G β
inst✝³ : MulAction H α
inst✝² : SMul H β
inst✝¹ : SMulCommClass G H β
inst✝ : SMulCommClass G H α
s t : Set α
b : β
g : H
h : Supports G s b
g' : G
hg' : ∀ ⦃a : α⦄, a ∈ g • s → g' • a = a
⊢ ∀ ⦃a : α⦄, a ∈ s →... | ((:c Eq) (:fv _uniq.1768) ((:c HSMul.hSMul) (:fv _uniq.1759) (:fv _uniq.1768) (:fv _uniq.1768) ((:c instHSMul) (:fv _uniq.1759) (:fv _uniq.1768) (:fv _uniq.1779)) (:fv _uniq.3869) ((:c HSMul.hSMul) (:fv _uniq.1762) (:fv _uniq.1768) (:fv _uniq.1768) ((:c instHSMul) (:fv _uniq.1762) (:fv _uniq.1768) (:fv _uniq.2005)) (:f... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁶","sexp":"((:c Group) (:fv _uniq.1762))"},{"name":"inst✝⁵","sexp":"((:c SMul) (:fv _uniq.1759) (:fv _uniq.1765))"},{"name":"inst✝⁴","sexp":"((:c... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c HSMul) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1759","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1762","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"rw","sourceEnd":1945,"sourceStart":1943,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1947,"sourceStart":1946,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"SMulCommClass.smul_c... | [] | [{"source":"smul_comm","source_end":1956,"source_start":1947,"syntax_kind":"ident"},{"source":"h","source_end":1959,"source_start":1958,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1759","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1762","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 20 | 5 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ab091213e79520bf1a5291276ee8b757227e42bac003ade378e69c45fd26bdf0 | ddd291b55e2c28d8e7a45c8803dd678b225624c7faaec21ab30e4a7d2d0c2b84 | 4f501aaf84d4ff0d791c8704f639b43f651d99e5efdd49f146e20b3b83464128 | a63f95ff7cae2741189bf2d01d5b34b02367e07cea1eb923f5074a6e8f8f4226 |
cat-searcher/leandojo-benchmark-4-random | test | 4,124 | MulAction.Supports.smul | Mathlib/GroupTheory/GroupAction/Support.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro a ha | case a
G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
inst✝⁶ : Group H
inst✝⁵ : SMul G α
inst✝⁴ : SMul G β
inst✝³ : MulAction H α
inst✝² : SMul H β
inst✝¹ : SMulCommClass G H β
inst✝ : SMulCommClass G H α
s t : Set α
b : β
g : H
h : Supports G s b
g' : G
hg' : ∀ ⦃a : α⦄, a ∈ g • s → g' • a = a
⊢ ∀ ⦃a : α⦄, a ∈ s →... | case a
G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
inst✝⁶ : Group H
inst✝⁵ : SMul G α
inst✝⁴ : SMul G β
inst✝³ : MulAction H α
inst✝² : SMul H β
inst✝¹ : SMulCommClass G H β
inst✝ : SMulCommClass G H α
s t : Set α
b : β
g : H
h : Supports G s b
g' : G
hg' : ∀ ⦃a : α⦄, a ∈ g • s → g' • a = a
a : α
ha : a ∈ s
⊢ g... | (:forall a (:fv _uniq.1765) (:forall _ ((:c Membership.mem) (:fv _uniq.1765) ((:c Set) (:fv _uniq.1765)) ((:c Set.instMembership) (:fv _uniq.1765)) 0 (:fv _uniq.2861)) ((:c Eq) (:fv _uniq.1765) ((:c HSMul.hSMul) (:fv _uniq.1759) (:fv _uniq.1765) (:fv _uniq.1765) ((:c instHSMul) (:fv _uniq.1759) (:fv _uniq.1765) (:fv _u... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁶","sexp":"((:c Group) (:fv _uniq.1762))"},{"name":"inst✝⁵","sexp":"((:c SMul) (:fv _uniq.1759) (:fv _uniq.1765))"},{"name":"inst✝⁴","sexp":"((:c... | (:forall a :strict-implicit (:fv FV2) (:forall _ :explicit (: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 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1759","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1762","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"rintro","sourceEnd":1969,"sourceStart":1963,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":1971,"sourceStart":1970,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"a","sourceEnd":1971,"sourceStart":1970,"tag":"... | [{"role":"fresh_name","source":"a","source_end":1971,"source_start":1970,"syntax_kind":"ident"},{"role":"fresh_name","source":"ha","source_end":1974,"source_start":1972,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1759","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1762","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 20 | 9 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b020c2a7277f754d0af48aaad92aacde829c5191f7ed027f45c4c4b61fbf7f6d | a63f95ff7cae2741189bf2d01d5b34b02367e07cea1eb923f5074a6e8f8f4226 | 4ea913ec073e58c8d03aef0b2b8b92aec0a6bfc340e4faad2b60b1f22e57ff1e | f536d7eed2b31b35bbaa37620a13d554cb7c07bac9191c73b8502ad712f58bd3 |
cat-searcher/leandojo-benchmark-4-random | test | 4,125 | MulAction.Supports.smul | Mathlib/GroupTheory/GroupAction/Support.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have := <a>Set.forall_mem_image</a>.1 hg' ha | case a
G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
inst✝⁶ : Group H
inst✝⁵ : SMul G α
inst✝⁴ : SMul G β
inst✝³ : MulAction H α
inst✝² : SMul H β
inst✝¹ : SMulCommClass G H β
inst✝ : SMulCommClass G H α
s t : Set α
b : β
g : H
h : Supports G s b
g' : G
hg' : ∀ ⦃a : α⦄, a ∈ g • s → g' • a = a
a : α
ha : a ∈ s
⊢ g... | case a
G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
inst✝⁶ : Group H
inst✝⁵ : SMul G α
inst✝⁴ : SMul G β
inst✝³ : MulAction H α
inst✝² : SMul H β
inst✝¹ : SMulCommClass G H β
inst✝ : SMulCommClass G H α
s t : Set α
b : β
g : H
h : Supports G s b
g' : G
hg' : ∀ ⦃a : α⦄, a ∈ g • s → g' • a = a
a : α
ha : a ∈ s
thi... | ((:c Eq) (:fv _uniq.1765) ((:c HSMul.hSMul) (:fv _uniq.1759) (:fv _uniq.1765) (:fv _uniq.1765) ((:c instHSMul) (:fv _uniq.1759) (:fv _uniq.1765) (:fv _uniq.1775)) (:fv _uniq.3869) (:fv _uniq.4209)) (:fv _uniq.4209)) | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁶","sexp":"((:c Group) (:fv _uniq.1762))"},{"name":"inst✝⁵","sexp":"((:c SMul) (:fv _uniq.1759) (:fv _uniq.1765))"},{"name":"inst✝⁴","sexp":"((:c... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c HSMul) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1759","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1762","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"have","sourceEnd":1981,"sourceStart":1977,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":1982,"sourceStart":1982,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":1982,"sourceStart":1982,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"Set.forall_mem_image.1 hg' ha","source_end":2014,"source_start":1985,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1759","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1762","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 20 | 10 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f1e6b20e8e87db51be1960d2444840fc5e311444cafdd7866079ebfb2cc76f8f | f536d7eed2b31b35bbaa37620a13d554cb7c07bac9191c73b8502ad712f58bd3 | d50c908d255243540ce7858e4c1941e28890d9816c9cf7f223631f2319a6df17 | da3ae426156703e22259b86aa47025916af1e84cc31e8b4feb1706a0babfc60a |
cat-searcher/leandojo-benchmark-4-random | test | 4,126 | MulAction.Supports.smul | Mathlib/GroupTheory/GroupAction/Support.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>SMulCommClass.smul_comm</a>, <a>smul_left_cancel_iff</a>] at this | case a
G : Type u_1
H : Type u_2
α : Type u_3
β : Type u_4
inst✝⁶ : Group H
inst✝⁵ : SMul G α
inst✝⁴ : SMul G β
inst✝³ : MulAction H α
inst✝² : SMul H β
inst✝¹ : SMulCommClass G H β
inst✝ : SMulCommClass G H α
s t : Set α
b : β
g : H
h : Supports G s b
g' : G
hg' : ∀ ⦃a : α⦄, a ∈ g • s → g' • a = a
a : α
ha : a ∈ s
thi... | ((:c Eq) (:fv _uniq.1765) ((:c HSMul.hSMul) (:fv _uniq.1759) (:fv _uniq.1765) (:fv _uniq.1765) ((:c instHSMul) (:fv _uniq.1759) (:fv _uniq.1765) (:fv _uniq.1775)) (:fv _uniq.3869) (:fv _uniq.4209)) (:fv _uniq.4209)) | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁶","sexp":"((:c Group) (:fv _uniq.1762))"},{"name":"inst✝⁵","sexp":"((:c SMul) (:fv _uniq.1759) (:fv _uniq.1765))"},{"name":"inst✝⁴","sexp":"((:c... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c HSMul) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1759","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1762","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"rwa","sourceEnd":2020,"sourceStart":2017,"tag":"atom"},{"children":[{"source":"[","sourceEnd":2022,"sourceStart":2021,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"SMulCommClass.smul_comm","semanticRole":"global","source":"smul_comm","sou... | [] | [{"source":"smul_comm","source_end":2031,"source_start":2022,"syntax_kind":"ident"},{"source":"this","source_end":2062,"source_start":2058,"syntax_kind":"ident"},{"source":"smul_left_cancel_iff","source_end":2053,"source_start":2033,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1759","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1762","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 20 | 11 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dd9a21d4d235fc2e7f98419dcdbe0e730da7a9a2ba03b462f613ff3b37ca83d7 | da3ae426156703e22259b86aa47025916af1e84cc31e8b4feb1706a0babfc60a | 97d315e460c2dee357a994e5430bb3804f1d6c62e986c1f7112cb777b51eefd5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,127 | Set.projIci_eq_self | Mathlib/Order/Interval/Set/ProjIcc.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Set.projIci</a>, <a>Subtype.ext_iff</a>] | α : Type u_1
β : Type u_2
inst✝ : LinearOrder α
a b : α
h : a ≤ b
x : α
⊢ projIci a x = ⟨a, ⋯⟩ ↔ x ≤ a | ((:c Iff) ((:c Eq) ((:c Set.Elem) (:fv _uniq.6162) ((:c Set.Ici) (:fv _uniq.6162) ((:c PartialOrder.toPreorder) (:fv _uniq.6162) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.6162) ((:c Lattice.toSemilatticeInf) (:fv _uniq.6162) ((:c DistribLattice.toLattice) (:fv _uniq.6162) ((:c instDistribLatticeOfLinearOrder) (:fv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.6162))"},{"name":"a","sexp":"(:fv _uniq.6162)"},{"name":"b","sexp":"(:fv _uniq.6162)"},{"name":"h","sexp":"((:c LE.le) (:fv _uniq.6162) ((:c Preorder.toLE) (:fv _uniq.6162) ((:c PartialO... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set.Ici) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV3)))))) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6162","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6165","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":3709,"sourceStart":3705,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"projIci","source_end":3718,"source_start":3711,"syntax_kind":"ident"},{"source":"Subtype.ext_iff","source_end":3735,"source_start":3720,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6162","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6165","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 34 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 18e39dc536fd3c4d0134289118b1dcb1411c4b14164635886123e44d7d7e2779 | bc596f6c0dc36c880af3ad4e7fabfbeecdc68301e5b0aa10d8e79c9e1931303e | aa89bf2a86935a6c2385ad1b1cd14cf63db2924c1d268da97e63a1bf683f999d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,128 | nnnorm_mul_le | Mathlib/Analysis/Normed/Field/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [← <a>norm_toNNReal</a>, ← <a>Real.toNNReal_mul</a> (<a>norm_nonneg</a> _)] using <a>Real.toNNReal_mono</a> (<a>norm_mul_le</a> _ _) | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
inst✝ : NonUnitalSeminormedRing α
a b : α
⊢ ‖a * b‖₊ ≤ ‖a‖₊ * ‖b‖₊ | ((:c LE.le) (:c NNReal) ((:c Preorder.toLE) (:c NNReal) ((:c PartialOrder.toPreorder) (:c NNReal) ((:c StrictOrderedSemiring.toPartialOrder) (:c NNReal) (:c instNNRealStrictOrderedSemiring)))) ((:c NNNorm.nnnorm) (:fv _uniq.14862) ((:c SeminormedAddGroup.toNNNorm) (:fv _uniq.14862) ((:c SeminormedAddCommGroup.toSeminor... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c NonUnitalSeminormedRing) (:fv _uniq.14862))"},{"name":"a","sexp":"(:fv _uniq.14862)"},{"name":"b","sexp":"(:fv _uniq.14862)"}] | (:app (:c LE.le) (:arg :implicit-type 0 (:c NNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c NNReal))))) (:arg :explicit 2 (:app (:c NNNorm.nnnorm) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NNNorm) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14862","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14865","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":10645,"sourceStart":10640,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"norm_toNNReal","source_end":10669,"source_start":10656,"syntax_kind":"ident"},{"source":"Real.toNNReal_mul (norm_nonneg _)","source_end":10708,"source_start":10675,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Real.toNNReal_mono (norm_mul_le _ _)","source_end":10756,"source_start":10720,"syntax_kind":"Le... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14862","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14865","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 63 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e4a71dffbc9ea1391b71f33c4f8b74a55e6ec76fb0137efe5a0e7dbdabc864b2 | 0931b8c390d0170f6c99f2552f3728779413adf19c5c9799a4067dd5a5f6f5a6 | f275d065435944810fe59dd2b6abf05a9796b4f28000efc5f648300de123bbf8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,129 | IsGLB.biUnion_Ioi_eq | Mathlib/Order/Interval/Set/Disjoint.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (<a>Set.iUnion₂_subset</a> fun x hx => ?_).<a>HasSubset.Subset.antisymm</a> fun x hx => ?_ | ι : Sort u
α : Type v
β : Type w
inst✝ : LinearOrder α
s : Set α
a : α
f : ι → α
h : IsGLB s a
⊢ ⋃ x ∈ s, Ioi x = Ioi a | case refine_1
ι : Sort u
α : Type v
β : Type w
inst✝ : LinearOrder α
s : Set α
a : α
f : ι → α
h : IsGLB s a
x : α
hx : x ∈ s
⊢ Ioi x ⊆ Ioi a
case refine_2
ι : Sort u
α : Type v
β : Type w
inst✝ : LinearOrder α
s : Set α
a : α
f : ι → α
h : IsGLB s a
x : α
hx : x ∈ Ioi a
⊢ x ∈ ⋃ i ∈ s, Ioi i | ((:c Eq) ((:c Set) (:fv _uniq.41455)) ((:c Set.iUnion) (:fv _uniq.41455) (:fv _uniq.41455) (:lambda x (:fv _uniq.41455) ((:c Set.iUnion) (:fv _uniq.41455) ((:c Membership.mem) (:fv _uniq.41455) ((:c Set) (:fv _uniq.41455)) ((:c Set.instMembership) (:fv _uniq.41455)) 0 (:fv _uniq.41463)) (:lambda _ ((:c Membership.mem) ... | [{"name":"ι","sexp":"(:sort u)"},{"name":"α","sexp":"(:sort (+ v 1))"},{"name":"β","sexp":"(:sort (+ w 1))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.41455))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.41455))"},{"name":"a","sexp":"(:fv _uniq.41455)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.41453) (:fv _un... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Set.iUnion) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:lambda x :explicit (:fv FV1) (:app (:c Set.iUnion) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41453","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41455","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":7384,"sourceStart":7378,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":7386,"sourceStart":7385,"tag":"atom"},{"children":[{"name":"Set.iUnion₂_subset","semanticRole":"global","source":"iUnion₂_subset","sourceEnd":7402,"sourceStart":7386,"tag":"... | [] | [{"source":"(iUnion₂_subset fun x hx => ?_).antisymm fun x hx => ?_","source_end":7442,"source_start":7385,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41453","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41455","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 70 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a9adebc82fa23dfa4d921aa03f8caa1856d04640d7852373fb2e6f581493be9a | c45e25b5212b357910ff36e7eaed752321462f0afe6e67785953ebca131647b7 | 656b42b0ca66047a323c63d49eab88382649e04d96c6e3fa9ebf32c3316817b6 | ddafe4b0cc5fa32f606be5d499b196d3da8ca3e9a435cb28e07cba4310046cae |
cat-searcher/leandojo-benchmark-4-random | test | 4,130 | IsGLB.biUnion_Ioi_eq | Mathlib/Order/Interval/Set/Disjoint.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Set.Ioi_subset_Ioi</a> (h.1 hx) | case refine_1
ι : Sort u
α : Type v
β : Type w
inst✝ : LinearOrder α
s : Set α
a : α
f : ι → α
h : IsGLB s a
x : α
hx : x ∈ s
⊢ Ioi x ⊆ Ioi a | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.41455)) ((:c Set.instHasSubset) (:fv _uniq.41455)) ((:c Set.Ioi) (:fv _uniq.41455) ((:c PartialOrder.toPreorder) (:fv _uniq.41455) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.41455) ((:c Lattice.toSemilatticeInf) (:fv _uniq.41455) ((:c DistribLattice.toLattice) (:fv _uniq.... | [{"name":"ι","sexp":"(:sort u)"},{"name":"α","sexp":"(:sort (+ v 1))"},{"name":"β","sexp":"(:sort (+ w 1))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.41455))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.41455))"},{"name":"a","sexp":"(:fv _uniq.41455)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.41453) (:fv _un... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 2 (:app (:c Set.Ioi) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41453","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41455","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":7453,"sourceStart":7448,"tag":"atom"},{"children":[{"name":"Set.Ioi_subset_Ioi","semanticRole":"global","source":"Ioi_subset_Ioi","sourceEnd":7468,"sourceStart":7454,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":... | [] | [{"source":"Ioi_subset_Ioi (h.1 hx)","source_end":7477,"source_start":7454,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41453","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41455","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 70 | 7 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 381790181d21f09ae013885e2bd4f8681ea06e1f1e0c678d7fdbc21f9f04cdc7 | 860c3f0f913f0ea172115d61135bacc440dbbc1503b2a5f59f95bf4b6f54064a | 3e9805c5218814435df8b1ad03aace978f6cd33d4ed22684d76087c1b159bdf0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,131 | IsGLB.biUnion_Ioi_eq | Mathlib/Order/Interval/Set/Disjoint.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases h.exists_between hx with ⟨y, hys, _, hyx⟩ | case refine_2
ι : Sort u
α : Type v
β : Type w
inst✝ : LinearOrder α
s : Set α
a : α
f : ι → α
h : IsGLB s a
x : α
hx : x ∈ Ioi a
⊢ x ∈ ⋃ i ∈ s, Ioi i | case refine_2.intro.intro.intro
ι : Sort u
α : Type v
β : Type w
inst✝ : LinearOrder α
s : Set α
a : α
f : ι → α
h : IsGLB s a
x : α
hx : x ∈ Ioi a
y : α
hys : y ∈ s
left✝ : a ≤ y
hyx : y < x
⊢ x ∈ ⋃ i ∈ s, Ioi i | ((:c Membership.mem) (:fv _uniq.41455) ((:c Set) (:fv _uniq.41455)) ((:c Set.instMembership) (:fv _uniq.41455)) (:fv _uniq.41830) ((:c Set.iUnion) (:fv _uniq.41455) (:fv _uniq.41455) (:lambda i (:fv _uniq.41455) ((:c Set.iUnion) (:fv _uniq.41455) ((:c Membership.mem) (:fv _uniq.41455) ((:c Set) (:fv _uniq.41455)) ((:c ... | [{"name":"ι","sexp":"(:sort u)"},{"name":"α","sexp":"(:sort (+ v 1))"},{"name":"β","sexp":"(:sort (+ w 1))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.41455))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.41455))"},{"name":"a","sexp":"(:fv _uniq.41455)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.41453) (:fv _un... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:fv FV9)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41453","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41455","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rcases","sourceEnd":7489,"sourceStart":7483,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"h.exists_between","sourceEnd":7506,"sourceStart":7490,"tag":"identifier"},{"children":[{"contextIndex":10,"semanticRole":"local","sou... | [] | [{"source":"h.exists_between hx","source_end":7509,"source_start":7490,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨y, hys, _, hyx⟩","source_end":7535,"source_start":7515,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41453","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41455","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 70 | 14 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2ac9627b6f9285fbf72cce828758560bfe2eacc314e90a97b2109fa853695cf5 | de6e2d5463b8ed6178f8c114a9ccd58ab5931f88e98ce97e03fcb9808ac50ea3 | 539e84467e054e6a0924fd9d988f882ad94a6f96b4f0249fa63367d401bc62af | da917ab6482b0d0f95d4f4035a8c9cbe9e557f90cebb3575ab8e26051d241f13 |
cat-searcher/leandojo-benchmark-4-random | test | 4,132 | IsGLB.biUnion_Ioi_eq | Mathlib/Order/Interval/Set/Disjoint.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Set.mem_biUnion</a> hys hyx | case refine_2.intro.intro.intro
ι : Sort u
α : Type v
β : Type w
inst✝ : LinearOrder α
s : Set α
a : α
f : ι → α
h : IsGLB s a
x : α
hx : x ∈ Ioi a
y : α
hys : y ∈ s
left✝ : a ≤ y
hyx : y < x
⊢ x ∈ ⋃ i ∈ s, Ioi i | ((:c Membership.mem) (:fv _uniq.41455) ((:c Set) (:fv _uniq.41455)) ((:c Set.instMembership) (:fv _uniq.41455)) (:fv _uniq.41830) ((:c Set.iUnion) (:fv _uniq.41455) (:fv _uniq.41455) (:lambda i (:fv _uniq.41455) ((:c Set.iUnion) (:fv _uniq.41455) ((:c Membership.mem) (:fv _uniq.41455) ((:c Set) (:fv _uniq.41455)) ((:c ... | [{"name":"ι","sexp":"(:sort u)"},{"name":"α","sexp":"(:sort (+ v 1))"},{"name":"β","sexp":"(:sort (+ w 1))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.41455))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.41455))"},{"name":"a","sexp":"(:fv _uniq.41455)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.41453) (:fv _un... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:fv FV9)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41453","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41455","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":7545,"sourceStart":7540,"tag":"atom"},{"children":[{"name":"Set.mem_biUnion","semanticRole":"global","source":"mem_biUnion","sourceEnd":7557,"sourceStart":7546,"tag":"identifier"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"hys","sourceEnd":7561,"sourceSta... | [] | [{"source":"mem_biUnion hys hyx","source_end":7565,"source_start":7546,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41453","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41455","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 70 | 15 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ef10a2d99362bd21adc99374326c10d25d40fef20b624d8866e2b39539c2ff6a | da917ab6482b0d0f95d4f4035a8c9cbe9e557f90cebb3575ab8e26051d241f13 | b8aa2ab1b10709e115a215069649dfd944f53d8c0326f421330438df4f4ebe9a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,133 | RCLike.conj_smul | Mathlib/Analysis/RCLike/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>RCLike.conj_eq_re_sub_im</a>, <a>RCLike.conj_eq_re_sub_im</a>, <a>RCLike.smul_re</a>, <a>RCLike.smul_im</a>, <a>RCLike.ofReal_mul</a>, <a>RCLike.ofReal_mul</a>, <a>RCLike.real_smul_eq_coe_mul</a> r (_ - _), <a>mul_sub</a>, <a>mul_assoc</a>] | K : Type u_1
E : Type u_2
inst✝ : RCLike K
r : ℝ
z : K
⊢ (starRingEnd K) (r • z) = r • (starRingEnd K) z | ((:c Eq) (:fv _uniq.75908) ((:c DFunLike.coe) ((:c RingHom) (:fv _uniq.75908) (:fv _uniq.75908) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.75908) ((:c CommSemiring.toSemiring) (:fv _uniq.75908) ((:c Semifield.toCommSemiring) (:fv _uniq.75908) ((:c Field.toSemifield) (:fv _uniq.75908) ((:c NormedField.toField) (:fv _u... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c RCLike) (:fv _uniq.75908))"},{"name":"r","sexp":"(:c Real)"},{"name":"z","sexp":"(:fv _uniq.75908)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c RingHom) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c NonAssocSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.75908","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.75911","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":13716,"sourceStart":13714,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13718,"sourceStart":13717,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"conj_eq_re_sub_im","source_end":13735,"source_start":13718,"syntax_kind":"ident"},{"source":"conj_eq_re_sub_im","source_end":13754,"source_start":13737,"syntax_kind":"ident"},{"source":"smul_re","source_end":13763,"source_start":13756,"syntax_kind":"ident"},{"source":"smul_im","source_end":13772,"source_sta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.75908","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.75911","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 125 | 2 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5b47ea6c9c29b6986549b524a5d2fe01019fdbd6fe4befc0f37d64ec539172b3 | 707dab59d4c2fa37adb0d444414ebbb1659cb7dd9c4198bb9a66d97786efca75 | 11fa3b3ca31e50d652486ea186ccd4a52bab3934184cade07d469bf7dbac5ecb | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,134 | Polynomial.isNilpotent_C_mul_pow_X_of_isNilpotent | Mathlib/RingTheory/Polynomial/Nilpotent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Commute.isNilpotent_mul_left</a> (<a>Polynomial.commute_X_pow</a> _ _).<a>Commute.symm</a> ?_ | R : Type u_1
r : R
inst✝ : Semiring R
P : R[X]
n : ℕ
hnil : IsNilpotent r
⊢ IsNilpotent (C r * X ^ n) | R : Type u_1
r : R
inst✝ : Semiring R
P : R[X]
n : ℕ
hnil : IsNilpotent r
⊢ IsNilpotent (C r) | ((:c IsNilpotent) ((:c Polynomial) (:fv _uniq.30) (:fv _uniq.35)) ((:c Polynomial.zero) (:fv _uniq.30) (:fv _uniq.35)) ((:c Monoid.toNatPow) ((:c Polynomial) (:fv _uniq.30) (:fv _uniq.35)) ((:c MonoidWithZero.toMonoid) ((:c Polynomial) (:fv _uniq.30) (:fv _uniq.35)) ((:c Semiring.toMonoidWithZero) ((:c Polynomial) (:fv... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"r","sexp":"(:fv _uniq.30)"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.30))"},{"name":"P","sexp":"((:c Polynomial) (:fv _uniq.30) (:fv _uniq.35))"},{"name":"n","sexp":"(:c Nat)"},{"name":"hnil","sexp":"((:c IsNilpotent) (:fv _uniq.30) ((:c MonoidWithZero.toZero) ... | (:app (:c IsNilpotent) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32","is_instance":false,"is_let":false,"name":"r","sexp":"(:fv FV0)"},{"binder_role":":instance-implicit","con... | {"children":[{"source":"refine","sourceEnd":943,"sourceStart":937,"tag":"atom"},{"children":[{"name":"Commute.isNilpotent_mul_left","semanticRole":"global","source":"Commute.isNilpotent_mul_left","sourceEnd":972,"sourceStart":944,"tag":"identifier"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":974,"... | [] | [{"source":"Commute.isNilpotent_mul_left (commute_X_pow _ _).symm ?_","source_end":1000,"source_start":944,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32","is_instance":false,"is_let":false,"user_name":"r"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"... | 5 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7fab297596773526272e83b80805918537dff996af31ce0bc90f2300b28e7b75 | d567298f8e2b1f8b2105fd2b8c07b179624ea40c02766fc989511b189d854652 | 23ccedcdbed47ed6394db46322cdacc87d831e5c731a190100b00fadd7bc4a5c | b67cecb0dcd099e05947d1b898aa5e4169601bbd6edef4df6c76027c9fd0f573 |
cat-searcher/leandojo-benchmark-4-random | test | 4,135 | Polynomial.isNilpotent_C_mul_pow_X_of_isNilpotent | Mathlib/RingTheory/Polynomial/Nilpotent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨m, hm⟩ := hnil | R : Type u_1
r : R
inst✝ : Semiring R
P : R[X]
n : ℕ
hnil : IsNilpotent r
⊢ IsNilpotent (C r) | case intro
R : Type u_1
r : R
inst✝ : Semiring R
P : R[X]
n m : ℕ
hm : r ^ m = 0
⊢ IsNilpotent (C r) | ((:c IsNilpotent) ((:c Polynomial) (:fv _uniq.30) (:fv _uniq.35)) ((:c MonoidWithZero.toZero) ((:c Polynomial) (:fv _uniq.30) (:fv _uniq.35)) ((:c Semiring.toMonoidWithZero) ((:c Polynomial) (:fv _uniq.30) (:fv _uniq.35)) ((:c Polynomial.semiring) (:fv _uniq.30) (:fv _uniq.35)))) ((:c Monoid.toNatPow) ((:c Polynomial) ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"r","sexp":"(:fv _uniq.30)"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.30))"},{"name":"P","sexp":"((:c Polynomial) (:fv _uniq.30) (:fv _uniq.35))"},{"name":"n","sexp":"(:c Nat)"},{"name":"hnil","sexp":"((:c IsNilpotent) (:fv _uniq.30) ((:c MonoidWithZero.toZero) ... | (:app (:c IsNilpotent) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32","is_instance":false,"is_let":false,"name":"r","sexp":"(:fv FV0)"},{"binder_role":":instance-implicit","con... | {"children":[{"source":"obtain","sourceEnd":1009,"sourceStart":1003,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":1013,"sourceStart":1010,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"m","sourceEnd":1... | [] | [{"source":"hnil","source_end":1029,"source_start":1025,"syntax_kind":"ident"},{"source":"⟨m, hm⟩","source_end":1021,"source_start":1010,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32","is_instance":false,"is_let":false,"user_name":"r"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"... | 5 | 5 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4b256c16183a7c11fec917ec3e4bc6056a96f68bb442bc9cf2be2eeacea1ad52 | b67cecb0dcd099e05947d1b898aa5e4169601bbd6edef4df6c76027c9fd0f573 | 1e358aa0a077aa0058acdd022af85e9c13f86e1a8ae9db3be6eebce5eae7d71f | 2f7c4bde6c71881671ce4185f178be9ddbbbba153363103dc42257ce069eea02 |
cat-searcher/leandojo-benchmark-4-random | test | 4,136 | Polynomial.isNilpotent_C_mul_pow_X_of_isNilpotent | Mathlib/RingTheory/Polynomial/Nilpotent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨m, ?_⟩ | case intro
R : Type u_1
r : R
inst✝ : Semiring R
P : R[X]
n m : ℕ
hm : r ^ m = 0
⊢ IsNilpotent (C r) | case intro
R : Type u_1
r : R
inst✝ : Semiring R
P : R[X]
n m : ℕ
hm : r ^ m = 0
⊢ C r ^ m = 0 | ((:c IsNilpotent) ((:c Polynomial) (:fv _uniq.30) (:fv _uniq.35)) ((:c MonoidWithZero.toZero) ((:c Polynomial) (:fv _uniq.30) (:fv _uniq.35)) ((:c Semiring.toMonoidWithZero) ((:c Polynomial) (:fv _uniq.30) (:fv _uniq.35)) ((:c Polynomial.semiring) (:fv _uniq.30) (:fv _uniq.35)))) ((:c Monoid.toNatPow) ((:c Polynomial) ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"r","sexp":"(:fv _uniq.30)"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.30))"},{"name":"P","sexp":"((:c Polynomial) (:fv _uniq.30) (:fv _uniq.35))"},{"name":"n","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"hm","sexp":"((:c Eq) (:fv _uniq.30) ((:c HPo... | (:app (:c IsNilpotent) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32","is_instance":false,"is_let":false,"name":"r","sexp":"(:fv FV0)"},{"binder_role":":instance-implicit","con... | {"children":[{"source":"refine","sourceEnd":1038,"sourceStart":1032,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":1042,"sourceStart":1039,"tag":"atom"},{"children":[{"contextIndex":6,"semanticRole":"local","source":"m","sourceEnd":1043,"sourceStart":1042,"tag":"identifier"},{"source":",","sourceEnd":1044,"source... | [] | [{"source":"⟨m, ?_⟩","source_end":1050,"source_start":1039,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32","is_instance":false,"is_let":false,"user_name":"r"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"... | 5 | 6 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 80eca887e57404d3a6fc2b8af9702326e349a051a6106c46ccbf64563deceffa | 2f7c4bde6c71881671ce4185f178be9ddbbbba153363103dc42257ce069eea02 | 92bc6f5600d69522f9a440fba129ff3e8db007218fd24a2cc5a6c7ba4f970533 | ff283f035f20426e1b01bd0c4210446c6ea63889b3e31bbdbe2fbaaa2ee88405 |
cat-searcher/leandojo-benchmark-4-random | test | 4,137 | Polynomial.isNilpotent_C_mul_pow_X_of_isNilpotent | Mathlib/RingTheory/Polynomial/Nilpotent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Polynomial.C_pow</a>, hm, <a>Polynomial.C_0</a>] | case intro
R : Type u_1
r : R
inst✝ : Semiring R
P : R[X]
n m : ℕ
hm : r ^ m = 0
⊢ C r ^ m = 0 | ((:c Eq) ((:c Polynomial) (:fv _uniq.30) (:fv _uniq.35)) ((:c HPow.hPow) ((:c Polynomial) (:fv _uniq.30) (:fv _uniq.35)) (:c Nat) ((:c Polynomial) (:fv _uniq.30) (:fv _uniq.35)) ((:c instHPow) ((:c Polynomial) (:fv _uniq.30) (:fv _uniq.35)) (:c Nat) ((:c Monoid.toNatPow) ((:c Polynomial) (:fv _uniq.30) (:fv _uniq.35)) ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"r","sexp":"(:fv _uniq.30)"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.30))"},{"name":"P","sexp":"((:c Polynomial) (:fv _uniq.30) (:fv _uniq.35))"},{"name":"n","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"hm","sexp":"((:c Eq) (:fv _uniq.30) ((:c HPo... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32","is_instance":false,"is_let":false,"name":"r","sexp":"(:fv FV0)"},{"binder_role":":instance-implicit","con... | {"children":[{"source":"rw","sourceEnd":1055,"sourceStart":1053,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1057,"sourceStart":1056,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":1060,"sourceStart":... | [] | [{"source":"C_pow","source_end":1066,"source_start":1061,"syntax_kind":"ident"},{"source":"hm","source_end":1070,"source_start":1068,"syntax_kind":"ident"},{"source":"C_0","source_end":1075,"source_start":1072,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32","is_instance":false,"is_let":false,"user_name":"r"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"... | 5 | 7 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 070425b0c2d2245655a38d43e0637ec9454ec6e25a2c3a618792954c057a5d66 | ff283f035f20426e1b01bd0c4210446c6ea63889b3e31bbdbe2fbaaa2ee88405 | 3399859fe049b3d8189256ef78460ab71e4e94f6b97f3f7280cb10f354887352 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,141 | Measurable.nnreal_tsum | Mathlib/MeasureTheory/Constructions/BorelSpace/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>NNReal.tsum_eq_toNNReal_tsum</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι✝ : Sort y
s t u : Set α
inst✝¹ : MeasurableSpace α
ι : Type u_5
inst✝ : Countable ι
f : ι → α → ℝ≥0
h : ∀ (i : ι), Measurable (f i)
⊢ Measurable fun x => ∑' (i : ι), f i x | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι✝ : Sort y
s t u : Set α
inst✝¹ : MeasurableSpace α
ι : Type u_5
inst✝ : Countable ι
f : ι → α → ℝ≥0
h : ∀ (i : ι), Measurable (f i)
⊢ Measurable fun x => (∑' (b : ι), ↑(f b x)).toNNReal | ((:c Measurable) (:fv _uniq.98055) (:c NNReal) (:fv _uniq.98078) (:c NNReal.measurableSpace) (:lambda x (:fv _uniq.98055) ((:c tsum) (:c NNReal) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:c NNReal) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:c NNReal) ((:c Semiring.toNonAssocSemiring) (:c NNReal) (:c in... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"ι✝","sexp":"(:sort y)"},{"name":"s","sexp":"((:c Set) (:fv _uniq.98055))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.98055))"},{"name":"u","sexp":"((:c... | (:app (:c Measurable) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c NNReal)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c NNReal))))) (:arg :explicit 4 (:lambda x :explicit (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98055","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98058","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp_rw","sourceEnd":20036,"sourceStart":20029,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":20038,"sourceStart":20037,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"NNReal.tsum... | [] | [{"source":"NNReal.tsum_eq_toNNReal_tsum","source_end":20066,"source_start":20038,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98055","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98058","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 101 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 01bf5a38b505fbfb749c0f60b8c8b0fb212e2c4ee458e0ecb748786acb1159fa | 6fd8fd3bede4ac23996a0fa8ecb4baf3aa048f5837729d91e0162126cb8ee1f1 | fbce0c7032a3f784bcb40f41cbc20ba65de8426cf90bf5f65b6eb8990afc12d0 | 80d12763a33eac4af064f7d4e86953ae19e6dc862361b5615b38210b5298a539 |
cat-searcher/leandojo-benchmark-4-random | test | 4,142 | Measurable.nnreal_tsum | Mathlib/MeasureTheory/Constructions/BorelSpace/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>Measurable.ennreal_tsum</a> fun i => (h i).<a>Measurable.coe_nnreal_ennreal</a>).<a>Measurable.ennreal_toNNReal</a> | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι✝ : Sort y
s t u : Set α
inst✝¹ : MeasurableSpace α
ι : Type u_5
inst✝ : Countable ι
f : ι → α → ℝ≥0
h : ∀ (i : ι), Measurable (f i)
⊢ Measurable fun x => (∑' (b : ι), ↑(f b x)).toNNReal | ((:c Measurable) (:fv _uniq.98055) (:c NNReal) (:fv _uniq.98078) (:c NNReal.measurableSpace) (:lambda x (:fv _uniq.98055) ((:c ENNReal.toNNReal) ((:c tsum) (:c ENNReal) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:c ENNReal) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:c ENNReal) ((:c Semiring.toNonAssocSe... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"ι✝","sexp":"(:sort y)"},{"name":"s","sexp":"((:c Set) (:fv _uniq.98055))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.98055))"},{"name":"u","sexp":"((:c... | (:app (:c Measurable) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c NNReal)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c NNReal))))) (:arg :explicit 4 (:lambda x :explicit (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98055","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98058","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":20075,"sourceStart":20070,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":20077,"sourceStart":20076,"tag":"atom"},{"children":[{"name":"Measurable.ennreal_tsum","semanticRole":"global","source":"Measurable.ennreal_tsum","sourceEnd":20100,"sourceStart":20077,"... | [] | [{"source":"(Measurable.ennreal_tsum fun i => (h i).coe_nnreal_ennreal).ennreal_toNNReal","source_end":20152,"source_start":20076,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98055","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98058","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 101 | 7 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c3277877412a44508ab74e1f76398ed16ecb92e5b83995fdc2baf8d4d39ee904 | 80d12763a33eac4af064f7d4e86953ae19e6dc862361b5615b38210b5298a539 | e26a7fd70b177d7ad298670ec6cad40b16952719f9020460ad3367d7f2c6e756 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,144 | Complex.add_conj | Mathlib/Data/Complex/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>two_mul</a>, <a>Complex.ofReal'</a>] | z : ℂ
⊢ (z + (starRingEnd ℂ) z).re = (↑(2 * z.re)).re ∧ (z + (starRingEnd ℂ) z).im = (↑(2 * z.re)).im | ((:c And) ((:c Eq) (:c Real) ((:c Complex.re) ((:c HAdd.hAdd) (:c Complex) (:c Complex) (:c Complex) ((:c instHAdd) (:c Complex) (:c Complex.instAdd)) (:fv _uniq.85909) ((:c DFunLike.coe) ((:c RingHom) (:c Complex) (:c Complex) ((:c Semiring.toNonAssocSemiring) (:c Complex) ((:c CommSemiring.toSemiring) (:c Complex) (:... | [{"name":"z","sexp":"(:c Complex)"}] | (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Complex.re) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Complex)) (:arg :implicit-type 1 (:c Complex)) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.85909","is_instance":false,"is_let":false,"name":"z","sexp":"(:c Complex)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":25088,"sourceStart":25084,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"two_mul","source_end":25097,"source_start":25090,"syntax_kind":"ident"},{"source":"ofReal'","source_end":25106,"source_start":25099,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.85909","is_instance":false,"is_let":false,"user_name":"z"}] | 274 | 2 | exact | true | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 57c9bae63696b8f786b0ae405947edf06af05e71209686fbe33fb0cda12c7764 | be124d059369e7d359769c8d522a42e95abad0fd6987ef61dde2f126befa9a15 | c2c89a33167e2deed3e49913706fead42bc812450aec6b0aa8e58a0ac3c3e22f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,145 | AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_symm_mk_mk | Mathlib/RingTheory/AdjoinRoot.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot</a>, <a>RingEquiv.symm_trans_apply</a>, <a>RingEquiv.symm_trans_apply</a>, <a>RingEquiv.symm_trans_apply</a>, <a>RingEquiv.symm_symm</a>, <a>AdjoinRoot.Polynomial.quotQuotEquivComm_mk</a>, <a>Ideal.quotEquivOfEq_symm</a>, <a>Ideal.quotEquivOfEq_mk</a>, ← <a>RingHo... | R : Type u
S : Type v
K : Type w
inst✝ : CommRing R
I : Ideal R
f p : R[X]
⊢ (quotAdjoinRootEquivQuotPolynomialQuot I f).symm
((Ideal.Quotient.mk (span {Polynomial.map (Ideal.Quotient.mk I) f})) (Polynomial.map (Ideal.Quotient.mk I) p)) =
(Ideal.Quotient.mk (Ideal.map (of f) I)) ((mk f) p) | ((:c Eq) ((:c HasQuotient.Quotient) ((:c AdjoinRoot) (:fv _uniq.316322) (:fv _uniq.316329) (:fv _uniq.316524)) ((:c Ideal) ((:c AdjoinRoot) (:fv _uniq.316322) (:fv _uniq.316329) (:fv _uniq.316524)) ((:c CommSemiring.toSemiring) ((:c AdjoinRoot) (:fv _uniq.316322) (:fv _uniq.316329) (:fv _uniq.316524)) ((:c CommRing.toC... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"K","sexp":"(:sort (+ w 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.316322))"},{"name":"I","sexp":"((:c Ideal) (:fv _uniq.316322) ((:c CommSemiring.toSemiring) (:fv _uniq.316322) ((:c CommRing.toCommSemiring) (:fv _uniq.316... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c HasQuotient.Quotient) (:arg :explicit 0 (:app (:c AdjoinRoot) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV5)))) (:arg :implicit-type 1 (:app (:c Ideal) (:arg :explicit 0 (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.316322","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.316324","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":35199,"sourceStart":35197,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":35201,"sourceStart":35200,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"quotAdjoinRootEquivQuotPolynomialQuot","source_end":35238,"source_start":35201,"syntax_kind":"ident"},{"source":"RingEquiv.symm_trans_apply","source_end":35266,"source_start":35240,"syntax_kind":"ident"},{"source":"RingEquiv.symm_trans_apply","source_end":35298,"source_start":35272,"syntax_kind":"ident"},{"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.316322","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.316324","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 230 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 51b425628784ebceeaef9ce522a3e4fc7e98a15d61f208bea368b4e26e4dc9d5 | 29855c68236ef6ec7d22ce9a96e3cac9d6bb63bea4734d419190eee0e8b4d179 | 7bbe408ddca367bec4906b100a2863250c88f77c85edff5f96b7f2fd81915f39 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,146 | Mathlib.Meta.NormNum.isRat_inv_pos | Mathlib/Tactic/NormNum/Inv.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨_, rfl⟩ | α : Type u_1
inst✝¹ : DivisionRing α
inst✝ : CharZero α
a : α
n d : ℕ
⊢ IsRat a (Int.ofNat n.succ) d → IsRat a⁻¹ (Int.ofNat d) n.succ | case mk
α : Type u_1
inst✝¹ : DivisionRing α
inst✝ : CharZero α
n d : ℕ
inv✝ : Invertible ↑d
⊢ IsRat (↑(Int.ofNat n.succ) * ⅟↑d)⁻¹ (Int.ofNat d) n.succ | (:forall _ ((:c Mathlib.Meta.NormNum.IsRat) (:fv _uniq.18023) ((:c DivisionRing.toRing) (:fv _uniq.18023) (:fv _uniq.18024)) (:fv _uniq.18026) ((:c Int.ofNat) ((:c Nat.succ) (:fv _uniq.18027))) (:fv _uniq.18028)) ((:c Mathlib.Meta.NormNum.IsRat) (:fv _uniq.18023) ((:c DivisionRing.toRing) (:fv _uniq.18023) (:fv _uniq.1... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c DivisionRing) (:fv _uniq.18023))"},{"name":"inst✝","sexp":"((:c CharZero) (:fv _uniq.18023) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.18023) ((:c Ring.toAddGroupWithOne) (:fv _uniq.18023) ((:c DivisionRing.toRing) (:fv _uniq.18023) (:fv _u... | (:forall _ :explicit (:app (:c Mathlib.Meta.NormNum.IsRat) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV4)) (:arg :explicit 3 (:app (:c Int.ofNat) (:arg :explicit 0 (:app (:c Nat.succ) (:arg :explicit 0 (:fv FV5)))))) (:arg :e... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18023","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.18024","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c DivisionRing) (:arg :ex... | {"children":[{"source":"rintro","sourceEnd":4940,"sourceStart":4934,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":4944,"sourceStart":4941,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"_","sourceEnd":4945,"sourceStart":4944,"tag":"atom"}],"kind... | [] | [{"source":"⟨_, rfl⟩","source_end":4953,"source_start":4941,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18023","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.18024","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 16 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a0bffdd75425bcf8bb2708eefafbd7bbe7440a06f9f770f8c1f6bbb43514b895 | 32c639a7377419adc4ad4ec2686a8959941171e36a522911991405c8601d3a3e | 4a440eeae1d24fa16d7a0b4866501514f4332c35e289ed2f89016032bd0e6ebb | 70c4aeb2886ca5ae8804716804244a25e0d23300c379d4b2c1c54c6d27177b0f |
cat-searcher/leandojo-benchmark-4-random | test | 4,147 | Mathlib.Meta.NormNum.isRat_inv_pos | Mathlib/Tactic/NormNum/Inv.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have := <a>invertibleOfNonzero</a> (α := α) (<a>Nat.cast_ne_zero</a>.2 (<a>Nat.succ_ne_zero</a> n)) | case mk
α : Type u_1
inst✝¹ : DivisionRing α
inst✝ : CharZero α
n d : ℕ
inv✝ : Invertible ↑d
⊢ IsRat (↑(Int.ofNat n.succ) * ⅟↑d)⁻¹ (Int.ofNat d) n.succ | case mk
α : Type u_1
inst✝¹ : DivisionRing α
inst✝ : CharZero α
n d : ℕ
inv✝ : Invertible ↑d
this : Invertible ↑n.succ
⊢ IsRat (↑(Int.ofNat n.succ) * ⅟↑d)⁻¹ (Int.ofNat d) n.succ | ((:c Mathlib.Meta.NormNum.IsRat) (:fv _uniq.18023) ((:c DivisionRing.toRing) (:fv _uniq.18023) (:fv _uniq.18024)) ((:c Inv.inv) (:fv _uniq.18023) ((:c DivisionRing.toInv) (:fv _uniq.18023) (:fv _uniq.18024)) ((:c HMul.hMul) (:fv _uniq.18023) (:fv _uniq.18023) (:fv _uniq.18023) ((:c instHMul) (:fv _uniq.18023) ((:c NonU... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c DivisionRing) (:fv _uniq.18023))"},{"name":"inst✝","sexp":"((:c CharZero) (:fv _uniq.18023) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.18023) ((:c Ring.toAddGroupWithOne) (:fv _uniq.18023) ((:c DivisionRing.toRing) (:fv _uniq.18023) (:fv _u... | (:app (:c Mathlib.Meta.NormNum.IsRat) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Inv.inv) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Inv) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18023","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.18024","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c DivisionRing) (:arg :ex... | {"children":[{"source":"have","sourceEnd":4960,"sourceStart":4956,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":4961,"sourceStart":4961,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":4961,"sourceStart":4961,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"invertibleOfNonzero (α := α) (Nat.cast_ne_zero.2 (Nat.succ_ne_zero n))","source_end":5036,"source_start":4964,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18023","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.18024","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 16 | 5 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d63c78717cea4240f565824080b79b5740ebda504811e61606c57b48934e7e64 | 70c4aeb2886ca5ae8804716804244a25e0d23300c379d4b2c1c54c6d27177b0f | d53a833a187e42e4e90e51dcc7abdba63a812907ec2abbe42d6a0e80c7473a8d | 101b171b647cf06993dbac9328a9dff1161d6ad8cf82a45843f72065a666a929 |
cat-searcher/leandojo-benchmark-4-random | test | 4,148 | Mathlib.Meta.NormNum.isRat_inv_pos | Mathlib/Tactic/NormNum/Inv.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨this, by simp⟩ | case mk
α : Type u_1
inst✝¹ : DivisionRing α
inst✝ : CharZero α
n d : ℕ
inv✝ : Invertible ↑d
this : Invertible ↑n.succ
⊢ IsRat (↑(Int.ofNat n.succ) * ⅟↑d)⁻¹ (Int.ofNat d) n.succ | ((:c Mathlib.Meta.NormNum.IsRat) (:fv _uniq.18023) ((:c DivisionRing.toRing) (:fv _uniq.18023) (:fv _uniq.18024)) ((:c Inv.inv) (:fv _uniq.18023) ((:c DivisionRing.toInv) (:fv _uniq.18023) (:fv _uniq.18024)) ((:c HMul.hMul) (:fv _uniq.18023) (:fv _uniq.18023) (:fv _uniq.18023) ((:c instHMul) (:fv _uniq.18023) ((:c NonU... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c DivisionRing) (:fv _uniq.18023))"},{"name":"inst✝","sexp":"((:c CharZero) (:fv _uniq.18023) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.18023) ((:c Ring.toAddGroupWithOne) (:fv _uniq.18023) ((:c DivisionRing.toRing) (:fv _uniq.18023) (:fv _u... | (:app (:c Mathlib.Meta.NormNum.IsRat) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Inv.inv) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Inv) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18023","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.18024","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c DivisionRing) (:arg :ex... | {"children":[{"source":"exact","sourceEnd":5044,"sourceStart":5039,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":5048,"sourceStart":5045,"tag":"atom"},{"children":[{"contextIndex":7,"semanticRole":"local","source":"this","sourceEnd":5052,"sourceStart":5048,"tag":"identifier"},{"source":",","sourceEnd":5053,"sour... | [] | [{"source":"⟨this, by simp⟩","source_end":5064,"source_start":5045,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18023","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.18024","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 16 | 6 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eb4738ff72b50ea28c665311a647bd869ba986c76a5194b50bc5ffa05288cf8a | 101b171b647cf06993dbac9328a9dff1161d6ad8cf82a45843f72065a666a929 | dd049ede8854a2f510bd4a50be3aecedfc251425807c0b213258eccc74cb3a99 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,149 | Mathlib.Meta.NormNum.isRat_inv_pos | Mathlib/Tactic/NormNum/Inv.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | α : Type u_1
inst✝¹ : DivisionRing α
inst✝ : CharZero α
n d : ℕ
inv✝ : Invertible ↑d
this : Invertible ↑n.succ
⊢ (↑(Int.ofNat n.succ) * ⅟↑d)⁻¹ = ↑(Int.ofNat d) * ⅟↑n.succ | ((:c Eq) (:fv _uniq.18023) ((:c Inv.inv) (:fv _uniq.18023) ((:c DivisionRing.toInv) (:fv _uniq.18023) (:fv _uniq.18024)) ((:c HMul.hMul) (:fv _uniq.18023) (:fv _uniq.18023) (:fv _uniq.18023) ((:c instHMul) (:fv _uniq.18023) ((:c NonUnitalNonAssocRing.toMul) (:fv _uniq.18023) ((:c NonAssocRing.toNonUnitalNonAssocRing) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c DivisionRing) (:fv _uniq.18023))"},{"name":"inst✝","sexp":"((:c CharZero) (:fv _uniq.18023) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.18023) ((:c Ring.toAddGroupWithOne) (:fv _uniq.18023) ((:c DivisionRing.toRing) (:fv _uniq.18023) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Inv.inv) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Inv) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18023","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.18024","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c DivisionRing) (:arg :ex... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":5061,"sourceStart":5057,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source... | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18023","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.18024","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 16 | 9 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7d8987498674a62c0fb80cfc05bd071bc153783f75d1fb2e19015ccf17960a4b | 123353ffc59fd3ee8dff659f1cf771f9654eabef49b4be7b3b4863939538bb0a | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,150 | ProbabilityTheory.kernel.density_nonneg | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Filter.le_limsup_of_frequently_le</a> ?_ ?_ | α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝ : CountablyGenerated γ
κ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
hκν : fst κ ≤ ν
a : α
x : γ
s : Set β
⊢ 0 ≤ density κ ν a x s | case refine_1
α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝ : CountablyGenerated γ
κ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
hκν : fst κ ≤ ν
a : α
x : γ
s : Set β
⊢ ∃ᶠ (x_1 : ℕ) in atTop, 0 ≤ densityProcess κ ν x_1 a x s
case refine_2
α : Type u_1
β : ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c ProbabilityTheory.kernel.density) (:fv _uniq.182730) (:fv _uniq.182733) (:fv _uniq.182736) (:fv _uniq.182739) (:fv _uniq.182742) (:fv _uniq.182745) (:fv _uniq.182755) (:fv _uniq.182838) (:... | [{"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.182730))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.182733))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.182736))"},{"na... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.182730","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.182733","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":27098,"sourceStart":27092,"tag":"atom"},{"children":[{"name":"Filter.le_limsup_of_frequently_le","semanticRole":"global","source":"le_limsup_of_frequently_le","sourceEnd":27125,"sourceStart":27099,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":27127,"... | [] | [{"source":"le_limsup_of_frequently_le ?_ ?_","source_end":27131,"source_start":27099,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.182730","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.182733","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 49 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c50f680f3c9b11ec6b521430d598e8ddb2218e6af301a7d1a100ef4f0d2731d4 | 8076d45c413ebc3463e895baaf62e0c7bb3d9cb6c6f6359dac3ec9a83f784554 | e91425c3f9c18bf85f5877955fd7fe20fb4be69b9b796af81e8fcb55d048f22c | 039c2d6cc93b886057f4e1f4f51723771550368b3ea88d637aabb904550709f1 |
cat-searcher/leandojo-benchmark-4-random | test | 4,151 | ProbabilityTheory.kernel.density_nonneg | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Filter.frequently_of_forall</a> (fun n ↦ <a>ProbabilityTheory.kernel.densityProcess_nonneg</a> _ _ _ _ _ _) | case refine_1
α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝ : CountablyGenerated γ
κ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
hκν : fst κ ≤ ν
a : α
x : γ
s : Set β
⊢ ∃ᶠ (x_1 : ℕ) in atTop, 0 ≤ densityProcess κ ν x_1 a x s | ((:c Filter.Frequently) (:c Nat) (:lambda x (:c Nat) ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c SemilatticeInf.toPartialOrder) (:c Real) ((:c Lattice.toSemilatticeInf) (:c Real) ((:c ConditionallyCompleteLattice.toLattice) (:c Real) ((:c ConditionallyCompleteLinearO... | [{"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.182730))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.182733))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.182736))"},{"na... | (:app (:c Filter.Frequently) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda x :explicit (:c Nat) (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.182730","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.182733","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":27142,"sourceStart":27137,"tag":"atom"},{"children":[{"name":"Filter.frequently_of_forall","semanticRole":"global","source":"frequently_of_forall","sourceEnd":27163,"sourceStart":27143,"tag":"identifier"},{"children":[{"children":[{"sourc... | [] | [{"source":"frequently_of_forall (fun n ↦ densityProcess_nonneg _ _ _ _ _ _)","source_end":27209,"source_start":27143,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.182730","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.182733","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 49 | 7 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9f152f62d45d0ad93628df691499f46738fdb5bd74617dea20c1be5d09bc943a | 09e5092e90326336b1e0f3547dc26cb0b9ef14bbe48bae479bd0ee8e261e1ae1 | 6187ce22849858f7bed769cd1e07c443b630e6468b17e1cf911564806fb4061b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,152 | ProbabilityTheory.kernel.density_nonneg | Mathlib/Probability/Kernel/Disintegration/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Filter.isBoundedUnder_of</a> ⟨1, fun n ↦ <a>ProbabilityTheory.kernel.densityProcess_le_one</a> hκν _ _ _ _⟩ | case refine_2
α : Type u_1
β : Type u_2
γ : Type u_3
mα : MeasurableSpace α
mβ : MeasurableSpace β
mγ : MeasurableSpace γ
inst✝ : CountablyGenerated γ
κ : ↥(kernel α (γ × β))
ν : ↥(kernel α γ)
hκν : fst κ ≤ ν
a : α
x : γ
s : Set β
⊢ IsBoundedUnder (fun x x_1 => x ≤ x_1) atTop fun n => densityProcess κ ν n a x s | ((:c Filter.IsBoundedUnder) (:c Real) (:c Nat) (:lambda _ (:c Real) (:lambda _ (:c Real) ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c SemilatticeInf.toPartialOrder) (:c Real) ((:c Lattice.toSemilatticeInf) (:c Real) ((:c ConditionallyCompleteLattice.toLattice) (:c Rea... | [{"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.182730))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.182733))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.182736))"},{"na... | (:app (:c Filter.IsBoundedUnder) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Nat)) (:arg :explicit 2 (:lambda _ :explicit (:c Real) (:lambda _ :explicit (:c Real) (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.182730","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.182733","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":27220,"sourceStart":27215,"tag":"atom"},{"children":[{"name":"Filter.isBoundedUnder_of","semanticRole":"global","source":"isBoundedUnder_of","sourceEnd":27238,"sourceStart":27221,"tag":"identifier"},{"children":[{"children":[{"source":"⟨"... | [] | [{"source":"isBoundedUnder_of ⟨1, fun n ↦ densityProcess_le_one hκν _ _ _ _⟩","source_end":27293,"source_start":27221,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.182730","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.182733","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 49 | 12 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0bed8d5ee5d6bd9d9cdf97183d7ce2a693829768c313616755e7d907f31f452f | aad6f2313634322fa06c4c74b716bf8cbc37e21ebd2a9f18baa3fbcbf2c44c78 | 889d528bf312ab2e13bed60f29cce1cb7046ea23ebbd1d3a2000bb6fa9ea50b6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,153 | Multiset.le_inter | Mathlib/Data/Multiset/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | revert s u | α : Type u_1
β : Type v
γ : Type u_2
inst✝ : DecidableEq α
s t u : Multiset α
a b : α
h₁ : s ≤ t
h₂ : s ≤ u
⊢ s ≤ t ∩ u | α : Type u_1
β : Type v
γ : Type u_2
inst✝ : DecidableEq α
t : Multiset α
a b : α
⊢ ∀ {s u : Multiset α}, s ≤ t → s ≤ u → s ≤ t ∩ u | ((:c LE.le) ((:c Multiset) (:fv _uniq.110210)) ((:c Preorder.toLE) ((:c Multiset) (:fv _uniq.110210)) ((:c PartialOrder.toPreorder) ((:c Multiset) (:fv _uniq.110210)) ((:c Multiset.instPartialOrder) (:fv _uniq.110210)))) (:fv _uniq.110227) ((:c Inter.inter) ((:c Multiset) (:fv _uniq.110210)) ((:c Multiset.instInter) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.110210))"},{"name":"s","sexp":"((:c Multiset) (:fv _uniq.110210))"},{"name":"t","sexp":"((:c Multiset) (:fv _uniq.110210))"},{"name":"u","sexp":"((:... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:fv FV4)) (:arg :explicit 3 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Multiset... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110210","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110212","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"revert","sourceEnd":75219,"sourceStart":75213,"tag":"atom"},{"children":[{"contextIndex":4,"semanticRole":"local","source":"s","sourceEnd":75221,"sourceStart":75220,"tag":"identifier"},{"contextIndex":6,"semanticRole":"local","source":"u","sourceEnd":75223,"sourceStart":75222,"tag":"identifier"}... | [] | [{"source":"s","source_end":75221,"source_start":75220,"syntax_kind":"ident"},{"source":"u","source_end":75223,"source_start":75222,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110210","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110212","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 652 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0f9e79f2f04bf5a5ef83e3f3b2cd603f671761d0931469edbe64328651d62bd3 | 94aaad4e20498d0961c3321bf38958c97df47a9d1e16b983d9bc630c151378a2 | 86c6e2f10ca2814dfaac4a8ed33f5d5bba2103651ac96a17b0d5322517fe4f3d | b1df7987a0a61e4846be2ff0627b2862690714e8acf19a1ec7ad07d2a4e08ad8 |
cat-searcher/leandojo-benchmark-4-random | test | 4,154 | Multiset.le_inter | Mathlib/Data/Multiset/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine @(<a>Multiset.induction_on</a> t ?_ fun a t IH => ?_) <;> intros s u h₁ h₂ | α : Type u_1
β : Type v
γ : Type u_2
inst✝ : DecidableEq α
t : Multiset α
a b : α
⊢ ∀ {s u : Multiset α}, s ≤ t → s ≤ u → s ≤ t ∩ u | case refine_1
α : Type u_1
β : Type v
γ : Type u_2
inst✝ : DecidableEq α
t : Multiset α
a b : α
s u : Multiset α
h₁ : s ≤ 0
h₂ : s ≤ u
⊢ s ≤ 0 ∩ u
case refine_2
α : Type u_1
β : Type v
γ : Type u_2
inst✝ : DecidableEq α
t✝ : Multiset α
a✝ b a : α
t : Multiset α
IH : ∀ {s u : Multiset α}, s ≤ t → s ≤ u → s ≤ t ∩ u
s u :... | (:forall s ((:c Multiset) (:fv _uniq.110210)) (:forall u ((:c Multiset) (:fv _uniq.110210)) (:forall h₁ ((:c LE.le) ((:c Multiset) (:fv _uniq.110210)) ((:c Preorder.toLE) ((:c Multiset) (:fv _uniq.110210)) ((:c PartialOrder.toPreorder) ((:c Multiset) (:fv _uniq.110210)) ((:c Multiset.instPartialOrder) (:fv _uniq.110210... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.110210))"},{"name":"t","sexp":"((:c Multiset) (:fv _uniq.110210))"},{"name":"a","sexp":"(:fv _uniq.110210)"},{"name":"b","sexp":"(:fv _uniq.110210)"... | (:forall s :implicit (:app (:c Multiset) (:arg :explicit 0 (:fv FV0))) (:forall u :implicit (:app (:c Multiset) (:arg :explicit 0 (:fv FV0))) (:forall h₁ :explicit (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110210","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110212","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"source":"refine","sourceEnd":75231,"sourceStart":75225,"tag":"atom"},{"children":[{"source":"@","sourceEnd":75233,"sourceStart":75232,"tag":"atom"},{"children":[{"source":"(","sourceEnd":75234,"sourceStart":75233,"tag":"atom"},{"children":[{"name":"Multiset.induction_on","semanticRole":"glob... | [] | [{"source":"@(Multiset.induction_on t ?_ fun a t IH => ?_)","source_end":75278,"source_start":75232,"syntax_kind":"Lean.Parser.Term.explicit"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110210","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110212","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 652 | 6 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d2ad8d28dbc9758f2cc092299e81d700e6c1f5c5b1ac3082e24a61ac894cd549 | b1df7987a0a61e4846be2ff0627b2862690714e8acf19a1ec7ad07d2a4e08ad8 | 7db215995c167cd795f0ba56f8fdb728e22b36044967a0088693debaba506af7 | 2c43e2f5cbd00150a9c0065004efcc31d470cb8e3ec7b89543996af08774722b |
cat-searcher/leandojo-benchmark-4-random | test | 4,155 | Multiset.le_inter | Mathlib/Data/Multiset/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases h : a ∈ u | case refine_2
α : Type u_1
β : Type v
γ : Type u_2
inst✝ : DecidableEq α
t✝ : Multiset α
a✝ b a : α
t : Multiset α
IH : ∀ {s u : Multiset α}, s ≤ t → s ≤ u → s ≤ t ∩ u
s u : Multiset α
h₁ : s ≤ a ::ₘ t
h₂ : s ≤ u
⊢ s ≤ (a ::ₘ t) ∩ u | case pos
α : Type u_1
β : Type v
γ : Type u_2
inst✝ : DecidableEq α
t✝ : Multiset α
a✝ b a : α
t : Multiset α
IH : ∀ {s u : Multiset α}, s ≤ t → s ≤ u → s ≤ t ∩ u
s u : Multiset α
h₁ : s ≤ a ::ₘ t
h₂ : s ≤ u
h : a ∈ u
⊢ s ≤ (a ::ₘ t) ∩ u
case neg
α : Type u_1
β : Type v
γ : Type u_2
inst✝ : DecidableEq α
t✝ : Multiset ... | ((:c LE.le) ((:c Multiset) (:fv _uniq.110210)) ((:c Preorder.toLE) ((:c Multiset) (:fv _uniq.110210)) ((:c PartialOrder.toPreorder) ((:c Multiset) (:fv _uniq.110210)) ((:c Multiset.instPartialOrder) (:fv _uniq.110210)))) (:fv _uniq.110371) ((:c Inter.inter) ((:c Multiset) (:fv _uniq.110210)) ((:c Multiset.instInter) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.110210))"},{"name":"t✝","sexp":"((:c Multiset) (:fv _uniq.110210))"},{"name":"a✝","sexp":"(:fv _uniq.110210)"},{"name":"b","sexp":"(:fv _uniq.110210... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:fv FV10)) (:arg :explicit 3 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Multise... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110210","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110212","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"by_cases","sourceEnd":75374,"sourceStart":75366,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":75376,"sourceStart":75375,"tag":"identifier"},{"source":":","sourceEnd":75378,"sourceStart":75377,"tag":"atom"}],"kind":"null","source":"h :","sourceEnd":75378,"sour... | [] | [{"source":"a ∈ u","source_end":75386,"source_start":75379,"syntax_kind":"«term_∈_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110210","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110212","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 652 | 16 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 21e5b856c5a3cf5d660f72aab7f324fbbef7be5b0fb71151e0750ae24613b55d | c8610c91b724fa4ae685e6e785313cfaf85f5542476dd986b2b7568e40fcc60d | 6ff761fde9c77665df1fb4173975192c9e5e0bf5549428236a62e9d70df316ca | 1d646b630ead4432090ed2c2f4fbf8448d804aec661d0564e74320b9247a7d0e |
cat-searcher/leandojo-benchmark-4-random | test | 4,156 | Multiset.le_inter | Mathlib/Data/Multiset/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>Multiset.zero_inter</a>, <a>nonpos_iff_eq_zero</a>] using h₁ | case refine_1
α : Type u_1
β : Type v
γ : Type u_2
inst✝ : DecidableEq α
t : Multiset α
a b : α
s u : Multiset α
h₁ : s ≤ 0
h₂ : s ≤ u
⊢ s ≤ 0 ∩ u | ((:c LE.le) ((:c Multiset) (:fv _uniq.110210)) ((:c Preorder.toLE) ((:c Multiset) (:fv _uniq.110210)) ((:c PartialOrder.toPreorder) ((:c Multiset) (:fv _uniq.110210)) ((:c Multiset.instPartialOrder) (:fv _uniq.110210)))) (:fv _uniq.110365) ((:c Inter.inter) ((:c Multiset) (:fv _uniq.110210)) ((:c Multiset.instInter) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.110210))"},{"name":"t","sexp":"((:c Multiset) (:fv _uniq.110210))"},{"name":"a","sexp":"(:fv _uniq.110210)"},{"name":"b","sexp":"(:fv _uniq.110210)"... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:fv FV7)) (:arg :explicit 3 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Multiset... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110210","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110212","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":75314,"sourceStart":75309,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"zero_inter","source_end":75331,"source_start":75321,"syntax_kind":"ident"},{"source":"nonpos_iff_eq_zero","source_end":75351,"source_start":75333,"syntax_kind":"ident"},{"source":"h₁","source_end":75363,"source_start":75359,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110210","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110212","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 652 | 13 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6b1694d9b57ac5530736c2d4aad6ce9fa1234bc67762b78166be6552dcc83b44 | 08f46a2809d38330a9e2900789fe8ff653c1289574e0103204df7327c4fce699 | c8dfc462e8cd5b22985863ce3e8c4c4ad8854042a2a6233f867ea3d38423171a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,157 | Multiset.le_inter | Mathlib/Data/Multiset/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Multiset.cons_inter_of_pos</a> _ h, ← <a>Multiset.erase_le_iff_le_cons</a>] | case pos
α : Type u_1
β : Type v
γ : Type u_2
inst✝ : DecidableEq α
t✝ : Multiset α
a✝ b a : α
t : Multiset α
IH : ∀ {s u : Multiset α}, s ≤ t → s ≤ u → s ≤ t ∩ u
s u : Multiset α
h₁ : s ≤ a ::ₘ t
h₂ : s ≤ u
h : a ∈ u
⊢ s ≤ (a ::ₘ t) ∩ u | case pos
α : Type u_1
β : Type v
γ : Type u_2
inst✝ : DecidableEq α
t✝ : Multiset α
a✝ b a : α
t : Multiset α
IH : ∀ {s u : Multiset α}, s ≤ t → s ≤ u → s ≤ t ∩ u
s u : Multiset α
h₁ : s ≤ a ::ₘ t
h₂ : s ≤ u
h : a ∈ u
⊢ s.erase a ≤ t ∩ u.erase a | ((:c LE.le) ((:c Multiset) (:fv _uniq.110210)) ((:c Preorder.toLE) ((:c Multiset) (:fv _uniq.110210)) ((:c PartialOrder.toPreorder) ((:c Multiset) (:fv _uniq.110210)) ((:c Multiset.instPartialOrder) (:fv _uniq.110210)))) (:fv _uniq.110371) ((:c Inter.inter) ((:c Multiset) (:fv _uniq.110210)) ((:c Multiset.instInter) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.110210))"},{"name":"t✝","sexp":"((:c Multiset) (:fv _uniq.110210))"},{"name":"a✝","sexp":"(:fv _uniq.110210)"},{"name":"b","sexp":"(:fv _uniq.110210... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:fv FV10)) (:arg :explicit 3 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Multise... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110210","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110212","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":75394,"sourceStart":75392,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":75396,"sourceStart":75395,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Mul... | [] | [{"source":"cons_inter_of_pos _ h","source_end":75417,"source_start":75396,"syntax_kind":"Lean.Parser.Term.app"},{"source":"erase_le_iff_le_cons","source_end":75443,"source_start":75423,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110210","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110212","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 652 | 21 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5d4866c58c9ac1c975db9774d8f6520088797d5b498ec0761f57c37dcbc3b2e5 | efe58a4bd9e3f25df93efaaab174288ecdcd917aa945e8c7efea2dc1f50de543 | c04a54d4113d5d98764a0ebe52d684c6e7499b5ab76d95c812928d684729d314 | 6e1caf2ff9104a8103d5c6d437c6fc57a0c33f245e43ab3ea48c59ce19028396 |
cat-searcher/leandojo-benchmark-4-random | test | 4,158 | Multiset.le_inter | Mathlib/Data/Multiset/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact IH (<a>Multiset.erase_le_iff_le_cons</a>.2 h₁) (<a>Multiset.erase_le_erase</a> _ h₂) | case pos
α : Type u_1
β : Type v
γ : Type u_2
inst✝ : DecidableEq α
t✝ : Multiset α
a✝ b a : α
t : Multiset α
IH : ∀ {s u : Multiset α}, s ≤ t → s ≤ u → s ≤ t ∩ u
s u : Multiset α
h₁ : s ≤ a ::ₘ t
h₂ : s ≤ u
h : a ∈ u
⊢ s.erase a ≤ t ∩ u.erase a | ((:c LE.le) ((:c Multiset) (:fv _uniq.110210)) ((:c Preorder.toLE) ((:c Multiset) (:fv _uniq.110210)) ((:c PartialOrder.toPreorder) ((:c Multiset) (:fv _uniq.110210)) ((:c Multiset.instPartialOrder) (:fv _uniq.110210)))) ((:c Multiset.erase) (:fv _uniq.110210) (:fv _uniq.110222) (:fv _uniq.110371) (:fv _uniq.110341)) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.110210))"},{"name":"t✝","sexp":"((:c Multiset) (:fv _uniq.110210))"},{"name":"a✝","sexp":"(:fv _uniq.110210)"},{"name":"b","sexp":"(:fv _uniq.110210... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:c Multiset.erase) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110210","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110212","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":75454,"sourceStart":75449,"tag":"atom"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"IH","sourceEnd":75457,"sourceStart":75455,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":75459,"sourceStart":75458,"tag":"atom"},{"children":[{"chil... | [] | [{"source":"IH (erase_le_iff_le_cons.2 h₁) (erase_le_erase _ h₂)","source_end":75511,"source_start":75455,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110210","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110212","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 652 | 25 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e48ef714fe22b818d9e9b13165537fe9c1745809edecb725fae5207259e7f30a | 6e1caf2ff9104a8103d5c6d437c6fc57a0c33f245e43ab3ea48c59ce19028396 | 7d1db65367ae165fd964d3a76d50e4b0b649d927df7619826d7d26a6c6650bea | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,159 | Multiset.le_inter | Mathlib/Data/Multiset/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Multiset.cons_inter_of_neg</a> _ h] | case neg
α : Type u_1
β : Type v
γ : Type u_2
inst✝ : DecidableEq α
t✝ : Multiset α
a✝ b a : α
t : Multiset α
IH : ∀ {s u : Multiset α}, s ≤ t → s ≤ u → s ≤ t ∩ u
s u : Multiset α
h₁ : s ≤ a ::ₘ t
h₂ : s ≤ u
h : a ∉ u
⊢ s ≤ (a ::ₘ t) ∩ u | case neg
α : Type u_1
β : Type v
γ : Type u_2
inst✝ : DecidableEq α
t✝ : Multiset α
a✝ b a : α
t : Multiset α
IH : ∀ {s u : Multiset α}, s ≤ t → s ≤ u → s ≤ t ∩ u
s u : Multiset α
h₁ : s ≤ a ::ₘ t
h₂ : s ≤ u
h : a ∉ u
⊢ s ≤ t ∩ u | ((:c LE.le) ((:c Multiset) (:fv _uniq.110210)) ((:c Preorder.toLE) ((:c Multiset) (:fv _uniq.110210)) ((:c PartialOrder.toPreorder) ((:c Multiset) (:fv _uniq.110210)) ((:c Multiset.instPartialOrder) (:fv _uniq.110210)))) (:fv _uniq.110371) ((:c Inter.inter) ((:c Multiset) (:fv _uniq.110210)) ((:c Multiset.instInter) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.110210))"},{"name":"t✝","sexp":"((:c Multiset) (:fv _uniq.110210))"},{"name":"a✝","sexp":"(:fv _uniq.110210)"},{"name":"b","sexp":"(:fv _uniq.110210... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:fv FV10)) (:arg :explicit 3 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Multise... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110210","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110212","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":75519,"sourceStart":75517,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":75521,"sourceStart":75520,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Mul... | [] | [{"source":"cons_inter_of_neg _ h","source_end":75542,"source_start":75521,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110210","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110212","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 652 | 30 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 49d0ce600ad1b36b38c480f78c3b3846d38ed91b57cb08654612841b0f1ddc1f | 021da807b59f123b483cbe84c9be6e3198b2cb28861dc38aa466955e27ae561c | f60bfc3c740fc072a9a6e8c32c61f51fb5c08a142bfa1b8d66d223f2983d5484 | 1c11f7c531dc75c515938dbceece89b0cf65a1ec4936c3e88b13df0a752c334f |
cat-searcher/leandojo-benchmark-4-random | test | 4,160 | Multiset.le_inter | Mathlib/Data/Multiset/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact IH ((<a>Multiset.le_cons_of_not_mem</a> <| <a>mt</a> (<a>Multiset.mem_of_le</a> h₂) h).1 h₁) h₂ | case neg
α : Type u_1
β : Type v
γ : Type u_2
inst✝ : DecidableEq α
t✝ : Multiset α
a✝ b a : α
t : Multiset α
IH : ∀ {s u : Multiset α}, s ≤ t → s ≤ u → s ≤ t ∩ u
s u : Multiset α
h₁ : s ≤ a ::ₘ t
h₂ : s ≤ u
h : a ∉ u
⊢ s ≤ t ∩ u | ((:c LE.le) ((:c Multiset) (:fv _uniq.110210)) ((:c Preorder.toLE) ((:c Multiset) (:fv _uniq.110210)) ((:c PartialOrder.toPreorder) ((:c Multiset) (:fv _uniq.110210)) ((:c Multiset.instPartialOrder) (:fv _uniq.110210)))) (:fv _uniq.110371) ((:c Inter.inter) ((:c Multiset) (:fv _uniq.110210)) ((:c Multiset.instInter) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.110210))"},{"name":"t✝","sexp":"((:c Multiset) (:fv _uniq.110210))"},{"name":"a✝","sexp":"(:fv _uniq.110210)"},{"name":"b","sexp":"(:fv _uniq.110210... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:fv FV10)) (:arg :explicit 3 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Multise... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110210","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110212","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":75553,"sourceStart":75548,"tag":"atom"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"IH","sourceEnd":75556,"sourceStart":75554,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":75558,"sourceStart":75557,"tag":"atom"},{"children":[{"chil... | [] | [{"source":"IH ((le_cons_of_not_mem <| mt (mem_of_le h₂) h).1 h₁) h₂","source_end":75616,"source_start":75554,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.110210","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.110212","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 652 | 33 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 040d31d000818ede76208d4de766f4c733b5d38c4d4e6c6fa837efd820ccbc69 | 1c11f7c531dc75c515938dbceece89b0cf65a1ec4936c3e88b13df0a752c334f | ed3b747557826a99502e9d4085689e136ef5230f2cf629dc7465debcb7665dc1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,161 | Nat.WithBot.add_one_le_of_lt | Mathlib/Data/Nat/WithBot.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases n | n m : WithBot ℕ
h : n < m
⊢ n + 1 ≤ m | ((:c LE.le) ((:c WithBot) (:c Nat)) ((:c Preorder.toLE) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c HAdd.hAdd) ((:c WithBot) (:c Nat)) ((:c WithBot) (:c Nat)) ((:c WithBot) ... | [{"name":"n","sexp":"((:c WithBot) (:c Nat))"},{"name":"m","sexp":"((:c WithBot) (:c Nat))"},{"name":"h","sexp":"((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c ... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:ar... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13824","is_instance":false,"is_let":false,"name":"n","sexp":"(:app (:c WithBot) (:arg :explicit 0 (:c Nat)))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.13825","is_instance":false,"is_let":false,"name":"m","sexp":"(:app (:c W... | {"children":[{"children":[{"children":[{"children":[{"source":"cases","sourceEnd":2884,"sourceStart":2879,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":1,"semanticRole":"local","source":"n","sourceEnd":2886,"sourceStart":2885,"tag":"identifier"}],"kind":"... | [] | [{"source":"n","source_end":2886,"source_start":2885,"syntax_kind":"ident"},{"source":"WithBot.bot_add","source_end":2918,"source_start":2903,"syntax_kind":"ident"},{"source":"bot_le","source_end":2926,"source_start":2920,"syntax_kind":"ident"},{"source":"m","source_end":2937,"source_start":2936,"syntax_kind":"ident"},... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13824","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.13825","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 21 | 2 | branch_opener | false | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b2bcf143c03f94fb0ddecb68c2ef8df2e5c42391f3e1e2ecd0b36c1c884099eb | 7ca173808894ff5a1fc526ae330295af3fa24e2d9eca53fb53478cddcd58de62 | 587af0ace40623dade91be1b78e831facc5de085c3c720b59185b89ff09878a4 | cc53e33ab5c4555004725552ba00176c2be10ce6c70de004c1bc540b668a86d6 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,163 | Nat.WithBot.add_one_le_of_lt | Mathlib/Data/Nat/WithBot.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>WithBot.bot_add</a>, <a>bot_le</a>] | case bot
m : WithBot ℕ
h : ⊥ < m
⊢ ⊥ + 1 ≤ m | ((:c LE.le) ((:c WithBot) (:c Nat)) ((:c Preorder.toLE) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c HAdd.hAdd) ((:c WithBot) (:c Nat)) ((:c WithBot) (:c Nat)) ((:c WithBot) ... | [{"name":"m","sexp":"((:c WithBot) (:c Nat))"},{"name":"h","sexp":"((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Bot.bo... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:ar... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13825","is_instance":false,"is_let":false,"name":"m","sexp":"(:app (:c WithBot) (:arg :explicit 0 (:c Nat)))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.13867","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c L... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":2896,"sourceStart":2892,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":2901,"sourceStart":2897,"tag":"atom"}],"kind":"nu... | [] | [{"source":"WithBot.bot_add","source_end":2918,"source_start":2903,"syntax_kind":"ident"},{"source":"bot_le","source_end":2926,"source_start":2920,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13825","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.13867","is_instance":false,"is_let":false,"user_name":"h"}] | 21 | 7 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d3d52a82c68b105ec9e83aff3f2f996beb1e59bac1c5a887b6a4acafb8fce176 | 6843a24be8515c29880ac92f1fceba0d496217e90f940aad2499f9ad21c15343 | ccb008eae7c6d2342ee4db3c93f5d29f5a6abc1a8c5416aee4e040572bccbd00 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,164 | Nat.WithBot.add_one_le_of_lt | Mathlib/Data/Nat/WithBot.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>not_lt_bot</a> h).<a>False.elim</a> | case coe.bot
a✝ : ℕ
h : ↑a✝ < ⊥
⊢ ↑a✝ + 1 ≤ ⊥ | ((:c LE.le) ((:c WithBot) (:c Nat)) ((:c Preorder.toLE) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c HAdd.hAdd) ((:c WithBot) (:c Nat)) ((:c WithBot) (:c Nat)) ((:c WithBot) ... | [{"name":"a✝","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c WithBot.some) (:c Na... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:ar... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.13870","is_instance":false,"is_let":false,"name":"a✝","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.14116","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":2948,"sourceStart":2943,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":2950,"sourceStart":2949,"tag":"atom"},{"children":[{"name":"not_lt_bot","semanticRole":"global","source":"not_lt_bot","sourceEnd":2960,"sourceStart"... | [] | [{"source":"(not_lt_bot h).elim","source_end":2968,"source_start":2949,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.13870","is_instance":false,"is_let":false,"user_name":"a✝"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.14116","is_instance":false,"is_let":false,"user_name":"h"}] | 21 | 13 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d463e5a099a65519d5d194ec9bd3f78240f8ca17e1addcd9a2430f9705bc70e7 | f6e8d0e0bf836dde93106ec1cd6eca6e33da379fb1c081c84a9e634fde595152 | 36c8fa24d719682327b9ca027fb5d0e68e256238627e1388672af6a140b2990a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,165 | Nat.WithBot.add_one_le_of_lt | Mathlib/Data/Nat/WithBot.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>WithBot.coe_lt_coe</a>, ← <a>Nat.add_one_le_iff</a>, ← <a>WithBot.coe_le_coe</a>, <a>WithBot.coe_add</a>, <a>WithBot.coe_one</a>] at h | case coe.coe
a✝¹ a✝ : ℕ
h : ↑a✝¹ < ↑a✝
⊢ ↑a✝¹ + 1 ≤ ↑a✝ | ((:c LE.le) ((:c WithBot) (:c Nat)) ((:c Preorder.toLE) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c HAdd.hAdd) ((:c WithBot) (:c Nat)) ((:c WithBot) (:c Nat)) ((:c WithBot) ... | [{"name":"a✝¹","sexp":"(:c Nat)"},{"name":"a✝","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiri... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:ar... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.13870","is_instance":false,"is_let":false,"name":"a✝¹","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.14119","is_instance":false,"is_let":false,"name":"a✝","sexp":"(:c Nat)"},{"binder_role":":explicit","context_... | {"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":2977,"sourceStart":2974,"tag":"atom"},{"children":[{"source":"[","sourceEnd":2979,"sourceStart":2978,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"WithBot.coe_lt_coe","semanticRole":... | [] | [{"source":"WithBot.coe_lt_coe","source_end":2997,"source_start":2979,"syntax_kind":"ident"},{"source":"h","source_end":3091,"source_start":3090,"syntax_kind":"ident"},{"source":"Nat.add_one_le_iff","source_end":3021,"source_start":3003,"syntax_kind":"ident"},{"source":"WithBot.coe_le_coe","source_end":3045,"source_sta... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.13870","is_instance":false,"is_let":false,"user_name":"a✝¹"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.14119","is_instance":false,"is_let":false,"user_name":"a✝"},{"binder_role":":explicit","context_index":3,"internal_name":"... | 21 | 18 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 48d56c4775d6bad8a64dbb0da27945326d1210b081989f2c3cf7c68500ad6a9b | 25f071afb1cd25a0c44966461d2444c203130a6f962c2c0cba7ee4471001d15e | f9b3914b278d5263bd7dab3b9e730e49d67618e66a43c8a0b56079e091c1c9ed | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,166 | Matrix.det_updateColumn_add_self | Mathlib/LinearAlgebra/Matrix/Determinant/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Matrix.det_transpose</a>, ← <a>Matrix.updateRow_transpose</a>, ← <a>Matrix.det_transpose</a> A] | m : Type u_1
n : Type u_2
inst✝⁴ : DecidableEq n
inst✝³ : Fintype n
inst✝² : DecidableEq m
inst✝¹ : Fintype m
R : Type v
inst✝ : CommRing R
A : Matrix n n R
i j : n
hij : i ≠ j
⊢ (A.updateColumn i fun k => A k i + A k j).det = A.det | m : Type u_1
n : Type u_2
inst✝⁴ : DecidableEq n
inst✝³ : Fintype n
inst✝² : DecidableEq m
inst✝¹ : Fintype m
R : Type v
inst✝ : CommRing R
A : Matrix n n R
i j : n
hij : i ≠ j
⊢ (Aᵀ.updateRow i fun k => A k i + A k j).det = Aᵀ.det | ((:c Eq) (:fv _uniq.244021) ((:c Matrix.det) (:fv _uniq.243995) (:fv _uniq.244002) (:fv _uniq.244007) (:fv _uniq.244021) (:fv _uniq.244024) ((:c Matrix.updateColumn) (:fv _uniq.243995) (:fv _uniq.243995) (:fv _uniq.244021) (:fv _uniq.244002) (:fv _uniq.244317) (:fv _uniq.244318) (:lambda k (:fv _uniq.243995) ((:c HAdd.... | [{"name":"m","sexp":"(:sort (+ u_1 1))"},{"name":"n","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.243995))"},{"name":"inst✝³","sexp":"((:c Fintype) (:fv _uniq.243995))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.243992))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uni... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Matrix.det) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c DecidableEq) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c Fintype) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 3 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.243992","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.243995","is_instance":false,"is_let":false,"name":"n","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rw","sourceEnd":20938,"sourceStart":20936,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":20940,"sourceStart":20939,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":20943,"sourceSt... | [] | [{"source":"det_transpose","source_end":20957,"source_start":20944,"syntax_kind":"ident"},{"source":"updateRow_transpose","source_end":20982,"source_start":20963,"syntax_kind":"ident"},{"source":"det_transpose A","source_end":21003,"source_start":20988,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.243992","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.243995","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":instance-implicit","context_index":2,"internal... | 126 | 4 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 62b98632088913c3a4085d694f751390ec511d450cb327648b99a4a1fabd955a | a0535f971cfa622a765abf93b3b04399989af698f1f2fff8e440597941aa3690 | 2eb02b661ebfa08813b561c560426c69183f53d10dd65fc26abf39d41bc14b44 | e7b7db84ef7b1ac5e6e617fd52fdd5e27ea691705c0f28279a603c86b18eacc5 |
cat-searcher/leandojo-benchmark-4-random | test | 4,167 | Matrix.det_updateColumn_add_self | Mathlib/LinearAlgebra/Matrix/Determinant/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Matrix.det_updateRow_add_self</a> Aᵀ hij | m : Type u_1
n : Type u_2
inst✝⁴ : DecidableEq n
inst✝³ : Fintype n
inst✝² : DecidableEq m
inst✝¹ : Fintype m
R : Type v
inst✝ : CommRing R
A : Matrix n n R
i j : n
hij : i ≠ j
⊢ (Aᵀ.updateRow i fun k => A k i + A k j).det = Aᵀ.det | ((:c Eq) (:fv _uniq.244021) ((:c Matrix.det) (:fv _uniq.243995) (:fv _uniq.244002) (:fv _uniq.244007) (:fv _uniq.244021) (:fv _uniq.244024) ((:c Matrix.updateRow) (:fv _uniq.243995) (:fv _uniq.243995) (:fv _uniq.244021) (:fv _uniq.244002) ((:c Matrix.transpose) (:fv _uniq.243995) (:fv _uniq.243995) (:fv _uniq.244021) (... | [{"name":"m","sexp":"(:sort (+ u_1 1))"},{"name":"n","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.243995))"},{"name":"inst✝³","sexp":"((:c Fintype) (:fv _uniq.243995))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.243992))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uni... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Matrix.det) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c DecidableEq) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c Fintype) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 3 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.243992","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.243995","is_instance":false,"is_let":false,"name":"n","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"exact","sourceEnd":21012,"sourceStart":21007,"tag":"atom"},{"children":[{"name":"Matrix.det_updateRow_add_self","semanticRole":"global","source":"det_updateRow_add_self","sourceEnd":21035,"sourceStart":21013,"tag":"identifier"},{"children":[{"children":[{"contextIndex":9,"semanticRole":"local","... | [] | [{"source":"det_updateRow_add_self Aᵀ hij","source_end":21044,"source_start":21013,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.243992","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.243995","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":instance-implicit","context_index":2,"internal... | 126 | 9 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9fa88f77d68930b848061d41581a82e4c0991dc59518bbfddeba3c681c156183 | e7b7db84ef7b1ac5e6e617fd52fdd5e27ea691705c0f28279a603c86b18eacc5 | e4770db240d0722d6460d8a3d69f6d548eec9c0b29fbd355ef40cc04df846001 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,168 | Subgroup.MemRightTransversals.toEquiv_apply | Mathlib/GroupTheory/Complement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (Subtype.ext_iff.mp ?_).<a>Eq.trans</a> (<a>Subtype.coe_mk</a> (f q) ⟨q, <a>rfl</a>⟩) | G : Type u_1
inst✝ : Group G
H K : Subgroup G
S T : Set G
f : Quotient (QuotientGroup.rightRel H) → G
hf : ∀ (q : Quotient (QuotientGroup.rightRel H)), Quotient.mk'' (f q) = q
q : Quotient (QuotientGroup.rightRel H)
⊢ ↑((toEquiv ⋯) q) = f q | G : Type u_1
inst✝ : Group G
H K : Subgroup G
S T : Set G
f : Quotient (QuotientGroup.rightRel H) → G
hf : ∀ (q : Quotient (QuotientGroup.rightRel H)), Quotient.mk'' (f q) = q
q : Quotient (QuotientGroup.rightRel H)
⊢ (toEquiv ⋯) q = ⟨f q, ⋯⟩ | ((:c Eq) (:fv _uniq.167797) ((:c Subtype.val) (:fv _uniq.167797) (:lambda x (:fv _uniq.167797) ((:c Membership.mem) (:fv _uniq.167797) ((:c Set) (:fv _uniq.167797)) ((:c Set.instMembership) (:fv _uniq.167797)) 0 ((:c Set.range) (:fv _uniq.167797) ((:c Quotient) (:fv _uniq.167797) ((:c QuotientGroup.rightRel) (:fv _uniq... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.167797))"},{"name":"H","sexp":"((:c Subgroup) (:fv _uniq.167797) (:fv _uniq.167800))"},{"name":"K","sexp":"((:c Subgroup) (:fv _uniq.167797) (:fv _uniq.167800))"},{"name":"S","sexp":"((:c Set) (:fv _uniq.167797))"},{"name":"T","sexp... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype.val) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Equiv) (:arg :explicit 0 (:app (:c Quotient) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.167797","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.167800","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Group) (:arg :explicit... | {"children":[{"source":"refine","sourceEnd":30469,"sourceStart":30463,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":30471,"sourceStart":30470,"tag":"atom"},{"children":[{"source":"Subtype.ext_iff.mp","sourceEnd":30489,"sourceStart":30471,"tag":"identifier"},{"children":[{"children":[{"s... | [] | [{"source":"(Subtype.ext_iff.mp ?_).trans (Subtype.coe_mk (f q) ⟨q, rfl⟩)","source_end":30535,"source_start":30470,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.167797","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.167800","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"inter... | 162 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 638ad6543438182ae62850e1696eb8e3d4e52f85df87d4e6ebc16c16204a8f95 | 487f58e12fa4f0dd088a4e53fb7889f7d67d9a8ff12b6ff439ae694cb74e0ff1 | 65e0cbeebd25792185be3c2b0b7b4b64bad68155dd860fab2604211ebc1b8e2b | 02453d6a8e5a93362da7522aaa916bc15985efd64f6c96cb89eb8f6487ec9759 |
cat-searcher/leandojo-benchmark-4-random | test | 4,169 | Subgroup.MemRightTransversals.toEquiv_apply | Mathlib/GroupTheory/Complement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>Subgroup.MemRightTransversals.toEquiv</a> (<a>Subgroup.range_mem_rightTransversals</a> hf)).apply_eq_iff_eq_symm_apply.mpr (hf q).<a>Eq.symm</a> | G : Type u_1
inst✝ : Group G
H K : Subgroup G
S T : Set G
f : Quotient (QuotientGroup.rightRel H) → G
hf : ∀ (q : Quotient (QuotientGroup.rightRel H)), Quotient.mk'' (f q) = q
q : Quotient (QuotientGroup.rightRel H)
⊢ (toEquiv ⋯) q = ⟨f q, ⋯⟩ | ((:c Eq) ((:c Subtype) (:fv _uniq.167797) (:lambda x (:fv _uniq.167797) ((:c Membership.mem) (:fv _uniq.167797) ((:c Set) (:fv _uniq.167797)) ((:c Set.instMembership) (:fv _uniq.167797)) 0 ((:c Set.range) (:fv _uniq.167797) ((:c Quotient) (:fv _uniq.167797) ((:c QuotientGroup.rightRel) (:fv _uniq.167797) (:fv _uniq.167... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.167797))"},{"name":"H","sexp":"((:c Subgroup) (:fv _uniq.167797) (:fv _uniq.167800))"},{"name":"K","sexp":"((:c Subgroup) (:fv _uniq.167797) (:fv _uniq.167800))"},{"name":"S","sexp":"((:c Set) (:fv _uniq.167797))"},{"name":"T","sexp... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.167797","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.167800","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Group) (:arg :explicit... | {"children":[{"source":"exact","sourceEnd":30543,"sourceStart":30538,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":30545,"sourceStart":30544,"tag":"atom"},{"children":[{"name":"Subgroup.MemRightTransversals.toEquiv","semanticRole":"global","source":"toEquiv","sourceEnd":30552,"sourceSta... | [] | [{"source":"(toEquiv (range_mem_rightTransversals hf)).apply_eq_iff_eq_symm_apply.mpr (hf q).symm","source_end":30629,"source_start":30544,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.167797","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.167800","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"inter... | 162 | 5 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 48d79795b2bb8d12b4286bd0cbd92d3dbc461480f128784f2248a075b111695d | 02453d6a8e5a93362da7522aaa916bc15985efd64f6c96cb89eb8f6487ec9759 | bd6510fffbff7338d2062cc9a55d3f95fb0f5ce55599aaaa801eea8eedb2a6cd | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,170 | Stream'.WSeq.exists_of_liftRel_right | Mathlib/Data/Seq/WSeq.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Stream'.WSeq.LiftRel.swap</a>] at H | α : Type u
β : Type v
γ : Type w
R : α → β → Prop
s : WSeq α
t : WSeq β
H : LiftRel R s t
b : β
h : b ∈ t
⊢ ∃ a, a ∈ s ∧ R a b | α : Type u
β : Type v
γ : Type w
R : α → β → Prop
s : WSeq α
t : WSeq β
H : swap (LiftRel fun x y => R y x) s t
b : β
h : b ∈ t
⊢ ∃ a, a ∈ s ∧ R a b | ((:c Exists) (:fv _uniq.55903) (:lambda a (:fv _uniq.55903) ((:c And) ((:c Membership.mem) (:fv _uniq.55903) ((:c Stream'.WSeq) (:fv _uniq.55903)) ((:c Stream'.WSeq.membership) (:fv _uniq.55903)) 0 (:fv _uniq.55995)) ((:fv _uniq.55994) 0 (:fv _uniq.55998))))) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"R","sexp":"(:forall _ (:fv _uniq.55903) (:forall _ (:fv _uniq.55905) (:sort 0)))"},{"name":"s","sexp":"((:c Stream'.WSeq) (:fv _uniq.55903))"},{"name":"t","sexp":"((:c Stream'.WSeq) (:fv _uniq.559... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda a :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Stream'.WSeq) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Member... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55903","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55905","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":41354,"sourceStart":41352,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":41356,"sourceStart":41355,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":41359,"sourceSt... | [] | [{"source":"LiftRel.swap","source_end":41372,"source_start":41360,"syntax_kind":"ident"},{"source":"H","source_end":41378,"source_start":41377,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55903","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55905","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 282 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 36253b694f3b227533074c76f4179c4c008799381ae379de429d65f003ac61ea | 805c454914c85c3e9fc3756dbf5b39784bbe7b7c611718c1eff2d004ec91ff3f | 98362e0c12c7f6b02c8b5c9ee72cc432126e6aef4a1f7a808648f9f7d046282c | c288f543d69c98057b1e88acd2d6f65ad7b1abc2cdc778044e44474181dc93b4 |
cat-searcher/leandojo-benchmark-4-random | test | 4,171 | Stream'.WSeq.exists_of_liftRel_right | Mathlib/Data/Seq/WSeq.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Stream'.WSeq.exists_of_liftRel_left</a> H h | α : Type u
β : Type v
γ : Type w
R : α → β → Prop
s : WSeq α
t : WSeq β
H : swap (LiftRel fun x y => R y x) s t
b : β
h : b ∈ t
⊢ ∃ a, a ∈ s ∧ R a b | ((:c Exists) (:fv _uniq.55903) (:lambda a (:fv _uniq.55903) ((:c And) ((:c Membership.mem) (:fv _uniq.55903) ((:c Stream'.WSeq) (:fv _uniq.55903)) ((:c Stream'.WSeq.membership) (:fv _uniq.55903)) 0 (:fv _uniq.55995)) ((:fv _uniq.55994) 0 (:fv _uniq.56054))))) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"R","sexp":"(:forall _ (:fv _uniq.55903) (:forall _ (:fv _uniq.55905) (:sort 0)))"},{"name":"s","sexp":"((:c Stream'.WSeq) (:fv _uniq.55903))"},{"name":"t","sexp":"((:c Stream'.WSeq) (:fv _uniq.559... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda a :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Stream'.WSeq) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Member... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55903","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55905","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":41385,"sourceStart":41380,"tag":"atom"},{"children":[{"name":"Stream'.WSeq.exists_of_liftRel_left","semanticRole":"global","source":"exists_of_liftRel_left","sourceEnd":41408,"sourceStart":41386,"tag":"identifier"},{"children":[{"contextIndex":7,"semanticRole":"local","source"... | [] | [{"source":"exists_of_liftRel_left H h","source_end":41412,"source_start":41386,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55903","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55905","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 282 | 8 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9d94fd9f998eee4ebad142ee01a66a6b205c7b727c5038d92f7ceed42429ae1f | c288f543d69c98057b1e88acd2d6f65ad7b1abc2cdc778044e44474181dc93b4 | 832db77da30926a2dbdd58a5cd065b44c83c5bb443269e14489c24e293dd039e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,172 | MeasureTheory.locallyIntegrableOn_of_locallyIntegrable_restrict | Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro x _ | X : Type u_1
Y : Type u_2
E : Type u_3
F : Type u_4
R : Type u_5
inst✝⁶ : MeasurableSpace X
inst✝⁵ : TopologicalSpace X
inst✝⁴ : MeasurableSpace Y
inst✝³ : TopologicalSpace Y
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedAddCommGroup F
f g : X → E
μ : Measure X
s : Set X
inst✝ : OpensMeasurableSpace X
hf : LocallyIntegr... | X : Type u_1
Y : Type u_2
E : Type u_3
F : Type u_4
R : Type u_5
inst✝⁶ : MeasurableSpace X
inst✝⁵ : TopologicalSpace X
inst✝⁴ : MeasurableSpace Y
inst✝³ : TopologicalSpace Y
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedAddCommGroup F
f g : X → E
μ : Measure X
s : Set X
inst✝ : OpensMeasurableSpace X
hf : LocallyIntegr... | ((:c MeasureTheory.LocallyIntegrableOn) (:fv _uniq.17688) (:fv _uniq.17694) (:fv _uniq.17703) (:fv _uniq.17706) (:fv _uniq.17715) (:fv _uniq.17722) (:fv _uniq.17738) (:fv _uniq.17735)) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"F","sexp":"(:sort (+ u_4 1))"},{"name":"R","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c MeasurableSpace) (:fv _uniq.17688))"},{"name":"inst✝⁵","sexp":"((:c TopologicalSpace) (:f... | (:app (:c MeasureTheory.LocallyIntegrableOn) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17688","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17691","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"intro","sourceEnd":11029,"sourceStart":11024,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":11031,"sourceStart":11030,"tag":"identifier"},{"children":[{"source":"_","sourceEnd":11033,"sourceStart":11032,"tag":"atom"}],"kind":"Lean.Parser.Term.hole","source":"_... | [{"role":"fresh_name","source":"x","source_end":11031,"source_start":11030,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17688","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17691","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 42 | 4 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1d101c1d7a830c924f9475c2cf6d1ab6bdd9bb39512bea110a1ef2481b477bd1 | 2543d2c68d79741efb92780410997e38627c35e01cc7e915b9a0006d2c204e7d | 855e34751cbbd74b656a44590e56b72f1bcd18a3cbccbdb9da20da354083a6c1 | 1f48c92588e46044eec0900ea006568706c1b24216d8c24186b4fce291c00fc3 |
cat-searcher/leandojo-benchmark-4-random | test | 4,173 | MeasureTheory.locallyIntegrableOn_of_locallyIntegrable_restrict | Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨t, ht_mem, ht_int⟩ := hf x | X : Type u_1
Y : Type u_2
E : Type u_3
F : Type u_4
R : Type u_5
inst✝⁶ : MeasurableSpace X
inst✝⁵ : TopologicalSpace X
inst✝⁴ : MeasurableSpace Y
inst✝³ : TopologicalSpace Y
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedAddCommGroup F
f g : X → E
μ : Measure X
s : Set X
inst✝ : OpensMeasurableSpace X
hf : LocallyIntegr... | case intro.intro
X : Type u_1
Y : Type u_2
E : Type u_3
F : Type u_4
R : Type u_5
inst✝⁶ : MeasurableSpace X
inst✝⁵ : TopologicalSpace X
inst✝⁴ : MeasurableSpace Y
inst✝³ : TopologicalSpace Y
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedAddCommGroup F
f g : X → E
μ : Measure X
s : Set X
inst✝ : OpensMeasurableSpace X
h... | ((:c MeasureTheory.IntegrableAtFilter) (:fv _uniq.17688) (:fv _uniq.17694) (:fv _uniq.17703) (:fv _uniq.17715) (:fv _uniq.17722) ((:c nhdsWithin) (:fv _uniq.17688) (:fv _uniq.17706) (:fv _uniq.18062) (:fv _uniq.17738)) (:fv _uniq.17735)) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"F","sexp":"(:sort (+ u_4 1))"},{"name":"R","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c MeasurableSpace) (:fv _uniq.17688))"},{"name":"inst✝⁵","sexp":"((:c TopologicalSpace) (:f... | (:app (:c MeasureTheory.IntegrableAtFilter) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 4 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17688","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17691","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"obtain","sourceEnd":11042,"sourceStart":11036,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":11046,"sourceStart":11043,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"t","sourceEn... | [] | [{"source":"hf x","source_end":11074,"source_start":11070,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨t, ht_mem, ht_int⟩","source_end":11066,"source_start":11043,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17688","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17691","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 42 | 5 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 589410fefd15b60b89c7b551e73657767279020d49e0db24a07c1e4be3855a52 | 1f48c92588e46044eec0900ea006568706c1b24216d8c24186b4fce291c00fc3 | 850f93374b68b415978e98ec99021eec51f038fcef2ed993eb0bb7d8e3d7dfd0 | 5f974300dd1082175abbbb84d842eaf73ad83ddcfe965e34fcb7c650074f1fbf |
cat-searcher/leandojo-benchmark-4-random | test | 4,174 | MeasureTheory.locallyIntegrableOn_of_locallyIntegrable_restrict | Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨u, hu_sub, hu_o, hu_mem⟩ := mem_nhds_iff.mp ht_mem | case intro.intro
X : Type u_1
Y : Type u_2
E : Type u_3
F : Type u_4
R : Type u_5
inst✝⁶ : MeasurableSpace X
inst✝⁵ : TopologicalSpace X
inst✝⁴ : MeasurableSpace Y
inst✝³ : TopologicalSpace Y
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedAddCommGroup F
f g : X → E
μ : Measure X
s : Set X
inst✝ : OpensMeasurableSpace X
h... | case intro.intro.intro.intro.intro
X : Type u_1
Y : Type u_2
E : Type u_3
F : Type u_4
R : Type u_5
inst✝⁶ : MeasurableSpace X
inst✝⁵ : TopologicalSpace X
inst✝⁴ : MeasurableSpace Y
inst✝³ : TopologicalSpace Y
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedAddCommGroup F
f g : X → E
μ : Measure X
s : Set X
inst✝ : OpensM... | ((:c MeasureTheory.IntegrableAtFilter) (:fv _uniq.17688) (:fv _uniq.17694) (:fv _uniq.17703) (:fv _uniq.17715) (:fv _uniq.17722) ((:c nhdsWithin) (:fv _uniq.17688) (:fv _uniq.17706) (:fv _uniq.18062) (:fv _uniq.17738)) (:fv _uniq.17735)) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"F","sexp":"(:sort (+ u_4 1))"},{"name":"R","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c MeasurableSpace) (:fv _uniq.17688))"},{"name":"inst✝⁵","sexp":"((:c TopologicalSpace) (:f... | (:app (:c MeasureTheory.IntegrableAtFilter) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 4 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17688","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17691","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"obtain","sourceEnd":11083,"sourceStart":11077,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":11087,"sourceStart":11084,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"u","sourceEn... | [] | [{"source":"mem_nhds_iff.mp ht_mem","source_end":11139,"source_start":11117,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨u, hu_sub, hu_o, hu_mem⟩","source_end":11113,"source_start":11084,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17688","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17691","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 42 | 6 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 72e4b9df49a1eef28f298f63eda12a06fbda42a448945d9be671864c32744e0b | 5f974300dd1082175abbbb84d842eaf73ad83ddcfe965e34fcb7c650074f1fbf | 28c849e1cae7c734cf1c39b7fe810caebe176fae24438e7696c9b97a0085232b | 5f0335df29ff5ed1997ca8b6b36686a37521d15da6c0087489c19975a318b001 |
cat-searcher/leandojo-benchmark-4-random | test | 4,175 | MeasureTheory.locallyIntegrableOn_of_locallyIntegrable_restrict | Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨_, <a>inter_mem_nhdsWithin</a> s (hu_o.mem_nhds hu_mem), ?_⟩ | case intro.intro.intro.intro.intro
X : Type u_1
Y : Type u_2
E : Type u_3
F : Type u_4
R : Type u_5
inst✝⁶ : MeasurableSpace X
inst✝⁵ : TopologicalSpace X
inst✝⁴ : MeasurableSpace Y
inst✝³ : TopologicalSpace Y
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedAddCommGroup F
f g : X → E
μ : Measure X
s : Set X
inst✝ : OpensM... | case intro.intro.intro.intro.intro
X : Type u_1
Y : Type u_2
E : Type u_3
F : Type u_4
R : Type u_5
inst✝⁶ : MeasurableSpace X
inst✝⁵ : TopologicalSpace X
inst✝⁴ : MeasurableSpace Y
inst✝³ : TopologicalSpace Y
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedAddCommGroup F
f g : X → E
μ : Measure X
s : Set X
inst✝ : OpensM... | ((:c MeasureTheory.IntegrableAtFilter) (:fv _uniq.17688) (:fv _uniq.17694) (:fv _uniq.17703) (:fv _uniq.17715) (:fv _uniq.17722) ((:c nhdsWithin) (:fv _uniq.17688) (:fv _uniq.17706) (:fv _uniq.18062) (:fv _uniq.17738)) (:fv _uniq.17735)) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"F","sexp":"(:sort (+ u_4 1))"},{"name":"R","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c MeasurableSpace) (:fv _uniq.17688))"},{"name":"inst✝⁵","sexp":"((:c TopologicalSpace) (:f... | (:app (:c MeasureTheory.IntegrableAtFilter) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 4 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17688","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17691","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":11148,"sourceStart":11142,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":11152,"sourceStart":11149,"tag":"atom"},{"children":[{"children":[{"source":"_","sourceEnd":11153,"sourceStart":11152,"tag":"atom"}],"kind":"Lean.Parser.Term.hole","source":"_","sourceEnd":11153,"s... | [] | [{"source":"⟨_, inter_mem_nhdsWithin s (hu_o.mem_nhds hu_mem), ?_⟩","source_end":11207,"source_start":11149,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17688","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17691","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 42 | 7 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 97d3eb3a845300ad2b10b401e882f80ff65557278adb871e31f41d7d4cc20b80 | 5f0335df29ff5ed1997ca8b6b36686a37521d15da6c0087489c19975a318b001 | 84e5a69f77a6b55d7f6b385be35031526bab2bc09d5379c9ff32b70da59f1808 | 3f003e2e0f68725650ebd508a968acaa02172a9bd8a6e3881efd18ad2a039916 |
cat-searcher/leandojo-benchmark-4-random | test | 4,176 | MeasureTheory.locallyIntegrableOn_of_locallyIntegrable_restrict | Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>MeasureTheory.IntegrableOn</a>, <a>MeasureTheory.Measure.restrict_restrict</a> hu_o.measurableSet, <a>Set.inter_comm</a>] using ht_int.mono_set hu_sub | case intro.intro.intro.intro.intro
X : Type u_1
Y : Type u_2
E : Type u_3
F : Type u_4
R : Type u_5
inst✝⁶ : MeasurableSpace X
inst✝⁵ : TopologicalSpace X
inst✝⁴ : MeasurableSpace Y
inst✝³ : TopologicalSpace Y
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedAddCommGroup F
f g : X → E
μ : Measure X
s : Set X
inst✝ : OpensM... | ((:c MeasureTheory.IntegrableOn) (:fv _uniq.17688) (:fv _uniq.17694) (:fv _uniq.17703) (:fv _uniq.17715) (:fv _uniq.17722) ((:c Inter.inter) ((:c Set) (:fv _uniq.17688)) ((:c Set.instInter) (:fv _uniq.17688)) (:fv _uniq.17738) (:fv _uniq.18218)) (:fv _uniq.17735)) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"F","sexp":"(:sort (+ u_4 1))"},{"name":"R","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c MeasurableSpace) (:fv _uniq.17688))"},{"name":"inst✝⁵","sexp":"((:c TopologicalSpace) (:f... | (:app (:c MeasureTheory.IntegrableOn) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 4 (:fv FV11))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17688","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17691","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simpa","sourceEnd":11215,"sourceStart":11210,"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":"IntegrableOn","source_end":11234,"source_start":11222,"syntax_kind":"ident"},{"source":"Measure.restrict_restrict hu_o.measurableSet","source_end":11280,"source_start":11236,"syntax_kind":"Lean.Parser.Term.app"},{"source":"inter_comm","source_end":11292,"source_start":11282,"syntax_kind":"ident"},{"source":... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.17688","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.17691","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 42 | 8 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9704714fab81b168294946d3e1b812610ef6d05e64d719af3ca98ab9e0dabe5d | 3f003e2e0f68725650ebd508a968acaa02172a9bd8a6e3881efd18ad2a039916 | cf79585f3a9dcd73467da5d78a130f68424d173a1a8c3ca971fc68467b6083c0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,177 | ENNReal.smul_sSup | Mathlib/Topology/Instances/ENNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [← <a>smul_one_mul</a> c (<a>SupSet.sSup</a> s), <a>ENNReal.mul_sSup</a>, <a>smul_one_mul</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
a b c✝ d : ℝ≥0∞
r p q : ℝ≥0
x y z ε ε₁ ε₂ : ℝ≥0∞
s✝ : Set ℝ≥0∞
R : Type u_4
inst✝¹ : SMul R ℝ≥0∞
inst✝ : IsScalarTower R ℝ≥0∞ ℝ≥0∞
s : Set ℝ≥0∞
c : R
⊢ c • sSup s = ⨆ i ∈ s, c • i | ((:c Eq) (:c ENNReal) ((:c HSMul.hSMul) (:fv _uniq.135076) (:c ENNReal) (:c ENNReal) ((:c instHSMul) (:fv _uniq.135076) (:c ENNReal) (:fv _uniq.135077)) (:fv _uniq.135080) ((:c SupSet.sSup) (:c ENNReal) ((:c ConditionallyCompleteLattice.toSupSet) (:c ENNReal) ((:c ConditionallyCompleteLinearOrder.toConditionallyComplet... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"a","sexp":"(:c ENNReal)"},{"name":"b","sexp":"(:c ENNReal)"},{"name":"c✝","sexp":"(:c ENNReal)"},{"name":"d","sexp":"(:c ENNReal)"},{"name":"r","sexp":"(:c NNReal)"},{"name":"p","sexp":"(:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:fv FV18)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:app (:c HSMul) (:arg :explicit 0 (:fv FV18)) (:arg :explicit 1 (:c ENNReal)) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.134689","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.134692","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":34849,"sourceStart":34842,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":34851,"sourceStart":34850,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children... | [] | [{"source":"smul_one_mul c (sSup s)","source_end":34878,"source_start":34855,"syntax_kind":"Lean.Parser.Term.app"},{"source":"ENNReal.mul_sSup","source_end":34896,"source_start":34880,"syntax_kind":"ident"},{"source":"smul_one_mul","source_end":34910,"source_start":34898,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.134689","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.134692","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 214 | 2 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | efb084af40fb34f3243c26e99408e021cc62c7f2f606cfa1505252e660a369e3 | 0d152c392dbffcaa7e86e3cb7d9e04ccb5e7eb6cd3b225620557c6d8fb62710b | ddea107132c7d06e3c3f175f4cc7196314d2d689f18c8efd234799e201e8f8f8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,178 | UniqueMul.of_image_filter | Mathlib/Algebra/Group/UniqueProds.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | specialize huH (<a>Finset.mem_image_of_mem</a> _ ha) (<a>Finset.mem_image_of_mem</a> _ hb) | G : Type u_1
H : Type u_2
inst✝² : Mul G
inst✝¹ : Mul H
A✝ B✝ : Finset G
a0 b0 : G
inst✝ : DecidableEq H
f : G →ₙ* H
A B : Finset G
aG bG : G
aH bH : H
hae : f aG = aH
hbe : f bG = bH
huH : UniqueMul (image (⇑f) A) (image (⇑f) B) aH bH
huG : UniqueMul (filter (fun x => f x = aH) A) (filter (fun x => f x = bH) B) aG bG
... | G : Type u_1
H : Type u_2
inst✝² : Mul G
inst✝¹ : Mul H
A✝ B✝ : Finset G
a0 b0 : G
inst✝ : DecidableEq H
f : G →ₙ* H
A B : Finset G
aG bG : G
aH bH : H
hae : f aG = aH
hbe : f bG = bH
huG : UniqueMul (filter (fun x => f x = aH) A) (filter (fun x => f x = bH) B) aG bG
a b : G
ha : a ∈ A
hb : b ∈ B
he : a * b = aG * bG
h... | ((:c And) ((:c Eq) (:fv _uniq.30116) (:fv _uniq.31029) (:fv _uniq.31017)) ((:c Eq) (:fv _uniq.30116) (:fv _uniq.31032) (:fv _uniq.31018))) | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Mul) (:fv _uniq.30116))"},{"name":"inst✝¹","sexp":"((:c Mul) (:fv _uniq.30119))"},{"name":"A✝","sexp":"((:c Finset) (:fv _uniq.30116))"},{"name":"B✝","sexp":"((:c Finset) (:fv _uniq.30116))"},{"name":"a0","sex... | (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV21)) (:arg :explicit 2 (:fv FV13)))) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV22)) (:arg :explicit 2 (:fv FV14))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30116","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30119","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"specialize","sourceEnd":10644,"sourceStart":10634,"tag":"atom"},{"children":[{"contextIndex":19,"semanticRole":"local","source":"huH","sourceEnd":10648,"sourceStart":10645,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":10650,"sourceStart":10649,"tag":"atom"},{"children":... | [] | [{"source":"huH (mem_image_of_mem _ ha) (mem_image_of_mem _ hb)","source_end":10696,"source_start":10645,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30116","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30119","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 40 | 4 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6a0453ae42dad50c5adb73900d2b46a9e8d87943bc089015c8fadff21b5fcf16 | 13818b1857541005f8505964f29588175f588586f3a2afa2f4831bf9ce9634ba | f287b7d2fba5a50c69e2952603abc557900e77241c7c2888aa8d875f6e2a7930 | 45cd7c7e9d4b8682a1b74d84ee3164d6cd5b5386ceea36fc34e25432ef44cf74 |
cat-searcher/leandojo-benchmark-4-random | test | 4,179 | UniqueMul.of_image_filter | Mathlib/Algebra/Group/UniqueProds.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>map_mul</a>, he, <a>map_mul</a>, hae, hbe] at huH | G : Type u_1
H : Type u_2
inst✝² : Mul G
inst✝¹ : Mul H
A✝ B✝ : Finset G
a0 b0 : G
inst✝ : DecidableEq H
f : G →ₙ* H
A B : Finset G
aG bG : G
aH bH : H
hae : f aG = aH
hbe : f bG = bH
huG : UniqueMul (filter (fun x => f x = aH) A) (filter (fun x => f x = bH) B) aG bG
a b : G
ha : a ∈ A
hb : b ∈ B
he : a * b = aG * bG
h... | G : Type u_1
H : Type u_2
inst✝² : Mul G
inst✝¹ : Mul H
A✝ B✝ : Finset G
a0 b0 : G
inst✝ : DecidableEq H
f : G →ₙ* H
A B : Finset G
aG bG : G
aH bH : H
hae : f aG = aH
hbe : f bG = bH
huG : UniqueMul (filter (fun x => f x = aH) A) (filter (fun x => f x = bH) B) aG bG
a b : G
ha : a ∈ A
hb : b ∈ B
he : a * b = aG * bG
h... | ((:c And) ((:c Eq) (:fv _uniq.30116) (:fv _uniq.31029) (:fv _uniq.31017)) ((:c Eq) (:fv _uniq.30116) (:fv _uniq.31032) (:fv _uniq.31018))) | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Mul) (:fv _uniq.30116))"},{"name":"inst✝¹","sexp":"((:c Mul) (:fv _uniq.30119))"},{"name":"A✝","sexp":"((:c Finset) (:fv _uniq.30116))"},{"name":"B✝","sexp":"((:c Finset) (:fv _uniq.30116))"},{"name":"a0","sex... | (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV20)) (:arg :explicit 2 (:fv FV13)))) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV21)) (:arg :explicit 2 (:fv FV14))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30116","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30119","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":10701,"sourceStart":10699,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10703,"sourceStart":10702,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":10706,"sourceSt... | [] | [{"source":"map_mul","source_end":10714,"source_start":10707,"syntax_kind":"ident"},{"source":"huH","source_end":10745,"source_start":10742,"syntax_kind":"ident"},{"source":"he","source_end":10718,"source_start":10716,"syntax_kind":"ident"},{"source":"map_mul","source_end":10727,"source_start":10720,"syntax_kind":"iden... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30116","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30119","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 40 | 5 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 175f2fce700a8ea4b817ddbdc2f419ea9740dcdfa511346a2a8744200ac9b7d9 | 45cd7c7e9d4b8682a1b74d84ee3164d6cd5b5386ceea36fc34e25432ef44cf74 | 859c169bebf0a7b2c248aa6a408b6e03b1e034b527ae09becce57a1d76711d54 | 6d5d212581d33b91556a071434215c72889115792e1ada43f02ece45a3773627 |
cat-searcher/leandojo-benchmark-4-random | test | 4,180 | UniqueMul.of_image_filter | Mathlib/Algebra/Group/UniqueProds.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine huG ?_ ?_ he <;> rw [<a>Finset.mem_filter</a>] | G : Type u_1
H : Type u_2
inst✝² : Mul G
inst✝¹ : Mul H
A✝ B✝ : Finset G
a0 b0 : G
inst✝ : DecidableEq H
f : G →ₙ* H
A B : Finset G
aG bG : G
aH bH : H
hae : f aG = aH
hbe : f bG = bH
huG : UniqueMul (filter (fun x => f x = aH) A) (filter (fun x => f x = bH) B) aG bG
a b : G
ha : a ∈ A
hb : b ∈ B
he : a * b = aG * bG
h... | case refine_1
G : Type u_1
H : Type u_2
inst✝² : Mul G
inst✝¹ : Mul H
A✝ B✝ : Finset G
a0 b0 : G
inst✝ : DecidableEq H
f : G →ₙ* H
A B : Finset G
aG bG : G
aH bH : H
hae : f aG = aH
hbe : f bG = bH
huG : UniqueMul (filter (fun x => f x = aH) A) (filter (fun x => f x = bH) B) aG bG
a b : G
ha : a ∈ A
hb : b ∈ B
he : a *... | ((:c And) ((:c Eq) (:fv _uniq.30116) (:fv _uniq.31029) (:fv _uniq.31017)) ((:c Eq) (:fv _uniq.30116) (:fv _uniq.31032) (:fv _uniq.31018))) | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Mul) (:fv _uniq.30116))"},{"name":"inst✝¹","sexp":"((:c Mul) (:fv _uniq.30119))"},{"name":"A✝","sexp":"((:c Finset) (:fv _uniq.30116))"},{"name":"B✝","sexp":"((:c Finset) (:fv _uniq.30116))"},{"name":"a0","sex... | (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV20)) (:arg :explicit 2 (:fv FV13)))) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV21)) (:arg :explicit 2 (:fv FV14))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30116","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30119","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"source":"refine","sourceEnd":10754,"sourceStart":10748,"tag":"atom"},{"children":[{"contextIndex":19,"semanticRole":"local","source":"huG","sourceEnd":10758,"sourceStart":10755,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":10760,"sourceStart":10759,"tag":"atom"},{"c... | [] | [{"source":"huG ?_ ?_ he","source_end":10767,"source_start":10755,"syntax_kind":"Lean.Parser.Term.app"},{"source":"mem_filter","source_end":10786,"source_start":10776,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30116","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30119","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 40 | 12 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bd005f06e3fcaf7ddaa710aa96b6a3f5a33c2daf350f3073856e8781717b53c2 | 6d5d212581d33b91556a071434215c72889115792e1ada43f02ece45a3773627 | 0123f8f34b700e1de566af16ac8ddf90451f1af51e7f8aa264f31c9ae846928e | 020af0e6df0434915d4ca8b35a8c87f1b43ba63fdb38c90c3b0756f1f5f7ea80 |
cat-searcher/leandojo-benchmark-4-random | test | 4,182 | Nat.prod_pow_pos_of_zero_not_mem_support | Mathlib/Algebra/BigOperators/Finsupp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | subst H | α : Type u_1
ι : Type u_2
γ : Type u_3
A : Type u_4
B : Type u_5
C : Type u_6
inst✝² : AddCommMonoid A
inst✝¹ : AddCommMonoid B
inst✝ : AddCommMonoid C
t : ι → A → C
h0 : ∀ (i : ι), t i 0 = 0
h1 : ∀ (i : ι) (x y : A), t i (x + y) = t i x + t i y
s : Finset α
f✝ : α → ι →₀ A
i : ι
g : ι →₀ A
k : ι → A → γ → B
x : γ
β : ... | α : Type u_1
ι : Type u_2
γ : Type u_3
A : Type u_4
B : Type u_5
C : Type u_6
inst✝² : AddCommMonoid A
inst✝¹ : AddCommMonoid B
inst✝ : AddCommMonoid C
t : ι → A → C
h0 : ∀ (i : ι), t i 0 = 0
h1 : ∀ (i : ι) (x y : A), t i (x + y) = t i x + t i y
s : Finset α
f✝ : α → ι →₀ A
i : ι
g : ι →₀ A
k : ι → A → γ → B
x : γ
β : ... | (:c False) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"A","sexp":"(:sort (+ u_4 1))"},{"name":"B","sexp":"(:sort (+ u_5 1))"},{"name":"C","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝²","sexp":"((:c AddCommMonoid) (:fv _uniq.412173))"},{"name":"ins... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.412164","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.412167","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"subst","sourceEnd":32169,"sourceStart":32164,"tag":"atom"},{"children":[{"contextIndex":32,"semanticRole":"local","source":"H","sourceEnd":32171,"sourceStart":32170,"tag":"identifier"}],"kind":"null","source":"H","sourceEnd":32171,"sourceStart":32170,"tag":"node"}],"kind":"Lean.Parser.Tactic.sub... | [] | [{"source":"H","source_end":32171,"source_start":32170,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.412164","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.412167","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 205 | 4 | exact | true | 1 | 32 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 52b528ea936d799c46b0ef993483628b1845318081bbf3a898a0b400728d211e | 65e3ca0c68ae3337be8cae16fa0313eb0ab7b89b68f8ea3257bf87795a02eb7e | 8e9125caa8154c4ffff9f8739939eb0de8378a15e141e3ddb3963b543f3cb6d7 | 23de579bab4275cdb9f52b436c9918966d248fc1f5d075fe33b7e1d5761e08cb |
cat-searcher/leandojo-benchmark-4-random | test | 4,183 | Nat.prod_pow_pos_of_zero_not_mem_support | Mathlib/Algebra/BigOperators/Finsupp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hf ha | α : Type u_1
ι : Type u_2
γ : Type u_3
A : Type u_4
B : Type u_5
C : Type u_6
inst✝² : AddCommMonoid A
inst✝¹ : AddCommMonoid B
inst✝ : AddCommMonoid C
t : ι → A → C
h0 : ∀ (i : ι), t i 0 = 0
h1 : ∀ (i : ι) (x y : A), t i (x + y) = t i x + t i y
s : Finset α
f✝ : α → ι →₀ A
i : ι
g : ι →₀ A
k : ι → A → γ → B
x : γ
β : ... | (:c False) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"A","sexp":"(:sort (+ u_4 1))"},{"name":"B","sexp":"(:sort (+ u_5 1))"},{"name":"C","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝²","sexp":"((:c AddCommMonoid) (:fv _uniq.412173))"},{"name":"ins... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.412164","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.412167","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":32178,"sourceStart":32173,"tag":"atom"},{"children":[{"contextIndex":29,"semanticRole":"local","source":"hf","sourceEnd":32181,"sourceStart":32179,"tag":"identifier"},{"children":[{"contextIndex":30,"semanticRole":"local","source":"ha","sourceEnd":32184,"sourceStart":32182,"ta... | [] | [{"source":"hf ha","source_end":32184,"source_start":32179,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.412164","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.412167","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 205 | 6 | exact | true | 1 | 30 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dc2707b2bd6a54c0c63173a12e6ce3bc1f0e72a03bf73800f2d0809298120c72 | 23de579bab4275cdb9f52b436c9918966d248fc1f5d075fe33b7e1d5761e08cb | 5d2100d9a223f6d3cbe4b88bdefc7378ce3173d4c56cd6370354f709b6b2bbdf | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,184 | Matrix.PosSemidef.fromBlocks₁₁ | Mathlib/LinearAlgebra/Matrix/SchurComplement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Matrix.PosSemidef</a>, <a>Matrix.IsHermitian.fromBlocks₁₁</a> _ _ hA.1] | l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible A
⊢ (fromBl... | l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible A
⊢ ((D - B... | ((:c Iff) ((:c Matrix.PosSemidef) ((:c Sum) (:fv _uniq.448121) (:fv _uniq.448124)) (:fv _uniq.448130) ((:c instFintypeSum) (:fv _uniq.448121) (:fv _uniq.448124) (:fv _uniq.451887) (:fv _uniq.451889)) (:fv _uniq.448133) (:fv _uniq.448136) (:fv _uniq.448219) (:fv _uniq.448325) ((:c Matrix.fromBlocks) (:fv _uniq.448121) (... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.448130))"},{"name":"inst✝⁶","sexp":"((:c PartialOrder) (:fv _uniq.4... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Matrix.PosSemidef) (:arg :implicit-type 0 (:app (:c Sum) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))) (:arg :implicit-type 1 (:fv FV4)) (:arg :instance 2 (:instance-of (:app (:c Fintype) (:arg :explicit 0 (:app (:c Sum) (:arg :explicit 0 (:fv FV1)) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":28605,"sourceStart":28603,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28607,"sourceStart":28606,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Matrix.PosSemide... | [] | [{"source":"PosSemidef","source_end":28617,"source_start":28607,"syntax_kind":"ident"},{"source":"IsHermitian.fromBlocks₁₁ _ _ hA.1","source_end":28656,"source_start":28619,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 98 | 4 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f793836877718659fec62560fe5dd99259a593c74faed82b9c0251e3fbd813d9 | 79b892dfb66b37152486626f43fae7d5551a971e1e2ffa628bc8e67cf51d54e0 | 2eebb993229dcde3651108fe34f123e3383276c7767c7cb6320b500187c9839a | 66fa2aa59075d00cd1396734b65d284268539901e4f251b3abc7839483a22508 |
cat-searcher/leandojo-benchmark-4-random | test | 4,185 | Matrix.PosSemidef.fromBlocks₁₁ | Mathlib/LinearAlgebra/Matrix/SchurComplement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible A
⊢ ((D - B... | case mp
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible A
⊢... | ((:c Iff) ((:c And) ((:c Matrix.IsHermitian) (:fv _uniq.448130) (:fv _uniq.448124) ((:c InvolutiveStar.toStar) (:fv _uniq.448130) ((:c StarAddMonoid.toInvolutiveStar) (:fv _uniq.448130) ((:c AddMonoidWithOne.toAddMonoid) (:fv _uniq.448130) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.448130) ((:c Ring.toAddGroup... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.448130))"},{"name":"inst✝⁶","sexp":"((:c PartialOrder) (:fv _uniq.4... | (:app (:c Iff) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c Matrix.IsHermitian) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c Star) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 3 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:app (:c Matr... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"constructor","sourceEnd":28671,"sourceStart":28660,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":28671,"sourceStart":28660,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 98 | 8 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b438685cc09da941f3587a2abcab430785e23ca7dceacc83622c121343369c15 | 66fa2aa59075d00cd1396734b65d284268539901e4f251b3abc7839483a22508 | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | d5771cb6446d68a695e2ef11d70f629d9362e4285ea172fd4ec886aa84b3da7a |
cat-searcher/leandojo-benchmark-4-random | test | 4,186 | Matrix.PosSemidef.fromBlocks₁₁ | Mathlib/LinearAlgebra/Matrix/SchurComplement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine fun h => ⟨h.1, fun x => ?_⟩ | case mp
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible A
⊢... | case mp
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible A
h... | (:forall _ ((:c And) ((:c Matrix.IsHermitian) (:fv _uniq.448130) (:fv _uniq.448124) ((:c InvolutiveStar.toStar) (:fv _uniq.448130) ((:c StarAddMonoid.toInvolutiveStar) (:fv _uniq.448130) ((:c AddMonoidWithOne.toAddMonoid) (:fv _uniq.448130) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.448130) ((:c Ring.toAddGrou... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.448130))"},{"name":"inst✝⁶","sexp":"((:c PartialOrder) (:fv _uniq.4... | (:forall _ :explicit (:app (:c And) (:arg :explicit 0 (:app (:c Matrix.IsHermitian) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c Star) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 3 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":28683,"sourceStart":28677,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":28687,"sourceStart":28684,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":28689,"sourceStart":28688,"tag":"identifier"}],"kind":"null","source":"h"... | [] | [{"source":"fun h => ⟨h.1, fun x => ?_⟩","source_end":28715,"source_start":28684,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 98 | 13 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 12165b0751fcd90e572f224d0b7d940b0b965979d0fdafb86adbf8dc8d28bfdc | c011370d1fb8c361d708989058f53177cfcb2df3b9cf3d9eaa8e1b2367efe01f | 458ee825b5bda93f33acf7d86759876f677555e2992f7d7b167803b02fb19abd | dda067e5c941603d632ce8ebda3fe32d9da8fce4440d21c385d566f842933c3d |
cat-searcher/leandojo-benchmark-4-random | test | 4,187 | Matrix.PosSemidef.fromBlocks₁₁ | Mathlib/LinearAlgebra/Matrix/SchurComplement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have := h.2 (-((A⁻¹ * B) *ᵥ x) ⊕ᵥ x) | case mp
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible A
h... | case mp
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible A
h... | ((:c LE.le) (:fv _uniq.448130) ((:c Preorder.toLE) (:fv _uniq.448130) ((:c PartialOrder.toPreorder) (:fv _uniq.448130) (:fv _uniq.448136))) ((:c OfNat.ofNat) (:fv _uniq.448130) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.448130) ((:c CommMonoidWithZero.toZero) (:fv _uniq.448130) ((:c CommSemiring.toCommMonoidWithZero) (:fv... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.448130))"},{"name":"inst✝⁶","sexp":"((:c PartialOrder) (:fv _uniq.4... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV4)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":28724,"sourceStart":28720,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":28725,"sourceStart":28725,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":28725,"sourceStart":28725,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"h.2 (-((A⁻¹ * B) *ᵥ x) ⊕ᵥ x)","source_end":28765,"source_start":28728,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 98 | 14 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0b07a7db3e30a27849cefa517f017eafdf311718bdd9a234945986150177af71 | dda067e5c941603d632ce8ebda3fe32d9da8fce4440d21c385d566f842933c3d | 91be8be31f1995cb545285f1d3bc6cebe2b61815722ed910f0ceab4f5fa52a65 | d9628956d71f6b5d0eaa24c9060c53eeb75a87b726c151079d553164a2a4ff9e |
cat-searcher/leandojo-benchmark-4-random | test | 4,188 | Matrix.PosSemidef.fromBlocks₁₁ | Mathlib/LinearAlgebra/Matrix/SchurComplement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Matrix.dotProduct_mulVec</a>, <a>Matrix.schur_complement_eq₁₁</a> B D _ _ hA.1, <a>neg_add_self</a>, <a>Matrix.dotProduct_zero</a>, <a>zero_add</a>] at this | case mp
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible A
h... | case mp
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible A
h... | ((:c LE.le) (:fv _uniq.448130) ((:c Preorder.toLE) (:fv _uniq.448130) ((:c PartialOrder.toPreorder) (:fv _uniq.448130) (:fv _uniq.448136))) ((:c OfNat.ofNat) (:fv _uniq.448130) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.448130) ((:c CommMonoidWithZero.toZero) (:fv _uniq.448130) ((:c CommSemiring.toCommMonoidWithZero) (:fv... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.448130))"},{"name":"inst✝⁶","sexp":"((:c PartialOrder) (:fv _uniq.4... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV4)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":28772,"sourceStart":28770,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28774,"sourceStart":28773,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Matrix.dotProduc... | [] | [{"source":"dotProduct_mulVec","source_end":28791,"source_start":28774,"syntax_kind":"ident"},{"source":"this","source_end":28887,"source_start":28883,"syntax_kind":"ident"},{"source":"schur_complement_eq₁₁ B D _ _ hA.1","source_end":28831,"source_start":28793,"syntax_kind":"Lean.Parser.Term.app"},{"source":"neg_add_se... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 98 | 15 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 79e76d2e21d6010fc49d8caa34ab4206c8872f5475733395b59591a262d4dcdc | d9628956d71f6b5d0eaa24c9060c53eeb75a87b726c151079d553164a2a4ff9e | 9e982654c258765284d2a432ce7891b6aba336c19b117816111267337e7cdf9d | 90b05fa2dce80b6ce394a70a2e6ade521fc8302391056c135f9005977e723819 |
cat-searcher/leandojo-benchmark-4-random | test | 4,189 | Matrix.PosSemidef.fromBlocks₁₁ | Mathlib/LinearAlgebra/Matrix/SchurComplement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Matrix.dotProduct_mulVec</a>] | case mp
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible A
h... | case mp
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible A
h... | ((:c LE.le) (:fv _uniq.448130) ((:c Preorder.toLE) (:fv _uniq.448130) ((:c PartialOrder.toPreorder) (:fv _uniq.448130) (:fv _uniq.448136))) ((:c OfNat.ofNat) (:fv _uniq.448130) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.448130) ((:c CommMonoidWithZero.toZero) (:fv _uniq.448130) ((:c CommSemiring.toCommMonoidWithZero) (:fv... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.448130))"},{"name":"inst✝⁶","sexp":"((:c PartialOrder) (:fv _uniq.4... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV4)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":28894,"sourceStart":28892,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28896,"sourceStart":28895,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Matrix.dotProduc... | [] | [{"source":"dotProduct_mulVec","source_end":28913,"source_start":28896,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 98 | 22 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d9a94027667503af33855016e49e6d9365092825d3ea0495742254e6c15afb23 | 90b05fa2dce80b6ce394a70a2e6ade521fc8302391056c135f9005977e723819 | 496548d2f0f78fa6a259a1b60b658869a0224928b2fa2c7066bb43634173b319 | 5d13162f190c4c99770e8d4ad66921c271901f4f7b02e0e6ef3c608d88a1d2df |
cat-searcher/leandojo-benchmark-4-random | test | 4,190 | Matrix.PosSemidef.fromBlocks₁₁ | Mathlib/LinearAlgebra/Matrix/SchurComplement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact this | case mp
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible A
h... | ((:c LE.le) (:fv _uniq.448130) ((:c Preorder.toLE) (:fv _uniq.448130) ((:c PartialOrder.toPreorder) (:fv _uniq.448130) (:fv _uniq.448136))) ((:c OfNat.ofNat) (:fv _uniq.448130) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.448130) ((:c CommMonoidWithZero.toZero) (:fv _uniq.448130) ((:c CommSemiring.toCommMonoidWithZero) (:fv... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.448130))"},{"name":"inst✝⁶","sexp":"((:c PartialOrder) (:fv _uniq.4... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV4)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":28921,"sourceStart":28916,"tag":"atom"},{"contextIndex":20,"semanticRole":"local","source":"this","sourceEnd":28926,"sourceStart":28922,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact this","sourceEnd":28926,"sourceStart":28916,"tag":"node"} | [] | [{"source":"this","source_end":28926,"source_start":28922,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 98 | 26 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 604ec07eb1ad40e95edaf46013c0e244d51d1806754ca987db2ac2c1f8fd90a3 | 5d13162f190c4c99770e8d4ad66921c271901f4f7b02e0e6ef3c608d88a1d2df | 4bf05ffe5319fff5c45a2736953c2c5d2fee7a5728be1458b77f126cd265f282 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,191 | Matrix.PosSemidef.fromBlocks₁₁ | Mathlib/LinearAlgebra/Matrix/SchurComplement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine fun h => ⟨h.1, fun x => ?_⟩ | case mpr
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible A
... | case mpr
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible A
... | (:forall _ ((:c Matrix.PosSemidef) (:fv _uniq.448124) (:fv _uniq.448130) (:fv _uniq.451889) (:fv _uniq.448133) (:fv _uniq.448136) (:fv _uniq.448219) (:fv _uniq.448325) ((:c HSub.hSub) ((:c Matrix) (:fv _uniq.448124) (:fv _uniq.448124) (:fv _uniq.448130)) ((:c Matrix) (:fv _uniq.448124) (:fv _uniq.448124) (:fv _uniq.448... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.448130))"},{"name":"inst✝⁶","sexp":"((:c PartialOrder) (:fv _uniq.4... | (:forall _ :explicit (:app (:c Matrix.PosSemidef) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV4)) (:arg :instance 2 (:instance-of (:app (:c Fintype) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 3 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV4))))) (:arg :instance 4 (:instance-of (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":28938,"sourceStart":28932,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":28942,"sourceStart":28939,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":28944,"sourceStart":28943,"tag":"identifier"}],"kind":"null","source":"h"... | [] | [{"source":"fun h => ⟨h.1, fun x => ?_⟩","source_end":28970,"source_start":28939,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 98 | 31 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e8009011be8d93d04e8fd5ce69f94271987c8b91363c2565b577b8687079a6e6 | 05d93a2ccd7c3e194c063ae383ea22e6aa2bd5d3beac9a01762f39d028b95fcb | 458ee825b5bda93f33acf7d86759876f677555e2992f7d7b167803b02fb19abd | fcfa271a7f230172f674930a3d3eae916b9124cd76310bd32d47555a4c493ef3 |
cat-searcher/leandojo-benchmark-4-random | test | 4,192 | Matrix.PosSemidef.fromBlocks₁₁ | Mathlib/LinearAlgebra/Matrix/SchurComplement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Matrix.dotProduct_mulVec</a>, ← <a>Sum.elim_comp_inl_inr</a> x, <a>Matrix.schur_complement_eq₁₁</a> B D _ _ hA.1] | case mpr
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible A
... | case mpr
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible A
... | ((:c LE.le) (:fv _uniq.448130) ((:c Preorder.toLE) (:fv _uniq.448130) ((:c PartialOrder.toPreorder) (:fv _uniq.448130) (:fv _uniq.448136))) ((:c OfNat.ofNat) (:fv _uniq.448130) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.448130) ((:c CommMonoidWithZero.toZero) (:fv _uniq.448130) ((:c CommSemiring.toCommMonoidWithZero) (:fv... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.448130))"},{"name":"inst✝⁶","sexp":"((:c PartialOrder) (:fv _uniq.4... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV4)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":28977,"sourceStart":28975,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28979,"sourceStart":28978,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Matrix.dotProduc... | [] | [{"source":"dotProduct_mulVec","source_end":28996,"source_start":28979,"syntax_kind":"ident"},{"source":"Sum.elim_comp_inl_inr x","source_end":29025,"source_start":29002,"syntax_kind":"Lean.Parser.Term.app"},{"source":"schur_complement_eq₁₁ B D _ _ hA.1","source_end":29065,"source_start":29027,"syntax_kind":"Lean.Parse... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 98 | 32 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 82f82b23728c9304389dd7e27722d84db9e25d20b16fa2d779338581a0f25a1f | fcfa271a7f230172f674930a3d3eae916b9124cd76310bd32d47555a4c493ef3 | 70d9d74f21bb212b2cbc618000644953065888aa21c706b74f52240baf59cc6d | 4cd6ee28a830fd930dc41e826425422dd839d5f45e8ae33250ccc595c6b23f1b |
cat-searcher/leandojo-benchmark-4-random | test | 4,193 | Matrix.PosSemidef.fromBlocks₁₁ | Mathlib/LinearAlgebra/Matrix/SchurComplement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>le_add_of_nonneg_of_le</a> | case mpr
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible A
... | case mpr.ha
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible... | ((:c LE.le) (:fv _uniq.448130) ((:c Preorder.toLE) (:fv _uniq.448130) ((:c PartialOrder.toPreorder) (:fv _uniq.448130) (:fv _uniq.448136))) ((:c OfNat.ofNat) (:fv _uniq.448130) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.448130) ((:c CommMonoidWithZero.toZero) (:fv _uniq.448130) ((:c CommSemiring.toCommMonoidWithZero) (:fv... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.448130))"},{"name":"inst✝⁶","sexp":"((:c PartialOrder) (:fv _uniq.4... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV4)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"apply","sourceEnd":29076,"sourceStart":29071,"tag":"atom"},{"name":"le_add_of_nonneg_of_le","semanticRole":"global","source":"le_add_of_nonneg_of_le","sourceEnd":29099,"sourceStart":29077,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply le_add_of_nonneg_of_le","sourceEnd":2... | [] | [{"source":"le_add_of_nonneg_of_le","source_end":29099,"source_start":29077,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 98 | 37 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c4b00d72132c3664efb4eed0b9cf484178e09ba52fa9a39e5f639e4fd7fbf37a | 4cd6ee28a830fd930dc41e826425422dd839d5f45e8ae33250ccc595c6b23f1b | d694a742179ebfc79c9e2e205be2d7be9ba2dbbabaf59ddffac509f3a596cfa2 | 3a866f2d5550d108a4be05941033ce0a5852c823e0b794669985743ffa7039c8 |
cat-searcher/leandojo-benchmark-4-random | test | 4,194 | Matrix.PosSemidef.fromBlocks₁₁ | Mathlib/LinearAlgebra/Matrix/SchurComplement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Matrix.dotProduct_mulVec</a>] | case mpr.ha
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible... | case mpr.ha
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible... | ((:c LE.le) (:fv _uniq.448130) ((:c Preorder.toLE) (:fv _uniq.448130) ((:c PartialOrder.toPreorder) (:fv _uniq.448130) (:fv _uniq.448136))) ((:c OfNat.ofNat) (:fv _uniq.448130) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.448130) ((:c AddZeroClass.toZero) (:fv _uniq.448130) ((:c AddMonoid.toAddZeroClass) (:fv _uniq.448130) ... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.448130))"},{"name":"inst✝⁶","sexp":"((:c PartialOrder) (:fv _uniq.4... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV4)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":29109,"sourceStart":29107,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":29111,"sourceStart":29110,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":29114,"sourceSt... | [] | [{"source":"dotProduct_mulVec","source_end":29132,"source_start":29115,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 98 | 42 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9f7a85d890a8320213f50e5ba9cddcba2e24a7ad55d922e849ec8fd005ed9f6c | de75725622ac787f8848428a88fe5e22d69eaa4739cb06af95b0a985284b95ac | 445cd3ae0ada887e13ec87f1eb9f15407d0e262c38eb1764f84d6bc6a47973da | 86cc1416ecf69c2c407f4d9b0bf43f2b1252126d7521be165f8efbc6ba08b51c |
cat-searcher/leandojo-benchmark-4-random | test | 4,195 | Matrix.PosSemidef.fromBlocks₁₁ | Mathlib/LinearAlgebra/Matrix/SchurComplement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply hA.posSemidef.2 | case mpr.ha
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertible... | ((:c LE.le) (:fv _uniq.448130) ((:c Preorder.toLE) (:fv _uniq.448130) ((:c PartialOrder.toPreorder) (:fv _uniq.448130) (:fv _uniq.448136))) ((:c OfNat.ofNat) (:fv _uniq.448130) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.448130) ((:c AddZeroClass.toZero) (:fv _uniq.448130) ((:c AddMonoid.toAddZeroClass) (:fv _uniq.448130) ... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.448130))"},{"name":"inst✝⁶","sexp":"((:c PartialOrder) (:fv _uniq.4... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV4)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"apply","sourceEnd":29145,"sourceStart":29140,"tag":"atom"},{"children":[{"source":"hA.posSemidef","sourceEnd":29159,"sourceStart":29146,"tag":"identifier"},{"source":".","sourceEnd":29160,"sourceStart":29159,"tag":"atom"},{"children":[{"source":"2","sourceEnd":29161,"sourceStart":29160,"tag":"at... | [] | [{"source":"hA.posSemidef.2","source_end":29161,"source_start":29146,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 98 | 45 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f29c3c3253325b90de08a62d96acd0f34bb05419c182c28c50ebd47023e4f3cd | 86cc1416ecf69c2c407f4d9b0bf43f2b1252126d7521be165f8efbc6ba08b51c | 17eae6f7e617f4c01528684f589c1984a26f0ac121ad3601b2522f07e712fc67 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,196 | Matrix.PosSemidef.fromBlocks₁₁ | Mathlib/LinearAlgebra/Matrix/SchurComplement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Matrix.dotProduct_mulVec</a> (<a>Star.star</a> (x ∘ <a>Sum.inr</a>))] | case mpr.hbc
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertibl... | case mpr.hbc
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertibl... | ((:c LE.le) (:fv _uniq.448130) ((:c Preorder.toLE) (:fv _uniq.448130) ((:c PartialOrder.toPreorder) (:fv _uniq.448130) (:fv _uniq.448136))) ((:c OfNat.ofNat) (:fv _uniq.448130) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.448130) ((:c CommMonoidWithZero.toZero) (:fv _uniq.448130) ((:c CommSemiring.toCommMonoidWithZero) (:fv... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.448130))"},{"name":"inst✝⁶","sexp":"((:c PartialOrder) (:fv _uniq.4... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV4)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":29171,"sourceStart":29169,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":29173,"sourceStart":29172,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":29176,"sourceSt... | [] | [{"source":"dotProduct_mulVec (star (x ∘ Sum.inr))","source_end":29217,"source_start":29177,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 98 | 50 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4648e4a80ba17fccb890af71da4aed9ef3fef34810f5997580081d0431e5b25c | c5bee4a36e990e13ad409e1d2efe4558ed1d4b80883aa9bfd3c70bfdd7a47505 | 96eb020ff7f732bd0e425fa5d54235321d8244490623325c7a69a9fd43c0a416 | 483a97a4c0611d0dc62a5e3703eb3c09913b6a2d4862acaf2358be6de23ec032 |
cat-searcher/leandojo-benchmark-4-random | test | 4,197 | Matrix.PosSemidef.fromBlocks₁₁ | Mathlib/LinearAlgebra/Matrix/SchurComplement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply h.2 | case mpr.hbc
l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
𝕜 : Type u_5
inst✝⁷ : CommRing 𝕜
inst✝⁶ : PartialOrder 𝕜
inst✝⁵ : StarRing 𝕜
inst✝⁴ : StarOrderedRing 𝕜
inst✝³ : Fintype m
inst✝² : DecidableEq m
inst✝¹ : Fintype n
A : Matrix m m 𝕜
B : Matrix m n 𝕜
D : Matrix n n 𝕜
hA : A.PosDef
inst✝ : Invertibl... | ((:c LE.le) (:fv _uniq.448130) ((:c Preorder.toLE) (:fv _uniq.448130) ((:c PartialOrder.toPreorder) (:fv _uniq.448130) (:fv _uniq.448136))) ((:c OfNat.ofNat) (:fv _uniq.448130) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.448130) ((:c CommMonoidWithZero.toZero) (:fv _uniq.448130) ((:c CommSemiring.toCommMonoidWithZero) (:fv... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"𝕜","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.448130))"},{"name":"inst✝⁶","sexp":"((:c PartialOrder) (:fv _uniq.4... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV4)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"apply","sourceEnd":29230,"sourceStart":29225,"tag":"atom"},{"children":[{"contextIndex":18,"semanticRole":"local","source":"h","sourceEnd":29232,"sourceStart":29231,"tag":"identifier"},{"source":".","sourceEnd":29233,"sourceStart":29232,"tag":"atom"},{"children":[{"source":"2","sourceEnd":29234,... | [] | [{"source":"h.2","source_end":29234,"source_start":29231,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.448118","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.448121","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 98 | 53 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 223da1beda02320da77d5307119a40c67d883e03ae9ada7fe1a3a3d579b67ebe | 483a97a4c0611d0dc62a5e3703eb3c09913b6a2d4862acaf2358be6de23ec032 | c7fdd5f2ad899a0915ba794ff12c1c6be526087b14587949fe8a9f6229ae1804 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,198 | Function.mulSupport_update_of_ne_one | Mathlib/Algebra/Group/Support.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext a | α : Type u_1
β : Type u_2
A : Type u_3
B : Type u_4
M : Type u_5
N : Type u_6
P : Type u_7
G : Type u_8
inst✝³ : One M
inst✝² : One N
inst✝¹ : One P
inst✝ : DecidableEq α
f : α → M
x : α
y : M
hy : y ≠ 1
⊢ mulSupport (update f x y) = insert x (mulSupport f) | case h
α : Type u_1
β : Type u_2
A : Type u_3
B : Type u_4
M : Type u_5
N : Type u_6
P : Type u_7
G : Type u_8
inst✝³ : One M
inst✝² : One N
inst✝¹ : One P
inst✝ : DecidableEq α
f : α → M
x : α
y : M
hy : y ≠ 1
a : α
⊢ a ∈ mulSupport (update f x y) ↔ a ∈ insert x (mulSupport f) | ((:c Eq) ((:c Set) (:fv _uniq.2873)) ((:c Function.mulSupport) (:fv _uniq.2873) (:fv _uniq.2885) (:fv _uniq.2897) ((:c Function.update) (:fv _uniq.2873) (:lambda _ (:fv _uniq.2873) (:fv _uniq.2885)) (:fv _uniq.3107) (:fv _uniq.3108) (:fv _uniq.3109) (:fv _uniq.3110))) ((:c Insert.insert) (:fv _uniq.2873) ((:c Set) (:fv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"A","sexp":"(:sort (+ u_3 1))"},{"name":"B","sexp":"(:sort (+ u_4 1))"},{"name":"M","sexp":"(:sort (+ u_5 1))"},{"name":"N","sexp":"(:sort (+ u_6 1))"},{"name":"P","sexp":"(:sort (+ u_7 1))"},{"name":"G","sexp":"(:sort (+ u_8 1))"}... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Function.mulSupport) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV4)) (:arg :instance 2 (:instance-of (:app (:c One) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 3 (:app (:c Function.upda... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2873","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2876","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"ext","sourceEnd":3480,"sourceStart":3477,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":3482,"sourceStart":3481,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"a","sourceEnd":3482,"sourceStart":3481,"tag":"nod... | [{"role":"fresh_name","source":"a","source_end":3482,"source_start":3481,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2873","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2876","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 33 | 4 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9c1b0d761b986e0232e620621318c6275d0c30cf735245d76b8a1101eeb03117 | a69d2dae8ec5159a28ce855443fec732bbef38e5c28139a0ec45d9afb51975ac | 5b5ebc7422a51c4513cd3c976db7ca97ca10150d1cf8ecd0c4817a56e5071333 | 457ebaafa0127b82285b3dfe707440f0555c6df0da42c639c1810847052b0827 |
cat-searcher/leandojo-benchmark-4-random | test | 4,199 | Function.mulSupport_update_of_ne_one | Mathlib/Algebra/Group/Support.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>eq_or_ne</a> a x with rfl | hne <;> simp [*] | case h
α : Type u_1
β : Type u_2
A : Type u_3
B : Type u_4
M : Type u_5
N : Type u_6
P : Type u_7
G : Type u_8
inst✝³ : One M
inst✝² : One N
inst✝¹ : One P
inst✝ : DecidableEq α
f : α → M
x : α
y : M
hy : y ≠ 1
a : α
⊢ a ∈ mulSupport (update f x y) ↔ a ∈ insert x (mulSupport f) | ((:c Iff) ((:c Membership.mem) (:fv _uniq.2873) ((:c Set) (:fv _uniq.2873)) ((:c Set.instMembership) (:fv _uniq.2873)) (:fv _uniq.3137) ((:c Function.mulSupport) (:fv _uniq.2873) (:fv _uniq.2885) (:fv _uniq.2897) ((:c Function.update) (:fv _uniq.2873) (:lambda _ (:fv _uniq.2873) (:fv _uniq.2885)) (:fv _uniq.3107) (:fv ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"A","sexp":"(:sort (+ u_3 1))"},{"name":"B","sexp":"(:sort (+ u_4 1))"},{"name":"M","sexp":"(:sort (+ u_5 1))"},{"name":"N","sexp":"(:sort (+ u_6 1))"},{"name":"P","sexp":"(:sort (+ u_7 1))"},{"name":"G","sexp":"(:sort (+ u_8 1))"}... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2873","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2876","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"source":"rcases","sourceEnd":3490,"sourceStart":3484,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"eq_or_ne","semanticRole":"global","source":"eq_or_ne","sourceEnd":3499,"sourceStart":3491,"tag":"identifier"},{"children":... | [] | [{"source":"eq_or_ne a x","source_end":3503,"source_start":3491,"syntax_kind":"Lean.Parser.Term.app"},{"source":"rfl | hne","source_end":3518,"source_start":3509,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2873","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2876","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 33 | 6 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0ac0ee6f2255c59bcac4c14132c44ffdd688a69151b5b5a06edfbf572b094dd2 | 457ebaafa0127b82285b3dfe707440f0555c6df0da42c639c1810847052b0827 | 395226b9e0e390131a7923ec8893e7ed9ccf8c03d72c662f577816e93ffee898 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,200 | Multiset.gcd_union | Mathlib/Algebra/GCDMonoid/Multiset.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Multiset.gcd_dedup</a>, <a>Multiset.dedup_ext</a>.2, <a>Multiset.gcd_dedup</a>, <a>Multiset.gcd_add</a>] | α : Type u_1
inst✝² : CancelCommMonoidWithZero α
inst✝¹ : NormalizedGCDMonoid α
inst✝ : DecidableEq α
s₁ s₂ : Multiset α
⊢ (s₁ ∪ s₂).gcd = GCDMonoid.gcd s₁.gcd s₂.gcd | α : Type u_1
inst✝² : CancelCommMonoidWithZero α
inst✝¹ : NormalizedGCDMonoid α
inst✝ : DecidableEq α
s₁ s₂ : Multiset α
⊢ ∀ (a : α), a ∈ s₁ ∪ s₂ ↔ a ∈ s₁ + s₂ | ((:c Eq) (:fv _uniq.24200) ((:c Multiset.gcd) (:fv _uniq.24200) (:fv _uniq.24203) (:fv _uniq.24212) ((:c Union.union) ((:c Multiset) (:fv _uniq.24200)) ((:c Multiset.instUnion) (:fv _uniq.24200) (:fv _uniq.24219)) (:fv _uniq.24313) (:fv _uniq.24314))) ((:c GCDMonoid.gcd) (:fv _uniq.24200) (:fv _uniq.24203) ((:c Normali... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CancelCommMonoidWithZero) (:fv _uniq.24200))"},{"name":"inst✝¹","sexp":"((:c NormalizedGCDMonoid) (:fv _uniq.24200) (:fv _uniq.24203))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.24200))"},{"name":"s₁","sexp":"((:c Multiset) (:fv _uniq.24... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Multiset.gcd) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CancelCommMonoidWithZero) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c NormalizedGCDMonoid) (:arg :explicit 0 (:fv FV0)) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24200","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24203","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CancelCommMonoidWithZer... | {"children":[{"source":"rw","sourceEnd":7415,"sourceStart":7413,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7417,"sourceStart":7416,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":7420,"sourceStart":... | [] | [{"source":"gcd_dedup","source_end":7430,"source_start":7421,"syntax_kind":"ident"},{"source":"dedup_ext.2","source_end":7443,"source_start":7432,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"gcd_dedup","source_end":7454,"source_start":7445,"syntax_kind":"ident"},{"source":"gcd_add","source_end":7463,"source_start"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24200","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24203","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":... | 66 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 615e0314e84b43130766641f64b88fc74b540bfb39af16f359c1d7cdfa258453 | 0e41ebf39ab84498205a248c569467cad0510f7805afe92a7a028383c04c6d18 | f98c8caff40c30f16d9243ea6b3c281217b1eef5a431d6515d420b04247d24c9 | 09a7641d356a894ba05032be65785b2d1955354b0912ff912e6a9af1241b0d24 |
cat-searcher/leandojo-benchmark-4-random | test | 4,201 | Multiset.gcd_union | Mathlib/Algebra/GCDMonoid/Multiset.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | α : Type u_1
inst✝² : CancelCommMonoidWithZero α
inst✝¹ : NormalizedGCDMonoid α
inst✝ : DecidableEq α
s₁ s₂ : Multiset α
⊢ ∀ (a : α), a ∈ s₁ ∪ s₂ ↔ a ∈ s₁ + s₂ | (:forall a (:fv _uniq.24200) ((:c Iff) ((:c Membership.mem) (:fv _uniq.24200) ((:c Multiset) (:fv _uniq.24200)) ((:c Multiset.instMembership) (:fv _uniq.24200)) 0 ((:c Union.union) ((:c Multiset) (:fv _uniq.24200)) ((:c Multiset.instUnion) (:fv _uniq.24200) (:fv _uniq.24219)) (:fv _uniq.24313) (:fv _uniq.24314))) ((:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CancelCommMonoidWithZero) (:fv _uniq.24200))"},{"name":"inst✝¹","sexp":"((:c NormalizedGCDMonoid) (:fv _uniq.24200) (:fv _uniq.24203))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.24200))"},{"name":"s₁","sexp":"((:c Multiset) (:fv _uniq.24... | (:forall a :explicit (:fv FV0) (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Multiset) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24200","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24203","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CancelCommMonoidWithZer... | {"children":[{"source":"simp","sourceEnd":7471,"sourceStart":7467,"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.24200","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24203","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":... | 66 | 10 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aa413a78df9492eff476423d3d6c75fccd9ec814dc18fc9868621e183c7ac477 | 09a7641d356a894ba05032be65785b2d1955354b0912ff912e6a9af1241b0d24 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,202 | Multiset.Icc_eq_zero_iff | Mathlib/Order/Interval/Multiset.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Multiset.Icc</a>, <a>Finset.val_eq_zero</a>, <a>Finset.Icc_eq_empty_iff</a>] | α : Type u_1
inst✝¹ : Preorder α
inst✝ : LocallyFiniteOrder α
a b c : α
⊢ Icc a b = 0 ↔ ¬a ≤ b | ((:c Iff) ((:c Eq) ((:c Multiset) (:fv _uniq.3012)) ((:c Multiset.Icc) (:fv _uniq.3012) (:fv _uniq.3015) (:fv _uniq.3023) (:fv _uniq.3025) (:fv _uniq.3027)) ((:c OfNat.ofNat) ((:c Multiset) (:fv _uniq.3012)) (:lit 0) ((:c Zero.toOfNat0) ((:c Multiset) (:fv _uniq.3012)) ((:c Multiset.instZero) (:fv _uniq.3012))))) ((:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Preorder) (:fv _uniq.3012))"},{"name":"inst✝","sexp":"((:c LocallyFiniteOrder) (:fv _uniq.3012) (:fv _uniq.3015))"},{"name":"a","sexp":"(:fv _uniq.3012)"},{"name":"b","sexp":"(:fv _uniq.3012)"},{"name":"c","sexp":"(:fv _uniq.3012)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Multiset.Icc) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3012","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.3015","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Preorder) (:arg :explicit... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":4650,"sourceStart":4648,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4652,"sourceStart":4651,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"Icc","source_end":4655,"source_start":4652,"syntax_kind":"ident"},{"source":"Finset.val_eq_zero","source_end":4675,"source_start":4657,"syntax_kind":"ident"},{"source":"Finset.Icc_eq_empty_iff","source_end":4700,"source_start":4677,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3012","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.3015","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":2,... | 55 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1024a0ee7472df1afabb1f94e410204acf0740515a0858665ae56b2c90426003 | 67551938304f474b937a7b93c36fae3c0642b69eed7af770491bcd158b703159 | f9aca35505f5ea4215aa936dcd8f1e60b4ed7a692b00408624f8020a0e661ff2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,203 | Set.pairwise_univ | Mathlib/Data/Set/Pairwise/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.Pairwise</a>, <a>Pairwise</a>, <a>Set.mem_univ</a>, <a>forall_const</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
ι' : Type u_5
r p q : α → α → Prop
f g : ι → α
s t u : Set α
a b : α
⊢ univ.Pairwise r ↔ Pairwise r | ((:c Iff) ((:c Set.Pairwise) (:fv _uniq.16297) ((:c Set.univ) (:fv _uniq.16297)) (:fv _uniq.16315)) ((:c Pairwise) (:fv _uniq.16297) (:fv _uniq.16315))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"ι'","sexp":"(:sort (+ u_5 1))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.16297) (:forall _ (:fv _uniq.16297) (:sort 0)))"},{"name":"p","sexp":"(:fora... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Set.Pairwise) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set.univ) (:arg :implicit-type 0 (:fv FV0)))) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:app (:c Pairwise) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16297","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16300","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":9360,"sourceStart":9356,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":9365,"sourceStart":9361,"tag":"atom"}],"kind":"nu... | [] | [{"source":"Set.Pairwise","source_end":9379,"source_start":9367,"syntax_kind":"ident"},{"source":"Pairwise","source_end":9389,"source_start":9381,"syntax_kind":"ident"},{"source":"mem_univ","source_end":9399,"source_start":9391,"syntax_kind":"ident"},{"source":"forall_const","source_end":9413,"source_start":9401,"synta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16297","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16300","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 65 | 2 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 972d852c98628f1c357d4516264d9456939e19035b1829f5f16ed7a3a4a5fb0f | 1b2fbfafee2d4eea63dfeb0b42f6ee04e5602eb5650d9c0a2dfc1b95e587e1ea | 6ce154d8dd98f88e042a8822a550969b036fa6e99fbdf5e36ea9b3832455a367 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,204 | Finset.affineCombination_filter_of_ne | Mathlib/LinearAlgebra/AffineSpace/Combination.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.affineCombination_apply</a>, <a>Finset.affineCombination_apply</a>, s.weightedVSubOfPoint_filter_of_ne _ _ _ h] | k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
S : AffineSpace V P
ι : Type u_4
s : Finset ι
ι₂ : Type u_5
s₂ : Finset ι₂
w : ι → k
p : ι → P
pred : ι → Prop
inst✝ : DecidablePred pred
h : ∀ i ∈ s, w i ≠ 0 → pred i
⊢ (affineCombination k (filter pred s) p) w = (affine... | ((:c Eq) (:fv _uniq.280270) ((:c DFunLike.coe) ((:c AffineMap) (:fv _uniq.280264) (:forall _ (:fv _uniq.280955) (:fv _uniq.280264)) (:forall _ (:fv _uniq.280955) (:fv _uniq.280264)) (:fv _uniq.280267) (:fv _uniq.280270) (:fv _uniq.280273) ((:c Pi.addCommGroup) (:fv _uniq.280955) (:lambda _ (:fv _uniq.280955) (:fv _uniq... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.280264))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.280267))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.280264) (:fv _uniq.280267)... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AffineMap) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:forall _ :explicit (:fv FV7) (:fv FV0))) (:arg :explicit 2 (:forall _ :explicit (:fv FV7) (:fv FV0))) (:arg :implicit-type 3 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280264","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.280267","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":30808,"sourceStart":30806,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":30810,"sourceStart":30809,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"affineCombination_apply","source_end":30833,"source_start":30810,"syntax_kind":"ident"},{"source":"affineCombination_apply","source_end":30858,"source_start":30835,"syntax_kind":"ident"},{"source":"s.weightedVSubOfPoint_filter_of_ne _ _ _ h","source_end":30906,"source_start":30864,"syntax_kind":"Lean.Parser... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.280264","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.280267","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 126 | 2 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 48b8c25e5379e8966140a0d846b8ec06ca038df6213e8931ccbda1a1fca9138d | 2c7f0b39680f1618f2fcad0be61a62406919280cba2b396dc1666484970c8a98 | e35caa553bf989b176a285060e4637b68ffced9de68ae3153fdf14bda40ab674 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,205 | Filter.pi_eq_bot | Mathlib/Order/Filter/Pi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using @<a>Filter.pi_inf_principal_univ_pi_eq_bot</a> ι α f fun _ => <a>Set.univ</a> | ι : Type u_1
α : ι → Type u_2
f f₁ f₂ : (i : ι) → Filter (α i)
s : (i : ι) → Set (α i)
p : (i : ι) → α i → Prop
⊢ pi f = ⊥ ↔ ∃ i, f i = ⊥ | ((:c Iff) ((:c Eq) ((:c Filter) (:forall i (:fv _uniq.32753) ((:fv _uniq.32758) 0))) ((:c Filter.pi) (:fv _uniq.32753) (:fv _uniq.32758) (:fv _uniq.32764)) ((:c Bot.bot) ((:c Filter) (:forall i (:fv _uniq.32753) ((:fv _uniq.32758) 0))) ((:c CompleteLattice.toBot) ((:c Filter) (:forall i (:fv _uniq.32753) ((:fv _uniq.32... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:forall _ (:fv _uniq.32753) (:sort (+ u_2 1)))"},{"name":"f","sexp":"(:forall i (:fv _uniq.32753) ((:c Filter) ((:fv _uniq.32758) 0)))"},{"name":"f₁","sexp":"(:forall i (:fv _uniq.32753) ((:c Filter) ((:fv _uniq.32758) 0)))"},{"name":"f₂","sexp":"(:forall i ... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:forall i :explicit (:fv FV0) (:app (:fv FV1) (:arg :explicit 0 0)))))) (:arg :explicit 1 (:app (:c Filter.pi) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV2)))) (:arg :explicit 2 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32753","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32758","is_instance":false,"is_let":false,"name":"α","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"}... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":7839,"sourceStart":7834,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"@pi_inf_principal_univ_pi_eq_bot ι α f fun _ => univ","source_end":7900,"source_start":7846,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32753","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.32758","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 52 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8e4c006fd77fb5818ed62a8a76b19405fa38431264cf04493649fe4daaf96bea | 382844c69deb2bd08db6279302f4fda0ffb26201905dd6f9c23e0da0a9f23c54 | 81c2a0e5d980fb1a26ea0999e9e0f0336fded4c0583eb300f11d57b7c3088ff6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,206 | iterateFrobeniusEquiv_symm_add_apply | Mathlib/FieldTheory/Perfect.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>RingEquiv.apply_symm_apply</a>, <a>add_comm</a>, <a>iterateFrobeniusEquiv_add_apply</a>, <a>RingEquiv.apply_symm_apply</a>, <a>RingEquiv.apply_symm_apply</a>] | R : Type u_1
p m n : ℕ
inst✝² : CommSemiring R
inst✝¹ : ExpChar R p
inst✝ : PerfectRing R p
x : R
⊢ (iterateFrobeniusEquiv R p (m + n)) ((iterateFrobeniusEquiv R p (m + n)).symm x) =
(iterateFrobeniusEquiv R p (m + n)) ((iterateFrobeniusEquiv R p m).symm ((iterateFrobeniusEquiv R p n).symm x)) | ((:c Eq) (:fv _uniq.12846) ((:c DFunLike.coe) ((:c RingEquiv) (:fv _uniq.12846) (:fv _uniq.12846) ((:c NonUnitalNonAssocSemiring.toMul) (:fv _uniq.12846) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.12846) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.12846) ((:c CommSemiring.toSemiring) (:fv _uniq.1284... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"p","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.12846))"},{"name":"inst✝¹","sexp":"((:c ExpChar) (:fv _uniq.12846) ((:c CommSemiring.toSemiring) (:fv _uniq.12846) (:fv _uniq.12855... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c RingEquiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Mul) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Mul) (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.12846","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.12848","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":explicit","context... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":4443,"sourceStart":4441,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4445,"sourceStart":4444,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"RingEquiv.apply_symm_apply","source_end":4471,"source_start":4445,"syntax_kind":"ident"},{"source":"add_comm","source_end":4481,"source_start":4473,"syntax_kind":"ident"},{"source":"iterateFrobeniusEquiv_add_apply","source_end":4518,"source_start":4487,"syntax_kind":"ident"},{"source":"RingEquiv.apply_symm_... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.12846","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.12848","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":explicit","context_index":2,"internal_name":"_un... | 23 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c42a2a27331631ac624e7fd3eb28eaf29d9b74b65d3a46fb97afa7bdd2978ba8 | 5bd46d7085c9eaf1175d7b97960b63f21975f2f9d34939753ba071236c8f233a | d166ef90eaf7aa1e1029c7b618cb95c159a8c3ca2e51bc6376cdf1cdf687083a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,207 | Set.Ioi_mul_Ici_subset' | Mathlib/Data/Set/Pointwise/Interval.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | haveI := <a>covariantClass_le_of_lt</a> | α : Type u_1
inst✝³ : Mul α
inst✝² : PartialOrder α
inst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1
inst✝ : CovariantClass α α (Function.swap HMul.hMul) LT.lt
a b : α
⊢ Ioi a * Ici b ⊆ Ioi (a * b) | α : Type u_1
inst✝³ : Mul α
inst✝² : PartialOrder α
inst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1
inst✝ : CovariantClass α α (Function.swap HMul.hMul) LT.lt
a b : α
this :
∀ (M : Type ?u.11667) (N : Type ?u.11666) (μ : M → N → N) [inst : PartialOrder N]
[inst_1 : CovariantClass M N μ fun... | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.11258)) ((:c Set.instHasSubset) (:fv _uniq.11258)) ((:c HMul.hMul) ((:c Set) (:fv _uniq.11258)) ((:c Set) (:fv _uniq.11258)) ((:c Set) (:fv _uniq.11258)) ((:c instHMul) ((:c Set) (:fv _uniq.11258)) ((:c Set.mul) (:fv _uniq.11258) (:fv _uniq.11261))) ((:c Set.Ioi) (:fv _uniq.1... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Mul) (:fv _uniq.11258))"},{"name":"inst✝²","sexp":"((:c PartialOrder) (:fv _uniq.11258))"},{"name":"inst✝¹","sexp":"((:c CovariantClass) (:fv _uniq.11258) (:fv _uniq.11258) (:lambda _ (:fv _uniq.11258) (:lambda _ (:fv _uniq.11258) ((:c HMul.hMul) (:... | (: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 HMul.hMul) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11258","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11261","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Mul) (:arg :explicit 0 ... | {"children":[{"source":"haveI","sourceEnd":4080,"sourceStart":4075,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":4081,"sourceStart":4081,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":4081,"sourceStart":4081,"tag":"node"}],"kind":"Lean.Parser.Term.haveId",... | [] | [{"source":"covariantClass_le_of_lt","source_end":4107,"source_start":4084,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11258","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11261","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":... | 22 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 897baa5a574c3a7231b02abdeb7a2c5f06c718707b4c21670feb27eb99802a2b | 975e5554c06d7d225e4f2fa9cb0eb00aab452ce487f0a90ae48bf8d0d3ceef63 | 41589fc32c2f0064272a4aca6d2123cf931a21b995061618fd2ca84928f0447c | e38ad9ad620b743889ca0394bb339831b57532d6593ab4c0316f4f157f6575a2 |
cat-searcher/leandojo-benchmark-4-random | test | 4,208 | Set.Ioi_mul_Ici_subset' | Mathlib/Data/Set/Pointwise/Interval.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro x ⟨y, hya, z, hzb, rfl⟩ | α : Type u_1
inst✝³ : Mul α
inst✝² : PartialOrder α
inst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1
inst✝ : CovariantClass α α (Function.swap HMul.hMul) LT.lt
a b : α
this :
∀ (M : Type ?u.11667) (N : Type ?u.11666) (μ : M → N → N) [inst : PartialOrder N]
[inst_1 : CovariantClass M N μ fun... | case intro.intro.intro.intro
α : Type u_1
inst✝³ : Mul α
inst✝² : PartialOrder α
inst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1
inst✝ : CovariantClass α α (Function.swap HMul.hMul) LT.lt
a b : α
this :
∀ (M : Type ?u.11667) (N : Type ?u.11666) (μ : M → N → N) [inst : PartialOrder N]
[inst... | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.11258)) ((:c Set.instHasSubset) (:fv _uniq.11258)) ((:c HMul.hMul) ((:c Set) (:fv _uniq.11258)) ((:c Set) (:fv _uniq.11258)) ((:c Set) (:fv _uniq.11258)) ((:c instHMul) ((:c Set) (:fv _uniq.11258)) ((:c Set.mul) (:fv _uniq.11258) (:fv _uniq.11261))) ((:c Set.Ioi) (:fv _uniq.1... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Mul) (:fv _uniq.11258))"},{"name":"inst✝²","sexp":"((:c PartialOrder) (:fv _uniq.11258))"},{"name":"inst✝¹","sexp":"((:c CovariantClass) (:fv _uniq.11258) (:fv _uniq.11258) (:lambda _ (:fv _uniq.11258) (:lambda _ (:fv _uniq.11258) ((:c HMul.hMul) (:... | (: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 HMul.hMul) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11258","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11261","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Mul) (:arg :explicit 0 ... | {"children":[{"source":"rintro","sourceEnd":4116,"sourceStart":4110,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":4118,"sourceStart":4117,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":4118,"sourceStart":4117,"tag":"... | [{"role":"fresh_name","source":"y","source_end":4123,"source_start":4122,"syntax_kind":"ident"},{"role":"fresh_name","source":"hya","source_end":4128,"source_start":4125,"syntax_kind":"ident"},{"role":"fresh_name","source":"z","source_end":4131,"source_start":4130,"syntax_kind":"ident"},{"role":"fresh_name","source":"h... | [{"source":"⟨y, hya, z, hzb, rfl⟩","source_end":4144,"source_start":4119,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11258","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11261","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":... | 22 | 5 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 04fab58069a78c4341dc35fc971471015a30a9b6372ec38263ce31aea9f39a17 | e38ad9ad620b743889ca0394bb339831b57532d6593ab4c0316f4f157f6575a2 | 1a99703e5cd2d30866d22cc7d98ea82f9810af858c2f09e742750ccfbc446b96 | 13b5882937b57f7adbf25196bf2f62ca4596ed24b56363e4c9a7e39c9dd269ce |
cat-searcher/leandojo-benchmark-4-random | test | 4,209 | Set.Ioi_mul_Ici_subset' | Mathlib/Data/Set/Pointwise/Interval.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>mul_lt_mul_of_lt_of_le</a> hya hzb | case intro.intro.intro.intro
α : Type u_1
inst✝³ : Mul α
inst✝² : PartialOrder α
inst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1
inst✝ : CovariantClass α α (Function.swap HMul.hMul) LT.lt
a b : α
this :
∀ (M : Type ?u.11667) (N : Type ?u.11666) (μ : M → N → N) [inst : PartialOrder N]
[inst... | ((:c Membership.mem) (:fv _uniq.11258) ((:c Set) (:fv _uniq.11258)) ((:c Set.instMembership) (:fv _uniq.11258)) ((:lambda _ (:fv _uniq.11258) (:lambda _ (:fv _uniq.11258) ((:c HMul.hMul) (:fv _uniq.11258) (:fv _uniq.11258) (:fv _uniq.11258) ((:c instHMul) (:fv _uniq.11258) (:fv _uniq.11261)) 1 0))) (:fv _uniq.11708) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Mul) (:fv _uniq.11258))"},{"name":"inst✝²","sexp":"((:c PartialOrder) (:fv _uniq.11258))"},{"name":"inst✝¹","sexp":"((:c CovariantClass) (:fv _uniq.11258) (:fv _uniq.11258) (:lambda _ (:fv _uniq.11258) (:lambda _ (:fv _uniq.11258) ((:c HMul.hMul) (:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:app (:lambda _ :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11258","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11261","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Mul) (:arg :explicit 0 ... | {"children":[{"source":"exact","sourceEnd":4152,"sourceStart":4147,"tag":"atom"},{"children":[{"name":"mul_lt_mul_of_lt_of_le","semanticRole":"global","source":"mul_lt_mul_of_lt_of_le","sourceEnd":4175,"sourceStart":4153,"tag":"identifier"},{"children":[{"contextIndex":10,"semanticRole":"local","source":"hya","sourceEn... | [] | [{"source":"mul_lt_mul_of_lt_of_le hya hzb","source_end":4183,"source_start":4153,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11258","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11261","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":... | 22 | 6 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 363fbcf468c231d183788e620f2fa3ceafb8cd049087fb5199cbd75b41f4e168 | 13b5882937b57f7adbf25196bf2f62ca4596ed24b56363e4c9a7e39c9dd269ce | 047749e3347f6d40a43556bdd088b0238e4f69410e9399dd1c9c0855f3e0aa3f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 |
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