Split (3)

test · 4.39k rows

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	2,470	MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top	Mathlib/MeasureTheory/OuterMeasure/Basic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact <a>Or.inl</a> (h' hjn hj)	case mk.intro.inl α : Type u_1 β : Type u_2 m✝ m : OuterMeasure α s : ℕ → Set α h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1) h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤ n : ℕ h' : Monotone s x : α this : ∃ i, x ∈ s i j : ℕ hj : x ∈ s j hlt : ∀ m < j, x ∉ s m hjn : j ≤ n ⊢ x ∈ s n ∪ ⋃ i, s (i + n + 1) \ s (i + n)		((:c Membership.mem) (:fv _uniq.91806) ((:c Set) (:fv _uniq.91806)) ((:c Set.instMembership) (:fv _uniq.91806)) (:fv _uniq.94775) ((:c Union.union) ((:c Set) (:fv _uniq.91806)) ((:c Set.instUnion) (:fv _uniq.91806)) ((:fv _uniq.92514) (:fv _uniq.93049)) ((:c Set.iUnion) (:fv _uniq.91806) (:c Nat) (:lambda i (:c Nat) ((...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m✝","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"m","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"s","sexp":"(:forall _ (:c Nat) ((:c Set) (:fv _uniq.91806)))"},{"name":"h_mono","...	(: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 (:fv FV10)) (:arg :expl...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...	{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":13793,"sourceStart":13788,"tag":"atom"},{"children":[{"name":"Or.inl","semanticRole":"constructor","source":"Or.inl","sourceEnd":13800,"sourceStart":13794,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":13802,"sour...	[]	[{"source":"Or.inl (h' hjn hj)","source_end":13812,"source_start":13794,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	79	18	exact	true	1	15	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	673febf806a9281f5c9b10c3cd7d66ea0cfc37ee9620802c0227c71eef69323e	02697db16e2760bc93ea26b560bbee636e152f436290d450348a968469b51b88	80e827a87bfadc71066cae0fc535a96333d3d45dc30dc1f03399b7bc1eaec022	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,471	MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top	Mathlib/MeasureTheory/OuterMeasure/Basic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	omega	α : Type u_1 β : Type u_2 m✝ m : OuterMeasure α s : ℕ → Set α h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1) h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤ n : ℕ h' : Monotone s x : α this : ∃ i, x ∈ s i j : ℕ hj : x ∈ s j hlt : ∀ m < j, x ∉ s m hnj : n < j ⊢ j - (n + 1) + n + 1 = j		((:c Eq) (:c Nat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HSub.hSub) (:c Nat) (:c Nat) (:c Nat) ((:c instHSub) (:c Nat) (:c instSubNat)) (:fv _uniq.94894) ((:c HAdd.hAdd) (:c Nat) (:c Nat...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m✝","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"m","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"s","sexp":"(:forall _ (:c Nat) ((:c Set) (:fv _uniq.91806)))"},{"name":"h_mono","...	(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...	{"children":[{"source":"omega","sourceEnd":13857,"sourceStart":13852,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.omega","source":"omega","sourceEnd":13857,"sourceStart":13852,"tag":"node"}	[]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	79	23	exact	true	1	15	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	38c7cd25ebde17bb835114df2d213c0ab60dba2618ee9490582c08df67f648de	cbed7806aa5b7c858af9b97ce3889d7d69e952466a50feb317df3fea42520be0	304b4a90a76a1cbe4c112e074b30e75181f54df43d60f883597457844293b341	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,472	MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top	Mathlib/MeasureTheory/OuterMeasure/Basic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rwa [this]	case mk.intro.inr.refine_1 α : Type u_1 β : Type u_2 m✝ m : OuterMeasure α s : ℕ → Set α h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1) h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤ n : ℕ h' : Monotone s x : α this✝ : ∃ i, x ∈ s i j : ℕ hj : x ∈ s j hlt : ∀ m < j, x ∉ s m hnj : n < j this : j - (n + 1) + n + 1 = j ⊢ x ∈ s (j - (n + 1)...		((:c Membership.mem) (:fv _uniq.91806) ((:c Set) (:fv _uniq.91806)) ((:c Set.instMembership) (:fv _uniq.91806)) (:fv _uniq.94775) ((:fv _uniq.92514) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m✝","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"m","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"s","sexp":"(:forall _ (:c Nat) ((:c Set) (:fv _uniq.91806)))"},{"name":"h_mono","...	(: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 (:fv FV10)) (:arg :expl...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...	{"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":13929,"sourceStart":13926,"tag":"atom"},{"children":[{"source":"[","sourceEnd":13931,"sourceStart":13930,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":16,"semanticRole":"local...	[]	[{"source":"this","source_end":13935,"source_start":13931,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	79	27	exact	true	1	16	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	ab921f93a5150ef62698837d947bb324e9e35821561a7a0b1d22a7a7523ae41c	0853ecb7297811a0ff7b522bf57f2daa9aaee83fe013ba156fcaac5e6c3d8849	a7328267c2b777cb8d5131a96fbb6b4099b9fbd3e4030475394134226f4cb398	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,473	MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top	Mathlib/MeasureTheory/OuterMeasure/Basic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [← <a>Nat.succ_le_iff</a>, <a>Nat.succ_eq_add_one</a>, this]	case mk.intro.inr.refine_2 α : Type u_1 β : Type u_2 m✝ m : OuterMeasure α s : ℕ → Set α h_mono : ∀ (n : ℕ), s n ⊆ s (n + 1) h0 : ∑' (k : ℕ), m (s (k + 1) \ s k) ≠ ⊤ n : ℕ h' : Monotone s x : α this✝ : ∃ i, x ∈ s i j : ℕ hj : x ∈ s j hlt : ∀ m < j, x ∉ s m hnj : n < j this : j - (n + 1) + n + 1 = j ⊢ j - (n + 1) + n < ...		((:c LT.lt) (:c Nat) (:c instLTNat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HSub.hSub) (:c Nat) (:c Nat) (:c Nat) ((:c instHSub) (:c Nat) (:c instSubNat)) (:fv _uniq.94894) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.930...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m✝","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"m","sexp":"((:c MeasureTheory.OuterMeasure) (:fv _uniq.91806))"},{"name":"s","sexp":"(:forall _ (:c Nat) ((:c Set) (:fv _uniq.91806)))"},{"name":"h_mono","...	(:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...	{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":13944,"sourceStart":13942,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13946,"sourceStart":13945,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"...	[]	[{"source":"Nat.succ_le_iff","source_end":13965,"source_start":13950,"syntax_kind":"ident"},{"source":"Nat.succ_eq_add_one","source_end":13986,"source_start":13967,"syntax_kind":"ident"},{"source":"this","source_end":13992,"source_start":13988,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91806","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91809","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	79	34	exact	true	1	16	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	2f794ebff9154ff7ed41bb3ac745f89112d48ffe31fd71c4badf4b32e0c864b1	32e8a91ab685abfb1a533c207f678c3bb1c0314a32db661334a4145b2eb44829	5196135bcf1be22b41078bf08f632f4ef1760f5879c814e36f41f03a2ead7bdf	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,474	Batteries.RBNode.lowerBound?_le'	.lake/packages/batteries/Batteries/Data/RBMap/Lemmas.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [← <a>Batteries.RBNode.reverse_reverse</a> t, <a>Batteries.RBNode.lowerBound?_reverse</a>, <a>Ne</a>, ← <a>Ordering.swap_inj</a>]	α : Type u_1 lb : Option α cut : α → Ordering x : α t : RBNode α H : ∀ {x : α}, x ∈ lb → cut x ≠ Ordering.lt ⊢ lowerBound? cut t lb = some x → cut x ≠ Ordering.lt	α : Type u_1 lb : Option α cut : α → Ordering x : α t : RBNode α H : ∀ {x : α}, x ∈ lb → cut x ≠ Ordering.lt ⊢ upperBound? (fun x => (cut x).swap) t.reverse lb = some x → ¬(cut x).swap = Ordering.lt.swap	(:forall _ ((:c Eq) ((:c Option) (:fv _uniq.81372)) ((:c Batteries.RBNode.lowerBound?) (:fv _uniq.81372) (:fv _uniq.81374) (:fv _uniq.81376) (:fv _uniq.81373)) ((:c Option.some) (:fv _uniq.81372) (:fv _uniq.81375))) ((:c Ne) (:c Ordering) ((:fv _uniq.81374) (:fv _uniq.81375)) (:c Ordering.lt)))	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"lb","sexp":"((:c Option) (:fv _uniq.81372))"},{"name":"cut","sexp":"(:forall _ (:fv _uniq.81372) (:c Ordering))"},{"name":"x","sexp":"(:fv _uniq.81372)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.81372))"},{"name":"H","sexp":"(:forall x (:fv _uniq.81372) (:f...	(:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Option) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Batteries.RBNode.lowerBound?) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:fv FV2)))) (:arg :explicit 2 (:app (:c Opti...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81372","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.81373","is_instance":false,"is_let":false,"name":"lb","sexp":"(:app (:c Option) (:arg :explicit 0 (:fv FV1)...	{"children":[{"source":"rw","sourceEnd":17855,"sourceStart":17853,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":17857,"sourceStart":17856,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":17860,"sourceSt...	[]	[{"source":"reverse_reverse t","source_end":17878,"source_start":17861,"syntax_kind":"Lean.Parser.Term.app"},{"source":"lowerBound?_reverse","source_end":17899,"source_start":17880,"syntax_kind":"ident"},{"source":"Ne","source_end":17903,"source_start":17901,"syntax_kind":"ident"},{"source":"Ordering.swap_inj","source_...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81372","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.81373","is_instance":false,"is_let":false,"user_name":"lb"},{"binder_role":":implicit","context_index":3,"internal_name":"_u...	90	4	exact	true	1	6	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	779b258bb0fb0a21e57ca2859ac5eaffdd7d65bb3acf0aa90d405f77228ba286	0281a7af5218d3e80e5c57b2014e03713e9a1f55dcf2f2bce8301688fe83e28f	c6ccb71a52cba29dd91b1cd9000dc8e8833decce53a77445745848232844a687	c5cf4ccb65e17ed3cd61cb7a636e1d9e18ec7d0031b8766a6b54b8a7b1a4806e
cat-searcher/leandojo-benchmark-4-random	test	2,475	Batteries.RBNode.lowerBound?_le'	.lake/packages/batteries/Batteries/Data/RBMap/Lemmas.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact <a>Batteries.RBNode.upperBound?_ge'</a> fun h => by specialize H h; rwa [<a>Ne</a>, ← <a>Ordering.swap_inj</a>] at H	α : Type u_1 lb : Option α cut : α → Ordering x : α t : RBNode α H : ∀ {x : α}, x ∈ lb → cut x ≠ Ordering.lt ⊢ upperBound? (fun x => (cut x).swap) t.reverse lb = some x → ¬(cut x).swap = Ordering.lt.swap		(:forall _ ((:c Eq) ((:c Option) (:fv _uniq.81372)) ((:c Batteries.RBNode.upperBound?) (:fv _uniq.81372) (:lambda _ (:fv _uniq.81372) ((:c Ordering.swap) ((:fv _uniq.81374) 0))) ((:c Batteries.RBNode.reverse) (:fv _uniq.81372) (:fv _uniq.81376)) (:fv _uniq.81373)) ((:c Option.some) (:fv _uniq.81372) (:fv _uniq.81375)))...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"lb","sexp":"((:c Option) (:fv _uniq.81372))"},{"name":"cut","sexp":"(:forall _ (:fv _uniq.81372) (:c Ordering))"},{"name":"x","sexp":"(:fv _uniq.81372)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.81372))"},{"name":"H","sexp":"(:forall x (:fv _uniq.81372) (:f...	(:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Option) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Batteries.RBNode.upperBound?) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda _ :explicit (:fv FV1) (:app (:c Ordering.swap) (:arg :explicit 0 (:app (:fv FV3) (:arg :explic...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81372","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.81373","is_instance":false,"is_let":false,"name":"lb","sexp":"(:app (:c Option) (:arg :explicit 0 (:fv FV1)...	{"children":[{"source":"exact","sourceEnd":17935,"sourceStart":17930,"tag":"atom"},{"children":[{"name":"Batteries.RBNode.upperBound?_ge'","semanticRole":"global","source":"upperBound?_ge'","sourceEnd":17951,"sourceStart":17936,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":17955,"sourceStart...	[]	[{"source":"upperBound?_ge' fun h => by specialize H h; rwa [Ne, ← Ordering.swap_inj] at H","source_end":18016,"source_start":17936,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81372","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.81373","is_instance":false,"is_let":false,"user_name":"lb"},{"binder_role":":implicit","context_index":3,"internal_name":"_u...	90	10	exact	true	1	6	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	90a40cda34d6799b699dc7a6bc85ff0e7c55c3db28b83411e5bd7da999e16e58	c5cf4ccb65e17ed3cd61cb7a636e1d9e18ec7d0031b8766a6b54b8a7b1a4806e	7b1694fd835c21ef07993364e0e90053c91014313de0f268805443bbf6c41a79	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,476	Batteries.RBNode.lowerBound?_le'	.lake/packages/batteries/Batteries/Data/RBMap/Lemmas.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	specialize H h	α : Type u_1 lb : Option α cut : α → Ordering x : α t : RBNode α H : ∀ {x : α}, x ∈ lb → cut x ≠ Ordering.lt x✝ : α h : x✝ ∈ lb ⊢ (cut x✝).swap ≠ Ordering.gt	α : Type u_1 lb : Option α cut : α → Ordering x : α t : RBNode α x✝ : α h : x✝ ∈ lb H : cut x✝ ≠ Ordering.lt ⊢ (cut x✝).swap ≠ Ordering.gt	((:c Ne) (:c Ordering) ((:c Ordering.swap) ((:fv _uniq.81374) (:fv _uniq.81487))) (:c Ordering.gt))	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"lb","sexp":"((:c Option) (:fv _uniq.81372))"},{"name":"cut","sexp":"(:forall _ (:fv _uniq.81372) (:c Ordering))"},{"name":"x","sexp":"(:fv _uniq.81372)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.81372))"},{"name":"H","sexp":"(:forall x (:fv _uniq.81372) (:f...	(:app (:c Ne) (:arg :implicit-type 0 (:c Ordering)) (:arg :explicit 1 (:app (:c Ordering.swap) (:arg :explicit 0 (:app (:fv FV3) (:arg :explicit 0 (:fv FV7)))))) (:arg :explicit 2 (:c Ordering.gt)))	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81372","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.81373","is_instance":false,"is_let":false,"name":"lb","sexp":"(:app (:c Option) (:arg :explicit 0 (:fv FV1)...	{"children":[{"source":"specialize","sourceEnd":17974,"sourceStart":17964,"tag":"atom"},{"children":[{"contextIndex":6,"semanticRole":"local","source":"H","sourceEnd":17976,"sourceStart":17975,"tag":"identifier"},{"children":[{"contextIndex":8,"semanticRole":"local","source":"h","sourceEnd":17978,"sourceStart":17977,"t...	[]	[{"source":"H h","source_end":17978,"source_start":17975,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81372","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.81373","is_instance":false,"is_let":false,"user_name":"lb"},{"binder_role":":implicit","context_index":3,"internal_name":"_u...	90	15	exact	true	1	8	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	561f16fcee6d2d059b7da096f3d87356d278575648ea8f0632c2c581dd46abd4	2ad5773ea9fbcff06f2c0fade667d771dfff5715aa2008ad40b8fa8ec5b7e556	121959ccf9e1fdcd1972fde10b0c52140d6d383e78277194e6918a052f613aa1	5d91573a372ea6be08cd31a8779b855402d66adb0bda7c69ceed7f491e454a6a
cat-searcher/leandojo-benchmark-4-random	test	2,477	Batteries.RBNode.lowerBound?_le'	.lake/packages/batteries/Batteries/Data/RBMap/Lemmas.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rwa [<a>Ne</a>, ← <a>Ordering.swap_inj</a>] at H	α : Type u_1 lb : Option α cut : α → Ordering x : α t : RBNode α x✝ : α h : x✝ ∈ lb H : cut x✝ ≠ Ordering.lt ⊢ (cut x✝).swap ≠ Ordering.gt		((:c Ne) (:c Ordering) ((:c Ordering.swap) ((:fv _uniq.81374) (:fv _uniq.81487))) (:c Ordering.gt))	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"lb","sexp":"((:c Option) (:fv _uniq.81372))"},{"name":"cut","sexp":"(:forall _ (:fv _uniq.81372) (:c Ordering))"},{"name":"x","sexp":"(:fv _uniq.81372)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.81372))"},{"name":"x✝","sexp":"(:fv _uniq.81372)"},{"name":"h"...	(:app (:c Ne) (:arg :implicit-type 0 (:c Ordering)) (:arg :explicit 1 (:app (:c Ordering.swap) (:arg :explicit 0 (:app (:fv FV3) (:arg :explicit 0 (:fv FV6)))))) (:arg :explicit 2 (:c Ordering.gt)))	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81372","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.81373","is_instance":false,"is_let":false,"name":"lb","sexp":"(:app (:c Option) (:arg :explicit 0 (:fv FV1)...	{"children":[{"source":"rwa","sourceEnd":17983,"sourceStart":17980,"tag":"atom"},{"children":[{"source":"[","sourceEnd":17985,"sourceStart":17984,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Ne","semanticRole":"global","source":"Ne","sourceEnd":17987,"sourceSta...	[]	[{"source":"Ne","source_end":17987,"source_start":17985,"syntax_kind":"ident"},{"source":"H","source_end":18016,"source_start":18015,"syntax_kind":"ident"},{"source":"Ordering.swap_inj","source_end":18010,"source_start":17993,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.81372","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.81373","is_instance":false,"is_let":false,"user_name":"lb"},{"binder_role":":implicit","context_index":3,"internal_name":"_u...	90	17	exact	true	1	8	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	cf5016be3c1a73c2f01eaa3582cd0d38311b5fb9930367b083322ac96192bcc1	5d91573a372ea6be08cd31a8779b855402d66adb0bda7c69ceed7f491e454a6a	91c26d66a47538117d77bc57d365080c832e78457ae5aa968f05a8efb49e946f	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,478	LieAlgebra.IsKilling.traceForm_eq_zero_of_mem_ker_of_mem_span_coroot	Mathlib/Algebra/Lie/Weights/Killing.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [← <a>LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton</a>, <a>LieSubmodule.mem_coeSubmodule</a>, <a>LieAlgebra.mem_corootSpace'</a>] at hy	R : Type u_1 K : Type u_2 L : Type u_3 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : Field K inst✝⁵ : LieAlgebra K L inst✝⁴ : FiniteDimensional K L H : LieSubalgebra K L inst✝³ : H.IsCartanSubalgebra inst✝² : IsTriangularizable K (↥H) L inst✝¹ : IsKilling K L inst✝ : CharZero K α : Weight K (↥...	R : Type u_1 K : Type u_2 L : Type u_3 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : Field K inst✝⁵ : LieAlgebra K L inst✝⁴ : FiniteDimensional K L H : LieSubalgebra K L inst✝³ : H.IsCartanSubalgebra inst✝² : IsTriangularizable K (↥H) L inst✝¹ : IsKilling K L inst✝ : CharZero K α : Weight K (↥...	((:c Eq) (:fv _uniq.616263) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.616263) (:fv _uniq.616263) ((:c CommSemiring.toSemiring) (:fv _uniq.616263) ((:c CommRing.toCommSemiring) (:fv _uniq.616263) ((:c EuclideanDomain.toCommRing) (:fv _uniq.616263) ((:c Field.toEuclideanDomain) (:fv _uniq.616263) (:fv _uniq.616292)))...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.616260))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.616266))"},{"name":"inst✝⁷","sexp":"((:c LieAlgebra) (:fv _uniq.616260) (:fv _uniq.6162...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"rw","sourceEnd":21662,"sourceStart":21660,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":21664,"sourceStart":21663,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":21667,"sourceSt...	[]	[{"source":"coe_corootSpace_eq_span_singleton","source_end":21701,"source_start":21668,"syntax_kind":"ident"},{"source":"hy","source_end":21757,"source_start":21755,"syntax_kind":"ident"},{"source":"LieSubmodule.mem_coeSubmodule","source_end":21732,"source_start":21703,"syntax_kind":"ident"},{"source":"mem_corootSpace'...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	49	4	exact	true	1	19	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	5be78f57928ff5703075eeb95361b570965b039d2206deba14d7c8b65940d0e6	c8b3c590de3469907cf70905b90cbbf1b5197efa2ad43c411af2df04080f6165	03ac644bba1269c60ca33cd953c2f4de89c2b7ce887499e0de002b09afaad3fa	f557302c876b9896607a6d3a764db5187ada2212b91ff2d01f8e57225dfcb0c7
cat-searcher/leandojo-benchmark-4-random	test	2,479	LieAlgebra.IsKilling.traceForm_eq_zero_of_mem_ker_of_mem_span_coroot	Mathlib/Algebra/Lie/Weights/Killing.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	induction hy using <a>Submodule.span_induction'</a> with \| mem z hz => obtain ⟨u, hu, v, -, huv⟩ := hz change <a>killingForm</a> K L (x : L) (z : L) = 0 replace hx : α x = 0 := by simpa using hx rw [← huv, ← <a>LieModule.traceForm_apply_lie_apply</a>, ← <a>LieSubalgebra.coe_bracket_of_module</a>, <a>LieAlgebra.IsKillin...	R : Type u_1 K : Type u_2 L : Type u_3 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : Field K inst✝⁵ : LieAlgebra K L inst✝⁴ : FiniteDimensional K L H : LieSubalgebra K L inst✝³ : H.IsCartanSubalgebra inst✝² : IsTriangularizable K (↥H) L inst✝¹ : IsKilling K L inst✝ : CharZero K α : Weight K (↥...		((:c Eq) (:fv _uniq.616263) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.616263) (:fv _uniq.616263) ((:c CommSemiring.toSemiring) (:fv _uniq.616263) ((:c CommRing.toCommSemiring) (:fv _uniq.616263) ((:c EuclideanDomain.toCommRing) (:fv _uniq.616263) ((:c Field.toEuclideanDomain) (:fv _uniq.616263) (:fv _uniq.616292)))...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.616260))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.616266))"},{"name":"inst✝⁷","sexp":"((:c LieAlgebra) (:fv _uniq.616260) (:fv _uniq.6162...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"induction","sourceEnd":21769,"sourceStart":21760,"tag":"atom"},{"children":[{"contextIndex":19,"semanticRole":"local","source":"hy","sourceEnd":21772,"sourceStart":21770,"tag":"identifier"}],"kind":"null","source":"hy","sourceEnd":21772,"sourceStart":21770,"tag":"node"},{"children":[{"source":"u...	[]	[{"source":"hy","source_end":21772,"source_start":21770,"syntax_kind":"ident"},{"source":"Submodule.span_induction'","source_end":21804,"source_start":21779,"syntax_kind":"ident"},{"source":"hz","source_end":21865,"source_start":21863,"syntax_kind":"ident"},{"source":"⟨u, hu, v, -, huv⟩","source_end":21859,"source_star...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	49	9	exact	true	1	19	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	116065bb26c950702cc8699f68a11efff846210322d11ffb5e2d3bf8bb017b99	f557302c876b9896607a6d3a764db5187ada2212b91ff2d01f8e57225dfcb0c7	1d76c465606b8c1832ae11dc5efbd1e17cd750868ec1f6df995499094abf6c42	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,480	LieAlgebra.IsKilling.traceForm_eq_zero_of_mem_ker_of_mem_span_coroot	Mathlib/Algebra/Lie/Weights/Killing.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	obtain ⟨u, hu, v, -, huv⟩ := hz	case mem R : Type u_1 K : Type u_2 L : Type u_3 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : Field K inst✝⁵ : LieAlgebra K L inst✝⁴ : FiniteDimensional K L H : LieSubalgebra K L inst✝³ : H.IsCartanSubalgebra inst✝² : IsTriangularizable K (↥H) L inst✝¹ : IsKilling K L inst✝ : CharZero K α : We...	case mem.intro.intro.intro.intro R : Type u_1 K : Type u_2 L : Type u_3 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : Field K inst✝⁵ : LieAlgebra K L inst✝⁴ : FiniteDimensional K L H : LieSubalgebra K L inst✝³ : H.IsCartanSubalgebra inst✝² : IsTriangularizable K (↥H) L inst✝¹ : IsKilling K L i...	((:c Eq) (:fv _uniq.616263) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.616263) (:fv _uniq.616263) ((:c CommSemiring.toSemiring) (:fv _uniq.616263) ((:c CommRing.toCommSemiring) (:fv _uniq.616263) ((:c EuclideanDomain.toCommRing) (:fv _uniq.616263) ((:c Field.toEuclideanDomain) (:fv _uniq.616263) (:fv _uniq.616292)))...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.616260))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.616266))"},{"name":"inst✝⁷","sexp":"((:c LieAlgebra) (:fv _uniq.616260) (:fv _uniq.6162...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"obtain","sourceEnd":21836,"sourceStart":21830,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":21840,"sourceStart":21837,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"u","sourceEn...	[]	[{"source":"hz","source_end":21865,"source_start":21863,"syntax_kind":"ident"},{"source":"⟨u, hu, v, -, huv⟩","source_end":21859,"source_start":21837,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	49	14	exact	true	1	20	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	43357fac3714bba5f85b1c2e1660d2913af9b68c14efe0260077a10db5b37f6a	255db8331a9fdbceee4f13c245c149ed3f09fd3c776637526f15297843ec744c	cf55135e35da4c6f7200db4f662230757771ea6ce1c0020367e635491286b94a	867e0a544bb338d6bb507ec0259e0f8211cf785ead95ce0936a8b6c0f64b0b41
cat-searcher/leandojo-benchmark-4-random	test	2,481	LieAlgebra.IsKilling.traceForm_eq_zero_of_mem_ker_of_mem_span_coroot	Mathlib/Algebra/Lie/Weights/Killing.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	change <a>killingForm</a> K L (x : L) (z : L) = 0	case mem.intro.intro.intro.intro R : Type u_1 K : Type u_2 L : Type u_3 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : Field K inst✝⁵ : LieAlgebra K L inst✝⁴ : FiniteDimensional K L H : LieSubalgebra K L inst✝³ : H.IsCartanSubalgebra inst✝² : IsTriangularizable K (↥H) L inst✝¹ : IsKilling K L i...	case mem.intro.intro.intro.intro R : Type u_1 K : Type u_2 L : Type u_3 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : Field K inst✝⁵ : LieAlgebra K L inst✝⁴ : FiniteDimensional K L H : LieSubalgebra K L inst✝³ : H.IsCartanSubalgebra inst✝² : IsTriangularizable K (↥H) L inst✝¹ : IsKilling K L i...	((:c Eq) (:fv _uniq.616263) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.616263) (:fv _uniq.616263) ((:c CommSemiring.toSemiring) (:fv _uniq.616263) ((:c CommRing.toCommSemiring) (:fv _uniq.616263) ((:c EuclideanDomain.toCommRing) (:fv _uniq.616263) ((:c Field.toEuclideanDomain) (:fv _uniq.616263) (:fv _uniq.616292)))...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.616260))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.616266))"},{"name":"inst✝⁷","sexp":"((:c LieAlgebra) (:fv _uniq.616260) (:fv _uniq.6162...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"change","sourceEnd":21876,"sourceStart":21870,"tag":"atom"},{"children":[{"children":[{"name":"killingForm","semanticRole":"global","source":"killingForm","sourceEnd":21888,"sourceStart":21877,"tag":"identifier"},{"children":[{"contextIndex":1,"semanticRole":"local","source":"K","sourceEnd":2189...	[]	[{"source":"killingForm K L (x : L) (z : L) = 0","source_end":21912,"source_start":21877,"syntax_kind":"«term_=_»"}]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	49	15	exact	true	1	23	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	13d230c4104c618231a60eb304942963c700afd237ed87280c8552c06e7116be	867e0a544bb338d6bb507ec0259e0f8211cf785ead95ce0936a8b6c0f64b0b41	54793f4698d09b817be24133310293c13af39ba686c2b613884fd4bbee671e80	9793796516dcc4fb2d6dd0a3cce3a76cffb971dd9227a25d749c136415e5fa13
cat-searcher/leandojo-benchmark-4-random	test	2,482	LieAlgebra.IsKilling.traceForm_eq_zero_of_mem_ker_of_mem_span_coroot	Mathlib/Algebra/Lie/Weights/Killing.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	replace hx : α x = 0 := by simpa using hx	case mem.intro.intro.intro.intro R : Type u_1 K : Type u_2 L : Type u_3 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : Field K inst✝⁵ : LieAlgebra K L inst✝⁴ : FiniteDimensional K L H : LieSubalgebra K L inst✝³ : H.IsCartanSubalgebra inst✝² : IsTriangularizable K (↥H) L inst✝¹ : IsKilling K L i...	case mem.intro.intro.intro.intro R : Type u_1 K : Type u_2 L : Type u_3 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : Field K inst✝⁵ : LieAlgebra K L inst✝⁴ : FiniteDimensional K L H : LieSubalgebra K L inst✝³ : H.IsCartanSubalgebra inst✝² : IsTriangularizable K (↥H) L inst✝¹ : IsKilling K L i...	((:c Eq) (:fv _uniq.616263) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.616263) (:fv _uniq.616263) ((:c CommSemiring.toSemiring) (:fv _uniq.616263) ((:c CommRing.toCommSemiring) (:fv _uniq.616263) ((:c EuclideanDomain.toCommRing) (:fv _uniq.616263) ((:c Field.toEuclideanDomain) (:fv _uniq.616263) (:fv _uniq.616292)))...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.616260))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.616266))"},{"name":"inst✝⁷","sexp":"((:c LieAlgebra) (:fv _uniq.616260) (:fv _uniq.6162...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"replace","sourceEnd":21924,"sourceStart":21917,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hx","sourceEnd":21927,"sourceStart":21925,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hx","sourceEnd":21927,"sourceStart":21925,"tag":"...	[]	[{"source":"α x = 0","source_end":21938,"source_start":21930,"syntax_kind":"«term_=_»"},{"source":"hx","source_end":21959,"source_start":21957,"syntax_kind":"ident"}]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	49	16	exact	true	1	23	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	7f3ced7d5b6cd86ba71eaa4af8920755f01c355de7912626ca249eeb5e6dac27	9793796516dcc4fb2d6dd0a3cce3a76cffb971dd9227a25d749c136415e5fa13	bbd81314c16f4beefeba02352829b60bb5da14dbed39da40f3f157c7f6b16557	87f09bc64666244f0be7dae1104c09f6ed4cdfe64b70ca22ceb9a9f971a92b98
cat-searcher/leandojo-benchmark-4-random	test	2,483	LieAlgebra.IsKilling.traceForm_eq_zero_of_mem_ker_of_mem_span_coroot	Mathlib/Algebra/Lie/Weights/Killing.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [← huv, ← <a>LieModule.traceForm_apply_lie_apply</a>, ← <a>LieSubalgebra.coe_bracket_of_module</a>, <a>LieAlgebra.IsKilling.lie_eq_smul_of_mem_rootSpace</a> hu, hx, <a>zero_smul</a>, <a>map_zero</a>, <a>LinearMap.zero_apply</a>]	case mem.intro.intro.intro.intro R : Type u_1 K : Type u_2 L : Type u_3 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : Field K inst✝⁵ : LieAlgebra K L inst✝⁴ : FiniteDimensional K L H : LieSubalgebra K L inst✝³ : H.IsCartanSubalgebra inst✝² : IsTriangularizable K (↥H) L inst✝¹ : IsKilling K L i...		((:c Eq) (:fv _uniq.616263) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.616263) (:fv _uniq.616263) ((:c CommSemiring.toSemiring) (:fv _uniq.616263) ((:c CommRing.toCommSemiring) (:fv _uniq.616263) ((:c EuclideanDomain.toCommRing) (:fv _uniq.616263) ((:c Field.toEuclideanDomain) (:fv _uniq.616263) (:fv _uniq.616292)))...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.616260))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.616266))"},{"name":"inst✝⁷","sexp":"((:c LieAlgebra) (:fv _uniq.616260) (:fv _uniq.6162...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"rw","sourceEnd":21966,"sourceStart":21964,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":21968,"sourceStart":21967,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":21971,"sourceSt...	[]	[{"source":"huv","source_end":21975,"source_start":21972,"syntax_kind":"ident"},{"source":"traceForm_apply_lie_apply","source_end":22006,"source_start":21981,"syntax_kind":"ident"},{"source":"LieSubalgebra.coe_bracket_of_module","source_end":22047,"source_start":22012,"syntax_kind":"ident"},{"source":"lie_eq_smul_of_me...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	49	19	exact	true	1	23	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	fd54fba4751831785ccdf313c4dedda76c312151ad7544e0eff923d2d630dc0b	87f09bc64666244f0be7dae1104c09f6ed4cdfe64b70ca22ceb9a9f971a92b98	789b8a7c569534e68d003f72eb74cd0625b47e865f536cb1be70fd15552f6397	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,484	LieAlgebra.IsKilling.traceForm_eq_zero_of_mem_ker_of_mem_span_coroot	Mathlib/Algebra/Lie/Weights/Killing.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simpa using hx	R : Type u_1 K : Type u_2 L : Type u_3 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : Field K inst✝⁵ : LieAlgebra K L inst✝⁴ : FiniteDimensional K L H : LieSubalgebra K L inst✝³ : H.IsCartanSubalgebra inst✝² : IsTriangularizable K (↥H) L inst✝¹ : IsKilling K L inst✝ : CharZero K α : Weight K (↥...		((:c Eq) (:fv _uniq.616263) ((:c DFunLike.coe) ((:c LieModule.Weight) (:fv _uniq.616263) ((:c Subtype) (:fv _uniq.616266) (:lambda x (:fv _uniq.616266) ((:c Membership.mem) (:fv _uniq.616266) ((:c LieSubalgebra) (:fv _uniq.616263) (:fv _uniq.616266) ((:c EuclideanDomain.toCommRing) (:fv _uniq.616263) ((:c Field.toEucli...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.616260))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.616266))"},{"name":"inst✝⁷","sexp":"((:c LieAlgebra) (:fv _uniq.616260) (:fv _uniq.6162...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LieModule.Weight) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda x :explicit (:fv FV2) (:app (:c Membership.mem) (:ar...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"simpa","sourceEnd":21950,"sourceStart":21945,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"ch...	[]	[{"source":"hx","source_end":21959,"source_start":21957,"syntax_kind":"ident"}]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	49	18	exact	true	1	23	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	be9661eb818a4cf77e4dc1711166c8b2704854c9af59a9f45ade143fa95e044e	044e04230df70980d73c7f9734bcfc295634f2bea1673d6e8b951181dd38ae80	1974ce2fe37f145b393fc7f91fbc4c8c354a914949a5a54eb847e3c50da7bcb5	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,485	LieAlgebra.IsKilling.traceForm_eq_zero_of_mem_ker_of_mem_span_coroot	Mathlib/Algebra/Lie/Weights/Killing.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp	case zero R : Type u_1 K : Type u_2 L : Type u_3 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : Field K inst✝⁵ : LieAlgebra K L inst✝⁴ : FiniteDimensional K L H : LieSubalgebra K L inst✝³ : H.IsCartanSubalgebra inst✝² : IsTriangularizable K (↥H) L inst✝¹ : IsKilling K L inst✝ : CharZero K α : W...		((:c Eq) (:fv _uniq.616263) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.616263) (:fv _uniq.616263) ((:c CommSemiring.toSemiring) (:fv _uniq.616263) ((:c CommRing.toCommSemiring) (:fv _uniq.616263) ((:c EuclideanDomain.toCommRing) (:fv _uniq.616263) ((:c Field.toEuclideanDomain) (:fv _uniq.616263) (:fv _uniq.616292)))...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.616260))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.616266))"},{"name":"inst✝⁷","sexp":"((:c LieAlgebra) (:fv _uniq.616260) (:fv _uniq.6162...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":22151,"sourceStart":22147,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","sour...	[]	[]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	49	30	exact	true	1	18	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	61fb253f094e8b9a32c6542149e89d9d3ff09dc1eb0cd635838460abceda2038	3d68e57c69a9dbddcc929711c4e30417b3a9feddba7231e9ab353338c61cd570	8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,486	LieAlgebra.IsKilling.traceForm_eq_zero_of_mem_ker_of_mem_span_coroot	Mathlib/Algebra/Lie/Weights/Killing.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp [hx, hy]	case add R : Type u_1 K : Type u_2 L : Type u_3 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : Field K inst✝⁵ : LieAlgebra K L inst✝⁴ : FiniteDimensional K L H : LieSubalgebra K L inst✝³ : H.IsCartanSubalgebra inst✝² : IsTriangularizable K (↥H) L inst✝¹ : IsKilling K L inst✝ : CharZero K α : We...		((:c Eq) (:fv _uniq.616263) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.616263) (:fv _uniq.616263) ((:c CommSemiring.toSemiring) (:fv _uniq.616263) ((:c CommRing.toCommSemiring) (:fv _uniq.616263) ((:c EuclideanDomain.toCommRing) (:fv _uniq.616263) ((:c Field.toEuclideanDomain) (:fv _uniq.616263) (:fv _uniq.616292)))...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.616260))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.616266))"},{"name":"inst✝⁷","sexp":"((:c LieAlgebra) (:fv _uniq.616260) (:fv _uniq.6162...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":22181,"sourceStart":22177,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...	[]	[{"source":"hx","source_end":22185,"source_start":22183,"syntax_kind":"ident"},{"source":"hy","source_end":22189,"source_start":22187,"syntax_kind":"ident"}]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	49	34	exact	true	1	24	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	1f46a1cf27c05134af5af9dc88b4ac2773e27ad315a5e7ecb8f415725417b31d	e447d7f9c1026cd45fbedaa076f51474fc36d4482149afa7549d8fcbfcc006ae	b25086c88baa5aad8780cf4a7915ce92894d4cc488f82bf5e3af03c938943dcf	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,487	LieAlgebra.IsKilling.traceForm_eq_zero_of_mem_ker_of_mem_span_coroot	Mathlib/Algebra/Lie/Weights/Killing.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp [hz]	case smul R : Type u_1 K : Type u_2 L : Type u_3 inst✝⁹ : CommRing R inst✝⁸ : LieRing L inst✝⁷ : LieAlgebra R L inst✝⁶ : Field K inst✝⁵ : LieAlgebra K L inst✝⁴ : FiniteDimensional K L H : LieSubalgebra K L inst✝³ : H.IsCartanSubalgebra inst✝² : IsTriangularizable K (↥H) L inst✝¹ : IsKilling K L inst✝ : CharZero K α : W...		((:c Eq) (:fv _uniq.616263) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.616263) (:fv _uniq.616263) ((:c CommSemiring.toSemiring) (:fv _uniq.616263) ((:c CommRing.toCommSemiring) (:fv _uniq.616263) ((:c EuclideanDomain.toCommRing) (:fv _uniq.616263) ((:c Field.toEuclideanDomain) (:fv _uniq.616263) (:fv _uniq.616292)))...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁹","sexp":"((:c CommRing) (:fv _uniq.616260))"},{"name":"inst✝⁸","sexp":"((:c LieRing) (:fv _uniq.616266))"},{"name":"inst✝⁷","sexp":"((:c LieAlgebra) (:fv _uniq.616260) (:fv _uniq.6162...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":22216,"sourceStart":22212,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...	[]	[{"source":"hz","source_end":22220,"source_start":22218,"syntax_kind":"ident"}]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.616260","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.616263","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	49	38	exact	true	1	22	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	b54c76cf53f15377cb49b62b2334345f3e258da635054047211b40ddc68c15fc	49c153da1f1c645584490134a17cb3ed7625b2dce970afbe3d69d8a5de5b1136	199d5d52adca245380d9314e9608af40c4fb728e85bf299c4c3d783f9a3759fc	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,488	one_le_pow_mul_abs_eval_div	Mathlib/Algebra/Polynomial/DenomsClearable.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	obtain ⟨ev, bi, bu, hF⟩ := <a>denomsClearable_natDegree</a> (b := b) (<a>algebraMap</a> ℤ K) f a (by rw [<a>eq_intCast</a>, <a>one_div_mul_cancel</a>] rw [<a>Int.cast_ne_zero</a>] exact b0.ne.symm)	K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ⊢ 1 ≤ ↑b ^ f.natDegree * \|eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f)\|	case intro.intro.intro K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ev : ℤ bi : K bu : bi * (algebraMap ℤ K) b = 1 hF : (algebraMap ℤ K) ev = (algebraMap ℤ K) b ^ f.natDegree * eval ((algebraMap ℤ K) a * bi) (Polynomial.map (alg...	((:c LE.le) (:fv _uniq.22794) ((:c Preorder.toLE) (:fv _uniq.22794) ((:c PartialOrder.toPreorder) (:fv _uniq.22794) ((:c StrictOrderedRing.toPartialOrder) (:fv _uniq.22794) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.22794) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.22794) ((:c LinearOrderedF...	[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedField) (:fv _uniq.22794))"},{"name":"f","sexp":"((:c Polynomial) (:c Int) (:c Int.instSemiring))"},{"name":"a","sexp":"(:c Int)"},{"name":"b","sexp":"(:c Int)"},{"name":"b0","sexp":"((:c LT.lt) (:c Int) (:c Int.instLTInt) ((:c OfNat.ofNa...	(:app (:c LE.le) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV1)) (:arg :exp...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedField) (:ar...	{"children":[{"source":"obtain","sourceEnd":4299,"sourceStart":4293,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":4303,"sourceStart":4300,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"ev","sourceEnd":...	[]	[{"source":"denomsClearable_natDegree (b := b) (algebraMap ℤ K) f a\n (by\n rw [eq_intCast, one_div_mul_cancel]\n rw [Int.cast_ne_zero]\n exact b0.ne.symm)","source_end":4495,"source_start":4328,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨ev, bi, bu, hF⟩","source_end":4320,"source_start"...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna...	21	4	exact	true	1	7	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	55d3296f87de0113a1ac25c1a0578c68c94e4666f19f8ee4d757dd732ce5b061	f8c0c0a71f61fb9ef8ec86b5279577d02191bb63f29cbd2682c1441927da2f12	0b6295d276efa72416fe92318f9b2a1a7d04200d29edeec19efcaaf7a5578410	1556e272801d9969c6116a7c820dd6991a928e3fa28c418aa796493deb7c6fab
cat-searcher/leandojo-benchmark-4-random	test	2,489	one_le_pow_mul_abs_eval_div	Mathlib/Algebra/Polynomial/DenomsClearable.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	obtain Fa := <a>congr_arg</a> <a>abs</a> hF	case intro.intro.intro K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ev : ℤ bi : K bu : bi * (algebraMap ℤ K) b = 1 hF : (algebraMap ℤ K) ev = (algebraMap ℤ K) b ^ f.natDegree * eval ((algebraMap ℤ K) a * bi) (Polynomial.map (alg...	case intro.intro.intro K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ev : ℤ bi : K bu : bi * (algebraMap ℤ K) b = 1 hF : (algebraMap ℤ K) ev = (algebraMap ℤ K) b ^ f.natDegree * eval ((algebraMap ℤ K) a * bi) (Polynomial.map (alg...	((:c LE.le) (:fv _uniq.22794) ((:c Preorder.toLE) (:fv _uniq.22794) ((:c PartialOrder.toPreorder) (:fv _uniq.22794) ((:c StrictOrderedRing.toPartialOrder) (:fv _uniq.22794) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.22794) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.22794) ((:c LinearOrderedF...	[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedField) (:fv _uniq.22794))"},{"name":"f","sexp":"((:c Polynomial) (:c Int) (:c Int.instSemiring))"},{"name":"a","sexp":"(:c Int)"},{"name":"b","sexp":"(:c Int)"},{"name":"b0","sexp":"((:c LT.lt) (:c Int) (:c Int.instLTInt) ((:c OfNat.ofNa...	(:app (:c LE.le) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV1)) (:arg :exp...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedField) (:ar...	{"children":[{"source":"obtain","sourceEnd":4504,"sourceStart":4498,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"Fa","sourceEnd":4507,"sourceStart":4505,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"Fa","sourceEnd":4507,"sourceStar...	[]	[{"source":"_root_.congr_arg abs hF","source_end":4534,"source_start":4511,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna...	21	17	exact	true	1	11	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	ca5047ee7131df1edb94c88ddf3e41b3f31134d3465251532351ec194b468050	1556e272801d9969c6116a7c820dd6991a928e3fa28c418aa796493deb7c6fab	b3c04e3ae126afe95a9ef6adfaf55aada05bc87dd17ecc5d2979059b5f0b0bfd	d709233a11d893131e5c8a0b8c91c2a63763cb4c50e20e4bd91203dfd4e3f692
cat-searcher/leandojo-benchmark-4-random	test	2,490	one_le_pow_mul_abs_eval_div	Mathlib/Algebra/Polynomial/DenomsClearable.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>eq_one_div_of_mul_eq_one_left</a> bu, <a>eq_intCast</a>, <a>eq_intCast</a>, <a>abs_mul</a>] at Fa	case intro.intro.intro K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ev : ℤ bi : K bu : bi * (algebraMap ℤ K) b = 1 hF : (algebraMap ℤ K) ev = (algebraMap ℤ K) b ^ f.natDegree * eval ((algebraMap ℤ K) a * bi) (Polynomial.map (alg...	case intro.intro.intro K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ev : ℤ bi : K bu : bi * (algebraMap ℤ K) b = 1 hF : (algebraMap ℤ K) ev = (algebraMap ℤ K) b ^ f.natDegree * eval ((algebraMap ℤ K) a * bi) (Polynomial.map (alg...	((:c LE.le) (:fv _uniq.22794) ((:c Preorder.toLE) (:fv _uniq.22794) ((:c PartialOrder.toPreorder) (:fv _uniq.22794) ((:c StrictOrderedRing.toPartialOrder) (:fv _uniq.22794) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.22794) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.22794) ((:c LinearOrderedF...	[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedField) (:fv _uniq.22794))"},{"name":"f","sexp":"((:c Polynomial) (:c Int) (:c Int.instSemiring))"},{"name":"a","sexp":"(:c Int)"},{"name":"b","sexp":"(:c Int)"},{"name":"b0","sexp":"((:c LT.lt) (:c Int) (:c Int.instLTInt) ((:c OfNat.ofNa...	(:app (:c LE.le) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV1)) (:arg :exp...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedField) (:ar...	{"children":[{"source":"rw","sourceEnd":4539,"sourceStart":4537,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4541,"sourceStart":4540,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"eq_one_...	[]	[{"source":"Fa","source_end":4613,"source_start":4611,"syntax_kind":"ident"},{"source":"eq_one_div_of_mul_eq_one_left bu","source_end":4573,"source_start":4541,"syntax_kind":"Lean.Parser.Term.app"},{"source":"eq_intCast","source_end":4585,"source_start":4575,"syntax_kind":"ident"},{"source":"eq_intCast","source_end":45...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna...	21	18	exact	true	1	12	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	74bc4f16fa124375121106dd474cf2761d1300ea84bf3a3dfea457f6d1720b20	d709233a11d893131e5c8a0b8c91c2a63763cb4c50e20e4bd91203dfd4e3f692	0ec96c9d7931daf8372d52516a2e403331d2f87ab9d89aee08c73ba495da99b6	822a986ae8e4690dcdba04e318e78390b89807ab1f8bfdd8a156ca438f3f0bc4
cat-searcher/leandojo-benchmark-4-random	test	2,491	one_le_pow_mul_abs_eval_div	Mathlib/Algebra/Polynomial/DenomsClearable.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>abs_of_pos</a> (<a>pow_pos</a> (Int.cast_pos.mpr b0) _ : 0 < (b : K) ^ _), <a>one_div</a>, <a>eq_intCast</a>] at Fa	case intro.intro.intro K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ev : ℤ bi : K bu : bi * (algebraMap ℤ K) b = 1 hF : (algebraMap ℤ K) ev = (algebraMap ℤ K) b ^ f.natDegree * eval ((algebraMap ℤ K) a * bi) (Polynomial.map (alg...	case intro.intro.intro K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ev : ℤ bi : K bu : bi * (algebraMap ℤ K) b = 1 hF : (algebraMap ℤ K) ev = (algebraMap ℤ K) b ^ f.natDegree * eval ((algebraMap ℤ K) a * bi) (Polynomial.map (alg...	((:c LE.le) (:fv _uniq.22794) ((:c Preorder.toLE) (:fv _uniq.22794) ((:c PartialOrder.toPreorder) (:fv _uniq.22794) ((:c StrictOrderedRing.toPartialOrder) (:fv _uniq.22794) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.22794) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.22794) ((:c LinearOrderedF...	[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedField) (:fv _uniq.22794))"},{"name":"f","sexp":"((:c Polynomial) (:c Int) (:c Int.instSemiring))"},{"name":"a","sexp":"(:c Int)"},{"name":"b","sexp":"(:c Int)"},{"name":"b0","sexp":"((:c LT.lt) (:c Int) (:c Int.instLTInt) ((:c OfNat.ofNa...	(:app (:c LE.le) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV1)) (:arg :exp...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedField) (:ar...	{"children":[{"source":"rw","sourceEnd":4618,"sourceStart":4616,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4620,"sourceStart":4619,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"abs_of_...	[]	[{"source":"Fa","source_end":4710,"source_start":4708,"syntax_kind":"ident"},{"source":"abs_of_pos (pow_pos (Int.cast_pos.mpr b0) _ : 0 < (b : K) ^ _)","source_end":4682,"source_start":4620,"syntax_kind":"Lean.Parser.Term.app"},{"source":"one_div","source_end":4691,"source_start":4684,"syntax_kind":"ident"},{"source":"...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna...	21	24	exact	true	1	12	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	ce1db2b32b2d6c9ed25883bd068f3d0a7500229399913d843066554037055310	822a986ae8e4690dcdba04e318e78390b89807ab1f8bfdd8a156ca438f3f0bc4	172c8c3e7a54aef9384e0eaf95b6f41ffd8f3c59dd443bbd9d4d5b1bef501676	f7ebb27e2e454153210c3fa2cfb91bf231bdeddc3091165556315dfecdc3c0a3
cat-searcher/leandojo-benchmark-4-random	test	2,492	one_le_pow_mul_abs_eval_div	Mathlib/Algebra/Polynomial/DenomsClearable.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>div_eq_mul_inv</a>, ← Fa, ← <a>Int.cast_abs</a>, ← <a>Int.cast_one</a>, <a>Int.cast_le</a>]	case intro.intro.intro K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ev : ℤ bi : K bu : bi * (algebraMap ℤ K) b = 1 hF : (algebraMap ℤ K) ev = (algebraMap ℤ K) b ^ f.natDegree * eval ((algebraMap ℤ K) a * bi) (Polynomial.map (alg...	case intro.intro.intro K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ev : ℤ bi : K bu : bi * (algebraMap ℤ K) b = 1 hF : (algebraMap ℤ K) ev = (algebraMap ℤ K) b ^ f.natDegree * eval ((algebraMap ℤ K) a * bi) (Polynomial.map (alg...	((:c LE.le) (:fv _uniq.22794) ((:c Preorder.toLE) (:fv _uniq.22794) ((:c PartialOrder.toPreorder) (:fv _uniq.22794) ((:c StrictOrderedRing.toPartialOrder) (:fv _uniq.22794) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.22794) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.22794) ((:c LinearOrderedF...	[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedField) (:fv _uniq.22794))"},{"name":"f","sexp":"((:c Polynomial) (:c Int) (:c Int.instSemiring))"},{"name":"a","sexp":"(:c Int)"},{"name":"b","sexp":"(:c Int)"},{"name":"b0","sexp":"((:c LT.lt) (:c Int) (:c Int.instLTInt) ((:c OfNat.ofNa...	(:app (:c LE.le) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV1)) (:arg :exp...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedField) (:ar...	{"children":[{"source":"rw","sourceEnd":4715,"sourceStart":4713,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4717,"sourceStart":4716,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"div_eq_mul_inv","sem...	[]	[{"source":"div_eq_mul_inv","source_end":4731,"source_start":4717,"syntax_kind":"ident"},{"source":"Fa","source_end":4739,"source_start":4737,"syntax_kind":"ident"},{"source":"Int.cast_abs","source_end":4757,"source_start":4745,"syntax_kind":"ident"},{"source":"Int.cast_one","source_end":4775,"source_start":4763,"synta...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna...	21	29	exact	true	1	12	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	59497154e1f96506aecbb5c59052ca78e0cd1b23ae399199716e9675cc4dc442	f7ebb27e2e454153210c3fa2cfb91bf231bdeddc3091165556315dfecdc3c0a3	3348ba9c20db1b6747122e7260582b8f7cc7d4c8c6d6346e819d07aa289d69aa	4bead60518982b16db7ec812c379d3977023ce079faa744120ffec6c022b760b
cat-searcher/leandojo-benchmark-4-random	test	2,493	one_le_pow_mul_abs_eval_div	Mathlib/Algebra/Polynomial/DenomsClearable.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	refine <a>Int.le_of_lt_add_one</a> ((<a>lt_add_iff_pos_left</a> 1).<a>Iff.mpr</a> (abs_pos.mpr fun F0 => fab ?_))	case intro.intro.intro K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ev : ℤ bi : K bu : bi * (algebraMap ℤ K) b = 1 hF : (algebraMap ℤ K) ev = (algebraMap ℤ K) b ^ f.natDegree * eval ((algebraMap ℤ K) a * bi) (Polynomial.map (alg...	case intro.intro.intro K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ev : ℤ bi : K bu : bi * (algebraMap ℤ K) b = 1 hF : (algebraMap ℤ K) ev = (algebraMap ℤ K) b ^ f.natDegree * eval ((algebraMap ℤ K) a * bi) (Polynomial.map (alg...	((:c LE.le) (:c Int) (:c Int.instLEInt) ((:c OfNat.ofNat) (:c Int) (:lit 1) ((:c instOfNat) (:lit 1))) ((:c abs) (:c Int) (:c instLatticeInt) (:c Int.instAddGroup) (:fv _uniq.23928)))	[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedField) (:fv _uniq.22794))"},{"name":"f","sexp":"((:c Polynomial) (:c Int) (:c Int.instSemiring))"},{"name":"a","sexp":"(:c Int)"},{"name":"b","sexp":"(:c Int)"},{"name":"b0","sexp":"((:c LT.lt) (:c Int) (:c Int.instLTInt) ((:c OfNat.ofNa...	(:app (:c LE.le) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Int)) (:arg :explici...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedField) (:ar...	{"children":[{"source":"refine","sourceEnd":4798,"sourceStart":4792,"tag":"atom"},{"children":[{"name":"Int.le_of_lt_add_one","semanticRole":"global","source":"Int.le_of_lt_add_one","sourceEnd":4819,"sourceStart":4799,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":4821,"sourceStart":4820,"tag":...	[]	[{"source":"Int.le_of_lt_add_one ((lt_add_iff_pos_left 1).mpr (abs_pos.mpr fun F0 => fab ?_))","source_end":4880,"source_start":4799,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna...	21	36	exact	true	1	12	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	c3d8469a3d61525afd8f94cb34c7e57b27bff13db757a10283062ac4d2478d2b	4bead60518982b16db7ec812c379d3977023ce079faa744120ffec6c022b760b	11c1e5a58403a2d7dd6413dd23f90bf2c9986d162134cab0247ecfef274ad0eb	2af9f434c57fcad044e4b378b2410d66500e88c26c7dd4db1027e32a447cfbf3
cat-searcher/leandojo-benchmark-4-random	test	2,494	one_le_pow_mul_abs_eval_div	Mathlib/Algebra/Polynomial/DenomsClearable.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>eq_one_div_of_mul_eq_one_left</a> bu, F0, <a>one_div</a>, <a>eq_intCast</a>, <a>Int.cast_zero</a>, <a>zero_eq_mul</a>] at hF	case intro.intro.intro K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ev : ℤ bi : K bu : bi * (algebraMap ℤ K) b = 1 hF : (algebraMap ℤ K) ev = (algebraMap ℤ K) b ^ f.natDegree * eval ((algebraMap ℤ K) a * bi) (Polynomial.map (alg...	case intro.intro.intro K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ev : ℤ bi : K bu : bi * (algebraMap ℤ K) b = 1 hF : (algebraMap ℤ K) b ^ f.natDegree = 0 ∨ eval ((algebraMap ℤ K) a * ((algebraMap ℤ K) b)⁻¹) (Polynomial.map (a...	((:c Eq) (:fv _uniq.22794) ((:c Polynomial.eval) (:fv _uniq.22794) ((:c StrictOrderedSemiring.toSemiring) (:fv _uniq.22794) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.22794) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.22794) ((:c LinearOrderedSemifield.toLinearOrderedCommSemir...	[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedField) (:fv _uniq.22794))"},{"name":"f","sexp":"((:c Polynomial) (:c Int) (:c Int.instSemiring))"},{"name":"a","sexp":"(:c Int)"},{"name":"b","sexp":"(:c Int)"},{"name":"b0","sexp":"((:c LT.lt) (:c Int) (:c Int.instLTInt) ((:c OfNat.ofNa...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Polynomial.eval) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedField) (:ar...	{"children":[{"source":"rw","sourceEnd":4885,"sourceStart":4883,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4887,"sourceStart":4886,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"eq_one_...	[]	[{"source":"hF","source_end":4979,"source_start":4977,"syntax_kind":"ident"},{"source":"eq_one_div_of_mul_eq_one_left bu","source_end":4919,"source_start":4887,"syntax_kind":"Lean.Parser.Term.app"},{"source":"F0","source_end":4923,"source_start":4921,"syntax_kind":"ident"},{"source":"one_div","source_end":4932,"source_...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna...	21	37	exact	true	1	13	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	abac81394a7bf85e4316ee34533f1ce5c5dcd6c05310801b55107d8ff123dfa0	2af9f434c57fcad044e4b378b2410d66500e88c26c7dd4db1027e32a447cfbf3	e62eafd1c60dc1de34f98b6e89dda9967e1afb15ad77e4c2649a5ef573a077fe	0742b0495594179c1040b031fe2bf34d39510f0aca74fd4e6beac00bb3fc754c
cat-searcher/leandojo-benchmark-4-random	test	2,495	one_le_pow_mul_abs_eval_div	Mathlib/Algebra/Polynomial/DenomsClearable.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	cases' hF with hF hF	case intro.intro.intro K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ev : ℤ bi : K bu : bi * (algebraMap ℤ K) b = 1 hF : (algebraMap ℤ K) b ^ f.natDegree = 0 ∨ eval ((algebraMap ℤ K) a * ((algebraMap ℤ K) b)⁻¹) (Polynomial.map (a...	case intro.intro.intro.inl K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ev : ℤ bi : K bu : bi * (algebraMap ℤ K) b = 1 Fa : \|↑ev\| = ↑b ^ f.natDegree * \|eval (↑a * (↑b)⁻¹) (Polynomial.map (algebraMap ℤ K) f)\| F0 : ev = 0 hF : (algebraM...	((:c Eq) (:fv _uniq.22794) ((:c Polynomial.eval) (:fv _uniq.22794) ((:c StrictOrderedSemiring.toSemiring) (:fv _uniq.22794) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.22794) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.22794) ((:c LinearOrderedSemifield.toLinearOrderedCommSemir...	[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedField) (:fv _uniq.22794))"},{"name":"f","sexp":"((:c Polynomial) (:c Int) (:c Int.instSemiring))"},{"name":"a","sexp":"(:c Int)"},{"name":"b","sexp":"(:c Int)"},{"name":"b0","sexp":"((:c LT.lt) (:c Int) (:c Int.instLTInt) ((:c OfNat.ofNa...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Polynomial.eval) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedField) (:ar...	{"children":[{"source":"cases'","sourceEnd":4988,"sourceStart":4982,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":11,"semanticRole":"local","source":"hF","sourceEnd":4991,"sourceStart":4989,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","sou...	[]	[{"source":"hF","source_end":4991,"source_start":4989,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna...	21	45	exact	true	1	13	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	dc5d5d1c91cf38d93668aa4fac12d331e7e50a3e9064df49ff1bdc84e1945297	0742b0495594179c1040b031fe2bf34d39510f0aca74fd4e6beac00bb3fc754c	c9a78618ae3e231e15d09122ec91bc025498e3d1930d28a68ccbc05c80de5b47	8aca3d15518ecf6f03da8d3800ffb22fab752565d58b240a73c292cc6452ece9
cat-searcher/leandojo-benchmark-4-random	test	2,496	one_le_pow_mul_abs_eval_div	Mathlib/Algebra/Polynomial/DenomsClearable.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>eq_intCast</a>, <a>one_div_mul_cancel</a>]	K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ⊢ ?m.22808 * (algebraMap ℤ K) b = 1	K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ⊢ ↑b ≠ 0	((:c Eq) (:fv _uniq.22794) ((:c HMul.hMul) (:fv _uniq.22794) (:fv _uniq.22794) (:fv _uniq.22794) ((:c instHMul) (:fv _uniq.22794) ((:c NonUnitalNonAssocSemiring.toMul) (:fv _uniq.22794) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.22794) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.22794) ((:c CommSemi...	[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedField) (:fv _uniq.22794))"},{"name":"f","sexp":"((:c Polynomial) (:c Int) (:c Int.instSemiring))"},{"name":"a","sexp":"(:c Int)"},{"name":"b","sexp":"(:c Int)"},{"name":"b0","sexp":"((:c LT.lt) (:c Int) (:c Int.instLTInt) ((:c OfNat.ofNa...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedField) (:ar...	{"children":[{"source":"rw","sourceEnd":4406,"sourceStart":4404,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4408,"sourceStart":4407,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"eq_intCast","semanti...	[]	[{"source":"eq_intCast","source_end":4418,"source_start":4408,"syntax_kind":"ident"},{"source":"one_div_mul_cancel","source_end":4438,"source_start":4420,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna...	21	9	exact	true	1	7	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	02837bcabfc9f259c86f8b57d942eae51dfb8e0df3386ce8de13bbd300903e0a	dd9800cd57aa3d39a10b3f674010d5672bbd56e6ce195d1abef3ad3a3747335f	7789c0124ce6931cf402235550264a9406f7130474238ac6e17f560fdc666775	bbd2c9857c16536c93fe7b553a5cdddba8d30e720ac22a834e8ff757c7ae2b84
cat-searcher/leandojo-benchmark-4-random	test	2,497	one_le_pow_mul_abs_eval_div	Mathlib/Algebra/Polynomial/DenomsClearable.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>Int.cast_ne_zero</a>]	K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ⊢ ↑b ≠ 0	K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ⊢ b ≠ 0	((:c Ne) (:fv _uniq.22794) ((:c Int.cast) (:fv _uniq.22794) ((:c NonAssocRing.toIntCast) (:fv _uniq.22794) ((:c Ring.toNonAssocRing) (:fv _uniq.22794) ((:c StrictOrderedRing.toRing) (:fv _uniq.22794) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.22794) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq...	[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedField) (:fv _uniq.22794))"},{"name":"f","sexp":"((:c Polynomial) (:c Int) (:c Int.instSemiring))"},{"name":"a","sexp":"(:c Int)"},{"name":"b","sexp":"(:c Int)"},{"name":"b0","sexp":"((:c LT.lt) (:c Int) (:c Int.instLTInt) ((:c OfNat.ofNa...	(:app (:c Ne) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Int.cast) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c IntCast) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV1)) (:arg :expl...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedField) (:ar...	{"children":[{"source":"rw","sourceEnd":4450,"sourceStart":4448,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4452,"sourceStart":4451,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Int.cast_ne_zero","s...	[]	[{"source":"Int.cast_ne_zero","source_end":4468,"source_start":4452,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna...	21	13	exact	true	1	7	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	ffdc3e64cd9ed43f4408769db218f8891719e20914d3c5e3eb4625a979c18064	bbd2c9857c16536c93fe7b553a5cdddba8d30e720ac22a834e8ff757c7ae2b84	aa5831d8932cc1b3cd73ebaf0d90ca30fba5d548827563055ea50c2f291663e5	28b4b450cf00e2aeecf14c4ee55412b83dd94e26a623c123a9fc27a8ce103339
cat-searcher/leandojo-benchmark-4-random	test	2,498	one_le_pow_mul_abs_eval_div	Mathlib/Algebra/Polynomial/DenomsClearable.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact b0.ne.symm	K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ⊢ b ≠ 0		((:c Ne) (:c Int) (:fv _uniq.22798) ((:c OfNat.ofNat) (:c Int) (:lit 0) ((:c instOfNat) (:lit 0))))	[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedField) (:fv _uniq.22794))"},{"name":"f","sexp":"((:c Polynomial) (:c Int) (:c Int.instSemiring))"},{"name":"a","sexp":"(:c Int)"},{"name":"b","sexp":"(:c Int)"},{"name":"b0","sexp":"((:c LT.lt) (:c Int) (:c Int.instLTInt) ((:c OfNat.ofNa...	(:app (:c Ne) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:fv FV5)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Int)) (:arg :explicit 1 (:lit 0))))))))	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedField) (:ar...	{"children":[{"source":"exact","sourceEnd":4483,"sourceStart":4478,"tag":"atom"},{"name":"Ne.symm","semanticRole":"global","source":"b0.ne.symm","sourceEnd":4494,"sourceStart":4484,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact b0.ne.symm","sourceEnd":4494,"sourceStart":4478,"tag":"node"}	[]	[{"source":"b0.ne.symm","source_end":4494,"source_start":4484,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna...	21	16	exact	true	1	7	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	097815b41759eae296ac9746f9949e934ff58415c2163f1bda46efed016afd0f	28b4b450cf00e2aeecf14c4ee55412b83dd94e26a623c123a9fc27a8ce103339	179cef2f28881f98fa0196055f6b1d10ad7f564691d3f0df9ac0752e5b94df2c	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,499	one_le_pow_mul_abs_eval_div	Mathlib/Algebra/Polynomial/DenomsClearable.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact (not_le.mpr b0 (<a>le_of_eq</a> (Int.cast_eq_zero.mp (<a>pow_eq_zero</a> hF)))).<a>False.elim</a>	case intro.intro.intro.inl K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ev : ℤ bi : K bu : bi * (algebraMap ℤ K) b = 1 Fa : \|↑ev\| = ↑b ^ f.natDegree * \|eval (↑a * (↑b)⁻¹) (Polynomial.map (algebraMap ℤ K) f)\| F0 : ev = 0 hF : (algebraM...		((:c Eq) (:fv _uniq.22794) ((:c Polynomial.eval) (:fv _uniq.22794) ((:c StrictOrderedSemiring.toSemiring) (:fv _uniq.22794) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.22794) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.22794) ((:c LinearOrderedSemifield.toLinearOrderedCommSemir...	[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedField) (:fv _uniq.22794))"},{"name":"f","sexp":"((:c Polynomial) (:c Int) (:c Int.instSemiring))"},{"name":"a","sexp":"(:c Int)"},{"name":"b","sexp":"(:c Int)"},{"name":"b0","sexp":"((:c LT.lt) (:c Int) (:c Int.instLTInt) ((:c OfNat.ofNa...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Polynomial.eval) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedField) (:ar...	{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":5013,"sourceStart":5008,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":5015,"sourceStart":5014,"tag":"atom"},{"children":[{"source":"not_le.mpr","sourceEnd":5025,"sourceStart":5015,"tag":"identifier"},{"children":[{"con...	[]	[{"source":"(not_le.mpr b0 (le_of_eq (Int.cast_eq_zero.mp (pow_eq_zero hF)))).elim","source_end":5084,"source_start":5014,"syntax_kind":"Lean.Parser.Term.proj"}]	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna...	21	48	exact	true	1	13	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	a3c946c4cc585d147b58a550cd32cce7e5c94795f77749dd45406393011d6494	8abab0fb10eecddefe98d07d38c1e7932e6a18318568c0efb5199ebdc75f5190	40081c1e85aac9e04066c5abbeab0a65de57a784a6f541382d078c9dc131e954	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,500	one_le_pow_mul_abs_eval_div	Mathlib/Algebra/Polynomial/DenomsClearable.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rwa [<a>div_eq_mul_inv</a>]	case intro.intro.intro.inr K : Type u_1 inst✝ : LinearOrderedField K f : ℤ[X] a b : ℤ b0 : 0 < b fab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0 ev : ℤ bi : K bu : bi * (algebraMap ℤ K) b = 1 Fa : \|↑ev\| = ↑b ^ f.natDegree * \|eval (↑a * (↑b)⁻¹) (Polynomial.map (algebraMap ℤ K) f)\| F0 : ev = 0 hF : eval ((al...		((:c Eq) (:fv _uniq.22794) ((:c Polynomial.eval) (:fv _uniq.22794) ((:c StrictOrderedSemiring.toSemiring) (:fv _uniq.22794) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.22794) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:fv _uniq.22794) ((:c LinearOrderedSemifield.toLinearOrderedCommSemir...	[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedField) (:fv _uniq.22794))"},{"name":"f","sexp":"((:c Polynomial) (:c Int) (:c Int.instSemiring))"},{"name":"a","sexp":"(:c Int)"},{"name":"b","sexp":"(:c Int)"},{"name":"b0","sexp":"((:c LT.lt) (:c Int) (:c Int.instLTInt) ((:c OfNat.ofNa...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Polynomial.eval) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedField) (:ar...	{"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":5093,"sourceStart":5090,"tag":"atom"},{"children":[{"source":"[","sourceEnd":5095,"sourceStart":5094,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"div_eq_mul_inv","semanticRole":"glo...	[]	[{"source":"div_eq_mul_inv","source_end":5109,"source_start":5095,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22794","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.22795","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna...	21	53	exact	true	1	13	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	e1b762e1d83e202204c7db1bbb5641139ecdcae118ffdbae4c48ea945b825eae	6b7ae5019141d331370cbc1a6064daaf3f3012f51cf516944579592d101ca1eb	50a18966dcf7ab2635936df2a65048779cee8c41a01f4c0afd0edb95fbc91b0f	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,501	ENNReal.iSup_add_iSup	Mathlib/Topology/Instances/ENNReal.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	cases <a>isEmpty_or_nonempty</a> ι	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∞ ι : Sort u_4 f g : ι → ℝ≥0∞ h : ∀ (i j : ι), ∃ k, f i + g j ≤ f k + g k ⊢ iSup f + iSup g = ⨆ a, f a + g a	case inl 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∞ ι : Sort u_4 f g : ι → ℝ≥0∞ h : ∀ (i j : ι), ∃ k, f i + g j ≤ f k + g k h✝ : IsEmpty ι ⊢ iSup f + iSup g = ⨆ a, f a + g a case inr 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 ...	((:c Eq) (:c ENNReal) ((:c HAdd.hAdd) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHAdd) (:c ENNReal) ((:c Distrib.toAdd) (:c ENNReal) ((:c NonUnitalNonAssocSemiring.toDistrib) (:c ENNReal) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:c ENNReal) ((:c Semiring.toNonAssocSemiring) (:c ENNReal) ((:c OrderedSemi...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"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 N...	(:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c ENNReal)) (:arg :explicit 1 (:c ENNReal)) (:arg :...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119346","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119349","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"cases","sourceEnd":32321,"sourceStart":32316,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"isEmpty_or_nonempty","semanticRole":"global","source":"isEmpty_or_nonempty","sourceEnd":32341,"sourceStart":32322,"tag":"identifier"},...	[]	[{"source":"isEmpty_or_nonempty ι","source_end":32344,"source_start":32322,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119346","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119349","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	200	4	exact	true	1	21	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	0a07021c2843fdbfaae542f5351570247e58cb98ef87c9977c7af8f494088fd6	8fa715852ec1886bebfdc6e0b6ad2ade613fb73b27569b8291485e2dac733bb9	6356799323e07ad70e18e3a15445ecad7892c2b02de792b86e9c4c338240579e	8b2463c2b45d270df3b74a94208b47cd6ff482f3eaecab5eab535060b7840d38
cat-searcher/leandojo-benchmark-4-random	test	2,502	ENNReal.iSup_add_iSup	Mathlib/Topology/Instances/ENNReal.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp only [<a>iSup_of_empty</a>, <a>ENNReal.bot_eq_zero</a>, <a>zero_add</a>]	case inl 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∞ ι : Sort u_4 f g : ι → ℝ≥0∞ h : ∀ (i j : ι), ∃ k, f i + g j ≤ f k + g k h✝ : IsEmpty ι ⊢ iSup f + iSup g = ⨆ a, f a + g a		((:c Eq) (:c ENNReal) ((:c HAdd.hAdd) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHAdd) (:c ENNReal) ((:c Distrib.toAdd) (:c ENNReal) ((:c NonUnitalNonAssocSemiring.toDistrib) (:c ENNReal) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:c ENNReal) ((:c Semiring.toNonAssocSemiring) (:c ENNReal) ((:c OrderedSemi...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"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 N...	(:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c ENNReal)) (:arg :explicit 1 (:c ENNReal)) (:arg :...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119346","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119349","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":32354,"sourceStart":32350,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":32359,"sourceStart":32355,"tag":"atom"}],"kind"...	[]	[{"source":"iSup_of_empty","source_end":32374,"source_start":32361,"syntax_kind":"ident"},{"source":"bot_eq_zero","source_end":32387,"source_start":32376,"syntax_kind":"ident"},{"source":"zero_add","source_end":32397,"source_start":32389,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119346","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119349","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	200	7	exact	true	1	22	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	5794a38eb5c7489ed9410b64f3830d7983900e89a4b3fe31c567a52b895aec4f	61bea2329c4a1fe5a7118b6f85617a3d2d5f4497c8e0baa9d07e50a2d1b7c641	80aea4207aefec7c0637611b4b03bac22cab05b091a721d60ae5618af9e3f343	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,503	ENNReal.iSup_add_iSup	Mathlib/Topology/Instances/ENNReal.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	refine <a>le_antisymm</a> ?_ (<a>iSup_le</a> fun a => <a>add_le_add</a> (<a>le_iSup</a> _ _) (<a>le_iSup</a> _ _))	case inr 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∞ ι : Sort u_4 f g : ι → ℝ≥0∞ h : ∀ (i j : ι), ∃ k, f i + g j ≤ f k + g k h✝ : Nonempty ι ⊢ iSup f + iSup g = ⨆ a, f a + g a	case inr 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∞ ι : Sort u_4 f g : ι → ℝ≥0∞ h : ∀ (i j : ι), ∃ k, f i + g j ≤ f k + g k h✝ : Nonempty ι ⊢ iSup f + iSup g ≤ ⨆ a, f a + g a	((:c Eq) (:c ENNReal) ((:c HAdd.hAdd) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHAdd) (:c ENNReal) ((:c Distrib.toAdd) (:c ENNReal) ((:c NonUnitalNonAssocSemiring.toDistrib) (:c ENNReal) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:c ENNReal) ((:c Semiring.toNonAssocSemiring) (:c ENNReal) ((:c OrderedSemi...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"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 N...	(:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c ENNReal)) (:arg :explicit 1 (:c ENNReal)) (:arg :...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119346","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119349","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"refine","sourceEnd":32410,"sourceStart":32404,"tag":"atom"},{"children":[{"name":"le_antisymm","semanticRole":"global","source":"le_antisymm","sourceEnd":32422,"sourceStart":32411,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":32424,"sourceStart":32423,"tag":"atom"},{"ch...	[]	[{"source":"le_antisymm ?_ (iSup_le fun a => add_le_add (le_iSup _ _) (le_iSup _ _))","source_end":32483,"source_start":32411,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119346","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119349","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	200	14	exact	true	1	22	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	c1c985d4721b6ea5dd3c4929c8690226848431416adfcb758fccfb6497304600	535fa98e3767eafcd6dba62d5605e3758c75ece46445d130706b5b6377d4fc7e	b56ca5310f35b438b44f8b21a5326bb4233f1a7ad5cac9b83944a7d2adb23a9c	c746b973817d03dd949fc9cb839caa53edbae375ac6ffc9fae0c8e3ebb1968c1
cat-searcher/leandojo-benchmark-4-random	test	2,504	ENNReal.iSup_add_iSup	Mathlib/Topology/Instances/ENNReal.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	refine <a>ENNReal.iSup_add_iSup_le</a> fun i j => ?_	case inr 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∞ ι : Sort u_4 f g : ι → ℝ≥0∞ h : ∀ (i j : ι), ∃ k, f i + g j ≤ f k + g k h✝ : Nonempty ι ⊢ iSup f + iSup g ≤ ⨆ a, f a + g a	case inr 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∞ ι : Sort u_4 f g : ι → ℝ≥0∞ h : ∀ (i j : ι), ∃ k, f i + g j ≤ f k + g k h✝ : Nonempty ι i j : ι ⊢ f i + g j ≤ ⨆ a, f a + g a	((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.toPartialOrder) (:c ENNReal) ((:c OrderedCommSemiring.toOrderedSemiring) (:c ENNReal) ((:c CanonicallyOrderedCommSemiring.toOrderedCommSemiring) (:c ENNReal) (:c ENNReal.instCanonicallyOrderedCommSe...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"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 N...	(:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:a...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119346","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119349","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"refine","sourceEnd":32494,"sourceStart":32488,"tag":"atom"},{"children":[{"name":"ENNReal.iSup_add_iSup_le","semanticRole":"global","source":"iSup_add_iSup_le","sourceEnd":32511,"sourceStart":32495,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":32515,"sourceStart":3251...	[]	[{"source":"iSup_add_iSup_le fun i j => ?_","source_end":32525,"source_start":32495,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119346","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119349","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	200	15	exact	true	1	22	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	a960801c844f767a0de3ae294976a119283ab5e9c6c1124cc32c3bf0fddf483d	c746b973817d03dd949fc9cb839caa53edbae375ac6ffc9fae0c8e3ebb1968c1	9ee5e4c7a5afcfc2a64796d99e0ca18ce36586727d2d3b18d24a169a6f8a98cb	7f5f0d2aed28e1f9a22739692ef0370c08f03ba2cc06369706e6f3a766a726c7
cat-searcher/leandojo-benchmark-4-random	test	2,505	ENNReal.iSup_add_iSup	Mathlib/Topology/Instances/ENNReal.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rcases h i j with ⟨k, hk⟩	case inr 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∞ ι : Sort u_4 f g : ι → ℝ≥0∞ h : ∀ (i j : ι), ∃ k, f i + g j ≤ f k + g k h✝ : Nonempty ι i j : ι ⊢ f i + g j ≤ ⨆ a, f a + g a	case inr.intro 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∞ ι : Sort u_4 f g : ι → ℝ≥0∞ h : ∀ (i j : ι), ∃ k, f i + g j ≤ f k + g k h✝ : Nonempty ι i j k : ι hk : f i + g j ≤ f k + g k ⊢ f i + g j ≤ ⨆ a, f a + g a	((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.toPartialOrder) (:c ENNReal) ((:c OrderedCommSemiring.toOrderedSemiring) (:c ENNReal) ((:c CanonicallyOrderedCommSemiring.toOrderedCommSemiring) (:c ENNReal) (:c ENNReal.instCanonicallyOrderedCommSe...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"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 N...	(:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:a...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119346","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119349","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"rcases","sourceEnd":32536,"sourceStart":32530,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"contextIndex":21,"semanticRole":"local","source":"h","sourceEnd":32538,"sourceStart":32537,"tag":"identifier"},{"children":[{"contextIndex":...	[]	[{"source":"h i j","source_end":32542,"source_start":32537,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨k, hk⟩","source_end":32559,"source_start":32548,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119346","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119349","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	200	16	exact	true	1	24	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	93b78f60f456c92eef9ab8fb6ab755ef86850196dca53164b907ab842bc4acf0	7f5f0d2aed28e1f9a22739692ef0370c08f03ba2cc06369706e6f3a766a726c7	dfd4af35acb5159291253847ecc004ede0b2e2137abb2e44e817559a19d1a1f1	bcb56b287b71cb133a1a9ce1047d1b094007431b0a76edcb7f3506ba1f58cfd3
cat-searcher/leandojo-benchmark-4-random	test	2,506	ENNReal.iSup_add_iSup	Mathlib/Topology/Instances/ENNReal.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact <a>le_iSup_of_le</a> k hk	case inr.intro 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∞ ι : Sort u_4 f g : ι → ℝ≥0∞ h : ∀ (i j : ι), ∃ k, f i + g j ≤ f k + g k h✝ : Nonempty ι i j k : ι hk : f i + g j ≤ f k + g k ⊢ f i + g j ≤ ⨆ a, f a + g a		((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.toPartialOrder) (:c ENNReal) ((:c OrderedCommSemiring.toOrderedSemiring) (:c ENNReal) ((:c CanonicallyOrderedCommSemiring.toOrderedCommSemiring) (:c ENNReal) (:c ENNReal.instCanonicallyOrderedCommSe...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"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 N...	(:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:a...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119346","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119349","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"exact","sourceEnd":32569,"sourceStart":32564,"tag":"atom"},{"children":[{"name":"le_iSup_of_le","semanticRole":"global","source":"le_iSup_of_le","sourceEnd":32583,"sourceStart":32570,"tag":"identifier"},{"children":[{"contextIndex":25,"semanticRole":"local","source":"k","sourceEnd":32585,"source...	[]	[{"source":"le_iSup_of_le k hk","source_end":32588,"source_start":32570,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.119346","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119349","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	200	17	exact	true	1	26	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	28c29653159151ccb2e125b08675bd29924917fa615ea9f2c7dcf49c5fb7a704	bcb56b287b71cb133a1a9ce1047d1b094007431b0a76edcb7f3506ba1f58cfd3	79dc8e4380c940ba252b857d4ba57f8be36c2c91d829c3eeff9ba0b89deb4e4e	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,507	le_egauge_smul_right	Mathlib/Analysis/Convex/EGauge.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>le_egauge_iff</a>]	𝕜 : Type u_1 inst✝² : NormedDivisionRing 𝕜 α : Type u_2 E : Type u_3 inst✝¹ : AddCommGroup E inst✝ : Module 𝕜 E c✝ : 𝕜 s✝ t : Set E x✝ y : E r : ℝ≥0∞ c : 𝕜 s : Set E x : E ⊢ ↑‖c‖₊ * egauge 𝕜 s x ≤ egauge 𝕜 s (c • x)	𝕜 : Type u_1 inst✝² : NormedDivisionRing 𝕜 α : Type u_2 E : Type u_3 inst✝¹ : AddCommGroup E inst✝ : Module 𝕜 E c✝ : 𝕜 s✝ t : Set E x✝ y : E r : ℝ≥0∞ c : 𝕜 s : Set E x : E ⊢ ∀ (c_1 : 𝕜), c • x ∈ c_1 • s → ↑‖c‖₊ * egauge 𝕜 s x ≤ ↑‖c_1‖₊	((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedDivisionRing) (:fv _uniq.61661))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.61670))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.61661) (:fv _u...	(:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:a...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61661","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61664","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedDivisionRing) (:...	{"children":[{"source":"rw","sourceEnd":5450,"sourceStart":5448,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5452,"sourceStart":5451,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"le_egauge_iff","sema...	[]	[{"source":"le_egauge_iff","source_end":5465,"source_start":5452,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61661","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61664","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inter...	31	4	exact	true	1	15	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	27f4e5ab5cee73564939efab494ff28eb728c3970ddf08c605da7565254b2c30	004dae3852b0b08fdaa7b1559edec2a7f9d0485c7b3bbed6c2cac334ce4a9091	09996861f6c00a3508f897863620ed43ff1ae3af2cbae502f4f640fca6177923	559efd8e572e8ee9810a9819063816fd0bcafe891618452ea4f651a6c3a24d69
cat-searcher/leandojo-benchmark-4-random	test	2,508	le_egauge_smul_right	Mathlib/Analysis/Convex/EGauge.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rintro a ⟨y, hy, hxy⟩	𝕜 : Type u_1 inst✝² : NormedDivisionRing 𝕜 α : Type u_2 E : Type u_3 inst✝¹ : AddCommGroup E inst✝ : Module 𝕜 E c✝ : 𝕜 s✝ t : Set E x✝ y : E r : ℝ≥0∞ c : 𝕜 s : Set E x : E ⊢ ∀ (c_1 : 𝕜), c • x ∈ c_1 • s → ↑‖c‖₊ * egauge 𝕜 s x ≤ ↑‖c_1‖₊	case intro.intro 𝕜 : Type u_1 inst✝² : NormedDivisionRing 𝕜 α : Type u_2 E : Type u_3 inst✝¹ : AddCommGroup E inst✝ : Module 𝕜 E c✝ : 𝕜 s✝ t : Set E x✝ y✝ : E r : ℝ≥0∞ c : 𝕜 s : Set E x : E a : 𝕜 y : E hy : y ∈ s hxy : (fun x => a • x) y = c • x ⊢ ↑‖c‖₊ * egauge 𝕜 s x ≤ ↑‖a‖₊	(:forall c (:fv _uniq.61661) (:forall _ ((:c Membership.mem) (:fv _uniq.61670) ((:c Set) (:fv _uniq.61670)) ((:c Set.instMembership) (:fv _uniq.61670)) ((:c HSMul.hSMul) (:fv _uniq.61661) (:fv _uniq.61670) (:fv _uniq.61670) ((:c instHSMul) (:fv _uniq.61661) (:fv _uniq.61670) ((:c SMulZeroClass.toSMul) (:fv _uniq.61661)...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedDivisionRing) (:fv _uniq.61661))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.61670))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.61661) (:fv _u...	(:forall c :explicit (:fv FV0) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv ...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61661","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61664","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedDivisionRing) (:...	{"children":[{"source":"rintro","sourceEnd":5475,"sourceStart":5469,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":5477,"sourceStart":5476,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"a","sourceEnd":5477,"sourceStart":5476,"tag":"...	[{"role":"fresh_name","source":"a","source_end":5477,"source_start":5476,"syntax_kind":"ident"},{"role":"fresh_name","source":"y","source_end":5482,"source_start":5481,"syntax_kind":"ident"},{"role":"fresh_name","source":"hy","source_end":5486,"source_start":5484,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx...	[{"source":"⟨y, hy, hxy⟩","source_end":5494,"source_start":5478,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61661","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61664","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inter...	31	7	exact	true	1	15	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	2cb27c9fb8f1a24827498e79d0a61f823bdbcc7e936dd6f22e3dc20dfadd2835	559efd8e572e8ee9810a9819063816fd0bcafe891618452ea4f651a6c3a24d69	2766e2666b0e33940a745dddd109c338387f6909283f10e81317ac7b48c850cb	c3734052b41ab893a5d9f09fbf326b8ba07e7ccdc5da8e31f1176d06c017a452
cat-searcher/leandojo-benchmark-4-random	test	2,509	le_egauge_smul_right	Mathlib/Analysis/Convex/EGauge.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rcases <a>eq_or_ne</a> c 0 with rfl \| hc	case intro.intro 𝕜 : Type u_1 inst✝² : NormedDivisionRing 𝕜 α : Type u_2 E : Type u_3 inst✝¹ : AddCommGroup E inst✝ : Module 𝕜 E c✝ : 𝕜 s✝ t : Set E x✝ y✝ : E r : ℝ≥0∞ c : 𝕜 s : Set E x : E a : 𝕜 y : E hy : y ∈ s hxy : (fun x => a • x) y = c • x ⊢ ↑‖c‖₊ * egauge 𝕜 s x ≤ ↑‖a‖₊	case intro.intro.inl 𝕜 : Type u_1 inst✝² : NormedDivisionRing 𝕜 α : Type u_2 E : Type u_3 inst✝¹ : AddCommGroup E inst✝ : Module 𝕜 E c : 𝕜 s✝ t : Set E x✝ y✝ : E r : ℝ≥0∞ s : Set E x : E a : 𝕜 y : E hy : y ∈ s hxy : (fun x => a • x) y = 0 • x ⊢ ↑‖0‖₊ * egauge 𝕜 s x ≤ ↑‖a‖₊ case intro.intro.inr 𝕜 : Type u_1 inst✝...	((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedDivisionRing) (:fv _uniq.61661))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.61670))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.61661) (:fv _u...	(:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:a...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61661","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61664","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedDivisionRing) (:...	{"children":[{"source":"rcases","sourceEnd":5503,"sourceStart":5497,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"eq_or_ne","semanticRole":"global","source":"eq_or_ne","sourceEnd":5512,"sourceStart":5504,"tag":"identifier"},{"children":[{"contextInd...	[]	[{"source":"eq_or_ne c 0","source_end":5516,"source_start":5504,"syntax_kind":"Lean.Parser.Term.app"},{"source":"rfl \| hc","source_end":5530,"source_start":5522,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61661","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61664","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inter...	31	8	exact	true	1	19	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	67da7fc1445b30fb9c8661abb51ea3b706857d01237e959757d86063ee304721	c3734052b41ab893a5d9f09fbf326b8ba07e7ccdc5da8e31f1176d06c017a452	38eb35d221fbb69e97f32ec7b2e70d18cdb392edd6d74ee1d4232796d7be3142	ee66af889a93a32db94a6f7e61fdae7910674ec8223dde4c0b0f3ee8866f2665
cat-searcher/leandojo-benchmark-4-random	test	2,510	le_egauge_smul_right	Mathlib/Analysis/Convex/EGauge.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp	case intro.intro.inl 𝕜 : Type u_1 inst✝² : NormedDivisionRing 𝕜 α : Type u_2 E : Type u_3 inst✝¹ : AddCommGroup E inst✝ : Module 𝕜 E c : 𝕜 s✝ t : Set E x✝ y✝ : E r : ℝ≥0∞ s : Set E x : E a : 𝕜 y : E hy : y ∈ s hxy : (fun x => a • x) y = 0 • x ⊢ ↑‖0‖₊ * egauge 𝕜 s x ≤ ↑‖a‖₊		((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedDivisionRing) (:fv _uniq.61661))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.61670))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.61661) (:fv _u...	(:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:a...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61661","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61664","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedDivisionRing) (:...	{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":5540,"sourceStart":5536,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source...	[]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61661","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61664","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inter...	31	11	exact	true	1	18	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	1af679ee32d28cf30d1952c7da0e7fec9c78d7f398915543906106ab9706a352	c1c828f3035306e7b0272166c6d3a4a8a0e674b933c1cd095e6287ea940b7078	8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,511	le_egauge_smul_right	Mathlib/Analysis/Convex/EGauge.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	refine <a>ENNReal.mul_le_of_le_div'</a> <\| <a>le_trans</a> ?_ <a>ENNReal.coe_div_le</a>	case intro.intro.inr 𝕜 : Type u_1 inst✝² : NormedDivisionRing 𝕜 α : Type u_2 E : Type u_3 inst✝¹ : AddCommGroup E inst✝ : Module 𝕜 E c✝ : 𝕜 s✝ t : Set E x✝ y✝ : E r : ℝ≥0∞ c : 𝕜 s : Set E x : E a : 𝕜 y : E hy : y ∈ s hxy : (fun x => a • x) y = c • x hc : c ≠ 0 ⊢ ↑‖c‖₊ * egauge 𝕜 s x ≤ ↑‖a‖₊	case intro.intro.inr 𝕜 : Type u_1 inst✝² : NormedDivisionRing 𝕜 α : Type u_2 E : Type u_3 inst✝¹ : AddCommGroup E inst✝ : Module 𝕜 E c✝ : 𝕜 s✝ t : Set E x✝ y✝ : E r : ℝ≥0∞ c : 𝕜 s : Set E x : E a : 𝕜 y : E hy : y ∈ s hxy : (fun x => a • x) y = c • x hc : c ≠ 0 ⊢ egauge 𝕜 s x ≤ ↑(‖a‖₊ / ‖c‖₊)	((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedDivisionRing) (:fv _uniq.61661))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.61670))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.61661) (:fv _u...	(:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:a...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61661","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61664","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedDivisionRing) (:...	{"children":[{"source":"refine","sourceEnd":5552,"sourceStart":5546,"tag":"atom"},{"children":[{"name":"ENNReal.mul_le_of_le_div'","semanticRole":"global","source":"ENNReal.mul_le_of_le_div'","sourceEnd":5578,"sourceStart":5553,"tag":"identifier"},{"source":"<\|","sourceEnd":5581,"sourceStart":5579,"tag":"atom"},{"child...	[]	[{"source":"ENNReal.mul_le_of_le_div' <\| le_trans ?_ ENNReal.coe_div_le","source_end":5612,"source_start":5553,"syntax_kind":"«term_<\|_»"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61661","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61664","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inter...	31	18	exact	true	1	20	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	70560123d6920a5f707ef5d10e0d386ab182efef1e9a549434abefb922e7f3ea	f5b075a18c18fc443d5d81d644c26f26c2324261b6f997cbf250ae4ff2590af5	83b8db78476609b648ad4395f30bca9e92f4df94e756ebbfb21fc9aab3ba1980	6940d53c8023de19eaad8e1a0bb9ae904832794f2bc93389ab512aceb5ac8738
cat-searcher/leandojo-benchmark-4-random	test	2,512	le_egauge_smul_right	Mathlib/Analysis/Convex/EGauge.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>div_eq_inv_mul</a>, ← <a>nnnorm_inv</a>, ← <a>nnnorm_mul</a>]	case intro.intro.inr 𝕜 : Type u_1 inst✝² : NormedDivisionRing 𝕜 α : Type u_2 E : Type u_3 inst✝¹ : AddCommGroup E inst✝ : Module 𝕜 E c✝ : 𝕜 s✝ t : Set E x✝ y✝ : E r : ℝ≥0∞ c : 𝕜 s : Set E x : E a : 𝕜 y : E hy : y ∈ s hxy : (fun x => a • x) y = c • x hc : c ≠ 0 ⊢ egauge 𝕜 s x ≤ ↑(‖a‖₊ / ‖c‖₊)	case intro.intro.inr 𝕜 : Type u_1 inst✝² : NormedDivisionRing 𝕜 α : Type u_2 E : Type u_3 inst✝¹ : AddCommGroup E inst✝ : Module 𝕜 E c✝ : 𝕜 s✝ t : Set E x✝ y✝ : E r : ℝ≥0∞ c : 𝕜 s : Set E x : E a : 𝕜 y : E hy : y ∈ s hxy : (fun x => a • x) y = c • x hc : c ≠ 0 ⊢ egauge 𝕜 s x ≤ ↑‖c⁻¹ * a‖₊	((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedDivisionRing) (:fv _uniq.61661))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.61670))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.61661) (:fv _u...	(:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c egauge) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NNNorm) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV3)) (:ar...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61661","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61664","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedDivisionRing) (:...	{"children":[{"source":"rw","sourceEnd":5619,"sourceStart":5617,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5621,"sourceStart":5620,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"div_eq_inv_mul","sem...	[]	[{"source":"div_eq_inv_mul","source_end":5635,"source_start":5621,"syntax_kind":"ident"},{"source":"nnnorm_inv","source_end":5651,"source_start":5641,"syntax_kind":"ident"},{"source":"nnnorm_mul","source_end":5667,"source_start":5657,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61661","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61664","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inter...	31	19	exact	true	1	20	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	348122f6f39aa783501de458c4055fc70285a766e524d8662902bd52cb0d08ab	6940d53c8023de19eaad8e1a0bb9ae904832794f2bc93389ab512aceb5ac8738	dc6771eeabdc4ded9ce6b7f7d3d2221dc5e8c71cd67a4437f02d6433b9d27484	b2aa3c323883c9fb4f2eda04f6006c0b004bea5bc11f5f73d2ad379cea235f93
cat-searcher/leandojo-benchmark-4-random	test	2,513	le_egauge_smul_right	Mathlib/Analysis/Convex/EGauge.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	refine <a>egauge_le_of_mem_smul</a> ⟨y, hy, ?_⟩	case intro.intro.inr 𝕜 : Type u_1 inst✝² : NormedDivisionRing 𝕜 α : Type u_2 E : Type u_3 inst✝¹ : AddCommGroup E inst✝ : Module 𝕜 E c✝ : 𝕜 s✝ t : Set E x✝ y✝ : E r : ℝ≥0∞ c : 𝕜 s : Set E x : E a : 𝕜 y : E hy : y ∈ s hxy : (fun x => a • x) y = c • x hc : c ≠ 0 ⊢ egauge 𝕜 s x ≤ ↑‖c⁻¹ * a‖₊	case intro.intro.inr 𝕜 : Type u_1 inst✝² : NormedDivisionRing 𝕜 α : Type u_2 E : Type u_3 inst✝¹ : AddCommGroup E inst✝ : Module 𝕜 E c✝ : 𝕜 s✝ t : Set E x✝ y✝ : E r : ℝ≥0∞ c : 𝕜 s : Set E x : E a : 𝕜 y : E hy : y ∈ s hxy : (fun x => a • x) y = c • x hc : c ≠ 0 ⊢ (fun x => (c⁻¹ * a) • x) y = x	((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedDivisionRing) (:fv _uniq.61661))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.61670))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.61661) (:fv _u...	(:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c egauge) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NNNorm) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV3)) (:ar...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61661","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61664","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedDivisionRing) (:...	{"children":[{"source":"refine","sourceEnd":5679,"sourceStart":5673,"tag":"atom"},{"children":[{"name":"egauge_le_of_mem_smul","semanticRole":"global","source":"egauge_le_of_mem_smul","sourceEnd":5701,"sourceStart":5680,"tag":"identifier"},{"children":[{"children":[{"source":"⟨","sourceEnd":5705,"sourceStart":5702,"tag...	[]	[{"source":"egauge_le_of_mem_smul ⟨y, hy, ?_⟩","source_end":5717,"source_start":5680,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61661","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61664","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inter...	31	24	exact	true	1	20	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	1839acb3561fcd11aee3573e8909bfb4ab44cd85e2f692b39d6d74ed6206bbdd	b2aa3c323883c9fb4f2eda04f6006c0b004bea5bc11f5f73d2ad379cea235f93	0e3eff5dfd8ee641ecffe1cfc098c262047b07aa69d38ebefa051ba7022a68e0	9263c001d26cbc5371da531bfd669eb5b2503b1896ecfd026d0c39b69f08ea20
cat-searcher/leandojo-benchmark-4-random	test	2,514	le_egauge_smul_right	Mathlib/Analysis/Convex/EGauge.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp only [<a>MulAction.mul_smul</a>, hxy, <a>inv_smul_smul₀</a> hc]	case intro.intro.inr 𝕜 : Type u_1 inst✝² : NormedDivisionRing 𝕜 α : Type u_2 E : Type u_3 inst✝¹ : AddCommGroup E inst✝ : Module 𝕜 E c✝ : 𝕜 s✝ t : Set E x✝ y✝ : E r : ℝ≥0∞ c : 𝕜 s : Set E x : E a : 𝕜 y : E hy : y ∈ s hxy : (fun x => a • x) y = c • x hc : c ≠ 0 ⊢ (fun x => (c⁻¹ * a) • x) y = x		((:c Eq) (:fv _uniq.61670) ((:lambda _ (:fv _uniq.61670) ((:c HSMul.hSMul) (:fv _uniq.61661) (:fv _uniq.61670) (:fv _uniq.61670) ((:c instHSMul) (:fv _uniq.61661) (:fv _uniq.61670) ((:c SMulZeroClass.toSMul) (:fv _uniq.61661) (:fv _uniq.61670) ((:c NegZeroClass.toZero) (:fv _uniq.61670) ((:c SubNegZeroMonoid.toNegZeroC...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedDivisionRing) (:fv _uniq.61661))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.61670))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.61661) (:fv _u...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:lambda _ :explicit (:fv FV3) (: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 :explici...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61661","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61664","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedDivisionRing) (:...	{"children":[{"source":"simp","sourceEnd":5726,"sourceStart":5722,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":5731,"sourceStart":5727,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":5731,"s...	[]	[{"source":"mul_smul","source_end":5741,"source_start":5733,"syntax_kind":"ident"},{"source":"hxy","source_end":5746,"source_start":5743,"syntax_kind":"ident"},{"source":"inv_smul_smul₀ hc","source_end":5767,"source_start":5748,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.61661","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.61664","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inter...	31	25	exact	true	1	20	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	da77cfcc24a7b8f67bf0a544d52b44b88cfe48ace571e2efd909b64f6917cf87	9263c001d26cbc5371da531bfd669eb5b2503b1896ecfd026d0c39b69f08ea20	1978e68a560148fd7a8ed3098cc4231c745cda2b23127dd654ea08f4c3b6dd71	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,515	subsingleton_or_nontrivial	Mathlib/Logic/Nontrivial/Defs.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [← <a>not_nontrivial_iff_subsingleton</a>, <a>or_comm</a>]	α✝ : Type u_1 β : Type u_2 α : Type u_3 ⊢ Subsingleton α ∨ Nontrivial α	α✝ : Type u_1 β : Type u_2 α : Type u_3 ⊢ Nontrivial α ∨ ¬Nontrivial α	((:c Or) ((:c Subsingleton) (:fv _uniq.1303)) ((:c Nontrivial) (:fv _uniq.1303)))	[{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"}]	(:app (:c Or) (:arg :explicit 0 (:app (:c Subsingleton) (:arg :explicit 0 (:fv FV3)))) (:arg :explicit 1 (:app (:c Nontrivial) (:arg :explicit 0 (:fv FV3)))))	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1292","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1295","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":explicit","cont...	{"children":[{"source":"rw","sourceEnd":3889,"sourceStart":3887,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3891,"sourceStart":3890,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":3894,"sourceStart":...	[]	[{"source":"not_nontrivial_iff_subsingleton","source_end":3926,"source_start":3895,"syntax_kind":"ident"},{"source":"or_comm","source_end":3935,"source_start":3928,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1292","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1295","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":explicit","context_index":3,"internal_name":"_uni...	29	4	exact	true	1	3	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	c17210e68e7c708a24a80df48b68e456cd98a2769bd23bf13849bdf931702476	501d0dc880205dfcb5fb574681cc55e8db7b0e2f8567e694e3572d4eaa070f18	8f573ca6a27833538be35886afce70f8cb44c8aab2478a32f9ae415aa4fb7c83	9a1c55da31ef53b732a254e9e9bdba305bb335f3b6ad31b1857b4d2cb39bf26c
cat-searcher/leandojo-benchmark-4-random	test	2,516	subsingleton_or_nontrivial	Mathlib/Logic/Nontrivial/Defs.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact <a>Classical.em</a> _	α✝ : Type u_1 β : Type u_2 α : Type u_3 ⊢ Nontrivial α ∨ ¬Nontrivial α		((:c Or) ((:c Nontrivial) (:fv _uniq.1303)) ((:c Not) ((:c Nontrivial) (:fv _uniq.1303))))	[{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"}]	(:app (:c Or) (:arg :explicit 0 (:app (:c Nontrivial) (:arg :explicit 0 (:fv FV3)))) (:arg :explicit 1 (:app (:c Not) (:arg :explicit 0 (:app (:c Nontrivial) (:arg :explicit 0 (:fv FV3)))))))	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1292","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1295","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":explicit","cont...	{"children":[{"source":"exact","sourceEnd":3944,"sourceStart":3939,"tag":"atom"},{"children":[{"name":"Classical.em","semanticRole":"global","source":"Classical.em","sourceEnd":3957,"sourceStart":3945,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":3959,"sourceStart":3958,"tag":"atom"}],"kind":"...	[]	[{"source":"Classical.em _","source_end":3959,"source_start":3945,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1292","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1295","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":explicit","context_index":3,"internal_name":"_uni...	29	8	exact	true	1	3	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	8a23f6bb5ff05a7100fd2e470f4b5f0fe1f06c38fb6cfd6a23aa6357294b1e97	9a1c55da31ef53b732a254e9e9bdba305bb335f3b6ad31b1857b4d2cb39bf26c	10dae30369e75d68e4b0c3f193726d96effda62cb6fe74aaa40b4f66d7be57dd	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,517	LinearMap.finiteDimensional_of_det_ne_one	Mathlib/LinearAlgebra/Determinant.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	by_cases H : ∃ s : <a>Finset</a> M, <a>Nonempty</a> (<a>Basis</a> s 𝕜 M)	R : Type u_1 inst✝¹¹ : CommRing R M : Type u_2 inst✝¹⁰ : AddCommGroup M inst✝⁹ : Module R M M' : Type u_3 inst✝⁸ : AddCommGroup M' inst✝⁷ : Module R M' ι : Type u_4 inst✝⁶ : DecidableEq ι inst✝⁵ : Fintype ι e : Basis ι R M A : Type u_5 inst✝⁴ : CommRing A inst✝³ : Module A M κ : Type u_6 inst✝² : Fintype κ 𝕜 : Type u_...	case pos R : Type u_1 inst✝¹¹ : CommRing R M : Type u_2 inst✝¹⁰ : AddCommGroup M inst✝⁹ : Module R M M' : Type u_3 inst✝⁸ : AddCommGroup M' inst✝⁷ : Module R M' ι : Type u_4 inst✝⁶ : DecidableEq ι inst✝⁵ : Fintype ι e : Basis ι R M A : Type u_5 inst✝⁴ : CommRing A inst✝³ : Module A M κ : Type u_6 inst✝² : Fintype κ 𝕜 ...	((:c FiniteDimensional) (:fv _uniq.257007) (:fv _uniq.252644) ((:c Field.toDivisionRing) (:fv _uniq.257007) (:fv _uniq.257008)) (:fv _uniq.252647) (:fv _uniq.257009))	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹¹","sexp":"((:c CommRing) (:fv _uniq.252638))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁰","sexp":"((:c AddCommGroup) (:fv _uniq.252644))"},{"name":"inst✝⁹","sexp":"((:c Module) (:fv _uniq.252638) (:fv _uniq.252644) ((:c CommSemiring.toSemiring) (:f...	(:app (:c FiniteDimensional) (:arg :explicit 0 (:fv FV18)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c DivisionRing) (:arg :explicit 0 (:fv FV18))))) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:app (:c Module) (:arg...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252638","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252641","is_instance":true,"is_let":false,"name":"inst✝¹¹","sexp":"(:app (:c CommRing) (:arg :exp...	{"children":[{"source":"by_cases","sourceEnd":14718,"sourceStart":14710,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"H","sourceEnd":14720,"sourceStart":14719,"tag":"identifier"},{"source":":","sourceEnd":14722,"sourceStart":14721,"tag":"atom"}],"kind":"null","source":"H :","sourceEnd":14722,"sour...	[]	[{"source":"∃ s : Finset M, Nonempty (Basis s 𝕜 M)","source_end":14766,"source_start":14723,"syntax_kind":"«term∃_,_»"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252638","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252641","is_instance":true,"is_let":false,"user_name":"inst✝¹¹"},{"binder_role":":implicit","context_index":2,"int...	79	4	exact	true	1	22	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	067d7b5310ad9ffd94cf34e2fc82ec98ed62769b55896ac0b5cbf4806f9b776c	39f741b580091e47732d5a574d58d07f04827d912486b9d35160840fa2a3ae7d	e4b2eb488c38c1191d542767a96792d656b8e65bea144962203babb78a8a835f	435730bf5932b4ec957965a00a7c6060c86ab0699535838b3892c1b6b660dd51
cat-searcher/leandojo-benchmark-4-random	test	2,518	LinearMap.finiteDimensional_of_det_ne_one	Mathlib/LinearAlgebra/Determinant.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rcases H with ⟨s, ⟨hs⟩⟩	case pos R : Type u_1 inst✝¹¹ : CommRing R M : Type u_2 inst✝¹⁰ : AddCommGroup M inst✝⁹ : Module R M M' : Type u_3 inst✝⁸ : AddCommGroup M' inst✝⁷ : Module R M' ι : Type u_4 inst✝⁶ : DecidableEq ι inst✝⁵ : Fintype ι e : Basis ι R M A : Type u_5 inst✝⁴ : CommRing A inst✝³ : Module A M κ : Type u_6 inst✝² : Fintype κ 𝕜 ...	case pos.intro.intro R : Type u_1 inst✝¹¹ : CommRing R M : Type u_2 inst✝¹⁰ : AddCommGroup M inst✝⁹ : Module R M M' : Type u_3 inst✝⁸ : AddCommGroup M' inst✝⁷ : Module R M' ι : Type u_4 inst✝⁶ : DecidableEq ι inst✝⁵ : Fintype ι e : Basis ι R M A : Type u_5 inst✝⁴ : CommRing A inst✝³ : Module A M κ : Type u_6 inst✝² : F...	((:c FiniteDimensional) (:fv _uniq.257007) (:fv _uniq.252644) ((:c Field.toDivisionRing) (:fv _uniq.257007) (:fv _uniq.257008)) (:fv _uniq.252647) (:fv _uniq.257009))	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹¹","sexp":"((:c CommRing) (:fv _uniq.252638))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁰","sexp":"((:c AddCommGroup) (:fv _uniq.252644))"},{"name":"inst✝⁹","sexp":"((:c Module) (:fv _uniq.252638) (:fv _uniq.252644) ((:c CommSemiring.toSemiring) (:f...	(:app (:c FiniteDimensional) (:arg :explicit 0 (:fv FV18)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c DivisionRing) (:arg :explicit 0 (:fv FV18))))) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:app (:c Module) (:arg...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252638","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252641","is_instance":true,"is_let":false,"name":"inst✝¹¹","sexp":"(:app (:c CommRing) (:arg :exp...	{"children":[{"source":"rcases","sourceEnd":14778,"sourceStart":14772,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":23,"semanticRole":"local","source":"H","sourceEnd":14780,"sourceStart":14779,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","...	[]	[{"source":"H","source_end":14780,"source_start":14779,"syntax_kind":"ident"},{"source":"⟨s, ⟨hs⟩⟩","source_end":14803,"source_start":14786,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252638","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252641","is_instance":true,"is_let":false,"user_name":"inst✝¹¹"},{"binder_role":":implicit","context_index":2,"int...	79	9	exact	true	1	23	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	0f50d8d8e6b5309cddc15950ea404bcd44db0485a39f2783a07ee4e8cde6398f	5c682b35d22effdae10749c5d07544b1e7d4c67b52c12804a3e26e3b86c47a06	89c79c0c52b1643e839d6cb02faf784c44e7555e30d6a7be59601b4bbf1f0e2b	4791c56a30384a82c7699df18b43aa06ec2e83c5c7bc10057603717291668bfc
cat-searcher/leandojo-benchmark-4-random	test	2,519	LinearMap.finiteDimensional_of_det_ne_one	Mathlib/LinearAlgebra/Determinant.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact <a>FiniteDimensional.of_fintype_basis</a> hs	case pos.intro.intro R : Type u_1 inst✝¹¹ : CommRing R M : Type u_2 inst✝¹⁰ : AddCommGroup M inst✝⁹ : Module R M M' : Type u_3 inst✝⁸ : AddCommGroup M' inst✝⁷ : Module R M' ι : Type u_4 inst✝⁶ : DecidableEq ι inst✝⁵ : Fintype ι e : Basis ι R M A : Type u_5 inst✝⁴ : CommRing A inst✝³ : Module A M κ : Type u_6 inst✝² : F...		((:c FiniteDimensional) (:fv _uniq.257007) (:fv _uniq.252644) ((:c Field.toDivisionRing) (:fv _uniq.257007) (:fv _uniq.257008)) (:fv _uniq.252647) (:fv _uniq.257009))	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹¹","sexp":"((:c CommRing) (:fv _uniq.252638))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁰","sexp":"((:c AddCommGroup) (:fv _uniq.252644))"},{"name":"inst✝⁹","sexp":"((:c Module) (:fv _uniq.252638) (:fv _uniq.252644) ((:c CommSemiring.toSemiring) (:f...	(:app (:c FiniteDimensional) (:arg :explicit 0 (:fv FV18)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c DivisionRing) (:arg :explicit 0 (:fv FV18))))) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:app (:c Module) (:arg...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252638","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252641","is_instance":true,"is_let":false,"name":"inst✝¹¹","sexp":"(:app (:c CommRing) (:arg :exp...	{"children":[{"source":"exact","sourceEnd":14813,"sourceStart":14808,"tag":"atom"},{"children":[{"name":"FiniteDimensional.of_fintype_basis","semanticRole":"global","source":"FiniteDimensional.of_fintype_basis","sourceEnd":14848,"sourceStart":14814,"tag":"identifier"},{"children":[{"contextIndex":24,"semanticRole":"loc...	[]	[{"source":"FiniteDimensional.of_fintype_basis hs","source_end":14851,"source_start":14814,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252638","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252641","is_instance":true,"is_let":false,"user_name":"inst✝¹¹"},{"binder_role":":implicit","context_index":2,"int...	79	10	exact	true	1	24	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	1eae89ed19c2342ff482dfbe417abdf9dffaf4b64fff5aef7f8eba1a2bccb4c9	4791c56a30384a82c7699df18b43aa06ec2e83c5c7bc10057603717291668bfc	e1b3e486f8bfc36f08f862af3b44d61ffa1988daaf9027441791972034ffa731	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,520	LinearMap.finiteDimensional_of_det_ne_one	Mathlib/LinearAlgebra/Determinant.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	classical simp [<a>LinearMap.coe_det</a>, H] at hf	case neg R : Type u_1 inst✝¹¹ : CommRing R M : Type u_2 inst✝¹⁰ : AddCommGroup M inst✝⁹ : Module R M M' : Type u_3 inst✝⁸ : AddCommGroup M' inst✝⁷ : Module R M' ι : Type u_4 inst✝⁶ : DecidableEq ι inst✝⁵ : Fintype ι e : Basis ι R M A : Type u_5 inst✝⁴ : CommRing A inst✝³ : Module A M κ : Type u_6 inst✝² : Fintype κ 𝕜 ...		((:c FiniteDimensional) (:fv _uniq.257007) (:fv _uniq.252644) ((:c Field.toDivisionRing) (:fv _uniq.257007) (:fv _uniq.257008)) (:fv _uniq.252647) (:fv _uniq.257009))	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹¹","sexp":"((:c CommRing) (:fv _uniq.252638))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁰","sexp":"((:c AddCommGroup) (:fv _uniq.252644))"},{"name":"inst✝⁹","sexp":"((:c Module) (:fv _uniq.252638) (:fv _uniq.252644) ((:c CommSemiring.toSemiring) (:f...	(:app (:c FiniteDimensional) (:arg :explicit 0 (:fv FV18)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c DivisionRing) (:arg :explicit 0 (:fv FV18))))) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:app (:c Module) (:arg...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252638","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252641","is_instance":true,"is_let":false,"name":"inst✝¹¹","sexp":"(:app (:c CommRing) (:arg :exp...	{"children":[{"children":[{"children":[{"children":[{"source":"classical","sourceEnd":14866,"sourceStart":14857,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":14871,"sourceStart":14867,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"ki...	[]	[{"source":"LinearMap.coe_det","source_end":14890,"source_start":14873,"syntax_kind":"ident"},{"source":"H","source_end":14893,"source_start":14892,"syntax_kind":"ident"},{"source":"hf","source_end":14900,"source_start":14898,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252638","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252641","is_instance":true,"is_let":false,"user_name":"inst✝¹¹"},{"binder_role":":implicit","context_index":2,"int...	79	13	exact	true	1	23	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	815e767cbad1ec54140d986f4da092dec3c6d6abda8536396d121ec6f9c5dd82	c8dfdbbce56babde0b10579f3c7700d041aaa9057a59a26b6a2d5e0b733783d9	5154e27aeb1909e9bb29a863193ab7c04be78aa9986cd71d76b1a2fb1446cd08	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,521	LinearMap.finiteDimensional_of_det_ne_one	Mathlib/LinearAlgebra/Determinant.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp [<a>LinearMap.coe_det</a>, H] at hf	case neg R : Type u_1 inst✝¹¹ : CommRing R M : Type u_2 inst✝¹⁰ : AddCommGroup M inst✝⁹ : Module R M M' : Type u_3 inst✝⁸ : AddCommGroup M' inst✝⁷ : Module R M' ι : Type u_4 inst✝⁶ : DecidableEq ι inst✝⁵ : Fintype ι e : Basis ι R M A : Type u_5 inst✝⁴ : CommRing A inst✝³ : Module A M κ : Type u_6 inst✝² : Fintype κ 𝕜 ...		((:c FiniteDimensional) (:fv _uniq.257007) (:fv _uniq.252644) ((:c Field.toDivisionRing) (:fv _uniq.257007) (:fv _uniq.257008)) (:fv _uniq.252647) (:fv _uniq.257009))	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹¹","sexp":"((:c CommRing) (:fv _uniq.252638))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁰","sexp":"((:c AddCommGroup) (:fv _uniq.252644))"},{"name":"inst✝⁹","sexp":"((:c Module) (:fv _uniq.252638) (:fv _uniq.252644) ((:c CommSemiring.toSemiring) (:f...	(:app (:c FiniteDimensional) (:arg :explicit 0 (:fv FV18)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c DivisionRing) (:arg :explicit 0 (:fv FV18))))) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:app (:c Module) (:arg...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252638","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252641","is_instance":true,"is_let":false,"name":"inst✝¹¹","sexp":"(:app (:c CommRing) (:arg :exp...	{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":14871,"sourceStart":14867,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...	[]	[{"source":"LinearMap.coe_det","source_end":14890,"source_start":14873,"syntax_kind":"ident"},{"source":"H","source_end":14893,"source_start":14892,"syntax_kind":"ident"},{"source":"hf","source_end":14900,"source_start":14898,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.252638","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.252641","is_instance":true,"is_let":false,"user_name":"inst✝¹¹"},{"binder_role":":implicit","context_index":2,"int...	79	16	exact	true	1	23	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	685ffe86396a216f5102442475d9cb84c07efcb6f8c266f5cd4731606f0e3a70	c8dfdbbce56babde0b10579f3c7700d041aaa9057a59a26b6a2d5e0b733783d9	50ca93cf64f490f73fb087cc741cd50de83a3176f094a9c0f69de15da7f58bdc	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,522	Int.even_pow	Mathlib/Algebra/Group/Int.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	induction' n with n ih <;> simp [*, <a>Int.even_mul</a>, <a>pow_succ</a>]	u v m n✝ : ℤ n : ℕ ⊢ Even (m ^ n) ↔ Even m ∧ n ≠ 0	case succ u v m n✝ : ℤ n : ℕ ih : Even (m ^ n) ↔ Even m ∧ n ≠ 0 ⊢ Even m → ¬n = 0 → Even m	((:c Iff) ((:c Even) (:c Int) (:c Int.instAdd) ((:c HPow.hPow) (:c Int) (:c Nat) (:c Int) (:c Int.instHPowNat) (:fv _uniq.21224) (:fv _uniq.21275))) ((:c And) ((:c Even) (:c Int) (:c Int.instAdd) (:fv _uniq.21224)) ((:c Ne) (:c Nat) (:fv _uniq.21275) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))))	[{"name":"u","sexp":"(:c Int)"},{"name":"v","sexp":"(:c Int)"},{"name":"m","sexp":"(:c Int)"},{"name":"n✝","sexp":"(:c Int)"},{"name":"n","sexp":"(:c Nat)"}]	(:app (:c Iff) (:arg :explicit 0 (:app (:c Even) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c Add) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Int)) (:arg :instance 3 (:in...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21220","is_instance":false,"is_let":false,"name":"u","sexp":"(:c Int)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.21222","is_instance":false,"is_let":false,"name":"v","sexp":"(:c Int)"},{"binder_role":":implicit","context_ind...	{"children":[{"children":[{"source":"induction'","sourceEnd":10106,"sourceStart":10096,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":5,"semanticRole":"local","source":"n","sourceEnd":10108,"sourceStart":10107,"tag":"identifier"}],"kind":"Lean.Parser.Tacti...	[]	[{"source":"n","source_end":10108,"source_start":10107,"syntax_kind":"ident"},{"source":"even_mul","source_end":10140,"source_start":10132,"syntax_kind":"ident"},{"source":"pow_succ","source_end":10150,"source_start":10142,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21220","is_instance":false,"is_let":false,"user_name":"u"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.21222","is_instance":false,"is_let":false,"user_name":"v"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	94	4	exact	true	1	5	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	4bd81ccbc27a13ebedfd066faaf7952b51e19a17e3ddf14830eef224363f5b6d	ff27757b70bba51b4786c89de5838269824bec71965e234ca1e62ff22ee8544a	14aa14535c8a9611bf8809780e38ec386ffdf56485b64812fc0926e0a801e9be	d37015827b56551e32d97a27f5fd96e1b03489b8a5afba8227e1876d5be49536
cat-searcher/leandojo-benchmark-4-random	test	2,523	Int.even_pow	Mathlib/Algebra/Group/Int.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	tauto	case succ u v m n✝ : ℤ n : ℕ ih : Even (m ^ n) ↔ Even m ∧ n ≠ 0 ⊢ Even m → ¬n = 0 → Even m		(:forall _ ((:c Even) (:c Int) (:c Int.instAdd) (:fv _uniq.21224)) (:forall _ ((:c Not) ((:c Eq) (:c Nat) (:fv _uniq.21292) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))) ((:c Even) (:c Int) (:c Int.instAdd) (:fv _uniq.21224))))	[{"name":"u","sexp":"(:c Int)"},{"name":"v","sexp":"(:c Int)"},{"name":"m","sexp":"(:c Int)"},{"name":"n✝","sexp":"(:c Int)"},{"name":"n","sexp":"(:c Nat)"},{"name":"ih","sexp":"((:c Iff) ((:c Even) (:c Int) (:c Int.instAdd) ((:c HPow.hPow) (:c Int) (:c Nat) (:c Int) (:c Int.instHPowNat) (:fv _uniq.21224) (:fv _uniq.21...	(:forall _ :explicit (:app (:c Even) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c Add) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:fv FV2))) (:forall _ :explicit (:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV5)) (:arg :expli...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21220","is_instance":false,"is_let":false,"name":"u","sexp":"(:c Int)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.21222","is_instance":false,"is_let":false,"name":"v","sexp":"(:c Int)"},{"binder_role":":implicit","context_ind...	{"children":[{"source":"tauto","sourceEnd":10158,"sourceStart":10153,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.Tauto.tauto","source":"tauto","sourceEnd":10158,"sourceStart":10153,"tag":"node"}	[]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21220","is_instance":false,"is_let":false,"user_name":"u"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.21222","is_instance":false,"is_let":false,"user_name":"v"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	94	10	exact	true	1	6	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	5e3dc59f235ba934271da5dcaaa93db6a01888e01c006b2fa402e1b3d50884d0	d37015827b56551e32d97a27f5fd96e1b03489b8a5afba8227e1876d5be49536	78175d0e14580017b7abde3d46f7acc510808867e2ea0a22535e39b5dff68317	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,524	Zsqrtd.le_antisymm	Mathlib/NumberTheory/Zsqrtd/Basic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rwa [<a>neg_sub</a>]	d : ℕ dnsq : Nonsquare d a b : ℤ√↑d ab : a ≤ b ba : b ≤ a ⊢ (-(a - b)).Nonneg		((:c Zsqrtd.Nonneg) (:fv _uniq.275489) ((:c Neg.neg) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.275489))) ((:c Zsqrtd.instNeg) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.275489))) ((:c HSub.hSub) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.275489))) ((:c Zsqr...	[{"name":"d","sexp":"(:c Nat)"},{"name":"dnsq","sexp":"((:c Zsqrtd.Nonsquare) (:fv _uniq.275489))"},{"name":"a","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.275489)))"},{"name":"b","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.275489)))"},{"name":"ab","sexp":...	(:app (:c Zsqrtd.Nonneg) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Neg.neg) (:arg :implicit-type 0 (:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:fv FV0)))))) (:arg :insta...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.275489","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.275491","is_instance":true,"is_let":false,"name":"dnsq","sexp":"(:app (:c Zsqrtd.Nonsquare) (:arg :ex...	{"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":35436,"sourceStart":35433,"tag":"atom"},{"children":[{"source":"[","sourceEnd":35438,"sourceStart":35437,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"neg_sub","semanticRole":"global...	[]	[{"source":"neg_sub","source_end":35445,"source_start":35438,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.275489","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.275491","is_instance":true,"is_let":false,"user_name":"dnsq"},{"binder_role":":implicit","context_index":3,"intern...	266	2	exact	true	1	6	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	bbe272b7ad583c16f55fc3be2986b806f404d40fd55c6503ad2a465f828b95f6	f0365a311dc7f3d2c5902f3b9bb7cd025c8e67eeff12632640d2a1f289142aa1	42fa0ef8f44e108e4d979620afe618000321d7eceb617f6d97a751c1cf2b5279	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,525	LinearMap.rank_comp_le_left	Mathlib/LinearAlgebra/Dimension/LinearMap.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	refine <a>rank_le_of_submodule</a> _ _ ?_	K : Type u V V₁ : Type v V' V'₁ : Type v' V'' : Type v'' inst✝⁸ : Ring K inst✝⁷ : AddCommGroup V inst✝⁶ : Module K V inst✝⁵ : AddCommGroup V₁ inst✝⁴ : Module K V₁ inst✝³ : AddCommGroup V' inst✝² : Module K V' inst✝¹ : AddCommGroup V'' inst✝ : Module K V'' g : V →ₗ[K] V' f : V' →ₗ[K] V'' ⊢ (f ∘ₗ g).rank ≤ f.rank	K : Type u V V₁ : Type v V' V'₁ : Type v' V'' : Type v'' inst✝⁸ : Ring K inst✝⁷ : AddCommGroup V inst✝⁶ : Module K V inst✝⁵ : AddCommGroup V₁ inst✝⁴ : Module K V₁ inst✝³ : AddCommGroup V' inst✝² : Module K V' inst✝¹ : AddCommGroup V'' inst✝ : Module K V'' g : V →ₗ[K] V' f : V' →ₗ[K] V'' ⊢ range (f ∘ₗ g) ≤ range f	((:c LE.le) (:c Cardinal) (:c Cardinal.instLE) ((:c LinearMap.rank) (:fv _uniq.23614) (:fv _uniq.23616) (:fv _uniq.23624) (:fv _uniq.23627) (:fv _uniq.23630) (:fv _uniq.24264) (:fv _uniq.25348) (:fv _uniq.25933) ((:c LinearMap.comp) (:fv _uniq.23614) (:fv _uniq.23614) (:fv _uniq.23614) (:fv _uniq.23616) (:fv _uniq.2362...	[{"name":"K","sexp":"(:sort (+ u 1))"},{"name":"V","sexp":"(:sort (+ v 1))"},{"name":"V₁","sexp":"(:sort (+ v 1))"},{"name":"V'","sexp":"(:sort (+ v' 1))"},{"name":"V'₁","sexp":"(:sort (+ v' 1))"},{"name":"V''","sexp":"(:sort (+ v'' 1))"},{"name":"inst✝⁸","sexp":"((:c Ring) (:fv _uniq.23614))"},{"name":"inst✝⁷","sexp":...	(:app (:c LE.le) (:arg :implicit-type 0 (:c Cardinal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Cardinal))))) (:arg :explicit 2 (:app (:c LinearMap.rank) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23614","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23616","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con...	{"children":[{"source":"refine","sourceEnd":1556,"sourceStart":1550,"tag":"atom"},{"children":[{"name":"rank_le_of_submodule","semanticRole":"global","source":"rank_le_of_submodule","sourceEnd":1577,"sourceStart":1557,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":1579,"sourceStart":1578,"tag":...	[]	[{"source":"rank_le_of_submodule _ _ ?_","source_end":1584,"source_start":1557,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23614","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23616","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	18	4	exact	true	1	17	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	2930c3bf49134036c624853d301b7e3092f87281afa5e46cbdff3946f1bdf446	1ee9c86368b9b4135e3d590d7f45c7f8a5e3e2297250c9641db924ad9cae1533	9e5aea3c4836c95c5e529953feb624a199cb507094f09fc57656fd666edb64fa	fce1a3a6636dc34a709d14fcd4c577fae32207cd3eb18a62484a9e4e8fc5758e
cat-searcher/leandojo-benchmark-4-random	test	2,526	LinearMap.rank_comp_le_left	Mathlib/LinearAlgebra/Dimension/LinearMap.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>LinearMap.range_comp</a>]	K : Type u V V₁ : Type v V' V'₁ : Type v' V'' : Type v'' inst✝⁸ : Ring K inst✝⁷ : AddCommGroup V inst✝⁶ : Module K V inst✝⁵ : AddCommGroup V₁ inst✝⁴ : Module K V₁ inst✝³ : AddCommGroup V' inst✝² : Module K V' inst✝¹ : AddCommGroup V'' inst✝ : Module K V'' g : V →ₗ[K] V' f : V' →ₗ[K] V'' ⊢ range (f ∘ₗ g) ≤ range f	K : Type u V V₁ : Type v V' V'₁ : Type v' V'' : Type v'' inst✝⁸ : Ring K inst✝⁷ : AddCommGroup V inst✝⁶ : Module K V inst✝⁵ : AddCommGroup V₁ inst✝⁴ : Module K V₁ inst✝³ : AddCommGroup V' inst✝² : Module K V' inst✝¹ : AddCommGroup V'' inst✝ : Module K V'' g : V →ₗ[K] V' f : V' →ₗ[K] V'' ⊢ Submodule.map f (range g) ≤ ra...	((:c LE.le) ((:c Submodule) (:fv _uniq.23614) (:fv _uniq.23624) ((:c Ring.toSemiring) (:fv _uniq.23614) (:fv _uniq.23627)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.23624) (:fv _uniq.25348)) (:fv _uniq.25933)) ((:c Preorder.toLE) ((:c Submodule) (:fv _uniq.23614) (:fv _uniq.23624) ((:c Ring.toSemiring) (:fv _uniq.2...	[{"name":"K","sexp":"(:sort (+ u 1))"},{"name":"V","sexp":"(:sort (+ v 1))"},{"name":"V₁","sexp":"(:sort (+ v 1))"},{"name":"V'","sexp":"(:sort (+ v' 1))"},{"name":"V'₁","sexp":"(:sort (+ v' 1))"},{"name":"V''","sexp":"(:sort (+ v'' 1))"},{"name":"inst✝⁸","sexp":"((:c Ring) (:fv _uniq.23614))"},{"name":"inst✝⁷","sexp":...	(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23614","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23616","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con...	{"children":[{"source":"rw","sourceEnd":1589,"sourceStart":1587,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1591,"sourceStart":1590,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"LinearMap.range_comp...	[]	[{"source":"LinearMap.range_comp","source_end":1611,"source_start":1591,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23614","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23616","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	18	5	exact	true	1	17	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	3c6a4ef4254c6fc011c963f10808a6bceb686ca78b0df92270022bd66f731b7a	fce1a3a6636dc34a709d14fcd4c577fae32207cd3eb18a62484a9e4e8fc5758e	6e955e66e826d42626e32494faf48492c9c28a6899e6ef5d025f64d4f52e7b04	5dc9cc3e0328ae3294ab2a3cd6c17f34119680def90879fbed6d3d3a7fde155c
cat-searcher/leandojo-benchmark-4-random	test	2,527	LinearMap.rank_comp_le_left	Mathlib/LinearAlgebra/Dimension/LinearMap.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact <a>LinearMap.map_le_range</a>	K : Type u V V₁ : Type v V' V'₁ : Type v' V'' : Type v'' inst✝⁸ : Ring K inst✝⁷ : AddCommGroup V inst✝⁶ : Module K V inst✝⁵ : AddCommGroup V₁ inst✝⁴ : Module K V₁ inst✝³ : AddCommGroup V' inst✝² : Module K V' inst✝¹ : AddCommGroup V'' inst✝ : Module K V'' g : V →ₗ[K] V' f : V' →ₗ[K] V'' ⊢ Submodule.map f (range g) ≤ ra...		((:c LE.le) ((:c Submodule) (:fv _uniq.23614) (:fv _uniq.23624) ((:c Ring.toSemiring) (:fv _uniq.23614) (:fv _uniq.23627)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.23624) (:fv _uniq.25348)) (:fv _uniq.25933)) ((:c Preorder.toLE) ((:c Submodule) (:fv _uniq.23614) (:fv _uniq.23624) ((:c Ring.toSemiring) (:fv _uniq.2...	[{"name":"K","sexp":"(:sort (+ u 1))"},{"name":"V","sexp":"(:sort (+ v 1))"},{"name":"V₁","sexp":"(:sort (+ v 1))"},{"name":"V'","sexp":"(:sort (+ v' 1))"},{"name":"V'₁","sexp":"(:sort (+ v' 1))"},{"name":"V''","sexp":"(:sort (+ v'' 1))"},{"name":"inst✝⁸","sexp":"((:c Ring) (:fv _uniq.23614))"},{"name":"inst✝⁷","sexp":...	(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23614","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23616","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con...	{"children":[{"source":"exact","sourceEnd":1620,"sourceStart":1615,"tag":"atom"},{"name":"LinearMap.map_le_range","semanticRole":"global","source":"LinearMap.map_le_range","sourceEnd":1643,"sourceStart":1621,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact LinearMap.map_le_range","sourceEnd":1643,...	[]	[{"source":"LinearMap.map_le_range","source_end":1643,"source_start":1621,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23614","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23616","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	18	8	exact	true	1	17	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	e5a28aa4e57ccd759d90db0769ba748d3e9394f0c2875fa6385e6099dd7e0159	5dc9cc3e0328ae3294ab2a3cd6c17f34119680def90879fbed6d3d3a7fde155c	b0b70b55be21101c2b5485b33721df6de08498cb6c36e71b11ca4eebc5d660e9	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,528	ENNReal.rpow_eq_top_of_nonneg	Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>ENNReal.rpow_eq_top_iff</a>]	x : ℝ≥0∞ y : ℝ hy0 : 0 ≤ y ⊢ x ^ y = ⊤ → x = ⊤	x : ℝ≥0∞ y : ℝ hy0 : 0 ≤ y ⊢ x = 0 ∧ y < 0 ∨ x = ⊤ ∧ 0 < y → x = ⊤	(:forall _ ((:c Eq) (:c ENNReal) ((:c HPow.hPow) (:c ENNReal) (:c Real) (:c ENNReal) ((:c instHPow) (:c ENNReal) (:c Real) (:c ENNReal.instPowReal)) (:fv _uniq.65974) (:fv _uniq.65975)) ((:c Top.top) (:c ENNReal) ((:c CompleteLattice.toTop) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c...	[{"name":"x","sexp":"(:c ENNReal)"},{"name":"y","sexp":"(:c Real)"},{"name":"hy0","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.65975))"}]	(:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c ENNReal)) (:arg :explicit 1 (:c...	[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.65974","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.65975","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"},{"binder_role":":explicit","contex...	{"children":[{"source":"rw","sourceEnd":21830,"sourceStart":21828,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":21832,"sourceStart":21831,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"ENNReal.rpow_eq_...	[]	[{"source":"ENNReal.rpow_eq_top_iff","source_end":21855,"source_start":21832,"syntax_kind":"ident"}]	[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.65974","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.65975","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":explicit","context_index":3,"internal_name":"_un...	176	4	exact	true	1	3	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	34e6c91d42e1f61fe4cbc51d0c685f8681560bb580efabd8c200ca8f3678d40f	fe5fadd365c43fad0ec0b65742f10071fddc5a1d48f09220c70a1248ac8a0ba6	0b2bd3594ed46e09dff95ed20dfd800d933c631d1abab0516101eb88edf5ff80	686fb76464a4c1df90853729829dd94fc1bc2bfa9606d0518a8f91ca89c6a0a0
cat-searcher/leandojo-benchmark-4-random	test	2,530	ENNReal.rpow_eq_top_of_nonneg	Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exfalso	case inl x : ℝ≥0∞ y : ℝ hy0 : 0 ≤ y h : x = 0 ∧ y < 0 ⊢ x = ⊤	case inl x : ℝ≥0∞ y : ℝ hy0 : 0 ≤ y h : x = 0 ∧ y < 0 ⊢ False	((:c Eq) (:c ENNReal) (:fv _uniq.65974) ((:c Top.top) (:c ENNReal) ((:c CompleteLattice.toTop) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompletelyDistribLattice) (:c ENNReal) (:c ENNReal.instCompleteLinearOrder))))))	[{"name":"x","sexp":"(:c ENNReal)"},{"name":"y","sexp":"(:c Real)"},{"name":"hy0","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.65975))"},{"name":"h","sexp":"((:c And) ((:c Eq) (:c ENNReal) (:fv _uniq.65974) ((:c OfNat.o...	(:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:app (:c Top.top) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c Top) (:arg :explicit 0 (:c ENNReal))))))))	[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.65974","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.65975","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"},{"binder_role":":explicit","contex...	{"children":[{"source":"exfalso","sourceEnd":21884,"sourceStart":21877,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticExfalso","source":"exfalso","sourceEnd":21884,"sourceStart":21877,"tag":"node"}	[]	[]	[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.65974","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.65975","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":explicit","context_index":3,"internal_name":"_un...	176	12	exact	true	1	4	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	04fe99750bf1f67d6eddcdcbcd2e979b3b7b5cefb865e58f751511974eb0794c	aa63020a4ad49fc217031f9929d8f3b515c9ef49a376e9611618daf3cbc42e90	c68edda11cdb69125c1486c6356b60cedaec50aa8c4d3442e85a91513f01648d	eb14d7412d906c32bd56d80754525a8c278fce8be3fdd676359326243ebff9d2
cat-searcher/leandojo-benchmark-4-random	test	2,531	ENNReal.rpow_eq_top_of_nonneg	Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>lt_iff_not_ge</a>] at h	case inl x : ℝ≥0∞ y : ℝ hy0 : 0 ≤ y h : x = 0 ∧ y < 0 ⊢ False	case inl x : ℝ≥0∞ y : ℝ hy0 : 0 ≤ y h : x = 0 ∧ ¬y ≥ 0 ⊢ False	(:c False)	[{"name":"x","sexp":"(:c ENNReal)"},{"name":"y","sexp":"(:c Real)"},{"name":"hy0","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.65975))"},{"name":"h","sexp":"((:c And) ((:c Eq) (:c ENNReal) (:fv _uniq.65974) ((:c OfNat.o...	(:c False)	[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.65974","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.65975","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"},{"binder_role":":explicit","contex...	{"children":[{"source":"rw","sourceEnd":21891,"sourceStart":21889,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":21893,"sourceStart":21892,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"lt_iff_not_ge","...	[]	[{"source":"lt_iff_not_ge","source_end":21906,"source_start":21893,"syntax_kind":"ident"},{"source":"h","source_end":21912,"source_start":21911,"syntax_kind":"ident"}]	[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.65974","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.65975","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":explicit","context_index":3,"internal_name":"_un...	176	13	exact	true	1	4	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	97e3a3f3b0aaa8e8f448852f389c0c2c09d8a36f3fc7a1e4bac5ffc39b9b8d89	eb14d7412d906c32bd56d80754525a8c278fce8be3fdd676359326243ebff9d2	239b779fb29b6553bef29f6ddfffb74975fe22ccc0825ff053094c741f84aa37	1638df0e0f6c73bcb31387f6e2e123ff5fd5fe49cd8811677ef5ffcb3f7a3792
cat-searcher/leandojo-benchmark-4-random	test	2,532	ENNReal.rpow_eq_top_of_nonneg	Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact h.right hy0	case inl x : ℝ≥0∞ y : ℝ hy0 : 0 ≤ y h : x = 0 ∧ ¬y ≥ 0 ⊢ False		(:c False)	[{"name":"x","sexp":"(:c ENNReal)"},{"name":"y","sexp":"(:c Real)"},{"name":"hy0","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.65975))"},{"name":"h","sexp":"((:c And) ((:c Eq) (:c ENNReal) (:fv _uniq.65974) ((:c OfNat.o...	(:c False)	[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.65974","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.65975","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"},{"binder_role":":explicit","contex...	{"children":[{"source":"exact","sourceEnd":21922,"sourceStart":21917,"tag":"atom"},{"children":[{"source":"h.right","sourceEnd":21930,"sourceStart":21923,"tag":"identifier"},{"children":[{"contextIndex":3,"semanticRole":"local","source":"hy0","sourceEnd":21934,"sourceStart":21931,"tag":"identifier"}],"kind":"null","sou...	[]	[{"source":"h.right hy0","source_end":21934,"source_start":21923,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.65974","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.65975","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":explicit","context_index":3,"internal_name":"_un...	176	16	exact	true	1	4	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	e3549ea1e2a6c46733dd56543ddef72701ddb36f57aeaff7bd8dc04744be7de9	1638df0e0f6c73bcb31387f6e2e123ff5fd5fe49cd8811677ef5ffcb3f7a3792	5e6963edf800338a750e768f3f789dcadd73812b5e9f3834394d826a442a9ce1	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,533	ENNReal.rpow_eq_top_of_nonneg	Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact h.left	case inr x : ℝ≥0∞ y : ℝ hy0 : 0 ≤ y h : x = ⊤ ∧ 0 < y ⊢ x = ⊤		((:c Eq) (:c ENNReal) (:fv _uniq.65974) ((:c Top.top) (:c ENNReal) ((:c CompleteLattice.toTop) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompletelyDistribLattice) (:c ENNReal) (:c ENNReal.instCompleteLinearOrder))))))	[{"name":"x","sexp":"(:c ENNReal)"},{"name":"y","sexp":"(:c Real)"},{"name":"hy0","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.65975))"},{"name":"h","sexp":"((:c And) ((:c Eq) (:c ENNReal) (:fv _uniq.65974) ((:c Top.top...	(:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:app (:c Top.top) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c Top) (:arg :explicit 0 (:c ENNReal))))))))	[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.65974","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.65975","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"},{"binder_role":":explicit","contex...	{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":21945,"sourceStart":21940,"tag":"atom"},{"name":"And.left","semanticRole":"global","source":"h.left","sourceEnd":21952,"sourceStart":21946,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact h.left","sourceEnd":21952,"s...	[]	[{"source":"h.left","source_end":21952,"source_start":21946,"syntax_kind":"ident"}]	[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.65974","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.65975","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":explicit","context_index":3,"internal_name":"_un...	176	19	exact	true	1	4	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	8ff7786f4e5216f182919294580be3236b2426f5d65b307eef6eb2f66948ea65	d9bf07a65fe7bc66b2a4745528da1dd2ca4b0155a8d4e47bb4c9a278bbad81c5	0b7215e9eaef2d844d4a4ad9770ac47b38c368cbe99c19d2a4ccd562f6b2a51f	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,534	PiNat.cylinder_eq_cylinder_of_le_firstDiff	Mathlib/Topology/MetricSpace/PiNat.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [← <a>PiNat.mem_cylinder_iff_eq</a>]	E : ℕ → Type u_1 x y : (n : ℕ) → E n n : ℕ hn : n ≤ firstDiff x y ⊢ cylinder x n = cylinder y n	E : ℕ → Type u_1 x y : (n : ℕ) → E n n : ℕ hn : n ≤ firstDiff x y ⊢ x ∈ cylinder y n	((:c Eq) ((:c Set) (:forall n (:c Nat) ((:fv _uniq.20676) 0))) ((:c PiNat.cylinder) (:fv _uniq.20676) (:fv _uniq.20729) (:fv _uniq.20731)) ((:c PiNat.cylinder) (:fv _uniq.20676) (:fv _uniq.20730) (:fv _uniq.20731)))	[{"name":"E","sexp":"(:forall _ (:c Nat) (:sort (+ u_1 1)))"},{"name":"x","sexp":"(:forall n (:c Nat) ((:fv _uniq.20676) 0))"},{"name":"y","sexp":"(:forall n (:c Nat) ((:fv _uniq.20676) 0))"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c LE.le) (:c Nat) (:c instLENat) (:fv _uniq.20731) ((:c PiNat.firstDiff) ...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:forall n :explicit (:c Nat) (:app (:fv FV0) (:arg :explicit 0 0)))))) (:arg :explicit 1 (:app (:c PiNat.cylinder) (:arg :implicit 0) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV4)))) (:arg :explicit 2 (:app (:c PiNat.cylinder) (:arg :impl...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20676","is_instance":false,"is_let":false,"name":"E","sexp":"(:forall _ :explicit (:c Nat) (:sort Type))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20729","is_instance":false,"is_let":false,"name":"x","sexp":"(:forall n :exp...	{"children":[{"source":"rw","sourceEnd":6950,"sourceStart":6948,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6952,"sourceStart":6951,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":6955,"sourceStart":...	[]	[{"source":"mem_cylinder_iff_eq","source_end":6975,"source_start":6956,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20676","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20729","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_un...	41	4	exact	true	1	5	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	2949f38f85b0d846c4637238bb985f00c32de3139c40cba382b6005302407974	e23a9e7c727211f7100142a8f570e71b2d5faebfe1eeef4bcc31110e46c8adaa	0092326e34da3ddd95a22e376c098ee0d119dfad8816bed69ab76aca5ce668ee	4a63553560f0697b491c7c25e7842a365c1118557a8365bb1ffeff82e9c52167
cat-searcher/leandojo-benchmark-4-random	test	2,535	PiNat.cylinder_eq_cylinder_of_le_firstDiff	Mathlib/Topology/MetricSpace/PiNat.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	intro i hi	E : ℕ → Type u_1 x y : (n : ℕ) → E n n : ℕ hn : n ≤ firstDiff x y ⊢ x ∈ cylinder y n	E : ℕ → Type u_1 x y : (n : ℕ) → E n n : ℕ hn : n ≤ firstDiff x y i : ℕ hi : i < n ⊢ x i = y i	((:c Membership.mem) (:forall n (:c Nat) ((:fv _uniq.20676) 0)) ((:c Set) (:forall n (:c Nat) ((:fv _uniq.20676) 0))) ((:c Set.instMembership) (:forall n (:c Nat) ((:fv _uniq.20676) 0))) (:fv _uniq.20729) ((:c PiNat.cylinder) (:fv _uniq.20676) (:fv _uniq.20730) (:fv _uniq.20731)))	[{"name":"E","sexp":"(:forall _ (:c Nat) (:sort (+ u_1 1)))"},{"name":"x","sexp":"(:forall n (:c Nat) ((:fv _uniq.20676) 0))"},{"name":"y","sexp":"(:forall n (:c Nat) ((:fv _uniq.20676) 0))"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c LE.le) (:c Nat) (:c instLENat) (:fv _uniq.20731) ((:c PiNat.firstDiff) ...	(:app (:c Membership.mem) (:arg :implicit-type 0 (:forall n :explicit (:c Nat) (:app (:fv FV0) (:arg :explicit 0 0)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:forall n :explicit (:c Nat) (:app (:fv FV0) (:arg :explicit 0 0)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20676","is_instance":false,"is_let":false,"name":"E","sexp":"(:forall _ :explicit (:c Nat) (:sort Type))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20729","is_instance":false,"is_let":false,"name":"x","sexp":"(:forall n :exp...	{"children":[{"source":"intro","sourceEnd":6984,"sourceStart":6979,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"i","sourceEnd":6986,"sourceStart":6985,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hi","sourceEnd":6989,"sourceStart":6987,"tag":"identifier"}],"kind":"null","source":"...	[{"role":"fresh_name","source":"i","source_end":6986,"source_start":6985,"syntax_kind":"ident"},{"role":"fresh_name","source":"hi","source_end":6989,"source_start":6987,"syntax_kind":"ident"}]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20676","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20729","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_un...	41	7	exact	true	1	5	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	014cc4e2d7a93872e134fa50c01d445c5c3796462002109a4f461ceaa3c0ec27	4a63553560f0697b491c7c25e7842a365c1118557a8365bb1ffeff82e9c52167	f8dc8efe385c2627ebbcb0000fbf509f2b0935edbac43a186e1157fab879513b	9a77194b84b0f16f52e2ef5959244d0054e9c1fd98422c64d2762440b1fb8852
cat-searcher/leandojo-benchmark-4-random	test	2,536	PiNat.cylinder_eq_cylinder_of_le_firstDiff	Mathlib/Topology/MetricSpace/PiNat.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact <a>PiNat.apply_eq_of_lt_firstDiff</a> (hi.trans_le hn)	E : ℕ → Type u_1 x y : (n : ℕ) → E n n : ℕ hn : n ≤ firstDiff x y i : ℕ hi : i < n ⊢ x i = y i		((:c Eq) ((:fv _uniq.20676) (:fv _uniq.20758)) ((:fv _uniq.20729) (:fv _uniq.20758)) ((:fv _uniq.20730) (:fv _uniq.20758)))	[{"name":"E","sexp":"(:forall _ (:c Nat) (:sort (+ u_1 1)))"},{"name":"x","sexp":"(:forall n (:c Nat) ((:fv _uniq.20676) 0))"},{"name":"y","sexp":"(:forall n (:c Nat) ((:fv _uniq.20676) 0))"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c LE.le) (:c Nat) (:c instLENat) (:fv _uniq.20731) ((:c PiNat.firstDiff) ...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:fv FV0) (:arg :explicit 0 (:fv FV6)))) (:arg :explicit 1 (:app (:fv FV2) (:arg :explicit 0 (:fv FV6)))) (:arg :explicit 2 (:app (:fv FV3) (:arg :explicit 0 (:fv FV6)))))	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20676","is_instance":false,"is_let":false,"name":"E","sexp":"(:forall _ :explicit (:c Nat) (:sort Type))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20729","is_instance":false,"is_let":false,"name":"x","sexp":"(:forall n :exp...	{"children":[{"source":"exact","sourceEnd":6997,"sourceStart":6992,"tag":"atom"},{"children":[{"name":"PiNat.apply_eq_of_lt_firstDiff","semanticRole":"global","source":"apply_eq_of_lt_firstDiff","sourceEnd":7022,"sourceStart":6998,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":7024,"sourceStart...	[]	[{"source":"apply_eq_of_lt_firstDiff (hi.trans_le hn)","source_end":7039,"source_start":6998,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20676","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20729","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_un...	41	8	exact	true	1	7	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	b22df687f9e990b4ccd998c1ac1762b6c7fa06f454849339c13247ec2c8c3402	9a77194b84b0f16f52e2ef5959244d0054e9c1fd98422c64d2762440b1fb8852	cc1ee21685fd2fe296e647874830822c4bfb20bf808b0007a98afc81d579f3d2	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,537	Function.invFun_eq_of_injective_of_rightInverse	Mathlib/Logic/Function/Basic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [hg b]	α : Sort u_1 β : Sort u_2 inst✝ : Nonempty α f : α → β a : α b✝ : β g : β → α hf : Injective f hg : RightInverse g f b : β ⊢ f (invFun f b) = f (g b)	α : Sort u_1 β : Sort u_2 inst✝ : Nonempty α f : α → β a : α b✝ : β g : β → α hf : Injective f hg : RightInverse g f b : β ⊢ f (invFun f b) = b	((:c Eq) (:fv _uniq.13010) ((:fv _uniq.13017) ((:c Function.invFun) (:fv _uniq.13007) (:fv _uniq.13010) (:fv _uniq.13013) (:fv _uniq.13017) (:fv _uniq.13089))) ((:fv _uniq.13017) ((:fv _uniq.13070) (:fv _uniq.13089))))	[{"name":"α","sexp":"(:sort u_1)"},{"name":"β","sexp":"(:sort u_2)"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.13007))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.13007) (:fv _uniq.13010))"},{"name":"a","sexp":"(:fv _uniq.13007)"},{"name":"b✝","sexp":"(:fv _uniq.13010)"},{"name":"g","sexp":"(:forall _ (:fv _uni...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:fv FV3) (:arg :explicit 0 (:app (:c Function.invFun) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Nonempty) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 3 (:fv FV3)) (:arg :expli...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13007","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13010","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli...	{"children":[{"source":"rw","sourceEnd":21449,"sourceStart":21447,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":21451,"sourceStart":21450,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"contextInd...	[]	[{"source":"hg b","source_end":21455,"source_start":21451,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13007","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13010","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n...	157	4	exact	true	1	10	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	ce2302acc021eb11695e30941077410de6963893ebdd2229aa3d7cb8a3b77a2f	f17d94a1f2c5370333442c1df30869c673fb6a7af1ed00019cfc997e0d1b2fea	21584f2e9d4634aaefb5689c30842c97b1cb8248ee8aada13cff9a5a186dd109	132488b18992ca7a7493ea628693eb6865b987d6e160c22b494413ffd4748fb7
cat-searcher/leandojo-benchmark-4-random	test	2,538	Function.invFun_eq_of_injective_of_rightInverse	Mathlib/Logic/Function/Basic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact <a>Function.invFun_eq</a> ⟨g b, hg b⟩	α : Sort u_1 β : Sort u_2 inst✝ : Nonempty α f : α → β a : α b✝ : β g : β → α hf : Injective f hg : RightInverse g f b : β ⊢ f (invFun f b) = b		((:c Eq) (:fv _uniq.13010) ((:fv _uniq.13017) ((:c Function.invFun) (:fv _uniq.13007) (:fv _uniq.13010) (:fv _uniq.13013) (:fv _uniq.13017) (:fv _uniq.13089))) (:fv _uniq.13089))	[{"name":"α","sexp":"(:sort u_1)"},{"name":"β","sexp":"(:sort u_2)"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.13007))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.13007) (:fv _uniq.13010))"},{"name":"a","sexp":"(:fv _uniq.13007)"},{"name":"b✝","sexp":"(:fv _uniq.13010)"},{"name":"g","sexp":"(:forall _ (:fv _uni...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:fv FV3) (:arg :explicit 0 (:app (:c Function.invFun) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Nonempty) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 3 (:fv FV3)) (:arg :expli...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13007","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13010","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli...	{"children":[{"source":"exact","sourceEnd":21470,"sourceStart":21465,"tag":"atom"},{"children":[{"name":"Function.invFun_eq","semanticRole":"global","source":"invFun_eq","sourceEnd":21480,"sourceStart":21471,"tag":"identifier"},{"children":[{"children":[{"source":"⟨","sourceEnd":21484,"sourceStart":21481,"tag":"atom"},...	[]	[{"source":"invFun_eq ⟨g b, hg b⟩","source_end":21496,"source_start":21471,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13007","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13010","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n...	157	7	exact	true	1	10	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	881d53275ce2a5466b62602d655bc62682cffd98036a7882ce89b4246ff6253e	132488b18992ca7a7493ea628693eb6865b987d6e160c22b494413ffd4748fb7	051c4e19c219bab581d445df72a92a6dac047f6790e4a6852446c844f98a83ce	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,539	MeasureTheory.tendsto_setToFun_filter_of_dominated_convergence	Mathlib/MeasureTheory/Integral/SetToL1.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>Filter.tendsto_iff_seq_tendsto</a>]	α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ : Measure ...	α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ : Measure ...	((:c Filter.Tendsto) (:fv _uniq.1285346) (:fv _uniq.1280751) (:lambda n (:fv _uniq.1285346) ((:c MeasureTheory.setToFun) (:fv _uniq.1280745) (:fv _uniq.1280748) (:fv _uniq.1280751) (:fv _uniq.1280765) (:fv _uniq.1280870) (:fv _uniq.1280873) (:fv _uniq.1280977) (:fv _uniq.1281090) (:fv _uniq.1281099) (:fv _uniq.1281197)...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁸","sexp":"((:c NormedAddCom...	(:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:fv FV27)) (:arg :implicit-type 1 (:fv FV2)) (:arg :explicit 2 (:lambda n :explicit (:fv FV27) (:app (:c MeasureTheory.setToFun) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit",...	{"children":[{"source":"rw","sourceEnd":97819,"sourceStart":97817,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":97821,"sourceStart":97820,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Filter.tendsto_i...	[]	[{"source":"tendsto_iff_seq_tendsto","source_end":97844,"source_start":97821,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":...	392	4	exact	true	1	36	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	cad47e0d18cb8eb82e078e4c3ba5a06eeb146b4fe47a666ed59c4515b377c858	e4bc2f0f5a32ac63def2899ae5979985f5d95d62a28653462ddf4da4062eefa0	80fe0fec15c87c109b0f664c256e9fe3afead211cdd75eee5d2f14ddd38491c7	24ba1a33a7188ac2739f38480fa1bfe960f7a7bc042d1a1aa057303d576fd8d1
cat-searcher/leandojo-benchmark-4-random	test	2,540	MeasureTheory.tendsto_setToFun_filter_of_dominated_convergence	Mathlib/MeasureTheory/Integral/SetToL1.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	intro x xl	α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ : Measure ...	α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ : Measure ...	(:forall x (:forall _ (:c Nat) (:fv _uniq.1285346)) (:forall _ ((:c Filter.Tendsto) (:c Nat) (:fv _uniq.1285346) 0 ((:c Filter.atTop) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring)))) (:fv _uniq.1285347)) ((:c Filter.Tendsto) (:c Na...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁸","sexp":"((:c NormedAddCom...	(:forall x :explicit (:forall _ :explicit (:c Nat) (:fv FV27)) (:forall _ :explicit (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV27)) (:arg :explicit 2 0) (:arg :explicit 3 (:app (:c Filter.atTop) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c Preo...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit",...	{"children":[{"source":"intro","sourceEnd":97853,"sourceStart":97848,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":97855,"sourceStart":97854,"tag":"identifier"},{"semanticRole":"scoped_local","source":"xl","sourceEnd":97858,"sourceStart":97856,"tag":"identifier"}],"kind":"null","sou...	[{"role":"fresh_name","source":"x","source_end":97855,"source_start":97854,"syntax_kind":"ident"},{"role":"fresh_name","source":"xl","source_end":97858,"source_start":97856,"syntax_kind":"ident"}]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":...	392	7	exact	true	1	36	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	ccd89d4231551c3cf3aff936d865c6ef4e9e257a2d197c06feb38f331c8d18ea	24ba1a33a7188ac2739f38480fa1bfe960f7a7bc042d1a1aa057303d576fd8d1	b98feee802c56dc9f5bec8e97b5be3136ea7c73bda361e9234643e212f8369e0	1e8840e4904d1842504052bb5ac4c1ee508ae1b9cf398992a9898596cb350178
cat-searcher/leandojo-benchmark-4-random	test	2,541	MeasureTheory.tendsto_setToFun_filter_of_dominated_convergence	Mathlib/MeasureTheory/Integral/SetToL1.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	have hxl : ∀ s ∈ l, ∃ a, ∀ b ≥ a, x b ∈ s := by rwa [<a>Filter.tendsto_atTop'</a>] at xl	α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ : Measure ...	α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ : Measure ...	((:c Filter.Tendsto) (:c Nat) (:fv _uniq.1280751) ((:c Function.comp) (:c Nat) (:fv _uniq.1285346) (:fv _uniq.1280751) (:lambda n (:fv _uniq.1285346) ((:c MeasureTheory.setToFun) (:fv _uniq.1280745) (:fv _uniq.1280748) (:fv _uniq.1280751) (:fv _uniq.1280765) (:fv _uniq.1280870) (:fv _uniq.1280873) (:fv _uniq.1280977) (...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁸","sexp":"((:c NormedAddCom...	(:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV2)) (:arg :explicit 2 (:app (:c Function.comp) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV27)) (:arg :implicit-type 2 (:fv FV2)) (:arg :explicit 3 (:lambda n :explicit (:fv FV27) (:app (:c MeasureTheory.setToFun...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit",...	{"children":[{"source":"have","sourceEnd":97865,"sourceStart":97861,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hxl","sourceEnd":97869,"sourceStart":97866,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hxl","sourceEnd":97869,"sourceStart":97866,"tag":"n...	[]	[{"source":"∀ s ∈ l, ∃ a, ∀ b ≥ a, x b ∈ s","source_end":97914,"source_start":97872,"syntax_kind":"Lean.«term∀__,_»"},{"source":"tendsto_atTop'","source_end":97940,"source_start":97926,"syntax_kind":"ident"},{"source":"xl","source_end":97947,"source_start":97945,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":...	392	8	exact	true	1	38	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	019aa7946894e611a467a8eedb11709030e7bb8c861178f7a4ada9d703b488a1	1e8840e4904d1842504052bb5ac4c1ee508ae1b9cf398992a9898596cb350178	04637b25c63f8b00b6669993b327035d766e6655a736fb7ae2b81e946fdb275e	3b0812f1f02c5c0120f80c16f4b7a7a6a50d34040df4feb9b3fe62d5ad7cfd6f
cat-searcher/leandojo-benchmark-4-random	test	2,542	MeasureTheory.tendsto_setToFun_filter_of_dominated_convergence	Mathlib/MeasureTheory/Integral/SetToL1.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	have h : { x : ι \| (fun n => <a>MeasureTheory.AEStronglyMeasurable</a> (fs n) μ) x } ∩ { x : ι \| (fun n => ∀ᵐ a ∂μ, ‖fs n a‖ ≤ bound a) x } ∈ l := <a>Filter.inter_mem</a> hfs_meas h_bound	α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ : Measure ...	α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ : Measure ...	((:c Filter.Tendsto) (:c Nat) (:fv _uniq.1280751) ((:c Function.comp) (:c Nat) (:fv _uniq.1285346) (:fv _uniq.1280751) (:lambda n (:fv _uniq.1285346) ((:c MeasureTheory.setToFun) (:fv _uniq.1280745) (:fv _uniq.1280748) (:fv _uniq.1280751) (:fv _uniq.1280765) (:fv _uniq.1280870) (:fv _uniq.1280873) (:fv _uniq.1280977) (...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁸","sexp":"((:c NormedAddCom...	(:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV2)) (:arg :explicit 2 (:app (:c Function.comp) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV27)) (:arg :implicit-type 2 (:fv FV2)) (:arg :explicit 3 (:lambda n :explicit (:fv FV27) (:app (:c MeasureTheory.setToFun...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit",...	{"children":[{"source":"have","sourceEnd":97954,"sourceStart":97950,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":97956,"sourceStart":97955,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":97956,"sourceStart":97955,"tag":"node"...	[]	[{"source":"{ x : ι \| (fun n => AEStronglyMeasurable (fs n) μ) x } ∩\n { x : ι \| (fun n => ∀ᵐ a ∂μ, ‖fs n a‖ ≤ bound a) x } ∈ l","source_end":98104,"source_start":97963,"syntax_kind":"«term_∈_»"},{"source":"inter_mem hfs_meas h_bound","source_end":98138,"source_start":98112,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":...	392	13	exact	true	1	39	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	f8d586046c2a0a6db90efe29dac86840a0cb8e892cb69172ed7dae295f4bc41b	3b0812f1f02c5c0120f80c16f4b7a7a6a50d34040df4feb9b3fe62d5ad7cfd6f	cc6dfc86b5638f552cb577ebd6a9586de0f989a92fe7c1bfc92fca76f24626b7	5d48e3124b8987b03b6b72d2e598d72762f705b8423cfdb68815a15d0042db66
cat-searcher/leandojo-benchmark-4-random	test	2,543	MeasureTheory.tendsto_setToFun_filter_of_dominated_convergence	Mathlib/MeasureTheory/Integral/SetToL1.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	obtain ⟨k, h⟩ := hxl _ h	α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ : Measure ...	case intro α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ...	((:c Filter.Tendsto) (:c Nat) (:fv _uniq.1280751) ((:c Function.comp) (:c Nat) (:fv _uniq.1285346) (:fv _uniq.1280751) (:lambda n (:fv _uniq.1285346) ((:c MeasureTheory.setToFun) (:fv _uniq.1280745) (:fv _uniq.1280748) (:fv _uniq.1280751) (:fv _uniq.1280765) (:fv _uniq.1280870) (:fv _uniq.1280873) (:fv _uniq.1280977) (...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁸","sexp":"((:c NormedAddCom...	(:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV2)) (:arg :explicit 2 (:app (:c Function.comp) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV27)) (:arg :implicit-type 2 (:fv FV2)) (:arg :explicit 3 (:lambda n :explicit (:fv FV27) (:app (:c MeasureTheory.setToFun...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit",...	{"children":[{"source":"obtain","sourceEnd":98147,"sourceStart":98141,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":98151,"sourceStart":98148,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"k","sourceEn...	[]	[{"source":"hxl _ h","source_end":98169,"source_start":98162,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨k, h⟩","source_end":98158,"source_start":98148,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":...	392	14	exact	true	1	40	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	3283cfc2b22e281dda3538d37dd768f71411fd10fe012dc0e9b49fb092b73586	5d48e3124b8987b03b6b72d2e598d72762f705b8423cfdb68815a15d0042db66	4d5af5e2f63bc003ba743d6dc89c6050e9c2211b792cf413c5f3476af5cca022	d0907edd21271ffd86d4f00ad38ae54323872f58a5eb705444e93e1c96472757
cat-searcher/leandojo-benchmark-4-random	test	2,544	MeasureTheory.tendsto_setToFun_filter_of_dominated_convergence	Mathlib/MeasureTheory/Integral/SetToL1.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [← <a>Filter.tendsto_add_atTop_iff_nat</a> k]	case intro α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ...	case intro α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ...	((:c Filter.Tendsto) (:c Nat) (:fv _uniq.1280751) ((:c Function.comp) (:c Nat) (:fv _uniq.1285346) (:fv _uniq.1280751) (:lambda n (:fv _uniq.1285346) ((:c MeasureTheory.setToFun) (:fv _uniq.1280745) (:fv _uniq.1280748) (:fv _uniq.1280751) (:fv _uniq.1280765) (:fv _uniq.1280870) (:fv _uniq.1280873) (:fv _uniq.1280977) (...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁸","sexp":"((:c NormedAddCom...	(:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV2)) (:arg :explicit 2 (:app (:c Function.comp) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV27)) (:arg :implicit-type 2 (:fv FV2)) (:arg :explicit 3 (:lambda n :explicit (:fv FV27) (:app (:c MeasureTheory.setToFun...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit",...	{"children":[{"source":"rw","sourceEnd":98174,"sourceStart":98172,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":98176,"sourceStart":98175,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":98179,"sourceSt...	[]	[{"source":"tendsto_add_atTop_iff_nat k","source_end":98207,"source_start":98180,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":...	392	15	exact	true	1	42	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	c413ea57bc54378d69dda0b999ea5d9f6c2927a7236b32d8af3e5f2ed2dbe22f	d0907edd21271ffd86d4f00ad38ae54323872f58a5eb705444e93e1c96472757	864ba2ef81e9624b3c56a2eb3258282eb2bd9f59760d83572ee271ee08371fc1	d5f22b9958e7972065d72d82def9f9d06f40a376fe96f7cea3aee8a873e76f14
cat-searcher/leandojo-benchmark-4-random	test	2,545	MeasureTheory.tendsto_setToFun_filter_of_dominated_convergence	Mathlib/MeasureTheory/Integral/SetToL1.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	refine <a>MeasureTheory.tendsto_setToFun_of_dominated_convergence</a> hT bound ?_ bound_integrable ?_ ?_	case intro α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ...	case intro.refine_1 α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : Measurable...	((:c Filter.Tendsto) (:c Nat) (:fv _uniq.1280751) (:lambda n (:c Nat) ((:c Function.comp) (:c Nat) (:fv _uniq.1285346) (:fv _uniq.1280751) (:lambda n (:fv _uniq.1285346) ((:c MeasureTheory.setToFun) (:fv _uniq.1280745) (:fv _uniq.1280748) (:fv _uniq.1280751) (:fv _uniq.1280765) (:fv _uniq.1280870) (:fv _uniq.1280873) (...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁸","sexp":"((:c NormedAddCom...	(:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV2)) (:arg :explicit 2 (:lambda n :explicit (:c Nat) (:app (:c Function.comp) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV27)) (:arg :implicit-type 2 (:fv FV2)) (:arg :explicit 3 (:lambda n :explicit (:fv FV27) (:...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit",...	{"children":[{"source":"refine","sourceEnd":98217,"sourceStart":98211,"tag":"atom"},{"children":[{"name":"MeasureTheory.tendsto_setToFun_of_dominated_convergence","semanticRole":"global","source":"tendsto_setToFun_of_dominated_convergence","sourceEnd":98259,"sourceStart":98218,"tag":"identifier"},{"children":[{"context...	[]	[{"source":"tendsto_setToFun_of_dominated_convergence hT bound ?_ bound_integrable ?_ ?_","source_end":98294,"source_start":98218,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":...	392	18	exact	true	1	42	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	6f01fe625953089546be1f34ae3c1ae787ae8e56b8152087a57502283fdbdd5b	d5f22b9958e7972065d72d82def9f9d06f40a376fe96f7cea3aee8a873e76f14	2de26202f7255ee91a69da4f4810f12b926f4824e8b4d17486165d80006b5add	0c60cb1b8a8945103723f91a573028a93e5951745b7653099f9bd22b7d123620
cat-searcher/leandojo-benchmark-4-random	test	2,546	MeasureTheory.tendsto_setToFun_filter_of_dominated_convergence	Mathlib/MeasureTheory/Integral/SetToL1.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rwa [<a>Filter.tendsto_atTop'</a>] at xl	α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ : Measure ...		(:forall s ((:c Set) (:fv _uniq.1285346)) (:forall _ ((:c Membership.mem) ((:c Set) (:fv _uniq.1285346)) ((:c Filter) (:fv _uniq.1285346)) ((:c instMembershipSetFilter) (:fv _uniq.1285346)) 0 (:fv _uniq.1285347)) ((:c Exists) (:c Nat) (:lambda a (:c Nat) (:forall b (:c Nat) (:forall _ ((:c GE.ge) (:c Nat) (:c instLENat...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁸","sexp":"((:c NormedAddCom...	(:forall s :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV27))) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV27)))) (:arg :implicit-type 1 (:app (:c Filter) (:arg :explicit 0 (:fv FV27)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :ex...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit",...	{"children":[{"source":"rwa","sourceEnd":97924,"sourceStart":97921,"tag":"atom"},{"children":[{"source":"[","sourceEnd":97926,"sourceStart":97925,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Filter.tendsto_atTop'","semanticRole":"global","source":"tendsto_atTop...	[]	[{"source":"tendsto_atTop'","source_end":97940,"source_start":97926,"syntax_kind":"ident"},{"source":"xl","source_end":97947,"source_start":97945,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":...	392	10	exact	true	1	38	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	02d4b6c979e2959119fcba51824b3ded382a3e2b6c1c492fcdc095e6556a2e62	2040fee2e8b16b709594a579637697e71f0f262e98a9a073cdad298ac412f4a2	a90327741d8592758b517e180976193ccd13df50d7cd4350e40f5f648a53c60b	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,547	MeasureTheory.tendsto_setToFun_filter_of_dominated_convergence	Mathlib/MeasureTheory/Integral/SetToL1.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact fun n => (h _ (<a>self_le_add_left</a> _ _)).1	case intro.refine_1 α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : Measurable...		(:forall n (:c Nat) ((:c MeasureTheory.AEStronglyMeasurable) (:fv _uniq.1280745) (:fv _uniq.1280748) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.1280748) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.1280748) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:fv _uniq.1280748) ((:c NormedAddCommGroup.toSeminor...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁸","sexp":"((:c NormedAddCom...	(:forall n :explicit (:c Nat) (:app (:c MeasureTheory.AEStronglyMeasurable) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit 3) (:arg :explicit 4 (:app (:fv FV30) (:arg :explicit 0 (:app (:fv F...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit",...	{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":98305,"sourceStart":98300,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":98309,"sourceStart":98306,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"n","sourceEnd":98311,"sourceStart":98310,"tag":"id...	[]	[{"source":"fun n => (h _ (self_le_add_left _ _)).1","source_end":98345,"source_start":98306,"syntax_kind":"Lean.Parser.Term.fun"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":...	392	21	exact	true	1	42	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	e023e6bdbd31b6956aaeabfba27e5a74675403c728c85fa3e789f50783e69d07	533b2135fe1e440531a222335c5e96f49e352cea08b0c2cd1c55da8286a1fcc9	0e416b54d0a5f740b1826b9ba140e34dce7861bdab5b5564bc4eb896d8ebc925	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,548	MeasureTheory.tendsto_setToFun_filter_of_dominated_convergence	Mathlib/MeasureTheory/Integral/SetToL1.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact fun n => (h _ (<a>self_le_add_left</a> _ _)).2	case intro.refine_2 α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : Measurable...		(:forall n (:c Nat) ((:c Filter.Eventually) (:fv _uniq.1280745) (:lambda a (:fv _uniq.1280745) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.1280748) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.1280748) (:fv _uniq.1280765)) ((:fv _uniq.1285349) ((:fv _uniq.1285469) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁸","sexp":"((:c NormedAddCom...	(:forall n :explicit (:c Nat) (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda a :explicit (:fv FV0) (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :imp...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit",...	{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":98356,"sourceStart":98351,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":98360,"sourceStart":98357,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"n","sourceEnd":98362,"sourceStart":98361,"tag":"id...	[]	[{"source":"fun n => (h _ (self_le_add_left _ _)).2","source_end":98396,"source_start":98357,"syntax_kind":"Lean.Parser.Term.fun"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":...	392	26	exact	true	1	42	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	9cfa01ae4241a6d79cf123888dc7ca0bb180fd1b3a96a94b87af5fbf78859d2f	1b989a974d1b5f9805608a6d923dd3ff2093f966a8614029f26161509021851e	b9a4c44625a156e4ae7ecc2a85139ccb4692945d47149c481be391fd90deee54	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,549	MeasureTheory.tendsto_setToFun_filter_of_dominated_convergence	Mathlib/MeasureTheory/Integral/SetToL1.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	filter_upwards [h_lim]	case intro.refine_3 α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : Measurable...	case h α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ : M...	((:c Filter.Eventually) (:fv _uniq.1280745) (:lambda a (:fv _uniq.1280745) ((:c Filter.Tendsto) (:c Nat) (:fv _uniq.1280748) (:lambda n (:c Nat) ((:fv _uniq.1285349) ((:fv _uniq.1285469) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) 0 (:fv _uniq.1286793))) 1)) ((:c Filter.atTop) (:...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁸","sexp":"((:c NormedAddCom...	(:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda a :explicit (:fv FV0) (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:lambda n :explicit (:c Nat) (:app (:fv FV30) (:arg :explicit 0 (:app (:fv FV37) (:arg :explicit...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit",...	{"children":[{"source":"filter_upwards","sourceEnd":98416,"sourceStart":98402,"tag":"atom"},{"children":[{"source":"[","sourceEnd":98418,"sourceStart":98417,"tag":"atom"},{"children":[{"contextIndex":36,"semanticRole":"local","source":"h_lim","sourceEnd":98423,"sourceStart":98418,"tag":"identifier"}],"kind":"null","sou...	[]	[{"source":"h_lim","source_end":98423,"source_start":98418,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":...	392	33	exact	true	1	42	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	bb5ccc4e5715b911200517cfbb24dbbdc3617df185a89fb6ff2a936cb2fd9a95	6c61f2c0b266de48a447ebdb521d5c0ea7f9cc8378a70fd4fa4c3d728e53e0a7	c4cefb98bc4cc11bd0a11a51c32f75eeab74783d16338d6542cfcaf9242ef359	c51704365f1b975d445ac4a20329c66f1ba5817d37ae51b5256caf7dd2255663
cat-searcher/leandojo-benchmark-4-random	test	2,550	MeasureTheory.tendsto_setToFun_filter_of_dominated_convergence	Mathlib/MeasureTheory/Integral/SetToL1.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	refine fun a h_lin => @<a>Filter.Tendsto.comp</a> _ _ _ (fun n => x (n + k)) (fun n => fs n a) _ _ _ h_lin ?_	case h α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ : M...	case h α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ : M...	(:forall a (:fv _uniq.1280745) (:forall _ ((:c Filter.Tendsto) (:fv _uniq.1285346) (:fv _uniq.1280748) (:lambda n (:fv _uniq.1285346) ((:fv _uniq.1285349) 0 1)) (:fv _uniq.1285347) ((:c nhds) (:fv _uniq.1280748) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.1280748) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq....	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁸","sexp":"((:c NormedAddCom...	(:forall a :explicit (:fv FV0) (:forall _ :explicit (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:fv FV27)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:lambda n :explicit (:fv FV27) (:app (:fv FV30) (:arg :explicit 0 0) (:arg :explicit 1 1)))) (:arg :explicit 3 (:fv FV28)) (:arg :explicit 4 (:app (:c nhd...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit",...	{"children":[{"source":"refine","sourceEnd":98435,"sourceStart":98429,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":98439,"sourceStart":98436,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":98441,"sourceStart":98440,"tag":"identifier"},{"semanticRole":"scoped_loc...	[]	[{"source":"fun a h_lin => @Tendsto.comp _ _ _ (fun n => x (n + k)) (fun n => fs n a) _ _ _ h_lin ?_","source_end":98524,"source_start":98436,"syntax_kind":"Lean.Parser.Term.fun"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":...	392	34	exact	true	1	42	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	3842734aeffda7eea7bbf144b7f92e10842158e52288e500a9ed358d89003d2f	c51704365f1b975d445ac4a20329c66f1ba5817d37ae51b5256caf7dd2255663	39aa4545c468f8b8174c023f3ad141d35f3d5ac26ceeaf72b26ea7bac0e1bb43	895d5614e8dd1783b9c18ebd4681505a2174172e6441ba036c9d76e8fe2366b8
cat-searcher/leandojo-benchmark-4-random	test	2,551	MeasureTheory.tendsto_setToFun_filter_of_dominated_convergence	Mathlib/MeasureTheory/Integral/SetToL1.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>Filter.tendsto_add_atTop_iff_nat</a>]	case h α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ : M...	case h α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ : M...	((:c Filter.Tendsto) (:c Nat) (:fv _uniq.1285346) (:lambda n (:c Nat) ((:fv _uniq.1285469) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) 0 (:fv _uniq.1286793)))) ((:c Filter.atTop) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁸","sexp":"((:c NormedAddCom...	(:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV27)) (:arg :explicit 2 (:lambda n :explicit (:c Nat) (:app (:fv FV37) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:ins...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit",...	{"children":[{"source":"rw","sourceEnd":98531,"sourceStart":98529,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":98533,"sourceStart":98532,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Filter.tendsto_a...	[]	[{"source":"tendsto_add_atTop_iff_nat","source_end":98558,"source_start":98533,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":...	392	35	exact	true	1	44	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	d04c7b3e07cc0ac29ab788a41d694d4b5f79c09f4c5d1879f66239b1fa6067c1	895d5614e8dd1783b9c18ebd4681505a2174172e6441ba036c9d76e8fe2366b8	b87c70222abab2ca5a6b4a39c3e6c0d103ad063c06326ca7ee7345d51f891d16	d1e3e9ce5de84d1e5da64b6734833e6b79c357bca902757cfb63ddb2d6cff84c
cat-searcher/leandojo-benchmark-4-random	test	2,552	MeasureTheory.tendsto_setToFun_filter_of_dominated_convergence	Mathlib/MeasureTheory/Integral/SetToL1.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	assumption	case h α : Type u_1 E : Type u_2 F : Type u_3 F' : Type u_4 G : Type u_5 𝕜 : Type u_6 p : ℝ≥0∞ inst✝⁸ : NormedAddCommGroup E inst✝⁷ : NormedSpace ℝ E inst✝⁶ : NormedAddCommGroup F inst✝⁵ : NormedSpace ℝ F inst✝⁴ : NormedAddCommGroup F' inst✝³ : NormedSpace ℝ F' inst✝² : NormedAddCommGroup G m : MeasurableSpace α μ : M...		((:c Filter.Tendsto) (:c Nat) (:fv _uniq.1285346) (:fv _uniq.1285469) ((:c Filter.atTop) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring)))) (:fv _uniq.1285347))	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁸","sexp":"((:c NormedAddCom...	(:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV27)) (:arg :explicit 2 (:fv FV37)) (:arg :explicit 3 (:app (:c Filter.atTop) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 4 (:fv FV28)))	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit",...	{"children":[{"source":"assumption","sourceEnd":98574,"sourceStart":98564,"tag":"atom"}],"kind":"Lean.Parser.Tactic.assumption","source":"assumption","sourceEnd":98574,"sourceStart":98564,"tag":"node"}	[]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1280745","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1280748","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":...	392	38	exact	true	1	44	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	2d47538d3217629da1a182bcd9eb9df6b5dc5be2ce32966d1c788fa05958e25c	d1e3e9ce5de84d1e5da64b6734833e6b79c357bca902757cfb63ddb2d6cff84c	c081dd376ba93a530dd044cffc81e70953e86d86f7d0796dc26bc1597302573d	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,553	LieAlgebra.zeroRootSubalgebra_normalizer_eq_self	Mathlib/Algebra/Lie/Weights/Cartan.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	refine <a>le_antisymm</a> ?_ (<a>LieSubalgebra.le_normalizer</a> _)	R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M ⊢ (zeroRootSubalgebra R L H).normalizer = zeroRootSubalgebra R L H	R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M ⊢ (zeroRootSubalgebra R L H).normalizer ≤ zeroRootSubalgebra R L H	((:c Eq) ((:c LieSubalgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964) (:fv _uniq.105981)) ((:c LieSubalgebra.normalizer) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964) (:fv _uniq.105981) ((:c LieAlgebra.zeroRootSubalgebra) (:fv _uniq.105955) (:fv _uniq.105...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.105955))"},{"name":"inst✝⁶","sexp":"((:c LieRing) (:fv _uniq.105958))"},{"name":"inst✝⁵","sexp":"((:c LieAlgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c LieSubalgebra) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"refine","sourceEnd":10639,"sourceStart":10633,"tag":"atom"},{"children":[{"name":"le_antisymm","semanticRole":"global","source":"le_antisymm","sourceEnd":10651,"sourceStart":10640,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":10653,"sourceStart":10652,"tag":"atom"},{"ch...	[]	[{"source":"le_antisymm ?_ (LieSubalgebra.le_normalizer _)","source_end":10686,"source_start":10640,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...	42	4	exact	true	1	12	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	b47d4a6e29da1ac66fd3012cd27bd5d1c742c385b089b96ef2ff6e067bf7585a	cfa2576372577e1a6c2a38064789578bfda34583477cbace3d52aae4bbba2e92	9b12c776311276e48f9287a5c8dc0b4d5ff003766ed55e682385fe2cce657d80	1ca3007d5eb6379542543ff81c2fd87aee26253665567bbb07f0caa512b4d775
cat-searcher/leandojo-benchmark-4-random	test	2,554	LieAlgebra.zeroRootSubalgebra_normalizer_eq_self	Mathlib/Algebra/Lie/Weights/Cartan.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	intro x hx	R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M ⊢ (zeroRootSubalgebra R L H).normalizer ≤ zeroRootSubalgebra R L H	R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M x : L hx : x ∈ (zeroRootSubalgebra R L H).normalizer ⊢ x ∈ zeroRootSubalgeb...	((:c LE.le) ((:c LieSubalgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964) (:fv _uniq.105981)) ((:c Preorder.toLE) ((:c LieSubalgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964) (:fv _uniq.105981)) ((:c PartialOrder.toPreorder) ((:c LieSubalgebra) (:fv _...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.105955))"},{"name":"inst✝⁶","sexp":"((:c LieRing) (:fv _uniq.105958))"},{"name":"inst✝⁵","sexp":"((:c LieAlgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964...	(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c LieSubalgebra) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-o...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"intro","sourceEnd":10694,"sourceStart":10689,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":10696,"sourceStart":10695,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hx","sourceEnd":10699,"sourceStart":10697,"tag":"identifier"}],"kind":"null","sou...	[{"role":"fresh_name","source":"x","source_end":10696,"source_start":10695,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":10699,"source_start":10697,"syntax_kind":"ident"}]	[]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...	42	5	exact	true	1	12	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	cb71469cec8d55194aa84bf5b626de75e1a88380ff002ed5aee0b2f95533f09e	1ca3007d5eb6379542543ff81c2fd87aee26253665567bbb07f0caa512b4d775	65777af1f444837568ec00c3040db2bdc96178d91d8bf83037116b747be939ac	93b39da7fcb551db6649a7c5f758fdb09fc22d99062b1c49d6a3e72b234759c4
cat-searcher/leandojo-benchmark-4-random	test	2,555	LieAlgebra.zeroRootSubalgebra_normalizer_eq_self	Mathlib/Algebra/Lie/Weights/Cartan.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>LieSubalgebra.mem_normalizer_iff</a>] at hx	R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M x : L hx : x ∈ (zeroRootSubalgebra R L H).normalizer ⊢ x ∈ zeroRootSubalgeb...	R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M x : L hx : ∀ y ∈ zeroRootSubalgebra R L H, ⁅x, y⁆ ∈ zeroRootSubalgebra R L ...	((:c Membership.mem) (:fv _uniq.105958) ((:c LieSubalgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964) (:fv _uniq.105981)) ((:c SetLike.instMembership) ((:c LieSubalgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964) (:fv _uniq.105981)) (:fv _uniq.105958) ...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.105955))"},{"name":"inst✝⁶","sexp":"((:c LieRing) (:fv _uniq.105958))"},{"name":"inst✝⁵","sexp":"((:c LieAlgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964...	(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c LieSubalgebra) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"rw","sourceEnd":10704,"sourceStart":10702,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10706,"sourceStart":10705,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"LieSubalgebra.me...	[]	[{"source":"LieSubalgebra.mem_normalizer_iff","source_end":10738,"source_start":10706,"syntax_kind":"ident"},{"source":"hx","source_end":10745,"source_start":10743,"syntax_kind":"ident"}]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...	42	6	exact	true	1	14	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	e2c2cf2865355b98afae1f57316c0d9d75b1768844caea0dffdf968f9137d103	93b39da7fcb551db6649a7c5f758fdb09fc22d99062b1c49d6a3e72b234759c4	bdfc1d2d0bfd1bde26e7b4d7890fc83fe674a4eaaae75b09d0362c5c54bfa5d5	2ac59698f1b105f3abf98b89af27fdcf6c9c37744ef981aa710ab8ab2e4384b7
cat-searcher/leandojo-benchmark-4-random	test	2,556	LieAlgebra.zeroRootSubalgebra_normalizer_eq_self	Mathlib/Algebra/Lie/Weights/Cartan.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>LieAlgebra.mem_zeroRootSubalgebra</a>]	R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M x : L hx : ∀ y ∈ zeroRootSubalgebra R L H, ⁅x, y⁆ ∈ zeroRootSubalgebra R L ...	R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M x : L hx : ∀ y ∈ zeroRootSubalgebra R L H, ⁅x, y⁆ ∈ zeroRootSubalgebra R L ...	((:c Membership.mem) (:fv _uniq.105958) ((:c LieSubalgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964) (:fv _uniq.105981)) ((:c SetLike.instMembership) ((:c LieSubalgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964) (:fv _uniq.105981)) (:fv _uniq.105958) ...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.105955))"},{"name":"inst✝⁶","sexp":"((:c LieRing) (:fv _uniq.105958))"},{"name":"inst✝⁵","sexp":"((:c LieAlgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964...	(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c LieSubalgebra) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"rw","sourceEnd":10750,"sourceStart":10748,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10752,"sourceStart":10751,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"LieAlgebra.mem_z...	[]	[{"source":"mem_zeroRootSubalgebra","source_end":10774,"source_start":10752,"syntax_kind":"ident"}]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...	42	9	exact	true	1	14	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	1029bc5aca73ebe779e05a22401b5c0073e1b1ba9ec5c33db34207c2165dee12	2ac59698f1b105f3abf98b89af27fdcf6c9c37744ef981aa710ab8ab2e4384b7	ffaf033a8a0af268c1a3adea8b5097c7e0722ea911862642ae86602e680b0f62	c457f15d0ddf2053412e4ad47921e2bac1b8f0db7e6ba8ae60ec166b63b410b5
cat-searcher/leandojo-benchmark-4-random	test	2,557	LieAlgebra.zeroRootSubalgebra_normalizer_eq_self	Mathlib/Algebra/Lie/Weights/Cartan.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rintro ⟨y, hy⟩	R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M x : L hx : ∀ y ∈ zeroRootSubalgebra R L H, ⁅x, y⁆ ∈ zeroRootSubalgebra R L ...	case mk R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M x : L hx : ∀ y ∈ zeroRootSubalgebra R L H, ⁅x, y⁆ ∈ zeroRootSubalge...	(:forall y ((:c Subtype) (:fv _uniq.105958) (:lambda x (:fv _uniq.105958) ((:c Membership.mem) (:fv _uniq.105958) ((:c LieSubalgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964) (:fv _uniq.105981)) ((:c SetLike.instMembership) ((:c LieSubalgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:f...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.105955))"},{"name":"inst✝⁶","sexp":"((:c LieRing) (:fv _uniq.105958))"},{"name":"inst✝⁵","sexp":"((:c LieAlgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964...	(:forall y :explicit (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c LieSubalgebra) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"rintro","sourceEnd":10784,"sourceStart":10778,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":10788,"sourceStart":10785,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":10789,"sou...	[{"role":"fresh_name","source":"y","source_end":10789,"source_start":10788,"syntax_kind":"ident"},{"role":"fresh_name","source":"hy","source_end":10793,"source_start":10791,"syntax_kind":"ident"}]	[{"source":"⟨y, hy⟩","source_end":10796,"source_start":10785,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...	42	12	exact	true	1	14	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	a802a4afcee34a1f0d8521c3fd0baccc7c6f3be7a13b248432bf007b7571d863	c457f15d0ddf2053412e4ad47921e2bac1b8f0db7e6ba8ae60ec166b63b410b5	813cc811905d2e7e9af04e80bc2c0ad03d98df053fe26eaaf7bb20ae162aefaf	2b163a33e896d421a73846a86e0c493e54edfb5f40aad926dd244a1b7945c5a1
cat-searcher/leandojo-benchmark-4-random	test	2,558	LieAlgebra.zeroRootSubalgebra_normalizer_eq_self	Mathlib/Algebra/Lie/Weights/Cartan.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	specialize hx y (<a>LieAlgebra.le_zeroRootSubalgebra</a> R L H hy)	case mk R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M x : L hx : ∀ y ∈ zeroRootSubalgebra R L H, ⁅x, y⁆ ∈ zeroRootSubalge...	case mk R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M x y : L hy : y ∈ H hx : ⁅x, y⁆ ∈ zeroRootSubalgebra R L H ⊢ ∃ k, ((...	((:c Exists) (:c Nat) (:lambda k (:c Nat) ((:c Eq) (:fv _uniq.105958) ((:c DFunLike.coe) ((:c Module.End) (:fv _uniq.105955) (:fv _uniq.105958) ((:c CommSemiring.toSemiring) (:fv _uniq.105955) ((:c CommRing.toCommSemiring) (:fv _uniq.105955) (:fv _uniq.105961))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.105958) ((:...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.105955))"},{"name":"inst✝⁶","sexp":"((:c LieRing) (:fv _uniq.105958))"},{"name":"inst✝⁵","sexp":"((:c LieAlgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964...	(:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda k :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Module.End) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"specialize","sourceEnd":10809,"sourceStart":10799,"tag":"atom"},{"children":[{"contextIndex":14,"semanticRole":"local","source":"hx","sourceEnd":10812,"sourceStart":10810,"tag":"identifier"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"y","sourceEnd":10814,"sourceStart":10813...	[]	[{"source":"hx y (le_zeroRootSubalgebra R L H hy)","source_end":10847,"source_start":10810,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...	42	13	exact	true	1	16	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	a0f2824cfbf2e0e4a71a606b40f2dc1b3a69f0d68037f6743318cf77171a2741	2b163a33e896d421a73846a86e0c493e54edfb5f40aad926dd244a1b7945c5a1	aaa0cc30e95c5314f22e425a5da4bad5d6bae56195df01be01ceab325ba09143	5e4b4d989f0eef52087a33db341c132a50e4097d9ec3156e2d2bf5375db9c197
cat-searcher/leandojo-benchmark-4-random	test	2,559	LieAlgebra.zeroRootSubalgebra_normalizer_eq_self	Mathlib/Algebra/Lie/Weights/Cartan.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>LieAlgebra.mem_zeroRootSubalgebra</a>] at hx	case mk R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M x y : L hy : y ∈ H hx : ⁅x, y⁆ ∈ zeroRootSubalgebra R L H ⊢ ∃ k, ((...	case mk R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M x y : L hy : y ∈ H hx : ∀ (y_1 : ↥H), ∃ k, ((toEnd R (↥H) L) y_1 ^ ...	((:c Exists) (:c Nat) (:lambda k (:c Nat) ((:c Eq) (:fv _uniq.105958) ((:c DFunLike.coe) ((:c Module.End) (:fv _uniq.105955) (:fv _uniq.105958) ((:c CommSemiring.toSemiring) (:fv _uniq.105955) ((:c CommRing.toCommSemiring) (:fv _uniq.105955) (:fv _uniq.105961))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.105958) ((:...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.105955))"},{"name":"inst✝⁶","sexp":"((:c LieRing) (:fv _uniq.105958))"},{"name":"inst✝⁵","sexp":"((:c LieAlgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964...	(:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda k :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Module.End) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"rw","sourceEnd":10852,"sourceStart":10850,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10854,"sourceStart":10853,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"LieAlgebra.mem_z...	[]	[{"source":"mem_zeroRootSubalgebra","source_end":10876,"source_start":10854,"syntax_kind":"ident"},{"source":"hx","source_end":10883,"source_start":10881,"syntax_kind":"ident"}]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...	42	14	exact	true	1	16	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	a79fb525349de3f6598be429bf4d5e84ece096470a6969e4bf2e3a6b73b1302a	5e4b4d989f0eef52087a33db341c132a50e4097d9ec3156e2d2bf5375db9c197	fdd9022c38bfd4649d9f6127743c73f71e01ae904d28b218631cbb3ce06faa24	ec501e3e56d5f6928ac1b2476b4d8da84dff6cc04572808deaa63ab8a8601f7e
cat-searcher/leandojo-benchmark-4-random	test	2,560	LieAlgebra.zeroRootSubalgebra_normalizer_eq_self	Mathlib/Algebra/Lie/Weights/Cartan.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	obtain ⟨k, hk⟩ := hx ⟨y, hy⟩	case mk R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M x y : L hy : y ∈ H hx : ∀ (y_1 : ↥H), ∃ k, ((toEnd R (↥H) L) y_1 ^ ...	case mk.intro R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M x y : L hy : y ∈ H hx : ∀ (y_1 : ↥H), ∃ k, ((toEnd R (↥H) L) ...	((:c Exists) (:c Nat) (:lambda k (:c Nat) ((:c Eq) (:fv _uniq.105958) ((:c DFunLike.coe) ((:c Module.End) (:fv _uniq.105955) (:fv _uniq.105958) ((:c CommSemiring.toSemiring) (:fv _uniq.105955) ((:c CommRing.toCommSemiring) (:fv _uniq.105955) (:fv _uniq.105961))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.105958) ((:...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.105955))"},{"name":"inst✝⁶","sexp":"((:c LieRing) (:fv _uniq.105958))"},{"name":"inst✝⁵","sexp":"((:c LieAlgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964...	(:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda k :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Module.End) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"obtain","sourceEnd":10892,"sourceStart":10886,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":10896,"sourceStart":10893,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"k","sourceEn...	[]	[{"source":"hx ⟨y, hy⟩","source_end":10922,"source_start":10908,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨k, hk⟩","source_end":10904,"source_start":10893,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...	42	17	exact	true	1	16	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	956a0d7d77204de488d91db74cb45fdec7c039b42883d9b413310e531c3562c9	ec501e3e56d5f6928ac1b2476b4d8da84dff6cc04572808deaa63ab8a8601f7e	effbe77e7e6c8b507f296c42c96aff8862ef10da9544c11f13c756b63a24ce24	e0f3eebd4ca8666d09534a1ad2626b195238983a79cfe8e60037cf6f97ef18c4
cat-searcher/leandojo-benchmark-4-random	test	2,561	LieAlgebra.zeroRootSubalgebra_normalizer_eq_self	Mathlib/Algebra/Lie/Weights/Cartan.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [← <a>lie_skew</a>, <a>LinearMap.map_neg</a>, <a>neg_eq_zero</a>] at hk	case mk.intro R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M x y : L hy : y ∈ H hx : ∀ (y_1 : ↥H), ∃ k, ((toEnd R (↥H) L) ...	case mk.intro R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M x y : L hy : y ∈ H hx : ∀ (y_1 : ↥H), ∃ k, ((toEnd R (↥H) L) ...	((:c Exists) (:c Nat) (:lambda k (:c Nat) ((:c Eq) (:fv _uniq.105958) ((:c DFunLike.coe) ((:c Module.End) (:fv _uniq.105955) (:fv _uniq.105958) ((:c CommSemiring.toSemiring) (:fv _uniq.105955) ((:c CommRing.toCommSemiring) (:fv _uniq.105955) (:fv _uniq.105961))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.105958) ((:...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.105955))"},{"name":"inst✝⁶","sexp":"((:c LieRing) (:fv _uniq.105958))"},{"name":"inst✝⁵","sexp":"((:c LieAlgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964...	(:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda k :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Module.End) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"rw","sourceEnd":10927,"sourceStart":10925,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10929,"sourceStart":10928,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":10932,"sourceSt...	[]	[{"source":"lie_skew","source_end":10941,"source_start":10933,"syntax_kind":"ident"},{"source":"hk","source_end":10980,"source_start":10978,"syntax_kind":"ident"},{"source":"LinearMap.map_neg","source_end":10960,"source_start":10943,"syntax_kind":"ident"},{"source":"neg_eq_zero","source_end":10973,"source_start":10962,...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...	42	18	exact	true	1	18	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	0d443fc81f225a3a8ad19aac1d64f5c5e8da0a74ddb912b4232592642933d385	e0f3eebd4ca8666d09534a1ad2626b195238983a79cfe8e60037cf6f97ef18c4	0dbe918007788381744678403c0ac15d63cca5ab65388675a2c7a4d566942f7d	a57d347eb6e42acae6ada0a239435afc0e21b63069726740a2364f71aa87d1e1
cat-searcher/leandojo-benchmark-4-random	test	2,562	LieAlgebra.zeroRootSubalgebra_normalizer_eq_self	Mathlib/Algebra/Lie/Weights/Cartan.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	use k + 1	case mk.intro R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M x y : L hy : y ∈ H hx : ∀ (y_1 : ↥H), ∃ k, ((toEnd R (↥H) L) ...	case h R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M x y : L hy : y ∈ H hx : ∀ (y_1 : ↥H), ∃ k, ((toEnd R (↥H) L) y_1 ^ k...	((:c Exists) (:c Nat) (:lambda k (:c Nat) ((:c Eq) (:fv _uniq.105958) ((:c DFunLike.coe) ((:c Module.End) (:fv _uniq.105955) (:fv _uniq.105958) ((:c CommSemiring.toSemiring) (:fv _uniq.105955) ((:c CommRing.toCommSemiring) (:fv _uniq.105955) (:fv _uniq.105961))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.105958) ((:...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.105955))"},{"name":"inst✝⁶","sexp":"((:c LieRing) (:fv _uniq.105958))"},{"name":"inst✝⁵","sexp":"((:c LieAlgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964...	(:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda k :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Module.End) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"use","sourceEnd":10986,"sourceStart":10983,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"children":[{"contextIndex":17,"semanticRole":"local","source":"k","sourceEnd":10988,"sourceStart":10987,"tag":"id...	[]	[{"source":"k + 1","source_end":10992,"source_start":10987,"syntax_kind":"«term_+_»"}]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...	42	23	exact	true	1	18	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	a79257b68303e089b47f7ff7bcd274917905ec6d96d84b989dfe1e5acade353c	a57d347eb6e42acae6ada0a239435afc0e21b63069726740a2364f71aa87d1e1	486f921950483d89d6d0e672f95d4bc55659bc4e8fcfef6a82963c18fd7f9c76	aa888cac0f86dc846439f33250bf94e8c7335dc6c84838fb7b4b9317f4892096
cat-searcher/leandojo-benchmark-4-random	test	2,563	LieAlgebra.zeroRootSubalgebra_normalizer_eq_self	Mathlib/Algebra/Lie/Weights/Cartan.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>LinearMap.iterate_succ</a>, <a>LinearMap.coe_comp</a>, <a>Function.comp_apply</a>, <a>LieModule.toEnd_apply_apply</a>, <a>LieSubalgebra.coe_bracket_of_module</a>, <a>Submodule.coe_mk</a>, hk]	case h R : Type u_1 L : Type u_2 inst✝⁷ : CommRing R inst✝⁶ : LieRing L inst✝⁵ : LieAlgebra R L H : LieSubalgebra R L inst✝⁴ : IsNilpotent R ↥H M : Type u_3 inst✝³ : AddCommGroup M inst✝² : Module R M inst✝¹ : LieRingModule L M inst✝ : LieModule R L M x y : L hy : y ∈ H hx : ∀ (y_1 : ↥H), ∃ k, ((toEnd R (↥H) L) y_1 ^ k...		((:c Eq) (:fv _uniq.105958) ((:c DFunLike.coe) ((:c Module.End) (:fv _uniq.105955) (:fv _uniq.105958) ((:c CommSemiring.toSemiring) (:fv _uniq.105955) ((:c CommRing.toCommSemiring) (:fv _uniq.105955) (:fv _uniq.105961))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.105958) ((:c LieRing.toAddCommGroup) (:fv _uniq.10595...	[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.105955))"},{"name":"inst✝⁶","sexp":"((:c LieRing) (:fv _uniq.105958))"},{"name":"inst✝⁵","sexp":"((:c LieAlgebra) (:fv _uniq.105955) (:fv _uniq.105958) (:fv _uniq.105961) (:fv _uniq.105964...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Module.End) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c A...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"rw","sourceEnd":10997,"sourceStart":10995,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10999,"sourceStart":10998,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"LinearMap.iterat...	[]	[{"source":"LinearMap.iterate_succ","source_end":11021,"source_start":10999,"syntax_kind":"ident"},{"source":"LinearMap.coe_comp","source_end":11041,"source_start":11023,"syntax_kind":"ident"},{"source":"Function.comp_apply","source_end":11062,"source_start":11043,"syntax_kind":"ident"},{"source":"toEnd_apply_apply","s...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.105955","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.105958","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...	42	24	exact	true	1	18	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	452848b00ad83bf75f733585d847032e11783e1a4595a812aa40e7c762cb9b9d	aa888cac0f86dc846439f33250bf94e8c7335dc6c84838fb7b4b9317f4892096	af7246946711d60736e543c9d27ac7f11d2018c59e1fb12cb7f3db68dce7264b	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,564	CategoryTheory.PresheafHom.IsSheafFor.exists_app	Mathlib/CategoryTheory/Sites/SheafHom.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	let c : <a>CategoryTheory.Limits.Cone</a> ((<a>CategoryTheory.Presieve.diagram</a> (<a>CategoryTheory.Sieve.pullback</a> g S).<a>CategoryTheory.Sieve.arrows</a>).<a>CategoryTheory.Functor.op</a> ⋙ G) := { pt := F.obj (<a>Opposite.op</a> Y) π := { app := fun ⟨Z, hZ⟩ => F.map Z.hom.op ≫ (x _ hZ).<a>CategoryTheory.NatTran...	C : Type u inst✝¹ : Category.{v, u} C J : GrothendieckTopology C A : Type u' inst✝ : Category.{v', u'} A F G : Cᵒᵖ ⥤ A X : C S : Sieve X hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op) x : Presieve.FamilyOfElements (presheafHom F G) S.arrows hx : x.Compatible Y : C g : Y ⟶ X ⊢ ∃ φ...	C : Type u inst✝¹ : Category.{v, u} C J : GrothendieckTopology C A : Type u' inst✝ : Category.{v', u'} A F G : Cᵒᵖ ⥤ A X : C S : Sieve X hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op) x : Presieve.FamilyOfElements (presheafHom F G) S.arrows hx : x.Compatible Y : C g : Y ⟶ X c : C...	((:c Exists) ((:c Quiver.Hom) (:fv _uniq.24589) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.24589) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.24589) (:fv _uniq.24592))) ((:c Prefunctor.obj) ((:c Opposite) (:fv _uniq.24569)) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c Opposite) (:fv _uni...	[{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.24569))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.24569) (:fv _uniq.24572))"},{"name":"A","sexp":"(:sort (+ u' 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq....	(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c Opposite) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:ins...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category...	{"children":[{"source":"let","sourceEnd":4710,"sourceStart":4707,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"c","sourceEnd":4712,"sourceStart":4711,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":4714,"so...	[]	[{"source":"Cone ((Presieve.diagram (Sieve.pullback g S).arrows).op ⋙ G)","source_end":4777,"source_start":4715,"syntax_kind":"Lean.Parser.Term.app"},{"source":"{ pt := F.obj (op Y)\n π :=\n { app := fun ⟨Z, hZ⟩ => F.map Z.hom.op ≫ (x _ hZ).app (op (Over.mk (𝟙 _)))\n naturality := by\n ...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern...	18	4	exact	true	1	14	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	7b869e9ef69a51953a5af23997c854af9919d26303fc0851a34c21f408e33084	559c0dd454eb17ee2f69254a8e52d7d1f5bb67b92090f49ca7a4a8cd3fee141d	a24d96b0ee56f32c2d32c41fd2d5b1abc01be35e282d1b7cccfb3d1e5659c3f5	a3e2cc9273181066330f6497582b599cdd02703c64dad2e513fa7c2c2138ee5d
cat-searcher/leandojo-benchmark-4-random	test	2,565	CategoryTheory.PresheafHom.IsSheafFor.exists_app	Mathlib/CategoryTheory/Sites/SheafHom.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	use (hG g).<a>CategoryTheory.Limits.IsLimit.lift</a> c	C : Type u inst✝¹ : Category.{v, u} C J : GrothendieckTopology C A : Type u' inst✝ : Category.{v', u'} A F G : Cᵒᵖ ⥤ A X : C S : Sieve X hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op) x : Presieve.FamilyOfElements (presheafHom F G) S.arrows hx : x.Compatible Y : C g : Y ⟶ X c : C...	case h C : Type u inst✝¹ : Category.{v, u} C J : GrothendieckTopology C A : Type u' inst✝ : Category.{v', u'} A F G : Cᵒᵖ ⥤ A X : C S : Sieve X hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op) x : Presieve.FamilyOfElements (presheafHom F G) S.arrows hx : x.Compatible Y : C g : Y ⟶ ...	((:c Exists) ((:c Quiver.Hom) (:fv _uniq.24589) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.24589) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.24589) (:fv _uniq.24592))) ((:c Prefunctor.obj) ((:c Opposite) (:fv _uniq.24569)) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c Opposite) (:fv _uni...	[{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.24569))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.24569) (:fv _uniq.24572))"},{"name":"A","sexp":"(:sort (+ u' 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq....	(:app (:c Exists) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c Opposite) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:ins...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category...	{"children":[{"source":"use","sourceEnd":5562,"sourceStart":5559,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"children":[{"children":[{"children":[{"source":"(","sourceEnd":5564,"sourceStart":5563,"tag":"atom"},{"children":[{...	[]	[{"source":"(hG g).lift c","source_end":5576,"source_start":5563,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern...	18	33	exact	true	1	15	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	032a66d11b3423b25db4f810b398d5284872d7ba5bca68bc4dc833e8f5b4de7c	a3e2cc9273181066330f6497582b599cdd02703c64dad2e513fa7c2c2138ee5d	f68a3f9087f4c0bdba0cc0ffba1d2db141a7d8bf3b7eb8ddf1bf477527afcd46	68fcb55b3bb0ad668fab86f41d7d2037bdbb5da5ac9df798cafc5cead95eb7cb
cat-searcher/leandojo-benchmark-4-random	test	2,566	CategoryTheory.PresheafHom.IsSheafFor.exists_app	Mathlib/CategoryTheory/Sites/SheafHom.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	intro Z p hp	case h C : Type u inst✝¹ : Category.{v, u} C J : GrothendieckTopology C A : Type u' inst✝ : Category.{v', u'} A F G : Cᵒᵖ ⥤ A X : C S : Sieve X hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op) x : Presieve.FamilyOfElements (presheafHom F G) S.arrows hx : x.Compatible Y : C g : Y ⟶ ...	case h C : Type u inst✝¹ : Category.{v, u} C J : GrothendieckTopology C A : Type u' inst✝ : Category.{v', u'} A F G : Cᵒᵖ ⥤ A X : C S : Sieve X hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op) x : Presieve.FamilyOfElements (presheafHom F G) S.arrows hx : x.Compatible Y : C g : Y ⟶ ...	(:forall Z (:fv _uniq.24569) (:forall p ((:c Quiver.Hom) (:fv _uniq.24569) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.24569) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.24569) (:fv _uniq.24572))) 0 (:fv _uniq.25918)) (:forall hp ((:c CategoryTheory.Sieve.arrows) (:fv _uniq.24569) (:fv _uniq.2...	[{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.24569))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.24569) (:fv _uniq.24572))"},{"name":"A","sexp":"(:sort (+ u' 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq....	(:forall Z :implicit (:fv FV0) (:forall p :explicit (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 0) (:arg :explicit 3 (:fv FV12))) (:forall hp :explicit (:app (:c CategoryTheory.Sieve.arrows) (:arg :implicit-t...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category...	{"children":[{"source":"intro","sourceEnd":5584,"sourceStart":5579,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"Z","sourceEnd":5586,"sourceStart":5585,"tag":"identifier"},{"semanticRole":"scoped_local","source":"p","sourceEnd":5588,"sourceStart":5587,"tag":"identifier"},{"semanticRole":"scoped_lo...	[{"role":"fresh_name","source":"Z","source_end":5586,"source_start":5585,"syntax_kind":"ident"},{"role":"fresh_name","source":"p","source_end":5588,"source_start":5587,"syntax_kind":"ident"},{"role":"fresh_name","source":"hp","source_end":5591,"source_start":5589,"syntax_kind":"ident"}]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern...	18	34	exact	true	1	15	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	2ddc1aea39af69bcc51bc4ad304553b7b1409cc5bed7ca50b12b58ecca743c88	68fcb55b3bb0ad668fab86f41d7d2037bdbb5da5ac9df798cafc5cead95eb7cb	d31b2767f788fb51ccf84169e79a59bc288cc37ff82cf1744c669b3ccef5611a	f72764fb583a7bc1510b892667ffa0985d6b6f2ed85405f92d145f9afc7d9680
cat-searcher/leandojo-benchmark-4-random	test	2,567	CategoryTheory.PresheafHom.IsSheafFor.exists_app	Mathlib/CategoryTheory/Sites/SheafHom.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact ((hG g).<a>CategoryTheory.Limits.IsLimit.fac</a> c ⟨<a>CategoryTheory.Over.mk</a> p, hp⟩)	case h C : Type u inst✝¹ : Category.{v, u} C J : GrothendieckTopology C A : Type u' inst✝ : Category.{v', u'} A F G : Cᵒᵖ ⥤ A X : C S : Sieve X hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op) x : Presieve.FamilyOfElements (presheafHom F G) S.arrows hx : x.Compatible Y : C g : Y ⟶ ...		((:c Eq) ((:c Quiver.Hom) (:fv _uniq.24589) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.24589) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.24589) (:fv _uniq.24592))) ((:c Prefunctor.obj) ((:c Opposite) (:fv _uniq.24569)) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c Opposite) (:fv _uniq.24...	[{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.24569))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.24569) (:fv _uniq.24572))"},{"name":"A","sexp":"(:sort (+ u' 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq....	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c Opposite) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instanc...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category...	{"children":[{"source":"exact","sourceEnd":5599,"sourceStart":5594,"tag":"atom"},{"children":[{"source":"(","sourceEnd":5601,"sourceStart":5600,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":5602,"sourceStart":5601,"tag":"atom"},{"children":[{"contextIndex":9,"semanticRole":"local","sour...	[]	[{"source":"((hG g).fac c ⟨Over.mk p, hp⟩)","source_end":5634,"source_start":5600,"syntax_kind":"Lean.Parser.Term.paren"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern...	18	35	exact	true	1	18	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	8e88f63d784673bd41a5887ce9d76f9606eb00af18dd5b137d86ca2bb77038d9	f72764fb583a7bc1510b892667ffa0985d6b6f2ed85405f92d145f9afc7d9680	74f4416b9bf81f11134ccfaa1540e7b752186e2c2b9a1f8d347ef343f0ccc59a	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	2,568	CategoryTheory.PresheafHom.IsSheafFor.exists_app	Mathlib/CategoryTheory/Sites/SheafHom.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rintro ⟨Z₁, hZ₁⟩ ⟨Z₂, hZ₂⟩ ⟨f : Z₂ ⟶ Z₁⟩	C : Type u inst✝¹ : Category.{v, u} C J : GrothendieckTopology C A : Type u' inst✝ : Category.{v', u'} A F G : Cᵒᵖ ⥤ A X : C S : Sieve X hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op) x : Presieve.FamilyOfElements (presheafHom F G) S.arrows hx : x.Compatible Y : C g : Y ⟶ X ⊢ ∀ ⦃...	case op.mk.op.mk.op C : Type u inst✝¹ : Category.{v, u} C J : GrothendieckTopology C A : Type u' inst✝ : Category.{v', u'} A F G : Cᵒᵖ ⥤ A X : C S : Sieve X hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op) x : Presieve.FamilyOfElements (presheafHom F G) S.arrows hx : x.Compatible Y...	(:forall X ((:c Opposite) ((:c CategoryTheory.Presieve.category) (:fv _uniq.24569) (:fv _uniq.24572) (:fv _uniq.25918) ((:c CategoryTheory.Sieve.arrows) (:fv _uniq.24569) (:fv _uniq.24572) (:fv _uniq.25918) ((:c CategoryTheory.Sieve.pullback) (:fv _uniq.24569) (:fv _uniq.24572) (:fv _uniq.24671) (:fv _uniq.25918) (:fv ...	[{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.24569))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.24569) (:fv _uniq.24572))"},{"name":"A","sexp":"(:sort (+ u' 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq....	(:forall X :strict-implicit (:app (:c Opposite) (:arg :explicit 0 (:app (:c CategoryTheory.Presieve.category) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit 2) (:arg :explicit 3 (:app (:c CategoryTheory.Sieve.arrows) (...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category...	{"children":[{"source":"rintro","sourceEnd":4955,"sourceStart":4949,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":4959,"sourceStart":4956,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"Z₁","sourceEnd":4963,"sourceS...	[{"role":"fresh_name","source":"Z₁","source_end":4963,"source_start":4959,"syntax_kind":"ident"},{"role":"fresh_name","source":"hZ₁","source_end":4970,"source_start":4965,"syntax_kind":"ident"},{"role":"fresh_name","source":"Z₂","source_end":4981,"source_start":4977,"syntax_kind":"ident"},{"role":"fresh_name","source":...	[{"source":"⟨Z₁, hZ₁⟩","source_end":4973,"source_start":4956,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"},{"source":"⟨Z₂, hZ₂⟩","source_end":4991,"source_start":4974,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"},{"source":"⟨f : Z₂ ⟶ Z₁⟩","source_end":5015,"source_start":4992,"syntax_kind":"Lean.Parser.Tact...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern...	18	9	exact	true	1	14	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	4a140cbe3f76ed5754eb5529950f065270041579fc0d48c9e505534a5a2dcf83	825939756bd2fc515325351eedb26a0dab0a8b7b44b8c41246c6b82119eebb8b	8c41f24d168be332c7c8bad633306702f4770cc30315626b10e3b02291cdb938	67f74b30b4ff5010d2b2092afba1f0946c49c597151bf3a39afa1ea9843c9338
cat-searcher/leandojo-benchmark-4-random	test	2,569	CategoryTheory.PresheafHom.IsSheafFor.exists_app	Mathlib/CategoryTheory/Sites/SheafHom.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	dsimp	case op.mk.op.mk.op C : Type u inst✝¹ : Category.{v, u} C J : GrothendieckTopology C A : Type u' inst✝ : Category.{v', u'} A F G : Cᵒᵖ ⥤ A X : C S : Sieve X hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op) x : Presieve.FamilyOfElements (presheafHom F G) S.arrows hx : x.Compatible Y...	case op.mk.op.mk.op C : Type u inst✝¹ : Category.{v, u} C J : GrothendieckTopology C A : Type u' inst✝ : Category.{v', u'} A F G : Cᵒᵖ ⥤ A X : C S : Sieve X hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op) x : Presieve.FamilyOfElements (presheafHom F G) S.arrows hx : x.Compatible Y...	((:c Eq) ((:c Quiver.Hom) (:fv _uniq.24589) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.24589) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.24589) (:fv _uniq.24592))) ((:c Prefunctor.obj) ((:c Opposite) ((:c CategoryTheory.Presieve.category) (:fv _uniq.24569) (:fv _uniq.24572) (:fv _uniq.25918)...	[{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.24569))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.24569) (:fv _uniq.24572))"},{"name":"A","sexp":"(:sort (+ u' 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq....	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c Opposite) (:arg :explicit 0 (:app (:c CategoryTheory.Presieve.catego...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category...	{"children":[{"source":"dsimp","sourceEnd":5033,"sourceStart":5028,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kin...	[]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern...	18	10	exact	true	1	19	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	a63b5d24203cbc22765a0bb8b9454cebe4d668300ceefdcab48172013079b0e3	67f74b30b4ff5010d2b2092afba1f0946c49c597151bf3a39afa1ea9843c9338	7854eab90b5d1f0eed9d2f7f6b885100cc44bc732b41c876b3af083c01260845	048df5fe2b2941a62d821bd905c9ac6b62b5332df291290f13e02008ef9c72e4
cat-searcher/leandojo-benchmark-4-random	test	2,570	CategoryTheory.PresheafHom.IsSheafFor.exists_app	Mathlib/CategoryTheory/Sites/SheafHom.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>CategoryTheory.Category.id_comp</a>, <a>CategoryTheory.Category.assoc</a>]	case op.mk.op.mk.op C : Type u inst✝¹ : Category.{v, u} C J : GrothendieckTopology C A : Type u' inst✝ : Category.{v', u'} A F G : Cᵒᵖ ⥤ A X : C S : Sieve X hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op) x : Presieve.FamilyOfElements (presheafHom F G) S.arrows hx : x.Compatible Y...	case op.mk.op.mk.op C : Type u inst✝¹ : Category.{v, u} C J : GrothendieckTopology C A : Type u' inst✝ : Category.{v', u'} A F G : Cᵒᵖ ⥤ A X : C S : Sieve X hG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op) x : Presieve.FamilyOfElements (presheafHom F G) S.arrows hx : x.Compatible Y...	((:c Eq) ((:c Quiver.Hom) (:fv _uniq.24589) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.24589) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.24589) (:fv _uniq.24592))) ((:c Prefunctor.obj) ((:c Opposite) (:fv _uniq.24569)) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c Opposite) (:fv _uniq.24...	[{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.24569))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.24569) (:fv _uniq.24572))"},{"name":"A","sexp":"(:sort (+ u' 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq....	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c Opposite) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instanc...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category...	{"children":[{"source":"rw","sourceEnd":5048,"sourceStart":5046,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5050,"sourceStart":5049,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"CategoryTheory.Categ...	[]	[{"source":"id_comp","source_end":5057,"source_start":5050,"syntax_kind":"ident"},{"source":"assoc","source_end":5064,"source_start":5059,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24569","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.24572","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern...	18	11	exact	true	1	19	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	3c27f71f6ba78b75e4aa7a5385ff168ef6fe481324642be5479e8ebba1dcb2db	048df5fe2b2941a62d821bd905c9ac6b62b5332df291290f13e02008ef9c72e4	be61d7412dfc2e172881489f7a8814439873582dd54fe18c47bf14c088fd16db	b8ace57e375173be4453efb58b017d832e97fd371c1cb4915181e4ddc46896de

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