Split (3)

test · 4.39k rows

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cat-searcher/leandojo-benchmark-4-random	test	935	ProbabilityTheory.eq_condKernel_of_measure_eq_compProd	Mathlib/Probability/Kernel/Disintegration/Unique.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	filter_upwards [heq] with x hx s hs	α : Type u_1 β : Type u_2 Ω : Type u_3 mα : MeasurableSpace α mβ : MeasurableSpace β inst✝⁴ : MeasurableSpace Ω inst✝³ : StandardBorelSpace Ω inst✝² : Nonempty Ω ρ : Measure (α × Ω) inst✝¹ : IsFiniteMeasure ρ κ : ↥(kernel α Ω) inst✝ : IsFiniteKernel κ hκ : ρ = ρ.fst ⊗ₘ κ f : Ω → ℝ := embeddingReal Ω hf : MeasurableEmbe...	case h α : Type u_1 β : Type u_2 Ω : Type u_3 mα : MeasurableSpace α mβ : MeasurableSpace β inst✝⁴ : MeasurableSpace Ω inst✝³ : StandardBorelSpace Ω inst✝² : Nonempty Ω ρ : Measure (α × Ω) inst✝¹ : IsFiniteMeasure ρ κ : ↥(kernel α Ω) inst✝ : IsFiniteKernel κ hκ : ρ = ρ.fst ⊗ₘ κ f : Ω → ℝ := embeddingReal Ω hf : Measura...	((:c Filter.Eventually) (:fv _uniq.18774) (:lambda x (:fv _uniq.18774) (:forall s ((:c Set) (:c Real)) (:forall _ ((:c MeasurableSet) (:c Real) (:c Real.measurableSpace) 0) ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:c Real) (:c Real.measurableSpace)) ((:c Set) (:c Real)) (:lambda _ ((:c Set)...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"Ω","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.18774))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.18777))"},{"name":"inst✝⁴","sexp":"((:c MeasurableSpace) (:fv _uniq.18780))"},{"n...	(:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:forall s :explicit (:app (:c Set) (:arg :explicit 0 (:c Real))) (:forall _ :explicit (:app (:c MeasurableSet) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:a...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18774","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18777","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...	{"children":[{"source":"filter_upwards","sourceEnd":5452,"sourceStart":5438,"tag":"atom"},{"children":[{"source":"[","sourceEnd":5454,"sourceStart":5453,"tag":"atom"},{"children":[{"contextIndex":21,"semanticRole":"local","source":"heq","sourceEnd":5457,"sourceStart":5454,"tag":"identifier"}],"kind":"null","source":"he...	[]	[{"source":"heq","source_end":5457,"source_start":5454,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18774","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18777","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	10	65	exact	true	1	21	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	d69436237f720426519da317e2bd343b99bb1468bbbbcaebc1103ced2bdabdf5	622e33c77724366d2fd576ab685a0937bcecdf1de90924bc767aa0f4afeb2ae5	9b47c24165a1cbf94e9e34487f88e63d9b06c8d07635f0e5674a26230b38e2cb	7925bac79b40c070a2463b38aee2cac362568334fd0ff91a278bb4ba202ff45a
cat-searcher/leandojo-benchmark-4-random	test	936	ProbabilityTheory.eq_condKernel_of_measure_eq_compProd	Mathlib/Probability/Kernel/Disintegration/Unique.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [← hx, <a>ProbabilityTheory.kernel.map_apply</a>, <a>MeasureTheory.Measure.map_apply</a> hf.measurable hs]	case h α : Type u_1 β : Type u_2 Ω : Type u_3 mα : MeasurableSpace α mβ : MeasurableSpace β inst✝⁴ : MeasurableSpace Ω inst✝³ : StandardBorelSpace Ω inst✝² : Nonempty Ω ρ : Measure (α × Ω) inst✝¹ : IsFiniteMeasure ρ κ : ↥(kernel α Ω) inst✝ : IsFiniteKernel κ hκ : ρ = ρ.fst ⊗ₘ κ f : Ω → ℝ := embeddingReal Ω hf : Measura...		((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:c Real) (:c Real.measurableSpace)) ((:c Set) (:c Real)) (:lambda _ ((:c Set) (:c Real)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:c Real) (:c Real.measurableSpace)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv _uniq.18774) ((:c Mea...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"Ω","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.18774))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.18777))"},{"name":"inst✝⁴","sexp":"((:c MeasurableSpace) (:fv _uniq.18780))"},{"n...	(:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c Real))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18774","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18777","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...	{"children":[{"source":"rw","sourceEnd":5480,"sourceStart":5478,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5482,"sourceStart":5481,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":5485,"sourceStart":...	[]	[{"source":"hx","source_end":5488,"source_start":5486,"syntax_kind":"ident"},{"source":"kernel.map_apply","source_end":5506,"source_start":5490,"syntax_kind":"ident"},{"source":"Measure.map_apply hf.measurable hs","source_end":5542,"source_start":5508,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18774","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18777","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	10	66	exact	true	1	25	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	58d478a8730a19355974c3abfac9107f7038516f59e7b7c811c07b78acd8f4ed	7925bac79b40c070a2463b38aee2cac362568334fd0ff91a278bb4ba202ff45a	9c633782f4e0bb97a6e1b2165e44ad9a7344fe666096091e69a5551ec3baf7ad	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	937	ProbabilityTheory.eq_condKernel_of_measure_eq_compProd	Mathlib/Probability/Kernel/Disintegration/Unique.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	congr with a	case h α : Type u_1 β : Type u_2 Ω : Type u_3 mα : MeasurableSpace α mβ : MeasurableSpace β inst✝⁴ : MeasurableSpace Ω inst✝³ : StandardBorelSpace Ω inst✝² : Nonempty Ω ρ : Measure (α × Ω) inst✝¹ : IsFiniteMeasure ρ κ : ↥(kernel α Ω) inst✝ : IsFiniteKernel κ hκ : ρ = ρ.fst ⊗ₘ κ f : Ω → ℝ := embeddingReal Ω hf : Measura...	case h.e_f.h α : Type u_1 β : Type u_2 Ω : Type u_3 mα : MeasurableSpace α mβ : MeasurableSpace β inst✝⁴ : MeasurableSpace Ω inst✝³ : StandardBorelSpace Ω inst✝² : Nonempty Ω ρ : Measure (α × Ω) inst✝¹ : IsFiniteMeasure ρ κ : ↥(kernel α Ω) inst✝ : IsFiniteKernel κ hκ : ρ = ρ.fst ⊗ₘ κ f : Ω → ℝ := embeddingReal Ω hf : M...	((:c Eq) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.18774) (:fv _uniq.18783) ((:c MeasureTheory.Measure.fst) (:fv _uniq.18774) (:fv _uniq.18780) (:fv _uniq.18783) (:fv _uniq.18789) (:fv _uniq.18832)) (:lambda a (:fv _uniq.18774) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.1878...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"Ω","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.18774))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.18777))"},{"name":"inst✝⁴","sexp":"((:c MeasurableSpace) (:fv _uniq.18780))"},{"n...	(:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure.fst) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18774","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18777","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...	{"children":[{"source":"congr","sourceEnd":5737,"sourceStart":5732,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":"with","sourceEnd":5742,"sourceStart":5738,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped...	[]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18774","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18777","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	10	86	exact	true	1	21	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	553f77624b882509c4ead7e68673758d2acb2852f5972c4c5e2415ae77ca6a8c	50b077a91788b8387d50d12f557aa3e73c963ad46ed970cb00a9c40123627811	5011123f861f9d949fd6e0a0e9aab90e2d65630d818d13307a95737d6d05b59a	1b0d8bb5cebc6014c5a1353a9df2607a31741c2294ecd21d5ddf24d37964017b
cat-searcher/leandojo-benchmark-4-random	test	938	ProbabilityTheory.eq_condKernel_of_measure_eq_compProd	Mathlib/Probability/Kernel/Disintegration/Unique.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>ProbabilityTheory.kernel.map_apply'</a>]	case h.e_f.h α : Type u_1 β : Type u_2 Ω : Type u_3 mα : MeasurableSpace α mβ : MeasurableSpace β inst✝⁴ : MeasurableSpace Ω inst✝³ : StandardBorelSpace Ω inst✝² : Nonempty Ω ρ : Measure (α × Ω) inst✝¹ : IsFiniteMeasure ρ κ : ↥(kernel α Ω) inst✝ : IsFiniteKernel κ hκ : ρ = ρ.fst ⊗ₘ κ f : Ω → ℝ := embeddingReal Ω hf : M...	case h.e_f.h α : Type u_1 β : Type u_2 Ω : Type u_3 mα : MeasurableSpace α mβ : MeasurableSpace β inst✝⁴ : MeasurableSpace Ω inst✝³ : StandardBorelSpace Ω inst✝² : Nonempty Ω ρ : Measure (α × Ω) inst✝¹ : IsFiniteMeasure ρ κ : ↥(kernel α Ω) inst✝ : IsFiniteKernel κ hκ : ρ = ρ.fst ⊗ₘ κ f : Ω → ℝ := embeddingReal Ω hf : M...	((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789)) ((:c Set) (:fv _uniq.18780)) (:lambda _ ((:c Set) (:fv _uniq.18780)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.18780) (:fv _uniq.18789)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv _uniq...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"Ω","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.18774))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.18777))"},{"name":"inst✝⁴","sexp":"((:c MeasurableSpace) (:fv _uniq.18780))"},{"n...	(:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV2))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18774","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18777","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...	{"children":[{"source":"rw","sourceEnd":5751,"sourceStart":5749,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5753,"sourceStart":5752,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"ProbabilityTheory.ke...	[]	[{"source":"kernel.map_apply'","source_end":5770,"source_start":5753,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18774","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18777","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	10	87	exact	true	1	22	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	56d2bc44965d676bc7f6c70c0ab6ad9b07cd9b23808d95f8132b804c357cd237	1b0d8bb5cebc6014c5a1353a9df2607a31741c2294ecd21d5ddf24d37964017b	f829cc648afc54758bd562643f9874447bb919cf6a99b411f1513397c6aa1937	b348778fb702cba25442763e808ecad61e907597b2961e081767c3408917d227
cat-searcher/leandojo-benchmark-4-random	test	940	ProbabilityTheory.eq_condKernel_of_measure_eq_compProd	Mathlib/Probability/Kernel/Disintegration/Unique.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact measurable_id.prod_map hf.measurable hs	case h α : Type u_1 β : Type u_2 Ω : Type u_3 mα : MeasurableSpace α mβ : MeasurableSpace β inst✝⁴ : MeasurableSpace Ω inst✝³ : StandardBorelSpace Ω inst✝² : Nonempty Ω ρ : Measure (α × Ω) inst✝¹ : IsFiniteMeasure ρ κ : ↥(kernel α Ω) inst✝ : IsFiniteKernel κ hκ : ρ = ρ.fst ⊗ₘ κ f : Ω → ℝ := embeddingReal Ω hf : Measura...		((:c MeasurableSet) ((:c Prod) (:fv _uniq.18774) (:fv _uniq.18780)) ((:c Prod.instMeasurableSpace) (:fv _uniq.18774) (:fv _uniq.18780) (:fv _uniq.18783) (:fv _uniq.18789)) ((:c Set.preimage) ((:c Prod) (:fv _uniq.18774) (:fv _uniq.18780)) ((:c Prod) (:fv _uniq.18774) (:c Real)) ((:c Prod.map) (:fv _uniq.18774) (:fv _un...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"Ω","sexp":"(:sort (+ u_3 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.18774))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.18777))"},{"name":"inst✝⁴","sexp":"((:c MeasurableSpace) (:fv _uniq.18780))"},{"n...	(:app (:c MeasurableSet) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2))))))) (:arg :explicit 2 (:app (:c Set.preimage...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18774","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18777","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...	{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":5827,"sourceStart":5822,"tag":"atom"},{"children":[{"source":"measurable_id.prod_map","sourceEnd":5850,"sourceStart":5828,"tag":"identifier"},{"children":[{"name":"MeasurableEmbedding.measurable","semanticRole":"global","source":"hf.measu...	[]	[{"source":"measurable_id.prod_map hf.measurable hs","source_end":5867,"source_start":5828,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18774","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18777","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	10	93	exact	true	1	21	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	997aa136f69a5df09da2406412da5cf2584ae150893df095742cfda8de1bfaa2	41c3b15f58686e59a99de74ab5f5c270dc8245a337c4a57cd47c0ccfa059fe1f	9295791d5c5ef6f41453cc1342b2470096bed322905e1eff67a3ba1cb0054b28	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	941	Ordinal.blsub_eq_zero_iff	Mathlib/SetTheory/Ordinal/Arithmetic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [← <a>Ordinal.lsub_eq_blsub</a>, <a>Ordinal.lsub_eq_zero_iff</a>]	α : Type u_1 β : Type u_2 γ : Type u_3 r : α → α → Prop s : β → β → Prop t : γ → γ → Prop o : Ordinal.{u_4} f : (a : Ordinal.{u_4}) → a < o → Ordinal.{max u_5 u_4} ⊢ o.blsub f = 0 ↔ o = 0	α : Type u_1 β : Type u_2 γ : Type u_3 r : α → α → Prop s : β → β → Prop t : γ → γ → Prop o : Ordinal.{u_4} f : (a : Ordinal.{u_4}) → a < o → Ordinal.{max u_5 u_4} ⊢ IsEmpty (Quotient.out o).α ↔ o = 0	((:c Iff) ((:c Eq) (:c Ordinal) ((:c Ordinal.blsub) (:fv _uniq.227514) (:fv _uniq.227515)) ((:c OfNat.ofNat) (:c Ordinal) (:lit 0) ((:c Zero.toOfNat0) (:c Ordinal) (:c Ordinal.zero)))) ((:c Eq) (:c Ordinal) (:fv _uniq.227514) ((:c OfNat.ofNat) (:c Ordinal) (:lit 0) ((:c Zero.toOfNat0) (:c Ordinal) (:c Ordinal.zero)))))	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.227233) (:forall _ (:fv _uniq.227233) (:sort 0)))"},{"name":"s","sexp":"(:forall _ (:fv _uniq.227236) (:forall _ (:fv _uniq.227236) (:sort 0)))"},{"name":"t"...	(:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:app (:c Ordinal.blsub) (:arg :explicit 0 (:fv FV7)) (:arg :explicit 1 (:fv FV8)))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instanc...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227233","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227236","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"rw","sourceEnd":83025,"sourceStart":83023,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":83027,"sourceStart":83026,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":83030,"sourceSt...	[]	[{"source":"lsub_eq_blsub","source_end":83044,"source_start":83031,"syntax_kind":"ident"},{"source":"lsub_eq_zero_iff","source_end":83062,"source_start":83046,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227233","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227236","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	573	4	exact	true	1	8	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	4addb416b813c8ea94a3ba1996a6259705db360aaaef480a8a99e9e29b3acb77	7cb455b63436a222b3dae3bb92707d154e16b3da7657b83984523dfe331a4c06	23295b42f3d1a18a56ed8b1219e09e699615fdf91250d8936a6cc5d22cfc51c1	8e435fee15e020ec8e11430c0028e5d107416ec78a0df8e30b5709ace7044c33
cat-searcher/leandojo-benchmark-4-random	test	942	Ordinal.blsub_eq_zero_iff	Mathlib/SetTheory/Ordinal/Arithmetic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact <a>Ordinal.out_empty_iff_eq_zero</a>	α : Type u_1 β : Type u_2 γ : Type u_3 r : α → α → Prop s : β → β → Prop t : γ → γ → Prop o : Ordinal.{u_4} f : (a : Ordinal.{u_4}) → a < o → Ordinal.{max u_5 u_4} ⊢ IsEmpty (Quotient.out o).α ↔ o = 0		((:c Iff) ((:c IsEmpty) ((:c WellOrder.α) ((:c Quotient.out) (:c WellOrder) (:c Ordinal.isEquivalent) (:fv _uniq.227514)))) ((:c Eq) (:c Ordinal) (:fv _uniq.227514) ((:c OfNat.ofNat) (:c Ordinal) (:lit 0) ((:c Zero.toOfNat0) (:c Ordinal) (:c Ordinal.zero)))))	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.227233) (:forall _ (:fv _uniq.227233) (:sort 0)))"},{"name":"s","sexp":"(:forall _ (:fv _uniq.227236) (:forall _ (:fv _uniq.227236) (:sort 0)))"},{"name":"t"...	(:app (:c Iff) (:arg :explicit 0 (:app (:c IsEmpty) (:arg :explicit 0 (:app (:c WellOrder.α) (:arg :explicit 0 (:app (:c Quotient.out) (:arg :implicit-type 0 (:c WellOrder)) (:arg :instance 1 (:instance-of (:app (:c Setoid) (:arg :explicit 0 (:c WellOrder))))) (:arg :explicit 2 (:fv FV7)))))))) (:arg :explicit 1 (:app ...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227233","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227236","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"exact","sourceEnd":83071,"sourceStart":83066,"tag":"atom"},{"name":"Ordinal.out_empty_iff_eq_zero","semanticRole":"global","source":"out_empty_iff_eq_zero","sourceEnd":83093,"sourceStart":83072,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact out_empty_iff_eq_zero","sourceE...	[]	[{"source":"out_empty_iff_eq_zero","source_end":83093,"source_start":83072,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227233","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227236","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	573	8	exact	true	1	8	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	1129f941138788e3162794808956a48d6a642613c46777cc5bc3da2b7c65f2a5	8e435fee15e020ec8e11430c0028e5d107416ec78a0df8e30b5709ace7044c33	df1440844233d975930378a92d2ac9a621975a45799699029f8107cf6cfc9de6	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	943	t0Space_iff_uniformity'	Mathlib/Topology/UniformSpace/Separation.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp [<a>t0Space_iff_not_inseparable</a>, <a>inseparable_iff_ker_uniformity</a>]	α : Type u β : Type v γ : Type w inst✝² : UniformSpace α inst✝¹ : UniformSpace β inst✝ : UniformSpace γ ⊢ T0Space α ↔ Pairwise fun x y => ∃ r ∈ 𝓤 α, (x, y) ∉ r		((:c Iff) ((:c T0Space) (:fv _uniq.2589) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.2589) (:fv _uniq.2596))) ((:c Pairwise) (:fv _uniq.2589) (:lambda x (:fv _uniq.2589) (:lambda y (:fv _uniq.2589) ((:c Exists) ((:c Set) ((:c Prod) (:fv _uniq.2589) (:fv _uniq.2589))) (:lambda r ((:c Set) ((:c Prod) (:fv _uniq.2589...	[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"inst✝²","sexp":"((:c UniformSpace) (:fv _uniq.2589))"},{"name":"inst✝¹","sexp":"((:c UniformSpace) (:fv _uniq.2591))"},{"name":"inst✝","sexp":"((:c UniformSpace) (:fv _uniq.2593))"}]	(:app (:c Iff) (:arg :explicit 0 (:app (:c T0Space) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c Pairwise) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:lambda y :explicit (:f...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2589","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2591","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte...	{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":6765,"sourceStart":6761,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn...	[]	[{"source":"t0Space_iff_not_inseparable","source_end":6794,"source_start":6767,"syntax_kind":"ident"},{"source":"inseparable_iff_ker_uniformity","source_end":6826,"source_start":6796,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2589","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2591","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq...	24	2	exact	true	1	6	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	70c0c16a5a7fdbe48ce72aaf14417bdb774eabb58fa3cda3f0a001ea56c11120	93dbd883a7188227513d6e3763e35d9826ab0e4911cd2740b09efc49b7813cac	ddd65edad0bc3eab53fd523e51cf48345964a3852c90232b4802e9d450fa47ec	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	944	ConvexOn.smul''	Mathlib/Analysis/Convex/Mul.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [← <a>neg_smul_neg</a>]	𝕜 : Type u_1 E : Type u_2 F : Type u_3 inst✝¹⁰ : LinearOrderedCommRing 𝕜 inst✝⁹ : LinearOrderedCommRing E inst✝⁸ : LinearOrderedAddCommGroup F inst✝⁷ : Module 𝕜 E inst✝⁶ : Module 𝕜 F inst✝⁵ : Module E F inst✝⁴ : IsScalarTower 𝕜 E F inst✝³ : SMulCommClass 𝕜 E F inst✝² : OrderedSMul 𝕜 E inst✝¹ : OrderedSMul 𝕜 F i...	𝕜 : Type u_1 E : Type u_2 F : Type u_3 inst✝¹⁰ : LinearOrderedCommRing 𝕜 inst✝⁹ : LinearOrderedCommRing E inst✝⁸ : LinearOrderedAddCommGroup F inst✝⁷ : Module 𝕜 E inst✝⁶ : Module 𝕜 F inst✝⁵ : Module E F inst✝⁴ : IsScalarTower 𝕜 E F inst✝³ : SMulCommClass 𝕜 E F inst✝² : OrderedSMul 𝕜 E inst✝¹ : OrderedSMul 𝕜 F i...	((:c ConcaveOn) (:fv _uniq.113468) (:fv _uniq.113468) (:fv _uniq.113474) ((:c OrderedCommSemiring.toOrderedSemiring) (:fv _uniq.113468) ((:c StrictOrderedCommSemiring.toOrderedCommSemiring) (:fv _uniq.113468) ((:c LinearOrderedCommSemiring.toStrictOrderedCommSemiring) (:fv _uniq.113468) ((:c LinearOrderedCommRing.toLin...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹⁰","sexp":"((:c LinearOrderedCommRing) (:fv _uniq.113468))"},{"name":"inst✝⁹","sexp":"((:c LinearOrderedCommRing) (:fv _uniq.113471))"},{"name":"inst✝⁸","sexp":"((:c LinearOrderedAddC...	(:app (:c ConcaveOn) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c OrderedSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 5 (:in...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.113468","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.113471","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...	{"children":[{"source":"rw","sourceEnd":3891,"sourceStart":3889,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3893,"sourceStart":3892,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":3896,"sourceStart":...	[]	[{"source":"neg_smul_neg","source_end":3909,"source_start":3897,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.113468","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.113471","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...	7	4	exact	true	1	22	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	1eb75a91789d376c77b4ec0ad20ef02167a1ffe15c8ec8e12721545afbd9b26e	8cf774b810b6893e67575d1df02a516ae564a01badee91dcb0ead7920f93b04f	d07ebb47e175afa99a6fbbe8a594935cd82d1d2e4b593c03e2a2d77108b8dc25	9928838e5e334659d9ded945a627a4f5959aa6ecd4d41c6d3cc047a6d44aec7d
cat-searcher/leandojo-benchmark-4-random	test	945	ConvexOn.smul''	Mathlib/Analysis/Convex/Mul.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact hf.neg.smul' hg.neg (fun x hx ↦ <a>neg_nonneg</a>.2 <\| hf₀ hx) (fun x hx ↦ <a>neg_nonneg</a>.2 <\| hg₀ hx) hfg.neg	𝕜 : Type u_1 E : Type u_2 F : Type u_3 inst✝¹⁰ : LinearOrderedCommRing 𝕜 inst✝⁹ : LinearOrderedCommRing E inst✝⁸ : LinearOrderedAddCommGroup F inst✝⁷ : Module 𝕜 E inst✝⁶ : Module 𝕜 F inst✝⁵ : Module E F inst✝⁴ : IsScalarTower 𝕜 E F inst✝³ : SMulCommClass 𝕜 E F inst✝² : OrderedSMul 𝕜 E inst✝¹ : OrderedSMul 𝕜 F i...		((:c ConcaveOn) (:fv _uniq.113468) (:fv _uniq.113468) (:fv _uniq.113474) ((:c OrderedCommSemiring.toOrderedSemiring) (:fv _uniq.113468) ((:c StrictOrderedCommSemiring.toOrderedCommSemiring) (:fv _uniq.113468) ((:c LinearOrderedCommSemiring.toStrictOrderedCommSemiring) (:fv _uniq.113468) ((:c LinearOrderedCommRing.toLin...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹⁰","sexp":"((:c LinearOrderedCommRing) (:fv _uniq.113468))"},{"name":"inst✝⁹","sexp":"((:c LinearOrderedCommRing) (:fv _uniq.113471))"},{"name":"inst✝⁸","sexp":"((:c LinearOrderedAddC...	(:app (:c ConcaveOn) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c OrderedSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 5 (:in...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.113468","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.113471","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","...	{"children":[{"source":"exact","sourceEnd":3918,"sourceStart":3913,"tag":"atom"},{"children":[{"source":"hf.neg.smul'","sourceEnd":3931,"sourceStart":3919,"tag":"identifier"},{"children":[{"name":"ConvexOn.neg","semanticRole":"global","source":"hg.neg","sourceEnd":3938,"sourceStart":3932,"tag":"identifier"},{"children"...	[]	[{"source":"hf.neg.smul' hg.neg (fun x hx ↦ neg_nonneg.2 <\| hf₀ hx) (fun x hx ↦ neg_nonneg.2 <\| hg₀ hx)\n hfg.neg","source_end":4030,"source_start":3919,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.113468","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.113471","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"...	7	7	exact	true	1	22	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	0d73ac1ac112965df73256a9f26f9833582f76cf3716b65a3a3d35dd9d8c0e50	9928838e5e334659d9ded945a627a4f5959aa6ecd4d41c6d3cc047a6d44aec7d	911f2ce1509b158ea56c03572b48c311db1bfee22621c76305baeeb83ad55db1	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	946	BoxIntegral.Box.biUnion_coe_eq_coe	Mathlib/Analysis/BoxIntegral/Box/Basic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	induction I <;> simp [<a>WithBot.coe_eq_coe</a>]	ι : Type u_1 I✝ J : Box ι x y : ι → ℝ I : WithBot (Box ι) ⊢ ⋃ J, ⋃ (_ : ↑J = I), ↑J = ↑I		((:c Eq) ((:c Set) (:forall _ (:fv _uniq.27294) (:c Real))) ((:c Set.iUnion) (:forall _ (:fv _uniq.27294) (:c Real)) ((:c BoxIntegral.Box) (:fv _uniq.27294)) (:lambda J ((:c BoxIntegral.Box) (:fv _uniq.27294)) ((:c Set.iUnion) (:forall _ (:fv _uniq.27294) (:c Real)) ((:c Eq) ((:c WithBot) ((:c BoxIntegral.Box) (:fv _un...	[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"I✝","sexp":"((:c BoxIntegral.Box) (:fv _uniq.27294))"},{"name":"J","sexp":"((:c BoxIntegral.Box) (:fv _uniq.27294))"},{"name":"x","sexp":"(:forall _ (:fv _uniq.27294) (:c Real))"},{"name":"y","sexp":"(:forall _ (:fv _uniq.27294) (:c Real))"},{"name":"I","sexp":"((:c Wit...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:forall _ :explicit (:fv FV0) (:c Real))))) (:arg :explicit 1 (:app (:c Set.iUnion) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:c Real))) (:arg :implicit-type 1 (:app (:c BoxIntegral.Box) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 2 ...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27294","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27297","is_instance":false,"is_let":false,"name":"I✝","sexp":"(:app (:c BoxIntegral.Box) (:arg :explicit 0 ...	{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"induction","sourceEnd":11649,"sourceStart":11640,"tag":"atom"},{"children":[{"contextIndex":6,"semanticRole":"local","source":"I","sourceEnd":11651,"sourceStart":11650,"tag":"identifier"}],"kind":"null","source":"I","sourceEnd":11651,"sourceSta...	[]	[{"source":"I","source_end":11651,"source_start":11650,"syntax_kind":"ident"},{"source":"WithBot.coe_eq_coe","source_end":11680,"source_start":11662,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27294","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27297","is_instance":false,"is_let":false,"user_name":"I✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...	94	2	exact	true	1	6	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	5b33266222042d02516092c34f68d61a615975aa08012fe4e9c71994ba60a9c3	19703e31a9d6f3acfd17e24f4862ace50ae81ae364d22178a0425abf9b40df62	1f0a219fbeee434b77a3a0ad6f3d8548a33d89ce9b9eb126fc0bd1f710727c0a	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	947	BoxIntegral.Prepartition.mem_iUnion	Mathlib/Analysis/BoxIntegral/Partition/Basic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	convert <a>Set.mem_iUnion₂</a>	ι : Type u_1 I J J₁ J₂ : Box ι π π₁ π₂ : Prepartition I x : ι → ℝ ⊢ x ∈ π.iUnion ↔ ∃ J ∈ π, x ∈ J	case h.e'_2.h.e'_2.h.a ι : Type u_1 I J J₁ J₂ : Box ι π π₁ π₂ : Prepartition I x : ι → ℝ x✝ : Box ι ⊢ x✝ ∈ π ∧ x ∈ x✝ ↔ ∃ (_ : x✝ ∈ π), x ∈ ↑x✝	((:c Iff) ((:c Membership.mem) (:forall _ (:fv _uniq.15298) (:c Real)) ((:c Set) (:forall _ (:fv _uniq.15298) (:c Real))) ((:c Set.instMembership) (:forall _ (:fv _uniq.15298) (:c Real))) (:fv _uniq.15330) ((:c BoxIntegral.Prepartition.iUnion) (:fv _uniq.15298) (:fv _uniq.15301) (:fv _uniq.15316))) ((:c Exists) ((:c Bo...	[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"I","sexp":"((:c BoxIntegral.Box) (:fv _uniq.15298))"},{"name":"J","sexp":"((:c BoxIntegral.Box) (:fv _uniq.15298))"},{"name":"J₁","sexp":"((:c BoxIntegral.Box) (:fv _uniq.15298))"},{"name":"J₂","sexp":"((:c BoxIntegral.Box) (:fv _uniq.15298))"},{"name":"π","sexp":"((:c ...	(:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:c Real))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:forall _ :explicit (:fv FV0) (:c Real))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:forall _ :explicit (...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15298","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15301","is_instance":false,"is_let":false,"name":"I","sexp":"(:app (:c BoxIntegral.Box) (:arg :explicit 0 (...	{"children":[{"source":"convert","sourceEnd":10084,"sourceStart":10077,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.mem_iUnion₂","semanticRole":"global","source":"Set.mem_iUnion₂","sourceEnd":10102,"sourceStart":10085,"tag":"ide...	[]	[{"source":"Set.mem_iUnion₂","source_end":10102,"source_start":10085,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15298","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15301","is_instance":false,"is_let":false,"user_name":"I"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	64	4	exact	true	1	9	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	2a5a7bacf9d896149ceed9fbd39c20676bcb136ec26aecef8106e343d88afe5c	0dfd43dd54da138efb3bd88cd7d502fe22ae6e12fe87f9d1e96687775af0475e	23717942ebb5899d734854977ad2f5f0a7d7a6e9962ac4af579f066037d869ad	d26c368f0ac4d0921c79a3e5edbf864b2a0c8e29d4f3ef96ba5c2743b674a390
cat-searcher/leandojo-benchmark-4-random	test	948	BoxIntegral.Prepartition.mem_iUnion	Mathlib/Analysis/BoxIntegral/Partition/Basic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>BoxIntegral.Box.mem_coe</a>, <a>exists_prop</a>]	case h.e'_2.h.e'_2.h.a ι : Type u_1 I J J₁ J₂ : Box ι π π₁ π₂ : Prepartition I x : ι → ℝ x✝ : Box ι ⊢ x✝ ∈ π ∧ x ∈ x✝ ↔ ∃ (_ : x✝ ∈ π), x ∈ ↑x✝		((:c Iff) ((:c And) ((:c Membership.mem) ((:c BoxIntegral.Box) (:fv _uniq.15298)) ((:c BoxIntegral.Prepartition) (:fv _uniq.15298) (:fv _uniq.15301)) ((:c BoxIntegral.Prepartition.instMembershipBox) (:fv _uniq.15298) (:fv _uniq.15301)) (:fv _uniq.17363) (:fv _uniq.15316)) ((:c Membership.mem) (:forall _ (:fv _uniq.1529...	[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"I","sexp":"((:c BoxIntegral.Box) (:fv _uniq.15298))"},{"name":"J","sexp":"((:c BoxIntegral.Box) (:fv _uniq.15298))"},{"name":"J₁","sexp":"((:c BoxIntegral.Box) (:fv _uniq.15298))"},{"name":"J₂","sexp":"((:c BoxIntegral.Box) (:fv _uniq.15298))"},{"name":"π","sexp":"((:c ...	(:app (:c Iff) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c BoxIntegral.Box) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c BoxIntegral.Prepartition) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))) (:arg :instance 2 (:ins...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15298","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15301","is_instance":false,"is_let":false,"name":"I","sexp":"(:app (:c BoxIntegral.Box) (:arg :explicit 0 (...	{"children":[{"source":"rw","sourceEnd":10107,"sourceStart":10105,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10109,"sourceStart":10108,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"BoxIntegral.Box....	[]	[{"source":"Box.mem_coe","source_end":10120,"source_start":10109,"syntax_kind":"ident"},{"source":"exists_prop","source_end":10133,"source_start":10122,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15298","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15301","is_instance":false,"is_let":false,"user_name":"I"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	64	5	exact	true	1	10	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	a2a0d4cc8ebbb72433e0ddb87a5a8f2911b40559c51cb278d9a020ad2cb1227a	d26c368f0ac4d0921c79a3e5edbf864b2a0c8e29d4f3ef96ba5c2743b674a390	3e19c2cd62f8107945083617b1ca5fa18b56348a220427209277d0407e372026	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	949	Submodule.comm_trans_rTensorOne	Mathlib/LinearAlgebra/TensorProduct/Submodule.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	refine <a>LinearEquiv.toLinearMap_injective</a> <\| <a>TensorProduct.ext'</a> fun r m ↦ ?_	R : Type u S : Type v inst✝² : CommSemiring R inst✝¹ : Semiring S inst✝ : Algebra R S M N : Submodule R S ⊢ TensorProduct.comm R ↥⊥ ↥M ≪≫ₗ M.rTensorOne = M.lTensorOne	R : Type u S : Type v inst✝² : CommSemiring R inst✝¹ : Semiring S inst✝ : Algebra R S M N : Submodule R S r : ↥⊥ m : ↥M ⊢ ↑(TensorProduct.comm R ↥⊥ ↥M ≪≫ₗ M.rTensorOne) (r ⊗ₜ[R] m) = ↑M.lTensorOne (r ⊗ₜ[R] m)	((:c Eq) ((:c LinearEquiv) (:fv _uniq.205847) (:fv _uniq.205847) ((:c CommSemiring.toSemiring) (:fv _uniq.205847) (:fv _uniq.205852)) ((:c CommSemiring.toSemiring) (:fv _uniq.205847) (:fv _uniq.205852)) ((:c RingHom.id) (:fv _uniq.205847) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.205847) ((:c CommSemiring.toSemiring...	[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.205847))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.205849))"},{"name":"inst✝","sexp":"((:c Algebra) (:fv _uniq.205847) (:fv _uniq.205849) (:fv _uniq.205852) (:fv _uniq.205855))"...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c LinearEquiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 4 (:app ...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.205847","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.205849","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"refine","sourceEnd":9893,"sourceStart":9887,"tag":"atom"},{"children":[{"name":"LinearEquiv.toLinearMap_injective","semanticRole":"global","source":"LinearEquiv.toLinearMap_injective","sourceEnd":9927,"sourceStart":9894,"tag":"identifier"},{"source":"<\|","sourceEnd":9930,"sourceStart":9928,"tag"...	[]	[{"source":"LinearEquiv.toLinearMap_injective <\| TensorProduct.ext' fun r m ↦ ?_","source_end":9964,"source_start":9894,"syntax_kind":"«term_<\|_»"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.205847","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.205849","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal...	38	4	exact	true	1	7	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	7ab8b6612832f504ba006e813ad733b48020d831565d9f11301fb52e4b969caa	4d2b7fc97a58993bdbd5c101d6bfda01e83512adb8a9d424b9306d82596b5d8d	d0164de64023157e35c54e2403c0890e2c8edc0b3ee4ee5488f310b1f6e1b180	341a45ef59c222f38f3d3a4135b73de4a87156bdb5c1eb484b4e7cbcd8e5f0c2
cat-searcher/leandojo-benchmark-4-random	test	950	Submodule.comm_trans_rTensorOne	Mathlib/LinearAlgebra/TensorProduct/Submodule.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	obtain ⟨x, h⟩ := <a>Algebra.mem_bot</a>.1 r.2	R : Type u S : Type v inst✝² : CommSemiring R inst✝¹ : Semiring S inst✝ : Algebra R S M N : Submodule R S r : ↥⊥ m : ↥M ⊢ ↑(TensorProduct.comm R ↥⊥ ↥M ≪≫ₗ M.rTensorOne) (r ⊗ₜ[R] m) = ↑M.lTensorOne (r ⊗ₜ[R] m)	case intro R : Type u S : Type v inst✝² : CommSemiring R inst✝¹ : Semiring S inst✝ : Algebra R S M N : Submodule R S r : ↥⊥ m : ↥M x : R h : (algebraMap R S) x = ↑r ⊢ ↑(TensorProduct.comm R ↥⊥ ↥M ≪≫ₗ M.rTensorOne) (r ⊗ₜ[R] m) = ↑M.lTensorOne (r ⊗ₜ[R] m)	((:c Eq) ((:c Subtype) (:fv _uniq.205849) (:lambda x (:fv _uniq.205849) ((:c Membership.mem) (:fv _uniq.205849) ((:c Submodule) (:fv _uniq.205847) (:fv _uniq.205849) ((:c CommSemiring.toSemiring) (:fv _uniq.205847) (:fv _uniq.205852)) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.205849) ((:c NonAssocSemir...	[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.205847))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.205849))"},{"name":"inst✝","sexp":"((:c Algebra) (:fv _uniq.205847) (:fv _uniq.205849) (:fv _uniq.205852) (:fv _uniq.205855))"...	(:app (:c Eq) (:arg :implicit-type 0 (: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 Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.205847","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.205849","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"obtain","sourceEnd":9973,"sourceStart":9967,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":9977,"sourceStart":9974,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":9...	[]	[{"source":"Algebra.mem_bot.1 r.2","source_end":10009,"source_start":9988,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨x, h⟩","source_end":9984,"source_start":9974,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.205847","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.205849","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal...	38	5	exact	true	1	9	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	f9089bd256cf775434060b8caa1dececfc4cac3189d932137208419cc5f3929f	341a45ef59c222f38f3d3a4135b73de4a87156bdb5c1eb484b4e7cbcd8e5f0c2	a11ec5ad298ea750b4ab4758412dd000e8023e96ec0413a70a66f2d3ec31336e	4be8bc5607fc2199b68f86e2910f36d4edf464d0b5226303c445ad5a238dbd78
cat-searcher/leandojo-benchmark-4-random	test	951	Submodule.comm_trans_rTensorOne	Mathlib/LinearAlgebra/TensorProduct/Submodule.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	replace h : <a>algebraMap</a> R _ x = r := <a>Subtype.val_injective</a> h	case intro R : Type u S : Type v inst✝² : CommSemiring R inst✝¹ : Semiring S inst✝ : Algebra R S M N : Submodule R S r : ↥⊥ m : ↥M x : R h : (algebraMap R S) x = ↑r ⊢ ↑(TensorProduct.comm R ↥⊥ ↥M ≪≫ₗ M.rTensorOne) (r ⊗ₜ[R] m) = ↑M.lTensorOne (r ⊗ₜ[R] m)	case intro R : Type u S : Type v inst✝² : CommSemiring R inst✝¹ : Semiring S inst✝ : Algebra R S M N : Submodule R S r : ↥⊥ m : ↥M x : R h : (algebraMap R ↥⊥) x = r ⊢ ↑(TensorProduct.comm R ↥⊥ ↥M ≪≫ₗ M.rTensorOne) (r ⊗ₜ[R] m) = ↑M.lTensorOne (r ⊗ₜ[R] m)	((:c Eq) ((:c Subtype) (:fv _uniq.205849) (:lambda x (:fv _uniq.205849) ((:c Membership.mem) (:fv _uniq.205849) ((:c Submodule) (:fv _uniq.205847) (:fv _uniq.205849) ((:c CommSemiring.toSemiring) (:fv _uniq.205847) (:fv _uniq.205852)) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.205849) ((:c NonAssocSemir...	[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.205847))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.205849))"},{"name":"inst✝","sexp":"((:c Algebra) (:fv _uniq.205847) (:fv _uniq.205849) (:fv _uniq.205852) (:fv _uniq.205855))"...	(:app (:c Eq) (:arg :implicit-type 0 (: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 Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.205847","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.205849","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"replace","sourceEnd":10019,"sourceStart":10012,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":10021,"sourceStart":10020,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":10021,"sourceStart":10020,"tag":"no...	[]	[{"source":"algebraMap R _ x = r","source_end":10044,"source_start":10024,"syntax_kind":"«term_=_»"},{"source":"Subtype.val_injective h","source_end":10071,"source_start":10048,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.205847","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.205849","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal...	38	6	exact	true	1	11	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	bb6632bb7719d4e5189a9c5cfc6490231261a8a866a662aa103d7e7f5834fe60	4be8bc5607fc2199b68f86e2910f36d4edf464d0b5226303c445ad5a238dbd78	4b030140cde0cc048ef7ebf5d975cc76b8866212b8ad5256c30a8c172acbf07d	c018ab50639aeb3ffa53c53a540d1e79215125f227f54597111403e739710a8f
cat-searcher/leandojo-benchmark-4-random	test	952	Submodule.comm_trans_rTensorOne	Mathlib/LinearAlgebra/TensorProduct/Submodule.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [← h]	case intro R : Type u S : Type v inst✝² : CommSemiring R inst✝¹ : Semiring S inst✝ : Algebra R S M N : Submodule R S r : ↥⊥ m : ↥M x : R h : (algebraMap R ↥⊥) x = r ⊢ ↑(TensorProduct.comm R ↥⊥ ↥M ≪≫ₗ M.rTensorOne) (r ⊗ₜ[R] m) = ↑M.lTensorOne (r ⊗ₜ[R] m)	case intro R : Type u S : Type v inst✝² : CommSemiring R inst✝¹ : Semiring S inst✝ : Algebra R S M N : Submodule R S r : ↥⊥ m : ↥M x : R h : (algebraMap R ↥⊥) x = r ⊢ ↑(TensorProduct.comm R ↥⊥ ↥M ≪≫ₗ M.rTensorOne) ((algebraMap R ↥⊥) x ⊗ₜ[R] m) = ↑M.lTensorOne ((algebraMap R ↥⊥) x ⊗ₜ[R] m)	((:c Eq) ((:c Subtype) (:fv _uniq.205849) (:lambda x (:fv _uniq.205849) ((:c Membership.mem) (:fv _uniq.205849) ((:c Submodule) (:fv _uniq.205847) (:fv _uniq.205849) ((:c CommSemiring.toSemiring) (:fv _uniq.205847) (:fv _uniq.205852)) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.205849) ((:c NonAssocSemir...	[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.205847))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.205849))"},{"name":"inst✝","sexp":"((:c Algebra) (:fv _uniq.205847) (:fv _uniq.205849) (:fv _uniq.205852) (:fv _uniq.205855))"...	(:app (:c Eq) (:arg :implicit-type 0 (: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 Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.205847","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.205849","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"rw","sourceEnd":10076,"sourceStart":10074,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10078,"sourceStart":10077,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":10081,"sourceSt...	[]	[{"source":"h","source_end":10083,"source_start":10082,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.205847","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.205849","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal...	38	7	exact	true	1	11	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	a3253d980fdf09d6548b79035feb8fce6360a53083b5a242e4fbfb050e185d45	c018ab50639aeb3ffa53c53a540d1e79215125f227f54597111403e739710a8f	b8f7ba4ddf00851760c0b1131d01447fed956b4cd76dde607f7e82015e941b84	f92983edef4e31f4af6e818b6c8b9fd3286e1958e27af21c28384743e7173035
cat-searcher/leandojo-benchmark-4-random	test	953	Submodule.comm_trans_rTensorOne	Mathlib/LinearAlgebra/TensorProduct/Submodule.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp	case intro R : Type u S : Type v inst✝² : CommSemiring R inst✝¹ : Semiring S inst✝ : Algebra R S M N : Submodule R S r : ↥⊥ m : ↥M x : R h : (algebraMap R ↥⊥) x = r ⊢ ↑(TensorProduct.comm R ↥⊥ ↥M ≪≫ₗ M.rTensorOne) ((algebraMap R ↥⊥) x ⊗ₜ[R] m) = ↑M.lTensorOne ((algebraMap R ↥⊥) x ⊗ₜ[R] m)		((:c Eq) ((:c Subtype) (:fv _uniq.205849) (:lambda x (:fv _uniq.205849) ((:c Membership.mem) (:fv _uniq.205849) ((:c Submodule) (:fv _uniq.205847) (:fv _uniq.205849) ((:c CommSemiring.toSemiring) (:fv _uniq.205847) (:fv _uniq.205852)) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.205849) ((:c NonAssocSemir...	[{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.205847))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.205849))"},{"name":"inst✝","sexp":"((:c Algebra) (:fv _uniq.205847) (:fv _uniq.205849) (:fv _uniq.205852) (:fv _uniq.205855))"...	(:app (:c Eq) (:arg :implicit-type 0 (: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 Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.205847","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.205849","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"simp","sourceEnd":10090,"sourceStart":10086,"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":[],"ki...	[]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.205847","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.205849","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal...	38	11	exact	true	1	11	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	ae38c042a6dcb5701c4169fa0976844d30f52c4d5adb1d49a52b1e5141a7b67e	f92983edef4e31f4af6e818b6c8b9fd3286e1958e27af21c28384743e7173035	8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	954	CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_hom_π	Mathlib/CategoryTheory/Limits/FunctorCategory.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	dsimp [<a>CategoryTheory.Limits.limitObjIsoLimitCompEvaluation</a>]	C : Type u inst✝⁴ : Category.{v, u} C D : Type u' inst✝³ : Category.{v', u'} D J : Type u₁ inst✝² : Category.{v₁, u₁} J K : Type u₂ inst✝¹ : Category.{v₂, u₂} K inst✝ : HasLimitsOfShape J C F : J ⥤ K ⥤ C j : J k : K ⊢ (limitObjIsoLimitCompEvaluation F k).hom ≫ limit.π (F ⋙ (evaluation K C).obj k) j = (limit.π F j).app ...	C : Type u inst✝⁴ : Category.{v, u} C D : Type u' inst✝³ : Category.{v', u'} D J : Type u₁ inst✝² : Category.{v₁, u₁} J K : Type u₂ inst✝¹ : Category.{v₂, u₂} K inst✝ : HasLimitsOfShape J C F : J ⥤ K ⥤ C j : J k : K ⊢ (preservesLimitIso ((evaluation K C).obj k) F).hom ≫ limit.π (F ⋙ (evaluation K C).obj k) j = (limit.π...	((:c Eq) ((:c Quiver.Hom) (:fv _uniq.50187) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.50187) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.50187) (:fv _uniq.50190))) ((:c Prefunctor.obj) (:fv _uniq.50202) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.50202) ((:c CategoryTheory.Catego...	[{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.50187))"},{"name":"D","sexp":"(:sort (+ u' 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.50192))"},{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Catego...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.50187","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.50190","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CategoryTheory.Category...	{"children":[{"source":"dsimp","sourceEnd":10639,"sourceStart":10634,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10641,"sourceStart":10640,"tag":"...	[]	[{"source":"limitObjIsoLimitCompEvaluation","source_end":10671,"source_start":10641,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.50187","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.50190","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"intern...	40	4	exact	true	1	12	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	04af2d975d8b3c9650cf1ecb5478d693cb128d4563f072aa7be0d347f08e2ca6	ca037bd1d7592a7e3dceb48bffa44e09381d66762d9f8cfd653e61d6dee3daec	b42bac7fec5a09b22e8ebdc737311179d6ceadc3cb706b1fead600e5901a781c	b373327bc3010b1291c8c9bb0aa162ed86a66c1e45d6eb4a302e72ced084bb5a
cat-searcher/leandojo-benchmark-4-random	test	955	CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_hom_π	Mathlib/CategoryTheory/Limits/FunctorCategory.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp	C : Type u inst✝⁴ : Category.{v, u} C D : Type u' inst✝³ : Category.{v', u'} D J : Type u₁ inst✝² : Category.{v₁, u₁} J K : Type u₂ inst✝¹ : Category.{v₂, u₂} K inst✝ : HasLimitsOfShape J C F : J ⥤ K ⥤ C j : J k : K ⊢ (preservesLimitIso ((evaluation K C).obj k) F).hom ≫ limit.π (F ⋙ (evaluation K C).obj k) j = (limit.π...		((:c Eq) ((:c Quiver.Hom) (:fv _uniq.50187) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.50187) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.50187) (:fv _uniq.50190))) ((:c Prefunctor.obj) (:fv _uniq.50202) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.50202) ((:c CategoryTheory.Catego...	[{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.50187))"},{"name":"D","sexp":"(:sort (+ u' 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.50192))"},{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Catego...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.50187","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.50190","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CategoryTheory.Category...	{"children":[{"source":"simp","sourceEnd":10679,"sourceStart":10675,"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":[],"ki...	[]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.50187","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.50190","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"intern...	40	5	exact	true	1	12	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	2402cd972813d5450bf798d651f34be393cec39a820b6bc7751695d43f1ba747	b373327bc3010b1291c8c9bb0aa162ed86a66c1e45d6eb4a302e72ced084bb5a	8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	956	Nat.gcd_mul_left_add_left	Mathlib/Data/Nat/GCD/Basic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>Nat.gcd_comm</a>, <a>Nat.gcd_mul_left_add_right</a>, <a>Nat.gcd_comm</a>]	m n k : ℕ ⊢ (n * k + m).gcd n = m.gcd n		((:c Eq) (:c Nat) ((:c Nat.gcd) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.1861) (:fv _uniq.1862)) (:fv _uniq.1860)) (:fv _uniq.1861)) ((:c Nat.gcd) (:fv _uniq.1860) (:fv _uniq.1861)))	[{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Nat)"}]	(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.gcd) (: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 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c ...	[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.1860","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.1861","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index...	{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":2557,"sourceStart":2555,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2559,"sourceStart":2558,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag...	[]	[{"source":"gcd_comm","source_end":2567,"source_start":2559,"syntax_kind":"ident"},{"source":"gcd_mul_left_add_right","source_end":2591,"source_start":2569,"syntax_kind":"ident"},{"source":"gcd_comm","source_end":2601,"source_start":2593,"syntax_kind":"ident"}]	[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.1860","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.1861","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq...	21	2	exact	true	1	3	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	84099139aa492bc4265a38a6cf6d9fa7712c0166b60bbbd6def978ee4dfe998b	f58a45a4d22eba9fded966e583a0ec36623f5c15f70e1625cc65b236fde94947	5b3c2fa26787b4622bfade4c6dcf94a6d08f819143360242107847555894df84	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	957	UniformInducing.of_comp_iff	Mathlib/Topology/UniformSpace/UniformEmbedding.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	refine ⟨fun h ↦ ?_, hg.comp⟩	α : Type u β : Type v γ : Type w inst✝² : UniformSpace α inst✝¹ : UniformSpace β inst✝ : UniformSpace γ g : β → γ hg : UniformInducing g f : α → β ⊢ UniformInducing (g ∘ f) ↔ UniformInducing f	α : Type u β : Type v γ : Type w inst✝² : UniformSpace α inst✝¹ : UniformSpace β inst✝ : UniformSpace γ g : β → γ hg : UniformInducing g f : α → β h : UniformInducing (g ∘ f) ⊢ UniformInducing f	((:c Iff) ((:c UniformInducing) (:fv _uniq.24955) (:fv _uniq.24959) (:fv _uniq.24962) (:fv _uniq.24968) ((:c Function.comp) (:fv _uniq.24955) (:fv _uniq.24957) (:fv _uniq.24959) (:fv _uniq.25061) (:fv _uniq.25063))) ((:c UniformInducing) (:fv _uniq.24955) (:fv _uniq.24957) (:fv _uniq.24962) (:fv _uniq.24965) (:fv _uniq...	[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"inst✝²","sexp":"((:c UniformSpace) (:fv _uniq.24955))"},{"name":"inst✝¹","sexp":"((:c UniformSpace) (:fv _uniq.24957))"},{"name":"inst✝","sexp":"((:c UniformSpace) (:fv _uniq.24959))"},{"name":"g"...	(:app (:c Iff) (:arg :explicit 0 (:app (:c UniformInducing) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c UniformSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c UniformSpace) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit ...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24955","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24957","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...	{"children":[{"source":"refine","sourceEnd":3528,"sourceStart":3522,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":3532,"sourceStart":3529,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":3535,"sourceStart":3532,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"h"...	[]	[{"source":"⟨fun h ↦ ?_, hg.comp⟩","source_end":3556,"source_start":3529,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24955","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24957","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	23	4	exact	true	1	9	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	e5ed5600d5a7f49f7c746fbbf819ab4f4cec8d090f6a20a4ed3c43fe81565e4f	45d52edeffc47f2e3f7ea9aa8afe262ee1a86ba4dec457d3033a9c357791deba	243a5e65aec7482c0c57b9eba903f55a70b493b25021b71af0f3237de7584dce	9437281d86145eef8c6acc44c017de9114a410bcc22af5f228b80cb3aeab759a
cat-searcher/leandojo-benchmark-4-random	test	958	UniformInducing.of_comp_iff	Mathlib/Topology/UniformSpace/UniformEmbedding.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>uniformInducing_iff</a>, ← hg.comap_uniformity, <a>Filter.comap_comap</a>, ← h.comap_uniformity, <a>Function.comp</a>, <a>Function.comp</a>]	α : Type u β : Type v γ : Type w inst✝² : UniformSpace α inst✝¹ : UniformSpace β inst✝ : UniformSpace γ g : β → γ hg : UniformInducing g f : α → β h : UniformInducing (g ∘ f) ⊢ UniformInducing f		((:c UniformInducing) (:fv _uniq.24955) (:fv _uniq.24957) (:fv _uniq.24962) (:fv _uniq.24965) (:fv _uniq.25063))	[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"inst✝²","sexp":"((:c UniformSpace) (:fv _uniq.24955))"},{"name":"inst✝¹","sexp":"((:c UniformSpace) (:fv _uniq.24957))"},{"name":"inst✝","sexp":"((:c UniformSpace) (:fv _uniq.24959))"},{"name":"g"...	(:app (:c UniformInducing) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c UniformSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c UniformSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 4 (:fv FV9)))	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24955","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24957","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...	{"children":[{"source":"rw","sourceEnd":3561,"sourceStart":3559,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3563,"sourceStart":3562,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"uniformInducing_iff"...	[]	[{"source":"uniformInducing_iff","source_end":3582,"source_start":3563,"syntax_kind":"ident"},{"source":"hg.comap_uniformity","source_end":3607,"source_start":3588,"syntax_kind":"ident"},{"source":"comap_comap","source_end":3620,"source_start":3609,"syntax_kind":"ident"},{"source":"h.comap_uniformity","source_end":3644...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24955","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24957","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	23	5	exact	true	1	10	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	b696fff4696183af2bf4120d5cbdf422edba599077f01cc783be3adfa59414d8	9437281d86145eef8c6acc44c017de9114a410bcc22af5f228b80cb3aeab759a	e15b1b2358403207e9b515c8f2a218c0d77afbedc8b1cdf5dde3177feda858d7	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	959	Ordnode.Bounded.to_sep	Mathlib/Data/Ordmap/Ordset.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	refine h₁.mem_lt.imp fun y yx => ?_	α : Type u_1 inst✝ : Preorder α t₁ t₂ : Ordnode α o₁ : WithBot α o₂ : WithTop α x : α h₁ : t₁.Bounded o₁ ↑x h₂ : t₂.Bounded (↑x) o₂ ⊢ All (fun y => All (fun z => y < z) t₂) t₁	α : Type u_1 inst✝ : Preorder α t₁ t₂ : Ordnode α o₁ : WithBot α o₂ : WithTop α x : α h₁ : t₁.Bounded o₁ ↑x h₂ : t₂.Bounded (↑x) o₂ y : α yx : y < x ⊢ All (fun z => y < z) t₂	((:c Ordnode.All) (:fv _uniq.239960) (:lambda y (:fv _uniq.239960) ((:c Ordnode.All) (:fv _uniq.239960) (:lambda z (:fv _uniq.239960) ((:c LT.lt) (:fv _uniq.239960) ((:c Preorder.toLT) (:fv _uniq.239960) (:fv _uniq.239963)) 1 0)) (:fv _uniq.240221))) (:fv _uniq.240220))	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Preorder) (:fv _uniq.239960))"},{"name":"t₁","sexp":"((:c Ordnode) (:fv _uniq.239960))"},{"name":"t₂","sexp":"((:c Ordnode) (:fv _uniq.239960))"},{"name":"o₁","sexp":"((:c WithBot) (:fv _uniq.239960))"},{"name":"o₂","sexp":"((:c WithTop) (:fv _uniq.2...	(:app (:c Ordnode.All) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda y :explicit (:fv FV0) (:app (:c Ordnode.All) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda z :explicit (:fv FV0) (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :expl...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.239960","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.239963","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Preorder) (:arg :expli...	{"children":[{"source":"refine","sourceEnd":44319,"sourceStart":44313,"tag":"atom"},{"children":[{"source":"h₁.mem_lt.imp","sourceEnd":44335,"sourceStart":44320,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":44339,"sourceStart":44336,"tag":"atom"},{"children":[{"children":[{"semanticRole":"sc...	[]	[{"source":"h₁.mem_lt.imp fun y yx => ?_","source_end":44350,"source_start":44320,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.239960","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.239963","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter...	276	4	exact	true	1	9	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	264cb02551d640a178554fc8dd7fa3040049d8038fe7b9b5485f230a79863b06	22a35a30d97494554abcf318dbdbfee0b3366330e2111251eb0f35f4c79cc151	aa2632acb2526f79ee9ab92267eca60911227d98945d1116c5349fb753f219e7	e7251e84626463f990b064975e39013acd31d967cb4a04af6e2918c5528f6292
cat-searcher/leandojo-benchmark-4-random	test	960	Ordnode.Bounded.to_sep	Mathlib/Data/Ordmap/Ordset.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact h₂.mem_gt.imp fun z xz => <a>lt_trans</a> yx xz	α : Type u_1 inst✝ : Preorder α t₁ t₂ : Ordnode α o₁ : WithBot α o₂ : WithTop α x : α h₁ : t₁.Bounded o₁ ↑x h₂ : t₂.Bounded (↑x) o₂ y : α yx : y < x ⊢ All (fun z => y < z) t₂		((:c Ordnode.All) (:fv _uniq.239960) (:lambda z (:fv _uniq.239960) ((:c LT.lt) (:fv _uniq.239960) ((:c Preorder.toLT) (:fv _uniq.239960) (:fv _uniq.239963)) (:fv _uniq.240274) 0)) (:fv _uniq.240221))	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Preorder) (:fv _uniq.239960))"},{"name":"t₁","sexp":"((:c Ordnode) (:fv _uniq.239960))"},{"name":"t₂","sexp":"((:c Ordnode) (:fv _uniq.239960))"},{"name":"o₁","sexp":"((:c WithBot) (:fv _uniq.239960))"},{"name":"o₂","sexp":"((:c WithTop) (:fv _uniq.2...	(:app (:c Ordnode.All) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda z :explicit (:fv FV0) (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV10)) (:arg :explicit 3 0)))) (:arg :explicit 2 (:fv FV4)))	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.239960","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.239963","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Preorder) (:arg :expli...	{"children":[{"source":"exact","sourceEnd":44358,"sourceStart":44353,"tag":"atom"},{"children":[{"source":"h₂.mem_gt.imp","sourceEnd":44374,"sourceStart":44359,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":44378,"sourceStart":44375,"tag":"atom"},{"children":[{"children":[{"semanticRole":"sco...	[]	[{"source":"h₂.mem_gt.imp fun z xz => lt_trans yx xz","source_end":44401,"source_start":44359,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.239960","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.239963","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter...	276	5	exact	true	1	11	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	00025cb4ee7e7296f00c84374949817b8b38715ed55c02839ccfb64fab1bd1c4	e7251e84626463f990b064975e39013acd31d967cb4a04af6e2918c5528f6292	84db2c6e76aeb6d2082737db7be6e55314ca8b1cd80cf2072ea9886f4d212b55	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	961	IsBoundedBilinearMap.contDiff	Mathlib/Analysis/Calculus/ContDiff/Basic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	suffices h : <a>ContDiff</a> 𝕜 ∞ b from h.of_le <a>le_top</a>	𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...	𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...	((:c ContDiff) (:fv _uniq.142971) (:fv _uniq.142974) ((:c Prod) (:fv _uniq.143094) (:fv _uniq.143207)) ((:c Prod.normedAddCommGroup) (:fv _uniq.143094) (:fv _uniq.143207) (:fv _uniq.143097) (:fv _uniq.143210)) ((:c Prod.normedSpace) (:fv _uniq.142971) (:fv _uniq.143094) (:fv _uniq.143207) ((:c NontriviallyNormedField.t...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.142971))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.142976))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.142971) (:fv _uniq.142976) ((:c Non...	(:app (:c ContDiff) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c Prod) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:fv FV8)))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :expl...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.142971","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.142974","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...	{"children":[{"source":"suffices","sourceEnd":7985,"sourceStart":7977,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":7987,"sourceStart":7986,"tag":"identifier"},{"source":":","sourceEnd":7989,"sourceStart":7988,"tag":"atom"}],"kind":"group","source":"h :","sourceEnd":798...	[]	[{"source":"ContDiff 𝕜 ∞ b","source_end":8009,"source_start":7990,"syntax_kind":"Lean.Parser.Term.app"},{"source":"h.of_le le_top","source_end":8029,"source_start":8015,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.142971","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.142974","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...	57	4	exact	true	1	32	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	2f80ab0dfa74d31170f8479b5e236e0f5404a1d2ee9d923a0ad5a1941bebf5c4	c1fa9e7b360d7f4a6bc6d9d494bab9713ab2852f828c7fa84f2cc29227aa97dc	bcb4c547bfe36367b06273792b028b810abecb937d9f38078fcf231d9f399655	396832a9b14593ea89bd93e6cb519788479f38ac896090618d5beabf16aa980c
cat-searcher/leandojo-benchmark-4-random	test	962	IsBoundedBilinearMap.contDiff	Mathlib/Analysis/Calculus/ContDiff/Basic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>contDiff_top_iff_fderiv</a>]	𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...	𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...	((:c ContDiff) (:fv _uniq.142971) (:fv _uniq.142974) ((:c Prod) (:fv _uniq.143094) (:fv _uniq.143207)) ((:c Prod.normedAddCommGroup) (:fv _uniq.143094) (:fv _uniq.143207) (:fv _uniq.143097) (:fv _uniq.143210)) ((:c Prod.normedSpace) (:fv _uniq.142971) (:fv _uniq.143094) (:fv _uniq.143207) ((:c NontriviallyNormedField.t...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.142971))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.142976))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.142971) (:fv _uniq.142976) ((:c Non...	(:app (:c ContDiff) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c Prod) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:fv FV8)))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :expl...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.142971","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.142974","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...	{"children":[{"source":"rw","sourceEnd":8034,"sourceStart":8032,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8036,"sourceStart":8035,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"contDiff_top_iff_fde...	[]	[{"source":"contDiff_top_iff_fderiv","source_end":8059,"source_start":8036,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.142971","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.142974","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...	57	5	exact	true	1	32	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	4efa8f1b952f30fac2959d8da08bbdd3229e85b410f936c39d7c6494166589d3	396832a9b14593ea89bd93e6cb519788479f38ac896090618d5beabf16aa980c	a23e3a343c4a9e23b90439565681184cd35b6b1b499f6b926e95af1a25ae455e	9db0d3aa6ac9ad22078e5485360d5e65be23686e99d1a2aa6f629f2308b02adf
cat-searcher/leandojo-benchmark-4-random	test	963	IsBoundedBilinearMap.contDiff	Mathlib/Analysis/Calculus/ContDiff/Basic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	refine ⟨hb.differentiable, ?_⟩	𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...	𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...	((:c And) ((:c Differentiable) (:fv _uniq.142971) (:fv _uniq.142974) ((:c Prod) (:fv _uniq.143094) (:fv _uniq.143207)) ((:c Prod.normedAddCommGroup) (:fv _uniq.143094) (:fv _uniq.143207) (:fv _uniq.143097) (:fv _uniq.143210)) ((:c Prod.normedSpace) (:fv _uniq.142971) (:fv _uniq.143094) (:fv _uniq.143207) ((:c Nontrivia...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.142971))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.142976))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.142971) (:fv _uniq.142976) ((:c Non...	(:app (:c And) (:arg :explicit 0 (:app (:c Differentiable) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c Prod) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:fv FV8)))) (:arg :instance 3 (:instance-of (:...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.142971","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.142974","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...	{"children":[{"source":"refine","sourceEnd":8069,"sourceStart":8063,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":8073,"sourceStart":8070,"tag":"atom"},{"children":[{"name":"IsBoundedBilinearMap.differentiable","semanticRole":"global","source":"hb.differentiable","sourceEnd":8090,"sourceStart":8073,"tag":"identi...	[]	[{"source":"⟨hb.differentiable, ?_⟩","source_end":8097,"source_start":8070,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.142971","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.142974","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...	57	8	exact	true	1	32	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	0294a0889d230b8551403b9d43ad90bbb294efdb8c9d0a9a0fffbcb6422c07d4	9db0d3aa6ac9ad22078e5485360d5e65be23686e99d1a2aa6f629f2308b02adf	756f04f0144d9b86d55ed7291e5a24d58df2e3ac1c7abf5861d8e4039a7d2d80	2871a08e6539d37854f909de9a2b46eb7ef5ebe7ba92f9b018aed3539d15e23a
cat-searcher/leandojo-benchmark-4-random	test	964	IsBoundedBilinearMap.contDiff	Mathlib/Analysis/Calculus/ContDiff/Basic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp only [hb.fderiv]	𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...	𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...	((:c ContDiff) (:fv _uniq.142971) (:fv _uniq.142974) ((:c Prod) (:fv _uniq.143094) (:fv _uniq.143207)) ((:c Prod.normedAddCommGroup) (:fv _uniq.143094) (:fv _uniq.143207) (:fv _uniq.143097) (:fv _uniq.143210)) ((:c Prod.normedSpace) (:fv _uniq.142971) (:fv _uniq.143094) (:fv _uniq.143207) ((:c NontriviallyNormedField.t...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.142971))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.142976))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.142971) (:fv _uniq.142976) ((:c Non...	(:app (:c ContDiff) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c Prod) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:fv FV8)))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :expl...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.142971","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.142974","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...	{"children":[{"source":"simp","sourceEnd":8104,"sourceStart":8100,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":8109,"sourceStart":8105,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":8109,"s...	[]	[{"source":"hb.fderiv","source_end":8120,"source_start":8111,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.142971","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.142974","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...	57	9	exact	true	1	32	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	d30baf2dc0ca03bfaf986b655aa2d7d203b6b77c62ddb2d380839ccdc2c24b97	2871a08e6539d37854f909de9a2b46eb7ef5ebe7ba92f9b018aed3539d15e23a	bded750211eb2d9dafe0dc6a93a651bf8537f9a15e2f17a7356288c562255085	1040da3a5585c6c5d5dc1c4fcc13dde96877e126a987c0cffaf9e868f87725ca
cat-searcher/leandojo-benchmark-4-random	test	965	IsBoundedBilinearMap.contDiff	Mathlib/Analysis/Calculus/ContDiff/Basic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact hb.isBoundedLinearMap_deriv.contDiff	𝕜 : Type u_1 inst✝¹⁰ : NontriviallyNormedField 𝕜 D : Type uD inst✝⁹ : NormedAddCommGroup D inst✝⁸ : NormedSpace 𝕜 D E : Type uE inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type uF inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type uG inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜...		((:c ContDiff) (:fv _uniq.142971) (:fv _uniq.142974) ((:c Prod) (:fv _uniq.143094) (:fv _uniq.143207)) ((:c Prod.normedAddCommGroup) (:fv _uniq.143094) (:fv _uniq.143207) (:fv _uniq.143097) (:fv _uniq.143210)) ((:c Prod.normedSpace) (:fv _uniq.142971) (:fv _uniq.143094) (:fv _uniq.143207) ((:c NontriviallyNormedField.t...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.142971))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.142976))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.142971) (:fv _uniq.142976) ((:c Non...	(:app (:c ContDiff) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c Prod) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:fv FV8)))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :expl...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.142971","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.142974","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF...	{"children":[{"source":"exact","sourceEnd":8129,"sourceStart":8124,"tag":"atom"},{"name":"IsBoundedLinearMap.contDiff","semanticRole":"global","source":"hb.isBoundedLinearMap_deriv.contDiff","sourceEnd":8166,"sourceStart":8130,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact hb.isBoundedLinearMap_...	[]	[{"source":"hb.isBoundedLinearMap_deriv.contDiff","source_end":8166,"source_start":8130,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.142971","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.142974","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in...	57	10	exact	true	1	32	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	382167850ad1314c3e2092e168603adfce751709305f22b209a1d72ca6934ba6	1040da3a5585c6c5d5dc1c4fcc13dde96877e126a987c0cffaf9e868f87725ca	457df611467d4a96c26c59ec1d00c616251b4b7dced6fdfc46d715471d54fcdd	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	966	ContinuousLinearEquiv.comp_right_differentiableWithinAt_iff	Mathlib/Analysis/Calculus/FDeriv/Equiv.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	refine ⟨fun H => ?_, fun H => H.comp x iso.differentiableWithinAt (<a>Set.mapsTo_preimage</a> _ s)⟩	𝕜 : Type u_1 inst✝⁸ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type u_3 inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type u_4 inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G G' : Type u_5 inst✝¹ : NormedAddCommGroup G' inst✝ : NormedSpac...	𝕜 : Type u_1 inst✝⁸ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type u_3 inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type u_4 inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G G' : Type u_5 inst✝¹ : NormedAddCommGroup G' inst✝ : NormedSpac...	((:c Iff) ((:c DifferentiableWithinAt) (:fv _uniq.210485) (:fv _uniq.210488) (:fv _uniq.210491) (:fv _uniq.210494) (:fv _uniq.210607) (:fv _uniq.210724) (:fv _uniq.210727) (:fv _uniq.210835) ((:c Function.comp) (:fv _uniq.210491) (:fv _uniq.210610) (:fv _uniq.210724) (:fv _uniq.213696) ((:c DFunLike.coe) ((:c Continuou...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.210485))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCommGroup) (:fv _uniq.210491))"},{"name":"inst✝⁶","sexp":"((:c NormedSpace) (:fv _uniq.210485) (:fv _uniq.210491) ((:c Non...	(:app (:c Iff) (:arg :explicit 0 (:app (:c DifferentiableWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2)))...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.210485","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.210488","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NontriviallyNormedFi...	{"children":[{"source":"refine","sourceEnd":10016,"sourceStart":10010,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":10020,"sourceStart":10017,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":10023,"sourceStart":10020,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","sourc...	[]	[{"source":"⟨fun H => ?_, fun H => H.comp x iso.differentiableWithinAt (mapsTo_preimage _ s)⟩","source_end":10102,"source_start":10017,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.210485","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.210488","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":implicit","context_index":2,"int...	64	4	exact	true	1	33	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	077a90445d8ec5f35a42cf962282b095679133002550eb183accb4d392b0b5ab	4c21c9a69c11c88b6c582ea8d7ea8fe4dec544183555f078f21ed8662300d3ad	e25a31b2162f007cb12d150b21c3dd88b2674206fc2f6708a8d1479e60fbe882	86d79514362854476b2692f1a26c1bb6dc051dcc024d5967bbe0e33b0098fa07
cat-searcher/leandojo-benchmark-4-random	test	967	ContinuousLinearEquiv.comp_right_differentiableWithinAt_iff	Mathlib/Analysis/Calculus/FDeriv/Equiv.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	have : <a>DifferentiableWithinAt</a> 𝕜 ((f ∘ iso) ∘ iso.symm) s (iso x) := by rw [← iso.symm_apply_apply x] at H apply H.comp (iso x) iso.symm.differentiableWithinAt intro y hy simpa only [<a>Set.mem_preimage</a>, <a>ContinuousLinearEquiv.apply_symm_apply</a>] using hy	𝕜 : Type u_1 inst✝⁸ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type u_3 inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type u_4 inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G G' : Type u_5 inst✝¹ : NormedAddCommGroup G' inst✝ : NormedSpac...	𝕜 : Type u_1 inst✝⁸ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type u_3 inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type u_4 inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G G' : Type u_5 inst✝¹ : NormedAddCommGroup G' inst✝ : NormedSpac...	((:c DifferentiableWithinAt) (:fv _uniq.210485) (:fv _uniq.210488) (:fv _uniq.210610) (:fv _uniq.210613) (:fv _uniq.210721) (:fv _uniq.210724) (:fv _uniq.210727) (:fv _uniq.210835) (:fv _uniq.213696) (:fv _uniq.213697) ((:c DFunLike.coe) ((:c ContinuousLinearEquiv) (:fv _uniq.210485) (:fv _uniq.210485) ((:c DivisionSem...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.210485))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCommGroup) (:fv _uniq.210491))"},{"name":"inst✝⁶","sexp":"((:c NormedSpace) (:fv _uniq.210485) (:fv _uniq.210491) ((:c Non...	(:app (:c DifferentiableWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-o...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.210485","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.210488","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NontriviallyNormedFi...	{"children":[{"source":"have","sourceEnd":10109,"sourceStart":10105,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":10110,"sourceStart":10110,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":10110,"sourceStart":10110,"tag":"node"}],"kind":"Lean.Parser.Term.hav...	[]	[{"source":"DifferentiableWithinAt 𝕜 ((f ∘ iso) ∘ iso.symm) s (iso x)","source_end":10176,"source_start":10112,"syntax_kind":"Lean.Parser.Term.app"},{"source":"H","source_end":10223,"source_start":10222,"syntax_kind":"ident"},{"source":"iso.symm_apply_apply x","source_end":10217,"source_start":10195,"syntax_kind":"Lea...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.210485","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.210488","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":implicit","context_index":2,"int...	64	5	exact	true	1	34	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	31d4ffee79c2935a8c3c36a3ffbecd984723b5ce9626130dfbd6f32275c21f85	86d79514362854476b2692f1a26c1bb6dc051dcc024d5967bbe0e33b0098fa07	f1fc566040d1a31b9218d84c92c9006c838776b239069931746aacc20b92dcd4	0fc78349de719b875c034152bbe50e5e38d86391464338c800321ee0d6bc7915
cat-searcher/leandojo-benchmark-4-random	test	968	ContinuousLinearEquiv.comp_right_differentiableWithinAt_iff	Mathlib/Analysis/Calculus/FDeriv/Equiv.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rwa [<a>Function.comp.assoc</a>, iso.self_comp_symm] at this	𝕜 : Type u_1 inst✝⁸ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type u_3 inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type u_4 inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G G' : Type u_5 inst✝¹ : NormedAddCommGroup G' inst✝ : NormedSpac...		((:c DifferentiableWithinAt) (:fv _uniq.210485) (:fv _uniq.210488) (:fv _uniq.210610) (:fv _uniq.210613) (:fv _uniq.210721) (:fv _uniq.210724) (:fv _uniq.210727) (:fv _uniq.210835) (:fv _uniq.213696) (:fv _uniq.213697) ((:c DFunLike.coe) ((:c ContinuousLinearEquiv) (:fv _uniq.210485) (:fv _uniq.210485) ((:c DivisionSem...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.210485))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCommGroup) (:fv _uniq.210491))"},{"name":"inst✝⁶","sexp":"((:c NormedSpace) (:fv _uniq.210485) (:fv _uniq.210491) ((:c Non...	(:app (:c DifferentiableWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-o...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.210485","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.210488","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NontriviallyNormedFi...	{"children":[{"source":"rwa","sourceEnd":10358,"sourceStart":10355,"tag":"atom"},{"children":[{"source":"[","sourceEnd":10360,"sourceStart":10359,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Function.comp.assoc","semanticRole":"global","source":"Function.comp.a...	[]	[{"source":"Function.comp.assoc","source_end":10379,"source_start":10360,"syntax_kind":"ident"},{"source":"this","source_end":10408,"source_start":10404,"syntax_kind":"ident"},{"source":"iso.self_comp_symm","source_end":10399,"source_start":10381,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.210485","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.210488","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":implicit","context_index":2,"int...	64	13	exact	true	1	35	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	a4542edcf10f1086ae0962688dd2287fe7bb65b980b99b893efd33792cff5f05	0fc78349de719b875c034152bbe50e5e38d86391464338c800321ee0d6bc7915	4badbb1c002954412fff7944d3f85c1ac51028bf8c91369b0c7c00474f400130	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	969	ContinuousLinearEquiv.comp_right_differentiableWithinAt_iff	Mathlib/Analysis/Calculus/FDeriv/Equiv.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [← iso.symm_apply_apply x] at H	𝕜 : Type u_1 inst✝⁸ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type u_3 inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type u_4 inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G G' : Type u_5 inst✝¹ : NormedAddCommGroup G' inst✝ : NormedSpac...	𝕜 : Type u_1 inst✝⁸ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type u_3 inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type u_4 inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G G' : Type u_5 inst✝¹ : NormedAddCommGroup G' inst✝ : NormedSpac...	((:c DifferentiableWithinAt) (:fv _uniq.210485) (:fv _uniq.210488) (:fv _uniq.210610) (:fv _uniq.210613) (:fv _uniq.210721) (:fv _uniq.210724) (:fv _uniq.210727) (:fv _uniq.210835) ((:c Function.comp) (:fv _uniq.210610) (:fv _uniq.210491) (:fv _uniq.210724) ((:c Function.comp) (:fv _uniq.210491) (:fv _uniq.210610) (:fv...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.210485))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCommGroup) (:fv _uniq.210491))"},{"name":"inst✝⁶","sexp":"((:c NormedSpace) (:fv _uniq.210485) (:fv _uniq.210491) ((:c Non...	(:app (:c DifferentiableWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-o...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.210485","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.210488","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NontriviallyNormedFi...	{"children":[{"source":"rw","sourceEnd":10189,"sourceStart":10187,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10191,"sourceStart":10190,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":10194,"sourceSt...	[]	[{"source":"H","source_end":10223,"source_start":10222,"syntax_kind":"ident"},{"source":"iso.symm_apply_apply x","source_end":10217,"source_start":10195,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.210485","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.210488","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":implicit","context_index":2,"int...	64	7	exact	true	1	34	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	3f03c68e7d03a86ea0a9bb9960018ba1b48019cd316b322c6f7ff501ddfe2e7b	44a85929a98ca8eecf1f6bfb4f84a63d4789f3127ef96f74f003f02ce43549f6	bf4683b11467729caae5b53ce5f34b6d29eac165b5329f6d6f4ac18ac43a793f	d0ad490d177a8a758bebca1049563c8f14836a2b7aeb5860b22202671da1b5bb
cat-searcher/leandojo-benchmark-4-random	test	970	ContinuousLinearEquiv.comp_right_differentiableWithinAt_iff	Mathlib/Analysis/Calculus/FDeriv/Equiv.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	apply H.comp (iso x) iso.symm.differentiableWithinAt	𝕜 : Type u_1 inst✝⁸ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type u_3 inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type u_4 inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G G' : Type u_5 inst✝¹ : NormedAddCommGroup G' inst✝ : NormedSpac...	𝕜 : Type u_1 inst✝⁸ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type u_3 inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type u_4 inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G G' : Type u_5 inst✝¹ : NormedAddCommGroup G' inst✝ : NormedSpac...	((:c DifferentiableWithinAt) (:fv _uniq.210485) (:fv _uniq.210488) (:fv _uniq.210610) (:fv _uniq.210613) (:fv _uniq.210721) (:fv _uniq.210724) (:fv _uniq.210727) (:fv _uniq.210835) ((:c Function.comp) (:fv _uniq.210610) (:fv _uniq.210491) (:fv _uniq.210724) ((:c Function.comp) (:fv _uniq.210491) (:fv _uniq.210610) (:fv...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.210485))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCommGroup) (:fv _uniq.210491))"},{"name":"inst✝⁶","sexp":"((:c NormedSpace) (:fv _uniq.210485) (:fv _uniq.210491) ((:c Non...	(:app (:c DifferentiableWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance-o...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.210485","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.210488","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NontriviallyNormedFi...	{"children":[{"source":"apply","sourceEnd":10233,"sourceStart":10228,"tag":"atom"},{"children":[{"source":"H.comp","sourceEnd":10240,"sourceStart":10234,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":10242,"sourceStart":10241,"tag":"atom"},{"children":[{"contextIndex":29,"semanticRole":"local",...	[]	[{"source":"H.comp (iso x) iso.symm.differentiableWithinAt","source_end":10280,"source_start":10234,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.210485","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.210488","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":implicit","context_index":2,"int...	64	10	exact	true	1	34	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	3ac792be2e79d3a82fda63ec8a06f17deac69900e6745c1ac160ea3c62553cb8	d0ad490d177a8a758bebca1049563c8f14836a2b7aeb5860b22202671da1b5bb	fccf28b9eecf4793cc7360bd8bce7d773844ea237fa7f8666a8b9d6381cd16c4	2dcd57b63ccce7273a4b62f6ca355e32c8000a0d40a81dc02632d3b4607f8cd7
cat-searcher/leandojo-benchmark-4-random	test	971	ContinuousLinearEquiv.comp_right_differentiableWithinAt_iff	Mathlib/Analysis/Calculus/FDeriv/Equiv.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	intro y hy	𝕜 : Type u_1 inst✝⁸ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type u_3 inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type u_4 inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G G' : Type u_5 inst✝¹ : NormedAddCommGroup G' inst✝ : NormedSpac...	𝕜 : Type u_1 inst✝⁸ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type u_3 inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type u_4 inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G G' : Type u_5 inst✝¹ : NormedAddCommGroup G' inst✝ : NormedSpac...	((:c Set.MapsTo) (:fv _uniq.210610) (:fv _uniq.210491) ((:c DFunLike.coe) ((:c ContinuousLinearEquiv) (:fv _uniq.210485) (:fv _uniq.210485) ((:c DivisionSemiring.toSemiring) (:fv _uniq.210485) ((:c Semifield.toDivisionSemiring) (:fv _uniq.210485) ((:c Field.toSemifield) (:fv _uniq.210485) ((:c NormedField.toField) (:fv...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.210485))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCommGroup) (:fv _uniq.210491))"},{"name":"inst✝⁶","sexp":"((:c NormedSpace) (:fv _uniq.210485) (:fv _uniq.210491) ((:c Non...	(:app (:c Set.MapsTo) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV2)) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c ContinuousLinearEquiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :expli...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.210485","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.210488","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NontriviallyNormedFi...	{"children":[{"source":"intro","sourceEnd":10290,"sourceStart":10285,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":10292,"sourceStart":10291,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hy","sourceEnd":10295,"sourceStart":10293,"tag":"identifier"}],"kind":"null","sou...	[{"role":"fresh_name","source":"y","source_end":10292,"source_start":10291,"syntax_kind":"ident"},{"role":"fresh_name","source":"hy","source_end":10295,"source_start":10293,"syntax_kind":"ident"}]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.210485","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.210488","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":implicit","context_index":2,"int...	64	11	exact	true	1	34	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	a9150547c506a7dae7ee8dd750a74575685ad3e867eb2e816a81b381e6d01aba	2dcd57b63ccce7273a4b62f6ca355e32c8000a0d40a81dc02632d3b4607f8cd7	69ac7ac9f4300ee3290568559761b10f79f65930316d628484707cb4cb9d79dc	59e2b342c7220212e72114970fba8a0e6149a46424d768b902499569da55899e
cat-searcher/leandojo-benchmark-4-random	test	972	ContinuousLinearEquiv.comp_right_differentiableWithinAt_iff	Mathlib/Analysis/Calculus/FDeriv/Equiv.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simpa only [<a>Set.mem_preimage</a>, <a>ContinuousLinearEquiv.apply_symm_apply</a>] using hy	𝕜 : Type u_1 inst✝⁸ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝⁷ : NormedAddCommGroup E inst✝⁶ : NormedSpace 𝕜 E F : Type u_3 inst✝⁵ : NormedAddCommGroup F inst✝⁴ : NormedSpace 𝕜 F G : Type u_4 inst✝³ : NormedAddCommGroup G inst✝² : NormedSpace 𝕜 G G' : Type u_5 inst✝¹ : NormedAddCommGroup G' inst✝ : NormedSpac...		((:c Membership.mem) (:fv _uniq.210491) ((:c Set) (:fv _uniq.210491)) ((:c Set.instMembership) (:fv _uniq.210491)) ((:c DFunLike.coe) ((:c ContinuousLinearEquiv) (:fv _uniq.210485) (:fv _uniq.210485) ((:c DivisionSemiring.toSemiring) (:fv _uniq.210485) ((:c Semifield.toDivisionSemiring) (:fv _uniq.210485) ((:c Field.to...	[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.210485))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCommGroup) (:fv _uniq.210491))"},{"name":"inst✝⁶","sexp":"((:c NormedSpace) (:fv _uniq.210485) (:fv _uniq.210491) ((:c Non...	(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 3 (:app (:c DFunLike.coe)...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.210485","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.210488","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NontriviallyNormedFi...	{"children":[{"source":"simpa","sourceEnd":10305,"sourceStart":10300,"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":"mem_preimage","source_end":10324,"source_start":10312,"syntax_kind":"ident"},{"source":"apply_symm_apply","source_end":10342,"source_start":10326,"syntax_kind":"ident"},{"source":"hy","source_end":10352,"source_start":10350,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.210485","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.210488","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":implicit","context_index":2,"int...	64	12	exact	true	1	36	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	f5c3d5935cdbc92ccdfaaeb334c34dfb9a91f8e5a6d084b6b5b73feeb6940fed	59e2b342c7220212e72114970fba8a0e6149a46424d768b902499569da55899e	4eafe20d15daf632aa93d880ce2c932ac9effa6c7fb0b7b25a88d28c324587d5	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	973	CategoryTheory.Adjunction.leftAdjointUniq_trans_app	Mathlib/CategoryTheory/Adjunction/Unique.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [← <a>CategoryTheory.Adjunction.leftAdjointUniq_trans</a> adj1 adj2 adj3]	C : Type u_1 D : Type u_2 inst✝¹ : Category.{u_3, u_1} C inst✝ : Category.{u_4, u_2} D F F' F'' : C ⥤ D G : D ⥤ C adj1 : F ⊣ G adj2 : F' ⊣ G adj3 : F'' ⊣ G x : C ⊢ (adj1.leftAdjointUniq adj2).hom.app x ≫ (adj2.leftAdjointUniq adj3).hom.app x = (adj1.leftAdjointUniq adj3).hom.app x	C : Type u_1 D : Type u_2 inst✝¹ : Category.{u_3, u_1} C inst✝ : Category.{u_4, u_2} D F F' F'' : C ⥤ D G : D ⥤ C adj1 : F ⊣ G adj2 : F' ⊣ G adj3 : F'' ⊣ G x : C ⊢ (adj1.leftAdjointUniq adj2).hom.app x ≫ (adj2.leftAdjointUniq adj3).hom.app x = ((adj1.leftAdjointUniq adj2).hom ≫ (adj2.leftAdjointUniq adj3).hom).app ...	((:c Eq) ((:c Quiver.Hom) (:fv _uniq.31461) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.31461) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.31461) (:fv _uniq.31469))) ((:c Prefunctor.obj) (:fv _uniq.31458) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.31458) ((:c CategoryTheory.Catego...	[{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"D","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.31458))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.31461))"},{"name":"F","sexp":"((:c CategoryTheory.Functor) (:fv _uniq.31458) (:fv _uniq.31465) (:f...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31458","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31461","is_instance":false,"is_let":false,"name":"D","sexp":"(:sort Type)"},{"binder_role":":instance-impli...	{"children":[{"source":"rw","sourceEnd":7765,"sourceStart":7763,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7767,"sourceStart":7766,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":7770,"sourceStart":...	[]	[{"source":"leftAdjointUniq_trans adj1 adj2 adj3","source_end":7807,"source_start":7771,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31458","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31461","is_instance":false,"is_let":false,"user_name":"D"},{"binder_role":":instance-implicit","context_index":2,"internal_n...	26	4	exact	true	1	12	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	891cfaed3cc0cf8c328c208ef2c475b66d1fcff526ad24054e4895a338e6d6b8	4755bac351ce8c863a2c94ebd8ff99b6a62af34987d6e8654b4e4862e034413f	cf965acec0d6301a746935e23023818db34645fb8af83f47f1473a922b7b845e	ae20f249cc6ac862a11b7bd83cca94506a4de84de782ea0b053f9aaf011aaa5f
cat-searcher/leandojo-benchmark-4-random	test	974	CategoryTheory.Adjunction.leftAdjointUniq_trans_app	Mathlib/CategoryTheory/Adjunction/Unique.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rfl	C : Type u_1 D : Type u_2 inst✝¹ : Category.{u_3, u_1} C inst✝ : Category.{u_4, u_2} D F F' F'' : C ⥤ D G : D ⥤ C adj1 : F ⊣ G adj2 : F' ⊣ G adj3 : F'' ⊣ G x : C ⊢ (adj1.leftAdjointUniq adj2).hom.app x ≫ (adj2.leftAdjointUniq adj3).hom.app x = ((adj1.leftAdjointUniq adj2).hom ≫ (adj2.leftAdjointUniq adj3).hom).app ...		((:c Eq) ((:c Quiver.Hom) (:fv _uniq.31461) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.31461) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.31461) (:fv _uniq.31469))) ((:c Prefunctor.obj) (:fv _uniq.31458) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.31458) ((:c CategoryTheory.Catego...	[{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"D","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.31458))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.31461))"},{"name":"F","sexp":"((:c CategoryTheory.Functor) (:fv _uniq.31458) (:fv _uniq.31465) (:f...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31458","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31461","is_instance":false,"is_let":false,"name":"D","sexp":"(:sort Type)"},{"binder_role":":instance-impli...	{"children":[{"source":"rfl","sourceEnd":7814,"sourceStart":7811,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":7814,"sourceStart":7811,"tag":"node"}	[]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31458","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31461","is_instance":false,"is_let":false,"user_name":"D"},{"binder_role":":instance-implicit","context_index":2,"internal_n...	26	7	exact	true	1	12	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	ecf9b0d67e3ff4c208d08495846ab5d380ad094920627a937017b67f28135207	ae20f249cc6ac862a11b7bd83cca94506a4de84de782ea0b053f9aaf011aaa5f	5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	975	ContinuousMap.continuous_comp_left	Mathlib/Topology/CompactOpen.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simpa only [<a>Set.mapsTo_image_iff</a>] using <a>ContinuousMap.isOpen_setOf_mapsTo</a> (hK.image f.2) hU	α : Type u_1 X : Type u_2 Y : Type u_3 Z : Type u_4 T : Type u_5 inst✝³ : TopologicalSpace X inst✝² : TopologicalSpace Y inst✝¹ : TopologicalSpace Z inst✝ : TopologicalSpace T K✝ : Set X U✝ : Set Y f : C(X, Y) K : Set X hK : IsCompact K U : Set Z hU : IsOpen U ⊢ IsOpen {x \| MapsTo (⇑(x.comp f)) K U}		((:c IsOpen) ((:c ContinuousMap) (:fv _uniq.18272) (:fv _uniq.18275) (:fv _uniq.18284) (:fv _uniq.18287)) ((:c ContinuousMap.compactOpen) (:fv _uniq.18272) (:fv _uniq.18275) (:fv _uniq.18284) (:fv _uniq.18287)) ((:c setOf) ((:c ContinuousMap) (:fv _uniq.18272) (:fv _uniq.18275) (:fv _uniq.18284) (:fv _uniq.18287)) (:la...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"X","sexp":"(:sort (+ u_2 1))"},{"name":"Y","sexp":"(:sort (+ u_3 1))"},{"name":"Z","sexp":"(:sort (+ u_4 1))"},{"name":"T","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.18269))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:...	(:app (:c IsOpen) (:arg :implicit-type 0 (:app (:c ContinuousMap) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV3))))))) (:arg :ins...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18266","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18269","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","con...	{"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":4684,"sourceStart":4679,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":...	[]	[{"source":"mapsTo_image_iff","source_end":4707,"source_start":4691,"syntax_kind":"ident"},{"source":"isOpen_setOf_mapsTo (hK.image f.2) hU","source_end":4752,"source_start":4715,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18266","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18269","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	29	2	exact	true	1	16	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	89b503c36f7b8e5cdce12ea077c5a62de37637fa80d9ce50302b67e504b2c2eb	6b30d34d7a7034e40df2708a140530296e607d3805e8dcd43bdb536ab013c4e3	e711cb1deabd7af0e44bf631090f0db88ae14cf404678de1c571114867befdb1	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	976	CategoryTheory.NatTrans.CommShift.app_shift	Mathlib/CategoryTheory/Shift/CommShift.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	erw [<a>CategoryTheory.NatTrans.CommShift.comm_app_assoc</a>, <a>CategoryTheory.Iso.hom_inv_id_app</a>, <a>CategoryTheory.Category.comp_id</a>]	C : Type u_1 D : Type u_2 E : Type u_3 J : Type u_4 inst✝¹⁵ : Category.{u_7, u_1} C inst✝¹⁴ : Category.{u_6, u_2} D inst✝¹³ : Category.{?u.111501, u_3} E inst✝¹² : Category.{?u.111505, u_4} J F₁ F₂ F₃ : C ⥤ D τ : F₁ ⟶ F₂ τ' : F₂ ⟶ F₃ e : F₁ ≅ F₂ G G' : D ⥤ E τ'' : G ⟶ G' H : E ⥤ J A : Type u_5 inst✝¹¹ : AddMonoid A ins...		((:c Eq) ((:c Quiver.Hom) (:fv _uniq.111484) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.111484) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.111484) (:fv _uniq.111498))) ((:c Prefunctor.obj) (:fv _uniq.111481) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.111481) ((:c CategoryTheory....	[{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"D","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"J","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹⁵","sexp":"((:c CategoryTheory.Category) (:fv _uniq.111481))"},{"name":"inst✝¹⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.111484))"},{"n...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.111481","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.111484","is_instance":false,"is_let":false,"name":"D","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"children":[{"children":[{"children":[{"source":"erw","sourceEnd":12211,"sourceStart":12208,"tag":"atom"},{"children":[{"source":"[","sourceEnd":12213,"sourceStart":12212,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"CategoryTheory.NatTrans.CommShi...	[]	[{"source":"comm_app_assoc","source_end":12227,"source_start":12213,"syntax_kind":"ident"},{"source":"Iso.hom_inv_id_app","source_end":12247,"source_start":12229,"syntax_kind":"ident"},{"source":"Category.comp_id","source_end":12265,"source_start":12249,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.111481","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.111484","is_instance":false,"is_let":false,"user_name":"D"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	49	2	exact	true	1	33	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	2492c58ce247af9fd2d140b576b1595de3d57f682cbb8ebec435ab20b1c98845	ee8d174ca6ecebc1c7d7505c8749ffc9cf8cea5240166f8b4f859414e3eb39f9	4510e7d598769f506843fdf4ed032ef0544d296b175801b0d8c35a43446e962d	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	977	Prod.ext_iff	Mathlib/Data/Prod/Basic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>Prod.mk.inj_iff</a>]	α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 p q : α × β ⊢ p = q ↔ p.fst = q.fst ∧ p.snd = q.snd		((:c Iff) ((:c Eq) ((:c Prod) (:fv _uniq.2662) (:fv _uniq.2665)) (:fv _uniq.2706) (:fv _uniq.2707)) ((:c And) ((:c Eq) (:fv _uniq.2662) ((:c Prod.fst) (:fv _uniq.2662) (:fv _uniq.2665) (:fv _uniq.2706)) ((:c Prod.fst) (:fv _uniq.2662) (:fv _uniq.2665) (:fv _uniq.2707))) ((:c Eq) (:fv _uniq.2665) ((:c Prod.snd) (:fv _un...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"p","sexp":"((:c Prod) (:fv _uniq.2662) (:fv _uniq.2665))"},{"name":"q","sexp":"((:c Prod) (:fv _uniq.2662) (:fv _uniq.2665))"}]	(:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))) (:arg :explicit 1 (:fv FV5)) (:arg :explicit 2 (:fv FV6)))) (:arg :explicit 1 (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2662","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2665","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte...	{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":4684,"sourceStart":4682,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4686,"sourceStart":4685,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag...	[]	[{"source":"mk.inj_iff","source_end":4696,"source_start":4686,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2662","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2665","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq...	43	2	exact	true	1	6	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	44f19a8d22342d902f48bf3952b0247ba7352eec5b59eca21a1a94283abc51fe	1b5cf9d46c76fdbdbd5abd7f616acca5b07c2e27fe6e0b739946eca002683489	362803c5fa02a88be70bf39134a14a32151bcde691c0c0cd874feaad2db67a7c	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	978	List.count_singleton	.lake/packages/batteries/Batteries/Data/List/Count.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp	α : Type u_1 inst✝ : DecidableEq α a : α ⊢ count a [a] = 1		((:c Eq) (:c Nat) ((:c List.count) (:fv _uniq.9641) ((:c instBEqOfDecidableEq) (:fv _uniq.9641) (:fv _uniq.9648)) (:fv _uniq.9705) ((:c List.cons) (:fv _uniq.9641) (:fv _uniq.9705) ((:c List.nil) (:fv _uniq.9641)))) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.9641))"},{"name":"a","sexp":"(:fv _uniq.9641)"}]	(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c List.count) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c BEq) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c List.cons) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 ...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9641","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.9648","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :explic...	{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":5460,"sourceStart":5456,"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.9641","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.9648","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":3,"internal_...	37	2	exact	true	1	3	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	46cb3b676d59317b7a9475b59d6757d188526d131a78565f7cf8cc8a7e61636d	2a8df6d25495d0190158618cd4af8d3de6f26e1476ac54a9999692262b00e643	8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	979	Substring.Valid.bsize	.lake/packages/batteries/Batteries/Data/String/Lemmas.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp [h.bsize, h.toString]	x✝ : Substring h✝ : x✝.Valid l m r : List Char h : ValidFor l m r x✝ ⊢ x✝.bsize = utf8Len x✝.toString.data		((:c Eq) (:c Nat) ((:c Substring.bsize) (:fv _uniq.169310)) ((:c String.utf8Len) ((:c String.data) ((:c Substring.toString) (:fv _uniq.169310)))))	[{"name":"x✝","sexp":"(:c Substring)"},{"name":"h✝","sexp":"((:c Substring.Valid) (:fv _uniq.169310))"},{"name":"l","sexp":"((:c List) (:c Char))"},{"name":"m","sexp":"((:c List) (:c Char))"},{"name":"r","sexp":"((:c List) (:c Char))"},{"name":"h","sexp":"((:c Substring.ValidFor) (:fv _uniq.169388) (:fv _uniq.169389) (...	(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Substring.bsize) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 2 (:app (:c String.utf8Len) (:arg :explicit 0 (:app (:c String.data) (:arg :explicit 0 (:app (:c Substring.toString) (:arg :explicit 0 (:fv FV1)))))))))	[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.169310","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Substring)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.169311","is_instance":false,"is_let":false,"name":"h✝","sexp":"(:app (:c Substring.Valid) (:arg :explic...	{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":42445,"sourceStart":42441,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...	[]	[{"source":"h.bsize","source_end":42454,"source_start":42447,"syntax_kind":"ident"},{"source":"h.toString","source_end":42466,"source_start":42456,"syntax_kind":"ident"}]	[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.169310","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.169311","is_instance":false,"is_let":false,"user_name":"h✝"},{"binder_role":":explicit","context_index":3,"internal_name":...	191	2	exact	true	1	6	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	079bd9821b10d76e96e9811528b92901635fcdf199cbb6b91fda8408dea7825b	ffd41f6631b16db84ddd4d5680fc0746eaf7ae31aa7bfd36754a01fdb6b26814	6cd2e8c9f75100f313f214a52bfadca2072a5a9c3a01e720df2345385083f751	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	980	MeasureTheory.integral_zero	Mathlib/MeasureTheory/Integral/Bochner.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	by_cases hG : <a>CompleteSpace</a> G	α : Type u_1 E : Type u_2 F : Type u_3 𝕜 : Type u_4 inst✝⁹ : NormedAddCommGroup E inst✝⁸ : NormedSpace ℝ E hE : CompleteSpace E inst✝⁷ : NontriviallyNormedField 𝕜 inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : SMulCommClass ℝ 𝕜 E inst✝⁴ : NormedAddCommGroup F inst✝³ : NormedSpace ℝ F inst✝² : CompleteSpace F G : Type u_5 inst✝¹...	case pos α : Type u_1 E : Type u_2 F : Type u_3 𝕜 : Type u_4 inst✝⁹ : NormedAddCommGroup E inst✝⁸ : NormedSpace ℝ E hE : CompleteSpace E inst✝⁷ : NontriviallyNormedField 𝕜 inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : SMulCommClass ℝ 𝕜 E inst✝⁴ : NormedAddCommGroup F inst✝³ : NormedSpace ℝ F inst✝² : CompleteSpace F G : Type u...	((:c Eq) (:fv _uniq.615847) ((:c MeasureTheory.integral) (:fv _uniq.613070) (:fv _uniq.615847) (:fv _uniq.615850) (:fv _uniq.615954) (:fv _uniq.615965) (:fv _uniq.615974) (:lambda _ (:fv _uniq.613070) ((:c OfNat.ofNat) (:fv _uniq.615847) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.615847) ((:c NegZeroClass.toZero) (:fv _un...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.613073))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.613073) (:c Real.norme...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV13)) (:arg :explicit 1 (:app (:c MeasureTheory.integral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV13)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV13))))) (:arg :instance 3 (:instance-of (:app (:c NormedSpace) ...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.613070","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.613073","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"by_cases","sourceEnd":40472,"sourceStart":40464,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hG","sourceEnd":40475,"sourceStart":40473,"tag":"identifier"},{"source":":","sourceEnd":40477,"sourceStart":40476,"tag":"atom"}],"kind":"null","source":"hG :","sourceEnd":40477,"so...	[]	[{"source":"CompleteSpace G","source_end":40493,"source_start":40478,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.613070","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.613073","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	231	4	exact	true	1	20	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	a7d193ff78d779441ff761944323ea3f183a169353912c275a913d0d1e3b5787	8e1d43ed3961efb4d3ca71737c4926facb1efdfb7816a106dbd87ebc9ceae10e	73d689db4fc67abcd8c179d795ffbe2babb764e3b1583a020c535a420dfe4586	e1c8381349e0a50cbd48b6e4c7f62ae8496c5fa23a962f02104e18fcc9ce4d50
cat-searcher/leandojo-benchmark-4-random	test	981	MeasureTheory.integral_zero	Mathlib/MeasureTheory/Integral/Bochner.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp only [<a>MeasureTheory.integral</a>, hG, <a>MeasureTheory.L1.integral</a>]	case pos α : Type u_1 E : Type u_2 F : Type u_3 𝕜 : Type u_4 inst✝⁹ : NormedAddCommGroup E inst✝⁸ : NormedSpace ℝ E hE : CompleteSpace E inst✝⁷ : NontriviallyNormedField 𝕜 inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : SMulCommClass ℝ 𝕜 E inst✝⁴ : NormedAddCommGroup F inst✝³ : NormedSpace ℝ F inst✝² : CompleteSpace F G : Type u...	case pos α : Type u_1 E : Type u_2 F : Type u_3 𝕜 : Type u_4 inst✝⁹ : NormedAddCommGroup E inst✝⁸ : NormedSpace ℝ E hE : CompleteSpace E inst✝⁷ : NontriviallyNormedField 𝕜 inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : SMulCommClass ℝ 𝕜 E inst✝⁴ : NormedAddCommGroup F inst✝³ : NormedSpace ℝ F inst✝² : CompleteSpace F G : Type u...	((:c Eq) (:fv _uniq.615847) ((:c MeasureTheory.integral) (:fv _uniq.613070) (:fv _uniq.615847) (:fv _uniq.615850) (:fv _uniq.615954) (:fv _uniq.615965) (:fv _uniq.615974) (:lambda _ (:fv _uniq.613070) ((:c OfNat.ofNat) (:fv _uniq.615847) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.615847) ((:c NegZeroClass.toZero) (:fv _un...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.613073))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.613073) (:c Real.norme...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV13)) (:arg :explicit 1 (:app (:c MeasureTheory.integral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV13)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV13))))) (:arg :instance 3 (:instance-of (:app (:c NormedSpace) ...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.613070","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.613073","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"simp","sourceEnd":40503,"sourceStart":40499,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":40508,"sourceStart":40504,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":405...	[]	[{"source":"integral","source_end":40518,"source_start":40510,"syntax_kind":"ident"},{"source":"hG","source_end":40522,"source_start":40520,"syntax_kind":"ident"},{"source":"L1.integral","source_end":40535,"source_start":40524,"syntax_kind":"ident"}]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.613070","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.613073","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	231	9	exact	true	1	21	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	99c34d2e765b0ea0832360c366fbed672231e6503ee3a5eb292111c4b3b3bf53	f19fc79c08e326ba926c97ecc547463881638cb32488bd65fbeca3f1836be74c	01d441d6bff320d0c3de861d5d8b66a63adbb78de02def9a9e593efcf58b6214	764d809b5fc686d0dedc45c4d0b0b9113b92b4f603b284022ec8443427526dd9
cat-searcher/leandojo-benchmark-4-random	test	982	MeasureTheory.integral_zero	Mathlib/MeasureTheory/Integral/Bochner.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact <a>MeasureTheory.setToFun_zero</a> (<a>MeasureTheory.dominatedFinMeasAdditive_weightedSMul</a> μ)	case pos α : Type u_1 E : Type u_2 F : Type u_3 𝕜 : Type u_4 inst✝⁹ : NormedAddCommGroup E inst✝⁸ : NormedSpace ℝ E hE : CompleteSpace E inst✝⁷ : NontriviallyNormedField 𝕜 inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : SMulCommClass ℝ 𝕜 E inst✝⁴ : NormedAddCommGroup F inst✝³ : NormedSpace ℝ F inst✝² : CompleteSpace F G : Type u...		((:c Eq) (:fv _uniq.615847) ((:c dite) (:fv _uniq.615847) (:c True) (:c instDecidableTrue) (:lambda h (:c True) ((:c dite) (:fv _uniq.615847) ((:c MeasureTheory.Integrable) (:fv _uniq.615847) (:fv _uniq.615850) (:fv _uniq.613070) (:fv _uniq.615965) (:lambda _ (:fv _uniq.613070) ((:c OfNat.ofNat) (:fv _uniq.615847) (:li...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.613073))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.613073) (:c Real.norme...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV13)) (:arg :explicit 1 (:app (:c dite) (:arg :implicit-type 0 (:fv FV13)) (:arg :explicit 1 (:c True)) (:arg :instance 2 (:instance-of (:app (:c Decidable) (:arg :explicit 0 (:c True))))) (:arg :explicit 3 (:lambda h :explicit (:c True) (:app (:c dite) (:arg :implicit-type 0 ...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.613070","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.613073","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"exact","sourceEnd":40546,"sourceStart":40541,"tag":"atom"},{"children":[{"name":"MeasureTheory.setToFun_zero","semanticRole":"global","source":"setToFun_zero","sourceEnd":40560,"sourceStart":40547,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":40562,"sourceStart":40561,"...	[]	[{"source":"setToFun_zero (dominatedFinMeasAdditive_weightedSMul μ)","source_end":40603,"source_start":40547,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.613070","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.613073","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	231	10	exact	true	1	21	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	a06d7b7011db96251e4f0336d1c98a869f7a0233ccbcb35078646854bd5ab4ab	764d809b5fc686d0dedc45c4d0b0b9113b92b4f603b284022ec8443427526dd9	3dc14a6accbe8c69a075fa0a117ad3c13d031691f5dc2080ed199dcf0d9cd1b8	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	983	MeasureTheory.integral_zero	Mathlib/MeasureTheory/Integral/Bochner.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp [<a>MeasureTheory.integral</a>, hG]	case neg α : Type u_1 E : Type u_2 F : Type u_3 𝕜 : Type u_4 inst✝⁹ : NormedAddCommGroup E inst✝⁸ : NormedSpace ℝ E hE : CompleteSpace E inst✝⁷ : NontriviallyNormedField 𝕜 inst✝⁶ : NormedSpace 𝕜 E inst✝⁵ : SMulCommClass ℝ 𝕜 E inst✝⁴ : NormedAddCommGroup F inst✝³ : NormedSpace ℝ F inst✝² : CompleteSpace F G : Type u...		((:c Eq) (:fv _uniq.615847) ((:c MeasureTheory.integral) (:fv _uniq.613070) (:fv _uniq.615847) (:fv _uniq.615850) (:fv _uniq.615954) (:fv _uniq.615965) (:fv _uniq.615974) (:lambda _ (:fv _uniq.613070) ((:c OfNat.ofNat) (:fv _uniq.615847) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.615847) ((:c NegZeroClass.toZero) (:fv _un...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.613073))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.613073) (:c Real.norme...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV13)) (:arg :explicit 1 (:app (:c MeasureTheory.integral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV13)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV13))))) (:arg :instance 3 (:instance-of (:app (:c NormedSpace) ...	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.613070","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.613073","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":40613,"sourceStart":40609,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...	[]	[{"source":"integral","source_end":40623,"source_start":40615,"syntax_kind":"ident"},{"source":"hG","source_end":40627,"source_start":40625,"syntax_kind":"ident"}]	[{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.613070","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.613073","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	231	13	exact	true	1	21	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	011bfb7ee74159633d916ae36ffb2f05fdea6ce0ad7fa2b9ac23c0c76d013983	a5a6715b14be0522a077afb7be236ccc1003b8352f3000cce9e5e40ad6351cc0	d59051a8d1df633dc0a9d35882b8d89c536e470b6349b10dedf6656a0f8d98d9	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	987	Finset.inv_smul_finset_distrib	Mathlib/Data/Finset/Pointwise.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	ext	F : Type u_1 α : Type u_2 β : Type u_3 γ : Type u_4 inst✝³ : DecidableEq β inst✝² : Group α inst✝¹ : MulAction α β s✝ t : Finset β a✝ : α b : β inst✝ : DecidableEq α a : α s : Finset α ⊢ (a • s)⁻¹ = op a⁻¹ • s⁻¹	case a F : Type u_1 α : Type u_2 β : Type u_3 γ : Type u_4 inst✝³ : DecidableEq β inst✝² : Group α inst✝¹ : MulAction α β s✝ t : Finset β a✝¹ : α b : β inst✝ : DecidableEq α a : α s : Finset α a✝ : α ⊢ a✝ ∈ (a • s)⁻¹ ↔ a✝ ∈ op a⁻¹ • s⁻¹	((:c Eq) ((:c Finset) (:fv _uniq.392007)) ((:c Inv.inv) ((:c Finset) (:fv _uniq.392007)) ((:c Finset.inv) (:fv _uniq.392007) (:fv _uniq.392345) ((:c InvOneClass.toInv) (:fv _uniq.392007) ((:c DivInvOneMonoid.toInvOneClass) (:fv _uniq.392007) ((:c DivisionMonoid.toDivInvOneMonoid) (:fv _uniq.392007) ((:c Group.toDivisio...	[{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝³","sexp":"((:c DecidableEq) (:fv _uniq.392010))"},{"name":"inst✝²","sexp":"((:c Group) (:fv _uniq.392007))"},{"name":"inst✝¹","sexp":"((:c MulAc...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Inv.inv) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c Inv) (:arg :explicit 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV1))))))) (:arg :e...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.392004","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.392007","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"ext","sourceEnd":86796,"sourceStart":86793,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":86796,"sourceStart":86793,"tag":"node"}	[]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.392004","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.392007","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	939	4	exact	true	1	14	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	55ba4d5827ae4bb7513ca6f2c556716121e722ed589251650f8978a988833e06	11e3b72c5fa0ba9a3882a5690bdf6fa6ad1d79b81456fe18abceba2d96d34df9	a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de	e2e4c0c86eaa29115d64aa3168ba75b5603f79ff726c64a393efb9dfb2047aaa
cat-searcher/leandojo-benchmark-4-random	test	988	Finset.inv_smul_finset_distrib	Mathlib/Data/Finset/Pointwise.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp [← <a>Finset.inv_smul_mem_iff</a>]	case a F : Type u_1 α : Type u_2 β : Type u_3 γ : Type u_4 inst✝³ : DecidableEq β inst✝² : Group α inst✝¹ : MulAction α β s✝ t : Finset β a✝¹ : α b : β inst✝ : DecidableEq α a : α s : Finset α a✝ : α ⊢ a✝ ∈ (a • s)⁻¹ ↔ a✝ ∈ op a⁻¹ • s⁻¹		((:c Iff) ((:c Membership.mem) (:fv _uniq.392007) ((:c Finset) (:fv _uniq.392007)) ((:c Finset.instMembership) (:fv _uniq.392007)) (:fv _uniq.394114) ((:c Inv.inv) ((:c Finset) (:fv _uniq.392007)) ((:c Finset.inv) (:fv _uniq.392007) (:fv _uniq.392345) ((:c InvOneClass.toInv) (:fv _uniq.392007) ((:c DivInvOneMonoid.toIn...	[{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝³","sexp":"((:c DecidableEq) (:fv _uniq.392010))"},{"name":"inst✝²","sexp":"((:c Group) (:fv _uniq.392007))"},{"name":"inst✝¹","sexp":"((:c MulAc...	(:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV1))))))) (:...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.392004","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.392007","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"simp","sourceEnd":86802,"sourceStart":86798,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":86804,"sourceStart":86803,"tag":"a...	[]	[{"source":"inv_smul_mem_iff","source_end":86824,"source_start":86808,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.392004","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.392007","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	939	6	exact	true	1	15	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	7f301e38e010fc90faadbed333e6e40f75a38e8de3942088f11fe56ebafccd0a	e2e4c0c86eaa29115d64aa3168ba75b5603f79ff726c64a393efb9dfb2047aaa	919ae11dd91702e8983183bcea6da788a8116c2fc8a7b3de368a51b964cdd4ae	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	989	CategoryTheory.LocalizerMorphism.isEquivalence_imp	Mathlib/CategoryTheory/Localization/LocalizerMorphism.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	let E₁ := <a>CategoryTheory.Localization.uniq</a> L₁ L₁' W₁	C₁ : Type u₁ C₂ : Type u₂ C₃ : Type u₃ D₁ : Type u₄ D₂ : Type u₅ D₃ : Type u₆ inst✝¹⁴ : Category.{v₁, u₁} C₁ inst✝¹³ : Category.{v₂, u₂} C₂ inst✝¹² : Category.{v₃, u₃} C₃ inst✝¹¹ : Category.{v₄, u₄} D₁ inst✝¹⁰ : Category.{v₅, u₅} D₂ inst✝⁹ : Category.{v₆, u₅} D₂ W₁ : MorphismProperty C₁ W₂ : MorphismProperty C₂ W₃ : Mo...	C₁ : Type u₁ C₂ : Type u₂ C₃ : Type u₃ D₁ : Type u₄ D₂ : Type u₅ D₃ : Type u₆ inst✝¹⁴ : Category.{v₁, u₁} C₁ inst✝¹³ : Category.{v₂, u₂} C₂ inst✝¹² : Category.{v₃, u₃} C₃ inst✝¹¹ : Category.{v₄, u₄} D₁ inst✝¹⁰ : Category.{v₅, u₅} D₂ inst✝⁹ : Category.{v₆, u₅} D₂ W₁ : MorphismProperty C₁ W₂ : MorphismProperty C₂ W₃ : Mo...	((:c CategoryTheory.Functor.IsEquivalence) (:fv _uniq.11744) (:fv _uniq.11749) (:fv _uniq.11746) (:fv _uniq.11752) (:fv _uniq.11896))	[{"name":"C₁","sexp":"(:sort (+ u₁ 1))"},{"name":"C₂","sexp":"(:sort (+ u₂ 1))"},{"name":"C₃","sexp":"(:sort (+ u₃ 1))"},{"name":"D₁","sexp":"(:sort (+ u₄ 1))"},{"name":"D₂","sexp":"(:sort (+ u₅ 1))"},{"name":"D₃","sexp":"(:sort (+ u₆ 1))"},{"name":"inst✝¹⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.10966))"},{"...	(:app (:c CategoryTheory.Functor.IsEquivalence) (:arg :implicit-type 0 (:fv FV22)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV22))))) (:arg :implicit-type 2 (:fv FV23)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV23))))) (:...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10966","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10968","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"let","sourceEnd":4184,"sourceStart":4181,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"E₁","sourceEnd":4189,"sourceStart":4185,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"so...	[]	[{"source":"Localization.uniq L₁ L₁' W₁","source_end":4226,"source_start":4193,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10966","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10968","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	20	4	exact	true	1	33	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	433ff7adb20fdd8b4d47da2c8bd7b5dea6063801439b9838d5aaba1fb0154e5a	0b2d756d7cd26ce2441026ee5344511222dbf1d7bc7997edcfb53fb4c3706010	64cf9b19d6192241c3714f37aab9b03445f713d457222e80b4b081db96ab19b1	c6b162352f3c6c4b43fccdf0c6a3055ce632383e9cf66a6ec8f87b88b53657a6
cat-searcher/leandojo-benchmark-4-random	test	990	CategoryTheory.LocalizerMorphism.isEquivalence_imp	Mathlib/CategoryTheory/Localization/LocalizerMorphism.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	let E₂ := <a>CategoryTheory.Localization.uniq</a> L₂ L₂' W₂	C₁ : Type u₁ C₂ : Type u₂ C₃ : Type u₃ D₁ : Type u₄ D₂ : Type u₅ D₃ : Type u₆ inst✝¹⁴ : Category.{v₁, u₁} C₁ inst✝¹³ : Category.{v₂, u₂} C₂ inst✝¹² : Category.{v₃, u₃} C₃ inst✝¹¹ : Category.{v₄, u₄} D₁ inst✝¹⁰ : Category.{v₅, u₅} D₂ inst✝⁹ : Category.{v₆, u₅} D₂ W₁ : MorphismProperty C₁ W₂ : MorphismProperty C₂ W₃ : Mo...	C₁ : Type u₁ C₂ : Type u₂ C₃ : Type u₃ D₁ : Type u₄ D₂ : Type u₅ D₃ : Type u₆ inst✝¹⁴ : Category.{v₁, u₁} C₁ inst✝¹³ : Category.{v₂, u₂} C₂ inst✝¹² : Category.{v₃, u₃} C₃ inst✝¹¹ : Category.{v₄, u₄} D₁ inst✝¹⁰ : Category.{v₅, u₅} D₂ inst✝⁹ : Category.{v₆, u₅} D₂ W₁ : MorphismProperty C₁ W₂ : MorphismProperty C₂ W₃ : Mo...	((:c CategoryTheory.Functor.IsEquivalence) (:fv _uniq.11744) (:fv _uniq.11749) (:fv _uniq.11746) (:fv _uniq.11752) (:fv _uniq.11896))	[{"name":"C₁","sexp":"(:sort (+ u₁ 1))"},{"name":"C₂","sexp":"(:sort (+ u₂ 1))"},{"name":"C₃","sexp":"(:sort (+ u₃ 1))"},{"name":"D₁","sexp":"(:sort (+ u₄ 1))"},{"name":"D₂","sexp":"(:sort (+ u₅ 1))"},{"name":"D₃","sexp":"(:sort (+ u₆ 1))"},{"name":"inst✝¹⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.10966))"},{"...	(:app (:c CategoryTheory.Functor.IsEquivalence) (:arg :implicit-type 0 (:fv FV22)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV22))))) (:arg :implicit-type 2 (:fv FV23)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV23))))) (:...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10966","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10968","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"let","sourceEnd":4232,"sourceStart":4229,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"E₂","sourceEnd":4237,"sourceStart":4233,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"so...	[]	[{"source":"Localization.uniq L₂ L₂' W₂","source_end":4274,"source_start":4241,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10966","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10968","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	20	5	exact	true	1	34	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	265be0cd4541879caf3e7fc55beaab5c11d830b8494c97c98528f4dde3a4488d	c6b162352f3c6c4b43fccdf0c6a3055ce632383e9cf66a6ec8f87b88b53657a6	c244814a618944803faf93d349e508784ed29eeaa198ff0d9da4f81822fcfbdc	225003710839e34ae42ab45c68cdd531c93270bf4a61f014e0422dd1fdf9b18b
cat-searcher/leandojo-benchmark-4-random	test	991	CategoryTheory.LocalizerMorphism.isEquivalence_imp	Mathlib/CategoryTheory/Localization/LocalizerMorphism.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	let e : L₁ ⋙ G ⋙ E₂.functor ≅ L₁ ⋙ E₁.functor ⋙ G' := calc L₁ ⋙ G ⋙ E₂.functor ≅ Φ.functor ⋙ L₂ ⋙ E₂.functor := (<a>CategoryTheory.Functor.associator</a> _ _ _).<a>CategoryTheory.Iso.symm</a> ≪≫ <a>CategoryTheory.isoWhiskerRight</a> (<a>CategoryTheory.CatCommSq.iso</a> Φ.functor L₁ L₂ G).<a>CategoryTheory.Iso.symm</a> ...	C₁ : Type u₁ C₂ : Type u₂ C₃ : Type u₃ D₁ : Type u₄ D₂ : Type u₅ D₃ : Type u₆ inst✝¹⁴ : Category.{v₁, u₁} C₁ inst✝¹³ : Category.{v₂, u₂} C₂ inst✝¹² : Category.{v₃, u₃} C₃ inst✝¹¹ : Category.{v₄, u₄} D₁ inst✝¹⁰ : Category.{v₅, u₅} D₂ inst✝⁹ : Category.{v₆, u₅} D₂ W₁ : MorphismProperty C₁ W₂ : MorphismProperty C₂ W₃ : Mo...	C₁ : Type u₁ C₂ : Type u₂ C₃ : Type u₃ D₁ : Type u₄ D₂ : Type u₅ D₃ : Type u₆ inst✝¹⁴ : Category.{v₁, u₁} C₁ inst✝¹³ : Category.{v₂, u₂} C₂ inst✝¹² : Category.{v₃, u₃} C₃ inst✝¹¹ : Category.{v₄, u₄} D₁ inst✝¹⁰ : Category.{v₅, u₅} D₂ inst✝⁹ : Category.{v₆, u₅} D₂ W₁ : MorphismProperty C₁ W₂ : MorphismProperty C₂ W₃ : Mo...	((:c CategoryTheory.Functor.IsEquivalence) (:fv _uniq.11744) (:fv _uniq.11749) (:fv _uniq.11746) (:fv _uniq.11752) (:fv _uniq.11896))	[{"name":"C₁","sexp":"(:sort (+ u₁ 1))"},{"name":"C₂","sexp":"(:sort (+ u₂ 1))"},{"name":"C₃","sexp":"(:sort (+ u₃ 1))"},{"name":"D₁","sexp":"(:sort (+ u₄ 1))"},{"name":"D₂","sexp":"(:sort (+ u₅ 1))"},{"name":"D₃","sexp":"(:sort (+ u₆ 1))"},{"name":"inst✝¹⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.10966))"},{"...	(:app (:c CategoryTheory.Functor.IsEquivalence) (:arg :implicit-type 0 (:fv FV22)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV22))))) (:arg :implicit-type 2 (:fv FV23)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV23))))) (:...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10966","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10968","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"let","sourceEnd":4280,"sourceStart":4277,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"e","sourceEnd":4282,"sourceStart":4281,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":4284,"so...	[]	[{"source":"L₁ ⋙ G ⋙ E₂.functor ≅ L₁ ⋙ E₁.functor ⋙ G'","source_end":4345,"source_start":4285,"syntax_kind":"CategoryTheory.«term_≅_»"},{"source":"calc\n L₁ ⋙ G ⋙ E₂.functor ≅ Φ.functor ⋙ L₂ ⋙ E₂.functor :=\n (Functor.associator _ _ _).symm ≪≫\n isoWhiskerRight (CatCommSq.iso Φ.functor L₁ L₂ G)...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10966","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10968","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	20	6	exact	true	1	35	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	1702ea2b8f5ad39cb29075e66e8747d13f748c9550956d52ebb523d92d8fbd31	225003710839e34ae42ab45c68cdd531c93270bf4a61f014e0422dd1fdf9b18b	aa384111fec354fab5cea14fd3683bacffca1e38b4af2ebb9e4f3e9e166e6bcb	68fa4aae7d74a09c5edb0565f9db9248d8764de436dd24ffd700e570524615dd
cat-searcher/leandojo-benchmark-4-random	test	992	CategoryTheory.LocalizerMorphism.isEquivalence_imp	Mathlib/CategoryTheory/Localization/LocalizerMorphism.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	have := <a>CategoryTheory.Functor.isEquivalence_of_iso</a> (<a>CategoryTheory.Localization.liftNatIso</a> L₁ W₁ _ _ (G ⋙ E₂.functor) (E₁.functor ⋙ G') e)	C₁ : Type u₁ C₂ : Type u₂ C₃ : Type u₃ D₁ : Type u₄ D₂ : Type u₅ D₃ : Type u₆ inst✝¹⁴ : Category.{v₁, u₁} C₁ inst✝¹³ : Category.{v₂, u₂} C₂ inst✝¹² : Category.{v₃, u₃} C₃ inst✝¹¹ : Category.{v₄, u₄} D₁ inst✝¹⁰ : Category.{v₅, u₅} D₂ inst✝⁹ : Category.{v₆, u₅} D₂ W₁ : MorphismProperty C₁ W₂ : MorphismProperty C₂ W₃ : Mo...	C₁ : Type u₁ C₂ : Type u₂ C₃ : Type u₃ D₁ : Type u₄ D₂ : Type u₅ D₃ : Type u₆ inst✝¹⁴ : Category.{v₁, u₁} C₁ inst✝¹³ : Category.{v₂, u₂} C₂ inst✝¹² : Category.{v₃, u₃} C₃ inst✝¹¹ : Category.{v₄, u₄} D₁ inst✝¹⁰ : Category.{v₅, u₅} D₂ inst✝⁹ : Category.{v₆, u₅} D₂ W₁ : MorphismProperty C₁ W₂ : MorphismProperty C₂ W₃ : Mo...	((:c CategoryTheory.Functor.IsEquivalence) (:fv _uniq.11744) (:fv _uniq.11749) (:fv _uniq.11746) (:fv _uniq.11752) (:fv _uniq.11896))	[{"name":"C₁","sexp":"(:sort (+ u₁ 1))"},{"name":"C₂","sexp":"(:sort (+ u₂ 1))"},{"name":"C₃","sexp":"(:sort (+ u₃ 1))"},{"name":"D₁","sexp":"(:sort (+ u₄ 1))"},{"name":"D₂","sexp":"(:sort (+ u₅ 1))"},{"name":"D₃","sexp":"(:sort (+ u₆ 1))"},{"name":"inst✝¹⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.10966))"},{"...	(:app (:c CategoryTheory.Functor.IsEquivalence) (:arg :implicit-type 0 (:fv FV22)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV22))))) (:arg :implicit-type 2 (:fv FV23)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV23))))) (:...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10966","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10968","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"have","sourceEnd":4930,"sourceStart":4926,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":4931,"sourceStart":4931,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":4931,"sourceStart":4931,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","...	[]	[{"source":"Functor.isEquivalence_of_iso\n (liftNatIso L₁ W₁ _ _ (G ⋙ E₂.functor) (E₁.functor ⋙ G') e)","source_end":5038,"source_start":4934,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10966","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10968","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	20	7	exact	true	1	36	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	13dc10c5ae15df4472b42509fc6b109bff0529403810293e3c98f7ba4ac9df35	68fa4aae7d74a09c5edb0565f9db9248d8764de436dd24ffd700e570524615dd	b6bbcd52d5b063faa7d9bb7f7d696c6e32651eb521215ae157436ada48cc7cb2	70478c0c2bc2dcbc533ef76323994cd14e21187ad6c5794d539e43206d61fb6e
cat-searcher/leandojo-benchmark-4-random	test	993	CategoryTheory.LocalizerMorphism.isEquivalence_imp	Mathlib/CategoryTheory/Localization/LocalizerMorphism.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact <a>CategoryTheory.Functor.isEquivalence_of_comp_left</a> E₁.functor G'	C₁ : Type u₁ C₂ : Type u₂ C₃ : Type u₃ D₁ : Type u₄ D₂ : Type u₅ D₃ : Type u₆ inst✝¹⁴ : Category.{v₁, u₁} C₁ inst✝¹³ : Category.{v₂, u₂} C₂ inst✝¹² : Category.{v₃, u₃} C₃ inst✝¹¹ : Category.{v₄, u₄} D₁ inst✝¹⁰ : Category.{v₅, u₅} D₂ inst✝⁹ : Category.{v₆, u₅} D₂ W₁ : MorphismProperty C₁ W₂ : MorphismProperty C₂ W₃ : Mo...		((:c CategoryTheory.Functor.IsEquivalence) (:fv _uniq.11744) (:fv _uniq.11749) (:fv _uniq.11746) (:fv _uniq.11752) (:fv _uniq.11896))	[{"name":"C₁","sexp":"(:sort (+ u₁ 1))"},{"name":"C₂","sexp":"(:sort (+ u₂ 1))"},{"name":"C₃","sexp":"(:sort (+ u₃ 1))"},{"name":"D₁","sexp":"(:sort (+ u₄ 1))"},{"name":"D₂","sexp":"(:sort (+ u₅ 1))"},{"name":"D₃","sexp":"(:sort (+ u₆ 1))"},{"name":"inst✝¹⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.10966))"},{"...	(:app (:c CategoryTheory.Functor.IsEquivalence) (:arg :implicit-type 0 (:fv FV22)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV22))))) (:arg :implicit-type 2 (:fv FV23)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV23))))) (:...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10966","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10968","is_instance":false,"is_let":false,"name":"C₂","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"source":"exact","sourceEnd":5046,"sourceStart":5041,"tag":"atom"},{"children":[{"name":"CategoryTheory.Functor.isEquivalence_of_comp_left","semanticRole":"global","source":"Functor.isEquivalence_of_comp_left","sourceEnd":5081,"sourceStart":5047,"tag":"identifier"},{"children":[{"name":"CategoryTheory.Equ...	[]	[{"source":"Functor.isEquivalence_of_comp_left E₁.functor G'","source_end":5097,"source_start":5047,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10966","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10968","is_instance":false,"is_let":false,"user_name":"C₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	20	8	exact	true	1	37	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	d114b06f8fe24466cef52882ba46c8f4a23bca951ba14234c377313501b61c0a	70478c0c2bc2dcbc533ef76323994cd14e21187ad6c5794d539e43206d61fb6e	60dd515ee63261a429712d5ce80d8adae4cd1ca578f8c4eeb3f1c99d33c7e389	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	994	MeasureTheory.lintegral_pos_iff_support	Mathlib/MeasureTheory/Integral/Lebesgue.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp [<a>pos_iff_ne_zero</a>, hf, <a>Filter.EventuallyEq</a>, <a>MeasureTheory.ae_iff</a>, <a>Function.support</a>]	α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 m : MeasurableSpace α μ ν : Measure α f : α → ℝ≥0∞ hf : Measurable f ⊢ 0 < ∫⁻ (a : α), f a ∂μ ↔ 0 < μ (support f)		((:c Iff) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrd...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.260320))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.260320) (:fv _uniq.260332))"},{"name...	(:app (:c Iff) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNa...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260320","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260323","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c...	{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":53827,"sourceStart":53823,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...	[]	[{"source":"pos_iff_ne_zero","source_end":53844,"source_start":53829,"syntax_kind":"ident"},{"source":"hf","source_end":53848,"source_start":53846,"syntax_kind":"ident"},{"source":"Filter.EventuallyEq","source_end":53869,"source_start":53850,"syntax_kind":"ident"},{"source":"ae_iff","source_end":53877,"source_start":53...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260320","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260323","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_...	223	2	exact	true	1	9	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	7eda669944b49ee97cdb3496ed34edcd08690be88d89e93ede0be32e4eb9951f	dc9167bcfa1e3dce5b78fcf92ab4f0e1e438db46f57d38fc803e93f1521af810	9053c1f79e573880209fe93bd924b8a7695f4eaa92b051a806e5f8b3055b842a	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	995	Matrix.cons_add	Mathlib/Data/Fin/VecNotation.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	ext i	α : Type u m n o : ℕ m' : Type u_1 n' : Type u_2 o' : Type u_3 inst✝ : Add α x : α v : Fin n → α w : Fin n.succ → α ⊢ vecCons x v + w = vecCons (x + vecHead w) (v + vecTail w)	case h α : Type u m n o : ℕ m' : Type u_1 n' : Type u_2 o' : Type u_3 inst✝ : Add α x : α v : Fin n → α w : Fin n.succ → α i : Fin n.succ ⊢ (vecCons x v + w) i = vecCons (x + vecHead w) (v + vecTail w) i	((:c Eq) (:forall _ ((:c Fin) ((:c Nat.succ) (:fv _uniq.45597))) (:fv _uniq.45593)) ((:c HAdd.hAdd) (:forall _ ((:c Fin) ((:c Nat.succ) (:fv _uniq.45597))) (:fv _uniq.45593)) (:forall _ ((:c Fin) ((:c Nat.succ) (:fv _uniq.45597))) (:fv _uniq.45593)) (:forall _ ((:c Fin) ((:c Nat.succ) (:fv _uniq.45597))) (:fv _uniq.455...	[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"o","sexp":"(:c Nat)"},{"name":"m'","sexp":"(:sort (+ u_1 1))"},{"name":"n'","sexp":"(:sort (+ u_2 1))"},{"name":"o'","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c Add) (:fv _uniq.45593))"},{"name":"x...	(:app (:c Eq) (:arg :implicit-type 0 (:forall _ :explicit (:app (:c Fin) (:arg :explicit 0 (:app (:c Nat.succ) (:arg :explicit 0 (:fv FV2))))) (:fv FV0))) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:forall _ :explicit (:app (:c Fin) (:arg :explicit 0 (:app (:c Nat.succ) (:arg :explicit 0 (:fv FV2)))...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45593","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45595","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":implicit","context...	{"children":[{"source":"ext","sourceEnd":16140,"sourceStart":16137,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"i","sourceEnd":16142,"sourceStart":16141,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"i","sourceEnd":16142,"sourceStart":16141,"tag...	[{"role":"fresh_name","source":"i","source_end":16142,"source_start":16141,"syntax_kind":"ident"}]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45593","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45595","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	117	4	exact	true	1	11	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	e386bd8674c08f87cd3cd3e417139d9b80a9773365aee666af8baf75c443e010	aaa8c32317d5bd6cc230708107d090e7d4f1d33ebab8c1286ddadd5e02a492de	dede2065f45c64314eb0d642cb3ec6d07cae33380d6ab9e7987679563298eb3f	dc0226021628a6fd4278e4093c90d830548ffcacad1997a47a1977c74ad4ccd2
cat-searcher/leandojo-benchmark-4-random	test	996	Matrix.cons_add	Mathlib/Data/Fin/VecNotation.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	refine <a>Fin.cases</a> ?_ ?_ i <;> simp [<a>Matrix.vecHead</a>, <a>Matrix.vecTail</a>]	case h α : Type u m n o : ℕ m' : Type u_1 n' : Type u_2 o' : Type u_3 inst✝ : Add α x : α v : Fin n → α w : Fin n.succ → α i : Fin n.succ ⊢ (vecCons x v + w) i = vecCons (x + vecHead w) (v + vecTail w) i		((:c Eq) (:fv _uniq.45593) ((:c HAdd.hAdd) (:forall _ ((:c Fin) ((:c Nat.succ) (:fv _uniq.45597))) (:fv _uniq.45593)) (:forall _ ((:c Fin) ((:c Nat.succ) (:fv _uniq.45597))) (:fv _uniq.45593)) (:forall _ ((:c Fin) ((:c Nat.succ) (:fv _uniq.45597))) (:fv _uniq.45593)) ((:c instHAdd) (:forall _ ((:c Fin) ((:c Nat.succ) (...	[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"o","sexp":"(:c Nat)"},{"name":"m'","sexp":"(:sort (+ u_1 1))"},{"name":"n'","sexp":"(:sort (+ u_2 1))"},{"name":"o'","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c Add) (:fv _uniq.45593))"},{"name":"x...	(:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:forall _ :explicit (:app (:c Fin) (:arg :explicit 0 (:app (:c Nat.succ) (:arg :explicit 0 (:fv FV2))))) (:fv FV0))) (:arg :implicit-type 1 (:forall _ :explicit (:app (:c Fin) (:arg :explicit 0 (:app (:c Nat.s...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45593","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45595","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":implicit","context...	{"children":[{"children":[{"source":"refine","sourceEnd":16151,"sourceStart":16145,"tag":"atom"},{"children":[{"name":"Fin.cases","semanticRole":"global","source":"Fin.cases","sourceEnd":16161,"sourceStart":16152,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":16163,"sourceStart":16162,"tag":"at...	[]	[{"source":"Fin.cases ?_ ?_ i","source_end":16169,"source_start":16152,"syntax_kind":"Lean.Parser.Term.app"},{"source":"vecHead","source_end":16187,"source_start":16180,"syntax_kind":"ident"},{"source":"vecTail","source_end":16196,"source_start":16189,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45593","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45595","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...	117	5	exact	true	1	12	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	9a6e7afd868ba7be196c2e3c269a850729047fa8bccc5d697738e90dc6bea7c1	dc0226021628a6fd4278e4093c90d830548ffcacad1997a47a1977c74ad4ccd2	8f62b011f70024457a43dfcd6f47258b341880375138f388fc89309a069c3f37	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	997	SimpleGraph.Walk.dropUntil_copy	Mathlib/Combinatorics/SimpleGraph/Connectivity.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	subst_vars	V : Type u V' : Type v V'' : Type w G : SimpleGraph V G' : SimpleGraph V' G'' : SimpleGraph V'' u✝ v✝ w✝ x y : V inst✝ : DecidableEq V u v w v' w' : V p : G.Walk v w hv : v = v' hw : w = w' h : u ∈ (p.copy hv hw).support ⊢ u ∈ p.support	V : Type u V' : Type v V'' : Type w G : SimpleGraph V G' : SimpleGraph V' G'' : SimpleGraph V'' u✝ v w x y : V inst✝ : DecidableEq V u v' w' : V p : G.Walk v' w' h : u ∈ (p.copy ⋯ ⋯).support ⊢ u ∈ p.support	((:c Membership.mem) (:fv _uniq.131831) ((:c List) (:fv _uniq.131831)) ((:c List.instMembership) (:fv _uniq.131831)) (:fv _uniq.131866) ((:c SimpleGraph.Walk.support) (:fv _uniq.131831) (:fv _uniq.131838) (:fv _uniq.131869) (:fv _uniq.131872) (:fv _uniq.131887)))	[{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"V'","sexp":"(:sort (+ v 1))"},{"name":"V''","sexp":"(:sort (+ w 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.131831))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.131833))"},{"name":"G''","sexp":"((:c SimpleGraph) (:fv _uniq.131835))"},{"name":"u✝","sexp"...	(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV12)) (:arg :ex...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.131831","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.131833","is_instance":false,"is_let":false,"name":"V'","sexp":"(:sort Type)"},{"binder_role":":implicit","...	{"children":[{"source":"subst_vars","sourceEnd":51728,"sourceStart":51718,"tag":"atom"}],"kind":"Lean.Parser.Tactic.substVars","source":"subst_vars","sourceEnd":51728,"sourceStart":51718,"tag":"node"}	[]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.131831","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.131833","is_instance":false,"is_let":false,"user_name":"V'"},{"binder_role":":implicit","context_index":2,"internal_name":"...	374	4	exact	true	1	21	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	52e0870776d7936acdd6e17259bce89aabdf06990dd5177be26aaaf2d938b5cd	aa4b9ae482cca3388854ab08693b931e89a9813c307566acdac6e3915d4f6834	ae631a3f403217044ab4580a43451a7dad14274ba5b1ee9b0ab353417fb12e40	763adeb8ca603fcdb4686ce16bc8345acc5a52161468bd79a03ccc88e33df6d4
cat-searcher/leandojo-benchmark-4-random	test	998	SimpleGraph.Walk.dropUntil_copy	Mathlib/Combinatorics/SimpleGraph/Connectivity.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact h	V : Type u V' : Type v V'' : Type w G : SimpleGraph V G' : SimpleGraph V' G'' : SimpleGraph V'' u✝ v w x y : V inst✝ : DecidableEq V u v' w' : V p : G.Walk v' w' h : u ∈ (p.copy ⋯ ⋯).support ⊢ u ∈ p.support		((:c Membership.mem) (:fv _uniq.131831) ((:c List) (:fv _uniq.131831)) ((:c List.instMembership) (:fv _uniq.131831)) (:fv _uniq.131866) ((:c SimpleGraph.Walk.support) (:fv _uniq.131831) (:fv _uniq.131838) (:fv _uniq.131875) (:fv _uniq.131878) (:fv _uniq.132094)))	[{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"V'","sexp":"(:sort (+ v 1))"},{"name":"V''","sexp":"(:sort (+ w 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.131831))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.131833))"},{"name":"G''","sexp":"((:c SimpleGraph) (:fv _uniq.131835))"},{"name":"u✝","sexp"...	(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV12)) (:arg :ex...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.131831","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.131833","is_instance":false,"is_let":false,"name":"V'","sexp":"(:sort Type)"},{"binder_role":":implicit","...	{"children":[{"source":"exact","sourceEnd":51735,"sourceStart":51730,"tag":"atom"},{"contextIndex":16,"semanticRole":"local","source":"h","sourceEnd":51737,"sourceStart":51736,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact h","sourceEnd":51737,"sourceStart":51730,"tag":"node"}	[]	[{"source":"h","source_end":51737,"source_start":51736,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.131831","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.131833","is_instance":false,"is_let":false,"user_name":"V'"},{"binder_role":":implicit","context_index":2,"internal_name":"...	374	6	exact	true	1	17	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	f669ea12d2f23a2ff0a6b32600ac078b9f5a9de9cd0119bcea34dd078e5c18e0	763adeb8ca603fcdb4686ce16bc8345acc5a52161468bd79a03ccc88e33df6d4	c2ce0e21ffddde69d6a80e187a5bf12b7761df4be076519945be8ed7a7a77294	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	999	SimpleGraph.Walk.dropUntil_copy	Mathlib/Combinatorics/SimpleGraph/Connectivity.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	subst_vars	V : Type u V' : Type v V'' : Type w G : SimpleGraph V G' : SimpleGraph V' G'' : SimpleGraph V'' u✝ v✝ w✝ x y : V inst✝ : DecidableEq V u v w v' w' : V p : G.Walk v w hv : v = v' hw : w = w' h : u ∈ (p.copy hv hw).support ⊢ (p.copy hv hw).dropUntil u h = (p.dropUntil u ⋯).copy ⋯ hw	V : Type u V' : Type v V'' : Type w G : SimpleGraph V G' : SimpleGraph V' G'' : SimpleGraph V'' u✝ v w x y : V inst✝ : DecidableEq V u v' w' : V p : G.Walk v' w' h : u ∈ (p.copy ⋯ ⋯).support ⊢ (p.copy ⋯ ⋯).dropUntil u h = (p.dropUntil u ⋯).copy ⋯ ⋯	((:c Eq) ((:c SimpleGraph.Walk) (:fv _uniq.131831) (:fv _uniq.131838) (:fv _uniq.132108) (:fv _uniq.132112)) ((:c SimpleGraph.Walk.dropUntil) (:fv _uniq.131831) (:fv _uniq.131838) (:fv _uniq.131861) (:fv _uniq.132111) (:fv _uniq.132112) ((:c SimpleGraph.Walk.copy) (:fv _uniq.131831) (:fv _uniq.131838) (:fv _uniq.132109...	[{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"V'","sexp":"(:sort (+ v 1))"},{"name":"V''","sexp":"(:sort (+ w 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.131831))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.131833))"},{"name":"G''","sexp":"((:c SimpleGraph) (:fv _uniq.131835))"},{"name":"u✝","sexp"...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c SimpleGraph.Walk) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV13)) (:arg :explicit 3 (:fv FV17)))) (:arg :explicit 1 (:app (:c SimpleGraph.Walk.dropUntil) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :instance 2 (:i...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.131831","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.131833","is_instance":false,"is_let":false,"name":"V'","sexp":"(:sort Type)"},{"binder_role":":implicit","...	{"children":[{"source":"subst_vars","sourceEnd":51770,"sourceStart":51760,"tag":"atom"}],"kind":"Lean.Parser.Tactic.substVars","source":"subst_vars","sourceEnd":51770,"sourceStart":51760,"tag":"node"}	[]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.131831","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.131833","is_instance":false,"is_let":false,"user_name":"V'"},{"binder_role":":implicit","context_index":2,"internal_name":"...	374	11	exact	true	1	21	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	b764c4a6482838b9939044229b3dbfcdbd6da60f431043def152c750a1c81164	5d43fd57ea875f9c62c5df31153867a710634b541f7ffccfc54c24ace55e9864	ae631a3f403217044ab4580a43451a7dad14274ba5b1ee9b0ab353417fb12e40	7ade96358dddf7562ed9ad5682434ae928da9da1dcac6a6626c663e652020101
cat-searcher/leandojo-benchmark-4-random	test	1,000	SimpleGraph.Walk.dropUntil_copy	Mathlib/Combinatorics/SimpleGraph/Connectivity.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rfl	V : Type u V' : Type v V'' : Type w G : SimpleGraph V G' : SimpleGraph V' G'' : SimpleGraph V'' u✝ v w x y : V inst✝ : DecidableEq V u v' w' : V p : G.Walk v' w' h : u ∈ (p.copy ⋯ ⋯).support ⊢ (p.copy ⋯ ⋯).dropUntil u h = (p.dropUntil u ⋯).copy ⋯ ⋯		((:c Eq) ((:c SimpleGraph.Walk) (:fv _uniq.131831) (:fv _uniq.131838) (:fv _uniq.132108) (:fv _uniq.132112)) ((:c SimpleGraph.Walk.dropUntil) (:fv _uniq.131831) (:fv _uniq.131838) (:fv _uniq.131861) (:fv _uniq.132111) (:fv _uniq.132112) ((:c SimpleGraph.Walk.copy) (:fv _uniq.131831) (:fv _uniq.131838) (:fv _uniq.132111...	[{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"V'","sexp":"(:sort (+ v 1))"},{"name":"V''","sexp":"(:sort (+ w 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.131831))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.131833))"},{"name":"G''","sexp":"((:c SimpleGraph) (:fv _uniq.131835))"},{"name":"u✝","sexp"...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c SimpleGraph.Walk) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV13)) (:arg :explicit 3 (:fv FV15)))) (:arg :explicit 1 (:app (:c SimpleGraph.Walk.dropUntil) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :instance 2 (:i...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.131831","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.131833","is_instance":false,"is_let":false,"name":"V'","sexp":"(:sort Type)"},{"binder_role":":implicit","...	{"children":[{"source":"rfl","sourceEnd":51776,"sourceStart":51773,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":51776,"sourceStart":51773,"tag":"node"}	[]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.131831","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.131833","is_instance":false,"is_let":false,"user_name":"V'"},{"binder_role":":implicit","context_index":2,"internal_name":"...	374	12	exact	true	1	17	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	dc0db1da0bc2fec10e51556a59797f46657647d631264cb940b5ae71d61a4e49	7ade96358dddf7562ed9ad5682434ae928da9da1dcac6a6626c663e652020101	5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	1,001	Nat.Partrec.Code.eval_prec_succ	Mathlib/Computability/PartrecCode.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>Nat.Partrec.Code.eval</a>, <a>Nat.unpaired</a>, <a>Part.bind_eq_bind</a>, <a>Nat.unpair_pair</a>]	cf cg : Code a k : ℕ ⊢ (cf.prec cg).eval (Nat.pair a k.succ) = do let ih ← (cf.prec cg).eval (Nat.pair a k) cg.eval (Nat.pair a (Nat.pair k ih))	cf cg : Code a k : ℕ ⊢ Nat.rec (cf.eval (a, k.succ).1) (fun y IH => do let i ← IH cg.eval (Nat.pair (a, k.succ).1 (Nat.pair y i))) (a, k.succ).2 = (unpaired (fun a n => Nat.rec (cf.eval a) (fun y IH => do let i ← IH cg.e...	((:c Eq) ((:c Part) (:c Nat)) ((:c Nat.Partrec.Code.eval) ((:c Nat.Partrec.Code.prec) (:fv _uniq.214126) (:fv _uniq.214127)) ((:c Nat.pair) (:fv _uniq.214128) ((:c Nat.succ) (:fv _uniq.214129)))) ((:c Bind.bind) (:c Part) ((:c Monad.toBind) (:c Part) (:c Part.instMonad)) (:c Nat) (:c Nat) ((:c Nat.Partrec.Code.eval) ((...	[{"name":"cf","sexp":"(:c Nat.Partrec.Code)"},{"name":"cg","sexp":"(:c Nat.Partrec.Code)"},{"name":"a","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Nat)"}]	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Part) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c Nat.Partrec.Code.eval) (:arg :explicit 0 (:app (:c Nat.Partrec.Code.prec) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))) (:arg :explicit 1 (:app (:c Nat.pair) (:arg :explicit 0 (:fv FV3)) (:arg :e...	[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.214126","is_instance":false,"is_let":false,"name":"cf","sexp":"(:c Nat.Partrec.Code)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.214127","is_instance":false,"is_let":false,"name":"cg","sexp":"(:c Nat.Partrec.Code)"},{"binder_...	{"children":[{"source":"rw","sourceEnd":23957,"sourceStart":23955,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":23959,"sourceStart":23958,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Nat.Partrec.Code...	[]	[{"source":"eval","source_end":23963,"source_start":23959,"syntax_kind":"ident"},{"source":"Nat.unpaired","source_end":23977,"source_start":23965,"syntax_kind":"ident"},{"source":"Part.bind_eq_bind","source_end":23996,"source_start":23979,"syntax_kind":"ident"},{"source":"Nat.unpair_pair","source_end":24013,"source_sta...	[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.214126","is_instance":false,"is_let":false,"user_name":"cf"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.214127","is_instance":false,"is_let":false,"user_name":"cg"},{"binder_role":":explicit","context_index":3,"internal_name":...	68	4	exact	true	1	4	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	c90d1843359ac94a5f89c81f0cef5b7a3603b8253d2275db4c9e6216e976a7a2	007072b7319c4d253621dcb4991ac739f5361cff1640cfa1d7f8191147492cdf	a8e72be5e92b17f07a806eaf57809ef3a5b1e6c9fa38228d5d211578df9a8923	f33fdfab99c86b0dd37687b8cb26070968adb0f75160bf9c5f2bfa42797ca089
cat-searcher/leandojo-benchmark-4-random	test	1,002	Nat.Partrec.Code.eval_prec_succ	Mathlib/Computability/PartrecCode.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp	cf cg : Code a k : ℕ ⊢ Nat.rec (cf.eval (a, k.succ).1) (fun y IH => do let i ← IH cg.eval (Nat.pair (a, k.succ).1 (Nat.pair y i))) (a, k.succ).2 = (unpaired (fun a n => Nat.rec (cf.eval a) (fun y IH => do let i ← IH cg.e...		((:c Eq) ((:c Part) (:c Nat)) ((:c Nat.rec) (:lambda _ (:c Nat) ((:c Part) (:c Nat))) ((:c Nat.Partrec.Code.eval) (:fv _uniq.214126) ((:c Prod.fst) (:c Nat) (:c Nat) ((:c Prod.mk) (:c Nat) (:c Nat) (:fv _uniq.214128) ((:c Nat.succ) (:fv _uniq.214129))))) (:lambda y (:c Nat) (:lambda IH ((:c Part) (:c Nat)) ((:c Bind.bi...	[{"name":"cf","sexp":"(:c Nat.Partrec.Code)"},{"name":"cg","sexp":"(:c Nat.Partrec.Code)"},{"name":"a","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Nat)"}]	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Part) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c Nat.rec) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Nat.Partrec.Code.eval) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Prod.fst) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat...	[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.214126","is_instance":false,"is_let":false,"name":"cf","sexp":"(:c Nat.Partrec.Code)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.214127","is_instance":false,"is_let":false,"name":"cg","sexp":"(:c Nat.Partrec.Code)"},{"binder_...	{"children":[{"source":"simp","sourceEnd":24021,"sourceStart":24017,"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":[],"ki...	[]	[]	[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.214126","is_instance":false,"is_let":false,"user_name":"cf"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.214127","is_instance":false,"is_let":false,"user_name":"cg"},{"binder_role":":explicit","context_index":3,"internal_name":...	68	10	exact	true	1	4	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	2ccf3510d0d98e0f40f7f2b49c785fc0d2b8ca9acc2e704e80be2228938076de	f33fdfab99c86b0dd37687b8cb26070968adb0f75160bf9c5f2bfa42797ca089	8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	1,003	CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_hom_π_π	Mathlib/CategoryTheory/Limits/Fubini.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	dsimp [<a>CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim</a>]	J K : Type v inst✝³ : SmallCategory J inst✝² : SmallCategory K C : Type u inst✝¹ : Category.{v, u} C F : J ⥤ K ⥤ C G : J × K ⥤ C inst✝ : HasLimits C j : J k : K ⊢ (limitCurrySwapCompLimIsoLimitCurryCompLim G).hom ≫ limit.π (curry.obj G ⋙ lim) j ≫ limit.π ((curry.obj G).obj j) k = limit.π (curry.obj (Prod.swap K J ⋙...	J K : Type v inst✝³ : SmallCategory J inst✝² : SmallCategory K C : Type u inst✝¹ : Category.{v, u} C F : J ⥤ K ⥤ C G : J × K ⥤ C inst✝ : HasLimits C j : J k : K ⊢ (((limitIsoLimitCurryCompLim (Prod.swap K J ⋙ G)).inv ≫ (HasLimit.isoOfEquivalence (Prod.braiding K J) (Iso.refl ((Prod.braiding K J).functor ⋙ G))...	((:c Eq) ((:c Quiver.Hom) (:fv _uniq.230774) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.230774) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.230774) (:fv _uniq.230777))) ((:c CategoryTheory.Limits.limit) (:fv _uniq.230766) (:fv _uniq.230772) (:fv _uniq.230774) (:fv _uniq.230777) ((:c CategoryT...	[{"name":"J","sexp":"(:sort (+ v 1))"},{"name":"K","sexp":"(:sort (+ v 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.SmallCategory) (:fv _uniq.230764))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.SmallCategory) (:fv _uniq.230766))"},{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryThe...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c CategoryTheory.Limits.limit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheo...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.230764","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.230766","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"dsimp","sourceEnd":21533,"sourceStart":21528,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":21535,"sourceStart":21534,"tag":"...	[]	[{"source":"limitCurrySwapCompLimIsoLimitCurryCompLim","source_end":21576,"source_start":21535,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.230764","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.230766","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal...	93	4	exact	true	1	11	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	b6436d4bdb5eac890734748b07f5ed59f242dde09421dd5c5c3edb7c076aefc6	a62594869602130023fc0f48a77305d14e85b077b021815ab4465c3ac0a73205	6d7f3715f499b8974f15088676c748c7556e4d714cf12450532c2dd97b88574a	6e32da1c8f20edb0282c76a4b6c641a20b05bc3d1c2f0f102a0e7d612736d90c
cat-searcher/leandojo-benchmark-4-random	test	1,004	CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_hom_π_π	Mathlib/CategoryTheory/Limits/Fubini.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp only [<a>CategoryTheory.Iso.refl_hom</a>, <a>CategoryTheory.Prod.braiding_counitIso_hom_app</a>, <a>CategoryTheory.Limits.HasLimit.isoOfEquivalence_hom_π</a>, <a>CategoryTheory.Iso.refl_inv</a>, <a>CategoryTheory.Limits.limitIsoLimitCurryCompLim_hom_π_π</a>, <a>CategoryTheory.eqToIso_refl</a>, <a>CategoryTheory.Ca...	J K : Type v inst✝³ : SmallCategory J inst✝² : SmallCategory K C : Type u inst✝¹ : Category.{v, u} C F : J ⥤ K ⥤ C G : J × K ⥤ C inst✝ : HasLimits C j : J k : K ⊢ (((limitIsoLimitCurryCompLim (Prod.swap K J ⋙ G)).inv ≫ (HasLimit.isoOfEquivalence (Prod.braiding K J) (Iso.refl ((Prod.braiding K J).functor ⋙ G))...	J K : Type v inst✝³ : SmallCategory J inst✝² : SmallCategory K C : Type u inst✝¹ : Category.{v, u} C F : J ⥤ K ⥤ C G : J × K ⥤ C inst✝ : HasLimits C j : J k : K ⊢ (limitIsoLimitCurryCompLim (Prod.swap K J ⋙ G)).inv ≫ limit.π (Prod.swap K J ⋙ G) ((Prod.braiding K J).inverse.obj (j, k)) ≫ (𝟙 ((Prod.braidin...	((:c Eq) ((:c Quiver.Hom) (:fv _uniq.230774) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.230774) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.230774) (:fv _uniq.230777))) ((:c CategoryTheory.Limits.limit) (:fv _uniq.230766) (:fv _uniq.230772) (:fv _uniq.230774) (:fv _uniq.230777) ((:c CategoryT...	[{"name":"J","sexp":"(:sort (+ v 1))"},{"name":"K","sexp":"(:sort (+ v 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.SmallCategory) (:fv _uniq.230764))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.SmallCategory) (:fv _uniq.230766))"},{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryThe...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c CategoryTheory.Limits.limit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheo...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.230764","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.230766","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"simp","sourceEnd":21584,"sourceStart":21580,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":21589,"sourceStart":21585,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":215...	[]	[{"source":"Iso.refl_hom","source_end":21603,"source_start":21591,"syntax_kind":"ident"},{"source":"Prod.braiding_counitIso_hom_app","source_end":21636,"source_start":21605,"syntax_kind":"ident"},{"source":"Limits.HasLimit.isoOfEquivalence_hom_π","source_end":21677,"source_start":21638,"syntax_kind":"ident"},{"source":...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.230764","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.230766","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal...	93	5	exact	true	1	11	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	18ea6ebf2294f342a78c2e8b4f1541fb2d8130adfe755fc3856de96a09d8b3ad	6e32da1c8f20edb0282c76a4b6c641a20b05bc3d1c2f0f102a0e7d612736d90c	a82e8fa9d44a44d260c59c2b91701fb8aa888115d0e079d3cd215b646a6d5e23	07e6086fd3f041721666d234080181ea17dccb3374ff5fe69ef57a1296d00090
cat-searcher/leandojo-benchmark-4-random	test	1,005	CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_hom_π_π	Mathlib/CategoryTheory/Limits/Fubini.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	erw [<a>CategoryTheory.NatTrans.id_app</a>]	J K : Type v inst✝³ : SmallCategory J inst✝² : SmallCategory K C : Type u inst✝¹ : Category.{v, u} C F : J ⥤ K ⥤ C G : J × K ⥤ C inst✝ : HasLimits C j : J k : K ⊢ (limitIsoLimitCurryCompLim (Prod.swap K J ⋙ G)).inv ≫ limit.π (Prod.swap K J ⋙ G) ((Prod.braiding K J).inverse.obj (j, k)) ≫ (𝟙 ((Prod.braidin...	J K : Type v inst✝³ : SmallCategory J inst✝² : SmallCategory K C : Type u inst✝¹ : Category.{v, u} C F : J ⥤ K ⥤ C G : J × K ⥤ C inst✝ : HasLimits C j : J k : K ⊢ (limitIsoLimitCurryCompLim (Prod.swap K J ⋙ G)).inv ≫ limit.π (Prod.swap K J ⋙ G) ((Prod.braiding K J).inverse.obj (j, k)) ≫ 𝟙 ((Prod.swap K J...	((:c Eq) ((:c Quiver.Hom) (:fv _uniq.230774) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.230774) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.230774) (:fv _uniq.230777))) ((:c CategoryTheory.Limits.limit) (:fv _uniq.230766) (:fv _uniq.230772) (:fv _uniq.230774) (:fv _uniq.230777) ((:c CategoryT...	[{"name":"J","sexp":"(:sort (+ v 1))"},{"name":"K","sexp":"(:sort (+ v 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.SmallCategory) (:fv _uniq.230764))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.SmallCategory) (:fv _uniq.230766))"},{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryThe...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c CategoryTheory.Limits.limit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheo...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.230764","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.230766","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"erw","sourceEnd":21769,"sourceStart":21766,"tag":"atom"},{"children":[{"source":"[","sourceEnd":21771,"sourceStart":21770,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"CategoryTheory.NatTrans.id_app","semanticRole":"global","source":"NatT...	[]	[{"source":"NatTrans.id_app","source_end":21786,"source_start":21771,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.230764","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.230766","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal...	93	6	exact	true	1	11	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	ce5d9d9ad380041df5fdaa508221fe735662ca8665fb2547e3738ed1d0185813	07e6086fd3f041721666d234080181ea17dccb3374ff5fe69ef57a1296d00090	08de52c3fab16d10f5317ee6ba73c872adf3ef33a1412054a38f446d199e747e	cf5fd39cbc369aaa11ae947f838e950ff4c21706331bd802bee077d0ee93ac22
cat-searcher/leandojo-benchmark-4-random	test	1,006	CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_hom_π_π	Mathlib/CategoryTheory/Limits/Fubini.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	dsimp	J K : Type v inst✝³ : SmallCategory J inst✝² : SmallCategory K C : Type u inst✝¹ : Category.{v, u} C F : J ⥤ K ⥤ C G : J × K ⥤ C inst✝ : HasLimits C j : J k : K ⊢ (limitIsoLimitCurryCompLim (Prod.swap K J ⋙ G)).inv ≫ limit.π (Prod.swap K J ⋙ G) ((Prod.braiding K J).inverse.obj (j, k)) ≫ 𝟙 ((Prod.swap K J...	J K : Type v inst✝³ : SmallCategory J inst✝² : SmallCategory K C : Type u inst✝¹ : Category.{v, u} C F : J ⥤ K ⥤ C G : J × K ⥤ C inst✝ : HasLimits C j : J k : K ⊢ (limitIsoLimitCurryCompLim (Prod.swap K J ⋙ G)).inv ≫ limit.π (Prod.swap K J ⋙ G) (k, j) ≫ 𝟙 (G.obj (j, k)) ≫ G.map (𝟙 j, 𝟙 k) = limit.π (curry....	((:c Eq) ((:c Quiver.Hom) (:fv _uniq.230774) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.230774) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.230774) (:fv _uniq.230777))) ((:c CategoryTheory.Limits.limit) (:fv _uniq.230766) (:fv _uniq.230772) (:fv _uniq.230774) (:fv _uniq.230777) ((:c CategoryT...	[{"name":"J","sexp":"(:sort (+ v 1))"},{"name":"K","sexp":"(:sort (+ v 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.SmallCategory) (:fv _uniq.230764))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.SmallCategory) (:fv _uniq.230766))"},{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryThe...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c CategoryTheory.Limits.limit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheo...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.230764","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.230766","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"dsimp","sourceEnd":21826,"sourceStart":21821,"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":[],"k...	[]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.230764","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.230766","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal...	93	9	exact	true	1	11	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	35e236f5101c52cee13462cb68a3677219718832dc24d03e9817735fd825d9ed	cf5fd39cbc369aaa11ae947f838e950ff4c21706331bd802bee077d0ee93ac22	7854eab90b5d1f0eed9d2f7f6b885100cc44bc732b41c876b3af083c01260845	ad8272757fe7390ebe974bc8d5241bb88713a88bdb433dd7ea33ba575f91eef5
cat-searcher/leandojo-benchmark-4-random	test	1,007	CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_hom_π_π	Mathlib/CategoryTheory/Limits/Fubini.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>CategoryTheory.Bifunctor.map_id</a>]	J K : Type v inst✝³ : SmallCategory J inst✝² : SmallCategory K C : Type u inst✝¹ : Category.{v, u} C F : J ⥤ K ⥤ C G : J × K ⥤ C inst✝ : HasLimits C j : J k : K ⊢ (limitIsoLimitCurryCompLim (Prod.swap K J ⋙ G)).inv ≫ limit.π (Prod.swap K J ⋙ G) (k, j) ≫ 𝟙 (G.obj (j, k)) ≫ G.map (𝟙 j, 𝟙 k) = limit.π (curry....	J K : Type v inst✝³ : SmallCategory J inst✝² : SmallCategory K C : Type u inst✝¹ : Category.{v, u} C F : J ⥤ K ⥤ C G : J × K ⥤ C inst✝ : HasLimits C j : J k : K ⊢ (limitIsoLimitCurryCompLim (Prod.swap K J ⋙ G)).inv ≫ limit.π (Prod.swap K J ⋙ G) (k, j) ≫ 𝟙 (G.obj (j, k)) ≫ 𝟙 (G.obj (j, k)) = limit.π (curry.o...	((:c Eq) ((:c Quiver.Hom) (:fv _uniq.230774) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.230774) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.230774) (:fv _uniq.230777))) ((:c CategoryTheory.Limits.limit) (:fv _uniq.230766) (:fv _uniq.230772) (:fv _uniq.230774) (:fv _uniq.230777) ((:c CategoryT...	[{"name":"J","sexp":"(:sort (+ v 1))"},{"name":"K","sexp":"(:sort (+ v 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.SmallCategory) (:fv _uniq.230764))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.SmallCategory) (:fv _uniq.230766))"},{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryThe...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c CategoryTheory.Limits.limit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheo...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.230764","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.230766","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"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":[],"kind":"null","source":"","tag":"node"},{"name":"CategoryTheory.B...	[]	[{"source":"CategoryTheory.Bifunctor.map_id","source_end":21999,"source_start":21968,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.230764","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.230766","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal...	93	10	exact	true	1	11	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	c5e17620a577d97b9778859244d6b99faa81a0438a4925c67e23ddc3c1f78ff9	ad8272757fe7390ebe974bc8d5241bb88713a88bdb433dd7ea33ba575f91eef5	e96a37e34d88b84ce1335d9ce2055e82efb0b3a2c408bc50f2d8ea580be9557b	b4886fec2d9540fe8a18cf1f5035175d2a042ecfebdd0f45216dc852eb3f647a
cat-searcher/leandojo-benchmark-4-random	test	1,008	CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_hom_π_π	Mathlib/CategoryTheory/Limits/Fubini.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp	J K : Type v inst✝³ : SmallCategory J inst✝² : SmallCategory K C : Type u inst✝¹ : Category.{v, u} C F : J ⥤ K ⥤ C G : J × K ⥤ C inst✝ : HasLimits C j : J k : K ⊢ (limitIsoLimitCurryCompLim (Prod.swap K J ⋙ G)).inv ≫ limit.π (Prod.swap K J ⋙ G) (k, j) ≫ 𝟙 (G.obj (j, k)) ≫ 𝟙 (G.obj (j, k)) = limit.π (curry.o...		((:c Eq) ((:c Quiver.Hom) (:fv _uniq.230774) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.230774) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.230774) (:fv _uniq.230777))) ((:c CategoryTheory.Limits.limit) (:fv _uniq.230766) (:fv _uniq.230772) (:fv _uniq.230774) (:fv _uniq.230777) ((:c CategoryT...	[{"name":"J","sexp":"(:sort (+ v 1))"},{"name":"K","sexp":"(:sort (+ v 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.SmallCategory) (:fv _uniq.230764))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.SmallCategory) (:fv _uniq.230766))"},{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryThe...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c CategoryTheory.Limits.limit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheo...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.230764","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.230766","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-imp...	{"children":[{"source":"simp","sourceEnd":22007,"sourceStart":22003,"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":[],"ki...	[]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.230764","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.230766","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal...	93	13	exact	true	1	11	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	0606deec801bab3f07960022cba788379247b81d5c748cf1e607cd0d5df2a87a	b4886fec2d9540fe8a18cf1f5035175d2a042ecfebdd0f45216dc852eb3f647a	8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	1,009	Bool.coe_false	Mathlib/Init/Data/Bool/Lemmas.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp	⊢ (false = true) = False		((:c Eq) (:sort 0) ((:c Eq) (:c Bool) (:c Bool.false) (:c Bool.true)) (:c False))	[]	(:app (:c Eq) (:arg :implicit-type 0 (:sort Prop)) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:c Bool)) (:arg :explicit 1 (:c Bool.false)) (:arg :explicit 2 (:c Bool.true)))) (:arg :explicit 2 (:c False)))	[]	{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":3318,"sourceStart":3314,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source...	[]	[]	[]	48	2	exact	true	1	0	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	fb16a1f8aa6725bc102c3be62ea873c895c4d874e03e8d910d78133329892782	57373351671f8e6697477a088796f1dcfcd67fea78b9654edd40632a6d54057d	8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	1,010	Rat.normalize.reduced'	.lake/packages/batteries/Batteries/Data/Rat/Lemmas.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [← <a>Int.div_eq_ediv_of_dvd</a> (e ▸ <a>Int.ofNat_dvd_left</a>.2 (<a>Nat.gcd_dvd_left</a> ..))]	num : Int den g : Nat den_nz : den ≠ 0 e : g = num.natAbs.gcd den ⊢ (num / ↑g).natAbs.Coprime (den / g)	num : Int den g : Nat den_nz : den ≠ 0 e : g = num.natAbs.gcd den ⊢ (num.div ↑g).natAbs.Coprime (den / g)	((:c Nat.Coprime) ((:c Int.natAbs) ((:c HDiv.hDiv) (:c Int) (:c Int) (:c Int) ((:c instHDiv) (:c Int) (:c Int.instDiv)) (:fv _uniq.1540) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.1542)))) ((:c HDiv.hDiv) (:c Nat) (:c Nat) (:c Nat) ((:c instHDiv) (:c Nat) (:c Nat.instDiv)) (:fv _uniq.1541) (:fv _uniq.1542))...	[{"name":"num","sexp":"(:c Int)"},{"name":"den","sexp":"(:c Nat)"},{"name":"g","sexp":"(:c Nat)"},{"name":"den_nz","sexp":"((:c Ne) (:c Nat) (:fv _uniq.1541) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"e","sexp":"((:c Eq) (:c Nat) (:fv _uniq.1542) ((:c Nat.gcd) ((:c Int.natAbs) (:fv _u...	(:app (:c Nat.Coprime) (:arg :explicit 0 (:app (:c Int.natAbs) (:arg :explicit 0 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:c Int)) (:arg :implicit-type 2 (:c Int)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:c Int)) (:arg :explicit 1 (:c Int)) (:arg :explicit...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1540","is_instance":false,"is_let":false,"name":"num","sexp":"(:c Int)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"name":"den","sexp":"(:c Nat)"},{"binder_role":":implicit","context_i...	{"children":[{"source":"rw","sourceEnd":1127,"sourceStart":1125,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1129,"sourceStart":1128,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":1132,"sourceStart":...	[]	[{"source":"Int.div_eq_ediv_of_dvd (e ▸ Int.ofNat_dvd_left.2 (Nat.gcd_dvd_left ..))","source_end":1206,"source_start":1133,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1540","is_instance":false,"is_let":false,"user_name":"num"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"user_name":"den"},{"binder_role":":implicit","context_index":3,"internal_name":"_...	9	4	exact	true	1	5	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	bcc9be8871f00caa584af54f7d4021470ab8386ccaa13a52a78b6c9eea86f9f3	397eda0d42e31809560627f11f4b7b2b0c75f17359d3e9d6acd8d795d65672bd	c992295dab8f14ea7432f0ac8ed6d069241a9f399ba81d92c73d4ffe48221213	85504bdbb14d92d2c81efedf989b516fdcb9c5f85396069178704438fba88727
cat-searcher/leandojo-benchmark-4-random	test	1,011	Rat.normalize.reduced'	.lake/packages/batteries/Batteries/Data/Rat/Lemmas.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact <a>Rat.normalize.reduced</a> den_nz e	num : Int den g : Nat den_nz : den ≠ 0 e : g = num.natAbs.gcd den ⊢ (num.div ↑g).natAbs.Coprime (den / g)		((:c Nat.Coprime) ((:c Int.natAbs) ((:c Int.div) (:fv _uniq.1540) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.1542)))) ((:c HDiv.hDiv) (:c Nat) (:c Nat) (:c Nat) ((:c instHDiv) (:c Nat) (:c Nat.instDiv)) (:fv _uniq.1541) (:fv _uniq.1542)))	[{"name":"num","sexp":"(:c Int)"},{"name":"den","sexp":"(:c Nat)"},{"name":"g","sexp":"(:c Nat)"},{"name":"den_nz","sexp":"((:c Ne) (:c Nat) (:fv _uniq.1541) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"e","sexp":"((:c Eq) (:c Nat) (:fv _uniq.1542) ((:c Nat.gcd) ((:c Int.natAbs) (:fv _u...	(:app (:c Nat.Coprime) (:arg :explicit 0 (:app (:c Int.natAbs) (:arg :explicit 0 (:app (:c Int.div) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (: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 FV3)))))))) (:a...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1540","is_instance":false,"is_let":false,"name":"num","sexp":"(:c Int)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"name":"den","sexp":"(:c Nat)"},{"binder_role":":implicit","context_i...	{"children":[{"source":"exact","sourceEnd":1215,"sourceStart":1210,"tag":"atom"},{"children":[{"name":"Rat.normalize.reduced","semanticRole":"global","source":"normalize.reduced","sourceEnd":1233,"sourceStart":1216,"tag":"identifier"},{"children":[{"contextIndex":4,"semanticRole":"local","source":"den_nz","sourceEnd":1...	[]	[{"source":"normalize.reduced den_nz e","source_end":1242,"source_start":1216,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1540","is_instance":false,"is_let":false,"user_name":"num"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"user_name":"den"},{"binder_role":":implicit","context_index":3,"internal_name":"_...	9	7	exact	true	1	5	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	85f1862a1cf986695c3c12d1cae4a38cc5179a154b488c18c9a0e7ba59956194	85504bdbb14d92d2c81efedf989b516fdcb9c5f85396069178704438fba88727	e03d542adda1976724ca9e6c61ecb2d751c1f9b9c9b4ec20eeb080d305f0e981	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	1,012	List.asString_inj	Mathlib/Data/String/Basic.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [← <a>List.toList_asString</a> l, ← <a>List.toList_asString</a> l', <a>String.toList_inj</a>, h]	l l' : List Char h : l.asString = l'.asString ⊢ l = l'		((:c Eq) ((:c List) (:c Char)) (:fv _uniq.43296) (:fv _uniq.43297))	[{"name":"l","sexp":"((:c List) (:c Char))"},{"name":"l'","sexp":"((:c List) (:c Char))"},{"name":"h","sexp":"((:c Eq) (:c String) ((:c List.asString) (:fv _uniq.43296)) ((:c List.asString) (:fv _uniq.43297)))"}]	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:c Char)))) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2)))	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.43296","is_instance":false,"is_let":false,"name":"l","sexp":"(:app (:c List) (:arg :explicit 0 (:c Char)))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.43297","is_instance":false,"is_let":false,"name":"l'","sexp":"(:app (:c Li...	{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":7793,"sourceStart":7791,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7795,"sourceStart":7794,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"sour...	[]	[{"source":"toList_asString l","source_end":7816,"source_start":7799,"syntax_kind":"Lean.Parser.Term.app"},{"source":"toList_asString l'","source_end":7840,"source_start":7822,"syntax_kind":"Lean.Parser.Term.app"},{"source":"toList_inj","source_end":7852,"source_start":7842,"syntax_kind":"ident"},{"source":"h","source_...	[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.43296","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.43297","is_instance":false,"is_let":false,"user_name":"l'"},{"binder_role":":explicit","context_index":3,"internal_name":"_u...	44	2	exact	true	1	3	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	f361a6fda084ab684025e4027cff030d014b75fcd912a7d173272681d2467f7c	cbde51af5630c169db32a500d9b360a00d4a5a1a75a3f470e625742414d208e2	07d344cfc8542e6e8dfcec0d1d331475597d8563db4ad1bc69277c4daf3416ec	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	1,013	SimpleGraph.IsSRGWith.compl_is_regular	Mathlib/Combinatorics/SimpleGraph/StronglyRegular.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [← h.card, <a>Nat.sub_sub</a>, <a>add_comm</a>, ← <a>Nat.sub_sub</a>]	V : Type u inst✝² : Fintype V inst✝¹ : DecidableEq V G : SimpleGraph V inst✝ : DecidableRel G.Adj n k ℓ μ : ℕ h : G.IsSRGWith n k ℓ μ ⊢ Gᶜ.IsRegularOfDegree (n - k - 1)	V : Type u inst✝² : Fintype V inst✝¹ : DecidableEq V G : SimpleGraph V inst✝ : DecidableRel G.Adj n k ℓ μ : ℕ h : G.IsSRGWith n k ℓ μ ⊢ Gᶜ.IsRegularOfDegree (Fintype.card V - 1 - k)	((:c SimpleGraph.IsRegularOfDegree) (:fv _uniq.21973) ((:c HasCompl.compl) ((:c SimpleGraph) (:fv _uniq.21973)) ((:c SimpleGraph.hasCompl) (:fv _uniq.21973)) (:fv _uniq.21988)) (:lambda v (:fv _uniq.21973) ((:c SimpleGraph.neighborSetFintype) (:fv _uniq.21973) ((:c HasCompl.compl) ((:c SimpleGraph) (:fv _uniq.21973)) (...	[{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c Fintype) (:fv _uniq.21973))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.21973))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.21973))"},{"name":"inst✝","sexp":"((:c DecidableRel) (:fv _uniq.21973) ((:c SimpleGraph.Adj) (:fv _uniq.2197...	(:app (:c SimpleGraph.IsRegularOfDegree) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HasCompl.compl) (:arg :implicit-type 0 (:app (:c SimpleGraph) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasCompl) (:arg :explicit 0 (:app (:c SimpleGraph) (:arg :explicit 0 (:fv FV0)))))...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21973","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21976","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Fintype) (:arg :explici...	{"children":[{"source":"rw","sourceEnd":6280,"sourceStart":6278,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6282,"sourceStart":6281,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":6285,"sourceStart":...	[]	[{"source":"h.card","source_end":6292,"source_start":6286,"syntax_kind":"ident"},{"source":"Nat.sub_sub","source_end":6305,"source_start":6294,"syntax_kind":"ident"},{"source":"add_comm","source_end":6315,"source_start":6307,"syntax_kind":"ident"},{"source":"Nat.sub_sub","source_end":6332,"source_start":6321,"syntax_ki...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21973","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21976","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...	24	4	exact	true	1	10	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	27a64690fdea566f68b7c4144bd3aacdf6dfe44d536eb45242a6bd17143fa9cd	4e4775a05bc7a5974bd50c63e677cadac52238ad2db4e59a9bb4e64dabf92028	24ac91eccf8479d193d4fb11d6d4b26c97fee754862aab545fecb77633980524	aef3a70ac7e1e08df35c3a0cf8a01a4cebdb870f4ee57e011ebcd47d9f8abc08
cat-searcher/leandojo-benchmark-4-random	test	1,014	SimpleGraph.IsSRGWith.compl_is_regular	Mathlib/Combinatorics/SimpleGraph/StronglyRegular.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact h.regular.compl	V : Type u inst✝² : Fintype V inst✝¹ : DecidableEq V G : SimpleGraph V inst✝ : DecidableRel G.Adj n k ℓ μ : ℕ h : G.IsSRGWith n k ℓ μ ⊢ Gᶜ.IsRegularOfDegree (Fintype.card V - 1 - k)		((:c SimpleGraph.IsRegularOfDegree) (:fv _uniq.21973) ((:c HasCompl.compl) ((:c SimpleGraph) (:fv _uniq.21973)) ((:c SimpleGraph.hasCompl) (:fv _uniq.21973)) (:fv _uniq.21988)) (:lambda v (:fv _uniq.21973) ((:c SimpleGraph.neighborSetFintype) (:fv _uniq.21973) ((:c HasCompl.compl) ((:c SimpleGraph) (:fv _uniq.21973)) (...	[{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c Fintype) (:fv _uniq.21973))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.21973))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.21973))"},{"name":"inst✝","sexp":"((:c DecidableRel) (:fv _uniq.21973) ((:c SimpleGraph.Adj) (:fv _uniq.2197...	(:app (:c SimpleGraph.IsRegularOfDegree) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HasCompl.compl) (:arg :implicit-type 0 (:app (:c SimpleGraph) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasCompl) (:arg :explicit 0 (:app (:c SimpleGraph) (:arg :explicit 0 (:fv FV0)))))...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21973","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21976","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Fintype) (:arg :explici...	{"children":[{"source":"exact","sourceEnd":6341,"sourceStart":6336,"tag":"atom"},{"name":"SimpleGraph.IsRegularOfDegree.compl","semanticRole":"global","source":"h.regular.compl","sourceEnd":6357,"sourceStart":6342,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact h.regular.compl","sourceEnd":6357,"...	[]	[{"source":"h.regular.compl","source_end":6357,"source_start":6342,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21973","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21976","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":...	24	10	exact	true	1	10	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	740b39c0ac40ed0b8f819c79c99f3bc37643d71fb0fa51490b9878e7a66b0a83	aef3a70ac7e1e08df35c3a0cf8a01a4cebdb870f4ee57e011ebcd47d9f8abc08	e865afa6e36b66eee3b8df3d9dbb110f56860d1dcf49b1011e700f7eb95aae99	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	1,015	Complex.differentiableOn_tsum_of_summable_norm	Mathlib/Analysis/Complex/LocallyUniformLimit.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	classical have hc := (<a>tendstoUniformlyOn_tsum</a> hu hF_le).<a>TendstoUniformlyOn.tendstoLocallyUniformlyOn</a> refine hc.differentiableOn (<a>Filter.eventually_of_forall</a> fun s => ?_) hU exact <a>DifferentiableOn.sum</a> fun i _ => hf i	E : Type u_1 ι : Type u_2 inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace ℂ E inst✝ : CompleteSpace E U K : Set ℂ z : ℂ M r δ : ℝ φ : Filter ι F : ι → ℂ → E f g : ℂ → E u : ι → ℝ hu : Summable u hf : ∀ (i : ι), DifferentiableOn ℂ (F i) U hU : IsOpen U hF_le : ∀ (i : ι), ∀ w ∈ U, ‖F i w‖ ≤ u i ⊢ DifferentiableOn ℂ (f...		((:c DifferentiableOn) (:c Complex) ((:c DenselyNormedField.toNontriviallyNormedField) (:c Complex) (:c Complex.instDenselyNormedField)) (:c Complex) (:c Complex.instNormedAddCommGroup) ((:c InnerProductSpace.toNormedSpace) (:c Complex) (:c Complex) (:c Complex.instRCLike) (:c Complex.instNormedAddCommGroup) ((:c RCLik...	[{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.55430))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Complex) (:fv _uniq.55430) (:c Complex.instNormedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.5543...	(:app (:c DifferentiableOn) (:arg :explicit 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:c Complex))))) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Complex))))) (:arg :instance 4 (:inst...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55430","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55433","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":instance-impli...	{"children":[{"children":[{"children":[{"children":[{"source":"classical","sourceEnd":9916,"sourceStart":9907,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"have","sourceEnd":9923,"sourceStart":9919,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source...	[]	[{"source":"(tendstoUniformlyOn_tsum hu hF_le).tendstoLocallyUniformlyOn","source_end":9990,"source_start":9930,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"hc.differentiableOn (eventually_of_forall fun s => ?_) hU","source_end":10057,"source_start":10000,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Differenti...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55430","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55433","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":instance-implicit","context_index":2,"internal_n...	33	2	exact	true	1	20	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	b30b1ef1c42f7feeb6ad1e95534f316b9aa656aba9ea0dbe516d04fafe9ec235	3ee6a32b4e5d8e47ec36c4bfe919076a33ae536167dcb5caeadf53798c338803	6c0b334787a43c21ebe5b9db5bab4b693426eda4d37b39d5923197796ed66b33	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	1,016	Complex.differentiableOn_tsum_of_summable_norm	Mathlib/Analysis/Complex/LocallyUniformLimit.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	have hc := (<a>tendstoUniformlyOn_tsum</a> hu hF_le).<a>TendstoUniformlyOn.tendstoLocallyUniformlyOn</a>	E : Type u_1 ι : Type u_2 inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace ℂ E inst✝ : CompleteSpace E U K : Set ℂ z : ℂ M r δ : ℝ φ : Filter ι F : ι → ℂ → E f g : ℂ → E u : ι → ℝ hu : Summable u hf : ∀ (i : ι), DifferentiableOn ℂ (F i) U hU : IsOpen U hF_le : ∀ (i : ι), ∀ w ∈ U, ‖F i w‖ ≤ u i ⊢ DifferentiableOn ℂ (f...	E : Type u_1 ι : Type u_2 inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace ℂ E inst✝ : CompleteSpace E U K : Set ℂ z : ℂ M r δ : ℝ φ : Filter ι F : ι → ℂ → E f g : ℂ → E u : ι → ℝ hu : Summable u hf : ∀ (i : ι), DifferentiableOn ℂ (F i) U hU : IsOpen U hF_le : ∀ (i : ι), ∀ w ∈ U, ‖F i w‖ ≤ u i hc : TendstoLocallyUnif...	((:c DifferentiableOn) (:c Complex) ((:c DenselyNormedField.toNontriviallyNormedField) (:c Complex) (:c Complex.instDenselyNormedField)) (:c Complex) (:c Complex.instNormedAddCommGroup) ((:c InnerProductSpace.toNormedSpace) (:c Complex) (:c Complex) (:c Complex.instRCLike) (:c Complex.instNormedAddCommGroup) ((:c RCLik...	[{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.55430))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Complex) (:fv _uniq.55430) (:c Complex.instNormedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.5543...	(:app (:c DifferentiableOn) (:arg :explicit 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:c Complex))))) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Complex))))) (:arg :instance 4 (:inst...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55430","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55433","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":instance-impli...	{"children":[{"source":"have","sourceEnd":9923,"sourceStart":9919,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hc","sourceEnd":9926,"sourceStart":9924,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hc","sourceEnd":9926,"sourceStart":9924,"tag":"node"},{"...	[]	[{"source":"(tendstoUniformlyOn_tsum hu hF_le).tendstoLocallyUniformlyOn","source_end":9990,"source_start":9930,"syntax_kind":"Lean.Parser.Term.proj"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55430","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55433","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":instance-implicit","context_index":2,"internal_n...	33	7	exact	true	1	20	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	0692087225b94fd2082cf51179134ac577473af6221a9760a253b65b14b18eea	3ee6a32b4e5d8e47ec36c4bfe919076a33ae536167dcb5caeadf53798c338803	6b1b54b6afeb6cec0269f41a02ff332eb1a71f52d1055d2fb82b6405bfda78dc	14b1c40cd8f7bb4d090b47be1e923f4804ac010e3e97b5b970a824017a0a47c3
cat-searcher/leandojo-benchmark-4-random	test	1,017	Complex.differentiableOn_tsum_of_summable_norm	Mathlib/Analysis/Complex/LocallyUniformLimit.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	refine hc.differentiableOn (<a>Filter.eventually_of_forall</a> fun s => ?_) hU	E : Type u_1 ι : Type u_2 inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace ℂ E inst✝ : CompleteSpace E U K : Set ℂ z : ℂ M r δ : ℝ φ : Filter ι F : ι → ℂ → E f g : ℂ → E u : ι → ℝ hu : Summable u hf : ∀ (i : ι), DifferentiableOn ℂ (F i) U hU : IsOpen U hF_le : ∀ (i : ι), ∀ w ∈ U, ‖F i w‖ ≤ u i hc : TendstoLocallyUnif...	E : Type u_1 ι : Type u_2 inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace ℂ E inst✝ : CompleteSpace E U K : Set ℂ z : ℂ M r δ : ℝ φ : Filter ι F : ι → ℂ → E f g : ℂ → E u : ι → ℝ hu : Summable u hf : ∀ (i : ι), DifferentiableOn ℂ (F i) U hU : IsOpen U hF_le : ∀ (i : ι), ∀ w ∈ U, ‖F i w‖ ≤ u i hc : TendstoLocallyUnif...	((:c DifferentiableOn) (:c Complex) ((:c DenselyNormedField.toNontriviallyNormedField) (:c Complex) (:c Complex.instDenselyNormedField)) (:c Complex) (:c Complex.instNormedAddCommGroup) ((:c InnerProductSpace.toNormedSpace) (:c Complex) (:c Complex) (:c Complex.instRCLike) (:c Complex.instNormedAddCommGroup) ((:c RCLik...	[{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.55430))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Complex) (:fv _uniq.55430) (:c Complex.instNormedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.5543...	(:app (:c DifferentiableOn) (:arg :explicit 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:c Complex))))) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Complex))))) (:arg :instance 4 (:inst...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55430","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55433","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":instance-impli...	{"children":[{"source":"refine","sourceEnd":9999,"sourceStart":9993,"tag":"atom"},{"children":[{"source":"hc.differentiableOn","sourceEnd":10019,"sourceStart":10000,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":10021,"sourceStart":10020,"tag":"atom"},{"children":[{"name":"Filter.eventually_of_...	[]	[{"source":"hc.differentiableOn (eventually_of_forall fun s => ?_) hU","source_end":10057,"source_start":10000,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55430","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55433","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":instance-implicit","context_index":2,"internal_n...	33	8	exact	true	1	21	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	11648c7f89f9257d452eae734caea1c31a384d5779b33dd85a7cccb1624af712	14b1c40cd8f7bb4d090b47be1e923f4804ac010e3e97b5b970a824017a0a47c3	48aa2090d096373722822f9beaf92ef6fc945d2ae72735de3a22c678cb3d89de	e04e98f2894edbb7d2e236b4e717e94eea9633ee7f53e140725833a9ea2e03db
cat-searcher/leandojo-benchmark-4-random	test	1,018	Complex.differentiableOn_tsum_of_summable_norm	Mathlib/Analysis/Complex/LocallyUniformLimit.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact <a>DifferentiableOn.sum</a> fun i _ => hf i	E : Type u_1 ι : Type u_2 inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace ℂ E inst✝ : CompleteSpace E U K : Set ℂ z : ℂ M r δ : ℝ φ : Filter ι F : ι → ℂ → E f g : ℂ → E u : ι → ℝ hu : Summable u hf : ∀ (i : ι), DifferentiableOn ℂ (F i) U hU : IsOpen U hF_le : ∀ (i : ι), ∀ w ∈ U, ‖F i w‖ ≤ u i hc : TendstoLocallyUnif...		((:c DifferentiableOn) (:c Complex) ((:c DenselyNormedField.toNontriviallyNormedField) (:c Complex) (:c Complex.instDenselyNormedField)) (:c Complex) (:c Complex.instNormedAddCommGroup) ((:c InnerProductSpace.toNormedSpace) (:c Complex) (:c Complex) (:c Complex.instRCLike) (:c Complex.instNormedAddCommGroup) ((:c RCLik...	[{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.55430))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Complex) (:fv _uniq.55430) (:c Complex.instNormedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.5543...	(:app (:c DifferentiableOn) (:arg :explicit 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:c Complex))))) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Complex))))) (:arg :instance 4 (:inst...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55430","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55433","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":instance-impli...	{"children":[{"source":"exact","sourceEnd":10065,"sourceStart":10060,"tag":"atom"},{"children":[{"name":"DifferentiableOn.sum","semanticRole":"global","source":"DifferentiableOn.sum","sourceEnd":10086,"sourceStart":10066,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":10090,"sourceStart":10087...	[]	[{"source":"DifferentiableOn.sum fun i _ => hf i","source_end":10102,"source_start":10066,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55430","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55433","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":instance-implicit","context_index":2,"internal_n...	33	9	exact	true	1	22	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	6571ca0091a1148c08fc7a45c948bc6932db66c33db8179d61643cca03ed1921	e04e98f2894edbb7d2e236b4e717e94eea9633ee7f53e140725833a9ea2e03db	c7c8d88fbe7adb66f9f5deb96ccf6586395baf8f39e9707ab411e39369edf75e	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	1,019	Matrix.Represents.add	Mathlib/LinearAlgebra/Matrix/Charpoly/LinearMap.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	delta <a>Matrix.Represents</a> at h h' ⊢	ι : Type u_1 inst✝⁴ : Fintype ι M : Type u_2 inst✝³ : AddCommGroup M R : Type u_3 inst✝² : CommRing R inst✝¹ : Module R M I : Ideal R b : ι → M hb : Submodule.span R (Set.range b) = ⊤ inst✝ : DecidableEq ι A A' : Matrix ι ι R f f' : Module.End R M h : Represents b A f h' : Represents b A' f' ⊢ Represents b (A + A') (f ...	ι : Type u_1 inst✝⁴ : Fintype ι M : Type u_2 inst✝³ : AddCommGroup M R : Type u_3 inst✝² : CommRing R inst✝¹ : Module R M I : Ideal R b : ι → M hb : Submodule.span R (Set.range b) = ⊤ inst✝ : DecidableEq ι A A' : Matrix ι ι R f f' : Module.End R M h : (PiToModule.fromMatrix R b) A = (PiToModule.fromEnd R b) f h' : (PiT...	((:c Matrix.Represents) (:fv _uniq.103949) (:fv _uniq.103952) (:fv _uniq.103955) (:fv _uniq.103958) (:fv _uniq.103961) (:fv _uniq.103964) (:fv _uniq.104577) (:fv _uniq.104727) (:fv _uniq.105198) ((:c HAdd.hAdd) ((:c Matrix) (:fv _uniq.103949) (:fv _uniq.103949) (:fv _uniq.103961)) ((:c Matrix) (:fv _uniq.103949) (:fv _...	[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Fintype) (:fv _uniq.103949))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c AddCommGroup) (:fv _uniq.103955))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c CommRing) (:fv _uniq.103961))"},{"name":"i...	(:app (:c Matrix.Represents) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Fintype) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :implicit-type 4 (:fv FV4)) (:arg :instance 5 ...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.103949","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.103952","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Fintype) (:arg :expli...	{"children":[{"source":"delta","sourceEnd":5892,"sourceStart":5887,"tag":"atom"},{"children":[{"name":"Matrix.Represents","semanticRole":"global","source":"Matrix.Represents","sourceEnd":5910,"sourceStart":5893,"tag":"identifier"}],"kind":"null","source":"Matrix.Represents","sourceEnd":5910,"sourceStart":5893,"tag":"no...	[]	[{"source":"Matrix.Represents","source_end":5910,"source_start":5893,"syntax_kind":"ident"},{"source":"h","source_end":5915,"source_start":5914,"syntax_kind":"ident"},{"source":"h'","source_end":5918,"source_start":5916,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.103949","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.103952","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...	35	4	exact	true	1	17	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	f0359315a8f2cb7431507b93949b27b5aa3eb35e75485634e7ad52bd2018163d	df49a98b024613c1836fa08701bd2e489be23833d5b433a7081aa52a1800dd09	80e308469cb3cce205233c80e1b2dda29a40d53cc363613f65786b2c3ad051c2	982c6155e4034ebc5928df9ff2b6e1b0a1146ecaff2453e8f6a458c5f2bd9995
cat-searcher/leandojo-benchmark-4-random	test	1,020	Matrix.Represents.add	Mathlib/LinearAlgebra/Matrix/Charpoly/LinearMap.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rw [<a>map_add</a>, <a>map_add</a>, h, h']	ι : Type u_1 inst✝⁴ : Fintype ι M : Type u_2 inst✝³ : AddCommGroup M R : Type u_3 inst✝² : CommRing R inst✝¹ : Module R M I : Ideal R b : ι → M hb : Submodule.span R (Set.range b) = ⊤ inst✝ : DecidableEq ι A A' : Matrix ι ι R f f' : Module.End R M h : (PiToModule.fromMatrix R b) A = (PiToModule.fromEnd R b) f h' : (PiT...		((:c Eq) ((:c LinearMap) (:fv _uniq.103961) (:fv _uniq.103961) ((:c CommSemiring.toSemiring) (:fv _uniq.103961) ((:c CommRing.toCommSemiring) (:fv _uniq.103961) (:fv _uniq.103964))) ((:c CommSemiring.toSemiring) (:fv _uniq.103961) ((:c CommRing.toCommSemiring) (:fv _uniq.103961) (:fv _uniq.103964))) ((:c RingHom.id) (:...	[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Fintype) (:fv _uniq.103949))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c AddCommGroup) (:fv _uniq.103955))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c CommRing) (:fv _uniq.103961))"},{"name":"i...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:fv FV4)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV4))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 4 (:app (:...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.103949","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.103952","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Fintype) (:arg :expli...	{"children":[{"source":"rw","sourceEnd":5926,"sourceStart":5924,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5928,"sourceStart":5927,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"map_add","semanticRo...	[]	[{"source":"map_add","source_end":5935,"source_start":5928,"syntax_kind":"ident"},{"source":"map_add","source_end":5944,"source_start":5937,"syntax_kind":"ident"},{"source":"h","source_end":5947,"source_start":5946,"syntax_kind":"ident"},{"source":"h'","source_end":5951,"source_start":5949,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.103949","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.103952","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...	35	6	exact	true	1	17	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	36a19c76eaaa356c902a57ce535e0caa382b038c91f343c516350119b7532594	982c6155e4034ebc5928df9ff2b6e1b0a1146ecaff2453e8f6a458c5f2bd9995	8a5cdec2aff34c3fd146420eebfe06140c33b6e64b1ad0a4ad6d9d8e7f23731e	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	1,021	le_of_forall_one_lt_div_le	Mathlib/Algebra/Order/Group/DenselyOrdered.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simpa only [<a>div_eq_mul_inv</a>, <a>inv_inv</a>] using h ε⁻¹ (<a>Left.one_lt_inv_iff</a>.2 ε1)	α : Type u_1 inst✝³ : Group α inst✝² : LinearOrder α inst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1 inst✝ : DenselyOrdered α a b c : α h : ∀ (ε : α), 1 < ε → a / ε ≤ b ε : α ε1 : ε < 1 ⊢ a * ε ≤ b		((:c LE.le) (:fv _uniq.2030) ((:c Preorder.toLE) (:fv _uniq.2030) ((:c PartialOrder.toPreorder) (:fv _uniq.2030) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.2030) ((:c Lattice.toSemilatticeInf) (:fv _uniq.2030) ((:c DistribLattice.toLattice) (:fv _uniq.2030) ((:c instDistribLatticeOfLinearOrder) (:fv _uniq.2030) (:f...	[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Group) (:fv _uniq.2030))"},{"name":"inst✝²","sexp":"((:c LinearOrder) (:fv _uniq.2030))"},{"name":"inst✝¹","sexp":"((:c CovariantClass) (:fv _uniq.2030) (:fv _uniq.2030) (:lambda _ (:fv _uniq.2030) (:lambda _ (:fv _uniq.2030) ((:c HMul.hMul) (:fv _u...	(:app (:c LE.le) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2030","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2033","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Group) (:arg :explicit 0 ...	{"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":1130,"sourceStart":1125,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":...	[]	[{"source":"div_eq_mul_inv","source_end":1151,"source_start":1137,"syntax_kind":"ident"},{"source":"inv_inv","source_end":1160,"source_start":1153,"syntax_kind":"ident"},{"source":"h ε⁻¹ (Left.one_lt_inv_iff.2 ε1)","source_end":1205,"source_start":1168,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2030","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2033","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":2,...	10	2	exact	true	1	11	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	742c2ad41ea610773fb75cea3051986c6ff73095680d4ed6f66b3861a2866b8a	6038c0954d756ce071a2b7319f4a5e073566e1913d551709aed739cd944edefa	a4d41a88abd6f70820a5138dddac46741741d2d48b748c8c0a6aa4565ec20a95	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	1,022	Directed.exists_mem_subset_of_finset_subset_biUnion	Mathlib/Data/Set/Finite.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	induction s using <a>Finset.cons_induction</a> with \| <a>Finset.empty</a> => simp \| <a>Finset.cons</a> b t hbt iht => simp only [<a>Finset.coe_cons</a>, <a>Set.insert_subset_iff</a>, <a>Set.mem_iUnion</a>] at hs ⊢ rcases hs.imp_right iht with ⟨⟨i, hi⟩, j, hj⟩ rcases h i j with ⟨k, hik, hjk⟩ exact ⟨k, hik hi, hj.trans h...	α✝ : Type u β : Type v ι✝ : Sort w γ : Type x inst✝¹ : LinearOrder α✝ s✝ : Set α✝ α : Type u_1 ι : Type u_2 inst✝ : Nonempty ι f : ι → Set α h : Directed (fun x x_1 => x ⊆ x_1) f s : Finset α hs : ↑s ⊆ ⋃ i, f i ⊢ ∃ i, ↑s ⊆ f i		((:c Exists) (:fv _uniq.201448) (:lambda i (:fv _uniq.201448) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.201447)) ((:c Set.instHasSubset) (:fv _uniq.201447)) ((:c Finset.toSet) (:fv _uniq.201447) (:fv _uniq.201452)) ((:fv _uniq.201450) 0))))	[{"name":"α✝","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"ι✝","sexp":"(:sort w)"},{"name":"γ","sexp":"(:sort (+ x 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrder) (:fv _uniq.201224))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.201224))"},{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"ι","...	(:app (:c Exists) (:arg :implicit-type 0 (:fv FV8)) (:arg :explicit 1 (:lambda i :explicit (:fv FV8) (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV7)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV7))))))) (:...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201224","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201226","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...	{"children":[{"children":[{"children":[{"children":[{"source":"induction","sourceEnd":78029,"sourceStart":78020,"tag":"atom"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"s","sourceEnd":78031,"sourceStart":78030,"tag":"identifier"}],"kind":"null","source":"s","sourceEnd":78031,"sourceStart":78030,"t...	[]	[{"source":"s","source_end":78031,"source_start":78030,"syntax_kind":"ident"},{"source":"Finset.cons_induction","source_end":78059,"source_start":78038,"syntax_kind":"ident"},{"source":"empty","source_end":78074,"source_start":78069,"syntax_kind":"ident"},{"source":"cons","source_end":78091,"source_start":78087,"syntax...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201224","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201226","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...	616	2	exact	true	1	13	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	c13405dbcb71f3f25a9c82b99cf0eec969addf11691674b74561381839949a6c	d98cb59421f4d153a94be8c0a9f0b3663802e02ae3ad9827284643e938738bca	1c0017ebd60e113045acb9dedacb47a1782166ca59a05c3b03e6289948288d55	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	1,023	Directed.exists_mem_subset_of_finset_subset_biUnion	Mathlib/Data/Set/Finite.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp	case empty α✝ : Type u β : Type v ι✝ : Sort w γ : Type x inst✝¹ : LinearOrder α✝ s : Set α✝ α : Type u_1 ι : Type u_2 inst✝ : Nonempty ι f : ι → Set α h : Directed (fun x x_1 => x ⊆ x_1) f hs : ↑∅ ⊆ ⋃ i, f i ⊢ ∃ i, ↑∅ ⊆ f i		((:c Exists) (:fv _uniq.201448) (:lambda i (:fv _uniq.201448) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.201447)) ((:c Set.instHasSubset) (:fv _uniq.201447)) ((:c Finset.toSet) (:fv _uniq.201447) ((:c EmptyCollection.emptyCollection) ((:c Finset) (:fv _uniq.201447)) ((:c Finset.instEmptyCollection) (:fv _uniq.201447))...	[{"name":"α✝","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"ι✝","sexp":"(:sort w)"},{"name":"γ","sexp":"(:sort (+ x 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrder) (:fv _uniq.201224))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.201224))"},{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"ι","s...	(:app (:c Exists) (:arg :implicit-type 0 (:fv FV8)) (:arg :explicit 1 (:lambda i :explicit (:fv FV8) (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV7)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV7))))))) (:...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201224","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201226","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...	{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":78082,"sourceStart":78078,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","sour...	[]	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201224","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201226","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...	616	7	exact	true	1	12	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	74608c82054935cab56bd85ee353a9c9f82e233fd67276fe655cb4fe5ea287fd	6fdf4721762e4838470242fa40a6a8e110624dd533943a2bb3f779de388fecd3	8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	1,024	Directed.exists_mem_subset_of_finset_subset_biUnion	Mathlib/Data/Set/Finite.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp only [<a>Finset.coe_cons</a>, <a>Set.insert_subset_iff</a>, <a>Set.mem_iUnion</a>] at hs ⊢	case cons α✝ : Type u β : Type v ι✝ : Sort w γ : Type x inst✝¹ : LinearOrder α✝ s : Set α✝ α : Type u_1 ι : Type u_2 inst✝ : Nonempty ι f : ι → Set α h : Directed (fun x x_1 => x ⊆ x_1) f b : α t : Finset α hbt : b ∉ t iht : ↑t ⊆ ⋃ i, f i → ∃ i, ↑t ⊆ f i hs : ↑(Finset.cons b t hbt) ⊆ ⋃ i, f i ⊢ ∃ i, ↑(Finset.cons b t h...	case cons α✝ : Type u β : Type v ι✝ : Sort w γ : Type x inst✝¹ : LinearOrder α✝ s : Set α✝ α : Type u_1 ι : Type u_2 inst✝ : Nonempty ι f : ι → Set α h : Directed (fun x x_1 => x ⊆ x_1) f b : α t : Finset α hbt : b ∉ t iht : ↑t ⊆ ⋃ i, f i → ∃ i, ↑t ⊆ f i hs : (∃ i, b ∈ f i) ∧ ↑t ⊆ ⋃ i, f i ⊢ ∃ i, b ∈ f i ∧ ↑t ⊆ f i	((:c Exists) (:fv _uniq.201448) (:lambda i (:fv _uniq.201448) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.201447)) ((:c Set.instHasSubset) (:fv _uniq.201447)) ((:c Finset.toSet) (:fv _uniq.201447) ((:c Finset.cons) (:fv _uniq.201447) (:fv _uniq.201609) (:fv _uniq.201610) (:fv _uniq.201611))) ((:fv _uniq.201450) 0))))	[{"name":"α✝","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"ι✝","sexp":"(:sort w)"},{"name":"γ","sexp":"(:sort (+ x 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrder) (:fv _uniq.201224))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.201224))"},{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"ι","s...	(:app (:c Exists) (:arg :implicit-type 0 (:fv FV8)) (:arg :explicit 1 (:lambda i :explicit (:fv FV8) (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV7)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV7))))))) (:...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201224","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201226","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...	{"children":[{"source":"simp","sourceEnd":78115,"sourceStart":78111,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":78120,"sourceStart":78116,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":781...	[]	[{"source":"Finset.coe_cons","source_end":78137,"source_start":78122,"syntax_kind":"ident"},{"source":"Set.insert_subset_iff","source_end":78160,"source_start":78139,"syntax_kind":"ident"},{"source":"Set.mem_iUnion","source_end":78176,"source_start":78162,"syntax_kind":"ident"},{"source":"hs","source_end":78183,"source...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201224","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201226","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...	616	13	exact	true	1	16	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	ecc9901cea3bc0145e15c655d0ac5626850bb5fe4fa50e3371f42eb5a3274ba2	a3761b4ff79a16005e4fb2eb0e59aa5e8b4f137e761583fa0e264c64bb51f86d	37073395c894d4af77261251935a639586b6d6df3f7b369d0e5065e3bd6c1692	999a2d07b8774fa61635bcf3f648376c9c240920a14f413938ab836c83cb50de
cat-searcher/leandojo-benchmark-4-random	test	1,025	Directed.exists_mem_subset_of_finset_subset_biUnion	Mathlib/Data/Set/Finite.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rcases hs.imp_right iht with ⟨⟨i, hi⟩, j, hj⟩	case cons α✝ : Type u β : Type v ι✝ : Sort w γ : Type x inst✝¹ : LinearOrder α✝ s : Set α✝ α : Type u_1 ι : Type u_2 inst✝ : Nonempty ι f : ι → Set α h : Directed (fun x x_1 => x ⊆ x_1) f b : α t : Finset α hbt : b ∉ t iht : ↑t ⊆ ⋃ i, f i → ∃ i, ↑t ⊆ f i hs : (∃ i, b ∈ f i) ∧ ↑t ⊆ ⋃ i, f i ⊢ ∃ i, b ∈ f i ∧ ↑t ⊆ f i	case cons.intro.intro.intro α✝ : Type u β : Type v ι✝ : Sort w γ : Type x inst✝¹ : LinearOrder α✝ s : Set α✝ α : Type u_1 ι : Type u_2 inst✝ : Nonempty ι f : ι → Set α h : Directed (fun x x_1 => x ⊆ x_1) f b : α t : Finset α hbt : b ∉ t iht : ↑t ⊆ ⋃ i, f i → ∃ i, ↑t ⊆ f i hs : (∃ i, b ∈ f i) ∧ ↑t ⊆ ⋃ i, f i i : ι hi : ...	((:c Exists) (:fv _uniq.201448) (:lambda i (:fv _uniq.201448) ((:c And) ((:c Membership.mem) (:fv _uniq.201447) ((:c Set) (:fv _uniq.201447)) ((:c Set.instMembership) (:fv _uniq.201447)) (:fv _uniq.201609) ((:fv _uniq.201450) 0)) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.201447)) ((:c Set.instHasSubset) (:fv _uniq.20...	[{"name":"α✝","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"ι✝","sexp":"(:sort w)"},{"name":"γ","sexp":"(:sort (+ x 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrder) (:fv _uniq.201224))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.201224))"},{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"ι","s...	(:app (:c Exists) (:arg :implicit-type 0 (:fv FV8)) (:arg :explicit 1 (:lambda i :explicit (:fv FV8) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV7)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV7)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201224","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201226","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...	{"children":[{"source":"rcases","sourceEnd":78198,"sourceStart":78192,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"hs.imp_right","sourceEnd":78211,"sourceStart":78199,"tag":"identifier"},{"children":[{"contextIndex":15,"semanticRole":"local","sou...	[]	[{"source":"hs.imp_right iht","source_end":78215,"source_start":78199,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨⟨i, hi⟩, j, hj⟩","source_end":78245,"source_start":78221,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201224","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201226","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...	616	14	exact	true	1	16	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	afc6b1b1c6bc556273f8ec5fb8b9e6484136f0543d5834ca454e0be707b24e71	999a2d07b8774fa61635bcf3f648376c9c240920a14f413938ab836c83cb50de	9a5f7a15c91d03c39acaf889515695802faf287f84d7387296e12e874cd0f9da	978c459c58287bb5d4ac408c9344855c1a2d5f329e7b2224fa22f52b3080d19d
cat-searcher/leandojo-benchmark-4-random	test	1,026	Directed.exists_mem_subset_of_finset_subset_biUnion	Mathlib/Data/Set/Finite.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	rcases h i j with ⟨k, hik, hjk⟩	case cons.intro.intro.intro α✝ : Type u β : Type v ι✝ : Sort w γ : Type x inst✝¹ : LinearOrder α✝ s : Set α✝ α : Type u_1 ι : Type u_2 inst✝ : Nonempty ι f : ι → Set α h : Directed (fun x x_1 => x ⊆ x_1) f b : α t : Finset α hbt : b ∉ t iht : ↑t ⊆ ⋃ i, f i → ∃ i, ↑t ⊆ f i hs : (∃ i, b ∈ f i) ∧ ↑t ⊆ ⋃ i, f i i : ι hi : ...	case cons.intro.intro.intro.intro.intro α✝ : Type u β : Type v ι✝ : Sort w γ : Type x inst✝¹ : LinearOrder α✝ s : Set α✝ α : Type u_1 ι : Type u_2 inst✝ : Nonempty ι f : ι → Set α h : Directed (fun x x_1 => x ⊆ x_1) f b : α t : Finset α hbt : b ∉ t iht : ↑t ⊆ ⋃ i, f i → ∃ i, ↑t ⊆ f i hs : (∃ i, b ∈ f i) ∧ ↑t ⊆ ⋃ i, f i...	((:c Exists) (:fv _uniq.201448) (:lambda i (:fv _uniq.201448) ((:c And) ((:c Membership.mem) (:fv _uniq.201447) ((:c Set) (:fv _uniq.201447)) ((:c Set.instMembership) (:fv _uniq.201447)) (:fv _uniq.201609) ((:fv _uniq.201450) 0)) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.201447)) ((:c Set.instHasSubset) (:fv _uniq.20...	[{"name":"α✝","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"ι✝","sexp":"(:sort w)"},{"name":"γ","sexp":"(:sort (+ x 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrder) (:fv _uniq.201224))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.201224))"},{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"ι","s...	(:app (:c Exists) (:arg :implicit-type 0 (:fv FV8)) (:arg :explicit 1 (:lambda i :explicit (:fv FV8) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV7)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV7)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201224","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201226","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...	{"children":[{"source":"rcases","sourceEnd":78256,"sourceStart":78250,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"h","sourceEnd":78258,"sourceStart":78257,"tag":"identifier"},{"children":[{"contextIndex":...	[]	[{"source":"h i j","source_end":78262,"source_start":78257,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨k, hik, hjk⟩","source_end":78285,"source_start":78268,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201224","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201226","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...	616	15	exact	true	1	20	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	1099c6ee6a47d7f04234799e99705030cf79ce2f71a3c36176a076f140519c27	978c459c58287bb5d4ac408c9344855c1a2d5f329e7b2224fa22f52b3080d19d	58f93f5683d98c8381fc13f17b04ffa7913081d4d19514654c023b5744a71685	758765b43be68bb2dcee8374cec336be21c06fe2f766b6c46cc772b45bf8b181
cat-searcher/leandojo-benchmark-4-random	test	1,027	Directed.exists_mem_subset_of_finset_subset_biUnion	Mathlib/Data/Set/Finite.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	exact ⟨k, hik hi, hj.trans hjk⟩	case cons.intro.intro.intro.intro.intro α✝ : Type u β : Type v ι✝ : Sort w γ : Type x inst✝¹ : LinearOrder α✝ s : Set α✝ α : Type u_1 ι : Type u_2 inst✝ : Nonempty ι f : ι → Set α h : Directed (fun x x_1 => x ⊆ x_1) f b : α t : Finset α hbt : b ∉ t iht : ↑t ⊆ ⋃ i, f i → ∃ i, ↑t ⊆ f i hs : (∃ i, b ∈ f i) ∧ ↑t ⊆ ⋃ i, f i...		((:c Exists) (:fv _uniq.201448) (:lambda i (:fv _uniq.201448) ((:c And) ((:c Membership.mem) (:fv _uniq.201447) ((:c Set) (:fv _uniq.201447)) ((:c Set.instMembership) (:fv _uniq.201447)) (:fv _uniq.201609) ((:fv _uniq.201450) 0)) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.201447)) ((:c Set.instHasSubset) (:fv _uniq.20...	[{"name":"α✝","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"ι✝","sexp":"(:sort w)"},{"name":"γ","sexp":"(:sort (+ x 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrder) (:fv _uniq.201224))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.201224))"},{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"ι","s...	(:app (:c Exists) (:arg :implicit-type 0 (:fv FV8)) (:arg :explicit 1 (:lambda i :explicit (:fv FV8) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV7)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV7)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201224","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201226","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","...	{"children":[{"source":"exact","sourceEnd":78295,"sourceStart":78290,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":78299,"sourceStart":78296,"tag":"atom"},{"children":[{"contextIndex":21,"semanticRole":"local","source":"k","sourceEnd":78300,"sourceStart":78299,"tag":"identifier"},{"source":",","sourceEnd":78301,...	[]	[{"source":"⟨k, hik hi, hj.trans hjk⟩","source_end":78325,"source_start":78296,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.201224","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.201226","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"...	616	16	exact	true	1	23	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	8072872e66c706dbc01173256e4dacc9b617f9fc892e143d0400b75e1f18231d	758765b43be68bb2dcee8374cec336be21c06fe2f766b6c46cc772b45bf8b181	96729249d9e4873576cda83a410f2b0584a7a97ca687b190a76b393d80521c4b	d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random	test	1,029	CategoryTheory.Limits.colimitLimitToLimitColimit_injective	Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	cases <a>nonempty_fintype</a> J	J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J ⊢ Function.Injective (colimitLimitToLimitColimit F)	case intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J ⊢ Function.Injective (colimitLimitToLimitColimit F)	((:c Function.Injective) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c Cate...	[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...	(:app (:c Function.Injective) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...	{"children":[{"source":"cases","sourceEnd":2624,"sourceStart":2619,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"nonempty_fintype","semanticRole":"global","source":"nonempty_fintype","sourceEnd":2641,"sourceStart":2625,"tag":"identifier"},{"children...	[]	[{"source":"nonempty_fintype J\n -- Suppose we have two terms `x y` in the colimit (over `K`) of the limits (over `J`),\n -- and that these have the same image under `colimitLimitToLimitColimit F`.","source_end":2643,"source_start":2625,"syntax_kind":"Lean.Parser.Term.app"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...	16	7	exact	true	1	8	true	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	0742c0ae5031c2472c2d2bea06a61965f111dcde237a6c2b313042ba12451b44	2f2902f38d34ef229b6869e9bcd214012652b102af08e74cf28c204904386346	30fc837fc6ae919c3b9cc1c2d00fcd494aeaab2f7060e8b8ec879700ff1cf61f	c5709bdf23b5c85aa4a04473345f681f0800a958cb3a7264daf0b2493ab14533
cat-searcher/leandojo-benchmark-4-random	test	1,030	CategoryTheory.Limits.colimitLimitToLimitColimit_injective	Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	intro x y h	case intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J ⊢ Function.Injective (colimitLimitToLimitColimit F)	case intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J x y : colimit (curry.obj (swap K J ⋙ F) ⋙ lim) h : colimitLimitToLimitColimit F x = colimitLimitToLimitColimit F y ⊢ x = y	((:c Function.Injective) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c Cate...	[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...	(:app (:c Function.Injective) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...	{"children":[{"source":"intro","sourceEnd":2824,"sourceStart":2819,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":2826,"sourceStart":2825,"tag":"identifier"},{"semanticRole":"scoped_local","source":"y","sourceEnd":2828,"sourceStart":2827,"tag":"identifier"},{"semanticRole":"scoped_lo...	[{"role":"fresh_name","source":"x","source_end":2826,"source_start":2825,"syntax_kind":"ident"},{"role":"fresh_name","source":"y","source_end":2828,"source_start":2827,"syntax_kind":"ident"},{"role":"fresh_name","source":"h\n -- These elements of the colimit have representatives somewhere:","source_end":2830,"source...	[]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...	16	8	exact	true	1	9	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	bdd38190a278e0cf3b4d898cc70379bed19d2b52a90dcf919597c48d9f6fd3c4	c5709bdf23b5c85aa4a04473345f681f0800a958cb3a7264daf0b2493ab14533	8f914c6a717df1f1cf291444b94ef2db34185ddd85ab5f36ec311cc73078055d	d3ebe29595f068ffef11f2c6a99e8fe1bb5370c43d567b9ad6672d1d9f93eb1c
cat-searcher/leandojo-benchmark-4-random	test	1,031	CategoryTheory.Limits.colimitLimitToLimitColimit_injective	Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	obtain ⟨kx, x, rfl⟩ := <a>CategoryTheory.Limits.Types.jointly_surjective'</a> x	case intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J x y : colimit (curry.obj (swap K J ⋙ F) ⋙ lim) h : colimitLimitToLimitColimit F x = colimitLimitToLimitColimit F y ⊢ x = y	case intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J y : colimit (curry.obj (swap K J ⋙ F) ⋙ lim) kx : K x : (curry.obj (swap K J ⋙ F) ⋙ lim).obj kx h : colimitLimitToL...	((:c Eq) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c CategoryTheory.Funct...	[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.LargeCategory) ...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...	{"children":[{"source":"obtain","sourceEnd":2910,"sourceStart":2904,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":2914,"sourceStart":2911,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"kx","sourceEnd":...	[]	[{"source":"jointly_surjective' x","source_end":2952,"source_start":2931,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨kx, x, rfl⟩","source_end":2927,"source_start":2911,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...	16	9	exact	true	1	12	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	90abe1854dff1ab20e583920d19a499f921d019ca846c0a55a2c94c7b36f2395	d3ebe29595f068ffef11f2c6a99e8fe1bb5370c43d567b9ad6672d1d9f93eb1c	9c2e57ca549f11a16347bbb6859762b08d1697cfcadee9e55718149d88cbfe90	568661c2826a006ea8ec1f2ed3c41e8a0608f55e0fdb0a8395e9a2d3df4d48fe
cat-searcher/leandojo-benchmark-4-random	test	1,032	CategoryTheory.Limits.colimitLimitToLimitColimit_injective	Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	obtain ⟨ky, y, rfl⟩ := <a>CategoryTheory.Limits.Types.jointly_surjective'</a> y	case intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J y : colimit (curry.obj (swap K J ⋙ F) ⋙ lim) kx : K x : (curry.obj (swap K J ⋙ F) ⋙ lim).obj kx h : colimitLimitToL...	case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : (curry.obj (swap K J ⋙ F) ⋙ lim).obj kx ky : K y : (curry.obj (swap K J ⋙ F) ⋙ lim).obj ky h...	((:c Eq) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c CategoryTheory.Funct...	[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.LargeCategory) ...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...	{"children":[{"source":"obtain","sourceEnd":2963,"sourceStart":2957,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":2967,"sourceStart":2964,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"ky","sourceEnd":...	[]	[{"source":"jointly_surjective' y","source_end":3005,"source_start":2984,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨ky, y, rfl⟩","source_end":2980,"source_start":2964,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...	16	10	exact	true	1	13	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	5cc3d1909569ac39fc0d460c71b25b98f4142cdb387491cd018cfa79e8a8ab4d	568661c2826a006ea8ec1f2ed3c41e8a0608f55e0fdb0a8395e9a2d3df4d48fe	742373f03d7ded6d0e7e8d56891cf3bb3686d42233cb9ad54755da3e16ea3a0b	d96fca5b5cd3ab623e5f8fd52d4de84300e7e6f36ee8f1090e605231b83c82fa
cat-searcher/leandojo-benchmark-4-random	test	1,033	CategoryTheory.Limits.colimitLimitToLimitColimit_injective	Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	dsimp at x y	case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : (curry.obj (swap K J ⋙ F) ⋙ lim).obj kx ky : K y : (curry.obj (swap K J ⋙ F) ⋙ lim).obj ky h...	case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...	((:c Eq) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c CategoryTheory.Funct...	[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.LargeCategory) ...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...	{"children":[{"source":"dsimp","sourceEnd":3015,"sourceStart":3010,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"chil...	[]	[{"source":"x","source_end":3020,"source_start":3019,"syntax_kind":"ident"},{"source":"y\n -- Since the images of `x` and `y` are equal in a limit, they are equal componentwise\n -- (indexed by `j : J`),","source_end":3022,"source_start":3021,"syntax_kind":"ident"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...	16	11	exact	true	1	14	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	70e32371431cac6f444a39c4266524830235f1861551741a9847cf48d2a97e03	d96fca5b5cd3ab623e5f8fd52d4de84300e7e6f36ee8f1090e605231b83c82fa	3fa6fbd8f0efad3bbd676ad833ad11fc77913ac95d4f1d3e26bf29fa0479bd4c	8867d96a3bb0b372559e05e9d3560591ccc881902adc19114dff9db6eab04699
cat-searcher/leandojo-benchmark-4-random	test	1,034	CategoryTheory.Limits.colimitLimitToLimitColimit_injective	Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	replace h := fun j => <a>congr_arg</a> (<a>CategoryTheory.Limits.limit.π</a> (curry.obj F ⋙ <a>CategoryTheory.Limits.colim</a>) j) h	case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...	case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...	((:c Eq) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c CategoryTheory.Funct...	[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.LargeCategory) ...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...	{"children":[{"source":"replace","sourceEnd":3153,"sourceStart":3146,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":3155,"sourceStart":3154,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":3155,"sourceStart":3154,"tag":"node"},{...	[]	[{"source":"fun j => congr_arg (limit.π (curry.obj F ⋙ colim) j) h\n -- and they are equations in a filtered colimit,\n -- so for each `j` we have some place `k j` to the right of both `kx` and `ky`","source_end":3216,"source_start":3159,"syntax_kind":"Lean.Parser.Term.fun"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...	16	12	exact	true	1	14	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	12aae3afb686a5b7a38c97899f9f04084c1886ed21efe74451330c47ab00ac53	8867d96a3bb0b372559e05e9d3560591ccc881902adc19114dff9db6eab04699	bba0835b36005f5e8a0a4a487c8c20203b19e7cbc90aa30de220405777cbf76b	6c8dd099f1aae6a0c5726e0bb434f74c96df2149d1fcea45bc493c251a94800f
cat-searcher/leandojo-benchmark-4-random	test	1,035	CategoryTheory.Limits.colimitLimitToLimitColimit_injective	Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	simp? [colimit_eq_iff] at h says simp only [<a>CategoryTheory.Functor.comp_obj</a>, <a>CategoryTheory.Limits.colim_obj</a>, <a>CategoryTheory.Limits.ι_colimitLimitToLimitColimit_π_apply</a>, <a>CategoryTheory.Limits.Types.FilteredColimit.colimit_eq_iff</a>, <a>CategoryTheory.curry_obj_obj_obj</a>, <a>CategoryTheory.cur...	case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...	case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...	((:c Eq) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c CategoryTheory.Funct...	[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.LargeCategory) ...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...	{"children":[{"children":[{"source":"simp?","sourceEnd":3362,"sourceStart":3357,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"...	[]	[{"source":"Functor.comp_obj","source_end":3423,"source_start":3407,"syntax_kind":"ident"},{"source":"colim_obj","source_end":3434,"source_start":3425,"syntax_kind":"ident"},{"source":"ι_colimitLimitToLimitColimit_π_apply","source_end":3474,"source_start":3436,"syntax_kind":"ident"},{"source":"colimit_eq_iff","source_e...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...	16	13	exact	true	1	14	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	2c223e501e4b9f941401c6ea6c2ec5f52c2340db9001c9be4537d42dabf46ec1	6c8dd099f1aae6a0c5726e0bb434f74c96df2149d1fcea45bc493c251a94800f	7e2f03346cca01fc50425e1f3c532e4914664622d5835eafaa19c805b7c20d95	3d7361fed9a133ee9157bd98c9fa0de2c736021983648919ea704e00b5cfef8e
cat-searcher/leandojo-benchmark-4-random	test	1,036	CategoryTheory.Limits.colimitLimitToLimitColimit_injective	Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	let k j := (h j).<a>Exists.choose</a>	case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...	case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...	((:c Eq) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c CategoryTheory.Funct...	[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.LargeCategory) ...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...	{"children":[{"source":"let","sourceEnd":3550,"sourceStart":3547,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"k","sourceEnd":3552,"sourceStart":3551,"tag":"identifier"},{"children":[{"semanticRole":"scoped_local","source":"j","sourceEnd":3554,"sourceStart":3553,"tag":"identifier"}],"...	[]	[{"source":"(h j).choose","source_end":3570,"source_start":3558,"syntax_kind":"Lean.Parser.Term.proj"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...	16	17	exact	true	1	14	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	73e503625c3cb7dc5176dfe92f3470aebf668c7ab8c721448ac99af7a7850873	3d7361fed9a133ee9157bd98c9fa0de2c736021983648919ea704e00b5cfef8e	719c51ffd447c2ccb095257b4cc26f5796c5c6f6423e9a3ca79720a4e1048624	48d7afa09cf2244493f1d7ed9184980ff7aab05af6d98ea91fdc52d331cf2d5b
cat-searcher/leandojo-benchmark-4-random	test	1,037	CategoryTheory.Limits.colimitLimitToLimitColimit_injective	Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	let f : ∀ j, kx ⟶ k j := fun j => (h j).choose_spec.choose	case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...	case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...	((:c Eq) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c CategoryTheory.Funct...	[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.LargeCategory) ...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...	{"children":[{"source":"let","sourceEnd":3578,"sourceStart":3575,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"f","sourceEnd":3580,"sourceStart":3579,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":3582,"so...	[]	[{"source":"∀ j, kx ⟶ k j","source_end":3600,"source_start":3583,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"fun j => (h j).choose_spec.choose","source_end":3637,"source_start":3604,"syntax_kind":"Lean.Parser.Term.fun"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...	16	18	exact	true	1	15	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	157910a2d06cc3953c042f31884362caaa32b711430849d7b32ec366b702b585	48d7afa09cf2244493f1d7ed9184980ff7aab05af6d98ea91fdc52d331cf2d5b	02cca81eb8a274e96fd0928aa2b076c907661870bdf0ca2c1d448f1fe1168035	bd19407e295a9b2909488f1c9cd43a16943360816f99da3a047bab4e2effa96e
cat-searcher/leandojo-benchmark-4-random	test	1,038	CategoryTheory.Limits.colimitLimitToLimitColimit_injective	Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	let g : ∀ j, ky ⟶ k j := fun j => (h j).choose_spec.choose_spec.choose	case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...	case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...	((:c Eq) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c CategoryTheory.Funct...	[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.LargeCategory) ...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...	{"children":[{"source":"let","sourceEnd":3645,"sourceStart":3642,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"g","sourceEnd":3647,"sourceStart":3646,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":3649,"so...	[]	[{"source":"∀ j, ky ⟶ k j","source_end":3667,"source_start":3650,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"fun j => (h j).choose_spec.choose_spec.choose\n -- where the images of the components of the representatives become equal:","source_end":3716,"source_start":3671,"syntax_kind":"Lean.Parser.Term.fun"}]	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...	16	19	exact	true	1	16	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	e951ed403c29e341de802f9e86c1ea0bc24739e014db7baa1af8efb007a6b6aa	bd19407e295a9b2909488f1c9cd43a16943360816f99da3a047bab4e2effa96e	d3c40f131d9fe75aef6aa69b671eba4cfdff2516e3c4392edce1bfb8acf0d439	e6c9fc965b57f84dce27bef70c0e80ca46070a74bc128653c8019abdb0f7e71a
cat-searcher/leandojo-benchmark-4-random	test	1,039	CategoryTheory.Limits.colimitLimitToLimitColimit_injective	Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean	https://github.com/leanprover-community/mathlib4	29dcec074de168ac2bf835a77ef68bbe069194c5	have w : ∀ j, F.map ((𝟙 j, f j) : (j, kx) ⟶ (j, k j)) (<a>CategoryTheory.Limits.limit.π</a> ((curry.obj (<a>CategoryTheory.Prod.swap</a> K J ⋙ F)).<a>Prefunctor.obj</a> kx) j x) = F.map ((𝟙 j, g j) : (j, ky) ⟶ (j, k j)) (<a>CategoryTheory.Limits.limit.π</a> ((curry.obj (<a>CategoryTheory.Prod.swap</a> K J ⋙ F)).<a>Pr...	case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...	case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...	((:c Eq) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c CategoryTheory.Funct...	[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...	(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.LargeCategory) ...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...	{"children":[{"source":"have","sourceEnd":3804,"sourceStart":3800,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"w","sourceEnd":3806,"sourceStart":3805,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"w","sourceEnd":3806,"sourceStart":3805,"tag":"node"},{"ch...	[]	[{"source":"∀ j, F.map ((𝟙 j, f j) :\n (j, kx) ⟶ (j, k j)) (limit.π ((curry.obj (swap K J ⋙ F)).obj kx) j x) =\n F.map ((𝟙 j, g j) : (j, ky) ⟶ (j, k j))\n (limit.π ((curry.obj (swap K J ⋙ F)).obj ky) j y)","source_end":4049,"source_start":3815,"syntax_kind":"Lean.Parser.Term.forall"},{"sour...	[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...	16	20	exact	true	1	17	false	4	source-invocation-v4	2	lean-model-sexp-v2	3	lean-action-trace-v3	73781c2d58456e4bf369dadd4a501e1b78a0b177	73781c2d58456e4bf369dadd4a501e1b78a0b177	9d5852300ba9b87adb6bebaef072a77206a601d2bb6f5cc94c47c4ceafc56d9a	e6c9fc965b57f84dce27bef70c0e80ca46070a74bc128653c8019abdb0f7e71a	20e5545d4f6ddbcf972b2926236756b10cb844ca45c0709e6b3ab1d590d06548	05f1ba678a1e02e3caad0a614a3a6916905d8da0aff538555916456cf57f19ef

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