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cat-searcher/leandojo-benchmark-4-random | test | 833 | Complex.Gamma_integrand_deriv_integrable_A | Mathlib/Analysis/SpecialFunctions/Gamma/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Complex.ofReal_exp</a>, <a>Complex.ofReal_neg</a>, <a>add_sub_cancel_right</a>] | case h.e'_3.h
s : ℂ
hs : 0 < s.re
X : ℝ
hX : 0 ≤ X
x✝ : ℝ
⊢ -(↑(rexp (-x✝)) * ↑x✝ ^ s) = (-fun x => ↑(rexp (-x)) * ↑x ^ (s + 1 - 1)) x✝ | case h.e'_3.h
s : ℂ
hs : 0 < s.re
X : ℝ
hX : 0 ≤ X
x✝ : ℝ
⊢ -(cexp (-↑x✝) * ↑x✝ ^ s) = (-fun x => cexp (-↑x) * ↑x ^ s) x✝ | ((:c Eq) (:c Complex) ((:c Neg.neg) (:c Complex) (:c Complex.instNeg) ((:c HMul.hMul) (:c Complex) (:c Complex) (:c Complex) ((:c instHMul) (:c Complex) (:c Complex.instMul)) ((:c Complex.ofReal') ((:c Real.exp) ((:c Neg.neg) (:c Real) (:c Real.instNeg) (:fv _uniq.31918)))) ((:c HPow.hPow) (:c Complex) (:c Complex) (:c... | [{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Complex.re) (:fv _uniq.31102)))"},{"name":"X","sexp":"(:c Real)"},{"name":"hX","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Complex))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Complex)) (:arg :implicit-type 1 (:c Complex)) ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31102","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.31103","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R... | {"children":[{"source":"simp","sourceEnd":7882,"sourceStart":7878,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":7887,"sourceStart":7883,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":7887,"s... | [] | [{"source":"ofReal_exp","source_end":7899,"source_start":7889,"syntax_kind":"ident"},{"source":"ofReal_neg","source_end":7911,"source_start":7901,"syntax_kind":"ident"},{"source":"add_sub_cancel_right","source_end":7933,"source_start":7913,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31102","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.31103","is_instance":false,"is_let":false,"user_name":"hs"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 32 | 9 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 150359b7f068b32aad148712d7bbdc0a27872bfb6837ec16371ec80a1f689b93 | ebf96cdfd84b6db9d987c5bb08175e242dda2c7f9ffa4c888b28c2b2be007fef | 33a7482a733f001637efffba2b248a6034d4af00f64f74480719a60c0c4b8137 | 4618d5cc4322ca2bfe239b0463eb8a37b9f0e3efda43bff76b8b017bd2ceffca |
cat-searcher/leandojo-benchmark-4-random | test | 834 | Complex.Gamma_integrand_deriv_integrable_A | Mathlib/Analysis/SpecialFunctions/Gamma/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case h.e'_3.h
s : ℂ
hs : 0 < s.re
X : ℝ
hX : 0 ≤ X
x✝ : ℝ
⊢ -(cexp (-↑x✝) * ↑x✝ ^ s) = (-fun x => cexp (-↑x) * ↑x ^ s) x✝ | ((:c Eq) (:c Complex) ((:c Neg.neg) (:c Complex) (:c Complex.instNeg) ((:c HMul.hMul) (:c Complex) (:c Complex) (:c Complex) ((:c instHMul) (:c Complex) (:c Complex.instMul)) ((:c Complex.exp) ((:c Neg.neg) (:c Complex) (:c Complex.instNeg) ((:c Complex.ofReal') (:fv _uniq.31918)))) ((:c HPow.hPow) (:c Complex) (:c Com... | [{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Complex.re) (:fv _uniq.31102)))"},{"name":"X","sexp":"(:c Real)"},{"name":"hX","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Complex))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Complex)) (:arg :implicit-type 1 (:c Complex)) ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31102","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.31103","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R... | {"children":[{"source":"rfl","sourceEnd":7939,"sourceStart":7936,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":7939,"sourceStart":7936,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31102","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.31103","is_instance":false,"is_let":false,"user_name":"hs"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 32 | 11 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 21149de25751842b8fa5f9f0d3d7e8688c5a6a221fb8129fc942862fef4fb3db | 4618d5cc4322ca2bfe239b0463eb8a37b9f0e3efda43bff76b8b017bd2ceffca | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 835 | Complex.Gamma_integrand_deriv_integrable_A | Mathlib/Analysis/SpecialFunctions/Gamma/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Complex.add_re</a>, <a>Complex.one_re</a>] | s : ℂ
hs : 0 < s.re
X : ℝ
hX : 0 ≤ X
⊢ 0 < (s + 1).re | s : ℂ
hs : 0 < s.re
X : ℝ
hX : 0 ≤ X
⊢ 0 < s.re + 1 | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Complex.re) ((:c HAdd.hAdd) (:c Complex) (:c Complex) (:c Complex) ((:c instHAdd) (:c Complex) (:c Complex.instAdd)) (:fv _uniq.31102) ((:c OfNat.ofNat) (:c Complex) (:lit 1) ((:c One.toOf... | [{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Complex.re) (:fv _uniq.31102)))"},{"name":"X","sexp":"(:c Real)"},{"name":"hX","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c ... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31102","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.31103","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R... | {"children":[{"source":"simp","sourceEnd":7949,"sourceStart":7945,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":7954,"sourceStart":7950,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":7954,"s... | [] | [{"source":"add_re","source_end":7962,"source_start":7956,"syntax_kind":"ident"},{"source":"one_re","source_end":7970,"source_start":7964,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31102","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.31103","is_instance":false,"is_let":false,"user_name":"hs"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 32 | 16 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fecd27a4ba71fd8dcf0022ab0aa1f210a060f3dd03bf7fa042780e9782ec5fbd | 29731936e8c79e470f277d2b2134ce2e744d3cc34999a5033da1e1cdc5c8d645 | 1356936b7ec412fc0f358bf58d04ead7fa4672f9cb8b7ae4b24980ac14aa4e05 | a3bfb76d7f7ce36e3744d16171d43693867495fec30b243aebc3ab06663bb2d4 |
cat-searcher/leandojo-benchmark-4-random | test | 836 | Complex.Gamma_integrand_deriv_integrable_A | Mathlib/Analysis/SpecialFunctions/Gamma/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith | s : ℂ
hs : 0 < s.re
X : ℝ
hX : 0 ≤ X
⊢ 0 < s.re + 1 | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) ((:c Complex.re) (:fv _uniq.31102)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (... | [{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Complex.re) (:fv _uniq.31102)))"},{"name":"X","sexp":"(:c Real)"},{"name":"hX","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c ... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31102","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.31103","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R... | {"children":[{"source":"linarith","sourceEnd":7981,"sourceStart":7973,"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":"node"}],"k... | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31102","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.31103","is_instance":false,"is_let":false,"user_name":"hs"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 32 | 18 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 89b1a0431d8b78e6ee81c8baf3fcddd3427eedfba939b90a4bcfaa6566e40d72 | a3bfb76d7f7ce36e3744d16171d43693867495fec30b243aebc3ab06663bb2d4 | 2c587e2f140ae41533b8e0551e8c940d4f70fbd4b1f4245ea1c9efcde110c9af | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 837 | Traversable.foldl_toList | Mathlib/Control/Fold.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>FreeMonoid.toList_ofList</a> (<a>Traversable.toList</a> xs), ← <a>Traversable.foldl.unop_ofFreeMonoid</a>] | α β γ : Type u
t : Type u → Type u
inst✝¹ : Traversable t
inst✝ : LawfulTraversable t
f : α → β → α
xs : t β
x : α
⊢ foldl f x xs = List.foldl f x (toList xs) | α β γ : Type u
t : Type u → Type u
inst✝¹ : Traversable t
inst✝ : LawfulTraversable t
f : α → β → α
xs : t β
x : α
⊢ foldl f x xs = unop ((Foldl.ofFreeMonoid f) (FreeMonoid.ofList (toList xs))) x | ((:c Eq) (:fv _uniq.15070) ((:c Traversable.foldl) (:fv _uniq.15070) (:fv _uniq.15072) (:fv _uniq.15078) (:fv _uniq.15084) (:fv _uniq.15151) (:fv _uniq.15153) (:fv _uniq.15152)) ((:c List.foldl) (:fv _uniq.15070) (:fv _uniq.15072) (:fv _uniq.15151) (:fv _uniq.15153) ((:c Traversable.toList) (:fv _uniq.15072) (:fv _uniq... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u 1))"},{"name":"γ","sexp":"(:sort (+ u 1))"},{"name":"t","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"inst✝¹","sexp":"((:c Traversable) (:fv _uniq.15078))"},{"name":"inst✝","sexp":"((:c LawfulTraversable) (:fv _uniq.15078) (:fv _uni... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Traversable.foldl) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c Traversable) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 4 (:fv FV7)) (:arg :explicit 5 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15070","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15072","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":13371,"sourceStart":13369,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13373,"sourceStart":13372,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":13376,"sourceSt... | [] | [{"source":"FreeMonoid.toList_ofList (toList xs)","source_end":13413,"source_start":13377,"syntax_kind":"Lean.Parser.Term.app"},{"source":"foldl.unop_ofFreeMonoid","source_end":13442,"source_start":13419,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15070","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15072","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 94 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aba354f0a979482a5d43787bb646d1f79f384e33d25a714a5d71b789492dab81 | dc85b6b90e8239697598b29f565c4bfb5bd4a0c4f159e7f907f7ad5c0043e1d9 | 5458e3753ae95cc378e64d3693acb2c1c5f93f62f443de538e31d656df8160c2 | 942deb0d9c4f4654da6aac4773425fa0a27a348d3fbd71e1da46583a966c71dd |
cat-searcher/leandojo-benchmark-4-random | test | 838 | Traversable.foldl_toList | Mathlib/Control/Fold.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Traversable.foldl</a>, <a>Traversable.toList_spec</a>, <a>Traversable.foldMap_hom_free</a>, <a>Traversable.foldl.ofFreeMonoid_comp_of</a>, <a>Monoid.Foldl.get</a>, <a>FreeMonoid.ofList_toList</a>] | α β γ : Type u
t : Type u → Type u
inst✝¹ : Traversable t
inst✝ : LawfulTraversable t
f : α → β → α
xs : t β
x : α
⊢ foldl f x xs = unop ((Foldl.ofFreeMonoid f) (FreeMonoid.ofList (toList xs))) x | ((:c Eq) (:fv _uniq.15070) ((:c Traversable.foldl) (:fv _uniq.15070) (:fv _uniq.15072) (:fv _uniq.15078) (:fv _uniq.15084) (:fv _uniq.15151) (:fv _uniq.15153) (:fv _uniq.15152)) ((:c MulOpposite.unop) ((:c CategoryTheory.End) (:sort (+ u 1)) ((:c CategoryTheory.Category.toCategoryStruct) (:sort (+ u 1)) (:c CategoryThe... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u 1))"},{"name":"γ","sexp":"(:sort (+ u 1))"},{"name":"t","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"inst✝¹","sexp":"((:c Traversable) (:fv _uniq.15078))"},{"name":"inst✝","sexp":"((:c LawfulTraversable) (:fv _uniq.15078) (:fv _uni... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Traversable.foldl) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c Traversable) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 4 (:fv FV7)) (:arg :explicit 5 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15070","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15072","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":13450,"sourceStart":13446,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":13455,"sourceStart":13451,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":134... | [] | [{"source":"foldl","source_end":13462,"source_start":13457,"syntax_kind":"ident"},{"source":"toList_spec","source_end":13475,"source_start":13464,"syntax_kind":"ident"},{"source":"foldMap_hom_free","source_end":13493,"source_start":13477,"syntax_kind":"ident"},{"source":"foldl.ofFreeMonoid_comp_of","source_end":13521,"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15070","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15072","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 94 | 8 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a922c6c79fdf5d794ff698d06853b05720ac9cbff5d33c1e7fac54ba402d1b78 | 942deb0d9c4f4654da6aac4773425fa0a27a348d3fbd71e1da46583a966c71dd | 28d36058024f6d39f9bc7b6f584665d2c6a6d26a431298c5d55fd84f5c7a2c51 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 839 | Polynomial.trinomial_leading_coeff' | Mathlib/Algebra/Polynomial/UnitTrinomial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Polynomial.trinomial_def</a>, <a>Polynomial.coeff_add</a>, <a>Polynomial.coeff_add</a>, <a>Polynomial.coeff_C_mul_X_pow</a>, <a>Polynomial.coeff_C_mul_X_pow</a>, <a>Polynomial.coeff_C_mul_X_pow</a>, <a>if_neg</a> (hkm.trans hmn).<a>LT.lt.ne'</a>, <a>if_neg</a> hmn.ne', <a>if_pos</a> <a>rfl</a>, <a>zero_add</a>, ... | R : Type u_1
inst✝ : Semiring R
k m n : ℕ
u v w : R
hkm : k < m
hmn : m < n
⊢ (trinomial k m n u v w).coeff n = w | ((:c Eq) (:fv _uniq.4746) ((:c Polynomial.coeff) (:fv _uniq.4746) (:fv _uniq.4749) ((:c Polynomial.trinomial) (:fv _uniq.4746) (:fv _uniq.4749) (:fv _uniq.4751) (:fv _uniq.4753) (:fv _uniq.4755) (:fv _uniq.4757) (:fv _uniq.4759) (:fv _uniq.4761)) (:fv _uniq.4755)) (:fv _uniq.4761)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.4746))"},{"name":"k","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"u","sexp":"(:fv _uniq.4746)"},{"name":"v","sexp":"(:fv _uniq.4746)"},{"name":"w","sexp":"(:fv _uniq.4746)"},{"name":"h... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Polynomial.coeff) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Polynomial.trinomial) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4746","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4749","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Semiring) (:arg :explicit ... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":1239,"sourceStart":1237,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1241,"sourceStart":1240,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"trinomial_def","source_end":1254,"source_start":1241,"syntax_kind":"ident"},{"source":"coeff_add","source_end":1265,"source_start":1256,"syntax_kind":"ident"},{"source":"coeff_add","source_end":1276,"source_start":1267,"syntax_kind":"ident"},{"source":"coeff_C_mul_X_pow","source_end":1295,"source_start":127... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4746","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4749","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"internal_... | 12 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ee5e8b541b6adc659b128ca3d58334ee6c2f8efe70cd458f30da6e1c51999aa5 | bf1e7fbd8b7a80e2397acda15dddb3fd482bbc442a519805a6d866e2c3558ac5 | 283e0fe257563847c8ab9c61f5233a269b3ce29da8e3a89ddb385d074484bc8d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 840 | AddSubgroup.norm_normedMk_le | Mathlib/Analysis/Normed/Group/Quotient.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>quotient_norm_mk_le'</a>] | M : Type u_1
N : Type u_2
inst✝¹ : SeminormedAddCommGroup M
inst✝ : SeminormedAddCommGroup N
S : AddSubgroup M
m : M
⊢ ‖S.normedMk m‖ ≤ 1 * ‖m‖ | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) ((:c HasQuotient.Quotient) (:fv _uniq.50437) ((:c AddSubgroup) (:fv _uniq.50437) ((:c SeminormedAddGroup.toAddGroup) (:fv _uniq.50437) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) (:fv _uniq.50437) (:fv _uniq.50443)))) ((:c QuotientAddGroup.instHasQuotientAddS... | [{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"N","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.50437))"},{"name":"inst✝","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.50440))"},{"name":"S","sexp":"((:c AddSubgroup) (:fv _uniq.50437) ((:c SeminormedAddGroup.toAddGroup... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c HasQuotient.Quotient) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c AddSubgroup) (:arg :explicit 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.50437","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.50440","is_instance":false,"is_let":false,"name":"N","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":15292,"sourceStart":15288,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"quotient_norm_mk_le'","source_end":15314,"source_start":15294,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.50437","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.50440","is_instance":false,"is_let":false,"user_name":"N"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 61 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 53bd2552013c20d15c16c7869255472e13e63cc77043374fb5614eb1800370d9 | 76b6be227f713b49c97aa395cca1fc15c2f63e032808d52afb209464f8446cc2 | dd46b04d413a7d5f0d204876e66152f600c615352a00dcd0bd3ab4436234861e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 841 | EuclideanGeometry.angle_eq_angle_of_angle_eq_pi_of_angle_eq_pi | Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith [<a>EuclideanGeometry.angle_add_angle_eq_pi_of_angle_eq_pi</a> p1 hbpd, <a>EuclideanGeometry.angle_comm</a> p4 p5 p1, <a>EuclideanGeometry.angle_add_angle_eq_pi_of_angle_eq_pi</a> p4 hapc, <a>EuclideanGeometry.angle_comm</a> p4 p5 p3] | V : Type u_1
P : Type u_2
inst✝³ : NormedAddCommGroup V
inst✝² : InnerProductSpace ℝ V
inst✝¹ : MetricSpace P
inst✝ : NormedAddTorsor V P
p p₀ p₁ p₂ p1 p2 p3 p4 p5 : P
hapc : ∠ p1 p5 p3 = π
hbpd : ∠ p2 p5 p4 = π
⊢ ∠ p1 p5 p2 = ∠ p3 p5 p4 | ((:c Eq) (:c Real) ((:c EuclideanGeometry.angle) (:fv _uniq.69636) (:fv _uniq.69639) (:fv _uniq.69642) (:fv _uniq.69655) (:fv _uniq.69658) (:fv _uniq.69946) (:fv _uniq.70615) (:fv _uniq.70619) (:fv _uniq.70616)) ((:c EuclideanGeometry.angle) (:fv _uniq.69636) (:fv _uniq.69639) (:fv _uniq.69642) (:fv _uniq.69655) (:fv _... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.69636))"},{"name":"inst✝²","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.69636) (:c Real.RCLike) (:fv _uniq.69642))"},{"name":"inst✝¹","sexp":"((:c MetricSpace) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c EuclideanGeometry.angle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c InnerProductSpa... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.69636","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69639","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"linarith","sourceEnd":9517,"sourceStart":9509,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"sour... | [] | [{"source":"angle_add_angle_eq_pi_of_angle_eq_pi p1 hbpd","source_end":9563,"source_start":9519,"syntax_kind":"Lean.Parser.Term.app"},{"source":"angle_comm p4 p5 p1","source_end":9584,"source_start":9565,"syntax_kind":"Lean.Parser.Term.app"},{"source":"angle_add_angle_eq_pi_of_angle_eq_pi p4 hapc","source_end":9634,"so... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.69636","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69639","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 57 | 2 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4139c7ef94d600dbff64473ab57801fc95684105494b45c4841cf9994c6159ef | 2e784e04f75583c10973abe088ed5df88ec49ddfb224c81483325349ad481af2 | b5ea047a33f69788f034d4561093e8d5da2c271b01ed1a68ad7858413580d982 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 842 | Multiset.eq_union_right | Mathlib/Data/Multiset/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Multiset.union_comm</a>, <a>Multiset.eq_union_left</a> h] | α : Type u_1
β : Type v
γ : Type u_2
inst✝ : DecidableEq α
s t u : Multiset α
a b : α
h : s ≤ t
⊢ s ∪ t = t | ((:c Eq) ((:c Multiset) (:fv _uniq.113352)) ((:c Union.union) ((:c Multiset) (:fv _uniq.113352)) ((:c Multiset.instUnion) (:fv _uniq.113352) (:fv _uniq.113364)) (:fv _uniq.113369) (:fv _uniq.113372)) (:fv _uniq.113372)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.113352))"},{"name":"s","sexp":"((:c Multiset) (:fv _uniq.113352))"},{"name":"t","sexp":"((:c Multiset) (:fv _uniq.113352))"},{"name":"u","sexp":"((:... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Union.union) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c Union) (:arg :explicit 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.113352","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.113354","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":77085,"sourceStart":77083,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":77087,"sourceStart":77086,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"union_comm","source_end":77097,"source_start":77087,"syntax_kind":"ident"},{"source":"eq_union_left h","source_end":77114,"source_start":77099,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.113352","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.113354","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 669 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 635360750305b1552891b87a0c6cbdfd52b2bb36b547730994b42e3d612e1293 | 2a032735d9933995983b4940bd84f93f4dd156201876e1c41e702a4cf26dcabb | c6d2cd90120d9c40a1990377715394d709941311c45a94a70d8447f22c6117f0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 843 | EReal.inv_pos_of_pos_ne_top | Mathlib/Data/Real/EReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction a with | h_bot => exact (<a>not_lt_bot</a> h).<a>False.rec</a> | h_real a => rw [← <a>EReal.coe_inv</a> a]; norm_cast at *; exact <a>inv_pos_of_pos</a> h | h_top => exact (h' (<a>Eq.refl</a> ⊤)).<a>False.rec</a> | a : EReal
h : 0 < a
h' : a ≠ ⊤
⊢ 0 < a⁻¹ | ((:c LT.lt) (:c EReal) ((:c Preorder.toLT) (:c EReal) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder))) ((:c OfNat.ofNat) (:c EReal) (:lit 0) ((:c Zero.toOfNat0) (:c EReal) (:c instERealZero))) ((:c Inv.inv) (:c EReal) (:c EReal.instInv) (:fv _uniq.210060))) | [{"name":"a","sexp":"(:c EReal)"},{"name":"h","sexp":"((:c LT.lt) (:c EReal) ((:c Preorder.toLT) (:c EReal) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder))) ((:c OfNat.ofNat) (:c EReal) (:lit 0) ((:c Zero.toOfNat0) (:c EReal) (:c instERealZero))) (:fv _uniq.210060))"},{"name":"h'","sexp":"((:c Ne) ... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c EReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c EReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c EReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c EReal)) (:arg ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.210060","is_instance":false,"is_let":false,"name":"a","sexp":"(:c EReal)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.210061","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c ER... | {"children":[{"children":[{"children":[{"children":[{"source":"induction","sourceEnd":59181,"sourceStart":59172,"tag":"atom"},{"children":[{"contextIndex":1,"semanticRole":"local","source":"a","sourceEnd":59183,"sourceStart":59182,"tag":"identifier"}],"kind":"null","source":"a","sourceEnd":59183,"sourceStart":59182,"ta... | [] | [{"source":"a","source_end":59183,"source_start":59182,"syntax_kind":"ident"},{"source":"(not_lt_bot h).rec","source_end":59226,"source_start":59208,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"coe_inv a","source_end":59261,"source_start":59252,"syntax_kind":"Lean.Parser.Term.app"},{"source":"inv_pos_of_pos h","so... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.210060","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.210061","is_instance":false,"is_let":false,"user_name":"h"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 438 | 2 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5f6260398ecb3513ed09ca893d5309e224ca9c2ce32dd0b9fe9e994f6043a16b | e95b02f7e17f5a484896f9d799014727d0685df34249546b95f9d5ea700c9d7d | fea36d1709a5f2028abd95915d719d97ecf6b2f16a00847923653f412935370e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 844 | EReal.inv_pos_of_pos_ne_top | Mathlib/Data/Real/EReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>not_lt_bot</a> h).<a>False.rec</a> | case h_bot
h : 0 < ⊥
h' : ⊥ ≠ ⊤
⊢ 0 < ⊥⁻¹ | ((:c LT.lt) (:c EReal) ((:c Preorder.toLT) (:c EReal) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder))) ((:c OfNat.ofNat) (:c EReal) (:lit 0) ((:c Zero.toOfNat0) (:c EReal) (:c instERealZero))) ((:c Inv.inv) (:c EReal) (:c EReal.instInv) ((:c Bot.bot) (:c EReal) (:c instERealBot)))) | [{"name":"h","sexp":"((:c LT.lt) (:c EReal) ((:c Preorder.toLT) (:c EReal) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder))) ((:c OfNat.ofNat) (:c EReal) (:lit 0) ((:c Zero.toOfNat0) (:c EReal) (:c instERealZero))) ((:c Bot.bot) (:c EReal) (:c instERealBot)))"},{"name":"h'","sexp":"((:c Ne) (:c ERea... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c EReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c EReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c EReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c EReal)) (:arg ... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.210084","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c EReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c EReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-t... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":59207,"sourceStart":59202,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":59209,"sourceStart":59208,"tag":"atom"},{"children":[{"name":"not_lt_bot","semanticRole":"global","source":"not_lt_bot","sourceEnd":59219,"sourceS... | [] | [{"source":"(not_lt_bot h).rec","source_end":59226,"source_start":59208,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.210084","is_instance":false,"is_let":false,"user_name":"h"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.210085","is_instance":false,"is_let":false,"user_name":"h'"}] | 438 | 7 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dcf6a33bcfd6e7002153933f43216cf61a48401b8c1c25f05161a475d01d79a6 | 2eabb1fea770e8da292de9f3ef2e0226f67ce0a133912c1c47d0945fd9c3b265 | 1d5ffa5bb32f517b9c8242a15273273852b12cf91bf54c39bd004c283a3b1de2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 845 | EReal.inv_pos_of_pos_ne_top | Mathlib/Data/Real/EReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>EReal.coe_inv</a> a] | case h_real
a : ℝ
h : 0 < ↑a
h' : ↑a ≠ ⊤
⊢ 0 < (↑a)⁻¹ | case h_real
a : ℝ
h : 0 < ↑a
h' : ↑a ≠ ⊤
⊢ 0 < ↑a⁻¹ | ((:c LT.lt) (:c EReal) ((:c Preorder.toLT) (:c EReal) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder))) ((:c OfNat.ofNat) (:c EReal) (:lit 0) ((:c Zero.toOfNat0) (:c EReal) (:c instERealZero))) ((:c Inv.inv) (:c EReal) (:c EReal.instInv) ((:c Real.toEReal) (:fv _uniq.210261)))) | [{"name":"a","sexp":"(:c Real)"},{"name":"h","sexp":"((:c LT.lt) (:c EReal) ((:c Preorder.toLT) (:c EReal) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder))) ((:c OfNat.ofNat) (:c EReal) (:lit 0) ((:c Zero.toOfNat0) (:c EReal) (:c instERealZero))) ((:c Real.toEReal) (:fv _uniq.210261)))"},{"name":"h'... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c EReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c EReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c EReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c EReal)) (:arg ... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.210261","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.210264","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c ERe... | {"children":[{"source":"rw","sourceEnd":59246,"sourceStart":59244,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":59248,"sourceStart":59247,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":59251,"sourceSt... | [] | [{"source":"coe_inv a","source_end":59261,"source_start":59252,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.210261","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.210264","is_instance":false,"is_let":false,"user_name":"h"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 438 | 13 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c9ea340278923f4b7caf17512f83763a902edfd5223314238bd9543e95f214de | 1a26a1bdb4935edea02104e8098d8e866ccf8806b9f887c99169e081f57c6910 | e3d671ad4a7f790050a1f4813d8dd0e0180e6955660cd7e4f4047df0b6b5f268 | 033589e78bf4702228fa1ae7f4c9bda297c61df5b98704f45004b45da9603ab3 |
cat-searcher/leandojo-benchmark-4-random | test | 846 | EReal.inv_pos_of_pos_ne_top | Mathlib/Data/Real/EReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_cast at * | case h_real
a : ℝ
h : 0 < ↑a
h' : ↑a ≠ ⊤
⊢ 0 < ↑a⁻¹ | case h_real
a : ℝ
h' : ¬↑a = ⊤
h : 0 < a
⊢ 0 < a⁻¹ | ((:c LT.lt) (:c EReal) ((:c Preorder.toLT) (:c EReal) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder))) ((:c OfNat.ofNat) (:c EReal) (:lit 0) ((:c Zero.toOfNat0) (:c EReal) (:c instERealZero))) ((:c Real.toEReal) ((:c Inv.inv) (:c Real) (:c Real.instInv) (:fv _uniq.210261)))) | [{"name":"a","sexp":"(:c Real)"},{"name":"h","sexp":"((:c LT.lt) (:c EReal) ((:c Preorder.toLT) (:c EReal) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder))) ((:c OfNat.ofNat) (:c EReal) (:lit 0) ((:c Zero.toOfNat0) (:c EReal) (:c instERealZero))) ((:c Real.toEReal) (:fv _uniq.210261)))"},{"name":"h'... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c EReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c EReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c EReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c EReal)) (:arg ... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.210261","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.210264","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c ERe... | {"children":[{"source":"norm_cast","sourceEnd":59273,"sourceStart":59264,"tag":"atom"},{"children":[{"children":[{"source":"at","sourceEnd":59276,"sourceStart":59274,"tag":"atom"},{"children":[{"source":"*","sourceEnd":59278,"sourceStart":59277,"tag":"atom"}],"kind":"Lean.Parser.Tactic.locationWildcard","source":"*","s... | [] | [] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.210261","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.210264","is_instance":false,"is_let":false,"user_name":"h"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 438 | 17 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ebfe7ae1e5225cd55efdabcdac10bffcf87be50dcdbebf64cf7f013675da1aee | 033589e78bf4702228fa1ae7f4c9bda297c61df5b98704f45004b45da9603ab3 | d0840c17d4ecc8da56829145fa177ff5194dabe5f6074ed3d8358f847267b529 | e910d34aef06bff7df73f4bdbdccf1a9d2fb04fbd5238ab2560ab2a4d8e40906 |
cat-searcher/leandojo-benchmark-4-random | test | 847 | EReal.inv_pos_of_pos_ne_top | Mathlib/Data/Real/EReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>inv_pos_of_pos</a> h | case h_real
a : ℝ
h' : ¬↑a = ⊤
h : 0 < a
⊢ 0 < a⁻¹ | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) ((:c AddMonoid.toZero) (:c Real) ((:c AddMonoidWithOne.toAddMonoid) (:c Real) ((:c AddGroupWithOne.toAddMonoidWithOne) (:c Real) ((:c Ring.toAddGroupWithOne) (:c Real) (:c Real.instRing))))))) ((:c Inv.inv) (:c Rea... | [{"name":"a","sexp":"(:c Real)"},{"name":"h'","sexp":"((:c Not) ((:c Eq) (:c EReal) ((:c Real.toEReal) (:fv _uniq.210261)) ((:c Top.top) (:c EReal) (:c EReal.instTop))))"},{"name":"h","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) ((:c AddMonoid.toZero)... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.210261","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.210265","is_instance":false,"is_let":false,"name":"h'","sexp":"(:app (:c Not) (:arg :explicit 0 (:app (:c Eq)... | {"children":[{"source":"exact","sourceEnd":59285,"sourceStart":59280,"tag":"atom"},{"children":[{"name":"inv_pos_of_pos","semanticRole":"global","source":"inv_pos_of_pos","sourceEnd":59300,"sourceStart":59286,"tag":"identifier"},{"children":[{"contextIndex":3,"semanticRole":"local","source":"h","sourceEnd":59302,"sourc... | [] | [{"source":"inv_pos_of_pos h","source_end":59302,"source_start":59286,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.210261","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.210265","is_instance":false,"is_let":false,"user_name":"h'"},{"binder_role":":explicit","context_index":3,"internal_name":"... | 438 | 19 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b62a4dc651c058cdb505f65f946cbcc1f2b5194964115e01e1dc65f496703c9c | e910d34aef06bff7df73f4bdbdccf1a9d2fb04fbd5238ab2560ab2a4d8e40906 | 9be077e559105675915bf0537700b332055ce65b2c9c143ee0b06c0a27202b7b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 848 | EReal.inv_pos_of_pos_ne_top | Mathlib/Data/Real/EReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (h' (<a>Eq.refl</a> ⊤)).<a>False.rec</a> | case h_top
h : 0 < ⊤
h' : ⊤ ≠ ⊤
⊢ 0 < ⊤⁻¹ | ((:c LT.lt) (:c EReal) ((:c Preorder.toLT) (:c EReal) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder))) ((:c OfNat.ofNat) (:c EReal) (:lit 0) ((:c Zero.toOfNat0) (:c EReal) (:c instERealZero))) ((:c Inv.inv) (:c EReal) (:c EReal.instInv) ((:c Top.top) (:c EReal) (:c EReal.instTop)))) | [{"name":"h","sexp":"((:c LT.lt) (:c EReal) ((:c Preorder.toLT) (:c EReal) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder))) ((:c OfNat.ofNat) (:c EReal) (:lit 0) ((:c Zero.toOfNat0) (:c EReal) (:c instERealZero))) ((:c Top.top) (:c EReal) (:c EReal.instTop)))"},{"name":"h'","sexp":"((:c Ne) (:c ERe... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c EReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c EReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c EReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c EReal)) (:arg ... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.211103","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c EReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c EReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-t... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":59321,"sourceStart":59316,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":59323,"sourceStart":59322,"tag":"atom"},{"children":[{"contextIndex":2,"semanticRole":"local","source":"h'","sourceEnd":59325,"sourceStart":59323,... | [] | [{"source":"(h' (Eq.refl ⊤)).rec","source_end":59344,"source_start":59322,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.211103","is_instance":false,"is_let":false,"user_name":"h"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.211104","is_instance":false,"is_let":false,"user_name":"h'"}] | 438 | 21 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8dd84f4200e4cd5e639926ca63613fc730dd016de9ce76463a7bd6d4dbf6aa6d | 18d971a16c612ae8361872400f385d45ea50a9a1fb082cfe92b706233ca9460a | 43a72ff68ec3b839b4f77e920c75b4549d764d87df38fbdc9cec31505bf18d26 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 849 | LinearMap.charpoly_natDegree | Mathlib/LinearAlgebra/Charpoly/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>LinearMap.charpoly</a>, <a>Matrix.charpoly_natDegree_eq_dim</a>, <a>FiniteDimensional.finrank_eq_card_chooseBasisIndex</a>] | R : Type u
M : Type v
inst✝⁶ : CommRing R
inst✝⁵ : Nontrivial R
inst✝⁴ : AddCommGroup M
inst✝³ : Module R M
inst✝² : Module.Free R M
inst✝¹ : Module.Finite R M
f : M →ₗ[R] M
inst✝ : StrongRankCondition R
⊢ f.charpoly.natDegree = finrank R M | ((:c Eq) (:c Nat) ((:c Polynomial.natDegree) (:fv _uniq.14592) ((:c CommSemiring.toSemiring) (:fv _uniq.14592) ((:c CommRing.toCommSemiring) (:fv _uniq.14592) (:fv _uniq.14597))) ((:c LinearMap.charpoly) (:fv _uniq.14592) (:fv _uniq.14594) (:fv _uniq.14597) (:fv _uniq.14603) (:fv _uniq.15216) (:fv _uniq.15702) (:fv _un... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁶","sexp":"((:c CommRing) (:fv _uniq.14592))"},{"name":"inst✝⁵","sexp":"((:c Nontrivial) (:fv _uniq.14592))"},{"name":"inst✝⁴","sexp":"((:c AddCommGroup) (:fv _uniq.14594))"},{"name":"inst✝³","sexp":"((:c Module) (:fv _uniq.14592... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Polynomial.natDegree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c LinearMap.charpoly) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14592","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14594","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":1736,"sourceStart":1734,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1738,"sourceStart":1737,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"charpoly","source_end":1746,"source_start":1738,"syntax_kind":"ident"},{"source":"Matrix.charpoly_natDegree_eq_dim","source_end":1780,"source_start":1748,"syntax_kind":"ident"},{"source":"finrank_eq_card_chooseBasisIndex","source_end":1814,"source_start":1782,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14592","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14594","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 18 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1156667bce6fbbe9900426f2ba9b4bcd3d2a618d08ae9b68482067845b9f64d3 | 238843548cec99676a4855fef62dd1618052df407a05b2c330ea234c97d26fc9 | c1eb1ddc7919191cb86a611d33d5168c6bf1cc69e947fa407c26eedc129fae42 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 850 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | unfold <a>Batteries.BinomialHeap.Imp.Heap.merge</a> | α✝ : Type u_1
le : α✝ → α✝ → Bool
s₁ s₂ : Heap α✝
n : Nat
h₁ : WF le n s₁
h₂ : WF le n s₂
⊢ WF le n (merge le s₁ s₂) ∧ ((s₁.rankGT n ↔ s₂.rankGT n) → (merge le s₁ s₂).rankGT n) | α✝ : Type u_1
le : α✝ → α✝ → Bool
s₁ s₂ : Heap α✝
n : Nat
h₁ : WF le n s₁
h₂ : WF le n s₂
⊢ WF le n
(match s₁, s₂ with
| Heap.nil, h => h
| h, Heap.nil => h
| s₁@h:(cons r₁ a₁ n₁ t₁), s₂@h_1:(cons r₂ a₂ n₂ t₂) =>
if r₁ < r₂ then cons r₁ a₁ n₁ (merge le t₁ s₂)
else
if r₂... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) ((:c Batteries.BinomialHeap.Imp.Heap.merge) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93572) (:fv _uniq.93573))) (:forall _ ((:c Iff) ((:c Batteries.BinomialHeap.Imp.Heap.rankGT) (:fv _uniq.93570) (:fv _uniq.93... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"s₁","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"s₂","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"n","sexp":"(:c N... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:app (:c Batteries.BinomialHeap.Imp.Heap.merge) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"unfold","sourceEnd":15050,"sourceStart":15044,"tag":"atom"},{"children":[{"name":"Batteries.BinomialHeap.Imp.Heap.merge","semanticRole":"global","source":"merge","sourceEnd":15056,"sourceStart":15051,"tag":"identifier"}],"kind":"null","source":"merge","sourceEnd":15056,"sourceStart":15051,"tag":... | [] | [{"source":"merge","source_end":15056,"source_start":15051,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5fac1bf1e2ce4a73c7c355380878f87f9fe959886f5dd378b8d8bed37a291660 | c3b1d3279ed96459f42389a44d3de88d1b761bc444103a8fde56c8eecabf45f0 | 07aebacd0167a21aa5a6655d1fa3b2c3b2fc56115c1028e3702337a3d7f292d0 | 12fbbe92c1d999ef8aa050264137d571643fa3d3ee368f191fee2ac87f2344c0 |
cat-searcher/leandojo-benchmark-4-random | test | 851 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split | α✝ : Type u_1
le : α✝ → α✝ → Bool
s₁ s₂ : Heap α✝
n : Nat
h₁ : WF le n s₁
h₂ : WF le n s₂
⊢ WF le n
(match s₁, s₂ with
| Heap.nil, h => h
| h, Heap.nil => h
| s₁@h:(cons r₁ a₁ n₁ t₁), s₂@h_1:(cons r₂ a₂ n₂ t₂) =>
if r₁ < r₂ then cons r₁ a₁ n₁ (merge le t₁ s₂)
else
if r₂... | case h_1
α✝ : Type u_1
le : α✝ → α✝ → Bool
s₂ : Heap α✝
n : Nat
h₂ : WF le n s₂
x✝¹ x✝ : Heap α✝
h₁ : WF le n Heap.nil
⊢ WF le n s₂ ∧ ((Heap.nil.rankGT n ↔ s₂.rankGT n) → s₂.rankGT n)
case h_2
α✝ : Type u_1
le : α✝ → α✝ → Bool
s₁ : Heap α✝
n : Nat
h₁ : WF le n s₁
x✝² x✝¹ : Heap α✝
x✝ : s₁ = Heap.nil → False
h₂ : WF le ... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) ((:c Batteries.BinomialHeap.Imp.Heap.merge.match_2) (:fv _uniq.93570) (:lambda _ ((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570)) (:lambda _ ((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570)) ((:c Batt... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"s₁","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"s₂","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"n","sexp":"(:c N... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:app (:c Batteries.BinomialHeap.Imp.Heap.merge.match_2) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda _ :explicit (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"split","sourceEnd":15063,"sourceStart":15058,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.split","source":"split","sourceEnd":15063,"sourceStart":15058,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 6 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b9f8d6b48f50182275761b12111e190ee7bec41f9ffc131456aac9c22d9e2c1e | 12fbbe92c1d999ef8aa050264137d571643fa3d3ee368f191fee2ac87f2344c0 | ad1a64057f9ab34fecfe3f4ee78660bb0316dbda9370581ffbeb1e8bddf3d598 | 3c5e7bfb51491b005014a32d3e66bc6bf800237a50b12a8db8c2a365bdbf31e7 |
cat-searcher/leandojo-benchmark-4-random | test | 852 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨h₂, fun h => h.1 h₁⟩ | case h_1
α✝ : Type u_1
le : α✝ → α✝ → Bool
s₂ : Heap α✝
n : Nat
h₂ : WF le n s₂
x✝¹ x✝ : Heap α✝
h₁ : WF le n Heap.nil
⊢ WF le n s₂ ∧ ((Heap.nil.rankGT n ↔ s₂.rankGT n) → s₂.rankGT n) | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) (:fv _uniq.93573)) (:forall _ ((:c Iff) ((:c Batteries.BinomialHeap.Imp.Heap.rankGT) (:fv _uniq.93570) ((:c Batteries.BinomialHeap.Imp.Heap.nil) (:fv _uniq.93570)) (:fv _uniq.93574)) ((:c Batteries.BinomialHeap.Imp.... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"s₂","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"n","sexp":"(:c Nat)"},{"name":"h₂","sexp":"((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.9... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV4)) (:arg :explicit 3 (:fv FV3)))) (:arg :explicit 1 (:forall _ :explicit (:app (:c Iff) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.rank... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":15074,"sourceStart":15069,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":15078,"sourceStart":15075,"tag":"atom"},{"children":[{"contextIndex":5,"semanticRole":"local","source":"h₂","sourceEnd":15082,"sourceStart":15078,"tag":"identi... | [] | [{"source":"⟨h₂, fun h => h.1 h₁⟩","source_end":15104,"source_start":15075,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 9 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1da1f991c5a281511b979f48deb9efc509001a87ab8e47944a8e1e93dbb0a491 | 0a7da2c72621b3e8cee74a0aaa23be4d63c1898cf110ac64b7f30fe99ee9921d | 715610dcbc37647080a2b5107fd46a05aba05118e80651f04da37cfb762bba2e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 853 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨h₁, fun h => h.2 h₂⟩ | case h_2
α✝ : Type u_1
le : α✝ → α✝ → Bool
s₁ : Heap α✝
n : Nat
h₁ : WF le n s₁
x✝² x✝¹ : Heap α✝
x✝ : s₁ = Heap.nil → False
h₂ : WF le n Heap.nil
⊢ WF le n s₁ ∧ ((s₁.rankGT n ↔ Heap.nil.rankGT n) → s₁.rankGT n) | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) (:fv _uniq.93572)) (:forall _ ((:c Iff) ((:c Batteries.BinomialHeap.Imp.Heap.rankGT) (:fv _uniq.93570) (:fv _uniq.93572) (:fv _uniq.93574)) ((:c Batteries.BinomialHeap.Imp.Heap.rankGT) (:fv _uniq.93570) ((:c Batteri... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"s₁","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"n","sexp":"(:c Nat)"},{"name":"h₁","sexp":"((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.9... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV4)) (:arg :explicit 3 (:fv FV3)))) (:arg :explicit 1 (:forall _ :explicit (:app (:c Iff) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.rank... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":15115,"sourceStart":15110,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":15119,"sourceStart":15116,"tag":"atom"},{"children":[{"contextIndex":5,"semanticRole":"local","source":"h₁","sourceEnd":15123,"sourceStart":15119,"tag":"identi... | [] | [{"source":"⟨h₁, fun h => h.2 h₂⟩","source_end":15145,"source_start":15116,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 14 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ce0324d6d1b3fd08efd7ef5e613a09a36be614ad446d87fb83e9cc6ee704b71a | 03a2b65702187b8990d112b6e352dbb30de9c97f4c3b6c492f749606b092ee28 | e1ea3334a5f94ac7bdf8460b8182707a85ff9dabc69b625d1cf7c8289828da6f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 854 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rename_i r₁ a₁ n₁ t₁ r₂ a₂ n₂ t₂ | case h_3
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝¹ x✝ : Heap α✝
r₁✝ : Nat
a₁✝ : α✝
n₁✝ : HeapNode α✝
t₁✝ : Heap α✝
r₂✝ : Nat
a₂✝ : α✝
n₂✝ : HeapNode α✝
t₂✝ : Heap α✝
h₁ : WF le n (cons r₁✝ a₁✝ n₁✝ t₁✝)
h₂ : WF le n (cons r₂✝ a₂✝ n₂✝ t₂✝)
⊢ WF le n
(if r₁✝ < r₂✝ then cons r₁✝ a₁✝ n₁✝ (merge le t₁✝ (cons r₂✝ a₂... | case h_3
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝¹ x✝ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
r₂ : Nat
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
h₂ : WF le n (cons r₂ a₂ n₂ t₂)
⊢ WF le n
(if r₁ < r₂ then cons r₁ a₁ n₁ (merge le t₁ (cons r₂ a₂ n₂ t₂))
else
... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) ((:c ite) ((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570)) ((:c LT.lt) (:c Nat) (:c instLTNat) (:fv _uniq.93860) (:fv _uniq.93864)) ((:c Nat.decLt) (:fv _uniq.93860) (:fv _uniq.93864)) ((:c Batteries.Binomia... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n","sexp":"(:c Nat)"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.935... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c ite) (:arg :implicit-type 0 (:app (:c Batteries.BinomialHeap.Imp.Heap) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"rename_i","sourceEnd":15159,"sourceStart":15151,"tag":"atom"},{"children":[{"children":[{"contextIndex":6,"semanticRole":"local","source":"r₁","sourceEnd":15164,"sourceStart":15160,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"r₁","sourceEnd":15164,"sourceStart":15160,"tag":"node"},{"... | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 21 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 03e41519bb5241b5e180eb5f65b1eed6a728735a53ab5d2bae68925a9cc39df3 | d3304147d93db6c621ba8cef770fd02e7aadb4cdbbf2e1778b786126f5fa4eb7 | 6f1595e6c927296228c20701b33e7ba020e18fa2f9ef9a4d0986a3d2c7cbb4f1 | d81397f8987fa4920c187ceb1e8928ad311898795c5ad4eb263e73e5b209f8a5 |
cat-searcher/leandojo-benchmark-4-random | test | 855 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let ⟨hr₁, hn₁, ht₁⟩ := h₁ | case h_3
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝¹ x✝ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
r₂ : Nat
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
h₂ : WF le n (cons r₂ a₂ n₂ t₂)
⊢ WF le n
(if r₁ < r₂ then cons r₁ a₁ n₁ (merge le t₁ (cons r₂ a₂ n₂ t₂))
else
... | case h_3
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝¹ x✝ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
r₂ : Nat
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
h₂ : WF le n (cons r₂ a₂ n₂ t₂)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
⊢ WF le n
(if r₁ < r₂... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) ((:c ite) ((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570)) ((:c LT.lt) (:c Nat) (:c instLTNat) (:fv _uniq.93860) (:fv _uniq.93864)) ((:c Nat.decLt) (:fv _uniq.93860) (:fv _uniq.93864)) ((:c Batteries.Binomia... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n","sexp":"(:c Nat)"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.935... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c ite) (:arg :implicit-type 0 (:app (:c Batteries.BinomialHeap.Imp.Heap) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"let","sourceEnd":15207,"sourceStart":15204,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":15211,"sourceStart":15208,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hr₁","sourceEnd":15216,"sourceStart":15211,"tag":"identifier"},{"source":",","so... | [] | [{"source":"h₁","source_end":15241,"source_start":15237,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 22 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 013d6c2f1b579f84e734968f9c111a1c2e8ccd01f7b0ca5c2210e438fefcb166 | d81397f8987fa4920c187ceb1e8928ad311898795c5ad4eb263e73e5b209f8a5 | 0b4376db4222b4d38eeff56c916345e4df55a8c6b02985cda64b09bcdfdc34f8 | 28c2be43fd7ec5bf815e9e5678dc7b038df2502b77174f58f83b92905ee8d8a1 |
cat-searcher/leandojo-benchmark-4-random | test | 856 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let ⟨hr₂, hn₂, ht₂⟩ := h₂ | case h_3
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝¹ x✝ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
r₂ : Nat
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
h₂ : WF le n (cons r₂ a₂ n₂ t₂)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
⊢ WF le n
(if r₁ < r₂... | case h_3
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝¹ x✝ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
r₂ : Nat
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
h₂ : WF le n (cons r₂ a₂ n₂ t₂)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
hr₂ : n ≤ r₂
hn₂ : HeapNode... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) ((:c ite) ((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570)) ((:c LT.lt) (:c Nat) (:c instLTNat) (:fv _uniq.93860) (:fv _uniq.93864)) ((:c Nat.decLt) (:fv _uniq.93860) (:fv _uniq.93864)) ((:c Batteries.Binomia... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n","sexp":"(:c Nat)"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.935... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c ite) (:arg :implicit-type 0 (:app (:c Batteries.BinomialHeap.Imp.Heap) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"let","sourceEnd":15249,"sourceStart":15246,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":15253,"sourceStart":15250,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hr₂","sourceEnd":15258,"sourceStart":15253,"tag":"identifier"},{"source":",","so... | [] | [{"source":"h₂","source_end":15283,"source_start":15279,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 23 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5f0fd93cbcb304d0544d661eb77d8a853a267f3d9ec965f5f4ea71b0e7e88627 | 28c2be43fd7ec5bf815e9e5678dc7b038df2502b77174f58f83b92905ee8d8a1 | 8fc65d05958d714d0e9e02b956736d356a6787f66384eb884427e1771d8c6265 | f8cae13b328c4d2ff28422b3a72f3fe95df091bd01abbb953292731cc82983be |
cat-searcher/leandojo-benchmark-4-random | test | 857 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split <;> rename_i lt₁ | case h_3
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝¹ x✝ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
r₂ : Nat
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
h₂ : WF le n (cons r₂ a₂ n₂ t₂)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
hr₂ : n ≤ r₂
hn₂ : HeapNode... | case h_3.isTrue
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝¹ x✝ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
r₂ : Nat
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
h₂ : WF le n (cons r₂ a₂ n₂ t₂)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
hr₂ : n ≤ r₂
hn₂ : H... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) ((:c ite) ((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570)) ((:c LT.lt) (:c Nat) (:c instLTNat) (:fv _uniq.93860) (:fv _uniq.93864)) ((:c Nat.decLt) (:fv _uniq.93860) (:fv _uniq.93864)) ((:c Batteries.Binomia... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n","sexp":"(:c Nat)"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.935... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c ite) (:arg :implicit-type 0 (:app (:c Batteries.BinomialHeap.Imp.Heap) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"children":[{"source":"split","sourceEnd":15293,"sourceStart":15288,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.split","source":"split","sourceEnd":15293,"sourceStart":15288,"tag":"node"},{"source":... | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 24 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3f81f0d07534b0fd2edd57a9cadc60028a924ce3fcb6a3adbcd2e8249ef4384c | f8cae13b328c4d2ff28422b3a72f3fe95df091bd01abbb953292731cc82983be | fe5d94f961fd0b90de8b9fff2335fe9d7072d65e7b64ce575948851c44a89614 | e4d71263986b7576f2eb0cbeabf32a9f80aa31d661552c9a049fe4482366a1d7 |
cat-searcher/leandojo-benchmark-4-random | test | 858 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split <;> rename_i lt₂ | case h_3.isFalse
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝¹ x✝ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
r₂ : Nat
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
h₂ : WF le n (cons r₂ a₂ n₂ t₂)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
hr₂ : n ≤ r₂
hn₂ : ... | case h_3.isFalse.isTrue
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝¹ x✝ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
r₂ : Nat
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
h₂ : WF le n (cons r₂ a₂ n₂ t₂)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
hr₂ : n ≤ r₂... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) ((:c ite) ((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570)) ((:c LT.lt) (:c Nat) (:c instLTNat) (:fv _uniq.93864) (:fv _uniq.93860)) ((:c Nat.decLt) (:fv _uniq.93864) (:fv _uniq.93860)) ((:c Batteries.Binomia... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n","sexp":"(:c Nat)"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.935... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c ite) (:arg :implicit-type 0 (:app (:c Batteries.BinomialHeap.Imp.Heap) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"children":[{"source":"split","sourceEnd":15475,"sourceStart":15470,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.split","source":"split","sourceEnd":15475,"sourceStart":15470,"tag":"node"},{"source":... | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 35 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b7fedb1c6ac3fd61c82adc7d2e054b14fecf5fe51ef02571d275234dd0a053b6 | 41797097b2b14d1adc87c32acb8aadd1464016b8127e6fcad77a57fc434ba2b0 | f8263dc4553aafb433c61a5f118703db6191f393b8400cdfb3021d4e8c72274c | dac9c881648e4d6db64ee70eda33e963a15cb6a691236bbe8811df96c86546d7 |
cat-searcher/leandojo-benchmark-4-random | test | 859 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases <a>Nat.le_antisymm</a> (<a>Nat.ge_of_not_lt</a> lt₂) (<a>Nat.ge_of_not_lt</a> lt₁) | case h_3.isFalse.isFalse
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝¹ x✝ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
r₂ : Nat
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
h₂ : WF le n (cons r₂ a₂ n₂ t₂)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
hr₂ : n ≤ r... | case h_3.isFalse.isFalse.refl
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝¹ x✝ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n (cons r₁ a₂ n₂ t₂)
hr₂ : n ≤ r₁
hn... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) ((:c Batteries.BinomialHeap.Imp.Heap.merge.match_1) (:fv _uniq.93570) (:lambda _ ((:c Prod) (:fv _uniq.93570) ((:c Batteries.BinomialHeap.Imp.HeapNode) (:fv _uniq.93570))) ((:c Batteries.BinomialHeap.Imp.Heap) (:fv ... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n","sexp":"(:c Nat)"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.935... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c Batteries.BinomialHeap.Imp.Heap.merge.match_1) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda _ :explicit (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"cases","sourceEnd":15657,"sourceStart":15652,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Nat.le_antisymm","semanticRole":"global","source":"Nat.le_antisymm","sourceEnd":15673,"sourceStart":15658,"tag":"identifier"},{"childr... | [] | [{"source":"Nat.le_antisymm (Nat.ge_of_not_lt lt₂) (Nat.ge_of_not_lt lt₁)","source_end":15723,"source_start":15658,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 46 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 884f7caea2ddd04e9094326657d39e29f57edf5ab682819d2f1bd080c9ad7e6f | 821ff19821f950ebca2dce40e3575b0a0afa32401ed4edc536ce330b650d55d4 | 415e5bc7cb311ec1d8d1e6a4d5b08a8fb494d483c9147d9e187fccf659f778c6 | 07616a00204a40f90c685850aae33c5a717ea7674767b7ee6f6ef2932d8fa8fb |
cat-searcher/leandojo-benchmark-4-random | test | 860 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split | case h_3.isFalse.isFalse.refl
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝¹ x✝ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n (cons r₁ a₂ n₂ t₂)
hr₂ : n ≤ r₁
hn... | case h_3.isFalse.isFalse.refl
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n (cons r₁ a₂ n₂ t₂)
hr₂ : n ≤ r₁
h... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) ((:c Batteries.BinomialHeap.Imp.Heap.merge.match_1) (:fv _uniq.93570) (:lambda _ ((:c Prod) (:fv _uniq.93570) ((:c Batteries.BinomialHeap.Imp.HeapNode) (:fv _uniq.93570))) ((:c Batteries.BinomialHeap.Imp.Heap) (:fv ... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n","sexp":"(:c Nat)"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.935... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c Batteries.BinomialHeap.Imp.Heap.merge.match_1) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda _ :explicit (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"split","sourceEnd":15733,"sourceStart":15728,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.split","source":"split","sourceEnd":15733,"sourceStart":15728,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 47 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6743271f45f1a6b72837207173311a257dc336aa250df813dac17cc0f4375e2b | 07616a00204a40f90c685850aae33c5a717ea7674767b7ee6f6ef2932d8fa8fb | ad1a64057f9ab34fecfe3f4ee78660bb0316dbda9370581ffbeb1e8bddf3d598 | fbd8e8b5cbda40a569480f650d8bf08eb9f2f9e074ef15326aeffc9d2a42212e |
cat-searcher/leandojo-benchmark-4-random | test | 861 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rename_i a n eq | case h_3.isFalse.isFalse.refl
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n (cons r₁ a₂ n₂ t₂)
hr₂ : n ≤ r₁
h... | case h_3.isFalse.isFalse.refl
α✝ : Type u_1
le : α✝ → α✝ → Bool
n✝ : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n✝ (cons r₁ a₁ n₁ t₁)
hr₁ : n✝ ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n✝ (cons r₁ a₂ n₂ t₂)
hr₂ : n✝ ≤... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) (:let r (:c Nat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.93860) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) ((:c ite) ((:c Batteries.Bino... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n","sexp":"(:c Nat)"},{"name":"x✝²","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:let r (:c Nat) (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"rename_i","sourceEnd":15743,"sourceStart":15735,"tag":"atom"},{"children":[{"children":[{"contextIndex":24,"semanticRole":"local","source":"a","sourceEnd":15745,"sourceStart":15744,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"a","sourceEnd":15745,"sourceStart":15744,"tag":"node"},{"c... | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 49 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e1bc66e53366c139e0d72c1822948491901db79dba0d9b120fac3f984c33f885 | fbd8e8b5cbda40a569480f650d8bf08eb9f2f9e074ef15326aeffc9d2a42212e | 0ebab1376b37c365da6b668dd1dfeadfd9109ce5be52331aaf0c6d2f2e563039 | adf5095233bf98485e6b4cb6f450d01bc94f6f0f47afca35731763e756e8fa50 |
cat-searcher/leandojo-benchmark-4-random | test | 862 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only | case h_3.isFalse.isFalse.refl
α✝ : Type u_1
le : α✝ → α✝ → Bool
n✝ : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n✝ (cons r₁ a₁ n₁ t₁)
hr₁ : n✝ ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n✝ (cons r₁ a₂ n₂ t₂)
hr₂ : n✝ ≤... | case h_3.isFalse.isFalse.refl
α✝ : Type u_1
le : α✝ → α✝ → Bool
n✝ : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n✝ (cons r₁ a₁ n₁ t₁)
hr₁ : n✝ ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n✝ (cons r₁ a₂ n₂ t₂)
hr₂ : n✝ ≤... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) (:let r (:c Nat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.93860) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) ((:c ite) ((:c Batteries.Bino... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"x✝²","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.9... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:let r (:c Nat) (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"simp","sourceEnd":15987,"sourceStart":15983,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":15992,"sourceStart":15988,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":159... | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 73 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 31e2cb3faf0d4572702245617854525064941818c952ab7824e364cf4f67d898 | ad7ca82e436aa1f1f317f321f40678bc6aaa07a0bef20ad16632d567c1b603e9 | 474d6f2fb64f6202b4a1fc099cb53cf41b343456b831e8c4f67099fd49f38f97 | 186d96115e224e9bdd8644ee83fcffd187f1c482b9d9bddaea4651a113caec6a |
cat-searcher/leandojo-benchmark-4-random | test | 863 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split <;> split <;> rename_i hl₁ hl₂ | case h_3.isFalse.isFalse.refl
α✝ : Type u_1
le : α✝ → α✝ → Bool
n✝ : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n✝ (cons r₁ a₁ n₁ t₁)
hr₁ : n✝ ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n✝ (cons r₁ a₂ n₂ t₂)
hr₂ : n✝ ≤... | case h_3.isFalse.isFalse.refl.isTrue.isTrue
α✝ : Type u_1
le : α✝ → α✝ → Bool
n✝ : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n✝ (cons r₁ a₁ n₁ t₁)
hr₁ : n✝ ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n✝ (cons r₁ a₂ n₂ ... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) ((:c ite) ((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570)) ((:c Batteries.BinomialHeap.Imp.Heap.rankGT) (:fv _uniq.93570) (:fv _uniq.93863) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) ... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"x✝²","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.9... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c ite) (:arg :implicit-type 0 (:app (:c Batteries.BinomialHeap.Imp.Heap) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"children":[{"children":[{"source":"split","sourceEnd":15999,"sourceStart":15994,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.split","source":"split","sourceEnd":15999,"sourceStart":15994,"tag":"node... | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 75 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 988274b099b5159f44e88a6ab41e2abda3ff0e23822bd3bdfc73fe375c84e9ee | 186d96115e224e9bdd8644ee83fcffd187f1c482b9d9bddaea4651a113caec6a | 7d960c8d3dd6c7153667196093b2b25b4568d743dc8e0ec2018c857dd16e4640 | b7aa3e60ee3e6b1520e1ba04bb90ee414f129e057b2425e68fc6a3fe1d5eac95 |
cat-searcher/leandojo-benchmark-4-random | test | 864 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨⟨hr₁, hn₁, <a>And.left</a> (merge' ht₁ ⟨lt₁, hn₂, ht₂⟩)⟩, fun h => ?_⟩ | case h_3.isTrue
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝¹ x✝ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
r₂ : Nat
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
h₂ : WF le n (cons r₂ a₂ n₂ t₂)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
hr₂ : n ≤ r₂
hn₂ : H... | case h_3.isTrue
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝¹ x✝ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
r₂ : Nat
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
h₂ : WF le n (cons r₂ a₂ n₂ t₂)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
hr₂ : n ≤ r₂
hn₂ : H... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) ((:c Batteries.BinomialHeap.Imp.Heap.cons) (:fv _uniq.93570) (:fv _uniq.93860) (:fv _uniq.93861) (:fv _uniq.93862) ((:c Batteries.BinomialHeap.Imp.Heap.merge) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93863) ((... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n","sexp":"(:c Nat)"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.935... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c Batteries.BinomialHeap.Imp.Heap.cons) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV6)) (:arg :explicit 2 (:... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"refine","sourceEnd":15326,"sourceStart":15320,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":15330,"sourceStart":15327,"tag":"atom"},{"children":[{"children":[{"source":"⟨","sourceEnd":15333,"sourceStart":15330,"tag":"atom"},{"children":[{"contextIndex":16,"semanticRole":"local","source":"... | [] | [{"source":"⟨⟨hr₁, hn₁, And.left (merge' ht₁ ⟨lt₁, hn₂, ht₂⟩)⟩, fun h => ?_⟩","source_end":15415,"source_start":15327,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 33 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a6dc9e5897a68b64e3bd5831ac42bb18b3094d71647906949bf8acb451b11606 | ed3fee8a6fc42492f384d8c661160233b754f803015f42feb52a7f5e6157f4b1 | 89e71f46b5a28db552e8ae4a2f428d8f19152eb3d703faa0f02813828a6f5640 | 7a299337879120f436ff20500c9582509bfb3f8701faa8e52424104ffc7656c3 |
cat-searcher/leandojo-benchmark-4-random | test | 865 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact h.2 <| <a>Nat.lt_of_le_of_lt</a> hr₁ lt₁ | case h_3.isTrue
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝¹ x✝ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
r₂ : Nat
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
h₂ : WF le n (cons r₂ a₂ n₂ t₂)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
hr₂ : n ≤ r₂
hn₂ : H... | ((:c Batteries.BinomialHeap.Imp.Heap.rankGT) (:fv _uniq.93570) ((:c Batteries.BinomialHeap.Imp.Heap.cons) (:fv _uniq.93570) (:fv _uniq.93860) (:fv _uniq.93861) (:fv _uniq.93862) ((:c Batteries.BinomialHeap.Imp.Heap.merge) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93863) ((:c Batteries.BinomialHeap.Imp.Heap.cons) (... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n","sexp":"(:c Nat)"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.935... | (:app (:c Batteries.BinomialHeap.Imp.Heap.rankGT) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.BinomialHeap.Imp.Heap.cons) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV6)) (:arg :explicit 2 (:fv FV7)) (:arg :explicit 3 (:fv FV8)) (:arg :explicit 4 (:app (:c Batteries.BinomialHea... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"exact","sourceEnd":15427,"sourceStart":15422,"tag":"atom"},{"children":[{"children":[{"contextIndex":23,"semanticRole":"local","source":"h","sourceEnd":15429,"sourceStart":15428,"tag":"identifier"},{"source":".","sourceEnd":15430,"sourceStart":15429,"tag":"atom"},{"children":[{"source":"2","sour... | [] | [{"source":"h.2 <| Nat.lt_of_le_of_lt hr₁ lt₁","source_end":15465,"source_start":15428,"syntax_kind":"«term_<|_»"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 34 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 551363515bbe079d9fe180232326a7f0d1c2d1c1a9edc62002c4aa231916b51b | 7a299337879120f436ff20500c9582509bfb3f8701faa8e52424104ffc7656c3 | fe6fd5d964cd3eaf4ef28ae523f53bc245ab61118b6ada2d90560c1cfd86743a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 866 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨⟨hr₂, hn₂, <a>And.left</a> (merge' ⟨lt₂, hn₁, ht₁⟩ ht₂)⟩, fun h => ?_⟩ | case h_3.isFalse.isTrue
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝¹ x✝ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
r₂ : Nat
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
h₂ : WF le n (cons r₂ a₂ n₂ t₂)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
hr₂ : n ≤ r₂... | case h_3.isFalse.isTrue
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝¹ x✝ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
r₂ : Nat
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
h₂ : WF le n (cons r₂ a₂ n₂ t₂)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
hr₂ : n ≤ r₂... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) ((:c Batteries.BinomialHeap.Imp.Heap.cons) (:fv _uniq.93570) (:fv _uniq.93864) (:fv _uniq.93865) (:fv _uniq.93866) ((:c Batteries.BinomialHeap.Imp.Heap.merge) (:fv _uniq.93570) (:fv _uniq.93571) ((:c Batteries.Binom... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n","sexp":"(:c Nat)"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.935... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c Batteries.BinomialHeap.Imp.Heap.cons) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV10)) (:arg :explicit 2 (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"refine","sourceEnd":15508,"sourceStart":15502,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":15512,"sourceStart":15509,"tag":"atom"},{"children":[{"children":[{"source":"⟨","sourceEnd":15515,"sourceStart":15512,"tag":"atom"},{"children":[{"contextIndex":19,"semanticRole":"local","source":"... | [] | [{"source":"⟨⟨hr₂, hn₂, And.left (merge' ⟨lt₂, hn₁, ht₁⟩ ht₂)⟩, fun h => ?_⟩","source_end":15597,"source_start":15509,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 44 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6085a50627569addcdbb56ddbf27e04a2429f8962e5c4bf89bcfeb2272515fbd | 0c6aa42c225b56864af73de9833850fe321859b660b2b4957f768904471a7d1e | 1656d41ab98f196670937dd7d557e02940e93d082e0765a7e4cb348386fadb60 | 287782345c685f5d5643fd719acdfa2fc223d554f47d03bd614edc0bc77c3fe3 |
cat-searcher/leandojo-benchmark-4-random | test | 867 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact h.1 <| <a>Nat.lt_of_le_of_lt</a> hr₂ lt₂ | case h_3.isFalse.isTrue
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝¹ x✝ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
r₂ : Nat
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
h₂ : WF le n (cons r₂ a₂ n₂ t₂)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
hr₂ : n ≤ r₂... | ((:c Batteries.BinomialHeap.Imp.Heap.rankGT) (:fv _uniq.93570) ((:c Batteries.BinomialHeap.Imp.Heap.cons) (:fv _uniq.93570) (:fv _uniq.93864) (:fv _uniq.93865) (:fv _uniq.93866) ((:c Batteries.BinomialHeap.Imp.Heap.merge) (:fv _uniq.93570) (:fv _uniq.93571) ((:c Batteries.BinomialHeap.Imp.Heap.cons) (:fv _uniq.93570) (... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n","sexp":"(:c Nat)"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.935... | (:app (:c Batteries.BinomialHeap.Imp.Heap.rankGT) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.BinomialHeap.Imp.Heap.cons) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV10)) (:arg :explicit 2 (:fv FV11)) (:arg :explicit 3 (:fv FV12)) (:arg :explicit 4 (:app (:c Batteries.Binomial... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"exact","sourceEnd":15609,"sourceStart":15604,"tag":"atom"},{"children":[{"children":[{"contextIndex":24,"semanticRole":"local","source":"h","sourceEnd":15611,"sourceStart":15610,"tag":"identifier"},{"source":".","sourceEnd":15612,"sourceStart":15611,"tag":"atom"},{"children":[{"source":"1","sour... | [] | [{"source":"h.1 <| Nat.lt_of_le_of_lt hr₂ lt₂","source_end":15647,"source_start":15610,"syntax_kind":"«term_<|_»"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 45 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 34142e1c4915bb5ef9026185403862d3721db7d8622965d0ca52903630697bd1 | 287782345c685f5d5643fd719acdfa2fc223d554f47d03bd614edc0bc77c3fe3 | f7519ee7d907167bced612aff6d0d7cc1983dbf9590fd617fed96921d4128fbb | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 868 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | unfold <a>Batteries.BinomialHeap.Imp.combine</a> at eq | α✝ : Type u_1
le : α✝ → α✝ → Bool
n✝ : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n✝ (cons r₁ a₁ n₁ t₁)
hr₁ : n✝ ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n✝ (cons r₁ a₂ n₂ t₂)
hr₂ : n✝ ≤ r₁
hn₂ : HeapNode.WF le a₂ n₂... | α✝ : Type u_1
le : α✝ → α✝ → Bool
n✝ : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n✝ (cons r₁ a₁ n₁ t₁)
hr₁ : n✝ ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n✝ (cons r₁ a₂ n₂ t₂)
hr₂ : n✝ ≤ r₁
hn₂ : HeapNode.WF le a₂ n₂... | ((:c Batteries.BinomialHeap.Imp.HeapNode.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.101854) (:fv _uniq.101855) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.93860) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"x✝²","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.9... | (:app (:c Batteries.BinomialHeap.Imp.HeapNode.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV24)) (:arg :explicit 3 (:fv FV25)) (:arg :explicit 4 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :in... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"unfold","sourceEnd":15799,"sourceStart":15793,"tag":"atom"},{"children":[{"name":"Batteries.BinomialHeap.Imp.combine","semanticRole":"global","source":"combine","sourceEnd":15807,"sourceStart":15800,"tag":"identifier"}],"kind":"null","source":"combine","sourceEnd":15807,"sourceStart":15800,"tag"... | [] | [{"source":"combine","source_end":15807,"source_start":15800,"syntax_kind":"ident"},{"source":"eq","source_end":15813,"source_start":15811,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 52 | exact | true | 1 | 26 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3ba34c7acbc7d036fb91159176cc7a9f46d22e2aed47043e73c0c5efd0e1d204 | 6ff38119cab68b8b6c4858f1e6477251d01cbf8ee842c307747990411b195410 | e8c603d1fe8fac63127b164e0e80050c6c8a9f07d0e4bad256b25df76a6b6829 | eaf4b4af041ac7f512d54cf99da12f086ed1fad02a1daf61c63a8442309c45cf |
cat-searcher/leandojo-benchmark-4-random | test | 869 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split at eq <;> cases eq <;> rename_i h | α✝ : Type u_1
le : α✝ → α✝ → Bool
n✝ : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n✝ (cons r₁ a₁ n₁ t₁)
hr₁ : n✝ ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n✝ (cons r₁ a₂ n₂ t₂)
hr₂ : n✝ ≤ r₁
hn₂ : HeapNode.WF le a₂ n₂... | case isTrue.refl
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n (cons r₁ a₂ n₂ t₂)
hr₂ : n ≤ r₁
hn₂ : HeapNode... | ((:c Batteries.BinomialHeap.Imp.HeapNode.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.101854) (:fv _uniq.101855) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.93860) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"x✝²","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.9... | (:app (:c Batteries.BinomialHeap.Imp.HeapNode.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV24)) (:arg :explicit 3 (:fv FV25)) (:arg :explicit 4 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :in... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"children":[{"children":[{"source":"split","sourceEnd":15820,"sourceStart":15815,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":"at","sourceEnd":15823,"sourceStart":15821,"tag":"atom"},{"children":[{"children":[{"contextIndex":26,"semanticRole":"lo... | [] | [{"source":"eq","source_end":15826,"source_start":15824,"syntax_kind":"ident"},{"source":"eq","source_end":15839,"source_start":15837,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 54 | exact | true | 1 | 26 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | edd6698bdd7573dfe1ca02a57245485c19a5e28f5e9700e98435b0e2471b9124 | eaf4b4af041ac7f512d54cf99da12f086ed1fad02a1daf61c63a8442309c45cf | 5ac7f2ce0965d96e99f94054ba156472dd993f939e45391755557a9e5cadec7a | d7205c784fc20d051418e4e8ef711ab072e234eb0272b7cd3154e63e8f8fd433 |
cat-searcher/leandojo-benchmark-4-random | test | 870 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨r₁, <a>rfl</a>, h, hn₂, hn₁⟩ | case isTrue.refl
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n (cons r₁ a₂ n₂ t₂)
hr₂ : n ≤ r₁
hn₂ : HeapNode... | ((:c Batteries.BinomialHeap.Imp.HeapNode.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93861) ((:c Batteries.BinomialHeap.Imp.HeapNode.node) (:fv _uniq.93570) (:fv _uniq.93865) (:fv _uniq.93866) (:fv _uniq.93862)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.93860)... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n","sexp":"(:c Nat)"},{"name":"x✝²","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93... | (:app (:c Batteries.BinomialHeap.Imp.HeapNode.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV7)) (:arg :explicit 3 (:app (:c Batteries.BinomialHeap.Imp.HeapNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV10)) (:arg :explicit 2 (:fv FV11)) (:arg :explici... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":15869,"sourceStart":15864,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":15873,"sourceStart":15870,"tag":"atom"},{"children":[{"contextIndex":6,"semanticRole":"local","source":"r₁","sourceEnd":15877,"sourceStart":15873,"tag":"identi... | [] | [{"source":"⟨r₁, rfl, h, hn₂, hn₁⟩","source_end":15902,"source_start":15870,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 65 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f19ee4c65b0b9193ad032a46faad2c13fa654b41d03d2e1d356bc7aa44e8a35d | 5aa5d38416ff31dc693c05fb2d5efefe193f5463bc2f8a32d3ac66d6e04278fe | 520308d6316e51d65bfcb88ad8482bf66085fa395f71ca2b9e609eeea04b4614 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 871 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨r₁, <a>rfl</a>, TotalBLE.total.resolve_left h, hn₁, hn₂⟩ | case isFalse.refl
α✝ : Type u_1
le : α✝ → α✝ → Bool
n : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n (cons r₁ a₁ n₁ t₁)
hr₁ : n ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n (cons r₁ a₂ n₂ t₂)
hr₂ : n ≤ r₁
hn₂ : HeapNod... | ((:c Batteries.BinomialHeap.Imp.HeapNode.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93865) ((:c Batteries.BinomialHeap.Imp.HeapNode.node) (:fv _uniq.93570) (:fv _uniq.93861) (:fv _uniq.93862) (:fv _uniq.93866)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.93860)... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n","sexp":"(:c Nat)"},{"name":"x✝²","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93... | (:app (:c Batteries.BinomialHeap.Imp.HeapNode.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV10)) (:arg :explicit 3 (:app (:c Batteries.BinomialHeap.Imp.HeapNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":15917,"sourceStart":15912,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":15921,"sourceStart":15918,"tag":"atom"},{"children":[{"contextIndex":6,"semanticRole":"local","source":"r₁","sourceEnd":15925,"sourceStart":15921,"tag":"identi... | [] | [{"source":"⟨r₁, rfl, TotalBLE.total.resolve_left h, hn₁, hn₂⟩","source_end":15978,"source_start":15918,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 70 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 863d8f623b47d899c61fedbf17b7cb24a89ffd18d91d49758946a5cc8444d1c1 | 06f49c22ca0acc25ef901e8ec3033fa891af033824761026711de8507676c41c | f55b3112e51ebcc544833fe6c9e07c882e39e6e778827e3f167a3d47fe0d856d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 872 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨⟨<a>Nat.le_succ_of_le</a> hr₁, this, (merge' (ht₁.of_rankGT hl₁) (ht₂.of_rankGT hl₂)).1⟩, fun _ => <a>Nat.lt_succ_of_le</a> hr₁⟩ | case h_3.isFalse.isFalse.refl.isTrue.isTrue
α✝ : Type u_1
le : α✝ → α✝ → Bool
n✝ : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n✝ (cons r₁ a₁ n₁ t₁)
hr₁ : n✝ ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n✝ (cons r₁ a₂ n₂ ... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) ((:c Batteries.BinomialHeap.Imp.Heap.cons) (:fv _uniq.93570) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.93860) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNa... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"x✝²","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.9... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c Batteries.BinomialHeap.Imp.Heap.cons) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :imp... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":16047,"sourceStart":16042,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":16051,"sourceStart":16048,"tag":"atom"},{"children":[{"children":[{"source":"⟨","sourceEnd":16054,"sourceStart":16051,"tag":"atom"},{"children":[{"children":[{... | [] | [{"source":"⟨⟨Nat.le_succ_of_le hr₁, this,\n (merge' (ht₁.of_rankGT hl₁) (ht₂.of_rankGT hl₂)).1⟩,\n fun _ => Nat.lt_succ_of_le hr₁⟩","source_end":16199,"source_start":16048,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 88 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 02ace842dd82171c422ccd00cbe4687556818014d1b85b77bcf6572788bed90e | 45ad1d4bf6f2427dcff3856a16203de12e7787895cbcb58032c1ceb7536b4403 | 32cee934b83a4647151db95ed6b00a6e957374558380b4f240d6089705df6f6b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 873 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let ⟨ih₁, ih₂⟩ := merge' (s₁ := .cons ..) ⟨<a>Nat.le_succ_of_le</a> hr₁, this, ht₁.of_rankGT hl₁⟩ (ht₂.of_le (<a>Nat.le_succ_of_le</a> hr₁)) | case h_3.isFalse.isFalse.refl.isTrue.isFalse
α✝ : Type u_1
le : α✝ → α✝ → Bool
n✝ : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n✝ (cons r₁ a₁ n₁ t₁)
hr₁ : n✝ ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n✝ (cons r₁ a₂ n₂... | case h_3.isFalse.isFalse.refl.isTrue.isFalse
α✝ : Type u_1
le : α✝ → α✝ → Bool
n✝ : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n✝ (cons r₁ a₁ n₁ t₁)
hr₁ : n✝ ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n✝ (cons r₁ a₂ n₂... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) ((:c Batteries.BinomialHeap.Imp.Heap.merge) (:fv _uniq.93570) (:fv _uniq.93571) ((:c Batteries.BinomialHeap.Imp.Heap.cons) (:fv _uniq.93570) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c ins... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"x✝²","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.9... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c Batteries.BinomialHeap.Imp.Heap.merge) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"let","sourceEnd":16210,"sourceStart":16207,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":16214,"sourceStart":16211,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"ih₁","sourceEnd":16219,"sourceStart":16214,"tag":"identifier"},{"source":",","so... | [] | [{"source":"merge' (s₁ := .cons ..)\n ⟨Nat.le_succ_of_le hr₁, this, ht₁.of_rankGT hl₁⟩\n (ht₂.of_le (Nat.le_succ_of_le hr₁))","source_end":16373,"source_start":16233,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 95 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 31dbd3ceaadaae56895d8a641f4f053bd99e44a0b19a0cb6807ea62e7de6b8b8 | bb21c2daa03a3168e61a480a4668d7c08f119332dbaa812ff0c9f1d0316a8187 | 93fe85b6fe474d75f5aa2a2d51bf1a0f76a5cb49986a97ae7520de093a9e2632 | 693c6652bc0e06258cb76c61d0f627304b7f44c45104ac882960c232eee33916 |
cat-searcher/leandojo-benchmark-4-random | test | 874 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨ih₁, fun _ => ih₂ ⟨fun _ => ht₂.rankGT.of_le hr₁, fun _ => <a>Nat.lt_succ_of_le</a> hr₁⟩⟩ | case h_3.isFalse.isFalse.refl.isTrue.isFalse
α✝ : Type u_1
le : α✝ → α✝ → Bool
n✝ : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n✝ (cons r₁ a₁ n₁ t₁)
hr₁ : n✝ ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n✝ (cons r₁ a₂ n₂... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) ((:c Batteries.BinomialHeap.Imp.Heap.merge) (:fv _uniq.93570) (:fv _uniq.93571) ((:c Batteries.BinomialHeap.Imp.Heap.cons) (:fv _uniq.93570) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c ins... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"x✝²","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.9... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c Batteries.BinomialHeap.Imp.Heap.merge) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"exact","sourceEnd":16385,"sourceStart":16380,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":16389,"sourceStart":16386,"tag":"atom"},{"children":[{"contextIndex":30,"semanticRole":"local","source":"ih₁","sourceEnd":16394,"sourceStart":16389,"tag":"identifier"},{"source":",","sourceEnd":1639... | [] | [{"source":"⟨ih₁, fun _ => ih₂ ⟨fun _ => ht₂.rankGT.of_le hr₁, fun _ => Nat.lt_succ_of_le hr₁⟩⟩","source_end":16487,"source_start":16386,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 96 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f6a390267137bde2c76778bf11d01723252707f800ee762ad7cd9684a2e7ce52 | 693c6652bc0e06258cb76c61d0f627304b7f44c45104ac882960c232eee33916 | 4327f25c6b0a9f91978c8ac1506b9abc9cc85bbb45a60d950b9f26400a7d253c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 875 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let ⟨ih₁, ih₂⟩ := merge' (s₂ := .cons ..) (ht₁.of_le (<a>Nat.le_succ_of_le</a> hr₁)) ⟨<a>Nat.le_succ_of_le</a> hr₁, this, ht₂.of_rankGT hl₂⟩ | case h_3.isFalse.isFalse.refl.isFalse.isTrue
α✝ : Type u_1
le : α✝ → α✝ → Bool
n✝ : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n✝ (cons r₁ a₁ n₁ t₁)
hr₁ : n✝ ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n✝ (cons r₁ a₂ n₂... | case h_3.isFalse.isFalse.refl.isFalse.isTrue
α✝ : Type u_1
le : α✝ → α✝ → Bool
n✝ : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n✝ (cons r₁ a₁ n₁ t₁)
hr₁ : n✝ ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n✝ (cons r₁ a₂ n₂... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) ((:c Batteries.BinomialHeap.Imp.Heap.merge) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93863) ((:c Batteries.BinomialHeap.Imp.Heap.cons) (:fv _uniq.93570) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"x✝²","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.9... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c Batteries.BinomialHeap.Imp.Heap.merge) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"let","sourceEnd":16498,"sourceStart":16495,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":16502,"sourceStart":16499,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"ih₁","sourceEnd":16507,"sourceStart":16502,"tag":"identifier"},{"source":",","so... | [] | [{"source":"merge' (s₂ := .cons ..) (ht₁.of_le (Nat.le_succ_of_le hr₁))\n ⟨Nat.le_succ_of_le hr₁, this, ht₂.of_rankGT hl₂⟩","source_end":16653,"source_start":16521,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 101 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 25dd5c40b25f7ce83145db8ff4515c1ee20a9bded29722dd1e9d41ef863daf58 | bccd7f25e41c65a203c36b10770e4bba5334638d036f8ccfcfffb4808301398e | 870f7a0f714097ad3c66d40cc79e19805b8b749066fd908d6a674b1a6eb45cf2 | 6451878c3b06aae0fbfbd0db2aabe891c907030ec486270bb601c3dfcd908595 |
cat-searcher/leandojo-benchmark-4-random | test | 876 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨ih₁, fun _ => ih₂ ⟨fun _ => <a>Nat.lt_succ_of_le</a> hr₁, fun _ => ht₁.rankGT.of_le hr₁⟩⟩ | case h_3.isFalse.isFalse.refl.isFalse.isTrue
α✝ : Type u_1
le : α✝ → α✝ → Bool
n✝ : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n✝ (cons r₁ a₁ n₁ t₁)
hr₁ : n✝ ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n✝ (cons r₁ a₂ n₂... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) ((:c Batteries.BinomialHeap.Imp.Heap.merge) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93863) ((:c Batteries.BinomialHeap.Imp.Heap.cons) (:fv _uniq.93570) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"x✝²","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.9... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c Batteries.BinomialHeap.Imp.Heap.merge) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"exact","sourceEnd":16665,"sourceStart":16660,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":16669,"sourceStart":16666,"tag":"atom"},{"children":[{"contextIndex":30,"semanticRole":"local","source":"ih₁","sourceEnd":16674,"sourceStart":16669,"tag":"identifier"},{"source":",","sourceEnd":1667... | [] | [{"source":"⟨ih₁, fun _ => ih₂ ⟨fun _ => Nat.lt_succ_of_le hr₁, fun _ => ht₁.rankGT.of_le hr₁⟩⟩","source_end":16767,"source_start":16666,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 102 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 95c20ccbd5f30ae4af09131e873c27ea991e57e5656f1c705e76b1827e8d11d6 | 6451878c3b06aae0fbfbd0db2aabe891c907030ec486270bb601c3dfcd908595 | d46e3edbe325f42f73acce5923b2bb8ae17f5dcb2aa968607c94e3da36885c3e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 877 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let ⟨ih₁, ih₂⟩ := merge' ht₁ ht₂ | case h_3.isFalse.isFalse.refl.isFalse.isFalse
α✝ : Type u_1
le : α✝ → α✝ → Bool
n✝ : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n✝ (cons r₁ a₁ n₁ t₁)
hr₁ : n✝ ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n✝ (cons r₁ a₂ n... | case h_3.isFalse.isFalse.refl.isFalse.isFalse
α✝ : Type u_1
le : α✝ → α✝ → Bool
n✝ : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n✝ (cons r₁ a₁ n₁ t₁)
hr₁ : n✝ ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n✝ (cons r₁ a₂ n... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) ((:c Batteries.BinomialHeap.Imp.Heap.cons) (:fv _uniq.93570) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.93860) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNa... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"x✝²","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.9... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c Batteries.BinomialHeap.Imp.Heap.cons) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :imp... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"let","sourceEnd":16778,"sourceStart":16775,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":16782,"sourceStart":16779,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"ih₁","sourceEnd":16787,"sourceStart":16782,"tag":"identifier"},{"source":",","so... | [] | [{"source":"merge' ht₁ ht₂","source_end":16819,"source_start":16801,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 107 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f253a57cc8a4ac7abef63e419c24c7ce4d21b78a5aa34d4268359072be8380dd | 9005ca1239de07e93eba1da7dee67d25c270fb17b2d6ff72e71a4037a06ac43b | 65af12fc4482c0da046b2ff59536b90b60c7454583cdde94f2c9f2dc6c1af0f5 | 84f82be71424b931436a5fc1b6b4217e8acfdffdcbdf493c7e509e8b098be9cb |
cat-searcher/leandojo-benchmark-4-random | test | 878 | Batteries.BinomialHeap.Imp.Heap.WF.merge' | .lake/packages/batteries/Batteries/Data/BinomialHeap/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨⟨<a>Nat.le_succ_of_le</a> hr₁, this, ih₁.of_rankGT (ih₂ (<a>iff_of_false</a> hl₁ hl₂))⟩, fun _ => <a>Nat.lt_succ_of_le</a> hr₁⟩ | case h_3.isFalse.isFalse.refl.isFalse.isFalse
α✝ : Type u_1
le : α✝ → α✝ → Bool
n✝ : Nat
x✝² x✝¹ : Heap α✝
r₁ : Nat
a₁ : α✝
n₁ : HeapNode α✝
t₁ : Heap α✝
a₂ : α✝
n₂ : HeapNode α✝
t₂ : Heap α✝
h₁ : WF le n✝ (cons r₁ a₁ n₁ t₁)
hr₁ : n✝ ≤ r₁
hn₁ : HeapNode.WF le a₁ n₁ r₁
ht₁ : WF le (r₁ + 1) t₁
h₂ : WF le n✝ (cons r₁ a₂ n... | ((:c And) ((:c Batteries.BinomialHeap.Imp.Heap.WF) (:fv _uniq.93570) (:fv _uniq.93571) (:fv _uniq.93574) ((:c Batteries.BinomialHeap.Imp.Heap.cons) (:fv _uniq.93570) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.93860) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNa... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"le","sexp":"(:forall _ (:fv _uniq.93570) (:forall _ (:fv _uniq.93570) (:c Bool)))"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"x✝²","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.93570))"},{"name":"x✝¹","sexp":"((:c Batteries.BinomialHeap.Imp.Heap) (:fv _uniq.9... | (:app (:c And) (:arg :explicit 0 (:app (:c Batteries.BinomialHeap.Imp.Heap.WF) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:app (:c Batteries.BinomialHeap.Imp.Heap.cons) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :imp... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"name":"le","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :e... | {"children":[{"source":"exact","sourceEnd":16831,"sourceStart":16826,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":16835,"sourceStart":16832,"tag":"atom"},{"children":[{"children":[{"source":"⟨","sourceEnd":16838,"sourceStart":16835,"tag":"atom"},{"children":[{"children":[{"name":"Nat.le_succ_of_le","semanticRol... | [] | [{"source":"⟨⟨Nat.le_succ_of_le hr₁, this, ih₁.of_rankGT (ih₂ (iff_of_false hl₁ hl₂))⟩,\n fun _ => Nat.lt_succ_of_le hr₁⟩","source_end":16967,"source_start":16832,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93570","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.93571","is_instance":false,"is_let":false,"user_name":"le"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 54 | 108 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a4920c3a82ec35cfb34f91788fff55e8fa6471bf7365376e2788ad66183b45a2 | 84f82be71424b931436a5fc1b6b4217e8acfdffdcbdf493c7e509e8b098be9cb | d952485521e35945e6471bd147c64006bbc0355e456579f6acc6ade421755c49 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 879 | Filter.HasBasis.equicontinuousAt_iff | Mathlib/Topology/UniformSpace/Equicontinuity.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>equicontinuousAt_iff_continuousAt</a>, <a>ContinuousAt</a>, hX.tendsto_iff (<a>UniformFun.hasBasis_nhds_of_basis</a> ι α _ hα)] | ι : Type u_1
κ : Type u_2
X : Type u_3
X' : Type u_4
Y : Type u_5
Z : Type u_6
α : Type u_7
α' : Type u_8
β : Type u_9
β' : Type u_10
γ : Type u_11
𝓕 : Type u_12
tX : TopologicalSpace X
tY : TopologicalSpace Y
tZ : TopologicalSpace Z
uα : UniformSpace α
uβ : UniformSpace β
uγ : UniformSpace γ
κ₁ : Type u_13
κ₂ : Type ... | ι : Type u_1
κ : Type u_2
X : Type u_3
X' : Type u_4
Y : Type u_5
Z : Type u_6
α : Type u_7
α' : Type u_8
β : Type u_9
β' : Type u_10
γ : Type u_11
𝓕 : Type u_12
tX : TopologicalSpace X
tY : TopologicalSpace Y
tZ : TopologicalSpace Z
uα : UniformSpace α
uβ : UniformSpace β
uγ : UniformSpace γ
κ₁ : Type u_13
κ₂ : Type ... | ((:c Iff) ((:c EquicontinuousAt) (:fv _uniq.88970) (:fv _uniq.88976) (:fv _uniq.88988) (:fv _uniq.89006) (:fv _uniq.89015) (:fv _uniq.89280) (:fv _uniq.89281)) (:forall k₂ (:fv _uniq.89275) (:forall _ ((:fv _uniq.89278) 0) ((:c Exists) (:fv _uniq.89274) (:lambda k₁ (:fv _uniq.89274) ((:c And) ((:fv _uniq.89276) 0) (:fo... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"κ","sexp":"(:sort (+ u_2 1))"},{"name":"X","sexp":"(:sort (+ u_3 1))"},{"name":"X'","sexp":"(:sort (+ u_4 1))"},{"name":"Y","sexp":"(:sort (+ u_5 1))"},{"name":"Z","sexp":"(:sort (+ u_6 1))"},{"name":"α","sexp":"(:sort (+ u_7 1))"},{"name":"α'","sexp":"(:sort (+ u_8 1))... | (:app (:c Iff) (:arg :explicit 0 (:app (:c EquicontinuousAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:fv FV6)) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:app (:c UniformSpace) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88970","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.88973","is_instance":false,"is_let":false,"name":"κ","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":37187,"sourceStart":37185,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":37189,"sourceStart":37188,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"equicontinuousAt... | [] | [{"source":"equicontinuousAt_iff_continuousAt","source_end":37222,"source_start":37189,"syntax_kind":"ident"},{"source":"ContinuousAt","source_end":37236,"source_start":37224,"syntax_kind":"ident"},{"source":"hX.tendsto_iff (UniformFun.hasBasis_nhds_of_basis ι α _ hα)","source_end":37304,"source_start":37242,"syntax_ki... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88970","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.88973","is_instance":false,"is_let":false,"user_name":"κ"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 136 | 4 | exact | true | 1 | 28 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3679ec30ef722c0c39888da68db3d3d46a3bdb83ca84b78b0ed71965a11016cd | a5a13acc63f960fcab654f90c2dd1a51643732ad3f66e29cca0b96d4a1389701 | 6b8c0828efeaeec606663294cb47a506d6a3306adc6e21fb0b5bfd45b8b7c9ff | f947f7939232c7a631b41899f6229ffd4ef1f39554c8cb407c6ab18ab92ecf4b |
cat-searcher/leandojo-benchmark-4-random | test | 880 | Filter.HasBasis.equicontinuousAt_iff | Mathlib/Topology/UniformSpace/Equicontinuity.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | ι : Type u_1
κ : Type u_2
X : Type u_3
X' : Type u_4
Y : Type u_5
Z : Type u_6
α : Type u_7
α' : Type u_8
β : Type u_9
β' : Type u_10
γ : Type u_11
𝓕 : Type u_12
tX : TopologicalSpace X
tY : TopologicalSpace Y
tZ : TopologicalSpace Z
uα : UniformSpace α
uβ : UniformSpace β
uγ : UniformSpace γ
κ₁ : Type u_13
κ₂ : Type ... | ((:c Iff) (:forall ib (:fv _uniq.89275) (:forall _ ((:fv _uniq.89278) 0) ((:c Exists) (:fv _uniq.89274) (:lambda ia (:fv _uniq.89274) ((:c And) ((:fv _uniq.89276) 0) (:forall x (:fv _uniq.88976) (:forall _ ((:c Membership.mem) (:fv _uniq.88976) ((:c Set) (:fv _uniq.88976)) ((:c Set.instMembership) (:fv _uniq.88976)) 0 ... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"κ","sexp":"(:sort (+ u_2 1))"},{"name":"X","sexp":"(:sort (+ u_3 1))"},{"name":"X'","sexp":"(:sort (+ u_4 1))"},{"name":"Y","sexp":"(:sort (+ u_5 1))"},{"name":"Z","sexp":"(:sort (+ u_6 1))"},{"name":"α","sexp":"(:sort (+ u_7 1))"},{"name":"α'","sexp":"(:sort (+ u_8 1))... | (:app (:c Iff) (:arg :explicit 0 (:forall ib :explicit (:fv FV20) (:forall _ :explicit (:app (:fv FV23) (:arg :explicit 0 0)) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV19)) (:arg :explicit 1 (:lambda ia :explicit (:fv FV19) (:app (:c And) (:arg :explicit 0 (:app (:fv FV21) (:arg :explicit 0 0))) (:arg :explicit 1... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88970","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.88973","is_instance":false,"is_let":false,"name":"κ","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rfl","sourceEnd":37311,"sourceStart":37308,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":37311,"sourceStart":37308,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88970","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.88973","is_instance":false,"is_let":false,"user_name":"κ"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 136 | 9 | exact | true | 1 | 28 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 896a9aa415cd64d1db523071b9168c5948e2d72560c03a6e380794d69426b7b9 | f947f7939232c7a631b41899f6229ffd4ef1f39554c8cb407c6ab18ab92ecf4b | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 881 | bddBelow_closure | Mathlib/Topology/Order/OrderClosed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>BddBelow</a>, <a>lowerBounds_closure</a>] | α : Type u
β : Type v
γ : Type w
inst✝² : TopologicalSpace α
inst✝¹ : Preorder α
inst✝ : ClosedIciTopology α
f : β → α
a b : α
s : Set α
⊢ BddBelow (closure s) ↔ BddBelow s | ((:c Iff) ((:c BddBelow) (:fv _uniq.63057) (:fv _uniq.63067) ((:c closure) (:fv _uniq.63057) (:fv _uniq.63064) (:fv _uniq.63091))) ((:c BddBelow) (:fv _uniq.63057) (:fv _uniq.63067) (:fv _uniq.63091))) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.63057))"},{"name":"inst✝¹","sexp":"((:c Preorder) (:fv _uniq.63057))"},{"name":"inst✝","sexp":"((:c ClosedIciTopology) (:fv _uniq.63057) (:fv _uni... | (:app (:c Iff) (:arg :explicit 0 (:app (:c BddBelow) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c closure) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.63057","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.63059","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":16463,"sourceStart":16456,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16465,"sourceStart":16464,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source... | [] | [{"source":"BddBelow","source_end":16473,"source_start":16465,"syntax_kind":"ident"},{"source":"lowerBounds_closure","source_end":16494,"source_start":16475,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.63057","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.63059","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 141 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 76e0a13d4a5bfc56c8f665ea05153710d8b0c34f006fc1d8726ac8da739f9de6 | d195ef1e7826f90a9357f009c6a14936fa838a9a767efe48445df677952b6278 | 7dad1e34f68a47c166eb4b0a4c9ad6167289ead552522a8ae1c89494b1f268a1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 882 | Subring.closure_induction' | Mathlib/Algebra/Ring/Subring/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Exists.elim</a> ?_ fun (ha : a ∈ <a>Subring.closure</a> s) (hc : p a ha) => hc | R : Type u
S : Type v
T : Type w
inst✝² : Ring R
inst✝¹ : Ring S
inst✝ : Ring T
s : Set R
p : (x : R) → x ∈ closure s → Prop
mem : ∀ (x : R) (h : x ∈ s), p x ⋯
zero : p 0 ⋯
one : p 1 ⋯
add : ∀ (x : R) (hx : x ∈ closure s) (y : R) (hy : y ∈ closure s), p x hx → p y hy → p (x + y) ⋯
neg : ∀ (x : R) (hx : x ∈ closure s), ... | R : Type u
S : Type v
T : Type w
inst✝² : Ring R
inst✝¹ : Ring S
inst✝ : Ring T
s : Set R
p : (x : R) → x ∈ closure s → Prop
mem : ∀ (x : R) (h : x ∈ s), p x ⋯
zero : p 0 ⋯
one : p 1 ⋯
add : ∀ (x : R) (hx : x ∈ closure s) (y : R) (hy : y ∈ closure s), p x hx → p y hy → p (x + y) ⋯
neg : ∀ (x : R) (hx : x ∈ closure s), ... | ((:fv _uniq.114995) (:fv _uniq.115002) (:fv _uniq.115003)) | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.112416))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.112418))"},{"name":"inst✝","sexp":"((:c Ring) (:fv _uniq.112420))"},{"name":"s","sexp":"((:c Set) (:... | (:app (:fv FV8) (:arg :explicit 0 (:fv FV15)) (:arg :proof 1 (:proof-of (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Subring) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 2 (:instance-of (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112416","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112418","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":32153,"sourceStart":32147,"tag":"atom"},{"children":[{"name":"Exists.elim","semanticRole":"global","source":"Exists.elim","sourceEnd":32165,"sourceStart":32154,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":32167,"sourceStart":32166,"tag":"atom"},{"ch... | [] | [{"source":"Exists.elim ?_ fun (ha : a ∈ closure s) (hc : p a ha) => hc","source_end":32215,"source_start":32154,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112416","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112418","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 306 | 4 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 95ee33cf433ed1ff9912e32f280993ceec4d3f463c73811fb888f5d8d78bd103 | a3aa078a893897f6dac231ae6014e2ab95c24ccc69e85ee6cfe9c21489077192 | b2c5278f4328fa0833a9c90e2203ff510212bb58c82b0583c2c493f94b3950ce | 07fdca91a1c3b14f76aef26b8cb0e2e01c73a9d2035a8a36cc3dab8dcb115841 |
cat-searcher/leandojo-benchmark-4-random | test | 883 | Subring.closure_induction' | Mathlib/Algebra/Ring/Subring/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Subring.closure_induction</a> ha (fun m hm => ⟨<a>Subring.subset_closure</a> hm, mem m hm⟩) ⟨<a>ZeroMemClass.zero_mem</a> _, zero⟩ ⟨<a>OneMemClass.one_mem</a> _, one⟩ ?_ (fun x hx => hx.elim fun hx' hx => ⟨<a>NegMemClass.neg_mem</a> hx', neg _ _ hx⟩) ?_ | R : Type u
S : Type v
T : Type w
inst✝² : Ring R
inst✝¹ : Ring S
inst✝ : Ring T
s : Set R
p : (x : R) → x ∈ closure s → Prop
mem : ∀ (x : R) (h : x ∈ s), p x ⋯
zero : p 0 ⋯
one : p 1 ⋯
add : ∀ (x : R) (hx : x ∈ closure s) (y : R) (hy : y ∈ closure s), p x hx → p y hy → p (x + y) ⋯
neg : ∀ (x : R) (hx : x ∈ closure s), ... | case refine_1
R : Type u
S : Type v
T : Type w
inst✝² : Ring R
inst✝¹ : Ring S
inst✝ : Ring T
s : Set R
p : (x : R) → x ∈ closure s → Prop
mem : ∀ (x : R) (h : x ∈ s), p x ⋯
zero : p 0 ⋯
one : p 1 ⋯
add : ∀ (x : R) (hx : x ∈ closure s) (y : R) (hy : y ∈ closure s), p x hx → p y hy → p (x + y) ⋯
neg : ∀ (x : R) (hx : x ... | ((:c Exists) ((:c Membership.mem) (:fv _uniq.112416) ((:c Subring) (:fv _uniq.112416) (:fv _uniq.112423)) ((:c SetLike.instMembership) ((:c Subring) (:fv _uniq.112416) (:fv _uniq.112423)) (:fv _uniq.112416) ((:c Subring.instSetLike) (:fv _uniq.112416) (:fv _uniq.112423))) (:fv _uniq.115002) ((:c Subring.closure) (:fv _... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.112416))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.112418))"},{"name":"inst✝","sexp":"((:c Ring) (:fv _uniq.112420))"},{"name":"s","sexp":"((:c Set) (:... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Subring) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112416","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112418","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":32224,"sourceStart":32218,"tag":"atom"},{"children":[{"name":"Subring.closure_induction","semanticRole":"global","source":"closure_induction","sourceEnd":32246,"sourceStart":32229,"tag":"identifier"},{"children":[{"contextIndex":16,"semanticRole":"local","source":"ha","source... | [] | [{"source":"closure_induction ha (fun m hm => ⟨subset_closure hm, mem m hm⟩) ⟨zero_mem _, zero⟩\n ⟨one_mem _, one⟩ ?_ (fun x hx => hx.elim fun hx' hx => ⟨neg_mem hx', neg _ _ hx⟩) ?_","source_end":32419,"source_start":32229,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112416","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112418","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 306 | 5 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 25542b7bf45b2cd846ed330f7f42f89c0428caf8b446883af994904010421490 | 07fdca91a1c3b14f76aef26b8cb0e2e01c73a9d2035a8a36cc3dab8dcb115841 | ccee8af4faa38a8ec91240cf2497aad1a398828ca485eb35dfc12e71b81d48d3 | c3cbef4081fa82c3d570821a300ad88b99e7683632423ed16d5539c89edbbf2b |
cat-searcher/leandojo-benchmark-4-random | test | 884 | Subring.closure_induction' | Mathlib/Algebra/Ring/Subring/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (fun x y hx hy => hx.elim fun hx' hx => hy.elim fun hy' hy => ⟨<a>AddMemClass.add_mem</a> hx' hy', add _ _ _ _ hx hy⟩) | case refine_1
R : Type u
S : Type v
T : Type w
inst✝² : Ring R
inst✝¹ : Ring S
inst✝ : Ring T
s : Set R
p : (x : R) → x ∈ closure s → Prop
mem : ∀ (x : R) (h : x ∈ s), p x ⋯
zero : p 0 ⋯
one : p 1 ⋯
add : ∀ (x : R) (hx : x ∈ closure s) (y : R) (hy : y ∈ closure s), p x hx → p y hy → p (x + y) ⋯
neg : ∀ (x : R) (hx : x ... | (:forall x (:fv _uniq.112416) (:forall y (:fv _uniq.112416) (:forall _ ((:c Exists) ((:c Membership.mem) (:fv _uniq.112416) ((:c Subring) (:fv _uniq.112416) (:fv _uniq.112423)) ((:c SetLike.instMembership) ((:c Subring) (:fv _uniq.112416) (:fv _uniq.112423)) (:fv _uniq.112416) ((:c Subring.instSetLike) (:fv _uniq.11241... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.112416))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.112418))"},{"name":"inst✝","sexp":"((:c Ring) (:fv _uniq.112420))"},{"name":"s","sexp":"((:c Set) (:... | (:forall x :explicit (:fv FV0) (:forall y :explicit (:fv FV0) (:forall _ :explicit (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Subring) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Ring) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112416","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112418","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":32430,"sourceStart":32425,"tag":"atom"},{"children":[{"source":"(","sourceEnd":32432,"sourceStart":32431,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":32435,"sourceStart":32432,"tag":"atom"},{"children":[{"children":[{"semanticRo... | [] | [{"source":"(fun x y hx hy => hx.elim fun hx' hx => hy.elim fun hy' hy =>\n ⟨add_mem hx' hy', add _ _ _ _ hx hy⟩)","source_end":32540,"source_start":32431,"syntax_kind":"Lean.Parser.Term.paren"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112416","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112418","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 306 | 8 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7835dae2d6b6d8a66bef6dc23bc8ccbcc958e0e446771b783bb64f2cbcb21aaf | 64f4370de4a49ee1828769b5503d0ec58527d69b318851da04006285c09ecf84 | 7b81f8f5931599197b0c7a6d7896145dd2e2f33ef2c7308cb6269c32d6653ef5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 885 | Subring.closure_induction' | Mathlib/Algebra/Ring/Subring/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (fun x y hx hy => hx.elim fun hx' hx => hy.elim fun hy' hy => ⟨<a>MulMemClass.mul_mem</a> hx' hy', mul _ _ _ _ hx hy⟩) | case refine_2
R : Type u
S : Type v
T : Type w
inst✝² : Ring R
inst✝¹ : Ring S
inst✝ : Ring T
s : Set R
p : (x : R) → x ∈ closure s → Prop
mem : ∀ (x : R) (h : x ∈ s), p x ⋯
zero : p 0 ⋯
one : p 1 ⋯
add : ∀ (x : R) (hx : x ∈ closure s) (y : R) (hy : y ∈ closure s), p x hx → p y hy → p (x + y) ⋯
neg : ∀ (x : R) (hx : x ... | (:forall x (:fv _uniq.112416) (:forall y (:fv _uniq.112416) (:forall _ ((:c Exists) ((:c Membership.mem) (:fv _uniq.112416) ((:c Subring) (:fv _uniq.112416) (:fv _uniq.112423)) ((:c SetLike.instMembership) ((:c Subring) (:fv _uniq.112416) (:fv _uniq.112423)) (:fv _uniq.112416) ((:c Subring.instSetLike) (:fv _uniq.11241... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.112416))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.112418))"},{"name":"inst✝","sexp":"((:c Ring) (:fv _uniq.112420))"},{"name":"s","sexp":"((:c Set) (:... | (:forall x :explicit (:fv FV0) (:forall y :explicit (:fv FV0) (:forall _ :explicit (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Subring) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Ring) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112416","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112418","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":32551,"sourceStart":32546,"tag":"atom"},{"children":[{"source":"(","sourceEnd":32553,"sourceStart":32552,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":32556,"sourceStart":32553,"tag":"atom"},{"children":[{"children":[{"semanticRo... | [] | [{"source":"(fun x y hx hy => hx.elim fun hx' hx => hy.elim fun hy' hy =>\n ⟨mul_mem hx' hy', mul _ _ _ _ hx hy⟩)","source_end":32661,"source_start":32552,"syntax_kind":"Lean.Parser.Term.paren"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112416","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112418","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 306 | 13 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a3ee347beb00f41f8c1f0380013eb889a64087db03c8237953f26c879182621b | b834d93b22cfe409318f4f9a363becb2461cc1081fc420e2046c5a7e8383c1cd | aa0a502b6444d66b9de05fc96685baf3e3165d258f3f82893c6d65a5cc3f60df | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 886 | MvPowerSeries.coeff_C_mul | Mathlib/RingTheory/MvPowerSeries/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using <a>MvPowerSeries.coeff_add_monomial_mul</a> 0 n φ a | σ : Type u_1
R : Type u_2
inst✝ : Semiring R
n : σ →₀ ℕ
φ : MvPowerSeries σ R
a : R
⊢ (coeff R n) ((C σ R) a * φ) = a * (coeff R n) φ | ((:c Eq) (:fv _uniq.139161) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.139161) (:fv _uniq.139161) (:fv _uniq.139164) (:fv _uniq.139164) ((:c RingHom.id) (:fv _uniq.139161) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.139161) (:fv _uniq.139164))) ((:c MvPowerSeries) (:fv _uniq.139158) (:fv _uniq.139161)) (:fv _uniq.1... | [{"name":"σ","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.139161))"},{"name":"n","sexp":"((:c Finsupp) (:fv _uniq.139158) (:c Nat) ((:c LinearOrderedCommMonoidWithZero.toZero) (:c Nat) (:c Nat.instLinearOrderedCommMonoidWithZero)))"},{"name":"φ","... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.139158","is_instance":false,"is_let":false,"name":"σ","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.139161","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":17441,"sourceStart":17436,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"coeff_add_monomial_mul 0 n φ a","source_end":17479,"source_start":17448,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.139158","is_instance":false,"is_let":false,"user_name":"σ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.139161","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal... | 120 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a7c0e59577811267f866bc81c7d7b726ce4d94955e6e21c89f0552082adfefec | 7a67e6f8666d9d77515bbd9ce999ebd975486765882d832a9da8f2843ef03e6e | fa3a3957d1b4ae9eec32920110be56f4b475d687c9a3b6746ca8dde514119ddf | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 887 | PMF.toOuterMeasure_apply_eq_zero_iff | Mathlib/Probability/ProbabilityMassFunction/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>PMF.toOuterMeasure_apply</a>, <a>ENNReal.tsum_eq_zero</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
p : PMF α
s t : Set α
⊢ p.toOuterMeasure s = 0 ↔ Disjoint p.support s | α : Type u_1
β : Type u_2
γ : Type u_3
p : PMF α
s t : Set α
⊢ (∀ (i : α), s.indicator (⇑p) i = 0) ↔ Disjoint p.support s | ((:c Iff) ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.OuterMeasure) (:fv _uniq.22994)) ((:c Set) (:fv _uniq.22994)) (:lambda _ ((:c Set) (:fv _uniq.22994)) (:c ENNReal)) ((:c MeasureTheory.OuterMeasure.instFunLikeSetENNReal) (:fv _uniq.22994)) ((:c PMF.toOuterMeasure) (:fv _uniq.22994) (:fv _uniq.23003)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"p","sexp":"((:c PMF) (:fv _uniq.22994))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.22994))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.22994))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.OuterMeasure) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit 2) (:arg :instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22994","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22997","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":8308,"sourceStart":8306,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8310,"sourceStart":8309,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"PMF.toOuterMeasure_a... | [] | [{"source":"toOuterMeasure_apply","source_end":8330,"source_start":8310,"syntax_kind":"ident"},{"source":"ENNReal.tsum_eq_zero","source_end":8352,"source_start":8332,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22994","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22997","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 61 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 30bbd543c1c086d95067897631e999b26faf134afe18c513a0c5bd8a71a88f0d | a80170af351f57c8ad64f29e6bdb264b2dcbbe4d07f85b2803025a479b06ec6a | 6f40097df20b681e81c5111199c9ce62c2c534ebf00a6861a5b8d80d100ff447 | fdea28cb780abb6ad9e4c2675898e7fbcaae8beb44661468024309f5c6984d5f |
cat-searcher/leandojo-benchmark-4-random | test | 888 | PMF.toOuterMeasure_apply_eq_zero_iff | Mathlib/Probability/ProbabilityMassFunction/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact Function.funext_iff.symm.trans <a>Set.indicator_eq_zero'</a> | α : Type u_1
β : Type u_2
γ : Type u_3
p : PMF α
s t : Set α
⊢ (∀ (i : α), s.indicator (⇑p) i = 0) ↔ Disjoint p.support s | ((:c Iff) (:forall i (:fv _uniq.22994) ((:c Eq) (:c ENNReal) ((:c Set.indicator) (:fv _uniq.22994) (:c ENNReal) (:c instENNRealZero) (:fv _uniq.23006) ((:c DFunLike.coe) ((:c PMF) (:fv _uniq.22994)) (:fv _uniq.22994) (:lambda _ (:fv _uniq.22994) (:c ENNReal)) ((:c PMF.instFunLike) (:fv _uniq.22994)) (:fv _uniq.23003)) ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"p","sexp":"((:c PMF) (:fv _uniq.22994))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.22994))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.22994))"}] | (:app (:c Iff) (:arg :explicit 0 (:forall i :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c Set.indicator) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :instance 2 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:c ENNReal))))) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22994","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22997","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":8361,"sourceStart":8356,"tag":"atom"},{"children":[{"source":"Function.funext_iff.symm.trans","sourceEnd":8392,"sourceStart":8362,"tag":"identifier"},{"children":[{"name":"Set.indicator_eq_zero'","semanticRole":"global","source":"Set.indicator_eq_zero'","sourceEnd":8415,"sourc... | [] | [{"source":"Function.funext_iff.symm.trans Set.indicator_eq_zero'","source_end":8415,"source_start":8362,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22994","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22997","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 61 | 8 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bcf78dc342378d1e5f2abe9c81a435f88193df49455c1775c599d49b26e17134 | fdea28cb780abb6ad9e4c2675898e7fbcaae8beb44661468024309f5c6984d5f | 9146d3608fa7b1caa33df70eadc78ae980af4795950e1cd7db3dc5c2b869ff08 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 889 | ModularForm.slash_action_eq'_iff | Mathlib/NumberTheory/ModularForms/SlashActions.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>ModularForm.subgroup_slash</a>, <a>ModularForm.slash_def</a>, <a>ModularForm.slash</a>] | Γ✝ : Subgroup SL(2, ℤ)
k✝ : ℤ
f✝ : ℍ → ℂ
k : ℤ
Γ : Subgroup SL(2, ℤ)
f : ℍ → ℂ
γ : ↥Γ
z : ℍ
⊢ (f ∣[k] γ) z = f z ↔ f (γ • z) = (↑(↑↑↑γ 1 0) * ↑z + ↑(↑↑↑γ 1 1)) ^ k * f z | Γ✝ : Subgroup SL(2, ℤ)
k✝ : ℤ
f✝ : ℍ → ℂ
k : ℤ
Γ : Subgroup SL(2, ℤ)
f : ℍ → ℂ
γ : ↥Γ
z : ℍ
⊢ f (↑↑γ • z) * ↑(↑↑↑↑γ).det ^ (k - 1) * denom (↑↑γ) z ^ (-k) = f z ↔
f (γ • z) = (↑(↑↑↑γ 1 0) * ↑z + ↑(↑↑↑γ 1 1)) ^ k * f z | ((:c Iff) ((:c Eq) (:c Complex) ((:c SlashAction.map) (:c Int) ((:c Subtype) ((:c Matrix.SpecialLinearGroup) ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c instDecidableEqFin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c Fin.fintype) ((:c OfNat.ofNat) (:c Na... | [{"name":"Γ✝","sexp":"((:c Subgroup) ((:c Matrix.SpecialLinearGroup) ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c instDecidableEqFin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c Fin.fintype) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2))... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c SlashAction.map) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c Matrix.SpecialLinearGroup) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit 0 (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154529","is_instance":false,"is_let":false,"name":"Γ✝","sexp":"(:app (:c Subgroup) (:arg :explicit 0 (:app (:c Matrix.SpecialLinearGroup) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg ... | {"children":[{"source":"simp","sourceEnd":8831,"sourceStart":8827,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":8836,"sourceStart":8832,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":8836,"s... | [] | [{"source":"subgroup_slash","source_end":8852,"source_start":8838,"syntax_kind":"ident"},{"source":"slash_def","source_end":8863,"source_start":8854,"syntax_kind":"ident"},{"source":"ModularForm.slash","source_end":8882,"source_start":8865,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154529","is_instance":false,"is_let":false,"user_name":"Γ✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.154531","is_instance":false,"is_let":false,"user_name":"k✝"},{"binder_role":":explicit","context_index":2,"internal_name":... | 49 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 02365ad08e4eed0afede0e5217315aaaefe57ce1af623bf8e2ae4f1de55c1e48 | 0de54b0f944dfe08607676ea443a55508fa31f5b4c0add0f5410a393643a8572 | 75eacacd92a5df9033c2a50bef69ff5cfd3649017ceabfd1a8c1ce6551d55684 | 2af68243ec25268d3624b8d876a2fb0b9fba0de9c9bc8066e49f74746fd71c77 |
cat-searcher/leandojo-benchmark-4-random | test | 890 | ModularForm.slash_action_eq'_iff | Mathlib/NumberTheory/ModularForms/SlashActions.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert <a>inv_mul_eq_iff_eq_mul₀</a> (G₀ := ℂ) _ using 2 | Γ✝ : Subgroup SL(2, ℤ)
k✝ : ℤ
f✝ : ℍ → ℂ
k : ℤ
Γ : Subgroup SL(2, ℤ)
f : ℍ → ℂ
γ : ↥Γ
z : ℍ
⊢ f (↑↑γ • z) * ↑(↑↑↑↑γ).det ^ (k - 1) * denom (↑↑γ) z ^ (-k) = f z ↔
f (γ • z) = (↑(↑↑↑γ 1 0) * ↑z + ↑(↑↑↑γ 1 1)) ^ k * f z | case h.e'_1.h.e'_2
Γ✝ : Subgroup SL(2, ℤ)
k✝ : ℤ
f✝ : ℍ → ℂ
k : ℤ
Γ : Subgroup SL(2, ℤ)
f : ℍ → ℂ
γ : ↥Γ
z : ℍ
⊢ f (↑↑γ • z) * ↑(↑↑↑↑γ).det ^ (k - 1) * denom (↑↑γ) z ^ (-k) = ((↑(↑↑↑γ 1 0) * ↑z + ↑(↑↑↑γ 1 1)) ^ k)⁻¹ * f (γ • z)
case convert_4
Γ✝ : Subgroup SL(2, ℤ)
k✝ : ℤ
f✝ : ℍ → ℂ
k : ℤ
Γ : Subgroup SL(2, ℤ)
f : ℍ → ... | ((:c Iff) ((:c Eq) (:c Complex) ((:c HMul.hMul) (:c Complex) (:c Complex) (:c Complex) ((:c instHMul) (:c Complex) (:c Complex.instMul)) ((:c HMul.hMul) (:c Complex) (:c Complex) (:c Complex) ((:c instHMul) (:c Complex) (:c Complex.instMul)) ((:fv _uniq.157187) ((:c HSMul.hSMul) ((:c Subtype) ((:c Matrix.GeneralLinearG... | [{"name":"Γ✝","sexp":"((:c Subgroup) ((:c Matrix.SpecialLinearGroup) ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c instDecidableEqFin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c Fin.fintype) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2))... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Complex)) (:arg :implicit-type 1 (:c Complex)) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Complex)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154529","is_instance":false,"is_let":false,"name":"Γ✝","sexp":"(:app (:c Subgroup) (:arg :explicit 0 (:app (:c Matrix.SpecialLinearGroup) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg ... | {"children":[{"source":"convert","sourceEnd":8893,"sourceStart":8886,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"inv_mul_eq_iff_eq_mul₀","semanticRole":"global","source":"inv_mul_eq_iff_eq_mul₀","sourceEnd":8918,"sourc... | [] | [{"source":"inv_mul_eq_iff_eq_mul₀ (G₀ := ℂ) _","source_end":8934,"source_start":8894,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154529","is_instance":false,"is_let":false,"user_name":"Γ✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.154531","is_instance":false,"is_let":false,"user_name":"k✝"},{"binder_role":":explicit","context_index":2,"internal_name":... | 49 | 5 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | be1c548a51d5cc2481422df871bfee8d3321091b50099da27fc85b045f0a8034 | 2af68243ec25268d3624b8d876a2fb0b9fba0de9c9bc8066e49f74746fd71c77 | 91871af0d00e414fed5df18d44d7e4d053496ddf6b3238a783658c43ad402dfe | fd13543c32aecc9dedcc3d9c85f1932b417f7a083e6e952995376cb7e4acda7c |
cat-searcher/leandojo-benchmark-4-random | test | 891 | ModularForm.slash_action_eq'_iff | Mathlib/NumberTheory/ModularForms/SlashActions.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>mul_comm</a>] | case h.e'_1.h.e'_2
Γ✝ : Subgroup SL(2, ℤ)
k✝ : ℤ
f✝ : ℍ → ℂ
k : ℤ
Γ : Subgroup SL(2, ℤ)
f : ℍ → ℂ
γ : ↥Γ
z : ℍ
⊢ f (↑↑γ • z) * ↑(↑↑↑↑γ).det ^ (k - 1) * denom (↑↑γ) z ^ (-k) = ((↑(↑↑↑γ 1 0) * ↑z + ↑(↑↑↑γ 1 1)) ^ k)⁻¹ * f (γ • z) | case h.e'_1.h.e'_2
Γ✝ : Subgroup SL(2, ℤ)
k✝ : ℤ
f✝ : ℍ → ℂ
k : ℤ
Γ : Subgroup SL(2, ℤ)
f : ℍ → ℂ
γ : ↥Γ
z : ℍ
⊢ denom (↑↑γ) z ^ (-k) * (f (↑↑γ • z) * ↑(↑↑↑↑γ).det ^ (k - 1)) = ((↑(↑↑↑γ 1 0) * ↑z + ↑(↑↑↑γ 1 1)) ^ k)⁻¹ * f (γ • z) | ((:c Eq) (:c Complex) ((:c HMul.hMul) (:c Complex) (:c Complex) (:c Complex) ((:c instHMul) (:c Complex) (:c Complex.instMul)) ((:c HMul.hMul) (:c Complex) (:c Complex) (:c Complex) ((:c instHMul) (:c Complex) (:c Complex.instMul)) ((:fv _uniq.157187) ((:c HSMul.hSMul) ((:c Subtype) ((:c Matrix.GeneralLinearGroup) ((:c... | [{"name":"Γ✝","sexp":"((:c Subgroup) ((:c Matrix.SpecialLinearGroup) ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c instDecidableEqFin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c Fin.fintype) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2))... | (:app (:c Eq) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Complex)) (:arg :implicit-type 1 (:c Complex)) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Complex)) (:arg :explicit 1 (:c Complex)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154529","is_instance":false,"is_let":false,"name":"Γ✝","sexp":"(:app (:c Subgroup) (:arg :explicit 0 (:app (:c Matrix.SpecialLinearGroup) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg ... | {"children":[{"source":"rw","sourceEnd":8950,"sourceStart":8948,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8952,"sourceStart":8951,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"mul_comm","semanticR... | [] | [{"source":"mul_comm","source_end":8960,"source_start":8952,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154529","is_instance":false,"is_let":false,"user_name":"Γ✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.154531","is_instance":false,"is_let":false,"user_name":"k✝"},{"binder_role":":explicit","context_index":2,"internal_name":... | 49 | 10 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3e105cb7f96c1383d6d415ddbc4b793114eac4f51f63e2714c7999bfa93d54be | a00fb5a6284ea37b94adc893cdb1db0a0d592b6f7ea00d1839ece534d05ac7b0 | b40139e2832d8f817070a6f57dda46abb72fcb05e2a85e2d0d7b1991ae7615d3 | b35d6e2911fc0f613d261c37ac6fedf7f4d484d1b3a8316b57ee499b4733f896 |
cat-searcher/leandojo-benchmark-4-random | test | 892 | ModularForm.slash_action_eq'_iff | Mathlib/NumberTheory/ModularForms/SlashActions.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>UpperHalfPlane.denom</a>, <a>zpow_neg</a>, <a>UpperHalfPlane.ModularGroup.det_coe'</a>, <a>Complex.ofReal_one</a>, <a>one_zpow</a>, <a>mul_one</a>, <a>UpperHalfPlane.ModularGroup.subgroup_to_sl_moeb</a>, <a>UpperHalfPlane.ModularGroup.sl_moeb</a>] | case h.e'_1.h.e'_2
Γ✝ : Subgroup SL(2, ℤ)
k✝ : ℤ
f✝ : ℍ → ℂ
k : ℤ
Γ : Subgroup SL(2, ℤ)
f : ℍ → ℂ
γ : ↥Γ
z : ℍ
⊢ denom (↑↑γ) z ^ (-k) * (f (↑↑γ • z) * ↑(↑↑↑↑γ).det ^ (k - 1)) = ((↑(↑↑↑γ 1 0) * ↑z + ↑(↑↑↑γ 1 1)) ^ k)⁻¹ * f (γ • z) | case h.e'_1.h.e'_2
Γ✝ : Subgroup SL(2, ℤ)
k✝ : ℤ
f✝ : ℍ → ℂ
k : ℤ
Γ : Subgroup SL(2, ℤ)
f : ℍ → ℂ
γ : ↥Γ
z : ℍ
⊢ ((↑(↑↑↑↑γ 1 0) * ↑z + ↑(↑↑↑↑γ 1 1)) ^ k)⁻¹ * f (↑↑γ • z) = ((↑(↑↑↑γ 1 0) * ↑z + ↑(↑↑↑γ 1 1)) ^ k)⁻¹ * f (↑↑γ • z) | ((:c Eq) (:c Complex) ((:c HMul.hMul) (:c Complex) (:c Complex) (:c Complex) ((:c instHMul) (:c Complex) ((:c CommMagma.toMul) (:c Complex) ((:c NonUnitalNonAssocCommSemiring.toCommMagma) (:c Complex) ((:c NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring) (:c Complex) ((:c NonUnitalCommRing.toNonUnitalNonAssoc... | [{"name":"Γ✝","sexp":"((:c Subgroup) ((:c Matrix.SpecialLinearGroup) ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c instDecidableEqFin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c Fin.fintype) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2))... | (:app (:c Eq) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Complex)) (:arg :implicit-type 1 (:c Complex)) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Complex)) (:arg :explicit 1 (:c Complex)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154529","is_instance":false,"is_let":false,"name":"Γ✝","sexp":"(:app (:c Subgroup) (:arg :explicit 0 (:app (:c Matrix.SpecialLinearGroup) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg ... | {"children":[{"source":"simp","sourceEnd":8970,"sourceStart":8966,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":8975,"sourceStart":8971,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":8975,"s... | [] | [{"source":"denom","source_end":8982,"source_start":8977,"syntax_kind":"ident"},{"source":"zpow_neg","source_end":8992,"source_start":8984,"syntax_kind":"ident"},{"source":"det_coe'","source_end":9002,"source_start":8994,"syntax_kind":"ident"},{"source":"ofReal_one","source_end":9014,"source_start":9004,"syntax_kind":"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154529","is_instance":false,"is_let":false,"user_name":"Γ✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.154531","is_instance":false,"is_let":false,"user_name":"k✝"},{"binder_role":":explicit","context_index":2,"internal_name":... | 49 | 13 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3a84aef16be91ba4b2a2d1d228d3ed38930610b8bdaef77ad7311137ce058d38 | b35d6e2911fc0f613d261c37ac6fedf7f4d484d1b3a8316b57ee499b4733f896 | d74ce06bf2a0bf6d0dfedcec05ae71f50bedb453de2cf06c916a92d2cf597a7f | a42ec4848ce0290d5f9427771d88b1805144816b4801cadd82f20e12e42b762c |
cat-searcher/leandojo-benchmark-4-random | test | 893 | ModularForm.slash_action_eq'_iff | Mathlib/NumberTheory/ModularForms/SlashActions.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case h.e'_1.h.e'_2
Γ✝ : Subgroup SL(2, ℤ)
k✝ : ℤ
f✝ : ℍ → ℂ
k : ℤ
Γ : Subgroup SL(2, ℤ)
f : ℍ → ℂ
γ : ↥Γ
z : ℍ
⊢ ((↑(↑↑↑↑γ 1 0) * ↑z + ↑(↑↑↑↑γ 1 1)) ^ k)⁻¹ * f (↑↑γ • z) = ((↑(↑↑↑γ 1 0) * ↑z + ↑(↑↑↑γ 1 1)) ^ k)⁻¹ * f (↑↑γ • z) | ((:c Eq) (:c Complex) ((:c HMul.hMul) (:c Complex) (:c Complex) (:c Complex) ((:c instHMul) (:c Complex) ((:c CommMagma.toMul) (:c Complex) ((:c NonUnitalNonAssocCommSemiring.toCommMagma) (:c Complex) ((:c NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring) (:c Complex) ((:c NonUnitalCommRing.toNonUnitalNonAssoc... | [{"name":"Γ✝","sexp":"((:c Subgroup) ((:c Matrix.SpecialLinearGroup) ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c instDecidableEqFin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c Fin.fintype) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2))... | (:app (:c Eq) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Complex)) (:arg :implicit-type 1 (:c Complex)) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Complex)) (:arg :explicit 1 (:c Complex)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154529","is_instance":false,"is_let":false,"name":"Γ✝","sexp":"(:app (:c Subgroup) (:arg :explicit 0 (:app (:c Matrix.SpecialLinearGroup) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg ... | {"children":[{"source":"rfl","sourceEnd":9078,"sourceStart":9075,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":9078,"sourceStart":9075,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154529","is_instance":false,"is_let":false,"user_name":"Γ✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.154531","is_instance":false,"is_let":false,"user_name":"k✝"},{"binder_role":":explicit","context_index":2,"internal_name":... | 49 | 14 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 46606a8beef246ad4f0ebdbf9cb380c29d98072ca70defbd25f57171166505a2 | a42ec4848ce0290d5f9427771d88b1805144816b4801cadd82f20e12e42b762c | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 894 | ModularForm.slash_action_eq'_iff | Mathlib/NumberTheory/ModularForms/SlashActions.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert <a>zpow_ne_zero</a> k (<a>UpperHalfPlane.denom_ne_zero</a> γ z) | case convert_4
Γ✝ : Subgroup SL(2, ℤ)
k✝ : ℤ
f✝ : ℍ → ℂ
k : ℤ
Γ : Subgroup SL(2, ℤ)
f : ℍ → ℂ
γ : ↥Γ
z : ℍ
⊢ (↑(↑↑↑γ 1 0) * ↑z + ↑(↑↑↑γ 1 1)) ^ k ≠ 0 | ((:c Ne) (:c Complex) ((:c HPow.hPow) (:c Complex) (:c Int) (:c Complex) ((:c instHPow) (:c Complex) (:c Int) ((:c DivInvMonoid.Pow) (:c Complex) (:c Complex.instDivInvMonoid))) ((:c HAdd.hAdd) (:c Complex) (:c Complex) (:c Complex) ((:c instHAdd) (:c Complex) (:c Complex.instAdd)) ((:c HMul.hMul) (:c Complex) (:c Comp... | [{"name":"Γ✝","sexp":"((:c Subgroup) ((:c Matrix.SpecialLinearGroup) ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c instDecidableEqFin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c Fin.fintype) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2))... | (:app (:c Ne) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Complex)) (:arg :implicit-type 1 (:c Int)) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c Complex)) (:arg :explicit 1 (:c Int)) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154529","is_instance":false,"is_let":false,"name":"Γ✝","sexp":"(:app (:c Subgroup) (:arg :explicit 0 (:app (:c Matrix.SpecialLinearGroup) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg ... | {"children":[{"children":[{"children":[{"children":[{"source":"convert","sourceEnd":9091,"sourceStart":9084,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"zpow_ne_zero","semanticRole":"global","source":"zpow_ne_zero","sou... | [] | [{"source":"zpow_ne_zero k (denom_ne_zero γ z)","source_end":9127,"source_start":9092,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.154529","is_instance":false,"is_let":false,"user_name":"Γ✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.154531","is_instance":false,"is_let":false,"user_name":"k✝"},{"binder_role":":explicit","context_index":2,"internal_name":... | 49 | 17 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e117b979726ea2b18216400d3a32293cf0122750b219be759435ad7f796158ae | d8f2c7feb31f379d785bfeec3bf2c91927667137fccf80ba002331c75457d06a | 5f943651b3365da6034fe7f8407edd74f6f899ca5f0e43adf3705250ceef2457 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 895 | List.map_permutationsAux2' | Mathlib/Data/List/Permutation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction' ys with ys_hd _ ys_ih generalizing f f' | α : Type u_1
β : Type u_2
α' : Type u_3
β' : Type u_4
g : α → α'
g' : β → β'
t : α
ts ys : List α
r : List β
f : List α → β
f' : List α' → β'
H : ∀ (a : List α), g' (f a) = f' (map g a)
⊢ map g' (permutationsAux2 t ts r ys f).2 = (permutationsAux2 (g t) (map g ts) (map g' r) (map g ys) f').2 | case nil
α : Type u_1
β : Type u_2
α' : Type u_3
β' : Type u_4
g : α → α'
g' : β → β'
t : α
ts : List α
r : List β
f : List α → β
f' : List α' → β'
H : ∀ (a : List α), g' (f a) = f' (map g a)
⊢ map g' (permutationsAux2 t ts r [] f).2 = (permutationsAux2 (g t) (map g ts) (map g' r) (map g []) f').2
case cons
α : Type u_... | ((:c Eq) ((:c List) (:fv _uniq.2252)) ((:c List.map) (:fv _uniq.2136) (:fv _uniq.2252) (:fv _uniq.2254) ((:c Prod.snd) ((:c List) (:fv _uniq.2133)) ((:c List) (:fv _uniq.2136)) ((:c List.permutationsAux2) (:fv _uniq.2133) (:fv _uniq.2136) (:fv _uniq.2255) (:fv _uniq.2256) (:fv _uniq.2258) (:fv _uniq.2257) (:fv _uniq.22... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"α'","sexp":"(:sort (+ u_3 1))"},{"name":"β'","sexp":"(:sort (+ u_4 1))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.2133) (:fv _uniq.2251))"},{"name":"g'","sexp":"(:forall _ (:fv _uniq.2136) (:fv _uniq.2252))"},{"name":"t","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV4)))) (:arg :explicit 1 (:app (:c List.map) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV4)) (:arg :explicit 2 (:fv FV6)) (:arg :explicit 3 (:app (:c Prod.snd) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2133","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2136","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"induction'","sourceEnd":4005,"sourceStart":3995,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":9,"semanticRole":"local","source":"ys","sourceEnd":4008,"sourceStart":4006,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","... | [] | [{"source":"ys","source_end":4008,"source_start":4006,"syntax_kind":"ident"},{"source":"f","source_end":4042,"source_start":4041,"syntax_kind":"ident"},{"source":"f'","source_end":4045,"source_start":4043,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2133","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2136","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_uniq... | 16 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 583a0e35704f2e762b19bb8928a2587d275504b3e177a0c03ce1817371e04a06 | 5ab9df5ebc57bfdeb018dd3a9b9d25e96d4bf474ee68e4483f6ec1351a5d9946 | 7db943add27c90c73938e3befe41d8783e6d5dfa33113db1bbcabe7492e349c3 | 2b9ff8578fe9e58f7a66057843c459bacea653c2c45d7238a50bc3e4de228dfb |
cat-searcher/leandojo-benchmark-4-random | test | 896 | List.map_permutationsAux2' | Mathlib/Data/List/Permutation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case nil
α : Type u_1
β : Type u_2
α' : Type u_3
β' : Type u_4
g : α → α'
g' : β → β'
t : α
ts : List α
r : List β
f : List α → β
f' : List α' → β'
H : ∀ (a : List α), g' (f a) = f' (map g a)
⊢ map g' (permutationsAux2 t ts r [] f).2 = (permutationsAux2 (g t) (map g ts) (map g' r) (map g []) f').2 | ((:c Eq) ((:c List) (:fv _uniq.2252)) ((:c List.map) (:fv _uniq.2136) (:fv _uniq.2252) (:fv _uniq.2254) ((:c Prod.snd) ((:c List) (:fv _uniq.2133)) ((:c List) (:fv _uniq.2136)) ((:c List.permutationsAux2) (:fv _uniq.2133) (:fv _uniq.2136) (:fv _uniq.2255) (:fv _uniq.2256) (:fv _uniq.2258) ((:c List.nil) (:fv _uniq.2133... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"α'","sexp":"(:sort (+ u_3 1))"},{"name":"β'","sexp":"(:sort (+ u_4 1))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.2133) (:fv _uniq.2251))"},{"name":"g'","sexp":"(:forall _ (:fv _uniq.2136) (:fv _uniq.2252))"},{"name":"t","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV4)))) (:arg :explicit 1 (:app (:c List.map) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV4)) (:arg :explicit 2 (:fv FV6)) (:arg :explicit 3 (:app (:c Prod.snd) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2133","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2136","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":4055,"sourceStart":4051,"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.2133","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2136","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_uniq... | 16 | 7 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 95a0e779871b7621957aa406c98e6c6546738d4815a74731949028fea220f548 | 7b46e68ee090a48b847c68a53fff7a4f30ea2aaaaa9039b881998ba68edd6618 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 897 | List.map_permutationsAux2' | Mathlib/Data/List/Permutation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>List.map</a>, <a>List.permutationsAux2_snd_cons</a>, <a>List.cons_append</a>, cons.injEq] | case cons
α : Type u_1
β : Type u_2
α' : Type u_3
β' : Type u_4
g : α → α'
g' : β → β'
t : α
ts : List α
r : List β
ys_hd : α
tail✝ : List α
ys_ih :
∀ (f : List α → β) (f' : List α' → β'),
(∀ (a : List α), g' (f a) = f' (map g a)) →
map g' (permutationsAux2 t ts r tail✝ f).2 = (permutationsAux2 (g t) (map g... | case cons
α : Type u_1
β : Type u_2
α' : Type u_3
β' : Type u_4
g : α → α'
g' : β → β'
t : α
ts : List α
r : List β
ys_hd : α
tail✝ : List α
ys_ih :
∀ (f : List α → β) (f' : List α' → β'),
(∀ (a : List α), g' (f a) = f' (map g a)) →
map g' (permutationsAux2 t ts r tail✝ f).2 = (permutationsAux2 (g t) (map g... | ((:c Eq) ((:c List) (:fv _uniq.2252)) ((:c List.map) (:fv _uniq.2136) (:fv _uniq.2252) (:fv _uniq.2254) ((:c Prod.snd) ((:c List) (:fv _uniq.2133)) ((:c List) (:fv _uniq.2136)) ((:c List.permutationsAux2) (:fv _uniq.2133) (:fv _uniq.2136) (:fv _uniq.2255) (:fv _uniq.2256) (:fv _uniq.2258) ((:c List.cons) (:fv _uniq.213... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"α'","sexp":"(:sort (+ u_3 1))"},{"name":"β'","sexp":"(:sort (+ u_4 1))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.2133) (:fv _uniq.2251))"},{"name":"g'","sexp":"(:forall _ (:fv _uniq.2136) (:fv _uniq.2252))"},{"name":"t","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV4)))) (:arg :explicit 1 (:app (:c List.map) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV4)) (:arg :explicit 2 (:fv FV6)) (:arg :explicit 3 (:app (:c Prod.snd) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2133","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2136","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"simp","sourceEnd":4065,"sourceStart":4061,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":4070,"sourceStart":4066,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":4070,"s... | [] | [{"source":"map","source_end":4075,"source_start":4072,"syntax_kind":"ident"},{"source":"permutationsAux2_snd_cons","source_end":4102,"source_start":4077,"syntax_kind":"ident"},{"source":"cons_append","source_end":4115,"source_start":4104,"syntax_kind":"ident"},{"source":"cons.injEq","source_end":4127,"source_start":41... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2133","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2136","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_uniq... | 16 | 14 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b2458967cbeaa72a43cfaf19555e58f3da054cf673d38a6bdf19e5759a9cfef4 | 9d2adfe4040d3f8eaa74d35ad087b0a084429bf03d9976d6092e25d98aaf80b6 | e58d027c6d3c17f507e1d42a64e2b9acc78392ddb269b5bbbc51a3819f854c5f | 3e5723f7aa6bb16c153ff2877714b91d4c7b8c56f6fafac8d75fbbe70112219b |
cat-searcher/leandojo-benchmark-4-random | test | 898 | List.map_permutationsAux2' | Mathlib/Data/List/Permutation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [ys_ih, <a>List.permutationsAux2_fst</a>] | case cons
α : Type u_1
β : Type u_2
α' : Type u_3
β' : Type u_4
g : α → α'
g' : β → β'
t : α
ts : List α
r : List β
ys_hd : α
tail✝ : List α
ys_ih :
∀ (f : List α → β) (f' : List α' → β'),
(∀ (a : List α), g' (f a) = f' (map g a)) →
map g' (permutationsAux2 t ts r tail✝ f).2 = (permutationsAux2 (g t) (map g... | case cons
α : Type u_1
β : Type u_2
α' : Type u_3
β' : Type u_4
g : α → α'
g' : β → β'
t : α
ts : List α
r : List β
ys_hd : α
tail✝ : List α
ys_ih :
∀ (f : List α → β) (f' : List α' → β'),
(∀ (a : List α), g' (f a) = f' (map g a)) →
map g' (permutationsAux2 t ts r tail✝ f).2 = (permutationsAux2 (g t) (map g... | ((:c And) ((:c Eq) (:fv _uniq.2252) ((:fv _uniq.2254) ((:fv _uniq.2303) ((:c List.cons) (:fv _uniq.2133) (:fv _uniq.2255) ((:c List.cons) (:fv _uniq.2133) (:fv _uniq.2295) ((:c Prod.fst) ((:c List) (:fv _uniq.2133)) ((:c List) (:fv _uniq.2136)) ((:c List.permutationsAux2) (:fv _uniq.2133) (:fv _uniq.2136) (:fv _uniq.22... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"α'","sexp":"(:sort (+ u_3 1))"},{"name":"β'","sexp":"(:sort (+ u_4 1))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.2133) (:fv _uniq.2251))"},{"name":"g'","sexp":"(:forall _ (:fv _uniq.2136) (:fv _uniq.2252))"},{"name":"t","sexp":"... | (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:app (:fv FV6) (:arg :explicit 0 (:app (:fv FV13) (:arg :explicit 0 (:app (:c List.cons) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:app (:c List.cons) (:arg :implicit-type 0 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2133","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2136","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"rw","sourceEnd":4135,"sourceStart":4133,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4137,"sourceStart":4136,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":12,"semanticR... | [] | [{"source":"ys_ih","source_end":4142,"source_start":4137,"syntax_kind":"ident"},{"source":"permutationsAux2_fst","source_end":4164,"source_start":4144,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2133","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2136","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_uniq... | 16 | 15 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8bd40df413516ba35fcaca0fc7e665561d12b4c573032d802987d5d6b6f9fcc2 | 3e5723f7aa6bb16c153ff2877714b91d4c7b8c56f6fafac8d75fbbe70112219b | 5fa3d3d563e95334d6f0bd53c5d12fc04f543b4f8b3d4157ee8c84026cf2a885 | 94fd6687450a846e1f4b679aa0d7c2f9f220fc8b7a9269c4370cc8c568ab1c8f |
cat-searcher/leandojo-benchmark-4-random | test | 899 | List.map_permutationsAux2' | Mathlib/Data/List/Permutation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨?_, <a>rfl</a>⟩ | case cons
α : Type u_1
β : Type u_2
α' : Type u_3
β' : Type u_4
g : α → α'
g' : β → β'
t : α
ts : List α
r : List β
ys_hd : α
tail✝ : List α
ys_ih :
∀ (f : List α → β) (f' : List α' → β'),
(∀ (a : List α), g' (f a) = f' (map g a)) →
map g' (permutationsAux2 t ts r tail✝ f).2 = (permutationsAux2 (g t) (map g... | case cons
α : Type u_1
β : Type u_2
α' : Type u_3
β' : Type u_4
g : α → α'
g' : β → β'
t : α
ts : List α
r : List β
ys_hd : α
tail✝ : List α
ys_ih :
∀ (f : List α → β) (f' : List α' → β'),
(∀ (a : List α), g' (f a) = f' (map g a)) →
map g' (permutationsAux2 t ts r tail✝ f).2 = (permutationsAux2 (g t) (map g... | ((:c And) ((:c Eq) (:fv _uniq.2252) ((:fv _uniq.2254) ((:fv _uniq.2303) ((:c List.cons) (:fv _uniq.2133) (:fv _uniq.2255) ((:c List.cons) (:fv _uniq.2133) (:fv _uniq.2295) ((:c HAppend.hAppend) ((:c List) (:fv _uniq.2133)) ((:c List) (:fv _uniq.2133)) ((:c List) (:fv _uniq.2133)) ((:c instHAppendOfAppend) ((:c List) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"α'","sexp":"(:sort (+ u_3 1))"},{"name":"β'","sexp":"(:sort (+ u_4 1))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.2133) (:fv _uniq.2251))"},{"name":"g'","sexp":"(:forall _ (:fv _uniq.2136) (:fv _uniq.2252))"},{"name":"t","sexp":"... | (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:app (:fv FV6) (:arg :explicit 0 (:app (:fv FV13) (:arg :explicit 0 (:app (:c List.cons) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:app (:c List.cons) (:arg :implicit-type 0 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2133","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2136","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"refine","sourceEnd":4179,"sourceStart":4173,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":4183,"sourceStart":4180,"tag":"atom"},{"children":[{"children":[{"source":"?","sourceEnd":4184,"sourceStart":4183,"tag":"atom"},{"children":[{"source":"_","sourceEnd":4185,"sourceStart":4184,"tag":"a... | [] | [{"source":"⟨?_, rfl⟩","source_end":4193,"source_start":4180,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2133","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2136","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_uniq... | 16 | 23 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 41667d15d7a9be9cbc39561145626255f979705087afc7a082fee68fcbba176d | 9191145edd4937e1a8100fa64cee259655261a93ea0749bd39f284015a3599af | 198666c0bf171b5c5ec3d8f31d7e011947de6c9b48083b5e716b157b1cb30e98 | 802003764c17e727164ecf1806cf4bb03085d20615829db39753f3a27b684739 |
cat-searcher/leandojo-benchmark-4-random | test | 900 | List.map_permutationsAux2' | Mathlib/Data/List/Permutation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [← <a>List.map_cons</a>, ← <a>List.map_append</a>] | case cons
α : Type u_1
β : Type u_2
α' : Type u_3
β' : Type u_4
g : α → α'
g' : β → β'
t : α
ts : List α
r : List β
ys_hd : α
tail✝ : List α
ys_ih :
∀ (f : List α → β) (f' : List α' → β'),
(∀ (a : List α), g' (f a) = f' (map g a)) →
map g' (permutationsAux2 t ts r tail✝ f).2 = (permutationsAux2 (g t) (map g... | case cons
α : Type u_1
β : Type u_2
α' : Type u_3
β' : Type u_4
g : α → α'
g' : β → β'
t : α
ts : List α
r : List β
ys_hd : α
tail✝ : List α
ys_ih :
∀ (f : List α → β) (f' : List α' → β'),
(∀ (a : List α), g' (f a) = f' (map g a)) →
map g' (permutationsAux2 t ts r tail✝ f).2 = (permutationsAux2 (g t) (map g... | ((:c Eq) (:fv _uniq.2252) ((:fv _uniq.2254) ((:fv _uniq.2303) ((:c List.cons) (:fv _uniq.2133) (:fv _uniq.2255) ((:c List.cons) (:fv _uniq.2133) (:fv _uniq.2295) ((:c HAppend.hAppend) ((:c List) (:fv _uniq.2133)) ((:c List) (:fv _uniq.2133)) ((:c List) (:fv _uniq.2133)) ((:c instHAppendOfAppend) ((:c List) (:fv _uniq.2... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"α'","sexp":"(:sort (+ u_3 1))"},{"name":"β'","sexp":"(:sort (+ u_4 1))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.2133) (:fv _uniq.2251))"},{"name":"g'","sexp":"(:forall _ (:fv _uniq.2136) (:fv _uniq.2252))"},{"name":"t","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:app (:fv FV6) (:arg :explicit 0 (:app (:fv FV13) (:arg :explicit 0 (:app (:c List.cons) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:app (:c List.cons) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV10)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2133","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2136","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"simp","sourceEnd":4204,"sourceStart":4200,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":4209,"sourceStart":4205,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":4209,"s... | [] | [{"source":"map_cons","source_end":4223,"source_start":4215,"syntax_kind":"ident"},{"source":"map_append","source_end":4239,"source_start":4229,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2133","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2136","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_uniq... | 16 | 24 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c671982111361a248ae27e8bc125825c9e0d63a798507bf87f7e760b071ae23b | 802003764c17e727164ecf1806cf4bb03085d20615829db39753f3a27b684739 | 0be8b1a1f25628912d35632263d2953417281b33f17360b0aa1b8619253c8ab8 | 4dae29020350081dc577baf2488a0c5127a3a302b891cdb2c594208aba38436c |
cat-searcher/leandojo-benchmark-4-random | test | 901 | List.map_permutationsAux2' | Mathlib/Data/List/Permutation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply H | case cons
α : Type u_1
β : Type u_2
α' : Type u_3
β' : Type u_4
g : α → α'
g' : β → β'
t : α
ts : List α
r : List β
ys_hd : α
tail✝ : List α
ys_ih :
∀ (f : List α → β) (f' : List α' → β'),
(∀ (a : List α), g' (f a) = f' (map g a)) →
map g' (permutationsAux2 t ts r tail✝ f).2 = (permutationsAux2 (g t) (map g... | ((:c Eq) (:fv _uniq.2252) ((:fv _uniq.2254) ((:fv _uniq.2303) ((:c List.cons) (:fv _uniq.2133) (:fv _uniq.2255) ((:c List.cons) (:fv _uniq.2133) (:fv _uniq.2295) ((:c HAppend.hAppend) ((:c List) (:fv _uniq.2133)) ((:c List) (:fv _uniq.2133)) ((:c List) (:fv _uniq.2133)) ((:c instHAppendOfAppend) ((:c List) (:fv _uniq.2... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"α'","sexp":"(:sort (+ u_3 1))"},{"name":"β'","sexp":"(:sort (+ u_4 1))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.2133) (:fv _uniq.2251))"},{"name":"g'","sexp":"(:forall _ (:fv _uniq.2136) (:fv _uniq.2252))"},{"name":"t","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:app (:fv FV6) (:arg :explicit 0 (:app (:fv FV13) (:arg :explicit 0 (:app (:c List.cons) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:app (:c List.cons) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV10)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2133","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2136","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"apply","sourceEnd":4247,"sourceStart":4242,"tag":"atom"},{"contextIndex":15,"semanticRole":"local","source":"H","sourceEnd":4249,"sourceStart":4248,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply H","sourceEnd":4249,"sourceStart":4242,"tag":"node"} | [] | [{"source":"H","source_end":4249,"source_start":4248,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2133","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2136","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_uniq... | 16 | 26 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d869b078a098fe2e2c957b6433deced0b846d2b7f148656fcd8633e6d5eb888b | 4dae29020350081dc577baf2488a0c5127a3a302b891cdb2c594208aba38436c | 658d46ec0cb4cfd169bca4cbb8446498ec3a4407cb616fb8625f722822f8e1e6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 902 | List.map_permutationsAux2' | Mathlib/Data/List/Permutation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro a | case cons.H
α : Type u_1
β : Type u_2
α' : Type u_3
β' : Type u_4
g : α → α'
g' : β → β'
t : α
ts : List α
r : List β
ys_hd : α
tail✝ : List α
ys_ih :
∀ (f : List α → β) (f' : List α' → β'),
(∀ (a : List α), g' (f a) = f' (map g a)) →
map g' (permutationsAux2 t ts r tail✝ f).2 = (permutationsAux2 (g t) (map... | case cons.H
α : Type u_1
β : Type u_2
α' : Type u_3
β' : Type u_4
g : α → α'
g' : β → β'
t : α
ts : List α
r : List β
ys_hd : α
tail✝ : List α
ys_ih :
∀ (f : List α → β) (f' : List α' → β'),
(∀ (a : List α), g' (f a) = f' (map g a)) →
map g' (permutationsAux2 t ts r tail✝ f).2 = (permutationsAux2 (g t) (map... | (:forall a ((:c List) (:fv _uniq.2133)) ((:c Eq) (:fv _uniq.2252) ((:fv _uniq.2254) ((:fv _uniq.2303) ((:c List.cons) (:fv _uniq.2133) (:fv _uniq.2295) 0))) ((:fv _uniq.2304) ((:c List.cons) (:fv _uniq.2251) ((:fv _uniq.2253) (:fv _uniq.2295)) ((:c List.map) (:fv _uniq.2133) (:fv _uniq.2251) (:fv _uniq.2253) 0))))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"α'","sexp":"(:sort (+ u_3 1))"},{"name":"β'","sexp":"(:sort (+ u_4 1))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.2133) (:fv _uniq.2251))"},{"name":"g'","sexp":"(:forall _ (:fv _uniq.2136) (:fv _uniq.2252))"},{"name":"t","sexp":"... | (:forall a :explicit (:app (:c List) (:arg :explicit 0 (:fv FV0))) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:app (:fv FV6) (:arg :explicit 0 (:app (:fv FV13) (:arg :explicit 0 (:app (:c List.cons) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV10)) (:arg :explicit 2 0))))))) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2133","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2136","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"intro","sourceEnd":4262,"sourceStart":4257,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":4264,"sourceStart":4263,"tag":"identifier"}],"kind":"null","source":"a","sourceEnd":4264,"sourceStart":4263,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source":"int... | [{"role":"fresh_name","source":"a","source_end":4264,"source_start":4263,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2133","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2136","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_uniq... | 16 | 31 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5ded89c714e3dee0b2c003c27c8d87a6432d67fe3992c31caaf666caee62d5e6 | e59b7b104640128a7dc80e76d21a596195e41898f7ff402f67cde46e94cbce70 | 103ef04ed94f5e0151a10e306e5d0cb73dbf1b66d45942dc8cdf5fe7b85f3ea9 | afb9fec3b4cd74ceb00b3f5fa67516cf8d2ac840220058d8954f9ec5883650b6 |
cat-searcher/leandojo-benchmark-4-random | test | 903 | List.map_permutationsAux2' | Mathlib/Data/List/Permutation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply H | case cons.H
α : Type u_1
β : Type u_2
α' : Type u_3
β' : Type u_4
g : α → α'
g' : β → β'
t : α
ts : List α
r : List β
ys_hd : α
tail✝ : List α
ys_ih :
∀ (f : List α → β) (f' : List α' → β'),
(∀ (a : List α), g' (f a) = f' (map g a)) →
map g' (permutationsAux2 t ts r tail✝ f).2 = (permutationsAux2 (g t) (map... | ((:c Eq) (:fv _uniq.2252) ((:fv _uniq.2254) ((:fv _uniq.2303) ((:c List.cons) (:fv _uniq.2133) (:fv _uniq.2295) (:fv _uniq.3023)))) ((:fv _uniq.2304) ((:c List.cons) (:fv _uniq.2251) ((:fv _uniq.2253) (:fv _uniq.2295)) ((:c List.map) (:fv _uniq.2133) (:fv _uniq.2251) (:fv _uniq.2253) (:fv _uniq.3023))))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"α'","sexp":"(:sort (+ u_3 1))"},{"name":"β'","sexp":"(:sort (+ u_4 1))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.2133) (:fv _uniq.2251))"},{"name":"g'","sexp":"(:forall _ (:fv _uniq.2136) (:fv _uniq.2252))"},{"name":"t","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:app (:fv FV6) (:arg :explicit 0 (:app (:fv FV13) (:arg :explicit 0 (:app (:c List.cons) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV10)) (:arg :explicit 2 (:fv FV16)))))))) (:arg :explicit 2 (:app (:fv FV14) (:arg :explicit 0 (:app (:c L... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2133","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2136","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"apply","sourceEnd":4271,"sourceStart":4266,"tag":"atom"},{"contextIndex":15,"semanticRole":"local","source":"H","sourceEnd":4273,"sourceStart":4272,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply H","sourceEnd":4273,"sourceStart":4266,"tag":"node"} | [] | [{"source":"H","source_end":4273,"source_start":4272,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2133","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2136","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_uniq... | 16 | 33 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0f2cad940ea31fe875695e421839719468191605bb50a72c1d31a8c6ae3ad779 | afb9fec3b4cd74ceb00b3f5fa67516cf8d2ac840220058d8954f9ec5883650b6 | 658d46ec0cb4cfd169bca4cbb8446498ec3a4407cb616fb8625f722822f8e1e6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 904 | MeasureTheory.ae_restrict_union_iff | Mathlib/MeasureTheory/Measure/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s✝ s' t✝ s t : Set α
p : α → Prop
⊢ (∀ᵐ (x : α) ∂μ.restrict (s ∪ t), p x) ↔ (∀ᵐ (x : α) ∂μ.restrict s, p x) ∧ ∀ᵐ (x : α) ∂μ.restrict... | ((:c Iff) ((:c Filter.Eventually) (:fv _uniq.93775) (:lambda x (:fv _uniq.93775) ((:fv _uniq.94423) 0)) ((:c MeasureTheory.ae) (:fv _uniq.93775) ((:c MeasureTheory.Measure) (:fv _uniq.93775) (:fv _uniq.93790)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.93775) (:fv _uniq.93790)) ((:c MeasureTheory.Measure.instOu... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.93775))"},{"name":"inst✝¹... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:fv FV23) (:arg :explicit 0 0)))) (:arg :explicit 2 (:app (:c MeasureTheory.ae) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c MeasureTheory.Measure... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.93772","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":31680,"sourceStart":31676,"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.93772","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.93775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 173 | 2 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 764b93e071a3975b285bab561696e369acd55453e4c3b1fb8d575f5819423052 | 29e48a5c512b149d7d8f8c9eea1f021d2242e3ad21e14170b6ab21fce1d65593 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 905 | ProbabilityTheory.kernel.rnDeriv_def' | Mathlib/Probability/Kernel/RadonNikodym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext | α : Type u_1
γ : Type u_2
mα : MeasurableSpace α
mγ : MeasurableSpace γ
κ✝ η✝ : ↥(kernel α γ)
hαγ : MeasurableSpace.CountableOrCountablyGenerated α γ
κ η : ↥(kernel α γ)
⊢ rnDeriv κ η = fun a x => ENNReal.ofReal (rnDerivAux κ (κ + η) a x) / ENNReal.ofReal (1 - rnDerivAux κ (κ + η) a x) | case h.h
α : Type u_1
γ : Type u_2
mα : MeasurableSpace α
mγ : MeasurableSpace γ
κ✝ η✝ : ↥(kernel α γ)
hαγ : MeasurableSpace.CountableOrCountablyGenerated α γ
κ η : ↥(kernel α γ)
x✝¹ : α
x✝ : γ
⊢ rnDeriv κ η x✝¹ x✝ = ENNReal.ofReal (rnDerivAux κ (κ + η) x✝¹ x✝) / ENNReal.ofReal (1 - rnDerivAux κ (κ + η) x✝¹ x✝) | ((:c Eq) (:forall a (:fv _uniq.45767) (:forall x (:fv _uniq.45770) (:c ENNReal))) ((:c ProbabilityTheory.kernel.rnDeriv) (:fv _uniq.45767) (:fv _uniq.45770) (:fv _uniq.45773) (:fv _uniq.45776) (:fv _uniq.45875) (:fv _uniq.46612) (:fv _uniq.46613)) (:lambda a (:fv _uniq.45767) (:lambda x (:fv _uniq.45770) ((:c HDiv.hDiv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.45767))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.45770))"},{"name":"κ✝","sexp":"((:c Subtype) (:forall _ (:fv _uniq.45767) ((:c MeasureTheory.Measure) (:fv _uniq.45770) (... | (:app (:c Eq) (:arg :implicit-type 0 (:forall a :explicit (:fv FV0) (:forall x :explicit (:fv FV1) (:c ENNReal)))) (:arg :explicit 1 (:app (:c ProbabilityTheory.kernel.rnDeriv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :implicit 3) (:arg :instance 4 (:instance-of (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45767","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45770","is_instance":false,"is_let":false,"name":"γ","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"ext","sourceEnd":12187,"sourceStart":12184,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":12187,"sourceStart":12184,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45767","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45770","is_instance":false,"is_let":false,"user_name":"γ"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 22 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | be5c49642deedb698c51b14e49c41c6123337add68430bf6f05c7590c1999239 | ae926ad383e0a9681e60351fd026728863d0a3e3e1f07449eceb0337aef4c180 | a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de | d659a0e033cf9bac75dbd61786d01852b74bb39c2fa5d26976dae02ba888dab2 |
cat-searcher/leandojo-benchmark-4-random | test | 906 | ProbabilityTheory.kernel.rnDeriv_def' | Mathlib/Probability/Kernel/RadonNikodym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>ProbabilityTheory.kernel.rnDeriv_def</a>] | case h.h
α : Type u_1
γ : Type u_2
mα : MeasurableSpace α
mγ : MeasurableSpace γ
κ✝ η✝ : ↥(kernel α γ)
hαγ : MeasurableSpace.CountableOrCountablyGenerated α γ
κ η : ↥(kernel α γ)
x✝¹ : α
x✝ : γ
⊢ rnDeriv κ η x✝¹ x✝ = ENNReal.ofReal (rnDerivAux κ (κ + η) x✝¹ x✝) / ENNReal.ofReal (1 - rnDerivAux κ (κ + η) x✝¹ x✝) | ((:c Eq) (:c ENNReal) ((:c ProbabilityTheory.kernel.rnDeriv) (:fv _uniq.45767) (:fv _uniq.45770) (:fv _uniq.45773) (:fv _uniq.45776) (:fv _uniq.45875) (:fv _uniq.46612) (:fv _uniq.46613) (:fv _uniq.46652) (:fv _uniq.46690)) ((:c HDiv.hDiv) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHDiv) (:c ENNReal) ((:c DivInvMo... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.45767))"},{"name":"mγ","sexp":"((:c MeasurableSpace) (:fv _uniq.45770))"},{"name":"κ✝","sexp":"((:c Subtype) (:forall _ (:fv _uniq.45767) ((:c MeasureTheory.Measure) (:fv _uniq.45770) (... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c ProbabilityTheory.kernel.rnDeriv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :implicit 3) (:arg :instance 4 (:instance-of (:app (:c MeasurableSpace.CountableOrCountablyGenerated) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45767","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45770","is_instance":false,"is_let":false,"name":"γ","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":12191,"sourceStart":12189,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12193,"sourceStart":12192,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"ProbabilityTheor... | [] | [{"source":"rnDeriv_def","source_end":12204,"source_start":12193,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45767","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45770","is_instance":false,"is_let":false,"user_name":"γ"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 22 | 6 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5ad9cdbe99ec458c0218fd9a523ceca3c41f4f5cb0772340e79591693782e498 | d659a0e033cf9bac75dbd61786d01852b74bb39c2fa5d26976dae02ba888dab2 | 2f51e6c9cb3de8e556d30d53fe6057c97c775dec403fa4aec5d75dee9f7b46e8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 907 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let f := <a>MeasureTheory.embeddingReal</a> Ω | 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
⊢ ∀ᵐ (x : α) ∂ρ.fst, κ x = ρ.condKernel x | 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
⊢ ∀ᵐ (x : α) ∂ρ.fst... | ((:c Filter.Eventually) (:fv _uniq.18774) (:lambda x (:fv _uniq.18774) ((:c Eq) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv _uniq.18774) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789))) (:lambda x (:forall _ (:fv _uniq.18774) ((:c Me... | [{"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) (:app (:c Eq) (: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 :explicit ... | [{"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":"let","sourceEnd":3958,"sourceStart":3955,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"f","sourceEnd":3960,"sourceStart":3959,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"sou... | [] | [{"source":"embeddingReal Ω","source_end":3980,"source_start":3964,"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 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 249ccbd9658dbb6788596eb09e4791bb4506de8c7ed5d64fa14ac13ac5fe9c6f | 45be4b9d7ba55c1fb0b4b75aee4b1d9cc587959ccbbb4488de6c28f7bccefd86 | 9c1c0da9adbeea264b2b67d3f5c6528b49980148b582f4b2c38a514b5abcd3f1 | 0004a069d90df88b320e5d6c7baedc560593facbf1ff59f389abd807a1c2629e |
cat-searcher/leandojo-benchmark-4-random | test | 908 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hf := <a>MeasureTheory.measurableEmbedding_embeddingReal</a> Ω | 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
⊢ ∀ᵐ (x : α) ∂ρ.fst... | 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... | ((:c Filter.Eventually) (:fv _uniq.18774) (:lambda x (:fv _uniq.18774) ((:c Eq) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv _uniq.18774) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789))) (:lambda x (:forall _ (:fv _uniq.18774) ((:c Me... | [{"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) (:app (:c Eq) (: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 :explicit ... | [{"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":"have","sourceEnd":3987,"sourceStart":3983,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hf","sourceEnd":3990,"sourceStart":3988,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hf","sourceEnd":3990,"sourceStart":3988,"tag":"node"},{"... | [] | [{"source":"measurableEmbedding_embeddingReal Ω","source_end":4030,"source_start":3994,"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 | 5 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0843e9f12481d0cc470db63a47e16a5a1e01af1bb24c8a6b789c50c6f193ee7e | 0004a069d90df88b320e5d6c7baedc560593facbf1ff59f389abd807a1c2629e | f6b0021309af43e5ca2f71c5c066452e2711d14953e8c3b3e7500cc8d7bef266 | 6a4ea19476da5dc3bdae92f2c55d0c8a7b15da4539fa80416d4ced02805448d0 |
cat-searcher/leandojo-benchmark-4-random | test | 909 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | set ρ' : <a>MeasureTheory.Measure</a> (α × ℝ) := ρ.map (<a>Prod.map</a> <a>id</a> f) with hρ'def | 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... | 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... | ((:c Filter.Eventually) (:fv _uniq.18774) (:lambda x (:fv _uniq.18774) ((:c Eq) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv _uniq.18774) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789))) (:lambda x (:forall _ (:fv _uniq.18774) ((:c Me... | [{"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) (:app (:c Eq) (: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 :explicit ... | [{"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":"set","sourceEnd":4036,"sourceStart":4033,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"semanticRole":"scoped_local","source":"ρ'","sourceEnd":4040,"sourceStart":4037,"tag":"identifier"},{"children":[{"source":":","sourceEnd":4042,"sourceStart":4041,"tag":"at... | [] | [{"source":"Measure (α × ℝ)","source_end":4062,"source_start":4043,"syntax_kind":"Lean.Parser.Term.app"},{"source":"ρ.map (Prod.map id f)","source_end":4088,"source_start":4066,"syntax_kind":"Lean.Parser.Term.app"},{"source":"ρ'","source_end":4040,"source_start":4037,"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 | 6 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ab42296cac2ef7857308573194da715a6567dad99f7bc4571e18dab928bf29c1 | 6a4ea19476da5dc3bdae92f2c55d0c8a7b15da4539fa80416d4ced02805448d0 | 857ce030ca8e06f45d18a751e27e05e8325476007e20780e48ae7539495b6d29 | 8c6804aeecda88f637d179a2c74675585e9f72849ee752f9ad4f625c6cbeeae9 |
cat-searcher/leandojo-benchmark-4-random | test | 910 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hρ' : ρ'.fst = ρ.fst := by ext s hs rw [hρ'def, <a>MeasureTheory.Measure.fst_apply</a>, <a>MeasureTheory.Measure.fst_apply</a>, <a>MeasureTheory.Measure.map_apply</a>] exacts [<a>rfl</a>, <a>Measurable.prod</a> <a>measurable_fst</a> <| hf.measurable.comp <a>measurable_snd</a>, <a>measurable_fst</a> hs, hs, 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... | 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... | ((:c Filter.Eventually) (:fv _uniq.18774) (:lambda x (:fv _uniq.18774) ((:c Eq) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv _uniq.18774) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789))) (:lambda x (:forall _ (:fv _uniq.18774) ((:c Me... | [{"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) (:app (:c Eq) (: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 :explicit ... | [{"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":"have","sourceEnd":4108,"sourceStart":4104,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hρ'","sourceEnd":4113,"sourceStart":4109,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hρ'","sourceEnd":4113,"sourceStart":4109,"tag":"node"},... | [] | [{"source":"ρ'.fst = ρ.fst","source_end":4132,"source_start":4116,"syntax_kind":"«term_=_»"},{"source":"hρ'def","source_end":4167,"source_start":4160,"syntax_kind":"ident"},{"source":"Measure.fst_apply","source_end":4186,"source_start":4169,"syntax_kind":"ident"},{"source":"Measure.fst_apply","source_end":4205,"source_... | [{"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 | 7 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3b787d09cabc511f029a6ed0bd1f848ff07699ba8a96338d3dc83d2571fe4267 | 8c6804aeecda88f637d179a2c74675585e9f72849ee752f9ad4f625c6cbeeae9 | ea5a0584521a40719592e4195ec00842540c183d44200abd39172d8dba915b48 | fbaa9793fdb99ec73da65af2810b82a78b614cf2c465f130bb685f50fb42b92b |
cat-searcher/leandojo-benchmark-4-random | test | 911 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hρ'' : ∀ᵐ x ∂ρ.fst, <a>ProbabilityTheory.kernel.map</a> κ f hf.measurable x = ρ'.condKernel x := by rw [← hρ'] refine <a>ProbabilityTheory.eq_condKernel_of_measure_eq_compProd_real</a> (<a>ProbabilityTheory.kernel.map</a> κ f hf.measurable) ?_ ext s hs conv_lhs => rw [hρ'def, hκ] rw [<a>MeasureTheory.Measure.map_a... | 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... | 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... | ((:c Filter.Eventually) (:fv _uniq.18774) (:lambda x (:fv _uniq.18774) ((:c Eq) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv _uniq.18774) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789))) (:lambda x (:forall _ (:fv _uniq.18774) ((:c Me... | [{"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) (:app (:c Eq) (: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 :explicit ... | [{"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":"have","sourceEnd":4351,"sourceStart":4347,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hρ''","sourceEnd":4357,"sourceStart":4352,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hρ''","sourceEnd":4357,"sourceStart":4352,"tag":"node"... | [] | [{"source":"∀ᵐ x ∂ρ.fst, kernel.map κ f hf.measurable x = ρ'.condKernel x","source_end":4430,"source_start":4360,"syntax_kind":"MeasureTheory.«term∀ᵐ_∂_,_»"},{"source":"hρ'","source_end":4453,"source_start":4449,"syntax_kind":"ident"},{"source":"eq_condKernel_of_measure_eq_compProd_real (kernel.map κ f hf.measurable) ?... | [{"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 | 17 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a2e325ad3d8598b79a643241f77324ae939537bf47e00160630710b93dfa17f7 | fbaa9793fdb99ec73da65af2810b82a78b614cf2c465f130bb685f50fb42b92b | 3a6d45f2b4f67f00d81f378bc1ec6d44d3bb54118c123443ab2609e53e9a6086 | 3afa8880d7bcba5e135f278bf2dce49210a8a239f0f2b48a53756b64c2c4298c |
cat-searcher/leandojo-benchmark-4-random | test | 912 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | suffices ∀ᵐ x ∂ρ.fst, ∀ s, <a>MeasurableSet</a> s → ρ'.condKernel x s = ρ.condKernel x (f ⁻¹' s) by filter_upwards [hρ'', this] with x hx h rw [<a>ProbabilityTheory.kernel.map_apply</a>] at hx ext s hs rw [← <a>Set.preimage_image_eq</a> s hf.injective, ← <a>MeasureTheory.Measure.map_apply</a> hf.measurable <| hf.measur... | 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... | 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... | ((:c Filter.Eventually) (:fv _uniq.18774) (:lambda x (:fv _uniq.18774) ((:c Eq) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv _uniq.18774) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789))) (:lambda x (:forall _ (:fv _uniq.18774) ((:c Me... | [{"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) (:app (:c Eq) (: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 :explicit ... | [{"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":"suffices","sourceEnd":4863,"sourceStart":4855,"tag":"atom"},{"children":[{"children":[{"source":"","sourceEnd":4864,"sourceStart":4864,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":4864,"sourceStart":4864,"tag":"node"},{"children":[{"source":"∀ᵐ","sourceEnd":4870,"sourceStart... | [] | [{"source":"∀ᵐ x ∂ρ.fst, ∀ s, MeasurableSet s → ρ'.condKernel x s = ρ.condKernel x (f ⁻¹' s)","source_end":4960,"source_start":4864,"syntax_kind":"MeasureTheory.«term∀ᵐ_∂_,_»"},{"source":"this","source_end":4995,"source_start":4991,"syntax_kind":"ident"},{"source":"hρ''","source_end":4989,"source_start":4984,"syntax_ki... | [{"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 | 41 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bb5b06aa039eb1d52e4a76adb2061f6bec10b4005dcb3abc2860510d2a38641f | 3afa8880d7bcba5e135f278bf2dce49210a8a239f0f2b48a53756b64c2c4298c | 71f7627bd99f28c32b0fc61095b43a3f4689c1c983318f4cf8d0450084677246 | 0910302a516c025ad1d2111a2e0028a14e1a573753e951001856ef97ef1489e4 |
cat-searcher/leandojo-benchmark-4-random | test | 913 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | suffices ρ.map (<a>Prod.map</a> <a>id</a> f) = (ρ.fst ⊗ₘ (<a>ProbabilityTheory.kernel.map</a> ρ.condKernel f hf.measurable)) by rw [← hρ'] at this have heq := <a>ProbabilityTheory.eq_condKernel_of_measure_eq_compProd_real</a> _ this rw [hρ'] at heq filter_upwards [heq] with x hx s hs rw [← hx, <a>ProbabilityTheory.kern... | 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... | 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... | ((: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":"suffices","sourceEnd":5234,"sourceStart":5226,"tag":"atom"},{"children":[{"children":[{"source":"","sourceEnd":5235,"sourceStart":5235,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":5235,"sourceStart":5235,"tag":"node"},{"children":[{"children":[{"source":"ρ.map","sourceEnd":5... | [] | [{"source":"ρ.map (Prod.map id f) = (ρ.fst ⊗ₘ (kernel.map ρ.condKernel f hf.measurable))","source_end":5318,"source_start":5235,"syntax_kind":"«term_=_»"},{"source":"hρ'","source_end":5338,"source_start":5334,"syntax_kind":"ident"},{"source":"this","source_end":5347,"source_start":5343,"syntax_kind":"ident"},{"source":... | [{"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 | 55 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 391b65cdc551186f1fc1241804dd4abe5caf22dbd904f899b9343f75b858a5b5 | 0910302a516c025ad1d2111a2e0028a14e1a573753e951001856ef97ef1489e4 | b5f8ec596f2a1436c34b6734b1e854afa9ceaf279bd8f946ad068c01d486704f | 167cb8666f378fa2e97a0882bf8fd7e3477f9a468bc78a40dfa30ef8699fe790 |
cat-searcher/leandojo-benchmark-4-random | test | 914 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext 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 Eq) ((:c MeasureTheory.Measure) ((:c Prod) (:fv _uniq.18774) (:c Real)) ((:c Prod.instMeasurableSpace) (:fv _uniq.18774) (:c Real) (:fv _uniq.18783) (:c Real.measurableSpace))) ((:c MeasureTheory.Measure.map) ((:c Prod) (:fv _uniq.18774) (:fv _uniq.18780)) ((:c Prod) (:fv _uniq.18774) (:c Real)) ((:c Prod.instMeas... | [{"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 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real))))))))... | [{"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":"ext","sourceEnd":5549,"sourceStart":5546,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"s","sourceEnd":5551,"sourceStart":5550,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"s","sourceEnd":5551,"sourceStart":5550,"tag":"nod... | [{"role":"fresh_name","source":"s","source_end":5551,"source_start":5550,"syntax_kind":"ident"},{"role":"fresh_name","source":"hs","source_end":5554,"source_start":5552,"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 | 71 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 29d8e1dd9f91bdcc6139aace1e4de9fe0736acf9b124733233f43f2c6170f4eb | 167cb8666f378fa2e97a0882bf8fd7e3477f9a468bc78a40dfa30ef8699fe790 | dd7716a830809b68143b6ea22f9be5b8009c7575f67ccc4d7333624fb8eb6eed | 5daae798efd4a71a9be524482743efa8cc803342102d16446f1ff5ce0a8c7a39 |
cat-searcher/leandojo-benchmark-4-random | test | 915 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | conv_lhs => rw [← ρ.compProd_fst_condKernel] | 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
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 Prod) (:fv _uniq.18774) (:c Real)) ((:c Prod.instMeasurableSpace) (:fv _uniq.18774) (:c Real) (:fv _uniq.18783) (:c Real.measurableSpace))) ((:c Set) ((:c Prod) (:fv _uniq.18774) (:c Real))) (:lambda _ ((:c Set) ((:c Prod) (:fv _uniq.18774) (:c R... | [{"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 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 ... | [{"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":"conv_lhs","sourceEnd":5565,"sourceStart":5557,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":"=>","sourceEnd":5568,"sourceStart":5566,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source"... | [] | [{"source":"ρ.compProd_fst_condKernel","source_end":5603,"source_start":5577,"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 | 72 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 255bbe1926b8a3564e29dd053c411a2a256d68f8fc62ca1565d6ca55e2373575 | 5daae798efd4a71a9be524482743efa8cc803342102d16446f1ff5ce0a8c7a39 | aeac856dade2d0e4f74d9edc00b0292636c797bed24229bf980076c1879c45ab | 7cc99d1c21dec949b066e4bc8b7ce9968ab006a9d4db0c2d3fbbfb694e5ae018 |
cat-searcher/leandojo-benchmark-4-random | test | 916 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.Measure.compProd_apply</a> hs, <a>MeasureTheory.Measure.map_apply</a> (measurable_id.prod_map hf.measurable) hs, <a>MeasureTheory.Measure.compProd_apply</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
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 Prod) (:fv _uniq.18774) (:c Real)) ((:c Prod.instMeasurableSpace) (:fv _uniq.18774) (:c Real) (:fv _uniq.18783) (:c Real.measurableSpace))) ((:c Set) ((:c Prod) (:fv _uniq.18774) (:c Real))) (:lambda _ ((:c Set) ((:c Prod) (:fv _uniq.18774) (:c R... | [{"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 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 ... | [{"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":5609,"sourceStart":5607,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5611,"sourceStart":5610,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Measure... | [] | [{"source":"Measure.compProd_apply hs","source_end":5636,"source_start":5611,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Measure.map_apply (measurable_id.prod_map hf.measurable) hs","source_end":5697,"source_start":5638,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Measure.compProd_apply","source_end":5725,"sou... | [{"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 | 77 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 055366695f2d7e4b6ffb50c942574de27fa57745d2f83e1e7e24a1f231591a18 | 7cc99d1c21dec949b066e4bc8b7ce9968ab006a9d4db0c2d3fbbfb694e5ae018 | 6adc4ff898873e9a4b5e0066a25ce3b15fb17c73fe2de6f3bdb9b38b713bec5d | fa29091ab8d1943bc883d3b70ce4923ce4cd332ce5ac98672b144e6c8989c47f |
cat-searcher/leandojo-benchmark-4-random | test | 917 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext 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 Eq) ((:c MeasureTheory.Measure) (:fv _uniq.18774) (:fv _uniq.18783)) ((:c MeasureTheory.Measure.fst) (:fv _uniq.18774) (:c Real) (:fv _uniq.18783) (:c Real.measurableSpace) (:fv _uniq.19664)) ((:c MeasureTheory.Measure.fst) (:fv _uniq.18774) (:fv _uniq.18780) (:fv _uniq.18783) (:fv _uniq.18789) (:fv _uniq.18832))) | [{"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 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c MeasureTheory.Measure.fst) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c Real)) (:arg... | [{"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":"ext","sourceEnd":4146,"sourceStart":4143,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"s","sourceEnd":4148,"sourceStart":4147,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"s","sourceEnd":4148,"sourceStart":4147,"tag":"nod... | [{"role":"fresh_name","source":"s","source_end":4148,"source_start":4147,"syntax_kind":"ident"},{"role":"fresh_name","source":"hs","source_end":4151,"source_start":4149,"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 | 9 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2e4b2fc610244011e8158b4097b8e0433b460a88b6689133037d67cddc37afbc | 7fd76c70db4c6b52f3fe23c910ab39b7a70a6e3fd6373f8ad2dba48186b6e359 | dd7716a830809b68143b6ea22f9be5b8009c7575f67ccc4d7333624fb8eb6eed | 54c64552fd02cc82dc5c0b2b00bda389c4da3c6624481aa80033eb828164b6d0 |
cat-searcher/leandojo-benchmark-4-random | test | 918 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hρ'def, <a>MeasureTheory.Measure.fst_apply</a>, <a>MeasureTheory.Measure.fst_apply</a>, <a>MeasureTheory.Measure.map_apply</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
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) (:fv _uniq.18774) (:fv _uniq.18783)) ((:c Set) (:fv _uniq.18774)) (:lambda _ ((:c Set) (:fv _uniq.18774)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.18774) (:fv _uniq.18783)) ((:c MeasureTheory.Measure.fst) (:fv _uniq.18774) (:c ... | [{"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 FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))))) (: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":4158,"sourceStart":4156,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4160,"sourceStart":4159,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":17,"semanticR... | [] | [{"source":"hρ'def","source_end":4167,"source_start":4160,"syntax_kind":"ident"},{"source":"Measure.fst_apply","source_end":4186,"source_start":4169,"syntax_kind":"ident"},{"source":"Measure.fst_apply","source_end":4205,"source_start":4188,"syntax_kind":"ident"},{"source":"Measure.map_apply","source_end":4224,"source_s... | [{"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 | 10 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cd719e00d6c5081cacf8cde89cd1f2ae80e46cd39f73997645a6b0d85c983332 | 54c64552fd02cc82dc5c0b2b00bda389c4da3c6624481aa80033eb828164b6d0 | 9c0af9ec76c0069a448af70c43611c5a6235161314f14a954be34b8443895f2a | 1a25fa25a140aabed034434a53b028aed5d3031ad5b171cba8cc4df4a58426bc |
cat-searcher/leandojo-benchmark-4-random | test | 920 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hρ'] | 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... | 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... | ((:c Filter.Eventually) (:fv _uniq.18774) (:lambda x (:fv _uniq.18774) ((:c Eq) ((:c MeasureTheory.Measure) (:c Real) (:c Real.measurableSpace)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv _uniq.18774) ((:c MeasureTheory.Measure) (:c Real) (:c Real.measurableSpace))) (:lambda x (:forall _ (:fv _uniq.18774) ((:c Me... | [{"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) (:app (:c Eq) (: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 :explicit ... | [{"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":4443,"sourceStart":4441,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4445,"sourceStart":4444,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":4448,"sourceStart":... | [] | [{"source":"hρ'","source_end":4453,"source_start":4449,"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 | 19 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c77c7cb8e40d94a6c6a5572561290898b88486b370fb52659dbb2fa4b0d2a815 | 9e2c29698e76f040419e2c0f33e9a664a618605f6174c3897fedba487e6c0977 | 091eb377fedfec16d8bd588f6fcafd06d8dadd74afb98e163faa403ea7f68cd5 | 99c03c7ad3a64cfc4dcfa97acb854f2794fa1724ffb7dad21077ac6a99bd281b |
cat-searcher/leandojo-benchmark-4-random | test | 921 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>ProbabilityTheory.eq_condKernel_of_measure_eq_compProd_real</a> (<a>ProbabilityTheory.kernel.map</a> κ f hf.measurable) ?_ | 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... | 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... | ((:c Filter.Eventually) (:fv _uniq.18774) (:lambda x (:fv _uniq.18774) ((:c Eq) ((:c MeasureTheory.Measure) (:c Real) (:c Real.measurableSpace)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv _uniq.18774) ((:c MeasureTheory.Measure) (:c Real) (:c Real.measurableSpace))) (:lambda x (:forall _ (:fv _uniq.18774) ((:c Me... | [{"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) (:app (:c Eq) (: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 :explicit ... | [{"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":"refine","sourceEnd":4465,"sourceStart":4459,"tag":"atom"},{"children":[{"name":"ProbabilityTheory.eq_condKernel_of_measure_eq_compProd_real","semanticRole":"global","source":"eq_condKernel_of_measure_eq_compProd_real","sourceEnd":4507,"sourceStart":4466,"tag":"identifier"},{"children":[{"childre... | [] | [{"source":"eq_condKernel_of_measure_eq_compProd_real (kernel.map κ f hf.measurable) ?_","source_end":4542,"source_start":4466,"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 | 22 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b55ba06de4163ff26451547b9c81d04d0b0258a2e1fd202b68c83257f4288031 | 99c03c7ad3a64cfc4dcfa97acb854f2794fa1724ffb7dad21077ac6a99bd281b | 3239a56279cc0066669b8b454778ff4f25d094b4cbbbc9823c907e5eca13342d | 6ac418a4904e944b31936647b0ebc71e02790d24016faf3699af4633bde1b8c4 |
cat-searcher/leandojo-benchmark-4-random | test | 922 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext 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 Eq) ((:c MeasureTheory.Measure) ((:c Prod) (:fv _uniq.18774) (:c Real)) ((:c Prod.instMeasurableSpace) (:fv _uniq.18774) (:c Real) (:fv _uniq.18783) (:c Real.measurableSpace))) (:fv _uniq.19664) ((:c MeasureTheory.Measure.compProd) (:fv _uniq.18774) (:c Real) (:fv _uniq.18783) (:c Real.measurableSpace) ((:c Measur... | [{"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 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real))))))))... | [{"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":"ext","sourceEnd":4550,"sourceStart":4547,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"s","sourceEnd":4552,"sourceStart":4551,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"s","sourceEnd":4552,"sourceStart":4551,"tag":"nod... | [{"role":"fresh_name","source":"s","source_end":4552,"source_start":4551,"syntax_kind":"ident"},{"role":"fresh_name","source":"hs","source_end":4555,"source_start":4553,"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 | 23 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 43be357e3bb6b1f0ab9f417ad3bed703b257381b1157011bda1ee44302d045a4 | 6ac418a4904e944b31936647b0ebc71e02790d24016faf3699af4633bde1b8c4 | dd7716a830809b68143b6ea22f9be5b8009c7575f67ccc4d7333624fb8eb6eed | ed0c30781dab862c7a207a82e0d3bca926d85b3ca346810b16d849d96ce3fd8d |
cat-searcher/leandojo-benchmark-4-random | test | 923 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | conv_lhs => rw [hρ'def, hκ] | 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
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 Prod) (:fv _uniq.18774) (:c Real)) ((:c Prod.instMeasurableSpace) (:fv _uniq.18774) (:c Real) (:fv _uniq.18783) (:c Real.measurableSpace))) ((:c Set) ((:c Prod) (:fv _uniq.18774) (:c Real))) (:lambda _ ((:c Set) ((:c Prod) (:fv _uniq.18774) (:c R... | [{"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 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 ... | [{"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":"conv_lhs","sourceEnd":4568,"sourceStart":4560,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":"=>","sourceEnd":4571,"sourceStart":4569,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source"... | [] | [{"source":"hρ'def","source_end":4583,"source_start":4576,"syntax_kind":"ident"},{"source":"hκ","source_end":4588,"source_start":4585,"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 | 24 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 71ba52e31f3252eb0e56d0e240bb56fa8712327ab4498b0d337a4a627001697e | ed0c30781dab862c7a207a82e0d3bca926d85b3ca346810b16d849d96ce3fd8d | 9a5d9363c11be36d4816772bb378ffc4b32dfea0d70227c6592c27a660c9fa98 | 6ce306b0eb02cf6d0114237341e5a60071f8f23a022afc90a27a5bb085a51d72 |
cat-searcher/leandojo-benchmark-4-random | test | 924 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.Measure.map_apply</a> (measurable_id.prod_map hf.measurable) hs, hρ', <a>MeasureTheory.Measure.compProd_apply</a> hs, <a>MeasureTheory.Measure.compProd_apply</a> (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... | 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 Prod) (:fv _uniq.18774) (:c Real)) ((:c Prod.instMeasurableSpace) (:fv _uniq.18774) (:c Real) (:fv _uniq.18783) (:c Real.measurableSpace))) ((:c Set) ((:c Prod) (:fv _uniq.18774) (:c Real))) (:lambda _ ((:c Set) ((:c Prod) (:fv _uniq.18774) (:c R... | [{"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 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 ... | [{"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":4596,"sourceStart":4594,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4598,"sourceStart":4597,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Measure... | [] | [{"source":"Measure.map_apply (measurable_id.prod_map hf.measurable) hs","source_end":4657,"source_start":4598,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hρ'","source_end":4663,"source_start":4659,"syntax_kind":"ident"},{"source":"Measure.compProd_apply hs","source_end":4696,"source_start":4671,"syntax_kind":"Lea... | [{"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 | 30 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6fc514a0d1c4ff6c2c1caa12a6303cf859b25773dd3b56840bedbfa99c8541dc | 6ce306b0eb02cf6d0114237341e5a60071f8f23a022afc90a27a5bb085a51d72 | c4bcb1ff86207fc021c96a62ce41d5b9edc4edae5a33c56a60d4ed52f1dac106 | c5b78d44991e90307b44950a13d5342847afc4ebb5fbba08ad598c822ae05c8a |
cat-searcher/leandojo-benchmark-4-random | test | 925 | 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":4773,"sourceStart":4768,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":"with","sourceEnd":4778,"sourceStart":4774,"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 | 36 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5dd4cce876841b2290ea8fe9ae25ff62ccdd2bc34a5dd540bd96dfe5ca4d8e23 | c5b78d44991e90307b44950a13d5342847afc4ebb5fbba08ad598c822ae05c8a | 5011123f861f9d949fd6e0a0e9aab90e2d65630d818d13307a95737d6d05b59a | 1547a73591e760fe92b3eb2df2c5715b836aac6c9c5c46385a182e19667aaf52 |
cat-searcher/leandojo-benchmark-4-random | test | 926 | 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":4787,"sourceStart":4785,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4789,"sourceStart":4788,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"ProbabilityTheory.ke... | [] | [{"source":"kernel.map_apply'","source_end":4806,"source_start":4789,"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 | 37 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9d16b74f93f3b2067a2e7724e50be2471b70d22fe9e5ef568ff058f7a81cc178 | 1547a73591e760fe92b3eb2df2c5715b836aac6c9c5c46385a182e19667aaf52 | f829cc648afc54758bd562643f9874447bb919cf6a99b411f1513397c6aa1937 | 1cc8b3f1b2bd64c899362bf133c58b5dfb55b33350574dc90e62249ef3cf2e1c |
cat-searcher/leandojo-benchmark-4-random | test | 928 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards [hρ'', this] with x hx 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 : 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) ((:c Eq) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv _uniq.18774) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789))) (:lambda x (:forall _ (:fv _uniq.18774) ((:c Me... | [{"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) (:app (:c Eq) (: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 :explicit ... | [{"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":4982,"sourceStart":4968,"tag":"atom"},{"children":[{"source":"[","sourceEnd":4984,"sourceStart":4983,"tag":"atom"},{"children":[{"contextIndex":19,"semanticRole":"local","source":"hρ''","sourceEnd":4989,"sourceStart":4984,"tag":"identifier"},{"source":",","sourceEnd":... | [] | [{"source":"this","source_end":4995,"source_start":4991,"syntax_kind":"ident"},{"source":"hρ''","source_end":4989,"source_start":4984,"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 | 44 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b14f70cdfa3bc1ebcf565f8e11ceed2d1beeb2c3ed14609264cfe9019b761e01 | bb6ece02081efe447c1477b0d0d5c108163f0a396258cc25685e6e3c76f714f1 | 3147d4785909da90d6245b52860e5fd258fded8fc4d3d5422b5b138f19732727 | 13c6faf794c26047594dbb46a15271e92b981cc7dd6040997c6a88dfb2258552 |
cat-searcher/leandojo-benchmark-4-random | test | 929 | 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>] at hx | 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
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 MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv _uniq.18774) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789))) (:lambda x (:forall _ (:fv _uniq.18774) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789))) ((:c Members... | [{"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 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:forall _ :explicit ... | [{"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":5015,"sourceStart":5013,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5017,"sourceStart":5016,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"ProbabilityTheory.ke... | [] | [{"source":"kernel.map_apply","source_end":5033,"source_start":5017,"syntax_kind":"ident"},{"source":"hx","source_end":5040,"source_start":5038,"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 | 45 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6af924cdf0bc00c868767e83cdd7630bb3157351db65aefc87f98d786146c450 | 13c6faf794c26047594dbb46a15271e92b981cc7dd6040997c6a88dfb2258552 | 1d8e0a39989748907fc48409515b2f48f9cbb1efc0f345f11505abb38675e9c0 | 3023448c6d2170db59dfa7bf247aa9657668069453e9d7eee3b14818a6e96b07 |
cat-searcher/leandojo-benchmark-4-random | test | 930 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext s 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... | case h.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 : Measu... | ((:c Eq) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv _uniq.18774) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789))) (:lambda x (:forall _ (:fv _uniq.18774) ((:c MeasureTheory.Measure) (:fv _uniq.18780) (:fv _uniq.18789))) ((:c Members... | [{"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 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:forall _ :explicit ... | [{"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":"ext","sourceEnd":5048,"sourceStart":5045,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"s","sourceEnd":5050,"sourceStart":5049,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"s","sourceEnd":5050,"sourceStart":5049,"tag":"nod... | [{"role":"fresh_name","source":"s","source_end":5050,"source_start":5049,"syntax_kind":"ident"},{"role":"fresh_name","source":"hs","source_end":5053,"source_start":5051,"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 | 48 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 890fb259219762e16e4189e493afef7dfe952cf6999d3671356869abd9109219 | 3023448c6d2170db59dfa7bf247aa9657668069453e9d7eee3b14818a6e96b07 | dd7716a830809b68143b6ea22f9be5b8009c7575f67ccc4d7333624fb8eb6eed | 7b945c284be9f89c793181aec16c06a516dc197c820be5ba7903c2c1009dd4ca |
cat-searcher/leandojo-benchmark-4-random | test | 931 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Set.preimage_image_eq</a> s hf.injective, ← <a>MeasureTheory.Measure.map_apply</a> hf.measurable <| hf.measurableSet_image.2 hs, hx, h _ <| hf.measurableSet_image.2 hs] | case h.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 : Measu... | ((: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":5060,"sourceStart":5058,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5062,"sourceStart":5061,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":5065,"sourceStart":... | [] | [{"source":"Set.preimage_image_eq s hf.injective","source_end":5102,"source_start":5066,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Measure.map_apply hf.measurable <| hf.measurableSet_image.2 hs","source_end":5176,"source_start":5114,"syntax_kind":"«term_<|_»"},{"source":"hx","source_end":5180,"source_start":5178,... | [{"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 | 49 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 68feda27a5a1d555675a457a925c643265f8f49ad51fbe8534b535292a629374 | 7b945c284be9f89c793181aec16c06a516dc197c820be5ba7903c2c1009dd4ca | 97e1d7d66309bdf9fa3483a49dbc2a486a44cbd09835a8d99122247c0f929345 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 932 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hρ'] at this | 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... | 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... | ((: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":"rw","sourceEnd":5328,"sourceStart":5326,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5330,"sourceStart":5329,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":5333,"sourceStart":... | [] | [{"source":"hρ'","source_end":5338,"source_start":5334,"syntax_kind":"ident"},{"source":"this","source_end":5347,"source_start":5343,"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 | 58 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4fc1efeba590a2d8987c4e6953b32da51bd4a341d0bc8db1d1186862f9f3d460 | 0bbce2a0ce4aeaa04847269f7cac09a98b5f3efec588bb3283976bbd9956f540 | da0fe75801aaf781085e1622dd70f13a733d2a0ac1a9def8f70c752f0338a002 | 6f12e1e097351bd86db79dd3d72a050f19693dd1a7c39df30aa6e14a780c3836 |
cat-searcher/leandojo-benchmark-4-random | test | 933 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have heq := <a>ProbabilityTheory.eq_condKernel_of_measure_eq_compProd_real</a> _ this | 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... | 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... | ((: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":"have","sourceEnd":5356,"sourceStart":5352,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"heq","sourceEnd":5360,"sourceStart":5357,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"heq","sourceEnd":5360,"sourceStart":5357,"tag":"node"},... | [] | [{"source":"eq_condKernel_of_measure_eq_compProd_real _ this","source_end":5412,"source_start":5364,"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 | 61 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 38e44d7618da1b0543b3ac3b839b22346296d7d4e437732565646f2af64b33ae | 6f12e1e097351bd86db79dd3d72a050f19693dd1a7c39df30aa6e14a780c3836 | be75fca4ccd602ee40a6315d99af24d360a1d09beaf462b3973271195482a423 | 287b2f12b921bc46b7b46f0ca4c958efd5a09f1c36e91f6b29c1dded6722bed8 |
cat-searcher/leandojo-benchmark-4-random | test | 934 | ProbabilityTheory.eq_condKernel_of_measure_eq_compProd | Mathlib/Probability/Kernel/Disintegration/Unique.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hρ'] at heq | 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... | 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... | ((: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":"rw","sourceEnd":5419,"sourceStart":5417,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5421,"sourceStart":5420,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":18,"semanticR... | [] | [{"source":"hρ'","source_end":5425,"source_start":5421,"syntax_kind":"ident"},{"source":"heq","source_end":5433,"source_start":5430,"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 | 62 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b6c6caa5f343cf1be950f7b77351ba935732228a8566bdd2827adcfee86055f7 | 287b2f12b921bc46b7b46f0ca4c958efd5a09f1c36e91f6b29c1dded6722bed8 | 602b309c9274bc6edf7f37640c9aecb8ce5a5ef4c63b6a18d56a2b05c363c95d | 622e33c77724366d2fd576ab685a0937bcecdf1de90924bc767aa0f4afeb2ae5 |
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