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value | tactic stringlengths 3 2.13k | text_state stringlengths 7 2.31k | text_target_state stringlengths 0 4.07k | raw_goal_sexp stringlengths 10 11.8M | raw_hyp_sexps stringlengths 2 15.6M | model_goal_sexp stringlengths 10 2.68M | model_hyp_sexps stringlengths 2 3.62M | source_syntax stringlengths 179 164k | syntax_args stringclasses 256
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classes | raw_schema_version int64 4 4 | raw_extractor_version stringclasses 1
value | model_schema_version int64 2 2 | model_normalization stringclasses 1
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value | pantograph_commit stringclasses 1
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value | raw_record_sha256 stringlengths 64 64 | state_sha256 stringlengths 64 64 | tactic_sha256 stringlengths 64 64 | target_state_sha256 stringlengths 64 64 |
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cat-searcher/leandojo-benchmark-4-random | test | 3,291 | IntermediateField.AdjoinSimple.norm_gen_eq_one | Mathlib/RingTheory/Norm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨s, ⟨b⟩⟩ := hx | case h
R : Type u_1
S : Type u_2
T : Type u_3
inst✝⁷ : CommRing R
inst✝⁶ : Ring S
inst✝⁵ : Algebra R S
K : Type u_4
L : Type u_5
F : Type u_6
inst✝⁴ : Field K
inst✝³ : Field L
inst✝² : Field F
inst✝¹ : Algebra K L
inst✝ : Algebra K F
ι : Type w
x : L
hx : ∃ s, Nonempty (Basis { x_1 // x_1 ∈ s } K ↥K⟮x⟯)
⊢ IsIntegral K ... | case h.intro.intro
R : Type u_1
S : Type u_2
T : Type u_3
inst✝⁷ : CommRing R
inst✝⁶ : Ring S
inst✝⁵ : Algebra R S
K : Type u_4
L : Type u_5
F : Type u_6
inst✝⁴ : Field K
inst✝³ : Field L
inst✝² : Field F
inst✝¹ : Algebra K L
inst✝ : Algebra K F
ι : Type w
x : L
s : Finset ↥K⟮x⟯
b : Basis { x_1 // x_1 ∈ s } K ↥K⟮x⟯
⊢ I... | ((:c IsIntegral) (:fv _uniq.99697) (:fv _uniq.99700) ((:c EuclideanDomain.toCommRing) (:fv _uniq.99697) ((:c Field.toEuclideanDomain) (:fv _uniq.99697) (:fv _uniq.99706))) ((:c DivisionRing.toRing) (:fv _uniq.99700) ((:c Field.toDivisionRing) (:fv _uniq.99700) (:fv _uniq.99709))) (:fv _uniq.99799) (:fv _uniq.100691)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"T","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.99372))"},{"name":"inst✝⁶","sexp":"((:c Ring) (:fv _uniq.99375))"},{"name":"inst✝⁵","sexp":"((:c Algebra) (:fv _uniq.99372) (:fv _uniq.99375) ((:c C... | (:app (:c IsIntegral) (:arg :explicit 0 (:fv FV6)) (:arg :implicit-type 1 (:fv FV7)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV6))))) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV7))))) (:arg :instance 4 (:instance-of (:app (:c Algebra) (:arg :explicit 0 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.99372","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.99375","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"obtain","sourceEnd":8942,"sourceStart":8936,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":8946,"sourceStart":8943,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"s","sourceEnd":8... | [] | [{"source":"hx","source_end":8965,"source_start":8963,"syntax_kind":"ident"},{"source":"⟨s, ⟨b⟩⟩","source_end":8959,"source_start":8943,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.99372","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.99375","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 56 | 8 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6532cf10b517bea3ff4f29dacb2c1a6b09300f9a0b6a0676c87f864c43535e18 | e70f212e17f38070fa6f7799b714153b22bc014dad8028ebbd49ab47daefa609 | a413d6e39ed46b04c52aca8055585ce5a2c97803c36e2f3be886bbd1d6c01651 | 6aa290c5cce20989635e8e20829f2c3a03f77626f4cd098ac2c6124bb39714f0 |
cat-searcher/leandojo-benchmark-4-random | test | 3,292 | IntermediateField.AdjoinSimple.norm_gen_eq_one | Mathlib/RingTheory/Norm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine .of_mem_of_fg K⟮x⟯.<a>IntermediateField.toSubalgebra</a> ?_ x ?_ | case h.intro.intro
R : Type u_1
S : Type u_2
T : Type u_3
inst✝⁷ : CommRing R
inst✝⁶ : Ring S
inst✝⁵ : Algebra R S
K : Type u_4
L : Type u_5
F : Type u_6
inst✝⁴ : Field K
inst✝³ : Field L
inst✝² : Field F
inst✝¹ : Algebra K L
inst✝ : Algebra K F
ι : Type w
x : L
s : Finset ↥K⟮x⟯
b : Basis { x_1 // x_1 ∈ s } K ↥K⟮x⟯
⊢ I... | case h.intro.intro.refine_1
R : Type u_1
S : Type u_2
T : Type u_3
inst✝⁷ : CommRing R
inst✝⁶ : Ring S
inst✝⁵ : Algebra R S
K : Type u_4
L : Type u_5
F : Type u_6
inst✝⁴ : Field K
inst✝³ : Field L
inst✝² : Field F
inst✝¹ : Algebra K L
inst✝ : Algebra K F
ι : Type w
x : L
s : Finset ↥K⟮x⟯
b : Basis { x_1 // x_1 ∈ s } K ... | ((:c IsIntegral) (:fv _uniq.99697) (:fv _uniq.99700) ((:c EuclideanDomain.toCommRing) (:fv _uniq.99697) ((:c Field.toEuclideanDomain) (:fv _uniq.99697) (:fv _uniq.99706))) ((:c DivisionRing.toRing) (:fv _uniq.99700) ((:c Field.toDivisionRing) (:fv _uniq.99700) (:fv _uniq.99709))) (:fv _uniq.99799) (:fv _uniq.100691)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"T","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.99372))"},{"name":"inst✝⁶","sexp":"((:c Ring) (:fv _uniq.99375))"},{"name":"inst✝⁵","sexp":"((:c Algebra) (:fv _uniq.99372) (:fv _uniq.99375) ((:c C... | (:app (:c IsIntegral) (:arg :explicit 0 (:fv FV6)) (:arg :implicit-type 1 (:fv FV7)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV6))))) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV7))))) (:arg :instance 4 (:instance-of (:app (:c Algebra) (:arg :explicit 0 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.99372","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.99375","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":8974,"sourceStart":8968,"tag":"atom"},{"children":[{"children":[{"source":".","sourceEnd":8976,"sourceStart":8975,"tag":"atom"},{"source":"of_mem_of_fg","sourceEnd":8988,"sourceStart":8976,"tag":"identifier"}],"kind":"Lean.Parser.Term.dotIdent","source":".of_mem_of_fg","sourc... | [] | [{"source":".of_mem_of_fg K⟮x⟯.toSubalgebra ?_ x ?_","source_end":9018,"source_start":8975,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.99372","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.99375","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 56 | 9 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 57e340cdacfbbf1faa7799b2f187a16d633a2c020716c990a68904404ed1fcd6 | 6aa290c5cce20989635e8e20829f2c3a03f77626f4cd098ac2c6124bb39714f0 | e95da5aa9ce6755652231571d73e5c6a7e7adbb0a4dfe84448bbab7058555f0e | 4ab6f88ff29fbdb96d2b68350e243251c5169c4f929107292279b954cf9075f8 |
cat-searcher/leandojo-benchmark-4-random | test | 3,293 | IntermediateField.AdjoinSimple.norm_gen_eq_one | Mathlib/RingTheory/Norm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>Submodule.fg_iff_finiteDimensional</a> _).<a>Iff.mpr</a> (<a>FiniteDimensional.of_fintype_basis</a> b) | case h.intro.intro.refine_1
R : Type u_1
S : Type u_2
T : Type u_3
inst✝⁷ : CommRing R
inst✝⁶ : Ring S
inst✝⁵ : Algebra R S
K : Type u_4
L : Type u_5
F : Type u_6
inst✝⁴ : Field K
inst✝³ : Field L
inst✝² : Field F
inst✝¹ : Algebra K L
inst✝ : Algebra K F
ι : Type w
x : L
s : Finset ↥K⟮x⟯
b : Basis { x_1 // x_1 ∈ s } K ... | ((:c Submodule.FG) (:fv _uniq.99697) (:fv _uniq.99700) ((:c CommSemiring.toSemiring) (:fv _uniq.99697) ((:c CommRing.toCommSemiring) (:fv _uniq.99697) ((:c EuclideanDomain.toCommRing) (:fv _uniq.99697) ((:c Field.toEuclideanDomain) (:fv _uniq.99697) (:fv _uniq.99706))))) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"T","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.99372))"},{"name":"inst✝⁶","sexp":"((:c Ring) (:fv _uniq.99375))"},{"name":"inst✝⁵","sexp":"((:c Algebra) (:fv _uniq.99372) (:fv _uniq.99375) ((:c C... | (:app (:c Submodule.FG) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1 (:fv FV7)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV6))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV7))))) (:arg :instance 4 (:instance-of (:app (:c Module) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.99372","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.99375","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":9029,"sourceStart":9024,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":9031,"sourceStart":9030,"tag":"atom"},{"children":[{"name":"Submodule.fg_iff_finiteDimensional","semanticRole":"global","source":"Submo... | [] | [{"source":"(Submodule.fg_iff_finiteDimensional _).mpr (of_fintype_basis b)","source_end":9093,"source_start":9030,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.99372","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.99375","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 56 | 12 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b79d7b2328242b6bfd2ea7b4a14740f7fef6c594450ffb9b2ee3f714e64d23be | c81a52f2e181f35b679e47aa0cc1438cd71faed114f2dc7cefd3cc8ad84a72c3 | ee66177cca2ca826d7c081e7c636bdec871397384b6fdf9485ef8411cdec9b3f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,294 | IntermediateField.AdjoinSimple.norm_gen_eq_one | Mathlib/RingTheory/Norm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>IntermediateField.subset_adjoin</a> K _ (<a>Set.mem_singleton</a> x) | case h.intro.intro.refine_2
R : Type u_1
S : Type u_2
T : Type u_3
inst✝⁷ : CommRing R
inst✝⁶ : Ring S
inst✝⁵ : Algebra R S
K : Type u_4
L : Type u_5
F : Type u_6
inst✝⁴ : Field K
inst✝³ : Field L
inst✝² : Field F
inst✝¹ : Algebra K L
inst✝ : Algebra K F
ι : Type w
x : L
s : Finset ↥K⟮x⟯
b : Basis { x_1 // x_1 ∈ s } K ... | ((:c Membership.mem) (:fv _uniq.99700) ((:c Subalgebra) (:fv _uniq.99697) (:fv _uniq.99700) ((:c CommRing.toCommSemiring) (:fv _uniq.99697) ((:c EuclideanDomain.toCommRing) (:fv _uniq.99697) ((:c Field.toEuclideanDomain) (:fv _uniq.99697) (:fv _uniq.99706)))) ((:c Ring.toSemiring) (:fv _uniq.99700) ((:c DivisionRing.to... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"T","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.99372))"},{"name":"inst✝⁶","sexp":"((:c Ring) (:fv _uniq.99375))"},{"name":"inst✝⁵","sexp":"((:c Algebra) (:fv _uniq.99372) (:fv _uniq.99375) ((:c C... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV7)) (:arg :implicit-type 1 (:app (:c Subalgebra) (:arg :explicit 0 (:fv FV6)) (:arg :explicit 1 (:fv FV7)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV6))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.99372","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.99375","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":9104,"sourceStart":9099,"tag":"atom"},{"children":[{"name":"IntermediateField.subset_adjoin","semanticRole":"global","source":"IntermediateField.subset_adjoin","sourceEnd":9136,"sourceStart":9105,"tag":"identifier"},{"children":[{"context... | [] | [{"source":"IntermediateField.subset_adjoin K _ (Set.mem_singleton x)","source_end":9162,"source_start":9105,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.99372","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.99375","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 56 | 17 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 41a092c2429fc84072628c3c9d284efdc8578bbf40a213ecf0de26318a3e22a8 | 5ab2a374083facf22bd87a1996ecb3e1cb10606eb97c332fd884fd75b0e76a64 | 21e1a60cdedd4248e731b9bc5a5047f27278d3ca307d17f0063f7cb3553878e4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,295 | List.permutationsAux2_fst | Mathlib/Data/List/Permutation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>List.permutationsAux2</a>, permutationsAux2_fst t _ _ ys] | α : Type u_1
β : Type u_2
t : α
ts : List α
r : List β
y : α
ys : List α
f : List α → β
⊢ (permutationsAux2 t ts r (y :: ys) f).1 = y :: ys ++ ts | ((:c Eq) ((:c List) (:fv _uniq.9)) ((:c Prod.fst) ((:c List) (:fv _uniq.9)) ((:c List) (:fv _uniq.12)) ((:c List.permutationsAux2) (:fv _uniq.9) (:fv _uniq.12) (:fv _uniq.89) (:fv _uniq.90) (:fv _uniq.91) ((:c List.cons) (:fv _uniq.9) (:fv _uniq.174) (:fv _uniq.175)) (:fv _uniq.176))) ((:c HAppend.hAppend) ((:c List) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"t","sexp":"(:fv _uniq.9)"},{"name":"ts","sexp":"((:c List) (:fv _uniq.9))"},{"name":"r","sexp":"((:c List) (:fv _uniq.12))"},{"name":"y","sexp":"(:fv _uniq.9)"},{"name":"ys","sexp":"((:c List) (:fv _uniq.9))"},{"name":"f","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Prod.fst) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 2 (:app (:c List.permutationsAux2) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":explicit","context_in... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":2091,"sourceStart":2087,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"permutationsAux2","source_end":2109,"source_start":2093,"syntax_kind":"ident"},{"source":"permutationsAux2_fst t _ _ ys","source_end":2140,"source_start":2111,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.89",... | 6 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7da89fef4f62ce3034209ef158035605f4406cb82ce178d7d9a8c1a0446c4209 | 84be5c3ff0fbfa2a144ec93ac8c33e7f18c88f41c5088489ed8322ca6c01be15 | f1839650107b7e6a6cf8d00431fe06de7917598e344d849864532a2255a3f8dc | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,296 | Set.image_iUnion₂ | Mathlib/Data/Set/Lattice.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>Set.image_iUnion</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
ι₂ : Sort u_6
κ : ι → Sort u_7
κ₁ : ι → Sort u_8
κ₂ : ι → Sort u_9
κ' : ι' → Sort u_10
f : α → β
s : (i : ι) → κ i → Set α
⊢ f '' ⋃ i, ⋃ j, s i j = ⋃ i, ⋃ j, f '' s i j | ((:c Eq) ((:c Set) (:fv _uniq.146734)) ((:c Set.image) (:fv _uniq.146731) (:fv _uniq.146734) (:fv _uniq.146856) ((:c Set.iUnion) (:fv _uniq.146731) (:fv _uniq.146740) (:lambda i (:fv _uniq.146740) ((:c Set.iUnion) (:fv _uniq.146731) ((:fv _uniq.146751) 0) (:lambda j ((:fv _uniq.146751) 0) ((:fv _uniq.146857) 1 0)))))) ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort u_4)"},{"name":"ι'","sexp":"(:sort u_5)"},{"name":"ι₂","sexp":"(:sort u_6)"},{"name":"κ","sexp":"(:forall _ (:fv _uniq.146740) (:sort u_7))"},{"name":"κ₁","sexp":"(:forall ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Set.image) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV11)) (:arg :explicit 3 (:app (:c Set.iUnion) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.146731","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.146734","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":73116,"sourceStart":73109,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":73118,"sourceStart":73117,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source... | [] | [{"source":"image_iUnion","source_end":73130,"source_start":73118,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.146731","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.146734","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 596 | 2 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 99b293f9dc29083f5f5ac44b25d12b041ba532d6ba8fc05d23cd96bea8b8d9fa | 301501708ebba663dfdb51c188debfc50d8f8d2df0becf698fba8a4fc4c90a29 | e0141a22b622fe741337f487be2af5c84f2ea69014fc71678dd468d55b353243 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,297 | Int.preimage_Ioc | Mathlib/Algebra/Order/Floor.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext | F : Type u_1
α : Type u_2
β : Type u_3
inst✝¹ : LinearOrderedRing α
inst✝ : FloorRing α
z : ℤ
a✝ a b : α
⊢ Int.cast ⁻¹' Ioc a b = Ioc ⌊a⌋ ⌊b⌋ | case h
F : Type u_1
α : Type u_2
β : Type u_3
inst✝¹ : LinearOrderedRing α
inst✝ : FloorRing α
z : ℤ
a✝ a b : α
x✝ : ℤ
⊢ x✝ ∈ Int.cast ⁻¹' Ioc a b ↔ x✝ ∈ Ioc ⌊a⌋ ⌊b⌋ | ((:c Eq) ((:c Set) (:c Int)) ((:c Set.preimage) (:c Int) (:fv _uniq.259464) ((:c Int.cast) (:fv _uniq.259464) ((:c Ring.toIntCast) (:fv _uniq.259464) ((:c StrictOrderedRing.toRing) (:fv _uniq.259464) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.259464) (:fv _uniq.259470))))) ((:c Set.Ioc) (:fv _uniq.259464) (... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedRing) (:fv _uniq.259464))"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.259464) (:fv _uniq.259470))"},{"name":"z","sexp":"(:c Int)"},{"name":"a✝","se... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:c Int)))) (:arg :explicit 1 (:app (:c Set.preimage) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:app (:c Int.cast) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c IntCast) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.259461","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.259464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"ext","sourceEnd":51317,"sourceStart":51314,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":51317,"sourceStart":51314,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.259461","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.259464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 452 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 74aa545606f91b612181a3b598bc13bb7d15f2bff6a11b1470d72165b8d4aa02 | 2875f5826e302f60c76ed078f570db1ec63a7403cf8bb9146dec0813b6657c07 | a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de | 81234a0a1631b662818564de136d15a5d0dafc7c437c6f8635afc7d83d218e5d |
cat-searcher/leandojo-benchmark-4-random | test | 3,298 | Int.preimage_Ioc | Mathlib/Algebra/Order/Floor.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Int.floor_lt</a>, <a>Int.le_floor</a>] | case h
F : Type u_1
α : Type u_2
β : Type u_3
inst✝¹ : LinearOrderedRing α
inst✝ : FloorRing α
z : ℤ
a✝ a b : α
x✝ : ℤ
⊢ x✝ ∈ Int.cast ⁻¹' Ioc a b ↔ x✝ ∈ Ioc ⌊a⌋ ⌊b⌋ | ((:c Iff) ((:c Membership.mem) (:c Int) ((:c Set) (:c Int)) ((:c Set.instMembership) (:c Int)) (:fv _uniq.259828) ((:c Set.preimage) (:c Int) (:fv _uniq.259464) ((:c Int.cast) (:fv _uniq.259464) ((:c Ring.toIntCast) (:fv _uniq.259464) ((:c StrictOrderedRing.toRing) (:fv _uniq.259464) ((:c LinearOrderedRing.toStrictOrde... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedRing) (:fv _uniq.259464))"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.259464) (:fv _uniq.259470))"},{"name":"z","sexp":"(:c Int)"},{"name":"a✝","se... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Int)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Int)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Int))))))) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.259461","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.259464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":51324,"sourceStart":51320,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":51326,"sourceStart":51325,"tag":"a... | [] | [{"source":"floor_lt","source_end":51334,"source_start":51326,"syntax_kind":"ident"},{"source":"le_floor","source_end":51344,"source_start":51336,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.259461","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.259464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 452 | 5 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bce70bde6639b753e0ddef9a0e52e332e790f5ac0d34848f333427e03a689bcb | 81234a0a1631b662818564de136d15a5d0dafc7c437c6f8635afc7d83d218e5d | 9ca11bad634fa69cef4a3663aea6824854397cde67c34be8ac7e049e395a6a08 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,299 | EuclideanGeometry.two_zsmul_oangle_of_vectorSpan_eq | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>vectorSpan_pair</a>] at h₁₂₄₅ h₃₂₆₅ | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ p₆ : P
h₁₂₄₅ : vectorSpan ℝ {p₁, p₂} = vectorSpan ℝ {p₄, p₅}
h₃₂₆₅ : vectorSpan ℝ {p₃, p₂} = vectorSp... | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ p₆ : P
h₁₂₄₅ : Submodule.span ℝ {p₁ -ᵥ p₂} = Submodule.span ℝ {p₄ -ᵥ p₅}
h₃₂₆₅ : Submodule.span ℝ {p₃... | ((:c Eq) (:c Real.Angle) ((:c HSMul.hSMul) (:c Int) (:c Real.Angle) (:c Real.Angle) ((:c instHSMul) (:c Int) (:c Real.Angle) ((:c SubNegMonoid.SMulInt) (:c Real.Angle) ((:c AddGroup.toSubNegMonoid) (:c Real.Angle) ((:c NormedAddGroup.toAddGroup) (:c Real.Angle) ((:c NormedAddCommGroup.toNormedAddGroup) (:c Real.Angle) ... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.125976))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.125976) (:c Real.RCLike) (:fv _uniq.125982))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:c Real.Angle)) (:arg :implicit-type 2 (:c Real.Angle)) (:arg :instance 3 (:instance-of (:app (:c HSMul) (:arg :explicit 0 (:c Int)) (:arg :explicit 1 (:c Real.Angle)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125976","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125979","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"simp_rw","sourceEnd":16162,"sourceStart":16155,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16164,"sourceStart":16163,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"vectorSpan_... | [] | [{"source":"h₁₂₄₅","source_end":16197,"source_start":16184,"syntax_kind":"ident"},{"source":"h₃₂₆₅","source_end":16211,"source_start":16198,"syntax_kind":"ident"},{"source":"vectorSpan_pair","source_end":16179,"source_start":16164,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125976","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125979","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 78 | 4 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fa7b3ba5c4d5f164971246ecbec5883c7b67bb4b095d5bbdfc8a33a8eb82c023 | fd3a0ecd591a48348c3e02abfa41874dd31bf24e314252bbcd5c53ff44b79f8f | d772bc45e177cb6344a4df249e2299e81c40813d95ffb60c56ed9439651ec2dd | b5ec1aa740ce111c83423424dfe634445422b53805bfacdfd96ad59f9a3ef841 |
cat-searcher/leandojo-benchmark-4-random | test | 3,300 | EuclideanGeometry.two_zsmul_oangle_of_vectorSpan_eq | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact o.two_zsmul_oangle_of_span_eq_of_span_eq h₁₂₄₅ h₃₂₆₅ | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ p₆ : P
h₁₂₄₅ : Submodule.span ℝ {p₁ -ᵥ p₂} = Submodule.span ℝ {p₄ -ᵥ p₅}
h₃₂₆₅ : Submodule.span ℝ {p₃... | ((:c Eq) (:c Real.Angle) ((:c HSMul.hSMul) (:c Int) (:c Real.Angle) (:c Real.Angle) ((:c instHSMul) (:c Int) (:c Real.Angle) ((:c SubNegMonoid.SMulInt) (:c Real.Angle) ((:c AddGroup.toSubNegMonoid) (:c Real.Angle) ((:c NormedAddGroup.toAddGroup) (:c Real.Angle) ((:c NormedAddCommGroup.toNormedAddGroup) (:c Real.Angle) ... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.125976))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.125976) (:c Real.RCLike) (:fv _uniq.125982))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:c Real.Angle)) (:arg :implicit-type 2 (:c Real.Angle)) (:arg :instance 3 (:instance-of (:app (:c HSMul) (:arg :explicit 0 (:c Int)) (:arg :explicit 1 (:c Real.Angle)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125976","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125979","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"exact","sourceEnd":16219,"sourceStart":16214,"tag":"atom"},{"children":[{"source":"o.two_zsmul_oangle_of_span_eq_of_span_eq","sourceEnd":16260,"sourceStart":16220,"tag":"identifier"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"h₁₂₄₅","sourceEnd":16274,"sourceStart":16261,"ta... | [] | [{"source":"o.two_zsmul_oangle_of_span_eq_of_span_eq h₁₂₄₅ h₃₂₆₅","source_end":16288,"source_start":16220,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125976","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125979","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 78 | 7 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d7e2fc89e9ee5946efab6d3b8e696ad1515a442c43f30556f43ede401758f5ed | b5ec1aa740ce111c83423424dfe634445422b53805bfacdfd96ad59f9a3ef841 | e376fb9091340d9c2ed311504be18de979001a9062790b06d8c701bdda986cbe | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,301 | Matrix.frobenius_nnnorm_diagonal | Mathlib/Analysis/Matrix.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>Matrix.frobenius_nnnorm_def</a>, ← <a>Finset.sum_product'</a>, <a>Finset.univ_product_univ</a>, <a>PiLp.nnnorm_eq_of_L2</a>] | R : Type u_1
l : Type u_2
m : Type u_3
n : Type u_4
α : Type u_5
β : Type u_6
ι : Type u_7
inst✝⁶ : Fintype l
inst✝⁵ : Fintype m
inst✝⁴ : Fintype n
inst✝³ : Unique ι
inst✝² : SeminormedAddCommGroup α
inst✝¹ : SeminormedAddCommGroup β
inst✝ : DecidableEq n
v : n → α
⊢ ‖diagonal v‖₊ = ‖(WithLp.equiv 2 (n → α)).symm v‖₊ | R : Type u_1
l : Type u_2
m : Type u_3
n : Type u_4
α : Type u_5
β : Type u_6
ι : Type u_7
inst✝⁶ : Fintype l
inst✝⁵ : Fintype m
inst✝⁴ : Fintype n
inst✝³ : Unique ι
inst✝² : SeminormedAddCommGroup α
inst✝¹ : SeminormedAddCommGroup β
inst✝ : DecidableEq n
v : n → α
⊢ (∑ x : n × n, ‖diagonal v x.1 x.2‖₊ ^ 2) ^ (1 / 2) =... | ((:c Eq) (:c NNReal) ((:c NNNorm.nnnorm) ((:c Matrix) (:fv _uniq.249169) (:fv _uniq.249169) (:fv _uniq.249172)) ((:c SeminormedAddGroup.toNNNorm) ((:c Matrix) (:fv _uniq.249169) (:fv _uniq.249169) (:fv _uniq.249172)) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) ((:c Matrix) (:fv _uniq.249169) (:fv _uniq.249169) (:... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"l","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"(:sort (+ u_3 1))"},{"name":"n","sexp":"(:sort (+ u_4 1))"},{"name":"α","sexp":"(:sort (+ u_5 1))"},{"name":"β","sexp":"(:sort (+ u_6 1))"},{"name":"ι","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁶","sexp":"((:c Fintype) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c NNReal)) (:arg :explicit 1 (:app (:c NNNorm.nnnorm) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV4)))) (:arg :instance 1 (:instance-of (:app (:c NNNorm) (:arg :explicit 0 (:app (:c Matrix) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp_rw","sourceEnd":27494,"sourceStart":27487,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27496,"sourceStart":27495,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Matrix.frob... | [] | [{"source":"frobenius_nnnorm_def","source_end":27516,"source_start":27496,"syntax_kind":"ident"},{"source":"Finset.sum_product'","source_end":27541,"source_start":27522,"syntax_kind":"ident"},{"source":"Finset.univ_product_univ","source_end":27567,"source_start":27543,"syntax_kind":"ident"},{"source":"PiLp.nnnorm_eq_of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 186 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2e280d52f6102c2594cc4274bfd3ed7646af5a8ec1ab8b72fc40e1bbbea9ef00 | 32f509a6b7510248356680f63c9329391d1607af8bda0ae2657ad9be4fe703ef | fe4f7f2850c3c03619b65e6f694a803c4b0a71bbbf7876985e68efe4fb70d2b6 | 3559f1cb8c1ff3ba22f1d1d44bec8317abf19423a2ec40d3ef64141355911a81 |
cat-searcher/leandojo-benchmark-4-random | test | 3,302 | Matrix.frobenius_nnnorm_diagonal | Mathlib/Analysis/Matrix.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let s := (<a>Finset.univ</a> : <a>Finset</a> n).<a>Finset.map</a> ⟨fun i : n => (i, i), fun i j h => <a>congr_arg</a> <a>Prod.fst</a> h⟩ | R : Type u_1
l : Type u_2
m : Type u_3
n : Type u_4
α : Type u_5
β : Type u_6
ι : Type u_7
inst✝⁶ : Fintype l
inst✝⁵ : Fintype m
inst✝⁴ : Fintype n
inst✝³ : Unique ι
inst✝² : SeminormedAddCommGroup α
inst✝¹ : SeminormedAddCommGroup β
inst✝ : DecidableEq n
v : n → α
⊢ (∑ x : n × n, ‖diagonal v x.1 x.2‖₊ ^ 2) ^ (1 / 2) =... | R : Type u_1
l : Type u_2
m : Type u_3
n : Type u_4
α : Type u_5
β : Type u_6
ι : Type u_7
inst✝⁶ : Fintype l
inst✝⁵ : Fintype m
inst✝⁴ : Fintype n
inst✝³ : Unique ι
inst✝² : SeminormedAddCommGroup α
inst✝¹ : SeminormedAddCommGroup β
inst✝ : DecidableEq n
v : n → α
s : Finset (n × n) := Finset.map { toFun := fun i => (... | ((:c Eq) (:c NNReal) ((:c HPow.hPow) (:c NNReal) (:c Real) (:c NNReal) ((:c instHPow) (:c NNReal) (:c Real) (:c NNReal.instPowReal)) ((:c Finset.sum) ((:c Prod) (:fv _uniq.249169) (:fv _uniq.249169)) (:c NNReal) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:c NNReal) ((:c NonAssocSemiring.toNonUnitalNonAssocSemirin... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"l","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"(:sort (+ u_3 1))"},{"name":"n","sexp":"(:sort (+ u_4 1))"},{"name":"α","sexp":"(:sort (+ u_5 1))"},{"name":"β","sexp":"(:sort (+ u_6 1))"},{"name":"ι","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁶","sexp":"((:c Fintype) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c NNReal)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c NNReal)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c NNReal)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c NNReal)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"let","sourceEnd":27600,"sourceStart":27597,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"s","sourceEnd":27602,"sourceStart":27601,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{... | [] | [{"source":"(Finset.univ : Finset n).map ⟨fun i : n => (i, i), fun i j h => congr_arg Prod.fst h⟩","source_end":27695,"source_start":27606,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 186 | 10 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6940d670fdbae17964aaadd5972a1cce9ccaa94219d4492c1dbc284058779145 | 3559f1cb8c1ff3ba22f1d1d44bec8317abf19423a2ec40d3ef64141355911a81 | d20a290b62cd0f231b375f77def5d926a45290ac2ccc5e17770ddc43d6666b85 | dbbe3521929efe9a9afbf42e9ec7de22e794da37daf3caa64406c1beedf42669 |
cat-searcher/leandojo-benchmark-4-random | test | 3,303 | Matrix.frobenius_nnnorm_diagonal | Mathlib/Analysis/Matrix.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Finset.sum_subset</a> (<a>Finset.subset_univ</a> s) fun i _hi his => ?_] | R : Type u_1
l : Type u_2
m : Type u_3
n : Type u_4
α : Type u_5
β : Type u_6
ι : Type u_7
inst✝⁶ : Fintype l
inst✝⁵ : Fintype m
inst✝⁴ : Fintype n
inst✝³ : Unique ι
inst✝² : SeminormedAddCommGroup α
inst✝¹ : SeminormedAddCommGroup β
inst✝ : DecidableEq n
v : n → α
s : Finset (n × n) := Finset.map { toFun := fun i => (... | R : Type u_1
l : Type u_2
m : Type u_3
n : Type u_4
α : Type u_5
β : Type u_6
ι : Type u_7
inst✝⁶ : Fintype l
inst✝⁵ : Fintype m
inst✝⁴ : Fintype n
inst✝³ : Unique ι
inst✝² : SeminormedAddCommGroup α
inst✝¹ : SeminormedAddCommGroup β
inst✝ : DecidableEq n
v : n → α
s : Finset (n × n) := Finset.map { toFun := fun i => (... | ((:c Eq) (:c NNReal) ((:c HPow.hPow) (:c NNReal) (:c Real) (:c NNReal) ((:c instHPow) (:c NNReal) (:c Real) (:c NNReal.instPowReal)) ((:c Finset.sum) ((:c Prod) (:fv _uniq.249169) (:fv _uniq.249169)) (:c NNReal) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:c NNReal) ((:c NonAssocSemiring.toNonUnitalNonAssocSemirin... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"l","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"(:sort (+ u_3 1))"},{"name":"n","sexp":"(:sort (+ u_4 1))"},{"name":"α","sexp":"(:sort (+ u_5 1))"},{"name":"β","sexp":"(:sort (+ u_6 1))"},{"name":"ι","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁶","sexp":"((:c Fintype) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c NNReal)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c NNReal)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c NNReal)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c NNReal)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":27700,"sourceStart":27698,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27702,"sourceStart":27701,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":27705,"sourceSt... | [] | [{"source":"Finset.sum_subset (Finset.subset_univ s) fun i _hi his => ?_","source_end":27766,"source_start":27706,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 186 | 11 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 33893751532d59301767a13d4b373dd0b27387f1d051f28000e9c2e196763fd8 | dbbe3521929efe9a9afbf42e9ec7de22e794da37daf3caa64406c1beedf42669 | 6b70ce6959c71c8f05508eb276d076293ca62aa86fc241f5897be84a1a24c419 | a3e5859038acaed7dff5c4ee43150e0ca5764bd7c19ab1fde100741553310c4b |
cat-searcher/leandojo-benchmark-4-random | test | 3,304 | Matrix.frobenius_nnnorm_diagonal | Mathlib/Analysis/Matrix.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.sum_map</a>, <a>NNReal.sqrt_eq_rpow</a>] | R : Type u_1
l : Type u_2
m : Type u_3
n : Type u_4
α : Type u_5
β : Type u_6
ι : Type u_7
inst✝⁶ : Fintype l
inst✝⁵ : Fintype m
inst✝⁴ : Fintype n
inst✝³ : Unique ι
inst✝² : SeminormedAddCommGroup α
inst✝¹ : SeminormedAddCommGroup β
inst✝ : DecidableEq n
v : n → α
s : Finset (n × n) := Finset.map { toFun := fun i => (... | R : Type u_1
l : Type u_2
m : Type u_3
n : Type u_4
α : Type u_5
β : Type u_6
ι : Type u_7
inst✝⁶ : Fintype l
inst✝⁵ : Fintype m
inst✝⁴ : Fintype n
inst✝³ : Unique ι
inst✝² : SeminormedAddCommGroup α
inst✝¹ : SeminormedAddCommGroup β
inst✝ : DecidableEq n
v : n → α
s : Finset (n × n) := Finset.map { toFun := fun i => (... | ((:c Eq) (:c NNReal) ((:c HPow.hPow) (:c NNReal) (:c Real) (:c NNReal) ((:c instHPow) (:c NNReal) (:c Real) (:c NNReal.instPowReal)) ((:c Finset.sum) ((:c Prod) (:fv _uniq.249169) (:fv _uniq.249169)) (:c NNReal) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:c NNReal) ((:c NonAssocSemiring.toNonUnitalNonAssocSemirin... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"l","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"(:sort (+ u_3 1))"},{"name":"n","sexp":"(:sort (+ u_4 1))"},{"name":"α","sexp":"(:sort (+ u_5 1))"},{"name":"β","sexp":"(:sort (+ u_6 1))"},{"name":"ι","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁶","sexp":"((:c Fintype) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c NNReal)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c NNReal)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c NNReal)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c NNReal)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":27775,"sourceStart":27773,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27777,"sourceStart":27776,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.sum_map",... | [] | [{"source":"Finset.sum_map","source_end":27791,"source_start":27777,"syntax_kind":"ident"},{"source":"NNReal.sqrt_eq_rpow","source_end":27812,"source_start":27793,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 186 | 18 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2963bf2896cb21e0aae664cd387f275e2e048c557fad58b5a6baa2109f6fd711 | 66d8a459868d05beb8737bff8223f9d8db1e02d24f332743e6a143f48881831f | 39fea362b8e24a6090ed6bca0f7333c822df72baec2eb0619f57877323ea67d7 | e4947187713cbcf980a5ea18bd82c4e8608359df0cf82055f2b7451511d243ce |
cat-searcher/leandojo-benchmark-4-random | test | 3,305 | Matrix.frobenius_nnnorm_diagonal | Mathlib/Analysis/Matrix.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp | R : Type u_1
l : Type u_2
m : Type u_3
n : Type u_4
α : Type u_5
β : Type u_6
ι : Type u_7
inst✝⁶ : Fintype l
inst✝⁵ : Fintype m
inst✝⁴ : Fintype n
inst✝³ : Unique ι
inst✝² : SeminormedAddCommGroup α
inst✝¹ : SeminormedAddCommGroup β
inst✝ : DecidableEq n
v : n → α
s : Finset (n × n) := Finset.map { toFun := fun i => (... | R : Type u_1
l : Type u_2
m : Type u_3
n : Type u_4
α : Type u_5
β : Type u_6
ι : Type u_7
inst✝⁶ : Fintype l
inst✝⁵ : Fintype m
inst✝⁴ : Fintype n
inst✝³ : Unique ι
inst✝² : SeminormedAddCommGroup α
inst✝¹ : SeminormedAddCommGroup β
inst✝ : DecidableEq n
v : n → α
s : Finset (n × n) := Finset.map { toFun := fun i => (... | ((:c Eq) (:c NNReal) ((:c HPow.hPow) (:c NNReal) (:c Real) (:c NNReal) ((:c instHPow) (:c NNReal) (:c Real) (:c NNReal.instPowReal)) ((:c Finset.sum) (:fv _uniq.249169) (:c NNReal) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:c NNReal) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:c NNReal) ((:c Semiring.to... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"l","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"(:sort (+ u_3 1))"},{"name":"n","sexp":"(:sort (+ u_4 1))"},{"name":"α","sexp":"(:sort (+ u_5 1))"},{"name":"β","sexp":"(:sort (+ u_6 1))"},{"name":"ι","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁶","sexp":"((:c Fintype) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c NNReal)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c NNReal)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c NNReal)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c NNReal)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"dsimp","sourceEnd":27823,"sourceStart":27818,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"k... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 186 | 22 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1dac4f3369575d707a51d5d5ce6bec0acf5514b12a7788321e395a1c25b9c899 | e4947187713cbcf980a5ea18bd82c4e8608359df0cf82055f2b7451511d243ce | 7854eab90b5d1f0eed9d2f7f6b885100cc44bc732b41c876b3af083c01260845 | e705895800c62a65cc90104528abe3fbeeaaab0c88c241915f0fdbf5e1c76f45 |
cat-searcher/leandojo-benchmark-4-random | test | 3,306 | Matrix.frobenius_nnnorm_diagonal | Mathlib/Analysis/Matrix.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>Matrix.diagonal_apply_eq</a>, <a>NNReal.rpow_two</a>] | R : Type u_1
l : Type u_2
m : Type u_3
n : Type u_4
α : Type u_5
β : Type u_6
ι : Type u_7
inst✝⁶ : Fintype l
inst✝⁵ : Fintype m
inst✝⁴ : Fintype n
inst✝³ : Unique ι
inst✝² : SeminormedAddCommGroup α
inst✝¹ : SeminormedAddCommGroup β
inst✝ : DecidableEq n
v : n → α
s : Finset (n × n) := Finset.map { toFun := fun i => (... | ((:c Eq) (:c NNReal) ((:c HPow.hPow) (:c NNReal) (:c Real) (:c NNReal) ((:c instHPow) (:c NNReal) (:c Real) (:c NNReal.instPowReal)) ((:c Finset.sum) (:fv _uniq.249169) (:c NNReal) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:c NNReal) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:c NNReal) ((:c Semiring.to... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"l","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"(:sort (+ u_3 1))"},{"name":"n","sexp":"(:sort (+ u_4 1))"},{"name":"α","sexp":"(:sort (+ u_5 1))"},{"name":"β","sexp":"(:sort (+ u_6 1))"},{"name":"ι","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁶","sexp":"((:c Fintype) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c NNReal)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c NNReal)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c NNReal)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c NNReal)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp_rw","sourceEnd":27835,"sourceStart":27828,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27837,"sourceStart":27836,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Matrix.diag... | [] | [{"source":"diagonal_apply_eq","source_end":27854,"source_start":27837,"syntax_kind":"ident"},{"source":"NNReal.rpow_two","source_end":27871,"source_start":27856,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 186 | 23 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7d3f78a26d4b2f1f568edf0828a524a658758e5ab2879339ac44762a0c56d384 | e705895800c62a65cc90104528abe3fbeeaaab0c88c241915f0fdbf5e1c76f45 | 1cc21f68ae59bbbe643389b6f0f77b0dba34fa6930c76e8d36cf82dba8695030 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,307 | Matrix.frobenius_nnnorm_diagonal | Mathlib/Analysis/Matrix.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | suffices i.1 ≠ i.2 by rw [<a>Matrix.diagonal_apply_ne</a> _ this, <a>nnnorm_zero</a>, <a>NNReal.zero_rpow</a> <a>two_ne_zero</a>] | R : Type u_1
l : Type u_2
m : Type u_3
n : Type u_4
α : Type u_5
β : Type u_6
ι : Type u_7
inst✝⁶ : Fintype l
inst✝⁵ : Fintype m
inst✝⁴ : Fintype n
inst✝³ : Unique ι
inst✝² : SeminormedAddCommGroup α
inst✝¹ : SeminormedAddCommGroup β
inst✝ : DecidableEq n
v : n → α
s : Finset (n × n) := Finset.map { toFun := fun i => (... | R : Type u_1
l : Type u_2
m : Type u_3
n : Type u_4
α : Type u_5
β : Type u_6
ι : Type u_7
inst✝⁶ : Fintype l
inst✝⁵ : Fintype m
inst✝⁴ : Fintype n
inst✝³ : Unique ι
inst✝² : SeminormedAddCommGroup α
inst✝¹ : SeminormedAddCommGroup β
inst✝ : DecidableEq n
v : n → α
s : Finset (n × n) := Finset.map { toFun := fun i => (... | ((:c Eq) (:c NNReal) ((:c HPow.hPow) (:c NNReal) (:c Real) (:c NNReal) ((:c instHPow) (:c NNReal) (:c Real) (:c NNReal.instPowReal)) ((:c NNNorm.nnnorm) (:fv _uniq.249172) ((:c SeminormedAddGroup.toNNNorm) (:fv _uniq.249172) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) (:fv _uniq.249172) (:fv _uniq.249193))) ((:c ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"l","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"(:sort (+ u_3 1))"},{"name":"n","sexp":"(:sort (+ u_4 1))"},{"name":"α","sexp":"(:sort (+ u_5 1))"},{"name":"β","sexp":"(:sort (+ u_6 1))"},{"name":"ι","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁶","sexp":"((:c Fintype) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c NNReal)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c NNReal)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c NNReal)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c NNReal)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"suffices","sourceEnd":27886,"sourceStart":27878,"tag":"atom"},{"children":[{"children":[{"source":"","sourceEnd":27887,"sourceStart":27887,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":27887,"sourceStart":27887,"tag":"node"},{"children":[{"children":[{"contextIndex":17,"seman... | [] | [{"source":"i.1 ≠ i.2","source_end":27898,"source_start":27887,"syntax_kind":"«term_≠_»"},{"source":"diagonal_apply_ne _ this","source_end":27930,"source_start":27906,"syntax_kind":"Lean.Parser.Term.app"},{"source":"nnnorm_zero","source_end":27943,"source_start":27932,"syntax_kind":"ident"},{"source":"NNReal.zero_rpow ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 186 | 31 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0ce757b25eca65beb3fae022823efa48e02f3d1225629a5ab73d1c5673cf2318 | f298ca3af68bbcd6c9df33e96c50f8fd1b90b7cd750438f3d445a2a53a5de16c | 385cfa66fe08fbcd6c0c006ccd7ba43c1c24d910822f9f15bc560f4bce02a04c | dcc23ac5d2215b58f00c74083c3bbf380515aea070004fe8dfab0eb31ca0297c |
cat-searcher/leandojo-benchmark-4-random | test | 3,308 | Matrix.frobenius_nnnorm_diagonal | Mathlib/Analysis/Matrix.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro h | R : Type u_1
l : Type u_2
m : Type u_3
n : Type u_4
α : Type u_5
β : Type u_6
ι : Type u_7
inst✝⁶ : Fintype l
inst✝⁵ : Fintype m
inst✝⁴ : Fintype n
inst✝³ : Unique ι
inst✝² : SeminormedAddCommGroup α
inst✝¹ : SeminormedAddCommGroup β
inst✝ : DecidableEq n
v : n → α
s : Finset (n × n) := Finset.map { toFun := fun i => (... | R : Type u_1
l : Type u_2
m : Type u_3
n : Type u_4
α : Type u_5
β : Type u_6
ι : Type u_7
inst✝⁶ : Fintype l
inst✝⁵ : Fintype m
inst✝⁴ : Fintype n
inst✝³ : Unique ι
inst✝² : SeminormedAddCommGroup α
inst✝¹ : SeminormedAddCommGroup β
inst✝ : DecidableEq n
v : n → α
s : Finset (n × n) := Finset.map { toFun := fun i => (... | ((:c Ne) (:fv _uniq.249169) ((:c Prod.fst) (:fv _uniq.249169) (:fv _uniq.249169) (:fv _uniq.252071)) ((:c Prod.snd) (:fv _uniq.249169) (:fv _uniq.249169) (:fv _uniq.252071))) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"l","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"(:sort (+ u_3 1))"},{"name":"n","sexp":"(:sort (+ u_4 1))"},{"name":"α","sexp":"(:sort (+ u_5 1))"},{"name":"β","sexp":"(:sort (+ u_6 1))"},{"name":"ι","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁶","sexp":"((:c Fintype) ... | (:app (:c Ne) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c Prod.fst) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:fv FV3)) (:arg :explicit 2 (:fv FV17)))) (:arg :explicit 2 (:app (:c Prod.snd) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:fv FV3)) (:arg :explicit 2 (:fv FV17)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"intro","sourceEnd":27984,"sourceStart":27979,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":27986,"sourceStart":27985,"tag":"identifier"}],"kind":"null","source":"h","sourceEnd":27986,"sourceStart":27985,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"h","source_end":27986,"source_start":27985,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 186 | 39 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8e669adb8ad7a1082871b8372954c3df272e72c3921387868305934f9d67829a | dcc23ac5d2215b58f00c74083c3bbf380515aea070004fe8dfab0eb31ca0297c | 5cf42e5c5e9faf9804f4b8005e32168f3a46b38347377087a457c72b727740cb | 3e3f57d6c7b0134991266ca0eaf76fb32189ae4b4398278deae0642e475eadf3 |
cat-searcher/leandojo-benchmark-4-random | test | 3,309 | Matrix.frobenius_nnnorm_diagonal | Mathlib/Analysis/Matrix.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact Finset.mem_map.not.mp his ⟨i.1, <a>Finset.mem_univ</a> _, <a>Prod.ext</a> <a>rfl</a> h⟩ | R : Type u_1
l : Type u_2
m : Type u_3
n : Type u_4
α : Type u_5
β : Type u_6
ι : Type u_7
inst✝⁶ : Fintype l
inst✝⁵ : Fintype m
inst✝⁴ : Fintype n
inst✝³ : Unique ι
inst✝² : SeminormedAddCommGroup α
inst✝¹ : SeminormedAddCommGroup β
inst✝ : DecidableEq n
v : n → α
s : Finset (n × n) := Finset.map { toFun := fun i => (... | (:c False) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"l","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"(:sort (+ u_3 1))"},{"name":"n","sexp":"(:sort (+ u_4 1))"},{"name":"α","sexp":"(:sort (+ u_5 1))"},{"name":"β","sexp":"(:sort (+ u_6 1))"},{"name":"ι","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁶","sexp":"((:c Fintype) ... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":27996,"sourceStart":27991,"tag":"atom"},{"children":[{"source":"Finset.mem_map.not.mp","sourceEnd":28018,"sourceStart":27997,"tag":"identifier"},{"children":[{"contextIndex":19,"semanticRole":"local","source":"his","sourceEnd":28022,"sourceStart":28019,"tag":"identifier"},{"ch... | [] | [{"source":"Finset.mem_map.not.mp his ⟨i.1, Finset.mem_univ _, Prod.ext rfl h⟩","source_end":28067,"source_start":27997,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 186 | 40 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c283a382536ed6cb3782f6fd54a0947ef878a98c01a4affc5dcc5559156d2f3c | 3e3f57d6c7b0134991266ca0eaf76fb32189ae4b4398278deae0642e475eadf3 | bc258a815ea6a4088c78eeb8db5e86124868bee09fd0e49385c52242d4afcfc5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,310 | Matrix.frobenius_nnnorm_diagonal | Mathlib/Analysis/Matrix.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Matrix.diagonal_apply_ne</a> _ this, <a>nnnorm_zero</a>, <a>NNReal.zero_rpow</a> <a>two_ne_zero</a>] | R : Type u_1
l : Type u_2
m : Type u_3
n : Type u_4
α : Type u_5
β : Type u_6
ι : Type u_7
inst✝⁶ : Fintype l
inst✝⁵ : Fintype m
inst✝⁴ : Fintype n
inst✝³ : Unique ι
inst✝² : SeminormedAddCommGroup α
inst✝¹ : SeminormedAddCommGroup β
inst✝ : DecidableEq n
v : n → α
s : Finset (n × n) := Finset.map { toFun := fun i => (... | ((:c Eq) (:c NNReal) ((:c HPow.hPow) (:c NNReal) (:c Real) (:c NNReal) ((:c instHPow) (:c NNReal) (:c Real) (:c NNReal.instPowReal)) ((:c NNNorm.nnnorm) (:fv _uniq.249172) ((:c SeminormedAddGroup.toNNNorm) (:fv _uniq.249172) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) (:fv _uniq.249172) (:fv _uniq.249193))) ((:c ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"l","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"(:sort (+ u_3 1))"},{"name":"n","sexp":"(:sort (+ u_4 1))"},{"name":"α","sexp":"(:sort (+ u_5 1))"},{"name":"β","sexp":"(:sort (+ u_6 1))"},{"name":"ι","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁶","sexp":"((:c Fintype) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c NNReal)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c NNReal)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c NNReal)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c NNReal)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":27904,"sourceStart":27902,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27906,"sourceStart":27905,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"diagonal_apply_ne _ this","source_end":27930,"source_start":27906,"syntax_kind":"Lean.Parser.Term.app"},{"source":"nnnorm_zero","source_end":27943,"source_start":27932,"syntax_kind":"ident"},{"source":"NNReal.zero_rpow two_ne_zero","source_end":27973,"source_start":27945,"syntax_kind":"Lean.Parser.Term.app"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.249160","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.249163","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 186 | 32 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6d14daa59cac8aff48f907f2d8cf406f1d203c1b69301cb42aed3c84f21fe66f | 48c574237d3091d5494b388d57c900a0183af01436b93fc0e75373e1068d33f4 | d682fbe94285846ed822587e2e91900a6e9764bcb46eb54ad9c37f4061a62b49 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,311 | LieModule.Weight.ext_iff | Mathlib/Algebra/Lie/Weights/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | aesop | K : Type u_1
R : Type u_2
L : Type u_3
M : Type u_4
inst✝⁷ : CommRing R
inst✝⁶ : LieRing L
inst✝⁵ : LieAlgebra R L
inst✝⁴ : LieAlgebra.IsNilpotent R L
inst✝³ : AddCommGroup M
inst✝² : Module R M
inst✝¹ : LieRingModule L M
inst✝ : LieModule R L M
χ₁ χ₂ : Weight R L M
⊢ ⇑χ₁ = ⇑χ₂ ↔ χ₁ = χ₂ | ((:c Iff) ((:c Eq) (:forall a (:fv _uniq.118607) (:fv _uniq.118604)) ((:c DFunLike.coe) ((:c LieModule.Weight) (:fv _uniq.118604) (:fv _uniq.118607) (:fv _uniq.118610) (:fv _uniq.118613) (:fv _uniq.118616) (:fv _uniq.118633) (:fv _uniq.118658) (:fv _uniq.118661) (:fv _uniq.119273) (:fv _uniq.119287) (:fv _uniq.119338))... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.118604))"},{"name":"inst✝⁶","sexp":"((:c LieRing) (:fv _uniq.118607))"},{"name":"inst✝⁵","sexp":"((:c LieAlg... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:forall a :explicit (:fv FV2) (:fv FV1))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LieModule.Weight) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :instance 3 (:instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.118601","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.118604","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"aesop","sourceEnd":9973,"sourceStart":9968,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Aesop.Frontend.Parser.aesopTactic","source":"aesop","sourceEnd":9973,"sourceStart":9968,"tag":"node"}],"kind":"null","source":"aesop","s... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.118601","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.118604","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 26 | 2 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5c7ae315ac5d222af7dd4f69deecd63516d6606b512e92a7b6131aed0c835ead | 31e13445d59eb18dcf3ae9316e2ff91a1d5aca140cd6c3517a91076c137e191a | bf61abd9c8c94e02103733c96be27852844483acbf580158f224257e620356a8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,312 | NoZeroSMulDivisors.trans | Mathlib/Algebra/Algebra/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨fun {r m} h => ?_⟩ | R✝ : Type u_1
inst✝²⁰ : CommSemiring R✝
A✝ : Type u_2
inst✝¹⁹ : Semiring A✝
inst✝¹⁸ : Algebra R✝ A✝
M✝ : Type u_3
inst✝¹⁷ : AddCommMonoid M✝
inst✝¹⁶ : Module A✝ M✝
inst✝¹⁵ : Module R✝ M✝
inst✝¹⁴ : IsScalarTower R✝ A✝ M✝
N : Type u_4
inst✝¹³ : AddCommMonoid N
inst✝¹² : Module A✝ N
inst✝¹¹ : Module R✝ N
inst✝¹⁰ : IsScala... | R✝ : Type u_1
inst✝²⁰ : CommSemiring R✝
A✝ : Type u_2
inst✝¹⁹ : Semiring A✝
inst✝¹⁸ : Algebra R✝ A✝
M✝ : Type u_3
inst✝¹⁷ : AddCommMonoid M✝
inst✝¹⁶ : Module A✝ M✝
inst✝¹⁵ : Module R✝ M✝
inst✝¹⁴ : IsScalarTower R✝ A✝ M✝
N : Type u_4
inst✝¹³ : AddCommMonoid N
inst✝¹² : Module A✝ N
inst✝¹¹ : Module R✝ N
inst✝¹⁰ : IsScala... | ((:c NoZeroSMulDivisors) (:fv _uniq.135884) (:fv _uniq.135886) ((:c CommMonoidWithZero.toZero) (:fv _uniq.135884) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.135884) ((:c CommRing.toCommSemiring) (:fv _uniq.135884) (:fv _uniq.135887)))) ((:c NegZeroClass.toZero) (:fv _uniq.135886) ((:c SubNegZeroMonoid.toNegZero... | [{"name":"R✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²⁰","sexp":"((:c CommSemiring) (:fv _uniq.125284))"},{"name":"A✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁹","sexp":"((:c Semiring) (:fv _uniq.125290))"},{"name":"inst✝¹⁸","sexp":"((:c Algebra) (:fv _uniq.125284) (:fv _uniq.125290) (:fv _uniq.125287) (:fv _uniq... | (:app (:c NoZeroSMulDivisors) (:arg :explicit 0 (:fv FV16)) (:arg :explicit 1 (:fv FV18)) (:arg :instance 2 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:fv FV16))))) (:arg :instance 3 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:fv FV18))))) (:arg :instance 4 (:instance-of (:app (:c SMul) (:arg :explicit 0 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125284","is_instance":false,"is_let":false,"name":"R✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.125287","is_instance":true,"is_let":false,"name":"inst✝²⁰","sexp":"(:app (:c CommSemiring) (:arg... | {"children":[{"source":"refine","sourceEnd":16000,"sourceStart":15994,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":16004,"sourceStart":16001,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":16007,"sourceStart":16004,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"{","sourceEnd... | [] | [{"source":"⟨fun {r m} h => ?_⟩","source_end":16024,"source_start":16001,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125284","is_instance":false,"is_let":false,"user_name":"R✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.125287","is_instance":true,"is_let":false,"user_name":"inst✝²⁰"},{"binder_role":":explicit","context_index":2,"in... | 150 | 4 | exact | true | 1 | 28 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ab1f3d5ed944388129c4a84c71ead2ca127238ad915a0bcffd0c44423c315917 | e6010f52950eca554e63d1ffddbaa129defe652d2274256c9b0eb958b6886b9b | a607deda97cec399039e657b98a7e9ea8bfa32672586cdde9d47784d337ad99c | c582ade33a31b3400ca5c0e8958d2a3432d792db2da43f4dc6634f8d694b7a89 |
cat-searcher/leandojo-benchmark-4-random | test | 3,313 | NoZeroSMulDivisors.trans | Mathlib/Algebra/Algebra/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>algebra_compatible_smul</a> A r m] at h | R✝ : Type u_1
inst✝²⁰ : CommSemiring R✝
A✝ : Type u_2
inst✝¹⁹ : Semiring A✝
inst✝¹⁸ : Algebra R✝ A✝
M✝ : Type u_3
inst✝¹⁷ : AddCommMonoid M✝
inst✝¹⁶ : Module A✝ M✝
inst✝¹⁵ : Module R✝ M✝
inst✝¹⁴ : IsScalarTower R✝ A✝ M✝
N : Type u_4
inst✝¹³ : AddCommMonoid N
inst✝¹² : Module A✝ N
inst✝¹¹ : Module R✝ N
inst✝¹⁰ : IsScala... | R✝ : Type u_1
inst✝²⁰ : CommSemiring R✝
A✝ : Type u_2
inst✝¹⁹ : Semiring A✝
inst✝¹⁸ : Algebra R✝ A✝
M✝ : Type u_3
inst✝¹⁷ : AddCommMonoid M✝
inst✝¹⁶ : Module A✝ M✝
inst✝¹⁵ : Module R✝ M✝
inst✝¹⁴ : IsScalarTower R✝ A✝ M✝
N : Type u_4
inst✝¹³ : AddCommMonoid N
inst✝¹² : Module A✝ N
inst✝¹¹ : Module R✝ N
inst✝¹⁰ : IsScala... | ((:c Or) ((:c Eq) (:fv _uniq.135884) (:fv _uniq.136144) ((:c OfNat.ofNat) (:fv _uniq.135884) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.135884) ((:c CommMonoidWithZero.toZero) (:fv _uniq.135884) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.135884) ((:c CommRing.toCommSemiring) (:fv _uniq.135884) (:fv _uniq.135887)))... | [{"name":"R✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²⁰","sexp":"((:c CommSemiring) (:fv _uniq.125284))"},{"name":"A✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁹","sexp":"((:c Semiring) (:fv _uniq.125290))"},{"name":"inst✝¹⁸","sexp":"((:c Algebra) (:fv _uniq.125284) (:fv _uniq.125290) (:fv _uniq.125287) (:fv _uniq... | (:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV16)) (:arg :explicit 1 (:fv FV29)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV16)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV16)) (:arg :explicit 1 (:lit 0)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125284","is_instance":false,"is_let":false,"name":"R✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.125287","is_instance":true,"is_let":false,"name":"inst✝²⁰","sexp":"(:app (:c CommSemiring) (:arg... | {"children":[{"source":"rw","sourceEnd":16029,"sourceStart":16027,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16031,"sourceStart":16030,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"alg... | [] | [{"source":"h","source_end":16066,"source_start":16065,"syntax_kind":"ident"},{"source":"algebra_compatible_smul A r m","source_end":16060,"source_start":16031,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125284","is_instance":false,"is_let":false,"user_name":"R✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.125287","is_instance":true,"is_let":false,"user_name":"inst✝²⁰"},{"binder_role":":explicit","context_index":2,"in... | 150 | 5 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bb612f2c72a1d19ac28bf954e53b9d5ddfda104270b90b6b1046be152b533b14 | c582ade33a31b3400ca5c0e8958d2a3432d792db2da43f4dc6634f8d694b7a89 | 9eb06ba17f8e3e03cfca0280cbd6d93ac8a87949c0a9894207eca77f6d4381bf | 1809e2c8ae6455a50c312f7bd31a1960d3b355ecf9a366237fd948fefa6bfea1 |
cat-searcher/leandojo-benchmark-4-random | test | 3,314 | NoZeroSMulDivisors.trans | Mathlib/Algebra/Algebra/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases' <a>smul_eq_zero</a>.1 h with H H | R✝ : Type u_1
inst✝²⁰ : CommSemiring R✝
A✝ : Type u_2
inst✝¹⁹ : Semiring A✝
inst✝¹⁸ : Algebra R✝ A✝
M✝ : Type u_3
inst✝¹⁷ : AddCommMonoid M✝
inst✝¹⁶ : Module A✝ M✝
inst✝¹⁵ : Module R✝ M✝
inst✝¹⁴ : IsScalarTower R✝ A✝ M✝
N : Type u_4
inst✝¹³ : AddCommMonoid N
inst✝¹² : Module A✝ N
inst✝¹¹ : Module R✝ N
inst✝¹⁰ : IsScala... | case inl
R✝ : Type u_1
inst✝²⁰ : CommSemiring R✝
A✝ : Type u_2
inst✝¹⁹ : Semiring A✝
inst✝¹⁸ : Algebra R✝ A✝
M✝ : Type u_3
inst✝¹⁷ : AddCommMonoid M✝
inst✝¹⁶ : Module A✝ M✝
inst✝¹⁵ : Module R✝ M✝
inst✝¹⁴ : IsScalarTower R✝ A✝ M✝
N : Type u_4
inst✝¹³ : AddCommMonoid N
inst✝¹² : Module A✝ N
inst✝¹¹ : Module R✝ N
inst✝¹⁰ ... | ((:c Or) ((:c Eq) (:fv _uniq.135884) (:fv _uniq.136144) ((:c OfNat.ofNat) (:fv _uniq.135884) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.135884) ((:c CommMonoidWithZero.toZero) (:fv _uniq.135884) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.135884) ((:c CommRing.toCommSemiring) (:fv _uniq.135884) (:fv _uniq.135887)))... | [{"name":"R✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²⁰","sexp":"((:c CommSemiring) (:fv _uniq.125284))"},{"name":"A✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁹","sexp":"((:c Semiring) (:fv _uniq.125290))"},{"name":"inst✝¹⁸","sexp":"((:c Algebra) (:fv _uniq.125284) (:fv _uniq.125290) (:fv _uniq.125287) (:fv _uniq... | (:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV16)) (:arg :explicit 1 (:fv FV29)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV16)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV16)) (:arg :explicit 1 (:lit 0)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125284","is_instance":false,"is_let":false,"name":"R✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.125287","is_instance":true,"is_let":false,"name":"inst✝²⁰","sexp":"(:app (:c CommSemiring) (:arg... | {"children":[{"source":"cases'","sourceEnd":16075,"sourceStart":16069,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"name":"smul_eq_zero","semanticRole":"global","source":"smul_eq_zero","sourceEnd":16088,"sourceStart":16076,"tag":"identifier"},... | [] | [{"source":"smul_eq_zero.1 h","source_end":16092,"source_start":16076,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125284","is_instance":false,"is_let":false,"user_name":"R✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.125287","is_instance":true,"is_let":false,"user_name":"inst✝²⁰"},{"binder_role":":explicit","context_index":2,"in... | 150 | 8 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 354d323af11d786e85f8e46a6333d17819756e757c0131907eca8b6b56bcd928 | 1809e2c8ae6455a50c312f7bd31a1960d3b355ecf9a366237fd948fefa6bfea1 | 86f609fb647b129b61024652d95b6f4503ba0e0de51bac01f9307a051a2db7cc | aa39f6bd0941618fc22893a8cf2686d6050b45b12db69ec383dbdf6384544bac |
cat-searcher/leandojo-benchmark-4-random | test | 3,315 | NoZeroSMulDivisors.trans | Mathlib/Algebra/Algebra/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>Function.Injective</a> (<a>algebraMap</a> R A) := <a>NoZeroSMulDivisors.iff_algebraMap_injective</a>.1 <a>inferInstance</a> | case inl
R✝ : Type u_1
inst✝²⁰ : CommSemiring R✝
A✝ : Type u_2
inst✝¹⁹ : Semiring A✝
inst✝¹⁸ : Algebra R✝ A✝
M✝ : Type u_3
inst✝¹⁷ : AddCommMonoid M✝
inst✝¹⁶ : Module A✝ M✝
inst✝¹⁵ : Module R✝ M✝
inst✝¹⁴ : IsScalarTower R✝ A✝ M✝
N : Type u_4
inst✝¹³ : AddCommMonoid N
inst✝¹² : Module A✝ N
inst✝¹¹ : Module R✝ N
inst✝¹⁰ ... | case inl
R✝ : Type u_1
inst✝²⁰ : CommSemiring R✝
A✝ : Type u_2
inst✝¹⁹ : Semiring A✝
inst✝¹⁸ : Algebra R✝ A✝
M✝ : Type u_3
inst✝¹⁷ : AddCommMonoid M✝
inst✝¹⁶ : Module A✝ M✝
inst✝¹⁵ : Module R✝ M✝
inst✝¹⁴ : IsScalarTower R✝ A✝ M✝
N : Type u_4
inst✝¹³ : AddCommMonoid N
inst✝¹² : Module A✝ N
inst✝¹¹ : Module R✝ N
inst✝¹⁰ ... | ((:c Or) ((:c Eq) (:fv _uniq.135884) (:fv _uniq.136144) ((:c OfNat.ofNat) (:fv _uniq.135884) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.135884) ((:c CommMonoidWithZero.toZero) (:fv _uniq.135884) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.135884) ((:c CommRing.toCommSemiring) (:fv _uniq.135884) (:fv _uniq.135887)))... | [{"name":"R✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²⁰","sexp":"((:c CommSemiring) (:fv _uniq.125284))"},{"name":"A✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁹","sexp":"((:c Semiring) (:fv _uniq.125290))"},{"name":"inst✝¹⁸","sexp":"((:c Algebra) (:fv _uniq.125284) (:fv _uniq.125290) (:fv _uniq.125287) (:fv _uniq... | (:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV16)) (:arg :explicit 1 (:fv FV29)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV16)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV16)) (:arg :explicit 1 (:lit 0)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125284","is_instance":false,"is_let":false,"name":"R✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.125287","is_instance":true,"is_let":false,"name":"inst✝²⁰","sexp":"(:app (:c CommSemiring) (:arg... | {"children":[{"source":"have","sourceEnd":16111,"sourceStart":16107,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":16112,"sourceStart":16112,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":16112,"sourceStart":16112,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"Function.Injective (algebraMap R A)","source_end":16149,"source_start":16114,"syntax_kind":"Lean.Parser.Term.app"},{"source":"NoZeroSMulDivisors.iff_algebraMap_injective.1 inferInstance","source_end":16218,"source_start":16159,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125284","is_instance":false,"is_let":false,"user_name":"R✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.125287","is_instance":true,"is_let":false,"user_name":"inst✝²⁰"},{"binder_role":":explicit","context_index":2,"in... | 150 | 13 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ae2b9609a5e33fac0a9fc16ced0a4d5a81e518844afaad77c9ba5f1f0d5334a6 | a6b229b5776859b0374ce81455b3a78b071fad51d102a4001dae7a5c8258f7b9 | 5471e5840ac805f9e4015ebed1772cae0f200e006731e4b6e0251895c8319f45 | 27ce802d1d0a1c3b23a642617bb3fd7215c3c8ec4e0ded8552f9fb5a0b9101ba |
cat-searcher/leandojo-benchmark-4-random | test | 3,316 | NoZeroSMulDivisors.trans | Mathlib/Algebra/Algebra/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | left | case inl
R✝ : Type u_1
inst✝²⁰ : CommSemiring R✝
A✝ : Type u_2
inst✝¹⁹ : Semiring A✝
inst✝¹⁸ : Algebra R✝ A✝
M✝ : Type u_3
inst✝¹⁷ : AddCommMonoid M✝
inst✝¹⁶ : Module A✝ M✝
inst✝¹⁵ : Module R✝ M✝
inst✝¹⁴ : IsScalarTower R✝ A✝ M✝
N : Type u_4
inst✝¹³ : AddCommMonoid N
inst✝¹² : Module A✝ N
inst✝¹¹ : Module R✝ N
inst✝¹⁰ ... | case inl.h
R✝ : Type u_1
inst✝²⁰ : CommSemiring R✝
A✝ : Type u_2
inst✝¹⁹ : Semiring A✝
inst✝¹⁸ : Algebra R✝ A✝
M✝ : Type u_3
inst✝¹⁷ : AddCommMonoid M✝
inst✝¹⁶ : Module A✝ M✝
inst✝¹⁵ : Module R✝ M✝
inst✝¹⁴ : IsScalarTower R✝ A✝ M✝
N : Type u_4
inst✝¹³ : AddCommMonoid N
inst✝¹² : Module A✝ N
inst✝¹¹ : Module R✝ N
inst✝¹... | ((:c Or) ((:c Eq) (:fv _uniq.135884) (:fv _uniq.136144) ((:c OfNat.ofNat) (:fv _uniq.135884) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.135884) ((:c CommMonoidWithZero.toZero) (:fv _uniq.135884) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.135884) ((:c CommRing.toCommSemiring) (:fv _uniq.135884) (:fv _uniq.135887)))... | [{"name":"R✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²⁰","sexp":"((:c CommSemiring) (:fv _uniq.125284))"},{"name":"A✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁹","sexp":"((:c Semiring) (:fv _uniq.125290))"},{"name":"inst✝¹⁸","sexp":"((:c Algebra) (:fv _uniq.125284) (:fv _uniq.125290) (:fv _uniq.125287) (:fv _uniq... | (:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV16)) (:arg :explicit 1 (:fv FV29)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV16)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV16)) (:arg :explicit 1 (:lit 0)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125284","is_instance":false,"is_let":false,"name":"R✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.125287","is_instance":true,"is_let":false,"name":"inst✝²⁰","sexp":"(:app (:c CommSemiring) (:arg... | {"children":[{"source":"left","sourceEnd":16227,"sourceStart":16223,"tag":"atom"}],"kind":"Lean.Parser.Tactic.left","source":"left","sourceEnd":16227,"sourceStart":16223,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125284","is_instance":false,"is_let":false,"user_name":"R✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.125287","is_instance":true,"is_let":false,"user_name":"inst✝²⁰"},{"binder_role":":explicit","context_index":2,"in... | 150 | 14 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d862b0419c7b611afb9aebb6da2b53bd21e59d9902f22e09e35e2f1036ef7641 | 27ce802d1d0a1c3b23a642617bb3fd7215c3c8ec4e0ded8552f9fb5a0b9101ba | 360f84035942243c6a36537ae2f8673485e6c04455a0a85a0db19690f2541480 | 9f6b9c7d190620a3f85e10167ee8dd54d10b6e057076d7625adfd9f717886691 |
cat-searcher/leandojo-benchmark-4-random | test | 3,317 | NoZeroSMulDivisors.trans | Mathlib/Algebra/Algebra/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>injective_iff_map_eq_zero</a> _).1 this _ H | case inl.h
R✝ : Type u_1
inst✝²⁰ : CommSemiring R✝
A✝ : Type u_2
inst✝¹⁹ : Semiring A✝
inst✝¹⁸ : Algebra R✝ A✝
M✝ : Type u_3
inst✝¹⁷ : AddCommMonoid M✝
inst✝¹⁶ : Module A✝ M✝
inst✝¹⁵ : Module R✝ M✝
inst✝¹⁴ : IsScalarTower R✝ A✝ M✝
N : Type u_4
inst✝¹³ : AddCommMonoid N
inst✝¹² : Module A✝ N
inst✝¹¹ : Module R✝ N
inst✝¹... | ((:c Eq) (:fv _uniq.135884) (:fv _uniq.136144) ((:c OfNat.ofNat) (:fv _uniq.135884) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.135884) ((:c CommMonoidWithZero.toZero) (:fv _uniq.135884) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.135884) ((:c CommRing.toCommSemiring) (:fv _uniq.135884) (:fv _uniq.135887))))))) | [{"name":"R✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²⁰","sexp":"((:c CommSemiring) (:fv _uniq.125284))"},{"name":"A✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁹","sexp":"((:c Semiring) (:fv _uniq.125290))"},{"name":"inst✝¹⁸","sexp":"((:c Algebra) (:fv _uniq.125284) (:fv _uniq.125290) (:fv _uniq.125287) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV16)) (:arg :explicit 1 (:fv FV29)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV16)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV16)) (:arg :explicit 1 (:lit 0)))))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125284","is_instance":false,"is_let":false,"name":"R✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.125287","is_instance":true,"is_let":false,"name":"inst✝²⁰","sexp":"(:app (:c CommSemiring) (:arg... | {"children":[{"source":"exact","sourceEnd":16237,"sourceStart":16232,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":16239,"sourceStart":16238,"tag":"atom"},{"children":[{"name":"injective_iff_map_eq_zero","semanticRole":"global","source":"injective_iff_map_eq_zero","sourceEnd":16264,"sou... | [] | [{"source":"(injective_iff_map_eq_zero _).1 this _ H","source_end":16278,"source_start":16238,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125284","is_instance":false,"is_let":false,"user_name":"R✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.125287","is_instance":true,"is_let":false,"user_name":"inst✝²⁰"},{"binder_role":":explicit","context_index":2,"in... | 150 | 15 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 21cd85143be2b125475e170d2a56d9d267e3a566acb0c8a4c623d124d172b2f8 | 9f6b9c7d190620a3f85e10167ee8dd54d10b6e057076d7625adfd9f717886691 | b2ff01a099959ee59000e7373bdba4623dec7703654f0a3906dd6a420423992b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,318 | NoZeroSMulDivisors.trans | Mathlib/Algebra/Algebra/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | right | case inr
R✝ : Type u_1
inst✝²⁰ : CommSemiring R✝
A✝ : Type u_2
inst✝¹⁹ : Semiring A✝
inst✝¹⁸ : Algebra R✝ A✝
M✝ : Type u_3
inst✝¹⁷ : AddCommMonoid M✝
inst✝¹⁶ : Module A✝ M✝
inst✝¹⁵ : Module R✝ M✝
inst✝¹⁴ : IsScalarTower R✝ A✝ M✝
N : Type u_4
inst✝¹³ : AddCommMonoid N
inst✝¹² : Module A✝ N
inst✝¹¹ : Module R✝ N
inst✝¹⁰ ... | case inr.h
R✝ : Type u_1
inst✝²⁰ : CommSemiring R✝
A✝ : Type u_2
inst✝¹⁹ : Semiring A✝
inst✝¹⁸ : Algebra R✝ A✝
M✝ : Type u_3
inst✝¹⁷ : AddCommMonoid M✝
inst✝¹⁶ : Module A✝ M✝
inst✝¹⁵ : Module R✝ M✝
inst✝¹⁴ : IsScalarTower R✝ A✝ M✝
N : Type u_4
inst✝¹³ : AddCommMonoid N
inst✝¹² : Module A✝ N
inst✝¹¹ : Module R✝ N
inst✝¹... | ((:c Or) ((:c Eq) (:fv _uniq.135884) (:fv _uniq.136144) ((:c OfNat.ofNat) (:fv _uniq.135884) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.135884) ((:c CommMonoidWithZero.toZero) (:fv _uniq.135884) ((:c CommSemiring.toCommMonoidWithZero) (:fv _uniq.135884) ((:c CommRing.toCommSemiring) (:fv _uniq.135884) (:fv _uniq.135887)))... | [{"name":"R✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²⁰","sexp":"((:c CommSemiring) (:fv _uniq.125284))"},{"name":"A✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁹","sexp":"((:c Semiring) (:fv _uniq.125290))"},{"name":"inst✝¹⁸","sexp":"((:c Algebra) (:fv _uniq.125284) (:fv _uniq.125290) (:fv _uniq.125287) (:fv _uniq... | (:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV16)) (:arg :explicit 1 (:fv FV29)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV16)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV16)) (:arg :explicit 1 (:lit 0)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125284","is_instance":false,"is_let":false,"name":"R✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.125287","is_instance":true,"is_let":false,"name":"inst✝²⁰","sexp":"(:app (:c CommSemiring) (:arg... | {"children":[{"source":"right","sourceEnd":16289,"sourceStart":16284,"tag":"atom"}],"kind":"Lean.Parser.Tactic.right","source":"right","sourceEnd":16289,"sourceStart":16284,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125284","is_instance":false,"is_let":false,"user_name":"R✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.125287","is_instance":true,"is_let":false,"user_name":"inst✝²⁰"},{"binder_role":":explicit","context_index":2,"in... | 150 | 20 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d11d5caac0206763e221c902a5705f7bdbf65281d6558ddf6bd65e4c885346fd | 75c0f6c50d9428f536a6fcc3d41269a66bf919c87a365f494844773f7ba67fe4 | 27042f4e6eca7d0b2a7ee4026df2ecfa51d3339e6d122aa099118ecd8563bad9 | efa68599e2083666ae50c41be4d6b54230360167dccbd9ff0909f127dfba1b26 |
cat-searcher/leandojo-benchmark-4-random | test | 3,319 | NoZeroSMulDivisors.trans | Mathlib/Algebra/Algebra/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact H | case inr.h
R✝ : Type u_1
inst✝²⁰ : CommSemiring R✝
A✝ : Type u_2
inst✝¹⁹ : Semiring A✝
inst✝¹⁸ : Algebra R✝ A✝
M✝ : Type u_3
inst✝¹⁷ : AddCommMonoid M✝
inst✝¹⁶ : Module A✝ M✝
inst✝¹⁵ : Module R✝ M✝
inst✝¹⁴ : IsScalarTower R✝ A✝ M✝
N : Type u_4
inst✝¹³ : AddCommMonoid N
inst✝¹² : Module A✝ N
inst✝¹¹ : Module R✝ N
inst✝¹... | ((:c Eq) (:fv _uniq.135886) (:fv _uniq.136147) ((:c OfNat.ofNat) (:fv _uniq.135886) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.135886) ((:c NegZeroClass.toZero) (:fv _uniq.135886) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.135886) ((:c SubtractionMonoid.toSubNegZeroMonoid) (:fv _uniq.135886) ((:c SubtractionCommMono... | [{"name":"R✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²⁰","sexp":"((:c CommSemiring) (:fv _uniq.125284))"},{"name":"A✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁹","sexp":"((:c Semiring) (:fv _uniq.125290))"},{"name":"inst✝¹⁸","sexp":"((:c Algebra) (:fv _uniq.125284) (:fv _uniq.125290) (:fv _uniq.125287) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV18)) (:arg :explicit 1 (:fv FV30)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV18)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV18)) (:arg :explicit 1 (:lit 0)))))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125284","is_instance":false,"is_let":false,"name":"R✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.125287","is_instance":true,"is_let":false,"name":"inst✝²⁰","sexp":"(:app (:c CommSemiring) (:arg... | {"children":[{"source":"exact","sourceEnd":16299,"sourceStart":16294,"tag":"atom"},{"contextIndex":32,"semanticRole":"local","source":"H","sourceEnd":16301,"sourceStart":16300,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact H","sourceEnd":16301,"sourceStart":16294,"tag":"node"} | [] | [{"source":"H","source_end":16301,"source_start":16300,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125284","is_instance":false,"is_let":false,"user_name":"R✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.125287","is_instance":true,"is_let":false,"user_name":"inst✝²⁰"},{"binder_role":":explicit","context_index":2,"in... | 150 | 21 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1f0acc88fac0992721ff232734a4fa78b6e671df3aea88a70af594cd9e76e848 | efa68599e2083666ae50c41be4d6b54230360167dccbd9ff0909f127dfba1b26 | a57c92f2767a684958740d7f97f4a6fb30e8e72bb4882d52df1d522e1d9070c0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,320 | CategoryTheory.Subobject.ofLEMk_comp | Mathlib/CategoryTheory/Subobject/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>CategoryTheory.Subobject.ofLEMk</a>] | C : Type u₁
inst✝² : Category.{v₁, u₁} C
X✝ Y Z : C
D : Type u₂
inst✝¹ : Category.{v₂, u₂} D
B A : C
X : Subobject B
f : A ⟶ B
inst✝ : Mono f
h : X ≤ mk f
⊢ X.ofLEMk f h ≫ f = X.arrow | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.41629) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.41629) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.41629) (:fv _uniq.41632))) ((:c Prefunctor.obj) ((:c CategoryTheory.Subobject) (:fv _uniq.41629) (:fv _uniq.41632) (:fv _uniq.42130)) ((:c CategoryTheory.C... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.41629))"},{"name":"X✝","sexp":"(:fv _uniq.41629)"},{"name":"Y","sexp":"(:fv _uniq.41629)"},{"name":"Z","sexp":"(:fv _uniq.41629)"},{"name":"D","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c CategoryTheory.Subobject) (:arg :implicit-type 0 (:fv FV0)) (:arg :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41629","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.41632","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":15553,"sourceStart":15549,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"ofLEMk","source_end":15561,"source_start":15555,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41629","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.41632","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern... | 83 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8f77a76f132ed48ab49e4c6fa9d11ec4218d6df8b181c2578d06141c7c828157 | ed3094cc107626c135f7d8d44e2ff62e18be81d5d6732445ab426187cd687fd0 | 5593754a60f60119a3a58f3b7ac309d6e633237ec1c3597f265a4d09c6bd9200 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,321 | EMetric.isClosed_subsets_of_isClosed | Mathlib/Topology/MetricSpace/Closeds.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>isClosed_of_closure_subset</a> fun (t : <a>TopologicalSpace.Closeds</a> α) (ht : t ∈ <a>closure</a> {t : <a>TopologicalSpace.Closeds</a> α | (t : <a>Set</a> α) ⊆ s}) (x : α) (hx : x ∈ t) => ?_ | α : Type u
inst✝ : EMetricSpace α
s : Set α
hs : IsClosed s
⊢ IsClosed {t | ↑t ⊆ s} | α : Type u
inst✝ : EMetricSpace α
s : Set α
hs : IsClosed s
t : Closeds α
ht : t ∈ closure {t | ↑t ⊆ s}
x : α
hx : x ∈ t
⊢ x ∈ s | ((:c IsClosed) ((:c TopologicalSpace.Closeds) (:fv _uniq.7061) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.7061) ((:c PseudoEMetricSpace.toUniformSpace) (:fv _uniq.7061) ((:c EMetricSpace.toPseudoEMetricSpace) (:fv _uniq.7061) (:fv _uniq.7064))))) ((:c UniformSpace.toTopologicalSpace) ((:c TopologicalSpace.Closeds... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c EMetricSpace) (:fv _uniq.7061))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.7061))"},{"name":"hs","sexp":"((:c IsClosed) (:fv _uniq.7061) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.7061) ((:c PseudoEMetricSpace.toUniformSpace) (:fv _uniq.7061) ((:... | (:app (:c IsClosed) (:arg :implicit-type 0 (:app (:c TopologicalSpace.Closeds) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:app (:c TopologicalSpace.Closeds) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7061","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.7064","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c EMetricSpace) (:arg :expli... | {"children":[{"source":"refine","sourceEnd":3017,"sourceStart":3011,"tag":"atom"},{"children":[{"name":"isClosed_of_closure_subset","semanticRole":"global","source":"isClosed_of_closure_subset","sourceEnd":3044,"sourceStart":3018,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":3048,"sourceStar... | [] | [{"source":"isClosed_of_closure_subset fun\n (t : Closeds α) (ht : t ∈ closure {t : Closeds α | (t : Set α) ⊆ s}) (x : α) (hx : x ∈ t) => ?_","source_end":3158,"source_start":3018,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7061","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.7064","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"internal_... | 15 | 4 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fde14c7249abd36a546012f3821bb7762b41ee2c3fcc50b46810100c9598946f | d5de312925c7a4f1576f9afc0d7f024bd10d6643ad915410e17734d15ab645f0 | 3cfe9e69b4daa19f2c86eb75fd50a075a7c8d227fcf37dfd83f81a662754abd2 | 1f40e5fc0e1065dd8628ba3b4a5d80f4a3bf101fb30c4795a325df66460f14c0 |
cat-searcher/leandojo-benchmark-4-random | test | 3,322 | EMetric.isClosed_subsets_of_isClosed | Mathlib/Topology/MetricSpace/Closeds.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : x ∈ <a>closure</a> s := by refine <a>EMetric.mem_closure_iff</a>.2 fun ε εpos => ?_ obtain ⟨u : <a>TopologicalSpace.Closeds</a> α, hu : u ∈ {t : <a>TopologicalSpace.Closeds</a> α | (t : <a>Set</a> α) ⊆ s}, Dtu : <a>EDist.edist</a> t u < ε⟩ := <a>EMetric.mem_closure_iff</a>.1 ht ε εpos obtain ⟨y : α, hy : y ∈ u, ... | α : Type u
inst✝ : EMetricSpace α
s : Set α
hs : IsClosed s
t : Closeds α
ht : t ∈ closure {t | ↑t ⊆ s}
x : α
hx : x ∈ t
⊢ x ∈ s | α : Type u
inst✝ : EMetricSpace α
s : Set α
hs : IsClosed s
t : Closeds α
ht : t ∈ closure {t | ↑t ⊆ s}
x : α
hx : x ∈ t
this : x ∈ closure s
⊢ x ∈ s | ((:c Membership.mem) (:fv _uniq.7061) ((:c Set) (:fv _uniq.7061)) ((:c Set.instMembership) (:fv _uniq.7061)) (:fv _uniq.7608) (:fv _uniq.7067)) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c EMetricSpace) (:fv _uniq.7061))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.7061))"},{"name":"hs","sexp":"((:c IsClosed) (:fv _uniq.7061) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.7061) ((:c PseudoEMetricSpace.toUniformSpace) (:fv _uniq.7061) ((:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV7)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7061","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.7064","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c EMetricSpace) (:arg :expli... | {"children":[{"source":"have","sourceEnd":3165,"sourceStart":3161,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":3166,"sourceStart":3166,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":3166,"sourceStart":3166,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"x ∈ closure s","source_end":3183,"source_start":3168,"syntax_kind":"«term_∈_»"},{"source":"mem_closure_iff.2 fun ε εpos => ?_","source_end":3237,"source_start":3201,"syntax_kind":"Lean.Parser.Term.app"},{"source":"mem_closure_iff.1 ht ε εpos","source_end":3380,"source_start":3351,"syntax_kind":"Lean.Parser.... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7061","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.7064","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"internal_... | 15 | 5 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | df42bc4f1fc81ed2d3c18ed762f7f1140c6641e0df6748aeaab7b5e13e703ee3 | 1f40e5fc0e1065dd8628ba3b4a5d80f4a3bf101fb30c4795a325df66460f14c0 | 0639c8aeb91faad318d7fd25366baeae345fd6bb311de86d948df9cfd945ac94 | 49f60f821c6b100b893171f84fdd43a759312ebd48e0ca0809e6d8e8dabcc80c |
cat-searcher/leandojo-benchmark-4-random | test | 3,323 | EMetric.isClosed_subsets_of_isClosed | Mathlib/Topology/MetricSpace/Closeds.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [hs.closure_eq] at this | α : Type u
inst✝ : EMetricSpace α
s : Set α
hs : IsClosed s
t : Closeds α
ht : t ∈ closure {t | ↑t ⊆ s}
x : α
hx : x ∈ t
this : x ∈ closure s
⊢ x ∈ s | ((:c Membership.mem) (:fv _uniq.7061) ((:c Set) (:fv _uniq.7061)) ((:c Set.instMembership) (:fv _uniq.7061)) (:fv _uniq.7608) (:fv _uniq.7067)) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c EMetricSpace) (:fv _uniq.7061))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.7061))"},{"name":"hs","sexp":"((:c IsClosed) (:fv _uniq.7061) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.7061) ((:c PseudoEMetricSpace.toUniformSpace) (:fv _uniq.7061) ((:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV7)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7061","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.7064","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c EMetricSpace) (:arg :expli... | {"children":[{"source":"rwa","sourceEnd":3523,"sourceStart":3520,"tag":"atom"},{"children":[{"source":"[","sourceEnd":3525,"sourceStart":3524,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"IsClosed.closure_eq","semanticRole":"global","source":"hs.closure_eq","sou... | [] | [{"source":"hs.closure_eq","source_end":3538,"source_start":3525,"syntax_kind":"ident"},{"source":"this","source_end":3547,"source_start":3543,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7061","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.7064","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"internal_... | 15 | 11 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fb23a495cef99627578d55d7f56bb7168568fec0be600315a59d11c3a4408a1b | 49f60f821c6b100b893171f84fdd43a759312ebd48e0ca0809e6d8e8dabcc80c | 7d99a78d08b0f21845fd01e763664cd97064c83c7e13c30ee5289e5a81ca10c2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,324 | EMetric.isClosed_subsets_of_isClosed | Mathlib/Topology/MetricSpace/Closeds.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>EMetric.mem_closure_iff</a>.2 fun ε εpos => ?_ | α : Type u
inst✝ : EMetricSpace α
s : Set α
hs : IsClosed s
t : Closeds α
ht : t ∈ closure {t | ↑t ⊆ s}
x : α
hx : x ∈ t
⊢ x ∈ closure s | α : Type u
inst✝ : EMetricSpace α
s : Set α
hs : IsClosed s
t : Closeds α
ht : t ∈ closure {t | ↑t ⊆ s}
x : α
hx : x ∈ t
ε : ℝ≥0∞
εpos : ε > 0
⊢ ∃ y ∈ s, edist x y < ε | ((:c Membership.mem) (:fv _uniq.7061) ((:c Set) (:fv _uniq.7061)) ((:c Set.instMembership) (:fv _uniq.7061)) (:fv _uniq.7608) ((:c closure) (:fv _uniq.7061) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.7061) ((:c PseudoEMetricSpace.toUniformSpace) (:fv _uniq.7061) ((:c EMetricSpace.toPseudoEMetricSpace) (:fv _uniq.... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c EMetricSpace) (:fv _uniq.7061))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.7061))"},{"name":"hs","sexp":"((:c IsClosed) (:fv _uniq.7061) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.7061) ((:c PseudoEMetricSpace.toUniformSpace) (:fv _uniq.7061) ((:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV7)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7061","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.7064","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c EMetricSpace) (:arg :expli... | {"children":[{"source":"refine","sourceEnd":3200,"sourceStart":3194,"tag":"atom"},{"children":[{"children":[{"name":"EMetric.mem_closure_iff","semanticRole":"global","source":"mem_closure_iff","sourceEnd":3216,"sourceStart":3201,"tag":"identifier"},{"source":".","sourceEnd":3217,"sourceStart":3216,"tag":"atom"},{"child... | [] | [{"source":"mem_closure_iff.2 fun ε εpos => ?_","source_end":3237,"source_start":3201,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7061","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.7064","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"internal_... | 15 | 7 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 55332ecabd6e6bacb825d7c02d1c17f288dca4e1e4db1f3718e0373c9582349c | 121d639eb01b9be8aa8869d85016849d98bef1f2bdbd5ff083dcdea211d3de73 | 887586824541699405adfaace0fe775653b60040639fb405a8709fffa62e6a0b | e772636d25d02fd1ff2e47c7c5cdfdfd04ec0809c797ef5858a018d4decf5bda |
cat-searcher/leandojo-benchmark-4-random | test | 3,325 | EMetric.isClosed_subsets_of_isClosed | Mathlib/Topology/MetricSpace/Closeds.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨u : <a>TopologicalSpace.Closeds</a> α, hu : u ∈ {t : <a>TopologicalSpace.Closeds</a> α | (t : <a>Set</a> α) ⊆ s}, Dtu : <a>EDist.edist</a> t u < ε⟩ := <a>EMetric.mem_closure_iff</a>.1 ht ε εpos | α : Type u
inst✝ : EMetricSpace α
s : Set α
hs : IsClosed s
t : Closeds α
ht : t ∈ closure {t | ↑t ⊆ s}
x : α
hx : x ∈ t
ε : ℝ≥0∞
εpos : ε > 0
⊢ ∃ y ∈ s, edist x y < ε | case intro.intro
α : Type u
inst✝ : EMetricSpace α
s : Set α
hs : IsClosed s
t : Closeds α
ht : t ∈ closure {t | ↑t ⊆ s}
x : α
hx : x ∈ t
ε : ℝ≥0∞
εpos : ε > 0
u : Closeds α
hu : u ∈ {t | ↑t ⊆ s}
Dtu : edist t u < ε
⊢ ∃ y ∈ s, edist x y < ε | ((:c Exists) (:fv _uniq.7061) (:lambda y (:fv _uniq.7061) ((:c And) ((:c Membership.mem) (:fv _uniq.7061) ((:c Set) (:fv _uniq.7061)) ((:c Set.instMembership) (:fv _uniq.7061)) 0 (:fv _uniq.7067)) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.t... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c EMetricSpace) (:fv _uniq.7061))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.7061))"},{"name":"hs","sexp":"((:c IsClosed) (:fv _uniq.7061) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.7061) ((:c PseudoEMetricSpace.toUniformSpace) (:fv _uniq.7061) ((:... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda y :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7061","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.7064","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c EMetricSpace) (:arg :expli... | {"children":[{"source":"obtain","sourceEnd":3248,"sourceStart":3242,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":3252,"sourceStart":3249,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"u","sourceEnd":3... | [] | [{"source":"mem_closure_iff.1 ht ε εpos","source_end":3380,"source_start":3351,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨u : Closeds α, hu : u ∈ {t : Closeds α | (t : Set α) ⊆ s}, Dtu : edist t u < ε⟩","source_end":3341,"source_start":3249,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7061","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.7064","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"internal_... | 15 | 8 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 21cbcbb2090fd2a96bbb1888b6fc6043830b73d50d79d78e29bb2f4d3db8e872 | e772636d25d02fd1ff2e47c7c5cdfdfd04ec0809c797ef5858a018d4decf5bda | a3431c77ddd8fea60f709a097e0ecb759c5b8a049681aaa9bd00b9a97f4a1d51 | 3b33b56f9a605d2268efe19d44c47af8488709493ef49a8a5f3d30719c80e268 |
cat-searcher/leandojo-benchmark-4-random | test | 3,326 | EMetric.isClosed_subsets_of_isClosed | Mathlib/Topology/MetricSpace/Closeds.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨y : α, hy : y ∈ u, Dxy : <a>EDist.edist</a> x y < ε⟩ := <a>EMetric.exists_edist_lt_of_hausdorffEdist_lt</a> hx Dtu | case intro.intro
α : Type u
inst✝ : EMetricSpace α
s : Set α
hs : IsClosed s
t : Closeds α
ht : t ∈ closure {t | ↑t ⊆ s}
x : α
hx : x ∈ t
ε : ℝ≥0∞
εpos : ε > 0
u : Closeds α
hu : u ∈ {t | ↑t ⊆ s}
Dtu : edist t u < ε
⊢ ∃ y ∈ s, edist x y < ε | case intro.intro.intro.intro
α : Type u
inst✝ : EMetricSpace α
s : Set α
hs : IsClosed s
t : Closeds α
ht : t ∈ closure {t | ↑t ⊆ s}
x : α
hx : x ∈ t
ε : ℝ≥0∞
εpos : ε > 0
u : Closeds α
hu : u ∈ {t | ↑t ⊆ s}
Dtu : edist t u < ε
y : α
hy : y ∈ u
Dxy : edist x y < ε
⊢ ∃ y ∈ s, edist x y < ε | ((:c Exists) (:fv _uniq.7061) (:lambda y (:fv _uniq.7061) ((:c And) ((:c Membership.mem) (:fv _uniq.7061) ((:c Set) (:fv _uniq.7061)) ((:c Set.instMembership) (:fv _uniq.7061)) 0 (:fv _uniq.7067)) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.t... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c EMetricSpace) (:fv _uniq.7061))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.7061))"},{"name":"hs","sexp":"((:c IsClosed) (:fv _uniq.7061) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.7061) ((:c PseudoEMetricSpace.toUniformSpace) (:fv _uniq.7061) ((:... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda y :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7061","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.7064","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c EMetricSpace) (:arg :expli... | {"children":[{"source":"obtain","sourceEnd":3391,"sourceStart":3385,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":3395,"sourceStart":3392,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":3... | [] | [{"source":"exists_edist_lt_of_hausdorffEdist_lt hx Dtu","source_end":3487,"source_start":3444,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨y : α, hy : y ∈ u, Dxy : edist x y < ε⟩","source_end":3440,"source_start":3392,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7061","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.7064","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"internal_... | 15 | 9 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 42622146947fa1bb40844be3d93ac8e7abb5807fb8024b29eb811daf0a6a34a6 | 3b33b56f9a605d2268efe19d44c47af8488709493ef49a8a5f3d30719c80e268 | f61b6cb2a3a81967c062ec6015f3c818b8c2172eb16ae66abc045b00ba629756 | fc63cba6d5f3cbd165276b83d4f8d8ba5aabbf031fef50272df608d48d644e43 |
cat-searcher/leandojo-benchmark-4-random | test | 3,327 | EMetric.isClosed_subsets_of_isClosed | Mathlib/Topology/MetricSpace/Closeds.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨y, hu hy, Dxy⟩ | case intro.intro.intro.intro
α : Type u
inst✝ : EMetricSpace α
s : Set α
hs : IsClosed s
t : Closeds α
ht : t ∈ closure {t | ↑t ⊆ s}
x : α
hx : x ∈ t
ε : ℝ≥0∞
εpos : ε > 0
u : Closeds α
hu : u ∈ {t | ↑t ⊆ s}
Dtu : edist t u < ε
y : α
hy : y ∈ u
Dxy : edist x y < ε
⊢ ∃ y ∈ s, edist x y < ε | ((:c Exists) (:fv _uniq.7061) (:lambda y (:fv _uniq.7061) ((:c And) ((:c Membership.mem) (:fv _uniq.7061) ((:c Set) (:fv _uniq.7061)) ((:c Set.instMembership) (:fv _uniq.7061)) 0 (:fv _uniq.7067)) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.t... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c EMetricSpace) (:fv _uniq.7061))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.7061))"},{"name":"hs","sexp":"((:c IsClosed) (:fv _uniq.7061) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.7061) ((:c PseudoEMetricSpace.toUniformSpace) (:fv _uniq.7061) ((:... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda y :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7061","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.7064","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c EMetricSpace) (:arg :expli... | {"children":[{"source":"exact","sourceEnd":3497,"sourceStart":3492,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":3501,"sourceStart":3498,"tag":"atom"},{"children":[{"contextIndex":14,"semanticRole":"local","source":"y","sourceEnd":3502,"sourceStart":3501,"tag":"identifier"},{"source":",","sourceEnd":3503,"source... | [] | [{"source":"⟨y, hu hy, Dxy⟩","source_end":3517,"source_start":3498,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7061","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.7064","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"internal_... | 15 | 10 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dbab12b6f96556d4ad4eb6292df69e6beae4751cc9a4ef0ecba36d008a4f500e | fc63cba6d5f3cbd165276b83d4f8d8ba5aabbf031fef50272df608d48d644e43 | b9b76f7a10ab2ec2d568c579d17fcdbc0d64106afc82c9d359fe4fb994e04e5f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,328 | ProbabilityTheory.kernel.iIndepFun.indepFun_prod_mk | Mathlib/Probability/Independence/Kernel.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | classical have h_right : f k = (fun p : ∀ j : ({k} : <a>Finset</a> ι), β j => p ⟨k, <a>Finset.mem_singleton_self</a> k⟩) ∘ fun a (j : ({k} : <a>Finset</a> ι)) => f j a := <a>rfl</a> have h_meas_right : <a>Measurable</a> fun p : ∀ j : ({k} : <a>Finset</a> ι), β j => p ⟨k, <a>Finset.mem_singleton_self</a> k⟩ := <a>measur... | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | ((:c ProbabilityTheory.kernel.IndepFun) (:fv _uniq.175986) (:fv _uniq.175989) (:fv _uniq.176007) ((:c Prod) ((:fv _uniq.176082) (:fv _uniq.176407)) ((:fv _uniq.176082) (:fv _uniq.176408))) ((:fv _uniq.176082) (:fv _uniq.176409)) (:fv _uniq.176010) ((:c Prod.instMeasurableSpace) ((:fv _uniq.176082) (:fv _uniq.176407)) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"Ω","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"β✝","sexp":"(:sort (+ u_4 1))"},{"name":"β'","sexp":"(:sort (+ u_5 1))"},{"name":"γ","sexp":"(:sort (+ u_6 1))"},{"name":"γ'","sexp":"(:sort (+ u_7 1))"},{"name":"_mα","sexp":"((:c Measurabl... | (:app (:c ProbabilityTheory.kernel.IndepFun) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :implicit-type 3 (:app (:c Prod) (:arg :explicit 0 (:app (:fv FV13) (:arg :explicit 0 (:fv FV20)))) (:arg :explicit 1 (:app (:fv FV13) (:arg :explicit 0 (:fv FV21)))))) (:arg :implic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"classical","sourceEnd":48598,"sourceStart":48589,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"have","sourceEnd":48605,"sourceStart":48601,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","so... | [] | [{"source":"f k =\n (fun p : ∀ j : ({k} : Finset ι), β j => p ⟨k, Finset.mem_singleton_self k⟩) ∘\n fun a (j : ({k} : Finset ι)) => f j a","source_end":48756,"source_start":48616,"syntax_kind":"«term_=_»"},{"source":"rfl","source_end":48763,"source_start":48760,"syntax_kind":"ident"},{"source":"Measurable fun p :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 113 | 2 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e9517f0dc06c40dacf714babdc52db0c8b91e685bc7e70f44f6c9ad2d7bacaa8 | e8a2ab43d47a406bb83716b71e5d44af9a25c0dcc2b67cba29539042eb8d6182 | 78909b193653b4ee987dcd45778c23e70d7f507cbebd067ee6877e66725874ec | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,329 | ProbabilityTheory.kernel.iIndepFun.indepFun_prod_mk | Mathlib/Probability/Independence/Kernel.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h_right : f k = (fun p : ∀ j : ({k} : <a>Finset</a> ι), β j => p ⟨k, <a>Finset.mem_singleton_self</a> k⟩) ∘ fun a (j : ({k} : <a>Finset</a> ι)) => f j a := <a>rfl</a> | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | ((:c ProbabilityTheory.kernel.IndepFun) (:fv _uniq.175986) (:fv _uniq.175989) (:fv _uniq.176007) ((:c Prod) ((:fv _uniq.176082) (:fv _uniq.176407)) ((:fv _uniq.176082) (:fv _uniq.176408))) ((:fv _uniq.176082) (:fv _uniq.176409)) (:fv _uniq.176010) ((:c Prod.instMeasurableSpace) ((:fv _uniq.176082) (:fv _uniq.176407)) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"Ω","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"β✝","sexp":"(:sort (+ u_4 1))"},{"name":"β'","sexp":"(:sort (+ u_5 1))"},{"name":"γ","sexp":"(:sort (+ u_6 1))"},{"name":"γ'","sexp":"(:sort (+ u_7 1))"},{"name":"_mα","sexp":"((:c Measurabl... | (:app (:c ProbabilityTheory.kernel.IndepFun) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :implicit-type 3 (:app (:c Prod) (:arg :explicit 0 (:app (:fv FV13) (:arg :explicit 0 (:fv FV20)))) (:arg :explicit 1 (:app (:fv FV13) (:arg :explicit 0 (:fv FV21)))))) (:arg :implic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":48605,"sourceStart":48601,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h_right","sourceEnd":48613,"sourceStart":48606,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h_right","sourceEnd":48613,"sourceStart":48606,... | [] | [{"source":"f k =\n (fun p : ∀ j : ({k} : Finset ι), β j => p ⟨k, Finset.mem_singleton_self k⟩) ∘\n fun a (j : ({k} : Finset ι)) => f j a","source_end":48756,"source_start":48616,"syntax_kind":"«term_=_»"},{"source":"rfl","source_end":48763,"source_start":48760,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 113 | 7 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ce562d8187df8acde442481d3c1ce1029f17933a0e0fb136513a6509e0fb1e19 | e8a2ab43d47a406bb83716b71e5d44af9a25c0dcc2b67cba29539042eb8d6182 | d17e9dd930b8ef407f2546f69ca9631a21991ba668e164a1f98a4a46427abdf6 | 6ef0250194ca981e4a6d11bf9b8e6abb99c8fa0714ce0748639f3f124e48cf06 |
cat-searcher/leandojo-benchmark-4-random | test | 3,330 | ProbabilityTheory.kernel.iIndepFun.indepFun_prod_mk | Mathlib/Probability/Independence/Kernel.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h_meas_right : <a>Measurable</a> fun p : ∀ j : ({k} : <a>Finset</a> ι), β j => p ⟨k, <a>Finset.mem_singleton_self</a> k⟩ := <a>measurable_pi_apply</a> _ | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | ((:c ProbabilityTheory.kernel.IndepFun) (:fv _uniq.175986) (:fv _uniq.175989) (:fv _uniq.176007) ((:c Prod) ((:fv _uniq.176082) (:fv _uniq.176407)) ((:fv _uniq.176082) (:fv _uniq.176408))) ((:fv _uniq.176082) (:fv _uniq.176409)) (:fv _uniq.176010) ((:c Prod.instMeasurableSpace) ((:fv _uniq.176082) (:fv _uniq.176407)) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"Ω","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"β✝","sexp":"(:sort (+ u_4 1))"},{"name":"β'","sexp":"(:sort (+ u_5 1))"},{"name":"γ","sexp":"(:sort (+ u_6 1))"},{"name":"γ'","sexp":"(:sort (+ u_7 1))"},{"name":"_mα","sexp":"((:c Measurabl... | (:app (:c ProbabilityTheory.kernel.IndepFun) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :implicit-type 3 (:app (:c Prod) (:arg :explicit 0 (:app (:fv FV13) (:arg :explicit 0 (:fv FV20)))) (:arg :explicit 1 (:app (:fv FV13) (:arg :explicit 0 (:fv FV21)))))) (:arg :implic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":48770,"sourceStart":48766,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h_meas_right","sourceEnd":48783,"sourceStart":48771,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h_meas_right","sourceEnd":48783,"sourceSta... | [] | [{"source":"Measurable fun p : ∀ j : ({k} : Finset ι),\n β j => p ⟨k, Finset.mem_singleton_self k⟩","source_end":48883,"source_start":48787,"syntax_kind":"Lean.Parser.Term.app"},{"source":"measurable_pi_apply _","source_end":48908,"source_start":48887,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 113 | 8 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dadd15067589b6292d4d07506653c533ef06378c25007c2ac625011a85a23a98 | 6ef0250194ca981e4a6d11bf9b8e6abb99c8fa0714ce0748639f3f124e48cf06 | d57ab5b9a32f14d6ed1c653679f77d391478c74c9c9da8a4788f0c0ad9629f96 | 3b7d858677fe16390aa64de334cd23bebf673e8a77c51381d55ea2dc6b6a4b32 |
cat-searcher/leandojo-benchmark-4-random | test | 3,331 | ProbabilityTheory.kernel.iIndepFun.indepFun_prod_mk | Mathlib/Probability/Independence/Kernel.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let s : <a>Finset</a> ι := {i, j} | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | ((:c ProbabilityTheory.kernel.IndepFun) (:fv _uniq.175986) (:fv _uniq.175989) (:fv _uniq.176007) ((:c Prod) ((:fv _uniq.176082) (:fv _uniq.176407)) ((:fv _uniq.176082) (:fv _uniq.176408))) ((:fv _uniq.176082) (:fv _uniq.176409)) (:fv _uniq.176010) ((:c Prod.instMeasurableSpace) ((:fv _uniq.176082) (:fv _uniq.176407)) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"Ω","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"β✝","sexp":"(:sort (+ u_4 1))"},{"name":"β'","sexp":"(:sort (+ u_5 1))"},{"name":"γ","sexp":"(:sort (+ u_6 1))"},{"name":"γ'","sexp":"(:sort (+ u_7 1))"},{"name":"_mα","sexp":"((:c Measurabl... | (:app (:c ProbabilityTheory.kernel.IndepFun) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :implicit-type 3 (:app (:c Prod) (:arg :explicit 0 (:app (:fv FV13) (:arg :explicit 0 (:fv FV20)))) (:arg :explicit 1 (:app (:fv FV13) (:arg :explicit 0 (:fv FV21)))))) (:arg :implic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"let","sourceEnd":48914,"sourceStart":48911,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"s","sourceEnd":48916,"sourceStart":48915,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":4891... | [] | [{"source":"Finset ι","source_end":48928,"source_start":48919,"syntax_kind":"Lean.Parser.Term.app"},{"source":"{i, j}","source_end":48938,"source_start":48932,"syntax_kind":"choice"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 113 | 9 | exact | true | 1 | 26 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 20a6c6c1857452baca2034ecc3f02e086e32f84af3d492151c8fd9bb21f7fc67 | 3b7d858677fe16390aa64de334cd23bebf673e8a77c51381d55ea2dc6b6a4b32 | 1e3feceb6d44de50b6af9c747f71c46ccb7988ed3516cd5d5af8cafa185db5ed | e89444ca8228f589dbb3ae3a281997b2f6f940bf14d7b4e44447b2320edcc03d |
cat-searcher/leandojo-benchmark-4-random | test | 3,332 | ProbabilityTheory.kernel.iIndepFun.indepFun_prod_mk | Mathlib/Probability/Independence/Kernel.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h_left : (fun ω => (f i ω, f j ω)) = (fun p : ∀ l : s, β l => (p ⟨i, <a>Finset.mem_insert_self</a> i _⟩, p ⟨j, <a>Finset.mem_insert_of_mem</a> (<a>Finset.mem_singleton_self</a> _)⟩)) ∘ fun a (j : s) => f j a := by ext1 a simp only [<a>Prod.mk.inj_iff</a>] constructor | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | ((:c ProbabilityTheory.kernel.IndepFun) (:fv _uniq.175986) (:fv _uniq.175989) (:fv _uniq.176007) ((:c Prod) ((:fv _uniq.176082) (:fv _uniq.176407)) ((:fv _uniq.176082) (:fv _uniq.176408))) ((:fv _uniq.176082) (:fv _uniq.176409)) (:fv _uniq.176010) ((:c Prod.instMeasurableSpace) ((:fv _uniq.176082) (:fv _uniq.176407)) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"Ω","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"β✝","sexp":"(:sort (+ u_4 1))"},{"name":"β'","sexp":"(:sort (+ u_5 1))"},{"name":"γ","sexp":"(:sort (+ u_6 1))"},{"name":"γ'","sexp":"(:sort (+ u_7 1))"},{"name":"_mα","sexp":"((:c Measurabl... | (:app (:c ProbabilityTheory.kernel.IndepFun) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :implicit-type 3 (:app (:c Prod) (:arg :explicit 0 (:app (:fv FV13) (:arg :explicit 0 (:fv FV20)))) (:arg :explicit 1 (:app (:fv FV13) (:arg :explicit 0 (:fv FV21)))))) (:arg :implic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":48945,"sourceStart":48941,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h_left","sourceEnd":48952,"sourceStart":48946,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h_left","sourceEnd":48952,"sourceStart":48946,"t... | [] | [{"source":"(fun ω => (f i ω, f j ω)) = (fun p : ∀ l : s, β l =>\n (p ⟨i, Finset.mem_insert_self i _⟩,\n p ⟨j, Finset.mem_insert_of_mem (Finset.mem_singleton_self _)⟩)) ∘ fun a (j : s) => f j a","source_end":49156,"source_start":48955,"syntax_kind":"«term_=_»"},{"source":"Prod.mk.inj_iff","source_end":49204,"sour... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 113 | 10 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6604510663e0839ea7432a1a02bf0d1dc0fd54a5edee19d5390995d54a6ec1ec | e89444ca8228f589dbb3ae3a281997b2f6f940bf14d7b4e44447b2320edcc03d | d52a277e883ac0f8297ed1c17a3c777439999d421660baf83e83b21cfd6e1c55 | 15f7819773031ca6262bf61bfee8723ba0e5b6f883a858ebe037ed15e5f9d4a8 |
cat-searcher/leandojo-benchmark-4-random | test | 3,333 | ProbabilityTheory.kernel.iIndepFun.indepFun_prod_mk | Mathlib/Probability/Independence/Kernel.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h_meas_left : <a>Measurable</a> fun p : ∀ l : s, β l => (p ⟨i, <a>Finset.mem_insert_self</a> i _⟩, p ⟨j, <a>Finset.mem_insert_of_mem</a> (<a>Finset.mem_singleton_self</a> _)⟩) := <a>Measurable.prod</a> (<a>measurable_pi_apply</a> _) (<a>measurable_pi_apply</a> _) | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | ((:c ProbabilityTheory.kernel.IndepFun) (:fv _uniq.175986) (:fv _uniq.175989) (:fv _uniq.176007) ((:c Prod) ((:fv _uniq.176082) (:fv _uniq.176407)) ((:fv _uniq.176082) (:fv _uniq.176408))) ((:fv _uniq.176082) (:fv _uniq.176409)) (:fv _uniq.176010) ((:c Prod.instMeasurableSpace) ((:fv _uniq.176082) (:fv _uniq.176407)) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"Ω","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"β✝","sexp":"(:sort (+ u_4 1))"},{"name":"β'","sexp":"(:sort (+ u_5 1))"},{"name":"γ","sexp":"(:sort (+ u_6 1))"},{"name":"γ'","sexp":"(:sort (+ u_7 1))"},{"name":"_mα","sexp":"((:c Measurabl... | (:app (:c ProbabilityTheory.kernel.IndepFun) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :implicit-type 3 (:app (:c Prod) (:arg :explicit 0 (:app (:fv FV13) (:arg :explicit 0 (:fv FV20)))) (:arg :explicit 1 (:app (:fv FV13) (:arg :explicit 0 (:fv FV21)))))) (:arg :implic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":49228,"sourceStart":49224,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h_meas_left","sourceEnd":49240,"sourceStart":49229,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h_meas_left","sourceEnd":49240,"sourceStart... | [] | [{"source":"Measurable fun p : ∀ l : s, β l =>\n (p ⟨i, Finset.mem_insert_self i _⟩,\n p ⟨j, Finset.mem_insert_of_mem (Finset.mem_singleton_self _)⟩)","source_end":49395,"source_start":49243,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Measurable.prod (measurable_pi_apply _) (measurable_pi_apply _)","source_e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 113 | 15 | exact | true | 1 | 28 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d3149ec2d7276e199d869b7834b8e9aed063ca54ea6fe1e29a077e15809642e4 | 15f7819773031ca6262bf61bfee8723ba0e5b6f883a858ebe037ed15e5f9d4a8 | ce3b8043f264ce7038667e618044200513b611fc54fe1581c0cadbc8a6649ac1 | fa47afdb8dd5363763022af74c7c677250e18ea4e81f990bda220986cfabba7d |
cat-searcher/leandojo-benchmark-4-random | test | 3,334 | ProbabilityTheory.kernel.iIndepFun.indepFun_prod_mk | Mathlib/Probability/Independence/Kernel.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [h_left, h_right] | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | ((:c ProbabilityTheory.kernel.IndepFun) (:fv _uniq.175986) (:fv _uniq.175989) (:fv _uniq.176007) ((:c Prod) ((:fv _uniq.176082) (:fv _uniq.176407)) ((:fv _uniq.176082) (:fv _uniq.176408))) ((:fv _uniq.176082) (:fv _uniq.176409)) (:fv _uniq.176010) ((:c Prod.instMeasurableSpace) ((:fv _uniq.176082) (:fv _uniq.176407)) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"Ω","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"β✝","sexp":"(:sort (+ u_4 1))"},{"name":"β'","sexp":"(:sort (+ u_5 1))"},{"name":"γ","sexp":"(:sort (+ u_6 1))"},{"name":"γ'","sexp":"(:sort (+ u_7 1))"},{"name":"_mα","sexp":"((:c Measurabl... | (:app (:c ProbabilityTheory.kernel.IndepFun) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :implicit-type 3 (:app (:c Prod) (:arg :explicit 0 (:app (:fv FV13) (:arg :explicit 0 (:fv FV20)))) (:arg :explicit 1 (:app (:fv FV13) (:arg :explicit 0 (:fv FV21)))))) (:arg :implic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":49473,"sourceStart":49471,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":49475,"sourceStart":49474,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":28,"seman... | [] | [{"source":"h_left","source_end":49481,"source_start":49475,"syntax_kind":"ident"},{"source":"h_right","source_end":49490,"source_start":49483,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 113 | 16 | exact | true | 1 | 29 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3bd0bba8a6fc9e62a72ccd6db90a937e7c9dd2fe8ef406e34dab2f24bf1753e8 | fa47afdb8dd5363763022af74c7c677250e18ea4e81f990bda220986cfabba7d | 80fec5d570f967a71e81adde73a2a0bed8c57c6ef51bb60d63ebdd1c26ce1ae7 | 1fd54d83c02fc150f66da4dd3b585b04d15dbe2e08d96c76e5593f535af89640 |
cat-searcher/leandojo-benchmark-4-random | test | 3,335 | ProbabilityTheory.kernel.iIndepFun.indepFun_prod_mk | Mathlib/Probability/Independence/Kernel.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (hf_Indep.indepFun_finset s {k} ?_ hf_meas).<a>ProbabilityTheory.kernel.IndepFun.comp</a> h_meas_left h_meas_right | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | ((:c ProbabilityTheory.kernel.IndepFun) (:fv _uniq.175986) (:fv _uniq.175989) (:fv _uniq.176007) ((:c Prod) ((:fv _uniq.176082) (:fv _uniq.176407)) ((:fv _uniq.176082) (:fv _uniq.176408))) ((:fv _uniq.176082) (:fv _uniq.176409)) (:fv _uniq.176010) ((:c Prod.instMeasurableSpace) ((:fv _uniq.176082) (:fv _uniq.176407)) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"Ω","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"β✝","sexp":"(:sort (+ u_4 1))"},{"name":"β'","sexp":"(:sort (+ u_5 1))"},{"name":"γ","sexp":"(:sort (+ u_6 1))"},{"name":"γ'","sexp":"(:sort (+ u_7 1))"},{"name":"_mα","sexp":"((:c Measurabl... | (:app (:c ProbabilityTheory.kernel.IndepFun) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :implicit-type 3 (:app (:c Prod) (:arg :explicit 0 (:app (:fv FV13) (:arg :explicit 0 (:fv FV20)))) (:arg :explicit 1 (:app (:fv FV13) (:arg :explicit 0 (:fv FV21)))))) (:arg :implic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":49500,"sourceStart":49494,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":49502,"sourceStart":49501,"tag":"atom"},{"children":[{"source":"hf_Indep.indepFun_finset","sourceEnd":49526,"sourceStart":49502,"tag":"identifier"},{"children":[{"contextI... | [] | [{"source":"(hf_Indep.indepFun_finset s {k} ?_ hf_meas).comp h_meas_left h_meas_right","source_end":49574,"source_start":49501,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 113 | 20 | exact | true | 1 | 29 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6880135c00172192706f32f6df1ef5ce98cdf8a6ac791af37392e8e92d44bdcd | 1fd54d83c02fc150f66da4dd3b585b04d15dbe2e08d96c76e5593f535af89640 | 32348cdfe381091e48c6be325e5c8b74a994c2271cdb3587b51add498c2fd2e4 | b3f2355b078452ac9ce3cd537fc18cb6acce286134aa51588822ce620f3feb18 |
cat-searcher/leandojo-benchmark-4-random | test | 3,336 | ProbabilityTheory.kernel.iIndepFun.indepFun_prod_mk | Mathlib/Probability/Independence/Kernel.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.disjoint_singleton_right</a>] | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | ((:c Disjoint) ((:c Finset) (:fv _uniq.175992)) ((:c Finset.partialOrder) (:fv _uniq.175992)) ((:c Finset.instOrderBot) (:fv _uniq.175992)) (:fv _uniq.177360) ((:c Singleton.singleton) (:fv _uniq.175992) ((:c Finset) (:fv _uniq.175992)) ((:c Finset.instSingleton) (:fv _uniq.175992)) (:fv _uniq.176409))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"Ω","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"β✝","sexp":"(:sort (+ u_4 1))"},{"name":"β'","sexp":"(:sort (+ u_5 1))"},{"name":"γ","sexp":"(:sort (+ u_6 1))"},{"name":"γ'","sexp":"(:sort (+ u_7 1))"},{"name":"_mα","sexp":"((:c Measurabl... | (:app (:c Disjoint) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV2))))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:app (:c Finset) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":49579,"sourceStart":49577,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":49581,"sourceStart":49580,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.disjoint_... | [] | [{"source":"Finset.disjoint_singleton_right","source_end":49612,"source_start":49581,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 113 | 21 | exact | true | 1 | 29 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ddbb870da4f42f4594a5492a56c87141ff2afea10a1d335e74c5b55f4c12c680 | b3f2355b078452ac9ce3cd537fc18cb6acce286134aa51588822ce620f3feb18 | 4625436d3475b9352d2dcd97f6ba2ca5628e311dccde3d53b4600d174fcfa583 | 9067dd51ca4430e8ccdeaf06d3fb028f6029d6a7726c9144654c8e5d36383438 |
cat-searcher/leandojo-benchmark-4-random | test | 3,337 | ProbabilityTheory.kernel.iIndepFun.indepFun_prod_mk | Mathlib/Probability/Independence/Kernel.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [s, <a>Finset.mem_insert</a>, <a>Finset.mem_singleton</a>, <a>not_or</a>] | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | ((:c Not) ((:c Membership.mem) (:fv _uniq.175992) ((:c Finset) (:fv _uniq.175992)) ((:c Finset.instMembership) (:fv _uniq.175992)) (:fv _uniq.176409) (:fv _uniq.177360))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"Ω","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"β✝","sexp":"(:sort (+ u_4 1))"},{"name":"β'","sexp":"(:sort (+ u_5 1))"},{"name":"γ","sexp":"(:sort (+ u_6 1))"},{"name":"γ'","sexp":"(:sort (+ u_7 1))"},{"name":"_mα","sexp":"((:c Measurabl... | (:app (:c Not) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV2))))))) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":49620,"sourceStart":49616,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":49625,"sourceStart":49621,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":496... | [] | [{"source":"s","source_end":49628,"source_start":49627,"syntax_kind":"ident"},{"source":"Finset.mem_insert","source_end":49647,"source_start":49630,"syntax_kind":"ident"},{"source":"Finset.mem_singleton","source_end":49669,"source_start":49649,"syntax_kind":"ident"},{"source":"not_or","source_end":49677,"source_start":... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 113 | 24 | exact | true | 1 | 29 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c2f48af18d757cd28f506b334cf8bc66649e694dfdefa53c0ebfae47943ba6e0 | 9067dd51ca4430e8ccdeaf06d3fb028f6029d6a7726c9144654c8e5d36383438 | 7038882e436986e52c0d970157549dd43cd52958e5b4ba480217588563c487a0 | 6e357d081e3a4d11b1d43ff47d1ff655797a43b1141bd2099ec96a1533e03874 |
cat-searcher/leandojo-benchmark-4-random | test | 3,338 | ProbabilityTheory.kernel.iIndepFun.indepFun_prod_mk | Mathlib/Probability/Independence/Kernel.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨hik.symm, hjk.symm⟩ | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | ((:c And) ((:c Not) ((:c Eq) (:fv _uniq.175992) (:fv _uniq.176409) (:fv _uniq.176407))) ((:c Not) ((:c Eq) (:fv _uniq.175992) (:fv _uniq.176409) (:fv _uniq.176408)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"Ω","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"β✝","sexp":"(:sort (+ u_4 1))"},{"name":"β'","sexp":"(:sort (+ u_5 1))"},{"name":"γ","sexp":"(:sort (+ u_6 1))"},{"name":"γ'","sexp":"(:sort (+ u_7 1))"},{"name":"_mα","sexp":"((:c Measurabl... | (:app (:c And) (:arg :explicit 0 (:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:fv FV22)) (:arg :explicit 2 (:fv FV20)))))) (:arg :explicit 1 (:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:fv FV22)) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":49686,"sourceStart":49681,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":49690,"sourceStart":49687,"tag":"atom"},{"children":[{"name":"Ne.symm","semanticRole":"global","source":"hik.symm","sourceEnd":49698,"sourceStart":49690,"tag":"identifier"},{"source":",","sourceEnd"... | [] | [{"source":"⟨hik.symm, hjk.symm⟩","source_end":49711,"source_start":49687,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 113 | 25 | exact | true | 1 | 29 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e0f930fad3922d98f90d712a270eb7627b4632ec049d9ca4e7f138eb5bb51a36 | 6e357d081e3a4d11b1d43ff47d1ff655797a43b1141bd2099ec96a1533e03874 | 27ec7b1415a424a7d044a066157f8fceee306b63ca179f5b1267fe5ba4d0d914 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,339 | ProbabilityTheory.kernel.iIndepFun.indepFun_prod_mk | Mathlib/Probability/Independence/Kernel.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext1 a | α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iIndepFun m ... | case h
α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iInde... | ((:c Eq) (:forall ω (:fv _uniq.175989) ((:c Prod) ((:fv _uniq.176082) (:fv _uniq.176407)) ((:fv _uniq.176082) (:fv _uniq.176408)))) (:lambda ω (:fv _uniq.175989) ((:c Prod.mk) ((:fv _uniq.176082) (:fv _uniq.176407)) ((:fv _uniq.176082) (:fv _uniq.176408)) ((:fv _uniq.176097) (:fv _uniq.176407) 0) ((:fv _uniq.176097) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"Ω","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"β✝","sexp":"(:sort (+ u_4 1))"},{"name":"β'","sexp":"(:sort (+ u_5 1))"},{"name":"γ","sexp":"(:sort (+ u_6 1))"},{"name":"γ'","sexp":"(:sort (+ u_7 1))"},{"name":"_mα","sexp":"((:c Measurabl... | (:app (:c Eq) (:arg :implicit-type 0 (:forall ω :explicit (:fv FV1) (:app (:c Prod) (:arg :explicit 0 (:app (:fv FV13) (:arg :explicit 0 (:fv FV20)))) (:arg :explicit 1 (:app (:fv FV13) (:arg :explicit 0 (:fv FV21))))))) (:arg :explicit 1 (:lambda ω :explicit (:fv FV1) (:app (:c Prod.mk) (:arg :implicit-type 0 (:app (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"ext1","sourceEnd":49171,"sourceStart":49167,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":49173,"sourceStart":49172,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"a","sourceEnd":49173,"sourceStart":49172,"ta... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 113 | 12 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e0b73476fe6efeb0ab73b66e7964799b65fc4c0830535357b87c69888ade90c2 | 93130b01e51930f88a2cff1fb9dacfa5372716bb44a5be1e04ffc9e2a58d310e | 0842c3c905ddfff77d4d78ac37d2bfb97666e48a897ec2fe6f4acee981c66048 | 65bf0a6d33dd42ab3499ecebbe754fb9e75691cdcd77c52539c4c2df01b61542 |
cat-searcher/leandojo-benchmark-4-random | test | 3,340 | ProbabilityTheory.kernel.iIndepFun.indepFun_prod_mk | Mathlib/Probability/Independence/Kernel.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | case h
α : Type u_1
Ω : Type u_2
ι : Type u_3
β✝ : Type u_4
β' : Type u_5
γ : Type u_6
γ' : Type u_7
_mα : MeasurableSpace α
_mΩ : MeasurableSpace Ω
κ : ↥(kernel α Ω)
μ : Measure α
f✝ : Ω → β✝
g : Ω → β'
β : ι → Type u_8
m : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
inst✝ : IsMarkovKernel κ
hf_Indep : iInde... | ((:c Eq) ((:c Prod) ((:fv _uniq.176082) (:fv _uniq.176407)) ((:fv _uniq.176082) (:fv _uniq.176408))) ((:c Prod.mk) ((:fv _uniq.176082) (:fv _uniq.176407)) ((:fv _uniq.176082) (:fv _uniq.176408)) ((:fv _uniq.176097) (:fv _uniq.176407) (:fv _uniq.177991)) ((:fv _uniq.176097) (:fv _uniq.176408) (:fv _uniq.177991))) ((:c F... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"Ω","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"β✝","sexp":"(:sort (+ u_4 1))"},{"name":"β'","sexp":"(:sort (+ u_5 1))"},{"name":"γ","sexp":"(:sort (+ u_6 1))"},{"name":"γ'","sexp":"(:sort (+ u_7 1))"},{"name":"_mα","sexp":"((:c Measurabl... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:fv FV13) (:arg :explicit 0 (:fv FV20)))) (:arg :explicit 1 (:app (:fv FV13) (:arg :explicit 0 (:fv FV21)))))) (:arg :explicit 1 (:app (:c Prod.mk) (:arg :implicit-type 0 (:app (:fv FV13) (:arg :explicit 0 (:fv FV20)))) (:arg :implicit-type 1... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"constructor","sourceEnd":49221,"sourceStart":49210,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":49221,"sourceStart":49210,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.175986","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.175989","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 113 | 14 | exact | true | 1 | 28 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1b4a09d8d850b6af9212aa71dfa55a58ebac49689e80cb005e28c74b95e19f6a | 65bf0a6d33dd42ab3499ecebbe754fb9e75691cdcd77c52539c4c2df01b61542 | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,341 | QPF.liftp_iff | Mathlib/Data/QPF/Univariate/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
⊢ Liftp p x ↔ ∃ a f, x = abs ⟨a, f⟩ ∧ ∀ (i : (P F).B a), p (f i) | case mp
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
⊢ Liftp p x → ∃ a f, x = abs ⟨a, f⟩ ∧ ∀ (i : (P F).B a), p (f i)
case mpr
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
⊢ (∃ a f, x = abs ⟨a, f⟩ ∧ ∀ (i : (P F).B a), p (f i)) → Liftp p x | ((:c Iff) ((:c Functor.Liftp) (:fv _uniq.1012) ((:c QPF.toFunctor) (:fv _uniq.1012) (:fv _uniq.1018)) (:fv _uniq.1104) (:fv _uniq.1105) (:fv _uniq.1106)) ((:c Exists) ((:c PFunctor.A) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018))) (:lambda a ((:c PFunctor.A) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018))) ((:c Exists)... | [{"name":"F","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c QPF) (:fv _uniq.1012))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.1104) (:sort 0))"},{"name":"x","sexp":"((:fv _uniq.1012) (:fv _uniq.1104))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Functor.Liftp) (:arg :implicit 0) (:arg :instance 1 (:instance-of (:app (:c Functor) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV3)) (:arg :explicit 3 (:fv FV4)) (:arg :explicit 4 (:fv FV5)))) (:arg :explicit 1 (:app (:c Exists) (:arg :implicit-type 0 (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"name":"F","sexp":"(:forall _ :explicit (:sort Type) (:sort Type))"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"name":"q","sexp":"(:app... | {"children":[{"source":"constructor","sourceEnd":2794,"sourceStart":2783,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":2794,"sourceStart":2783,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":3,"internal_name... | 16 | 4 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e32b7ef9c5ed6912ca08496137e56ae4710216394267e20274c7e8f4a7503717 | e068af9d428bdaba94da01aa6a428a2feafc1c7a6e05d0424f3a5cc18cf79dd2 | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | 87797da5bbf5ac3f71548749639d3ddb5554920720bd4ec7e403d7bb298dae86 |
cat-searcher/leandojo-benchmark-4-random | test | 3,342 | QPF.liftp_iff | Mathlib/Data/QPF/Univariate/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨a, f, h₀, h₁⟩ | case mpr
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
⊢ (∃ a f, x = abs ⟨a, f⟩ ∧ ∀ (i : (P F).B a), p (f i)) → Liftp p x | case mpr.intro.intro.intro
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
a : (P F).A
f : (P F).B a → α
h₀ : x = abs ⟨a, f⟩
h₁ : ∀ (i : (P F).B a), p (f i)
⊢ Liftp p x | (:forall _ ((:c Exists) ((:c PFunctor.A) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018))) (:lambda a ((:c PFunctor.A) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018))) ((:c Exists) (:forall _ ((:c PFunctor.B) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018)) 0) (:fv _uniq.1104)) (:lambda f (:forall _ ((:c PFunctor.B) ((:c QP... | [{"name":"F","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c QPF) (:fv _uniq.1012))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.1104) (:sort 0))"},{"name":"x","sexp":"((:fv _uniq.1012) (:fv _uniq.1104))"}] | (:forall _ :explicit (:app (:c Exists) (:arg :implicit-type 0 (:app (:c PFunctor.A) (:arg :explicit 0 (:app (:c QPF.P) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c QPF) (:arg :explicit 0 (:fv FV0))))))))) (:arg :explicit 1 (:lambda a :explicit (:app (:c PFunctor.A) (:arg :explicit 0 (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"name":"F","sexp":"(:forall _ :explicit (:sort Type) (:sort Type))"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"name":"q","sexp":"(:app... | {"children":[{"source":"rintro","sourceEnd":3002,"sourceStart":2996,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":3006,"sourceStart":3003,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":3007,"sourceSt... | [{"role":"fresh_name","source":"a","source_end":3007,"source_start":3006,"syntax_kind":"ident"},{"role":"fresh_name","source":"f","source_end":3010,"source_start":3009,"syntax_kind":"ident"},{"role":"fresh_name","source":"h₀","source_end":3016,"source_start":3012,"syntax_kind":"ident"},{"role":"fresh_name","source":"h₁... | [{"source":"⟨a, f, h₀, h₁⟩","source_end":3025,"source_start":3003,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":3,"internal_name... | 16 | 26 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 87113f72209be8e75431fffd1fb91c47a1bc0584c59910c65786d10d22f5c722 | d47e956aa433c762295756c4ac544066fb6238f00a507b6e0ed48737cbd45c0e | a4c9c34f48796ba056b4276977e89b610e907959810f59ac6b22d7b70de7ecbb | fa1cf5184026c6683668f331273d3397aae75bfd841890c5803ed18c9c3f8da3 |
cat-searcher/leandojo-benchmark-4-random | test | 3,343 | QPF.liftp_iff | Mathlib/Data/QPF/Univariate/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | use <a>QPF.abs</a> ⟨a, fun i => ⟨f i, h₁ i⟩⟩ | case mpr.intro.intro.intro
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
a : (P F).A
f : (P F).B a → α
h₀ : x = abs ⟨a, f⟩
h₁ : ∀ (i : (P F).B a), p (f i)
⊢ Liftp p x | case h
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
a : (P F).A
f : (P F).B a → α
h₀ : x = abs ⟨a, f⟩
h₁ : ∀ (i : (P F).B a), p (f i)
⊢ Subtype.val <$> abs ⟨a, fun i => ⟨f i, ⋯⟩⟩ = x | ((:c Functor.Liftp) (:fv _uniq.1012) ((:c QPF.toFunctor) (:fv _uniq.1012) (:fv _uniq.1018)) (:fv _uniq.1104) (:fv _uniq.1105) (:fv _uniq.1106)) | [{"name":"F","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c QPF) (:fv _uniq.1012))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.1104) (:sort 0))"},{"name":"x","sexp":"((:fv _uniq.1012) (:fv _uniq.1104))"},{"name":"a","sexp":"((:c PFunctor.A) ((:c QPF.... | (:app (:c Functor.Liftp) (:arg :implicit 0) (:arg :instance 1 (:instance-of (:app (:c Functor) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV3)) (:arg :explicit 3 (:fv FV4)) (:arg :explicit 4 (:fv FV5))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"name":"F","sexp":"(:forall _ :explicit (:sort Type) (:sort Type))"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"name":"q","sexp":"(:app... | {"children":[{"source":"use","sourceEnd":3031,"sourceStart":3028,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"children":[{"name":"QPF.abs","semanticRole":"global","source":"abs","sourceEnd":3035,"sourceStart":3032,"tag":"iden... | [] | [{"source":"abs ⟨a, fun i => ⟨f i, h₁ i⟩⟩","source_end":3071,"source_start":3032,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":3,"internal_name... | 16 | 27 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e639199786f6c8ace3e64223b248f76f56c25a9f739099ec2af53ad13b2408c2 | fa1cf5184026c6683668f331273d3397aae75bfd841890c5803ed18c9c3f8da3 | f8480ded46683f4de7f49bf236271c1c8b2b2847ffa699553fd3e06c431c1ee5 | a2f50e06362c3ca992e9669fe08eebe678b345840b04c08b96ef83dbdb81af5e |
cat-searcher/leandojo-benchmark-4-random | test | 3,344 | QPF.liftp_iff | Mathlib/Data/QPF/Univariate/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>QPF.abs_map</a>, h₀] | case h
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
a : (P F).A
f : (P F).B a → α
h₀ : x = abs ⟨a, f⟩
h₁ : ∀ (i : (P F).B a), p (f i)
⊢ Subtype.val <$> abs ⟨a, fun i => ⟨f i, ⋯⟩⟩ = x | case h
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
a : (P F).A
f : (P F).B a → α
h₀ : x = abs ⟨a, f⟩
h₁ : ∀ (i : (P F).B a), p (f i)
⊢ abs ((P F).map Subtype.val ⟨a, fun i => ⟨f i, ⋯⟩⟩) = abs ⟨a, f⟩ | ((:c Eq) ((:fv _uniq.1012) (:fv _uniq.1104)) ((:c Functor.map) (:fv _uniq.1012) ((:c QPF.toFunctor) (:fv _uniq.1012) (:fv _uniq.1018)) ((:c Subtype) (:fv _uniq.1104) (:fv _uniq.1105)) (:fv _uniq.1104) ((:c Subtype.val) (:fv _uniq.1104) (:fv _uniq.1105)) ((:c QPF.abs) (:fv _uniq.1012) (:fv _uniq.1018) ((:c Subtype) (:fv... | [{"name":"F","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c QPF) (:fv _uniq.1012))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.1104) (:sort 0))"},{"name":"x","sexp":"((:fv _uniq.1012) (:fv _uniq.1104))"},{"name":"a","sexp":"((:c PFunctor.A) ((:c QPF.... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:fv FV0) (:arg :explicit 0 (:fv FV3)))) (:arg :explicit 1 (:app (:c Functor.map) (:arg :implicit 0) (:arg :instance 1 (:instance-of (:app (:c Functor) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"name":"F","sexp":"(:forall _ :explicit (:sort Type) (:sort Type))"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"name":"q","sexp":"(:app... | {"children":[{"source":"rw","sourceEnd":3076,"sourceStart":3074,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3078,"sourceStart":3077,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":3081,"sourceStart":... | [] | [{"source":"abs_map","source_end":3089,"source_start":3082,"syntax_kind":"ident"},{"source":"h₀","source_end":3095,"source_start":3091,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":3,"internal_name... | 16 | 28 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e9cd9954643d9d57e91b0acc4cf9c0c57dfd64d23beefb718c522c218373a3ee | a2f50e06362c3ca992e9669fe08eebe678b345840b04c08b96ef83dbdb81af5e | b47b75bb448f265202a356a5088fa583b59b35408283ea2cd868f5da26b0aeeb | 631dbffe14e9aecc3a897f93187359e64f8c8cf303b77bb2c131548e26bea085 |
cat-searcher/leandojo-benchmark-4-random | test | 3,345 | QPF.liftp_iff | Mathlib/Data/QPF/Univariate/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case h
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
a : (P F).A
f : (P F).B a → α
h₀ : x = abs ⟨a, f⟩
h₁ : ∀ (i : (P F).B a), p (f i)
⊢ abs ((P F).map Subtype.val ⟨a, fun i => ⟨f i, ⋯⟩⟩) = abs ⟨a, f⟩ | ((:c Eq) ((:fv _uniq.1012) (:fv _uniq.1104)) ((:c QPF.abs) (:fv _uniq.1012) (:fv _uniq.1018) (:fv _uniq.1104) ((:c PFunctor.map) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018)) ((:c Subtype) (:fv _uniq.1104) (:fv _uniq.1105)) (:fv _uniq.1104) ((:c Subtype.val) (:fv _uniq.1104) (:fv _uniq.1105)) ((:c Sigma.mk) ((:c PFunc... | [{"name":"F","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c QPF) (:fv _uniq.1012))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.1104) (:sort 0))"},{"name":"x","sexp":"((:fv _uniq.1012) (:fv _uniq.1104))"},{"name":"a","sexp":"((:c PFunctor.A) ((:c QPF.... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:fv FV0) (:arg :explicit 0 (:fv FV3)))) (:arg :explicit 1 (:app (:c QPF.abs) (:arg :implicit 0) (:arg :instance 1 (:instance-of (:app (:c QPF) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV3)) (:arg :explicit 3 (:app (:c PFunctor.map) (:arg :explicit 0 (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"name":"F","sexp":"(:forall _ :explicit (:sort Type) (:sort Type))"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"name":"q","sexp":"(:app... | {"children":[{"source":"rfl","sourceEnd":3101,"sourceStart":3098,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":3101,"sourceStart":3098,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":3,"internal_name... | 16 | 33 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 677f91a4ae5b81a372822bc7b30bda5efe9b7e8b6fe69c52686f3b70424a95c1 | 631dbffe14e9aecc3a897f93187359e64f8c8cf303b77bb2c131548e26bea085 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,346 | QPF.liftp_iff | Mathlib/Data/QPF/Univariate/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨y, hy⟩ | case mp
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
⊢ Liftp p x → ∃ a f, x = abs ⟨a, f⟩ ∧ ∀ (i : (P F).B a), p (f i) | case mp.intro
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
y : F (Subtype p)
hy : Subtype.val <$> y = x
⊢ ∃ a f, x = abs ⟨a, f⟩ ∧ ∀ (i : (P F).B a), p (f i) | (:forall _ ((:c Functor.Liftp) (:fv _uniq.1012) ((:c QPF.toFunctor) (:fv _uniq.1012) (:fv _uniq.1018)) (:fv _uniq.1104) (:fv _uniq.1105) (:fv _uniq.1106)) ((:c Exists) ((:c PFunctor.A) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018))) (:lambda a ((:c PFunctor.A) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018))) ((:c Exists... | [{"name":"F","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c QPF) (:fv _uniq.1012))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.1104) (:sort 0))"},{"name":"x","sexp":"((:fv _uniq.1012) (:fv _uniq.1104))"}] | (:forall _ :explicit (:app (:c Functor.Liftp) (:arg :implicit 0) (:arg :instance 1 (:instance-of (:app (:c Functor) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV3)) (:arg :explicit 3 (:fv FV4)) (:arg :explicit 4 (:fv FV5))) (:app (:c Exists) (:arg :implicit-type 0 (:app (:c PFunctor.A) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"name":"F","sexp":"(:forall _ :explicit (:sort Type) (:sort Type))"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"name":"q","sexp":"(:app... | {"children":[{"source":"rintro","sourceEnd":2806,"sourceStart":2800,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":2810,"sourceStart":2807,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":2811,"sourceSt... | [{"role":"fresh_name","source":"y","source_end":2811,"source_start":2810,"syntax_kind":"ident"},{"role":"fresh_name","source":"hy","source_end":2815,"source_start":2813,"syntax_kind":"ident"}] | [{"source":"⟨y, hy⟩","source_end":2818,"source_start":2807,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":3,"internal_name... | 16 | 9 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5442c3e4d5022a6a47f8725879a1f35f8acedfa0c95e289f942e3c8e3f76ffe7 | 696cd7ab976f8f13ba06c9f50f9b1478a5ce1e7e8d90889ae701e58bcc90eb97 | 813cc811905d2e7e9af04e80bc2c0ad03d98df053fe26eaaf7bb20ae162aefaf | 7c843723b20a2fa897b9be4358b8d290e36ca85fb7cf5d6d16d42b9e9aeb38ce |
cat-searcher/leandojo-benchmark-4-random | test | 3,347 | QPF.liftp_iff | Mathlib/Data/QPF/Univariate/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases' h : <a>QPF.repr</a> y with a f | case mp.intro
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
y : F (Subtype p)
hy : Subtype.val <$> y = x
⊢ ∃ a f, x = abs ⟨a, f⟩ ∧ ∀ (i : (P F).B a), p (f i) | case mp.intro.mk
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
y : F (Subtype p)
hy : Subtype.val <$> y = x
a : (P F).A
f : (P F).B a → Subtype p
h : repr y = ⟨a, f⟩
⊢ ∃ a f, x = abs ⟨a, f⟩ ∧ ∀ (i : (P F).B a), p (f i) | ((:c Exists) ((:c PFunctor.A) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018))) (:lambda a ((:c PFunctor.A) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018))) ((:c Exists) (:forall _ ((:c PFunctor.B) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018)) 0) (:fv _uniq.1104)) (:lambda f (:forall _ ((:c PFunctor.B) ((:c QPF.P) (:fv _... | [{"name":"F","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c QPF) (:fv _uniq.1012))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.1104) (:sort 0))"},{"name":"x","sexp":"((:fv _uniq.1012) (:fv _uniq.1104))"},{"name":"y","sexp":"((:fv _uniq.1012) ((:c Sub... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c PFunctor.A) (:arg :explicit 0 (:app (:c QPF.P) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c QPF) (:arg :explicit 0 (:fv FV0))))))))) (:arg :explicit 1 (:lambda a :explicit (:app (:c PFunctor.A) (:arg :explicit 0 (:app (:c QPF.P) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"name":"F","sexp":"(:forall _ :explicit (:sort Type) (:sort Type))"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"name":"q","sexp":"(:app... | {"children":[{"source":"cases'","sourceEnd":2829,"sourceStart":2823,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":2831,"sourceStart":2830,"tag":"identifier"},{"source":":","sourceEnd":2833,"sourceStart":2832,"tag":"atom"}],"kind":"null","source":"h :","sour... | [] | [{"source":"repr y","source_end":2840,"source_start":2834,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":3,"internal_name... | 16 | 10 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6f163f208ece5ae64940cdc1bdd0237d8972eb0b0a53ddccd438a73f2b01d323 | 7c843723b20a2fa897b9be4358b8d290e36ca85fb7cf5d6d16d42b9e9aeb38ce | ac80e233cf3b9abb75de77cecb30e610176ce89165437c3bb9e0d8b01df8a96d | 727e2dee256e5c1cd33ce397913ac7d30fb423e8d0c9e9e60ea92c67bf20a8ed |
cat-searcher/leandojo-benchmark-4-random | test | 3,348 | QPF.liftp_iff | Mathlib/Data/QPF/Univariate/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | use a, fun i => (f i).<a>Subtype.val</a> | case mp.intro.mk
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
y : F (Subtype p)
hy : Subtype.val <$> y = x
a : (P F).A
f : (P F).B a → Subtype p
h : repr y = ⟨a, f⟩
⊢ ∃ a f, x = abs ⟨a, f⟩ ∧ ∀ (i : (P F).B a), p (f i) | case h
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
y : F (Subtype p)
hy : Subtype.val <$> y = x
a : (P F).A
f : (P F).B a → Subtype p
h : repr y = ⟨a, f⟩
⊢ x = abs ⟨a, fun i => ↑(f i)⟩ ∧ ∀ (i : (P F).B a), p ↑(f i) | ((:c Exists) ((:c PFunctor.A) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018))) (:lambda a ((:c PFunctor.A) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018))) ((:c Exists) (:forall _ ((:c PFunctor.B) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018)) 0) (:fv _uniq.1104)) (:lambda f (:forall _ ((:c PFunctor.B) ((:c QPF.P) (:fv _... | [{"name":"F","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c QPF) (:fv _uniq.1012))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.1104) (:sort 0))"},{"name":"x","sexp":"((:fv _uniq.1012) (:fv _uniq.1104))"},{"name":"y","sexp":"((:fv _uniq.1012) ((:c Sub... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c PFunctor.A) (:arg :explicit 0 (:app (:c QPF.P) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c QPF) (:arg :explicit 0 (:fv FV0))))))))) (:arg :explicit 1 (:lambda a :explicit (:app (:c PFunctor.A) (:arg :explicit 0 (:app (:c QPF.P) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"name":"F","sexp":"(:forall _ :explicit (:sort Type) (:sort Type))"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"name":"q","sexp":"(:app... | {"children":[{"source":"use","sourceEnd":2857,"sourceStart":2854,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"contextIndex":8,"semanticRole":"local","source":"a","sourceEnd":2859,"sourceStart":2858,"tag":"identifier"},{"sourc... | [] | [{"source":"a","source_end":2859,"source_start":2858,"syntax_kind":"ident"},{"source":"fun i => (f i).val","source_end":2879,"source_start":2861,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":3,"internal_name... | 16 | 11 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b59476c66a3286344e4f580522d9b72ae9cb9eb87544ea58754af42df491481f | 727e2dee256e5c1cd33ce397913ac7d30fb423e8d0c9e9e60ea92c67bf20a8ed | 7c546d4607ff54088524ac545ba0c06bee41c34dc53ecf8ab55c65abf349b85a | e634c0a66181e00b062d247f99e247051f6501def3cb4dc79878138ed1ac8df8 |
cat-searcher/leandojo-benchmark-4-random | test | 3,349 | QPF.liftp_iff | Mathlib/Data/QPF/Univariate/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | case h
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
y : F (Subtype p)
hy : Subtype.val <$> y = x
a : (P F).A
f : (P F).B a → Subtype p
h : repr y = ⟨a, f⟩
⊢ x = abs ⟨a, fun i => ↑(f i)⟩ ∧ ∀ (i : (P F).B a), p ↑(f i) | case h.left
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
y : F (Subtype p)
hy : Subtype.val <$> y = x
a : (P F).A
f : (P F).B a → Subtype p
h : repr y = ⟨a, f⟩
⊢ x = abs ⟨a, fun i => ↑(f i)⟩
case h.right
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
y : F (Subtype p)
hy : Subtype.val <$... | ((:c And) ((:c Eq) ((:fv _uniq.1012) (:fv _uniq.1104)) (:fv _uniq.1106) ((:c QPF.abs) (:fv _uniq.1012) (:fv _uniq.1018) (:fv _uniq.1104) ((:c Sigma.mk) ((:c PFunctor.A) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018))) (:lambda x ((:c PFunctor.A) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018))) (:forall _ ((:c PFunctor.B)... | [{"name":"F","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c QPF) (:fv _uniq.1012))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.1104) (:sort 0))"},{"name":"x","sexp":"((:fv _uniq.1012) (:fv _uniq.1104))"},{"name":"y","sexp":"((:fv _uniq.1012) ((:c Sub... | (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:fv FV0) (:arg :explicit 0 (:fv FV3)))) (:arg :explicit 1 (:fv FV5)) (:arg :explicit 2 (:app (:c QPF.abs) (:arg :implicit 0) (:arg :instance 1 (:instance-of (:app (:c QPF) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV3)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"name":"F","sexp":"(:forall _ :explicit (:sort Type) (:sort Type))"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"name":"q","sexp":"(:app... | {"children":[{"source":"constructor","sourceEnd":2895,"sourceStart":2884,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":2895,"sourceStart":2884,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":3,"internal_name... | 16 | 12 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 132677a90650e43162ddc48cab08986cbc3db1b569706dd4249186c6228ab1ea | e634c0a66181e00b062d247f99e247051f6501def3cb4dc79878138ed1ac8df8 | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | e7126ba7b82f646dc55c5f6925413843e0c877a90638b71098fc49063259d76e |
cat-searcher/leandojo-benchmark-4-random | test | 3,350 | QPF.liftp_iff | Mathlib/Data/QPF/Univariate/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro i | case h.right
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
y : F (Subtype p)
hy : Subtype.val <$> y = x
a : (P F).A
f : (P F).B a → Subtype p
h : repr y = ⟨a, f⟩
⊢ ∀ (i : (P F).B a), p ↑(f i) | case h.right
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
y : F (Subtype p)
hy : Subtype.val <$> y = x
a : (P F).A
f : (P F).B a → Subtype p
h : repr y = ⟨a, f⟩
i : (P F).B a
⊢ p ↑(f i) | (:forall i ((:c PFunctor.B) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018)) (:fv _uniq.1204)) ((:fv _uniq.1105) ((:c Subtype.val) (:fv _uniq.1104) (:fv _uniq.1105) ((:fv _uniq.1205) 0)))) | [{"name":"F","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c QPF) (:fv _uniq.1012))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.1104) (:sort 0))"},{"name":"x","sexp":"((:fv _uniq.1012) (:fv _uniq.1104))"},{"name":"y","sexp":"((:fv _uniq.1012) ((:c Sub... | (:forall i :explicit (:app (:c PFunctor.B) (:arg :explicit 0 (:app (:c QPF.P) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c QPF) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:fv FV8))) (:app (:fv FV4) (:arg :explicit 0 (:app (:c Subtype.val) (:arg :implicit-type 0 (:fv FV3)) (:arg :impl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"name":"F","sexp":"(:forall _ :explicit (:sort Type) (:sort Type))"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"name":"q","sexp":"(:app... | {"children":[{"source":"intro","sourceEnd":2966,"sourceStart":2961,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"i","sourceEnd":2968,"sourceStart":2967,"tag":"identifier"}],"kind":"null","source":"i","sourceEnd":2968,"sourceStart":2967,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source":"int... | [{"role":"fresh_name","source":"i","source_end":2968,"source_start":2967,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":3,"internal_name... | 16 | 24 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 14473f0af3346abb216ca1fb34287d4ef8714a25c5e367df38145fbc36d199b2 | 41540a2e1a437ed714e21037974da66f2f87ce95ac2a1e237d20be0378ba9731 | dbbb5bd97a735e823e818f7e277169eb5193225c74d8cc1ad07622a04037f7c3 | e0760ba3f6520e3d94854407243a541dc519d6b762963e09d8decd1657a7e4da |
cat-searcher/leandojo-benchmark-4-random | test | 3,351 | QPF.liftp_iff | Mathlib/Data/QPF/Univariate/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply (f i).<a>Subtype.property</a> | case h.right
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
y : F (Subtype p)
hy : Subtype.val <$> y = x
a : (P F).A
f : (P F).B a → Subtype p
h : repr y = ⟨a, f⟩
i : (P F).B a
⊢ p ↑(f i) | ((:fv _uniq.1105) ((:c Subtype.val) (:fv _uniq.1104) (:fv _uniq.1105) ((:fv _uniq.1205) (:fv _uniq.1405)))) | [{"name":"F","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c QPF) (:fv _uniq.1012))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.1104) (:sort 0))"},{"name":"x","sexp":"((:fv _uniq.1012) (:fv _uniq.1104))"},{"name":"y","sexp":"((:fv _uniq.1012) ((:c Sub... | (:app (:fv FV4) (:arg :explicit 0 (:app (:c Subtype.val) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit 1) (:arg :explicit 2 (:app (:fv FV9) (:arg :explicit 0 (:fv FV11))))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"name":"F","sexp":"(:forall _ :explicit (:sort Type) (:sort Type))"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"name":"q","sexp":"(:app... | {"children":[{"source":"apply","sourceEnd":2978,"sourceStart":2973,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":2980,"sourceStart":2979,"tag":"atom"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"f","sourceEnd":2981,"sourceStart":2980,"tag":"identifier"},{"children":[{"contextInde... | [] | [{"source":"(f i).property","source_end":2993,"source_start":2979,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":3,"internal_name... | 16 | 25 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 062e1c1409d08beee74961497ddb1c307771a5a8227aa24a2d33ca3d315b2cf1 | e0760ba3f6520e3d94854407243a541dc519d6b762963e09d8decd1657a7e4da | 9379bf291b45f322670266340407a0c73ec5648133f46e57d665ff9f63dfddc5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,352 | QPF.liftp_iff | Mathlib/Data/QPF/Univariate/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hy, ← <a>QPF.abs_repr</a> y, h, ← <a>QPF.abs_map</a>] | case h.left
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
y : F (Subtype p)
hy : Subtype.val <$> y = x
a : (P F).A
f : (P F).B a → Subtype p
h : repr y = ⟨a, f⟩
⊢ x = abs ⟨a, fun i => ↑(f i)⟩ | case h.left
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
y : F (Subtype p)
hy : Subtype.val <$> y = x
a : (P F).A
f : (P F).B a → Subtype p
h : repr y = ⟨a, f⟩
⊢ abs ((P F).map Subtype.val ⟨a, f⟩) = abs ⟨a, fun i => ↑(f i)⟩ | ((:c Eq) ((:fv _uniq.1012) (:fv _uniq.1104)) (:fv _uniq.1106) ((:c QPF.abs) (:fv _uniq.1012) (:fv _uniq.1018) (:fv _uniq.1104) ((:c Sigma.mk) ((:c PFunctor.A) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018))) (:lambda x ((:c PFunctor.A) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018))) (:forall _ ((:c PFunctor.B) ((:c QPF.... | [{"name":"F","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c QPF) (:fv _uniq.1012))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.1104) (:sort 0))"},{"name":"x","sexp":"((:fv _uniq.1012) (:fv _uniq.1104))"},{"name":"y","sexp":"((:fv _uniq.1012) ((:c Sub... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:fv FV0) (:arg :explicit 0 (:fv FV3)))) (:arg :explicit 1 (:fv FV5)) (:arg :explicit 2 (:app (:c QPF.abs) (:arg :implicit 0) (:arg :instance 1 (:instance-of (:app (:c QPF) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV3)) (:arg :explicit 3 (:app (:c Sigma.mk) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"name":"F","sexp":"(:forall _ :explicit (:sort Type) (:sort Type))"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"name":"q","sexp":"(:app... | {"children":[{"source":"rw","sourceEnd":2905,"sourceStart":2903,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2907,"sourceStart":2906,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":2910,"sourceStart":... | [] | [{"source":"hy","source_end":2913,"source_start":2911,"syntax_kind":"ident"},{"source":"abs_repr y","source_end":2929,"source_start":2919,"syntax_kind":"Lean.Parser.Term.app"},{"source":"h","source_end":2932,"source_start":2931,"syntax_kind":"ident"},{"source":"abs_map","source_end":2945,"source_start":2938,"syntax_kin... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":3,"internal_name... | 16 | 17 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2b641a7d64d8e53154423f8dea55bec1f38287af5dc212df123c80c5c617ea30 | 97fb0976b17b18609798ba7c18c1f8f9bafd77d3ee794b994c504f1c16399d38 | 27f0784fe4ce3de1754239465bb955eda5ea47143f248fe7d0fb6b686aa48d26 | c4dfabfde2f482cfb211d4c19975edbf600fd1d9b7974813ce8e71d0f7018b8b |
cat-searcher/leandojo-benchmark-4-random | test | 3,353 | QPF.liftp_iff | Mathlib/Data/QPF/Univariate/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case h.left
F : Type u → Type u
q : QPF F
α : Type u
p : α → Prop
x : F α
y : F (Subtype p)
hy : Subtype.val <$> y = x
a : (P F).A
f : (P F).B a → Subtype p
h : repr y = ⟨a, f⟩
⊢ abs ((P F).map Subtype.val ⟨a, f⟩) = abs ⟨a, fun i => ↑(f i)⟩ | ((:c Eq) ((:fv _uniq.1012) (:fv _uniq.1104)) ((:c QPF.abs) (:fv _uniq.1012) (:fv _uniq.1018) (:fv _uniq.1104) ((:c PFunctor.map) ((:c QPF.P) (:fv _uniq.1012) (:fv _uniq.1018)) ((:c Subtype) (:fv _uniq.1104) (:fv _uniq.1105)) (:fv _uniq.1104) ((:c Subtype.val) (:fv _uniq.1104) (:fv _uniq.1105)) ((:c Sigma.mk) ((:c PFunc... | [{"name":"F","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c QPF) (:fv _uniq.1012))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.1104) (:sort 0))"},{"name":"x","sexp":"((:fv _uniq.1012) (:fv _uniq.1104))"},{"name":"y","sexp":"((:fv _uniq.1012) ((:c Sub... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:fv FV0) (:arg :explicit 0 (:fv FV3)))) (:arg :explicit 1 (:app (:c QPF.abs) (:arg :implicit 0) (:arg :instance 1 (:instance-of (:app (:c QPF) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV3)) (:arg :explicit 3 (:app (:c PFunctor.map) (:arg :explicit 0 (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"name":"F","sexp":"(:forall _ :explicit (:sort Type) (:sort Type))"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"name":"q","sexp":"(:app... | {"children":[{"source":"rfl","sourceEnd":2956,"sourceStart":2953,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":2956,"sourceStart":2953,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1012","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1018","is_instance":true,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":3,"internal_name... | 16 | 23 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5fc6dfd038a7d3798ef1bd454cdf746e981d61e5d65e95391efcc2b63f7c353b | c4dfabfde2f482cfb211d4c19975edbf600fd1d9b7974813ce8e71d0f7018b8b | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,354 | differentiableWithinAt_univ | Mathlib/Analysis/Calculus/FDeriv/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>DifferentiableWithinAt</a>, <a>hasFDerivWithinAt_univ</a>, <a>DifferentiableAt</a>] | 𝕜 : Type u_1
inst✝⁸ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
F : Type u_3
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
G : Type u_4
inst✝³ : NormedAddCommGroup G
inst✝² : NormedSpace 𝕜 G
G' : Type u_5
inst✝¹ : NormedAddCommGroup G'
inst✝ : NormedSpac... | ((:c Iff) ((:c DifferentiableWithinAt) (:fv _uniq.343532) (:fv _uniq.343535) (:fv _uniq.343538) (:fv _uniq.343541) (:fv _uniq.343649) (:fv _uniq.343652) (:fv _uniq.343655) (:fv _uniq.343758) (:fv _uniq.343980) ((:c Set.univ) (:fv _uniq.343538)) (:fv _uniq.346206)) ((:c DifferentiableAt) (:fv _uniq.343532) (:fv _uniq.34... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.343532))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCommGroup) (:fv _uniq.343538))"},{"name":"inst✝⁶","sexp":"((:c NormedSpace) (:fv _uniq.343532) (:fv _uniq.343538) ((:c Non... | (:app (:c Iff) (:arg :explicit 0 (:app (:c DifferentiableWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2)))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.343532","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.343535","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":31900,"sourceStart":31896,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":31905,"sourceStart":31901,"tag":"atom"}],"kind"... | [] | [{"source":"DifferentiableWithinAt","source_end":31929,"source_start":31907,"syntax_kind":"ident"},{"source":"hasFDerivWithinAt_univ","source_end":31953,"source_start":31931,"syntax_kind":"ident"},{"source":"DifferentiableAt","source_end":31971,"source_start":31955,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.343532","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.343535","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":implicit","context_index":2,"int... | 156 | 2 | exact | true | 1 | 29 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9942bb6357f9a0b3ca2d39403a7498173306591213b8d9641db18a2dfce6b8aa | 5ea658c58783df72882b9e067f4582295adf2d357636e85f259dd20bde70dd29 | 73d3f74647209135a3e1fe416b3934788647618f2f1600bd63d6b98fa9a30b94 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,355 | FirstOrder.Language.Embedding.coe_injective | Mathlib/ModelTheory/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases f | L : Language
L' : Language
M : Type w
N : Type w'
inst✝³ : L.Structure M
inst✝² : L.Structure N
P : Type u_1
inst✝¹ : L.Structure P
Q : Type u_2
inst✝ : L.Structure Q
f g : M ↪[L] N
h : ⇑f = ⇑g
⊢ f = g | case mk
L : Language
L' : Language
M : Type w
N : Type w'
inst✝³ : L.Structure M
inst✝² : L.Structure N
P : Type u_1
inst✝¹ : L.Structure P
Q : Type u_2
inst✝ : L.Structure Q
g : M ↪[L] N
toEmbedding✝ : M ↪ N
map_fun'✝ :
∀ {n : ℕ} (f : L.Functions n) (x : Fin n → M), toEmbedding✝.toFun (funMap f x) = funMap f (toEmbe... | ((:c Eq) ((:c FirstOrder.Language.Embedding) (:fv _uniq.96302) (:fv _uniq.96306) (:fv _uniq.96308) (:fv _uniq.96315) (:fv _uniq.96322)) (:fv _uniq.96482) (:fv _uniq.96483)) | [{"name":"L","sexp":"(:c FirstOrder.Language)"},{"name":"L'","sexp":"(:c FirstOrder.Language)"},{"name":"M","sexp":"(:sort (+ w 1))"},{"name":"N","sexp":"(:sort (+ w' 1))"},{"name":"inst✝³","sexp":"((:c FirstOrder.Language.Structure) (:fv _uniq.96302) (:fv _uniq.96306))"},{"name":"inst✝²","sexp":"((:c FirstOrder.Langua... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c FirstOrder.Language.Embedding) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c FirstOrder.Language.Structure) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2))))) (:arg :instance 4 (:i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.96302","is_instance":false,"is_let":false,"name":"L","sexp":"(:c FirstOrder.Language)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.96304","is_instance":false,"is_let":false,"name":"L'","sexp":"(:c FirstOrder.Language)"},{"bind... | {"children":[{"source":"cases","sourceEnd":28731,"sourceStart":28726,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":11,"semanticRole":"local","source":"f","sourceEnd":28733,"sourceStart":28732,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","s... | [] | [{"source":"f","source_end":28733,"source_start":28732,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.96302","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.96304","is_instance":false,"is_let":false,"user_name":"L'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 198 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a53777c9b90b9ccc2889841df3e8d93fe282ad2280cb1f7dd8b6cd4f27573625 | faa8a01e8019c360756596bf9de6dd1cfc65a489b6d0e7dabc595a02f346cc30 | 8933eda3eb04918aa220940c3af5081708ccaaf69fc8e82139d499b98a43bc01 | 78a417a71da6abb8253d30155a7550e61ba68265ad6c89a08cc17ada70a57cc4 |
cat-searcher/leandojo-benchmark-4-random | test | 3,356 | FirstOrder.Language.Embedding.coe_injective | Mathlib/ModelTheory/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases g | case mk
L : Language
L' : Language
M : Type w
N : Type w'
inst✝³ : L.Structure M
inst✝² : L.Structure N
P : Type u_1
inst✝¹ : L.Structure P
Q : Type u_2
inst✝ : L.Structure Q
g : M ↪[L] N
toEmbedding✝ : M ↪ N
map_fun'✝ :
∀ {n : ℕ} (f : L.Functions n) (x : Fin n → M), toEmbedding✝.toFun (funMap f x) = funMap f (toEmbe... | case mk.mk
L : Language
L' : Language
M : Type w
N : Type w'
inst✝³ : L.Structure M
inst✝² : L.Structure N
P : Type u_1
inst✝¹ : L.Structure P
Q : Type u_2
inst✝ : L.Structure Q
toEmbedding✝¹ : M ↪ N
map_fun'✝¹ :
∀ {n : ℕ} (f : L.Functions n) (x : Fin n → M), toEmbedding✝¹.toFun (funMap f x) = funMap f (toEmbedding✝¹... | ((:c Eq) ((:c FirstOrder.Language.Embedding) (:fv _uniq.96302) (:fv _uniq.96306) (:fv _uniq.96308) (:fv _uniq.96315) (:fv _uniq.96322)) ((:c FirstOrder.Language.Embedding.mk) (:fv _uniq.96302) (:fv _uniq.96306) (:fv _uniq.96308) (:fv _uniq.96315) (:fv _uniq.96322) (:fv _uniq.96599) (:fv _uniq.96600) (:fv _uniq.96601)) ... | [{"name":"L","sexp":"(:c FirstOrder.Language)"},{"name":"L'","sexp":"(:c FirstOrder.Language)"},{"name":"M","sexp":"(:sort (+ w 1))"},{"name":"N","sexp":"(:sort (+ w' 1))"},{"name":"inst✝³","sexp":"((:c FirstOrder.Language.Structure) (:fv _uniq.96302) (:fv _uniq.96306))"},{"name":"inst✝²","sexp":"((:c FirstOrder.Langua... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c FirstOrder.Language.Embedding) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c FirstOrder.Language.Structure) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2))))) (:arg :instance 4 (:i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.96302","is_instance":false,"is_let":false,"name":"L","sexp":"(:c FirstOrder.Language)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.96304","is_instance":false,"is_let":false,"name":"L'","sexp":"(:c FirstOrder.Language)"},{"bind... | {"children":[{"source":"cases","sourceEnd":28743,"sourceStart":28738,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":11,"semanticRole":"local","source":"g","sourceEnd":28745,"sourceStart":28744,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","s... | [] | [{"source":"g","source_end":28745,"source_start":28744,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.96302","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.96304","is_instance":false,"is_let":false,"user_name":"L'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 198 | 5 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6400678e6ab494086124b0b9ce81199f27cbcaf662c51ad40ff071a93cfc7a70 | 78a417a71da6abb8253d30155a7550e61ba68265ad6c89a08cc17ada70a57cc4 | a3f2f74e996d2bff612576f3ab3419ce0806ba4e6a7852cdcbbf7ae6f094797f | 3337aa2384f8924331671d78a092a585aae897c22d61ad53156c3bf80bced006 |
cat-searcher/leandojo-benchmark-4-random | test | 3,357 | FirstOrder.Language.Embedding.coe_injective | Mathlib/ModelTheory/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr | case mk.mk
L : Language
L' : Language
M : Type w
N : Type w'
inst✝³ : L.Structure M
inst✝² : L.Structure N
P : Type u_1
inst✝¹ : L.Structure P
Q : Type u_2
inst✝ : L.Structure Q
toEmbedding✝¹ : M ↪ N
map_fun'✝¹ :
∀ {n : ℕ} (f : L.Functions n) (x : Fin n → M), toEmbedding✝¹.toFun (funMap f x) = funMap f (toEmbedding✝¹... | case mk.mk.e_toEmbedding
L : Language
L' : Language
M : Type w
N : Type w'
inst✝³ : L.Structure M
inst✝² : L.Structure N
P : Type u_1
inst✝¹ : L.Structure P
Q : Type u_2
inst✝ : L.Structure Q
toEmbedding✝¹ : M ↪ N
map_fun'✝¹ :
∀ {n : ℕ} (f : L.Functions n) (x : Fin n → M), toEmbedding✝¹.toFun (funMap f x) = funMap f ... | ((:c Eq) ((:c FirstOrder.Language.Embedding) (:fv _uniq.96302) (:fv _uniq.96306) (:fv _uniq.96308) (:fv _uniq.96315) (:fv _uniq.96322)) ((:c FirstOrder.Language.Embedding.mk) (:fv _uniq.96302) (:fv _uniq.96306) (:fv _uniq.96308) (:fv _uniq.96315) (:fv _uniq.96322) (:fv _uniq.96599) (:fv _uniq.96600) (:fv _uniq.96601)) ... | [{"name":"L","sexp":"(:c FirstOrder.Language)"},{"name":"L'","sexp":"(:c FirstOrder.Language)"},{"name":"M","sexp":"(:sort (+ w 1))"},{"name":"N","sexp":"(:sort (+ w' 1))"},{"name":"inst✝³","sexp":"((:c FirstOrder.Language.Structure) (:fv _uniq.96302) (:fv _uniq.96306))"},{"name":"inst✝²","sexp":"((:c FirstOrder.Langua... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c FirstOrder.Language.Embedding) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c FirstOrder.Language.Structure) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2))))) (:arg :instance 4 (:i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.96302","is_instance":false,"is_let":false,"name":"L","sexp":"(:c FirstOrder.Language)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.96304","is_instance":false,"is_let":false,"name":"L'","sexp":"(:c FirstOrder.Language)"},{"bind... | {"children":[{"source":"congr","sourceEnd":28755,"sourceStart":28750,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.congr","source":"congr","sourceEnd":28755,"sourceStart":28750,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.96302","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.96304","is_instance":false,"is_let":false,"user_name":"L'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 198 | 6 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1a450fedfc0fc96fc289f01522a4eeb89dfc27fd32777482fd276c5c3b48e62d | 3337aa2384f8924331671d78a092a585aae897c22d61ad53156c3bf80bced006 | 092b163cac48997cb6cc327c63cda260e694055f56ff3698a70cdfda80ffbb2b | 4dd21f0e68679cc9a9ab1c859ef9b5e8f22490739fbd376754f9e1bb587eb1a6 |
cat-searcher/leandojo-benchmark-4-random | test | 3,358 | FirstOrder.Language.Embedding.coe_injective | Mathlib/ModelTheory/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext x | case mk.mk.e_toEmbedding
L : Language
L' : Language
M : Type w
N : Type w'
inst✝³ : L.Structure M
inst✝² : L.Structure N
P : Type u_1
inst✝¹ : L.Structure P
Q : Type u_2
inst✝ : L.Structure Q
toEmbedding✝¹ : M ↪ N
map_fun'✝¹ :
∀ {n : ℕ} (f : L.Functions n) (x : Fin n → M), toEmbedding✝¹.toFun (funMap f x) = funMap f ... | case mk.mk.e_toEmbedding.h
L : Language
L' : Language
M : Type w
N : Type w'
inst✝³ : L.Structure M
inst✝² : L.Structure N
P : Type u_1
inst✝¹ : L.Structure P
Q : Type u_2
inst✝ : L.Structure Q
toEmbedding✝¹ : M ↪ N
map_fun'✝¹ :
∀ {n : ℕ} (f : L.Functions n) (x : Fin n → M), toEmbedding✝¹.toFun (funMap f x) = funMap ... | ((:c Eq) ((:c Function.Embedding) (:fv _uniq.96306) (:fv _uniq.96308)) (:fv _uniq.96599) (:fv _uniq.96662)) | [{"name":"L","sexp":"(:c FirstOrder.Language)"},{"name":"L'","sexp":"(:c FirstOrder.Language)"},{"name":"M","sexp":"(:sort (+ w 1))"},{"name":"N","sexp":"(:sort (+ w' 1))"},{"name":"inst✝³","sexp":"((:c FirstOrder.Language.Structure) (:fv _uniq.96302) (:fv _uniq.96306))"},{"name":"inst✝²","sexp":"((:c FirstOrder.Langua... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Function.Embedding) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV3)))) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:fv FV14))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.96302","is_instance":false,"is_let":false,"name":"L","sexp":"(:c FirstOrder.Language)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.96304","is_instance":false,"is_let":false,"name":"L'","sexp":"(:c FirstOrder.Language)"},{"bind... | {"children":[{"source":"ext","sourceEnd":28763,"sourceStart":28760,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":28765,"sourceStart":28764,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":28765,"sourceStart":28764,"tag... | [{"role":"fresh_name","source":"x","source_end":28765,"source_start":28764,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.96302","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.96304","is_instance":false,"is_let":false,"user_name":"L'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 198 | 7 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3162815ad9c1f3191621962abdf1f24d45a054265980ed728f72715646f89bce | 4dd21f0e68679cc9a9ab1c859ef9b5e8f22490739fbd376754f9e1bb587eb1a6 | ee522618587c4a8062e9541e92fad69d5c6e7dbdf5366e9d82c63ebe3c1e08c5 | 5055392c8c5c56865a5ebc3f3fdf080505c76f8188d8e0f83ed1d5031283ce68 |
cat-searcher/leandojo-benchmark-4-random | test | 3,359 | FirstOrder.Language.Embedding.coe_injective | Mathlib/ModelTheory/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Function.funext_iff</a>.1 h x | case mk.mk.e_toEmbedding.h
L : Language
L' : Language
M : Type w
N : Type w'
inst✝³ : L.Structure M
inst✝² : L.Structure N
P : Type u_1
inst✝¹ : L.Structure P
Q : Type u_2
inst✝ : L.Structure Q
toEmbedding✝¹ : M ↪ N
map_fun'✝¹ :
∀ {n : ℕ} (f : L.Functions n) (x : Fin n → M), toEmbedding✝¹.toFun (funMap f x) = funMap ... | ((:c Eq) (:fv _uniq.96308) ((:c DFunLike.coe) ((:c Function.Embedding) (:fv _uniq.96306) (:fv _uniq.96308)) (:fv _uniq.96306) (:lambda _ (:fv _uniq.96306) (:fv _uniq.96308)) ((:c Function.instFunLikeEmbedding) (:fv _uniq.96306) (:fv _uniq.96308)) (:fv _uniq.96599) (:fv _uniq.96957)) ((:c DFunLike.coe) ((:c Function.Emb... | [{"name":"L","sexp":"(:c FirstOrder.Language)"},{"name":"L'","sexp":"(:c FirstOrder.Language)"},{"name":"M","sexp":"(:sort (+ w 1))"},{"name":"N","sexp":"(:sort (+ w' 1))"},{"name":"inst✝³","sexp":"((:c FirstOrder.Language.Structure) (:fv _uniq.96302) (:fv _uniq.96306))"},{"name":"inst✝²","sexp":"((:c FirstOrder.Langua... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Function.Embedding) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV3)))) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c FunLike) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.96302","is_instance":false,"is_let":false,"name":"L","sexp":"(:c FirstOrder.Language)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.96304","is_instance":false,"is_let":false,"name":"L'","sexp":"(:c FirstOrder.Language)"},{"bind... | {"children":[{"source":"exact","sourceEnd":28775,"sourceStart":28770,"tag":"atom"},{"children":[{"children":[{"name":"Function.funext_iff","semanticRole":"global","source":"Function.funext_iff","sourceEnd":28795,"sourceStart":28776,"tag":"identifier"},{"source":".","sourceEnd":28796,"sourceStart":28795,"tag":"atom"},{"... | [] | [{"source":"Function.funext_iff.1 h x","source_end":28801,"source_start":28776,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.96302","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.96304","is_instance":false,"is_let":false,"user_name":"L'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 198 | 8 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0ad5b3c2838398c13bf6458a7938d721abba977bd702f7228ae0d48db17e4cde | 5055392c8c5c56865a5ebc3f3fdf080505c76f8188d8e0f83ed1d5031283ce68 | 0492dc53a4fa63f0e181cf53defd3a14a58b1f146c423374169637cb1170fce2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,360 | Polynomial.Monic.mul_left_ne_zero | Mathlib/Algebra/Polynomial/Monic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases h : p = 1 | R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p : R[X]
hp : p.Monic
q : R[X]
hq : q ≠ 0
⊢ q * p ≠ 0 | case pos
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p : R[X]
hp : p.Monic
q : R[X]
hq : q ≠ 0
h : p = 1
⊢ q * p ≠ 0
case neg
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p : R[X]
hp : p.Monic
q : R[X]
hq : q ≠ 0
h : ¬p = 1
⊢ q * p ≠ 0 | ((:c Ne) ((:c Polynomial) (:fv _uniq.101176) (:fv _uniq.101191)) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.101176) (:fv _uniq.101191)) ((:c Polynomial) (:fv _uniq.101176) (:fv _uniq.101191)) ((:c Polynomial) (:fv _uniq.101176) (:fv _uniq.101191)) ((:c instHMul) ((:c Polynomial) (:fv _uniq.101176) (:fv _uniq.101191)) ... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.101176)"},{"name":"b","sexp":"(:fv _uniq.101176)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.101176))"},... | (:app (:c Ne) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.101176","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.101178","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"by_cases","sourceEnd":18464,"sourceStart":18456,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":18466,"sourceStart":18465,"tag":"identifier"},{"source":":","sourceEnd":18468,"sourceStart":18467,"tag":"atom"}],"kind":"null","source":"h :","sourceEnd":18468,"sour... | [] | [{"source":"p = 1","source_end":18474,"source_start":18469,"syntax_kind":"«term_=_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.101176","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.101178","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 137 | 4 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a400c27c8e073d1197a9d4f43fc508279e8c04713fa6f6e4be018280465793bb | f30acee767c8c9480efd904dcda09473fc147798142e65e6df2921bfaacfbd04 | 1cfaa6f8c7f2ef0cc2bfb848e4249bf94ae613126ccdf3897f8c1240abf84d30 | f913eb4a9b827b3b49e850b35441de1b20e1be06c828ed23b9bd36c2bd501ec4 |
cat-searcher/leandojo-benchmark-4-random | test | 3,361 | Polynomial.Monic.mul_left_ne_zero | Mathlib/Algebra/Polynomial/Monic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Ne</a>, ← <a>Polynomial.degree_eq_bot</a>, hp.degree_mul, <a>WithBot.add_eq_bot</a>, <a>not_or</a>, <a>Polynomial.degree_eq_bot</a>] | case neg
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p : R[X]
hp : p.Monic
q : R[X]
hq : q ≠ 0
h : ¬p = 1
⊢ q * p ≠ 0 | case neg
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p : R[X]
hp : p.Monic
q : R[X]
hq : q ≠ 0
h : ¬p = 1
⊢ ¬q = 0 ∧ ¬p.degree = ⊥ | ((:c Ne) ((:c Polynomial) (:fv _uniq.101176) (:fv _uniq.101191)) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.101176) (:fv _uniq.101191)) ((:c Polynomial) (:fv _uniq.101176) (:fv _uniq.101191)) ((:c Polynomial) (:fv _uniq.101176) (:fv _uniq.101191)) ((:c instHMul) ((:c Polynomial) (:fv _uniq.101176) (:fv _uniq.101191)) ... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.101176)"},{"name":"b","sexp":"(:fv _uniq.101176)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.101176))"},... | (:app (:c Ne) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.101176","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.101178","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":18494,"sourceStart":18492,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":18496,"sourceStart":18495,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Ne","semanticRol... | [] | [{"source":"Ne","source_end":18498,"source_start":18496,"syntax_kind":"ident"},{"source":"degree_eq_bot","source_end":18517,"source_start":18504,"syntax_kind":"ident"},{"source":"hp.degree_mul","source_end":18532,"source_start":18519,"syntax_kind":"ident"},{"source":"WithBot.add_eq_bot","source_end":18552,"source_start... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.101176","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.101178","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 137 | 10 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 57fbd1df524ed79fa2f0357f27a006585ccb5e29d6c8fb4866257d2db95c954a | 685a25559860e9bc5340357eaa47d212b72d68cdcd5a04d094f6c2e887eb15c3 | 06cb50ecc658463bacc0fa6f2a1e93ef81822f4a1cd973e8df39870098ce128d | 951daed6d07cedc744731cb9fe5f09f69f0e8d3e8d5f04b8f7131d15b8ac556d |
cat-searcher/leandojo-benchmark-4-random | test | 3,362 | Polynomial.Monic.mul_left_ne_zero | Mathlib/Algebra/Polynomial/Monic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨hq, ?_⟩ | case neg
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p : R[X]
hp : p.Monic
q : R[X]
hq : q ≠ 0
h : ¬p = 1
⊢ ¬q = 0 ∧ ¬p.degree = ⊥ | case neg
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p : R[X]
hp : p.Monic
q : R[X]
hq : q ≠ 0
h : ¬p = 1
⊢ ¬p.degree = ⊥ | ((:c And) ((:c Not) ((:c Eq) ((:c Polynomial) (:fv _uniq.101176) (:fv _uniq.101191)) (:fv _uniq.101360) ((:c OfNat.ofNat) ((:c Polynomial) (:fv _uniq.101176) (:fv _uniq.101191)) (:lit 0) ((:c Zero.toOfNat0) ((:c Polynomial) (:fv _uniq.101176) (:fv _uniq.101191)) ((:c Polynomial.zero) (:fv _uniq.101176) (:fv _uniq.10119... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.101176)"},{"name":"b","sexp":"(:fv _uniq.101176)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.101176))"},... | (:app (:c And) (:arg :explicit 0 (:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :im... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.101176","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.101178","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":18585,"sourceStart":18579,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":18589,"sourceStart":18586,"tag":"atom"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"hq","sourceEnd":18591,"sourceStart":18589,"tag":"identifier"},{"source":",","sourceEnd":1859... | [] | [{"source":"⟨hq, ?_⟩","source_end":18598,"source_start":18586,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.101176","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.101178","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 137 | 18 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 33b13c8752b7fd6bec811a626ab15844208cb0a8705eb3a1e283bb350b51a525 | 951daed6d07cedc744731cb9fe5f09f69f0e8d3e8d5f04b8f7131d15b8ac556d | 5e3e2617c0b32c42aaa59db9e6bf8207841cd718548950d9aece888db9bdb0be | a7c588c6119c935558c31f28de83f61c6e7b3341b8f36f29acb9507136adf181 |
cat-searcher/leandojo-benchmark-4-random | test | 3,363 | Polynomial.Monic.mul_left_ne_zero | Mathlib/Algebra/Polynomial/Monic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hp.degree_le_zero_iff_eq_one, <a>not_le</a>] at h | case neg
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p : R[X]
hp : p.Monic
q : R[X]
hq : q ≠ 0
h : ¬p = 1
⊢ ¬p.degree = ⊥ | case neg
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p : R[X]
hp : p.Monic
q : R[X]
hq : q ≠ 0
h : 0 < p.degree
⊢ ¬p.degree = ⊥ | ((:c Not) ((:c Eq) ((:c WithBot) (:c Nat)) ((:c Polynomial.degree) (:fv _uniq.101176) (:fv _uniq.101191) (:fv _uniq.101204)) ((:c Bot.bot) ((:c WithBot) (:c Nat)) ((:c WithBot.bot) (:c Nat))))) | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.101176)"},{"name":"b","sexp":"(:fv _uniq.101176)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.101176))"},... | (:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV8)))) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.101176","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.101178","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":18603,"sourceStart":18601,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":18605,"sourceStart":18604,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":18608,"sourceSt... | [] | [{"source":"hp.degree_le_zero_iff_eq_one","source_end":18637,"source_start":18609,"syntax_kind":"ident"},{"source":"h","source_end":18651,"source_start":18650,"syntax_kind":"ident"},{"source":"not_le","source_end":18645,"source_start":18639,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.101176","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.101178","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 137 | 19 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 091f080a250ef89bfd8860e33a5080b721e3efbe726f279d9ae3f9f9c1f0a94c | a7c588c6119c935558c31f28de83f61c6e7b3341b8f36f29acb9507136adf181 | c596816ebc8d97d88e851798fe3b1f6695393fc39167f982d1a3e0112b0ca23a | 77f2c1e19131fad8bcba00e25296cd5f5d58ca5b59cd42db0b59b0aa66867bcf |
cat-searcher/leandojo-benchmark-4-random | test | 3,364 | Polynomial.Monic.mul_left_ne_zero | Mathlib/Algebra/Polynomial/Monic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (<a>lt_trans</a> ?_ h).<a>LT.lt.ne'</a> | case neg
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p : R[X]
hp : p.Monic
q : R[X]
hq : q ≠ 0
h : 0 < p.degree
⊢ ¬p.degree = ⊥ | case neg
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p : R[X]
hp : p.Monic
q : R[X]
hq : q ≠ 0
h : 0 < p.degree
⊢ ⊥ < 0 | ((:c Not) ((:c Eq) ((:c WithBot) (:c Nat)) ((:c Polynomial.degree) (:fv _uniq.101176) (:fv _uniq.101191) (:fv _uniq.101204)) ((:c Bot.bot) ((:c WithBot) (:c Nat)) ((:c WithBot.bot) (:c Nat))))) | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.101176)"},{"name":"b","sexp":"(:fv _uniq.101176)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.101176))"},... | (:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV8)))) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.101176","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.101178","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":18660,"sourceStart":18654,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":18662,"sourceStart":18661,"tag":"atom"},{"children":[{"name":"lt_trans","semanticRole":"global","source":"lt_trans","sourceEnd":18670,"sourceStart":18662,"tag":"identifier"},{"children... | [] | [{"source":"(lt_trans ?_ h).ne'","source_end":18680,"source_start":18661,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.101176","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.101178","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 137 | 23 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 19fcfc4a61996fdc313e10a759b3756154e17777ea40c1323e97af73ef3b6186 | 77f2c1e19131fad8bcba00e25296cd5f5d58ca5b59cd42db0b59b0aa66867bcf | 7ba3e08c349a0a127745da100b7e3074e18e86714349defa300ac19f9f10aca6 | 76a9706207fceec1c16c46d83c796c5d2c54feebf8cf2c1c631a21cd7c68aee7 |
cat-searcher/leandojo-benchmark-4-random | test | 3,365 | Polynomial.Monic.mul_left_ne_zero | Mathlib/Algebra/Polynomial/Monic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case neg
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p : R[X]
hp : p.Monic
q : R[X]
hq : q ≠ 0
h : 0 < p.degree
⊢ ⊥ < 0 | ((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Bot.bot) ((:c WithBot) (:c Nat)) ((:c WithBot.bot) (:c Nat))) ((:c OfNat.... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.101176)"},{"name":"b","sexp":"(:fv _uniq.101176)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.101176))"},... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Bot.bot) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.101176","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.101178","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":18687,"sourceStart":18683,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"ki... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.101176","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.101178","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 137 | 24 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 21ce10bb9fdfd1a3775291ab85d998631ead5f0b3aa891062c0fab25d2473313 | 76a9706207fceec1c16c46d83c796c5d2c54feebf8cf2c1c631a21cd7c68aee7 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,366 | Polynomial.Monic.mul_left_ne_zero | Mathlib/Algebra/Polynomial/Monic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [h] | case pos
R : Type u
S : Type v
a b : R
m n : ℕ
ι : Type y
inst✝ : Semiring R
p : R[X]
hp : p.Monic
q : R[X]
hq : q ≠ 0
h : p = 1
⊢ q * p ≠ 0 | ((:c Ne) ((:c Polynomial) (:fv _uniq.101176) (:fv _uniq.101191)) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.101176) (:fv _uniq.101191)) ((:c Polynomial) (:fv _uniq.101176) (:fv _uniq.101191)) ((:c Polynomial) (:fv _uniq.101176) (:fv _uniq.101191)) ((:c instHMul) ((:c Polynomial) (:fv _uniq.101176) (:fv _uniq.101191)) ... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.101176)"},{"name":"b","sexp":"(:fv _uniq.101176)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.101176))"},... | (:app (:c Ne) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.101176","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.101178","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":18485,"sourceStart":18480,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"h","source_end":18488,"source_start":18487,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.101176","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.101178","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 137 | 7 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 40811e85798e7741b65e2b3690c96c19597c404b2b67a884e51c04087a6d28e0 | 78ed5e7abf6da639ac1ef1b5561c0ca9f4047ea3d58b3b0fa8b8acfb69f4f6de | 06080447ea48c1992e73b6575319d32f720bdeff271033602d56247fd6256120 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,367 | Filter.principal_mono | Mathlib/Order/Filter/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Filter.le_principal_iff</a>, <a>iff_self_iff</a>, <a>Filter.mem_principal</a>] | α : Type u
β : Type v
γ : Type w
δ : Type u_1
ι : Sort x
f g : Filter α
s✝ t✝ s t : Set α
⊢ 𝓟 s ≤ 𝓟 t ↔ s ⊆ t | ((:c Iff) ((:c LE.le) ((:c Filter) (:fv _uniq.43081)) ((:c Preorder.toLE) ((:c Filter) (:fv _uniq.43081)) ((:c PartialOrder.toPreorder) ((:c Filter) (:fv _uniq.43081)) ((:c Filter.instPartialOrder) (:fv _uniq.43081)))) ((:c Filter.principal) (:fv _uniq.43081) (:fv _uniq.43162)) ((:c Filter.principal) (:fv _uniq.43081) ... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"δ","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort x)"},{"name":"f","sexp":"((:c Filter) (:fv _uniq.43081))"},{"name":"g","sexp":"((:c Filter) (:fv _uniq.43081))"},{"name":"s✝","sexp":"((:c... | (:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:c Filter.principal) (:arg :implicit-type 0 (:fv FV0)) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43081","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.43083","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":29648,"sourceStart":29644,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":29653,"sourceStart":29649,"tag":"atom"}],"kind"... | [] | [{"source":"le_principal_iff","source_end":29671,"source_start":29655,"syntax_kind":"ident"},{"source":"iff_self_iff","source_end":29685,"source_start":29673,"syntax_kind":"ident"},{"source":"mem_principal","source_end":29700,"source_start":29687,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.43081","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.43083","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 197 | 2 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5102220287844d9a819a8be1819f233f9562ee2a9438330ff78a2ab385ab790d | 5778807ab36c32f6a28614dbfc43485107e51274f70bcd59127027703dd16239 | bdc6c72361dc7b2886238e6320df01d3bde5d1ee7227066fc2699c4af6d7462a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,368 | denseRange_discrete | Mathlib/Topology/Order.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>DenseRange</a>, <a>dense_discrete</a>, <a>Set.range_iff_surjective</a>] | α : Type u_1
t t₁ t₂ : TopologicalSpace α
s : Set α
inst✝¹ : TopologicalSpace α
inst✝ : DiscreteTopology α
β : Type u_2
ι : Type u_3
f : ι → α
⊢ DenseRange f ↔ Surjective f | ((:c Iff) ((:c DenseRange) (:fv _uniq.14687) (:fv _uniq.14702) (:fv _uniq.14740) (:fv _uniq.14741)) ((:c Function.Surjective) (:fv _uniq.14740) (:fv _uniq.14687) (:fv _uniq.14741))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"t","sexp":"((:c TopologicalSpace) (:fv _uniq.14687))"},{"name":"t₁","sexp":"((:c TopologicalSpace) (:fv _uniq.14687))"},{"name":"t₂","sexp":"((:c TopologicalSpace) (:fv _uniq.14687))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.14687))"},{"name":"inst✝¹","sexp":"((:c Topo... | (:app (:c Iff) (:arg :explicit 0 (:app (:c DenseRange) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV9)) (:arg :explicit 3 (:fv FV10)))) (:arg :explicit 1 (:app (:c Function.Surjective) (:arg :implicit-type 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14687","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14690","is_instance":false,"is_let":false,"name":"t","sexp":"(:app (:c TopologicalSpace) (:arg :explicit 0 ... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":14083,"sourceStart":14081,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":14085,"sourceStart":14084,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"DenseRange","source_end":14095,"source_start":14085,"syntax_kind":"ident"},{"source":"dense_discrete","source_end":14111,"source_start":14097,"syntax_kind":"ident"},{"source":"range_iff_surjective","source_end":14133,"source_start":14113,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14687","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14690","is_instance":false,"is_let":false,"user_name":"t"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 76 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2f253cf27402e64830169ba3d38584ff62b73badb1d5d7476527d1d0facf4f9f | 0fe5034ae3d013aefb59492d65607eb11380a2805ab797d8548faec5030a207a | 1688229cd4e5fb6643700e82c326e3a22f271482746b8bb800d36db2964ab03a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,369 | MulAction.map_stabilizer_le | Mathlib/Algebra/Pointwise/Stabilizer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro a | G : Type u_1
H : Type u_2
α : Type u_3
inst✝² : Group G
inst✝¹ : Group H
inst✝ : MulAction G α
a : G
f : G →* H
s : Set G
⊢ Subgroup.map f (stabilizer G s) ≤ stabilizer H (⇑f '' s) | G : Type u_1
H : Type u_2
α : Type u_3
inst✝² : Group G
inst✝¹ : Group H
inst✝ : MulAction G α
a✝ : G
f : G →* H
s : Set G
a : H
⊢ a ∈ Subgroup.map f (stabilizer G s) → a ∈ stabilizer H (⇑f '' s) | ((:c LE.le) ((:c Subgroup) (:fv _uniq.7266) (:fv _uniq.7275)) ((:c Preorder.toLE) ((:c Subgroup) (:fv _uniq.7266) (:fv _uniq.7275)) ((:c PartialOrder.toPreorder) ((:c Subgroup) (:fv _uniq.7266) (:fv _uniq.7275)) ((:c CompleteSemilatticeInf.toPartialOrder) ((:c Subgroup) (:fv _uniq.7266) (:fv _uniq.7275)) ((:c CompleteL... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c Group) (:fv _uniq.7263))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.7266))"},{"name":"inst✝","sexp":"((:c MulAction) (:fv _uniq.7263) (:fv _uniq.7269) ((:c DivInv... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Subgroup) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV1))))))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Subgroup) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7263","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7266","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"rintro","sourceEnd":1492,"sourceStart":1486,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":1494,"sourceStart":1493,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"a","sourceEnd":1494,"sourceStart":1493,"tag":"... | [{"role":"fresh_name","source":"a","source_end":1494,"source_start":1493,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7263","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7266","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 11 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 052825616b039de3010b7b0751dcf6ae169a83857c6da70ac1c73d1f621def28 | fec0f232acac2392f8f572773b4563c842b0174e5785925466cd898776d74a89 | efc95b73c960e10a957b866f3c0191414a0fe8fc98d61334358d6f0f07d877aa | ff685239d49479f7808ea0611e4f487bdaf22d06d1d167eced56c814051442e1 |
cat-searcher/leandojo-benchmark-4-random | test | 3,370 | MulAction.map_stabilizer_le | Mathlib/Algebra/Pointwise/Stabilizer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Subgroup.mem_map</a>, <a>MulAction.mem_stabilizer_iff</a>, <a>exists_prop</a>, <a>forall_exists_index</a>, <a>and_imp</a>] | G : Type u_1
H : Type u_2
α : Type u_3
inst✝² : Group G
inst✝¹ : Group H
inst✝ : MulAction G α
a✝ : G
f : G →* H
s : Set G
a : H
⊢ a ∈ Subgroup.map f (stabilizer G s) → a ∈ stabilizer H (⇑f '' s) | G : Type u_1
H : Type u_2
α : Type u_3
inst✝² : Group G
inst✝¹ : Group H
inst✝ : MulAction G α
a✝ : G
f : G →* H
s : Set G
a : H
⊢ ∀ (x : G), x • s = s → f x = a → a • ⇑f '' s = ⇑f '' s | (:forall _ ((:c Membership.mem) (:fv _uniq.7266) ((:c Subgroup) (:fv _uniq.7266) (:fv _uniq.7275)) ((:c SetLike.instMembership) ((:c Subgroup) (:fv _uniq.7266) (:fv _uniq.7275)) (:fv _uniq.7266) ((:c Subgroup.instSetLike) (:fv _uniq.7266) (:fv _uniq.7275))) (:fv _uniq.10448) ((:c Subgroup.map) (:fv _uniq.7263) (:fv _un... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c Group) (:fv _uniq.7263))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.7266))"},{"name":"inst✝","sexp":"((:c MulAction) (:fv _uniq.7263) (:fv _uniq.7269) ((:c DivInv... | (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Subgroup) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV1))))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7263","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7266","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"simp","sourceEnd":1501,"sourceStart":1497,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":1506,"sourceStart":1502,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":1506,"s... | [] | [{"source":"Subgroup.mem_map","source_end":1524,"source_start":1508,"syntax_kind":"ident"},{"source":"mem_stabilizer_iff","source_end":1544,"source_start":1526,"syntax_kind":"ident"},{"source":"exists_prop","source_end":1557,"source_start":1546,"syntax_kind":"ident"},{"source":"forall_exists_index","source_end":1578,"s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7263","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7266","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 11 | 5 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e9dbdb4379665663f86844127dcd82131457d2913830bf89226f993497722ddb | ff685239d49479f7808ea0611e4f487bdaf22d06d1d167eced56c814051442e1 | 773f29620948cb7d88651289026036867cfb6b8c5bd27dc6ae0d8f6e60862de0 | 8bc2b47962f051652bfaa19dcd6dfb32c5a669df7afd239d5623d0725d9b7c91 |
cat-searcher/leandojo-benchmark-4-random | test | 3,371 | MulAction.map_stabilizer_le | Mathlib/Algebra/Pointwise/Stabilizer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro a ha rfl | G : Type u_1
H : Type u_2
α : Type u_3
inst✝² : Group G
inst✝¹ : Group H
inst✝ : MulAction G α
a✝ : G
f : G →* H
s : Set G
a : H
⊢ ∀ (x : G), x • s = s → f x = a → a • ⇑f '' s = ⇑f '' s | G : Type u_1
H : Type u_2
α : Type u_3
inst✝² : Group G
inst✝¹ : Group H
inst✝ : MulAction G α
a✝ : G
f : G →* H
s : Set G
a : G
ha : a • s = s
⊢ f a • ⇑f '' s = ⇑f '' s | (:forall x (:fv _uniq.7263) (:forall _ ((:c Eq) ((:c Set) (:fv _uniq.7263)) ((:c HSMul.hSMul) (:fv _uniq.7263) ((:c Set) (:fv _uniq.7263)) ((:c Set) (:fv _uniq.7263)) ((:c instHSMul) (:fv _uniq.7263) ((:c Set) (:fv _uniq.7263)) ((:c MulAction.toSMul) (:fv _uniq.7263) ((:c Set) (:fv _uniq.7263)) ((:c DivInvMonoid.toMono... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c Group) (:fv _uniq.7263))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.7266))"},{"name":"inst✝","sexp":"((:c MulAction) (:fv _uniq.7263) (:fv _uniq.7269) ((:c DivInv... | (:forall x :explicit (:fv FV0) (:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 2 (:app (:c Set) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7263","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7266","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"rintro","sourceEnd":1597,"sourceStart":1591,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":1599,"sourceStart":1598,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"a","sourceEnd":1599,"sourceStart":1598,"tag":"... | [{"role":"fresh_name","source":"a","source_end":1599,"source_start":1598,"syntax_kind":"ident"},{"role":"fresh_name","source":"ha","source_end":1602,"source_start":1600,"syntax_kind":"ident"}] | [{"source":"rfl","source_end":1606,"source_start":1603,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7263","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7266","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 11 | 6 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2aba4593192b053a90736177f98e3ad02f47aea1e3e63bcc197db4fdce8caa7a | 8bc2b47962f051652bfaa19dcd6dfb32c5a669df7afd239d5623d0725d9b7c91 | 56082308706c9193dfdcaf520742024c730f61d37e46acbd9939d6aaadb1f7c5 | a2d07a6d3d74600c178c625a586ccfb947019954258c2b78029dfb9732fd14b4 |
cat-searcher/leandojo-benchmark-4-random | test | 3,372 | MulAction.map_stabilizer_le | Mathlib/Algebra/Pointwise/Stabilizer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Set.image_smul_distrib</a>, ha] | G : Type u_1
H : Type u_2
α : Type u_3
inst✝² : Group G
inst✝¹ : Group H
inst✝ : MulAction G α
a✝ : G
f : G →* H
s : Set G
a : G
ha : a • s = s
⊢ f a • ⇑f '' s = ⇑f '' s | ((:c Eq) ((:c Set) (:fv _uniq.7266)) ((:c HSMul.hSMul) (:fv _uniq.7266) ((:c Set) (:fv _uniq.7266)) ((:c Set) (:fv _uniq.7266)) ((:c instHSMul) (:fv _uniq.7266) ((:c Set) (:fv _uniq.7266)) ((:c MulAction.toSMul) (:fv _uniq.7266) ((:c Set) (:fv _uniq.7266)) ((:c DivInvMonoid.toMonoid) (:fv _uniq.7266) ((:c Group.toDivIn... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"H","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c Group) (:fv _uniq.7263))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.7266))"},{"name":"inst✝","sexp":"((:c MulAction) (:fv _uniq.7263) (:fv _uniq.7269) ((:c DivInv... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 2 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 3 (:inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7263","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7266","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"rw","sourceEnd":1611,"sourceStart":1609,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1613,"sourceStart":1612,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":1616,"sourceStart":... | [] | [{"source":"image_smul_distrib","source_end":1635,"source_start":1617,"syntax_kind":"ident"},{"source":"ha","source_end":1639,"source_start":1637,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7263","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.7266","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 11 | 7 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5afe425490798b8db836fe941e1bf7f82ca8aa9332bb6fbfd0499561c08ad17f | a2d07a6d3d74600c178c625a586ccfb947019954258c2b78029dfb9732fd14b4 | 69663eb8ac39a22afbce35c3d5d0fcabd5e73977860e0c1a58d7790ca7451bc5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,373 | AffineSubspace.wSameSide_vadd_left_iff | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : StrictOrderedCommRing R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y : P
v : V
hv : v ∈ s.direction
⊢ s.WSameSide (v +ᵥ x) y ... | case mp
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : StrictOrderedCommRing R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y : P
v : V
hv : v ∈ s.direction
⊢ s.WSameSide (v ... | ((:c Iff) ((:c AffineSubspace.WSameSide) (:fv _uniq.125871) (:fv _uniq.125874) (:fv _uniq.125880) (:fv _uniq.125886) (:fv _uniq.125889) (:fv _uniq.126494) (:fv _uniq.126689) (:fv _uniq.128643) ((:c HVAdd.hVAdd) (:fv _uniq.125874) (:fv _uniq.125880) (:fv _uniq.125880) ((:c instHVAdd) (:fv _uniq.125874) (:fv _uniq.125880... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c StrictOrderedCommRing) (:fv _uniq.125871))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup... | (:app (:c Iff) (:arg :explicit 0 (:app (:c AffineSubspace.WSameSide) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c StrictOrderedCommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c AddCommGro... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125871","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125874","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"constructor","sourceEnd":12764,"sourceStart":12753,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":12764,"sourceStart":12753,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125871","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125874","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 92 | 4 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5d014d69d94c60eae4989021a8e0e331eb8c2baeea057ffc872c274b13aff3d6 | be87b4800d0a31739b53ce4220cf6252c517dd71efeb03b474b71b67328802e8 | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | 29fc6100252144682672068f2f408d39e03bcd408d8033f8b7ab13fe8582331c |
cat-searcher/leandojo-benchmark-4-random | test | 3,374 | AffineSubspace.wSameSide_vadd_left_iff | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨p₁, hp₁, p₂, hp₂, h⟩ | case mp
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : StrictOrderedCommRing R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y : P
v : V
hv : v ∈ s.direction
⊢ s.WSameSide (v ... | case mp.intro.intro.intro.intro
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : StrictOrderedCommRing R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y : P
v : V
hv : v ∈ s.dir... | (:forall _ ((:c AffineSubspace.WSameSide) (:fv _uniq.125871) (:fv _uniq.125874) (:fv _uniq.125880) (:fv _uniq.125886) (:fv _uniq.125889) (:fv _uniq.126494) (:fv _uniq.126689) (:fv _uniq.128643) ((:c HVAdd.hVAdd) (:fv _uniq.125874) (:fv _uniq.125880) (:fv _uniq.125880) ((:c instHVAdd) (:fv _uniq.125874) (:fv _uniq.12588... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c StrictOrderedCommRing) (:fv _uniq.125871))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup... | (:forall _ :explicit (:app (:c AffineSubspace.WSameSide) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c StrictOrderedCommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c AddCommGroup) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125871","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125874","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rintro","sourceEnd":12776,"sourceStart":12770,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":12780,"sourceStart":12777,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"p₁","sourceEnd":12784,"so... | [{"role":"fresh_name","source":"p₁","source_end":12784,"source_start":12780,"syntax_kind":"ident"},{"role":"fresh_name","source":"hp₁","source_end":12791,"source_start":12786,"syntax_kind":"ident"},{"role":"fresh_name","source":"p₂","source_end":12797,"source_start":12793,"syntax_kind":"ident"},{"role":"fresh_name","so... | [{"source":"⟨p₁, hp₁, p₂, hp₂, h⟩","source_end":12810,"source_start":12777,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125871","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125874","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 92 | 9 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3d8f3e82a0402a4ba5467322524a3cca5670576e7949441e4698ede7ff119e84 | a6357019218517bbf9172777200cac43dc671f945620490ee1c6fd7265fa06a8 | b7429f3688269eacda3952ea4c09c3efc1f9dc9bcb0ba71e15766024c555f0c2 | 6fa6663fd2e6c254ed3a9e062425133d33d22c75b624254e746125ef85fe8809 |
cat-searcher/leandojo-benchmark-4-random | test | 3,375 | AffineSubspace.wSameSide_vadd_left_iff | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨-v +ᵥ p₁, <a>AffineSubspace.vadd_mem_of_mem_direction</a> (<a>Submodule.neg_mem</a> _ hv) hp₁, p₂, hp₂, ?_⟩ | case mp.intro.intro.intro.intro
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : StrictOrderedCommRing R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y : P
v : V
hv : v ∈ s.dir... | case mp.intro.intro.intro.intro
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : StrictOrderedCommRing R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y : P
v : V
hv : v ∈ s.dir... | ((:c AffineSubspace.WSameSide) (:fv _uniq.125871) (:fv _uniq.125874) (:fv _uniq.125880) (:fv _uniq.125886) (:fv _uniq.125889) (:fv _uniq.126494) (:fv _uniq.126689) (:fv _uniq.128643) (:fv _uniq.128644) (:fv _uniq.128645)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c StrictOrderedCommRing) (:fv _uniq.125871))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup... | (:app (:c AffineSubspace.WSameSide) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c StrictOrderedCommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV1)))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125871","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125874","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":12821,"sourceStart":12815,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":12831,"sourceStart":12828,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"-","sourceEnd":12832,"sourceStart":12831,"tag":"atom"},{"contextIndex":16,"semanticRole":"local","source":"... | [] | [{"source":"⟨-v +ᵥ p₁, AffineSubspace.vadd_mem_of_mem_direction (Submodule.neg_mem _ hv) hp₁, p₂, hp₂, ?_⟩","source_end":12936,"source_start":12828,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125871","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125874","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 92 | 10 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 20dca1dc5117a26bc2791627e132ba49573fd54e33bb096758c4290b569555d2 | 6fa6663fd2e6c254ed3a9e062425133d33d22c75b624254e746125ef85fe8809 | e1e463894e9fc126f6c247b6a8e28009a22d3e668a857ae019257b4f8026b3c1 | 29111edeaaa2a1543f16eac0d66dc5744bc44af849d5d8d2a5d07ca4e0d46b42 |
cat-searcher/leandojo-benchmark-4-random | test | 3,376 | AffineSubspace.wSameSide_vadd_left_iff | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>vsub_vadd_eq_vsub_sub</a>, <a>sub_neg_eq_add</a>, <a>add_comm</a>, ← <a>vadd_vsub_assoc</a>] | case mp.intro.intro.intro.intro
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : StrictOrderedCommRing R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y : P
v : V
hv : v ∈ s.dir... | ((:c SameRay) (:fv _uniq.125871) ((:c StrictOrderedCommRing.toStrictOrderedCommSemiring) (:fv _uniq.125871) (:fv _uniq.125886)) (:fv _uniq.125874) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.125874) (:fv _uniq.125889)) (:fv _uniq.126494) ((:c VSub.vsub) (:fv _uniq.125874) (:fv _uniq.125880) ((:c AddTorsor.toVSub) (:f... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c StrictOrderedCommRing) (:fv _uniq.125871))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup... | (:app (:c SameRay) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c StrictOrderedCommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:app (:c Module... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125871","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125874","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rwa","sourceEnd":12944,"sourceStart":12941,"tag":"atom"},{"children":[{"source":"[","sourceEnd":12946,"sourceStart":12945,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"vsub_vadd_eq_vsub_sub","semanticRole":"global","source":"vsub_vadd_eq_... | [] | [{"source":"vsub_vadd_eq_vsub_sub","source_end":12967,"source_start":12946,"syntax_kind":"ident"},{"source":"sub_neg_eq_add","source_end":12983,"source_start":12969,"syntax_kind":"ident"},{"source":"add_comm","source_end":12993,"source_start":12985,"syntax_kind":"ident"},{"source":"vadd_vsub_assoc","source_end":13014,"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125871","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125874","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 92 | 11 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3dbdd4628ce580ce3c361f049adcdf8c710cef3cdcc334e964ddf958354c7a0b | 29111edeaaa2a1543f16eac0d66dc5744bc44af849d5d8d2a5d07ca4e0d46b42 | 442326ab34b2a19b4be27d8b9e358d9f6ccbd3e14229fbe6d7ce4fd3df25c24c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,377 | AffineSubspace.wSameSide_vadd_left_iff | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨p₁, hp₁, p₂, hp₂, h⟩ | case mpr
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : StrictOrderedCommRing R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y : P
v : V
hv : v ∈ s.direction
⊢ s.WSameSide x ... | case mpr.intro.intro.intro.intro
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : StrictOrderedCommRing R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y : P
v : V
hv : v ∈ s.di... | (:forall _ ((:c AffineSubspace.WSameSide) (:fv _uniq.125871) (:fv _uniq.125874) (:fv _uniq.125880) (:fv _uniq.125886) (:fv _uniq.125889) (:fv _uniq.126494) (:fv _uniq.126689) (:fv _uniq.128643) (:fv _uniq.128644) (:fv _uniq.128645)) ((:c AffineSubspace.WSameSide) (:fv _uniq.125871) (:fv _uniq.125874) (:fv _uniq.125880)... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c StrictOrderedCommRing) (:fv _uniq.125871))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup... | (:forall _ :explicit (:app (:c AffineSubspace.WSameSide) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c StrictOrderedCommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c AddCommGroup) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125871","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125874","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rintro","sourceEnd":13027,"sourceStart":13021,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":13031,"sourceStart":13028,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"p₁","sourceEnd":13035,"so... | [{"role":"fresh_name","source":"p₁","source_end":13035,"source_start":13031,"syntax_kind":"ident"},{"role":"fresh_name","source":"hp₁","source_end":13042,"source_start":13037,"syntax_kind":"ident"},{"role":"fresh_name","source":"p₂","source_end":13048,"source_start":13044,"syntax_kind":"ident"},{"role":"fresh_name","so... | [{"source":"⟨p₁, hp₁, p₂, hp₂, h⟩","source_end":13061,"source_start":13028,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125871","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125874","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 92 | 21 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | db531652e3ab0f0c58b611ebf3e6da0c28ba2df6693e1d6bfd76abd410528b02 | 5a21e47094d222b097b18df065fd4926d4b38abd2ef3ccb6e8992f6ddd77bc22 | b7429f3688269eacda3952ea4c09c3efc1f9dc9bcb0ba71e15766024c555f0c2 | c8e14e60869cb52c609047e129f7cfcafd05b395f0a54aace52d4ec6464774ec |
cat-searcher/leandojo-benchmark-4-random | test | 3,378 | AffineSubspace.wSameSide_vadd_left_iff | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨v +ᵥ p₁, <a>AffineSubspace.vadd_mem_of_mem_direction</a> hv hp₁, p₂, hp₂, ?_⟩ | case mpr.intro.intro.intro.intro
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : StrictOrderedCommRing R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y : P
v : V
hv : v ∈ s.di... | case mpr.intro.intro.intro.intro
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : StrictOrderedCommRing R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y : P
v : V
hv : v ∈ s.di... | ((:c AffineSubspace.WSameSide) (:fv _uniq.125871) (:fv _uniq.125874) (:fv _uniq.125880) (:fv _uniq.125886) (:fv _uniq.125889) (:fv _uniq.126494) (:fv _uniq.126689) (:fv _uniq.128643) ((:c HVAdd.hVAdd) (:fv _uniq.125874) (:fv _uniq.125880) (:fv _uniq.125880) ((:c instHVAdd) (:fv _uniq.125874) (:fv _uniq.125880) ((:c Add... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c StrictOrderedCommRing) (:fv _uniq.125871))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup... | (:app (:c AffineSubspace.WSameSide) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c StrictOrderedCommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV1)))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125871","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125874","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":13072,"sourceStart":13066,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":13076,"sourceStart":13073,"tag":"atom"},{"children":[{"children":[{"contextIndex":16,"semanticRole":"local","source":"v","sourceEnd":13077,"sourceStart":13076,"tag":"identifier"},{"source":"+ᵥ","so... | [] | [{"source":"⟨v +ᵥ p₁, AffineSubspace.vadd_mem_of_mem_direction hv hp₁, p₂, hp₂, ?_⟩","source_end":13158,"source_start":13073,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125871","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125874","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 92 | 22 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ff1f658696450a2b1c28ec57def5d8bbd0c8b14a809ebe8f6e1a4d3fb1c2743a | c8e14e60869cb52c609047e129f7cfcafd05b395f0a54aace52d4ec6464774ec | 50f62fef2df1eade300d0ac84d162542e001c244f5f4f8780656ef2f4887560d | 56013a40309234120f701b796fc2e56a6b45a563606d5abc00ec03bd3d69aa37 |
cat-searcher/leandojo-benchmark-4-random | test | 3,379 | AffineSubspace.wSameSide_vadd_left_iff | Mathlib/Analysis/Convex/Side.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>vadd_vsub_vadd_cancel_left</a>] | case mpr.intro.intro.intro.intro
R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁶ : StrictOrderedCommRing R
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
s : AffineSubspace R P
x y : P
v : V
hv : v ∈ s.di... | ((:c SameRay) (:fv _uniq.125871) ((:c StrictOrderedCommRing.toStrictOrderedCommSemiring) (:fv _uniq.125871) (:fv _uniq.125886)) (:fv _uniq.125874) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.125874) (:fv _uniq.125889)) (:fv _uniq.126494) ((:c VSub.vsub) (:fv _uniq.125874) (:fv _uniq.125880) ((:c AddTorsor.toVSub) (:f... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁶","sexp":"((:c StrictOrderedCommRing) (:fv _uniq.125871))"},{"name":"inst✝⁵","sexp":"((:c AddCommGroup... | (:app (:c SameRay) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c StrictOrderedCommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:app (:c Module... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125871","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125874","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rwa","sourceEnd":13166,"sourceStart":13163,"tag":"atom"},{"children":[{"source":"[","sourceEnd":13168,"sourceStart":13167,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"vadd_vsub_vadd_cancel_left","semanticRole":"global","source":"vadd_vsu... | [] | [{"source":"vadd_vsub_vadd_cancel_left","source_end":13194,"source_start":13168,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125871","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125874","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 92 | 23 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7325d349db5e50d4993478569d4be55aa455b079e00c6d7130bc181557ada9ad | 56013a40309234120f701b796fc2e56a6b45a563606d5abc00ec03bd3d69aa37 | a868c02ac947634d5f92246753072f7e9611c44a33cfdb072d8a205d5ed2c9d8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,380 | CategoryTheory.eqToIso_map | Mathlib/CategoryTheory/EqToHom.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext | C : Type u₁
inst✝¹ : Category.{v₁, u₁} C
β : Sort u_1
D : Type u₂
inst✝ : Category.{v₂, u₂} D
F : C ⥤ D
X Y : C
p : X = Y
⊢ F.mapIso (eqToIso p) = eqToIso ⋯ | case w
C : Type u₁
inst✝¹ : Category.{v₁, u₁} C
β : Sort u_1
D : Type u₂
inst✝ : Category.{v₂, u₂} D
F : C ⥤ D
X Y : C
p : X = Y
⊢ (F.mapIso (eqToIso p)).hom = (eqToIso ⋯).hom | ((:c Eq) ((:c CategoryTheory.Iso) (:fv _uniq.22708) (:fv _uniq.22711) ((:c Prefunctor.obj) (:fv _uniq.22700) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.22700) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.22700) (:fv _uniq.22703))) (:fv _uniq.22708) ((:c CategoryTheory.CategoryStruct.toQuiver) ... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.22700))"},{"name":"β","sexp":"(:sort u_1)"},{"name":"D","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.22708))"},{"name":"F","sexp":"((:c CategoryTheory.Functor) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Iso) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22700","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.22703","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"ext","sourceEnd":13145,"sourceStart":13142,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":13145,"sourceStart":13142,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22700","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.22703","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 77 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | baf7675efee70f96e4d644683d2ce089be81ba38c4eb0f7f733d62dd42b8813c | 0f68851afe589293ac4229ee9bf4dd3e55ecef06738a1d52be8e8ab425f3ad68 | a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de | 9f5ed61a24a76cce6d3a481db917a6e9b87d47dd7d863afbaa49d00d50376ce4 |
cat-searcher/leandojo-benchmark-4-random | test | 3,381 | CategoryTheory.eqToIso_map | Mathlib/CategoryTheory/EqToHom.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases p | case w
C : Type u₁
inst✝¹ : Category.{v₁, u₁} C
β : Sort u_1
D : Type u₂
inst✝ : Category.{v₂, u₂} D
F : C ⥤ D
X Y : C
p : X = Y
⊢ (F.mapIso (eqToIso p)).hom = (eqToIso ⋯).hom | case w.refl
C : Type u₁
inst✝¹ : Category.{v₁, u₁} C
β : Sort u_1
D : Type u₂
inst✝ : Category.{v₂, u₂} D
F : C ⥤ D
X : C
⊢ (F.mapIso (eqToIso ⋯)).hom = (eqToIso ⋯).hom | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.22708) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.22708) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.22708) (:fv _uniq.22711))) ((:c Prefunctor.obj) (:fv _uniq.22700) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.22700) ((:c CategoryTheory.Catego... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.22700))"},{"name":"β","sexp":"(:sort u_1)"},{"name":"D","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.22708))"},{"name":"F","sexp":"((:c CategoryTheory.Functor) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22700","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.22703","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"cases","sourceEnd":13152,"sourceStart":13147,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":9,"semanticRole":"local","source":"p","sourceEnd":13154,"sourceStart":13153,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","so... | [] | [{"source":"p","source_end":13154,"source_start":13153,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22700","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.22703","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 77 | 6 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1a41cfb8b00476aac7d40e0fc15c2f6dc29e42c30e163bcf7c2dc725630c27c4 | 9f5ed61a24a76cce6d3a481db917a6e9b87d47dd7d863afbaa49d00d50376ce4 | 621334f724a1980244c408c3fff2d5208cff98a17d072327b497f1db7f8e313e | ae6e4670584bad6f7d18a8109db3ca34e14317409d3fdf96ed36985369f6ad08 |
cat-searcher/leandojo-benchmark-4-random | test | 3,382 | CategoryTheory.eqToIso_map | Mathlib/CategoryTheory/EqToHom.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case w.refl
C : Type u₁
inst✝¹ : Category.{v₁, u₁} C
β : Sort u_1
D : Type u₂
inst✝ : Category.{v₂, u₂} D
F : C ⥤ D
X : C
⊢ (F.mapIso (eqToIso ⋯)).hom = (eqToIso ⋯).hom | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.22708) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.22708) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.22708) (:fv _uniq.22711))) ((:c Prefunctor.obj) (:fv _uniq.22700) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.22700) ((:c CategoryTheory.Catego... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.22700))"},{"name":"β","sexp":"(:sort u_1)"},{"name":"D","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.22708))"},{"name":"F","sexp":"((:c CategoryTheory.Functor) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22700","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.22703","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"simp","sourceEnd":13160,"sourceStart":13156,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"ki... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22700","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.22703","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 77 | 8 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dba0ce2793df9bf3e3c5e5bf8850bc34edbedfa2a5df19154bd3720a7094d036 | ae6e4670584bad6f7d18a8109db3ca34e14317409d3fdf96ed36985369f6ad08 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,383 | le_iff_compact_le_imp | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>sSup_compact_le_eq</a> a, ← <a>sSup_compact_le_eq</a> b] | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : CompleteLattice α
inst✝ : IsCompactlyGenerated α
a✝ b✝ : α
s : Set α
a b : α
h : ∀ (c : α), CompleteLattice.IsCompactElement c → c ≤ a → c ≤ b
⊢ a ≤ b | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : CompleteLattice α
inst✝ : IsCompactlyGenerated α
a✝ b✝ : α
s : Set α
a b : α
h : ∀ (c : α), CompleteLattice.IsCompactElement c → c ≤ a → c ≤ b
⊢ sSup {c | CompleteLattice.IsCompactElement c ∧ c ≤ a} ≤ sSup {c | CompleteLattice.IsCompactElement c ∧ ... | ((:c LE.le) (:fv _uniq.41364) ((:c Preorder.toLE) (:fv _uniq.41364) ((:c PartialOrder.toPreorder) (:fv _uniq.41364) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.41364) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.41364) (:fv _uniq.41374))))) (:fv _uniq.41544) (:fv _uniq.41545)) | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.41364))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.41361) (:fv _uniq.41364))"},{"name":"inst✝¹","sexp":"((:c CompleteLattice) (:fv _uniq.41364))"},{"name":"inst✝","sexp":"((:c IsCompactl... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV10)) (:arg :explicit 3 (:fv FV11))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41361","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41364","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":16841,"sourceStart":16839,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16843,"sourceStart":16842,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":16846,"sourceSt... | [] | [{"source":"sSup_compact_le_eq a","source_end":16867,"source_start":16847,"syntax_kind":"Lean.Parser.Term.app"},{"source":"sSup_compact_le_eq b","source_end":16893,"source_start":16873,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41361","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41364","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 59 | 4 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 43942baf198fa4f0076a30147d645ef6964289286b60b644aa29fb4c56eb2bab | 4016342b04454f1dc05d7366c16eeca51fe88bba523bbb0821f80a0bc987aa32 | 6ca59ade80a78bbaaf6e491ca6b5ea61726189ec8e912894c25fe3a0426a44df | 105c59c371d18b9063468ae1d8b7ad5129c2d295a68fb0f96a90031674cc30f5 |
cat-searcher/leandojo-benchmark-4-random | test | 3,384 | le_iff_compact_le_imp | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>sSup_le_sSup</a> fun c hc => ⟨hc.1, h c hc.1 hc.2⟩ | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : CompleteLattice α
inst✝ : IsCompactlyGenerated α
a✝ b✝ : α
s : Set α
a b : α
h : ∀ (c : α), CompleteLattice.IsCompactElement c → c ≤ a → c ≤ b
⊢ sSup {c | CompleteLattice.IsCompactElement c ∧ c ≤ a} ≤ sSup {c | CompleteLattice.IsCompactElement c ∧ ... | ((:c LE.le) (:fv _uniq.41364) ((:c Preorder.toLE) (:fv _uniq.41364) ((:c PartialOrder.toPreorder) (:fv _uniq.41364) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.41364) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.41364) (:fv _uniq.41374))))) ((:c SupSet.sSup) (:fv _uniq.41364) ((:c ConditionallyC... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.41364))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.41361) (:fv _uniq.41364))"},{"name":"inst✝¹","sexp":"((:c CompleteLattice) (:fv _uniq.41364))"},{"name":"inst✝","sexp":"((:c IsCompactl... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c SupSet.sSup) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c SupSet) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c setOf)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41361","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41364","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":16904,"sourceStart":16899,"tag":"atom"},{"children":[{"name":"sSup_le_sSup","semanticRole":"global","source":"sSup_le_sSup","sourceEnd":16917,"sourceStart":16905,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":16921,"sourceStart":16918,"tag":"atom"},{... | [] | [{"source":"sSup_le_sSup fun c hc => ⟨hc.1, h c hc.1 hc.2⟩","source_end":16955,"source_start":16905,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41361","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41364","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 59 | 8 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9484a17a4cff50dec1eada9a17dd25bcd9a4f629c38a95ffcadc2e7d5078400f | 105c59c371d18b9063468ae1d8b7ad5129c2d295a68fb0f96a90031674cc30f5 | bb7f2c72de22e7991c4e19ab5fd0383da6c220295463abe0958120b228b77b1a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,385 | LucasLehmer.X.card_units_lt | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>Fact</a> (1 < (q : ℕ)) := ⟨w⟩ | q : ℕ+
w : 1 < q
⊢ Fintype.card (X q)ˣ < ↑q ^ 2 | q : ℕ+
w : 1 < q
this : Fact (1 < ↑q)
⊢ Fintype.card (X q)ˣ < ↑q ^ 2 | ((:c LT.lt) (:c Nat) (:c instLTNat) ((:c Fintype.card) ((:c Units) ((:c LucasLehmer.X) (:fv _uniq.52868)) ((:c LucasLehmer.X.instMonoid) (:fv _uniq.52868))) ((:c instFintypeUnitsOfDecidableEq) ((:c LucasLehmer.X) (:fv _uniq.52868)) ((:c LucasLehmer.X.instMonoid) (:fv _uniq.52868)) ((:c LucasLehmer.X.instFintype) (:fv _... | [{"name":"q","sexp":"(:c PNat)"},{"name":"w","sexp":"((:c LT.lt) (:c PNat) ((:c Preorder.toLT) (:c PNat) ((:c PartialOrder.toPreorder) (:c PNat) ((:c OrderedCommMonoid.toPartialOrder) (:c PNat) ((:c LinearOrderedCommMonoid.toOrderedCommMonoid) (:c PNat) ((:c LinearOrderedCancelCommMonoid.toLinearOrderedCommMonoid) (:c ... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Fintype.card) (:arg :explicit 0 (:app (:c Units) (:arg :explicit 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52868","is_instance":false,"is_let":false,"name":"q","sexp":"(:c PNat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.53542","is_instance":false,"is_let":false,"name":"w","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c PNat)... | {"children":[{"source":"have","sourceEnd":14408,"sourceStart":14404,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":14409,"sourceStart":14409,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":14409,"sourceStart":14409,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"Fact (1 < (q : ℕ))","source_end":14431,"source_start":14411,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨w⟩","source_end":14442,"source_start":14435,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52868","is_instance":false,"is_let":false,"user_name":"q"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.53542","is_instance":false,"is_let":false,"user_name":"w"}] | 120 | 4 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 744725b9b7e4f008c74e133e9afaea91e2e005fca88ebd4601ce19d850a49afe | 9de2708132df642da276a06aad03181e4cc35d8d426cbea5330ca4aa837ef44a | f7931c4047b40936d1950a404a9070d95d0eafb3873c0739641106b3c19cca0e | 706952a7ae979145bc1ee97924f3bc56ddc2f22cf04671c5deed8fd6c904b232 |
cat-searcher/leandojo-benchmark-4-random | test | 3,386 | LucasLehmer.X.card_units_lt | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert <a>card_units_lt</a> (<a>LucasLehmer.X</a> q) | q : ℕ+
w : 1 < q
this : Fact (1 < ↑q)
⊢ Fintype.card (X q)ˣ < ↑q ^ 2 | case h.e'_4
q : ℕ+
w : 1 < q
this : Fact (1 < ↑q)
⊢ ↑q ^ 2 = Fintype.card (X q) | ((:c LT.lt) (:c Nat) (:c instLTNat) ((:c Fintype.card) ((:c Units) ((:c LucasLehmer.X) (:fv _uniq.52868)) ((:c LucasLehmer.X.instMonoid) (:fv _uniq.52868))) ((:c instFintypeUnitsOfDecidableEq) ((:c LucasLehmer.X) (:fv _uniq.52868)) ((:c LucasLehmer.X.instMonoid) (:fv _uniq.52868)) ((:c LucasLehmer.X.instFintype) (:fv _... | [{"name":"q","sexp":"(:c PNat)"},{"name":"w","sexp":"((:c LT.lt) (:c PNat) ((:c Preorder.toLT) (:c PNat) ((:c PartialOrder.toPreorder) (:c PNat) ((:c OrderedCommMonoid.toPartialOrder) (:c PNat) ((:c LinearOrderedCommMonoid.toOrderedCommMonoid) (:c PNat) ((:c LinearOrderedCancelCommMonoid.toLinearOrderedCommMonoid) (:c ... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Fintype.card) (:arg :explicit 0 (:app (:c Units) (:arg :explicit 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52868","is_instance":false,"is_let":false,"name":"q","sexp":"(:c PNat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.53542","is_instance":false,"is_let":false,"name":"w","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c PNat)... | {"children":[{"source":"convert","sourceEnd":14452,"sourceStart":14445,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"card_units_lt","semanticRole":"global","source":"card_units_lt","sourceEnd":14466,"sourceStart":14453,"... | [] | [{"source":"card_units_lt (X q)","source_end":14472,"source_start":14453,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52868","is_instance":false,"is_let":false,"user_name":"q"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.53542","is_instance":false,"is_let":false,"user_name":"w"},{"binder_role":":explicit","context_index":2,"internal_name":"_un... | 120 | 5 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6be43ee0bfedaac18756639bb5e559f43ab510095f23d78d8a02dc70ba6f6239 | 706952a7ae979145bc1ee97924f3bc56ddc2f22cf04671c5deed8fd6c904b232 | da2819268cf9f7793d7606c56694e857c3130e66af8d2b97e3d0fd2844d18e3e | 1105c2b4f7755dbb488c65e9e9c33c4cca84e55007beaa8ccb3aa7d98c9267fa |
cat-searcher/leandojo-benchmark-4-random | test | 3,387 | LucasLehmer.X.card_units_lt | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>LucasLehmer.X.card_eq</a>] | case h.e'_4
q : ℕ+
w : 1 < q
this : Fact (1 < ↑q)
⊢ ↑q ^ 2 = Fintype.card (X q) | ((:c Eq) (:c Nat) ((:c HPow.hPow) (:c Nat) (:c Nat) (:c Nat) ((:c instHPow) (:c Nat) (:c Nat) ((:c Monoid.toNatPow) (:c Nat) (:c Nat.instMonoid))) ((:c PNat.val) (:fv _uniq.52868)) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c Fintype.card) ((:c LucasLehmer.X) (:fv _uniq.52868)) ((:c LucasLehm... | [{"name":"q","sexp":"(:c PNat)"},{"name":"w","sexp":"((:c LT.lt) (:c PNat) ((:c Preorder.toLT) (:c PNat) ((:c PartialOrder.toPreorder) (:c PNat) ((:c OrderedCommMonoid.toPartialOrder) (:c PNat) ((:c LinearOrderedCommMonoid.toOrderedCommMonoid) (:c PNat) ((:c LinearOrderedCancelCommMonoid.toLinearOrderedCommMonoid) (:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52868","is_instance":false,"is_let":false,"name":"q","sexp":"(:c PNat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.53542","is_instance":false,"is_let":false,"name":"w","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c PNat)... | {"children":[{"source":"rw","sourceEnd":14477,"sourceStart":14475,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":14479,"sourceStart":14478,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"LucasLehmer.X.ca... | [] | [{"source":"card_eq","source_end":14486,"source_start":14479,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.52868","is_instance":false,"is_let":false,"user_name":"q"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.53542","is_instance":false,"is_let":false,"user_name":"w"},{"binder_role":":explicit","context_index":2,"internal_name":"_un... | 120 | 6 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a1d93d85d7b83e06cf508be84871c4257dab3de87b725d8c3c588a32b5c03294 | 1105c2b4f7755dbb488c65e9e9c33c4cca84e55007beaa8ccb3aa7d98c9267fa | e0fd1ddd6f9e7de763d9953d43a68d932c4af7a2ffeeb30b24aa96f2e2724a66 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,388 | Batteries.RBNode.Path.zoom_zoomed₂ | .lake/packages/batteries/Batteries/Data/RBMap/Alter.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | revert e | α✝ : Type u_1
cut : α✝ → Ordering
t : RBNode α✝
path : Path α✝
t'✝ : RBNode α✝
path'✝ : Path α✝
e✝ : zoom cut t path = (t'✝, path'✝)
hp : Zoomed cut path
path' : Path α✝
t' : RBNode α✝
c✝ : RBColor
l✝ : RBNode α✝
v✝ : α✝
r✝ : RBNode α✝
e : zoom cut (node c✝ l✝ v✝ r✝) path = (t', path')
⊢ Zoomed cut path' | α✝ : Type u_1
cut : α✝ → Ordering
t : RBNode α✝
path : Path α✝
t'✝ : RBNode α✝
path'✝ : Path α✝
e : zoom cut t path = (t'✝, path'✝)
hp : Zoomed cut path
path' : Path α✝
t' : RBNode α✝
c✝ : RBColor
l✝ : RBNode α✝
v✝ : α✝
r✝ : RBNode α✝
⊢ zoom cut (node c✝ l✝ v✝ r✝) path = (t', path') → Zoomed cut path' | ((:c Batteries.RBNode.Path.Zoomed) (:fv _uniq.26202) (:fv _uniq.26203) (:fv _uniq.26620)) | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"cut","sexp":"(:forall _ (:fv _uniq.26202) (:c Ordering))"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":"path","sexp":"((:c Batteries.RBNode.Path) (:fv _uniq.26202))"},{"name":"t'✝","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":... | (:app (:c Batteries.RBNode.Path.Zoomed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV9))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"name":"cut","sexp":"(:forall _ :explicit (:fv FV1) (:c Ordering... | {"children":[{"source":"revert","sourceEnd":6373,"sourceStart":6367,"tag":"atom"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"e","sourceEnd":6375,"sourceStart":6374,"tag":"identifier"}],"kind":"null","source":"e","sourceEnd":6375,"sourceStart":6374,"tag":"node"}],"kind":"Lean.Parser.Tactic.revert",... | [] | [{"source":"e","source_end":6375,"source_start":6374,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"user_name":"cut"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 18 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ad19b3fb7cadeaa5a00a85499dbbfe6ce9638f039f387efcd7455795ded7e430 | 2e1f65b48bc594bce0bb89ef6d317328f0f0d50c06509c43449eaa0bca61558c | 95a7a60fa1d232bca171847d2ce0aca383d33438d4ed21be09f95198aa989120 | 17bea9d3baaa5d1cc0fc36dcabc11f53acc5caf0c19be8f70620e97f47f19c03 |
cat-searcher/leandojo-benchmark-4-random | test | 3,389 | Batteries.RBNode.Path.zoom_zoomed₂ | .lake/packages/batteries/Batteries/Data/RBMap/Alter.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | unfold <a>Batteries.RBNode.zoom</a> | α✝ : Type u_1
cut : α✝ → Ordering
t : RBNode α✝
path : Path α✝
t'✝ : RBNode α✝
path'✝ : Path α✝
e : zoom cut t path = (t'✝, path'✝)
hp : Zoomed cut path
path' : Path α✝
t' : RBNode α✝
c✝ : RBColor
l✝ : RBNode α✝
v✝ : α✝
r✝ : RBNode α✝
⊢ zoom cut (node c✝ l✝ v✝ r✝) path = (t', path') → Zoomed cut path' | α✝ : Type u_1
cut : α✝ → Ordering
t : RBNode α✝
path : Path α✝
t'✝ : RBNode α✝
path'✝ : Path α✝
e : zoom cut t path = (t'✝, path'✝)
hp : Zoomed cut path
path' : Path α✝
t' : RBNode α✝
c✝ : RBColor
l✝ : RBNode α✝
v✝ : α✝
r✝ : RBNode α✝
⊢ (match cut v✝ with
| Ordering.lt => zoom cut l✝ (left c✝ path v✝ r✝)
| ... | (:forall e ((:c Eq) ((:c Prod) ((:c Batteries.RBNode) (:fv _uniq.26202)) ((:c Batteries.RBNode.Path) (:fv _uniq.26202))) ((:c Batteries.RBNode.zoom) (:fv _uniq.26202) (:fv _uniq.26203) ((:c Batteries.RBNode.node) (:fv _uniq.26202) (:fv _uniq.26622) (:fv _uniq.26623) (:fv _uniq.26624) (:fv _uniq.26625)) (:fv _uniq.26205... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"cut","sexp":"(:forall _ (:fv _uniq.26202) (:c Ordering))"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":"path","sexp":"((:c Batteries.RBNode.Path) (:fv _uniq.26202))"},{"name":"t'✝","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":... | (:forall e :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c Batteries.RBNode) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Batteries.RBNode.Path) (:arg :explicit 0 (:fv FV1)))))) (:arg :explicit 1 (:app (:c Batteries.RBNode.zoom) (:arg :implicit-type 0 (:fv FV1)) ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"name":"cut","sexp":"(:forall _ :explicit (:fv FV1) (:c Ordering... | {"children":[{"source":"unfold","sourceEnd":6383,"sourceStart":6377,"tag":"atom"},{"children":[{"name":"Batteries.RBNode.zoom","semanticRole":"global","source":"zoom","sourceEnd":6388,"sourceStart":6384,"tag":"identifier"}],"kind":"null","source":"zoom","sourceEnd":6388,"sourceStart":6384,"tag":"node"},{"children":[],"... | [] | [{"source":"zoom","source_end":6388,"source_start":6384,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"user_name":"cut"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 18 | 6 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7cc54d576ebe343bbbd774084661e80cc39bf491ff6bebc479e1e6e3ab5b227c | 17bea9d3baaa5d1cc0fc36dcabc11f53acc5caf0c19be8f70620e97f47f19c03 | 763e9d1dafada6e26d6fde2a41ad5f2f12c215079b0557a6b668fbde82b22ae7 | 16eb5f3088c3a6fc60eaa518b47539ff93e800b6f71063c22b5914396fc4a7cb |
cat-searcher/leandojo-benchmark-4-random | test | 3,390 | Batteries.RBNode.Path.zoom_zoomed₂ | .lake/packages/batteries/Batteries/Data/RBMap/Alter.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split | α✝ : Type u_1
cut : α✝ → Ordering
t : RBNode α✝
path : Path α✝
t'✝ : RBNode α✝
path'✝ : Path α✝
e : zoom cut t path = (t'✝, path'✝)
hp : Zoomed cut path
path' : Path α✝
t' : RBNode α✝
c✝ : RBColor
l✝ : RBNode α✝
v✝ : α✝
r✝ : RBNode α✝
⊢ (match cut v✝ with
| Ordering.lt => zoom cut l✝ (left c✝ path v✝ r✝)
| ... | case h_1
α✝ : Type u_1
cut : α✝ → Ordering
t : RBNode α✝
path : Path α✝
t'✝ : RBNode α✝
path'✝ : Path α✝
e : zoom cut t path = (t'✝, path'✝)
hp : Zoomed cut path
path' : Path α✝
t' : RBNode α✝
c✝ : RBColor
l✝ : RBNode α✝
v✝ : α✝
r✝ : RBNode α✝
x✝ : Ordering
heq✝ : cut v✝ = Ordering.lt
⊢ zoom cut l✝ (left c✝ path v✝ r✝)... | (:forall e ((:c Eq) ((:c Prod) ((:c Batteries.RBNode) (:fv _uniq.26202)) ((:c Batteries.RBNode.Path) (:fv _uniq.26202))) ((:c Batteries.RBNode.ins.match_1) (:lambda _ (:c Ordering) ((:c Prod) ((:c Batteries.RBNode) (:fv _uniq.26202)) ((:c Batteries.RBNode.Path) (:fv _uniq.26202)))) ((:fv _uniq.26203) (:fv _uniq.26624))... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"cut","sexp":"(:forall _ (:fv _uniq.26202) (:c Ordering))"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":"path","sexp":"((:c Batteries.RBNode.Path) (:fv _uniq.26202))"},{"name":"t'✝","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":... | (:forall e :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c Batteries.RBNode) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Batteries.RBNode.Path) (:arg :explicit 0 (:fv FV1)))))) (:arg :explicit 1 (:app (:c Batteries.RBNode.ins.match_1) (:arg :explicit 0 (:lambda ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"name":"cut","sexp":"(:forall _ :explicit (:fv FV1) (:c Ordering... | {"children":[{"source":"split","sourceEnd":6395,"sourceStart":6390,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.split","source":"split","sourceEnd":6395,"sourceStart":6390,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"user_name":"cut"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 18 | 8 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d97341843952c140b60be6b37226aa374ceee8c766c5fa834ca66655db013937 | 16eb5f3088c3a6fc60eaa518b47539ff93e800b6f71063c22b5914396fc4a7cb | ad1a64057f9ab34fecfe3f4ee78660bb0316dbda9370581ffbeb1e8bddf3d598 | 9c9ed081588d63821eedd39970098ae8f90feebc9ef7d91bf3553752b4f441cf |
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