dataset stringclasses 1
value | split stringclasses 1
value | row_index int64 0 4.5k | theorem stringlengths 7 81 | file_path stringclasses 723
values | repo_url stringclasses 1
value | repo_commit stringclasses 1
value | tactic stringlengths 3 2.13k | text_state stringlengths 7 2.31k | text_target_state stringlengths 0 4.07k | raw_goal_sexp stringlengths 10 11.8M | raw_hyp_sexps stringlengths 2 15.6M | model_goal_sexp stringlengths 10 2.68M | model_hyp_sexps stringlengths 2 3.62M | source_syntax stringlengths 179 164k | syntax_args stringclasses 256
values | term_ranges stringlengths 2 6.01k | local_context stringlengths 2 10.3k | unit_index int64 3 1.26k | invocation_index int64 0 357 | alignment_kind stringclasses 2
values | target_state_matches_invocation bool 2
classes | pending_goal_count int64 1 1 | hypothesis_count int64 0 77 | hypothesis_names_match bool 2
classes | raw_schema_version int64 4 4 | raw_extractor_version stringclasses 1
value | model_schema_version int64 2 2 | model_normalization stringclasses 1
value | trace_schema_version int64 3 3 | trace_extractor_version stringclasses 1
value | pantograph_commit stringclasses 1
value | model_pantograph_commit stringclasses 1
value | raw_record_sha256 stringlengths 64 64 | state_sha256 stringlengths 64 64 | tactic_sha256 stringlengths 64 64 | target_state_sha256 stringlengths 64 64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
cat-searcher/leandojo-benchmark-4-random | test | 2,984 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨x, hx⟩ - | case a.right
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : J' = I
⊢ ⊤ ≤ J | case a.right.mk
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : J' = I
x : L
hx : x ∈ ... | ((:c LE.le) ((:c LieIdeal) (:fv _uniq.14419) ((:c Subtype) (:fv _uniq.14422) (:lambda x (:fv _uniq.14422) ((:c Membership.mem) (:fv _uniq.14422) ((:c Submodule) (:fv _uniq.14419) (:fv _uniq.14422) ((:c CommSemiring.toSemiring) (:fv _uniq.14419) ((:c CommRing.toCommSemiring) (:fv _uniq.14419) (:fv _uniq.14425))) ((:c Ad... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c LieIdeal) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rintro","sourceEnd":7188,"sourceStart":7182,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":7192,"sourceStart":7189,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":7193,"sourceSt... | [{"role":"fresh_name","source":"x","source_end":7193,"source_start":7192,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":7197,"source_start":7195,"syntax_kind":"ident"}] | [{"source":"⟨x, hx⟩","source_end":7200,"source_start":7189,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"},{"source":"-","source_end":7202,"source_start":7201,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.clear"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 86 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2a1d4c07e9776811e2e8d6ea776d2e8c7ec40919aa0a7e2e17b6132eb9929527 | 6fefbe006071259ff33f9f6ef25c94aa8f82e5ef8e03bc5802bb5b51b59d366a | 366cbe3f31b4e224018ad77652cabe392f9778af80fa84ce191156558ad83481 | f0d8c893b184d324b6e0bd9d75c4ab3a8ded5fb338482095df2f7554e17834aa |
cat-searcher/leandojo-benchmark-4-random | test | 2,985 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hJ] at hx | case a.right.mk
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : J' = I
x : L
hx : x ∈ ... | case a.right.mk
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : J' = I
x : L
hx✝ : x ∈... | ((:c Membership.mem) ((:c Subtype) (:fv _uniq.14422) (:lambda x (:fv _uniq.14422) ((:c Membership.mem) (:fv _uniq.14422) ((:c Submodule) (:fv _uniq.14419) (:fv _uniq.14422) ((:c CommSemiring.toSemiring) (:fv _uniq.14419) ((:c CommRing.toCommSemiring) (:fv _uniq.14419) (:fv _uniq.14425))) ((:c AddCommGroup.toAddCommMono... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":7209,"sourceStart":7207,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7211,"sourceStart":7210,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":7214,"sourceStart":... | [] | [{"source":"hJ","source_end":7217,"source_start":7215,"syntax_kind":"ident"},{"source":"hx","source_end":7224,"source_start":7222,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 87 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 31a611c8596c760738b009075fdc8194be5500a3c31eaa43956ec761b7c70b9c | f0d8c893b184d324b6e0bd9d75c4ab3a8ded5fb338482095df2f7554e17834aa | f837a5c549767cb56406f67c035af7f33520a51e0b27ac3a1d37751ea6cebbd6 | 2a6f83eb3a72dd2be8e4bfef853668ee1de287f446245415a2b63798caf4665d |
cat-searcher/leandojo-benchmark-4-random | test | 2,986 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases hx with ⟨y, hy, rfl⟩ | case a.right.mk
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : J' = I
x : L
hx✝ : x ∈... | case a.right.mk.intro.intro
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : J' = I
y :... | ((:c Membership.mem) ((:c Subtype) (:fv _uniq.14422) (:lambda x (:fv _uniq.14422) ((:c Membership.mem) (:fv _uniq.14422) ((:c Submodule) (:fv _uniq.14419) (:fv _uniq.14422) ((:c CommSemiring.toSemiring) (:fv _uniq.14419) ((:c CommRing.toCommSemiring) (:fv _uniq.14419) (:fv _uniq.14425))) ((:c AddCommGroup.toAddCommMono... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rcases","sourceEnd":7235,"sourceStart":7229,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":14,"semanticRole":"local","source":"hx","sourceEnd":7238,"sourceStart":7236,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","sou... | [] | [{"source":"hx","source_end":7238,"source_start":7236,"syntax_kind":"ident"},{"source":"⟨y, hy, rfl⟩","source_end":7260,"source_start":7244,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 90 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 958a80432a032f2ec34c8471a9cfda52d9cea564620ca23b2005300fffcf1b37 | 2a6f83eb3a72dd2be8e4bfef853668ee1de287f446245415a2b63798caf4665d | 68221d8c8cbb0911b66ea65413229dcd0805080d9d4b30f3101731a11bf3cb0f | 1ae8c8e5c61aa80a082d17548cbe06dcc4cbfa83ba4b219036c5ace352f93e7d |
cat-searcher/leandojo-benchmark-4-random | test | 2,987 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hy | case a.right.mk.intro.intro
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : J' = I
y :... | ((:c Membership.mem) ((:c Subtype) (:fv _uniq.14422) (:lambda x (:fv _uniq.14422) ((:c Membership.mem) (:fv _uniq.14422) ((:c Submodule) (:fv _uniq.14419) (:fv _uniq.14422) ((:c CommSemiring.toSemiring) (:fv _uniq.14419) ((:c CommRing.toCommSemiring) (:fv _uniq.14419) (:fv _uniq.14425))) ((:c AddCommGroup.toAddCommMono... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":7270,"sourceStart":7265,"tag":"atom"},{"contextIndex":13,"semanticRole":"local","source":"hy","sourceEnd":7273,"sourceStart":7271,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact hy","sourceEnd":7273,"sourceStart":7265,"tag":"node"} | [] | [{"source":"hy","source_end":7273,"source_start":7271,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 91 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f2e546c953708e017590ad8c87e4ddd2ba060475921e3daf9ba04ceb2f35d532 | 1ae8c8e5c61aa80a082d17548cbe06dcc4cbfa83ba4b219036c5ace352f93e7d | 5088a32eabea2e75b7e26e342cc75ebb2a7788e64a60064017c9476437cad0a1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,988 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro x _ ⟨y, hy, rfl⟩ | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
⊢ ∀ {x m : L}, m ∈ __spread✝⁻⁰.carrier → ⁅x, m⁆ ∈ __spread✝⁻⁰.carrier | case intro.intro
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
x : L
y : ↥↑I
hy : y ∈ ↑↑J
⊢ ⁅x, ↑I.incl y⁆ ∈ __spread✝⁻⁰.carrier | (:forall x (:fv _uniq.14422) (:forall m (:fv _uniq.14422) (:forall _ ((:c Membership.mem) (:fv _uniq.14422) ((:c Set) (:fv _uniq.14422)) ((:c Set.instMembership) (:fv _uniq.14422)) 0 ((:c AddSubsemigroup.carrier) (:fv _uniq.14422) ((:c AddZeroClass.toAdd) (:fv _uniq.14422) ((:c AddMonoid.toAddZeroClass) (:fv _uniq.1442... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:forall x :implicit (:fv FV1) (:forall m :implicit (:fv FV1) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rintro","sourceEnd":4614,"sourceStart":4608,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":4616,"sourceStart":4615,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":4616,"sourceStart":4615,"tag":"... | [{"role":"fresh_name","source":"x","source_end":4616,"source_start":4615,"syntax_kind":"ident"},{"role":"fresh_name","source":"y","source_end":4623,"source_start":4622,"syntax_kind":"ident"},{"role":"fresh_name","source":"hy","source_end":4627,"source_start":4625,"syntax_kind":"ident"}] | [{"source":"⟨y, hy, rfl⟩","source_end":4635,"source_start":4619,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 10 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 16c01647452da8432a1537ec9067977dcda19af8010ca102c036b55c148107c7 | 8cc38eb756a14eee7247fadec57e6452417f50cbf2d5df03981a2aa6cb827a86 | 7705434637a18fa818fe9e86309b0887c98f4a5906e5de64b8d54b6bbd4bf900 | 9d77f832989b2b352ece4f08152f6d1ece421ca0b6c91d585af692381e25e7f9 |
cat-searcher/leandojo-benchmark-4-random | test | 2,989 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp | case intro.intro
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
x : L
y : ↥↑I
hy : y ∈ ↑↑J
⊢ ⁅x, ↑I.incl y⁆ ∈ __spread✝⁻⁰.carrier | case intro.intro
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
x : L
y : ↥↑I
hy : y ∈ ↑↑J
⊢ ⁅x, ↑y⁆ ∈ (Submodule.map (↑I).subtype ↑J).carrier | ((:c Membership.mem) (:fv _uniq.14422) ((:c Set) (:fv _uniq.14422)) ((:c Set.instMembership) (:fv _uniq.14422)) ((:c Bracket.bracket) (:fv _uniq.14422) (:fv _uniq.14422) ((:c LieRingModule.toBracket) (:fv _uniq.14422) (:fv _uniq.14422) (:fv _uniq.14428) ((:c LieRing.toAddCommGroup) (:fv _uniq.14422) (:fv _uniq.14428)) ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:app (:c Bracket.brack... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"dsimp","sourceEnd":4649,"sourceStart":4644,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kin... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 11 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 404bad7f1436b7680d65664dfda5de87facaacd205d59e2b780d9ccea4264ea1 | 9d77f832989b2b352ece4f08152f6d1ece421ca0b6c91d585af692381e25e7f9 | 7854eab90b5d1f0eed9d2f7f6b885100cc44bc732b41c876b3af083c01260845 | e926d60e322bf488672b25a7ac3770e20746d354023900b97f6ffa8056f9135b |
cat-searcher/leandojo-benchmark-4-random | test | 2,990 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>LieSubmodule.mem_sup</a>] at hx | case intro.intro
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
x : L
y : ↥↑I
hy : y ∈ ↑↑J
hx : x ∈ I ⊔ sSup ({I' | IsAtom I'} \ {I})
⊢ ⁅x, ↑y⁆ ∈ (Submodule.map (↑I).subtype ↑J).carrier | case intro.intro
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
x : L
y : ↥↑I
hy : y ∈ ↑↑J
hx : ∃ y ∈ I, ∃ z ∈ sSup ({I' | IsAtom I'} \ {I}), y + z = x
⊢ ⁅x, ↑y⁆ ∈ (Submodule.map (↑I).subtype ↑J).carrier | ((:c Membership.mem) (:fv _uniq.14422) ((:c Set) (:fv _uniq.14422)) ((:c Set.instMembership) (:fv _uniq.14422)) ((:c Bracket.bracket) (:fv _uniq.14422) (:fv _uniq.14422) ((:c LieRingModule.toBracket) (:fv _uniq.14422) (:fv _uniq.14422) (:fv _uniq.14428) ((:c LieRing.toAddCommGroup) (:fv _uniq.14422) (:fv _uniq.14428)) ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:app (:c Bracket.brack... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":5365,"sourceStart":5363,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5367,"sourceStart":5366,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"LieSubmodule.mem_sup... | [] | [{"source":"LieSubmodule.mem_sup","source_end":5387,"source_start":5367,"syntax_kind":"ident"},{"source":"hx","source_end":5394,"source_start":5392,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 33 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c2d120e46834d944d03aa85fb551d54d1f5900e2af0ed3b5bb5f266d87b40559 | 74eef7d69cd47678deacee9921b0a5f8fc1568dccb340617720bc87c8d8f298a | 2ce614931ebdcf9d331da1317bca8548c9d8106070862a560d89553d02ebcfed | 6e0430e75479560a789a1b24153d4f281811cc9367e1a407a043c7fb184bcd49 |
cat-searcher/leandojo-benchmark-4-random | test | 2,991 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨a, ha, b, hb, rfl⟩ := hx | case intro.intro
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
x : L
y : ↥↑I
hy : y ∈ ↑↑J
hx : ∃ y ∈ I, ∃ z ∈ sSup ({I' | IsAtom I'} \ {I}), y + z = x
⊢ ⁅x, ↑y⁆ ∈ (Submodule.map (↑I).subtype ↑J).carrier | case intro.intro.intro.intro.intro.intro
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
y : ↥↑I
hy : y ∈ ↑↑J
a : L
ha : a ∈ I
b : L
hb : b ∈ sSup ({I' | IsAtom I'} \ {I})
⊢ ⁅a + b, ↑y⁆ ∈ (Submodule.map (... | ((:c Membership.mem) (:fv _uniq.14422) ((:c Set) (:fv _uniq.14422)) ((:c Set.instMembership) (:fv _uniq.14422)) ((:c Bracket.bracket) (:fv _uniq.14422) (:fv _uniq.14422) ((:c LieRingModule.toBracket) (:fv _uniq.14422) (:fv _uniq.14422) (:fv _uniq.14428) ((:c LieRing.toAddCommGroup) (:fv _uniq.14422) (:fv _uniq.14428)) ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:app (:c Bracket.brack... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"obtain","sourceEnd":5409,"sourceStart":5403,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":5413,"sourceStart":5410,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":5... | [] | [{"source":"hx\n -- Therefore it suffices to show that `⁅a, y⁆ ∈ J` and `⁅b, y⁆ ∈ J`.","source_end":5439,"source_start":5437,"syntax_kind":"ident"},{"source":"⟨a, ha, b, hb, rfl⟩","source_end":5433,"source_start":5410,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 36 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 51067c91633c522afdc7449d9eaf175b04497c4f898a937e85260f814726bb51 | 6e0430e75479560a789a1b24153d4f281811cc9367e1a407a043c7fb184bcd49 | e8d60e6bb1848f84c1abe305eab1389fca42ae7b2dd0645db4dccc83c48a9915 | dcae18388ded97fd139b921c63a1e18d118c9005272747dc67d5bca0d3ab0994 |
cat-searcher/leandojo-benchmark-4-random | test | 2,992 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>add_lie</a>, <a>AddSubsemigroup.mem_carrier</a>, <a>AddSubmonoid.mem_toSubsemigroup</a>, <a>Submodule.mem_toAddSubmonoid</a>] | case intro.intro.intro.intro.intro.intro
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
y : ↥↑I
hy : y ∈ ↑↑J
a : L
ha : a ∈ I
b : L
hb : b ∈ sSup ({I' | IsAtom I'} \ {I})
⊢ ⁅a + b, ↑y⁆ ∈ (Submodule.map (... | case intro.intro.intro.intro.intro.intro
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
y : ↥↑I
hy : y ∈ ↑↑J
a : L
ha : a ∈ I
b : L
hb : b ∈ sSup ({I' | IsAtom I'} \ {I})
⊢ ⁅a, ↑y⁆ + ⁅b, ↑y⁆ ∈ Submodule.... | ((:c Membership.mem) (:fv _uniq.14422) ((:c Set) (:fv _uniq.14422)) ((:c Set.instMembership) (:fv _uniq.14422)) ((:c Bracket.bracket) (:fv _uniq.14422) (:fv _uniq.14422) ((:c LieRingModule.toBracket) (:fv _uniq.14422) (:fv _uniq.14422) (:fv _uniq.14428) ((:c LieRing.toAddCommGroup) (:fv _uniq.14422) (:fv _uniq.14428)) ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:app (:c Bracket.brack... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"simp","sourceEnd":5541,"sourceStart":5537,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":5546,"sourceStart":5542,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":5546,"s... | [] | [{"source":"add_lie","source_end":5555,"source_start":5548,"syntax_kind":"ident"},{"source":"AddSubsemigroup.mem_carrier","source_end":5584,"source_start":5557,"syntax_kind":"ident"},{"source":"AddSubmonoid.mem_toSubsemigroup","source_end":5617,"source_start":5586,"syntax_kind":"ident"},{"source":"Submodule.mem_toAddSu... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 37 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6074795f150fa5cbab4aa9e4cb063d358af5f9bb8ef7eb4d0d8b59a3e6528aee | dcae18388ded97fd139b921c63a1e18d118c9005272747dc67d5bca0d3ab0994 | e40f28fbe7777bd904b2ed5add016380a47e185efec394fdead62b4ca9a06d32 | 8fe8c0ae068e0668a763da88548635c06dc15dff158482d66f037c28e194637b |
cat-searcher/leandojo-benchmark-4-random | test | 2,993 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>AddMemClass.add_mem</a> | case intro.intro.intro.intro.intro.intro
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
y : ↥↑I
hy : y ∈ ↑↑J
a : L
ha : a ∈ I
b : L
hb : b ∈ sSup ({I' | IsAtom I'} \ {I})
⊢ ⁅a, ↑y⁆ + ⁅b, ↑y⁆ ∈ Submodule.... | case intro.intro.intro.intro.intro.intro.a
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
y : ↥↑I
hy : y ∈ ↑↑J
a : L
ha : a ∈ I
b : L
hb : b ∈ sSup ({I' | IsAtom I'} \ {I})
⊢ ⁅a, ↑y⁆ ∈ Submodule.map (↑I)... | ((:c Membership.mem) (:fv _uniq.14422) ((:c Submodule) (:fv _uniq.14419) (:fv _uniq.14422) ((:c CommSemiring.toSemiring) (:fv _uniq.14419) ((:c CommRing.toCommSemiring) (:fv _uniq.14419) (:fv _uniq.14425))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.14422) ((:c LieRing.toAddCommGroup) (:fv _uniq.14422) (:fv _uniq.14... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"apply","sourceEnd":5672,"sourceStart":5667,"tag":"atom"},{"name":"AddMemClass.add_mem","semanticRole":"global","source":"add_mem","sourceEnd":5680,"sourceStart":5673,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply add_mem\n -- Now `⁅a, y⁆ ∈ J` since `a ∈ I`, `y ∈ J`... | [] | [{"source":"add_mem\n -- Now `⁅a, y⁆ ∈ J` since `a ∈ I`, `y ∈ J`, and `J` is an ideal of `I`.","source_end":5680,"source_start":5673,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 38 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cf0d6ce327235e6086814b62c6025236180ed28e88c4dfc1815ea4de5e0611a0 | 8fe8c0ae068e0668a763da88548635c06dc15dff158482d66f037c28e194637b | 14f37de2dc12c4c5a6b4ab81987a27b4a27fccdeec9761cde5b88f2218dff5a8 | c9f5d64f75acab6f0bc191ca5edcd2abe8afc1ac295d3108a47c3c604900a89d |
cat-searcher/leandojo-benchmark-4-random | test | 2,994 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | nth_rewrite 1 [← <a>sSup_singleton</a> (a := I)] | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
x : L
y : ↥↑I
hy : y ∈ ↑↑J
⊢ x ∈ I ⊔ sSup ({I' | IsAtom I'} \ {I}) | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
x : L
y : ↥↑I
hy : y ∈ ↑↑J
⊢ x ∈ sSup {I} ⊔ sSup ({I' | IsAtom I'} \ {I}) | ((:c Membership.mem) (:fv _uniq.14422) ((:c LieIdeal) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) (:fv _uniq.14445)) ((:c SetLike.instMembership) ((:c LieIdeal) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) (:fv _uniq.14445)) (:fv _uniq.14422) ((:c LieSubmodule.inst... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c LieIdeal) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"nth_rewrite","sourceEnd":4955,"sourceStart":4944,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"1","sourceEnd":4957,"sourceStart":4956,"tag":"atom"}],"kind":"num","source":"1","sourceEnd":4957,"sourceStart":4956,"tag":"node"},{"children":[{"source":"... | [] | [{"source":"sSup_singleton (a := I)","source_end":4986,"source_start":4963,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 14 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a57a1850d227a08adb1327cac24563870aa6776b3587f255a60647520d8416fe | 9839dc606a4f70dd01df5a56b893861a6b6b4f9083ce0379b3a99ae016068f20 | 3e2862b13aceeadfa04866c29a763ba31e2ab2d778bfd901a04425e9919cf220 | c32120197b6db90c79d32f594de8f61d916b331514912c4adac3029a2e686a7a |
cat-searcher/leandojo-benchmark-4-random | test | 2,995 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>sSup_union</a>, <a>Set.union_diff_self</a>, <a>Set.union_eq_self_of_subset_left</a>, <a>LieAlgebra.IsSemisimple.sSup_atoms_eq_top</a>] | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
x : L
y : ↥↑I
hy : y ∈ ↑↑J
⊢ x ∈ sSup {I} ⊔ sSup ({I' | IsAtom I'} \ {I}) | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
x : L
y : ↥↑I
hy : y ∈ ↑↑J
⊢ x ∈ ⊤
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : Lie... | ((:c Membership.mem) (:fv _uniq.14422) ((:c LieIdeal) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) (:fv _uniq.14445)) ((:c SetLike.instMembership) ((:c LieIdeal) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) (:fv _uniq.14445)) (:fv _uniq.14422) ((:c LieSubmodule.inst... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c LieIdeal) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":5000,"sourceStart":4998,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5002,"sourceStart":5001,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":5005,"sourceStart":... | [] | [{"source":"sSup_union","source_end":5016,"source_start":5006,"syntax_kind":"ident"},{"source":"Set.union_diff_self","source_end":5037,"source_start":5018,"syntax_kind":"ident"},{"source":"Set.union_eq_self_of_subset_left","source_end":5071,"source_start":5039,"syntax_kind":"ident"},{"source":"IsSemisimple.sSup_atoms_e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 17 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3a551529fe6993b80fac5358b7853e67b1920ee9a7c3b2d8b939fab74db45248 | c32120197b6db90c79d32f594de8f61d916b331514912c4adac3029a2e686a7a | eeffecb48f72af89bfd88221c6a39d0d2cd2212e15bfa1918c43b6e76d92a676 | 1f4ce3f3108d4f1178e849e89750da002dbce30156c123b37191e8ba756eb73e |
cat-searcher/leandojo-benchmark-4-random | test | 2,996 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>LieSubmodule.mem_top</a> | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
x : L
y : ↥↑I
hy : y ∈ ↑↑J
⊢ x ∈ ⊤ | ((:c Membership.mem) (:fv _uniq.14422) ((:c LieIdeal) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) (:fv _uniq.14445)) ((:c SetLike.instMembership) ((:c LieIdeal) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) (:fv _uniq.14445)) (:fv _uniq.14422) ((:c LieSubmodule.inst... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c LieIdeal) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"apply","sourceEnd":5135,"sourceStart":5130,"tag":"atom"},{"name":"LieSubmodule.mem_top","semanticRole":"global","source":"LieSubmodule.mem_top","sourceEnd":5156,"sourceStart":5136,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply LieSub... | [] | [{"source":"LieSubmodule.mem_top","source_end":5156,"source_start":5136,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 25 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7d2d66d9b3a0ca57e29531c6569de39f8d4e878d50f0f809476710d3bd90f0d1 | d3b19e39bc092ac90c24f3025bc138ae7a55ebc6b62eff762ecb68351b07fde7 | 71a2e768a9b545f153378ae1377818f39036dc46cc46fe9b83250c6d3a95975a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,997 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.singleton_subset_iff</a>, <a>Set.mem_setOf_eq</a>, hI] | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
x : L
y : ↥↑I
hy : y ∈ ↑↑J
⊢ {I} ⊆ {I' | IsAtom I'} | ((:c HasSubset.Subset) ((:c Set) ((:c LieIdeal) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) (:fv _uniq.14445))) ((:c Set.instHasSubset) ((:c LieIdeal) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) (:fv _uniq.14445))) ((:c Singleton.singleton) ((:c LieIdeal) (:fv _un... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c LieIdeal) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":5174,"sourceStart":5170,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":5179,"sourceStart":5175,"tag":"atom"}],"kind":"nu... | [] | [{"source":"Set.singleton_subset_iff","source_end":5205,"source_start":5181,"syntax_kind":"ident"},{"source":"Set.mem_setOf_eq","source_end":5223,"source_start":5207,"syntax_kind":"ident"},{"source":"hI","source_end":5227,"source_start":5225,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 30 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e56788cbe21052ca14e6b695670d68a5c19e31f312b4349198edf8c922f794e2 | a962af995e496d15d784ea57522c4f3e2031dc7389389613e215b202070a7337 | 9938ff625c5066a34733a2153070407105fdee5a4e8d77c5fc7afc80125d0756 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,998 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Submodule.mem_map</a>, <a>LieSubmodule.mem_coeSubmodule</a>, <a>Submodule.coeSubtype</a>, <a>Subtype.exists</a>, <a>exists_and_right</a>, <a>exists_eq_right</a>, ha, <a>lie_mem_left</a>, <a>exists_true_left</a>] | case intro.intro.intro.intro.intro.intro.a
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
y : ↥↑I
hy : y ∈ ↑↑J
a : L
ha : a ∈ I
b : L
hb : b ∈ sSup ({I' | IsAtom I'} \ {I})
⊢ ⁅a, ↑y⁆ ∈ Submodule.map (↑I)... | case intro.intro.intro.intro.intro.intro.a
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
y : ↥↑I
hy : y ∈ ↑↑J
a : L
ha : a ∈ I
b : L
hb : b ∈ sSup ({I' | IsAtom I'} \ {I})
⊢ ⟨⁅a, ↑y⁆, ⋯⟩ ∈ J | ((:c Membership.mem) (:fv _uniq.14422) ((:c Submodule) (:fv _uniq.14419) (:fv _uniq.14422) ((:c CommSemiring.toSemiring) (:fv _uniq.14419) ((:c CommRing.toCommSemiring) (:fv _uniq.14419) (:fv _uniq.14425))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.14422) ((:c LieRing.toAddCommGroup) (:fv _uniq.14422) (:fv _uniq.14... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"simp","sourceEnd":5786,"sourceStart":5782,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":5791,"sourceStart":5787,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":5791,"s... | [] | [{"source":"Submodule.mem_map","source_end":5810,"source_start":5793,"syntax_kind":"ident"},{"source":"LieSubmodule.mem_coeSubmodule","source_end":5841,"source_start":5812,"syntax_kind":"ident"},{"source":"Submodule.coeSubtype","source_end":5863,"source_start":5843,"syntax_kind":"ident"},{"source":"Subtype.exists","sou... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 43 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9b64336b4e2bc884b0ebe1701827515062382b8815212079642db1ded834eec9 | 81e6dc7b98576d6579a28aa292821c99d9ab22c2440f6a95d9db84105b034f6f | 8c28cb3dbeee47660f49d6f91a75f10efac130c95af6077318b492589df2b422 | 4885250dda976b4a3141a83eec96b50471edc6194021e64ef8c4cc2f4c50a9df |
cat-searcher/leandojo-benchmark-4-random | test | 2,999 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>lie_mem_right</a> R I J ⟨a, ha⟩ y hy | case intro.intro.intro.intro.intro.intro.a
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
y : ↥↑I
hy : y ∈ ↑↑J
a : L
ha : a ∈ I
b : L
hb : b ∈ sSup ({I' | IsAtom I'} \ {I})
⊢ ⟨⁅a, ↑y⁆, ⋯⟩ ∈ J | ((:c Membership.mem) ((:c Subtype) (:fv _uniq.14422) (:lambda x (:fv _uniq.14422) ((:c Membership.mem) (:fv _uniq.14422) ((:c Submodule) (:fv _uniq.14419) (:fv _uniq.14422) ((:c CommSemiring.toSemiring) (:fv _uniq.14419) ((:c CommRing.toCommSemiring) (:fv _uniq.14419) (:fv _uniq.14425))) ((:c AddCommGroup.toAddCommMono... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":5979,"sourceStart":5974,"tag":"atom"},{"children":[{"name":"lie_mem_right","semanticRole":"global","source":"lie_mem_right","sourceEnd":5993,"sourceStart":5980,"tag":"identifier"},{"children":[{"contextIndex":0,"semanticRole":"local","source":"R","sourceEnd":5995,"sourceStart"... | [] | [{"source":"lie_mem_right R I J ⟨a, ha⟩ y hy\n -- Finally `⁅b, y⁆ = 0`, by the independence of the atoms.","source_end":6016,"source_start":5980,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 44 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2c73711378c302fa9ead86542e1e33289675ec15a9ed33a0b7eba4c79d57f7c2 | 4885250dda976b4a3141a83eec96b50471edc6194021e64ef8c4cc2f4c50a9df | 771ebab156debb20184588a427be48ee9f9731e662d05c99cb651ded0960e187 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,000 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | suffices ⁅b, y.val⁆ = 0 by simp only [this, <a>ZeroMemClass.zero_mem</a>] | case intro.intro.intro.intro.intro.intro.a
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
y : ↥↑I
hy : y ∈ ↑↑J
a : L
ha : a ∈ I
b : L
hb : b ∈ sSup ({I' | IsAtom I'} \ {I})
⊢ ⁅b, ↑y⁆ ∈ Submodule.map (↑I)... | case intro.intro.intro.intro.intro.intro.a
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
y : ↥↑I
hy : y ∈ ↑↑J
a : L
ha : a ∈ I
b : L
hb : b ∈ sSup ({I' | IsAtom I'} \ {I})
⊢ ⁅b, ↑y⁆ = 0 | ((:c Membership.mem) (:fv _uniq.14422) ((:c Submodule) (:fv _uniq.14419) (:fv _uniq.14422) ((:c CommSemiring.toSemiring) (:fv _uniq.14419) ((:c CommRing.toCommSemiring) (:fv _uniq.14419) (:fv _uniq.14425))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.14422) ((:c LieRing.toAddCommGroup) (:fv _uniq.14422) (:fv _uniq.14... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"suffices","sourceEnd":6107,"sourceStart":6099,"tag":"atom"},{"children":[{"children":[{"source":"","sourceEnd":6108,"sourceStart":6108,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":6108,"sourceStart":6108,"tag":"node"},{"children":[{"children":[{"source":"⁅","sourceEnd":6111,... | [] | [{"source":"⁅b, y.val⁆ = 0","source_end":6126,"source_start":6108,"syntax_kind":"«term_=_»"},{"source":"this","source_end":6145,"source_start":6141,"syntax_kind":"ident"},{"source":"zero_mem","source_end":6155,"source_start":6147,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 49 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8782e6f3188274b5cc7cd0d9de28469b30d5060bc9546abba954b0ceb0df8b5f | 9071c9414e13c9218c81f38d797aef0b2753b420273cddf67c5097465d734e93 | 53a4272e8b7e2eb27c930bd4eba57741e93f5248b9b6eeb1eb6073d04493c7ac | bb7a285412003c7c32291a11a73e2591967baf3b64d9409e3957b8edbfee90b5 |
cat-searcher/leandojo-benchmark-4-random | test | 3,001 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>LieSubmodule.mem_bot</a> (R := R) (L := L), ← (<a>LieAlgebra.IsSemisimple.setIndependent_isAtom</a> hI).<a>Disjoint.eq_bot</a>] | case intro.intro.intro.intro.intro.intro.a
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
y : ↥↑I
hy : y ∈ ↑↑J
a : L
ha : a ∈ I
b : L
hb : b ∈ sSup ({I' | IsAtom I'} \ {I})
⊢ ⁅b, ↑y⁆ = 0 | case intro.intro.intro.intro.intro.intro.a
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
y : ↥↑I
hy : y ∈ ↑↑J
a : L
ha : a ∈ I
b : L
hb : b ∈ sSup ({I' | IsAtom I'} \ {I})
⊢ ⁅b, ↑y⁆ ∈ I ⊓ sSup ({I | IsA... | ((:c Eq) (:fv _uniq.14422) ((:c Bracket.bracket) (:fv _uniq.14422) (:fv _uniq.14422) ((:c LieRingModule.toBracket) (:fv _uniq.14422) (:fv _uniq.14422) (:fv _uniq.14428) ((:c LieRing.toAddCommGroup) (:fv _uniq.14422) (:fv _uniq.14428)) ((:c lieRingSelfModule) (:fv _uniq.14422) (:fv _uniq.14428))) (:fv _uniq.18996) ((:c ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Bracket.bracket) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Bracket) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1))))) (:arg :explicit 3 (:fv FV15)) (:arg :explicit 4... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":6169,"sourceStart":6167,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6171,"sourceStart":6170,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":6174,"sourceStart":... | [] | [{"source":"LieSubmodule.mem_bot (R := R) (L := L)","source_end":6213,"source_start":6175,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(IsSemisimple.setIndependent_isAtom hI).eq_bot","source_end":6279,"source_start":6233,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 53 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d18aa0da58df458bac4f3c00e059cf742331be72275db2cffed8534f8c425345 | bb7a285412003c7c32291a11a73e2591967baf3b64d9409e3957b8edbfee90b5 | cd0ced285331ae05263ffecc3bc81afeb9d109007a7fc995270d2c5a0ff8a0f2 | 8b1b2ed9653cd135b5e88f1ba115f77c5da4eb7b5658e74b76acd876f69606cf |
cat-searcher/leandojo-benchmark-4-random | test | 3,002 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨<a>lie_mem_right</a> R L I b y y.2, <a>lie_mem_left</a> _ _ _ _ _ hb⟩ | case intro.intro.intro.intro.intro.intro.a
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
y : ↥↑I
hy : y ∈ ↑↑J
a : L
ha : a ∈ I
b : L
hb : b ∈ sSup ({I' | IsAtom I'} \ {I})
⊢ ⁅b, ↑y⁆ ∈ I ⊓ sSup ({I | IsA... | ((:c Membership.mem) (:fv _uniq.14422) ((:c LieSubmodule) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) ((:c LieRing.toAddCommGroup) (:fv _uniq.14422) (:fv _uniq.14428)) ((:c LieAlgebra.toModule) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) (:fv _un... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c LieSubmodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":6296,"sourceStart":6291,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":6300,"sourceStart":6297,"tag":"atom"},{"children":[{"children":[{"name":"lie_mem_right","semanticRole":"global","source":"lie_mem_right","sourceEnd":6313,"sourceStart":6300,"tag":"identifier"},{"child... | [] | [{"source":"⟨lie_mem_right R L I b y y.2, lie_mem_left _ _ _ _ _ hb⟩","source_end":6357,"source_start":6297,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 57 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cc6858ce1bd1f26a34f2bd5feedb1a34885890c6f5ba01e5409a09827be3cdbd | 8b1b2ed9653cd135b5e88f1ba115f77c5da4eb7b5658e74b76acd876f69606cf | 4ee4730972fcbb638f8c14d49d6e524f31c5a335c501bb9bdb061b65f6b72681 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,003 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [this, <a>ZeroMemClass.zero_mem</a>] | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
y : ↥↑I
hy : y ∈ ↑↑J
a : L
ha : a ∈ I
b : L
hb : b ∈ sSup ({I' | IsAtom I'} \ {I})
this : ⁅b, ↑y⁆ = 0
⊢ ⁅b, ↑y⁆ ∈ Submodule.map (↑I).subtype ↑J | ((:c Membership.mem) (:fv _uniq.14422) ((:c Submodule) (:fv _uniq.14419) (:fv _uniq.14422) ((:c CommSemiring.toSemiring) (:fv _uniq.14419) ((:c CommRing.toCommSemiring) (:fv _uniq.14419) (:fv _uniq.14425))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.14422) ((:c LieRing.toAddCommGroup) (:fv _uniq.14422) (:fv _uniq.14... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":6134,"sourceStart":6130,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":6139,"sourceStart":6135,"tag":"atom"}],"kind":"nu... | [] | [{"source":"this","source_end":6145,"source_start":6141,"syntax_kind":"ident"},{"source":"zero_mem","source_end":6155,"source_start":6147,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 50 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2582501a6bded02408eb9c811d1a2ecc225d138811ded3b80aa9f1cc735d86d5 | 4612b8a3f694a992a30bb9a4778e5b667cdba81ea35db241bed1724271991234 | 2920e7bf9d6a06d8d1f456546be3e587e8ef4515f3085eaa06ef4c6c91c57878 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,004 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>eq_bot_iff</a>] at this ⊢ | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
this : J' = ⊥
⊢ J = ⊥ | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
this : J' ≤ ⊥
⊢ J ≤ ⊥ | ((:c Eq) ((:c LieIdeal) (:fv _uniq.14419) ((:c Subtype) (:fv _uniq.14422) (:lambda x (:fv _uniq.14422) ((:c Membership.mem) (:fv _uniq.14422) ((:c Submodule) (:fv _uniq.14419) (:fv _uniq.14422) ((:c CommSemiring.toSemiring) (:fv _uniq.14419) ((:c CommRing.toCommSemiring) (:fv _uniq.14419) (:fv _uniq.14425))) ((:c AddCo... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LieIdeal) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":6586,"sourceStart":6584,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6588,"sourceStart":6587,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"eq_bot_iff","semanti... | [] | [{"source":"eq_bot_iff","source_end":6598,"source_start":6588,"syntax_kind":"ident"},{"source":"this","source_end":6607,"source_start":6603,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 65 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cc521c9d0fdd2793e88846efeedc6d15198cbe0b7caf0b4093773b1388b7d347 | 298c293f77c789db5c2d0c845b7ada0e9ae5d5306b3e364c1ed9e5b4de220487 | 2aba0ebdf9aab131f372ebca42a5b14d5fe78004b786014c0d02a010959cc8dd | a9c5f085c14eae24d60f772dc74b14c000f1e1106a16722d29acada28401e63d |
cat-searcher/leandojo-benchmark-4-random | test | 3,005 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro x hx | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
this : J' ≤ ⊥
⊢ J ≤ ⊥ | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
this : J' ≤ ⊥
x : ↥↑I
hx : x ∈ ... | ((:c LE.le) ((:c LieIdeal) (:fv _uniq.14419) ((:c Subtype) (:fv _uniq.14422) (:lambda x (:fv _uniq.14422) ((:c Membership.mem) (:fv _uniq.14422) ((:c Submodule) (:fv _uniq.14419) (:fv _uniq.14422) ((:c CommSemiring.toSemiring) (:fv _uniq.14419) ((:c CommRing.toCommSemiring) (:fv _uniq.14419) (:fv _uniq.14425))) ((:c Ad... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c LieIdeal) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"intro","sourceEnd":6623,"sourceStart":6618,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":6625,"sourceStart":6624,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hx","sourceEnd":6628,"sourceStart":6626,"tag":"identifier"}],"kind":"null","source":"... | [{"role":"fresh_name","source":"x","source_end":6625,"source_start":6624,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":6628,"source_start":6626,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 68 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d99d6261c56f453ebbd18b17f3d4c2ec198143a6beaebd378fd47fca1dfb5a41 | a9c5f085c14eae24d60f772dc74b14c000f1e1106a16722d29acada28401e63d | 65777af1f444837568ec00c3040db2bdc96178d91d8bf83037116b747be939ac | 9610dc6633dd21546bc5a02541f132bb9708c26c3fabc80e40d61cc88de4f61a |
cat-searcher/leandojo-benchmark-4-random | test | 3,006 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | suffices x ∈ J → x = 0 from this hx | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
this : J' ≤ ⊥
x : ↥↑I
hx : x ∈ ... | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
this : J' ≤ ⊥
x : ↥↑I
hx : x ∈ ... | ((:c Membership.mem) ((:c Subtype) (:fv _uniq.14422) (:lambda x (:fv _uniq.14422) ((:c Membership.mem) (:fv _uniq.14422) ((:c Submodule) (:fv _uniq.14419) (:fv _uniq.14422) ((:c CommSemiring.toSemiring) (:fv _uniq.14419) ((:c CommRing.toCommSemiring) (:fv _uniq.14419) (:fv _uniq.14425))) ((:c AddCommGroup.toAddCommMono... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"suffices","sourceEnd":6643,"sourceStart":6635,"tag":"atom"},{"children":[{"children":[{"source":"","sourceEnd":6644,"sourceStart":6644,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":6644,"sourceStart":6644,"tag":"node"},{"children":[{"children":[{"contextIndex":13,"semanticRol... | [] | [{"source":"x ∈ J → x = 0","source_end":6661,"source_start":6644,"syntax_kind":"Lean.Parser.Term.arrow"},{"source":"this hx","source_end":6674,"source_start":6667,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 69 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | efe251ae4d84aef665be69625d6a825c03b8644fa35d794ece089703e5f413ec | 9610dc6633dd21546bc5a02541f132bb9708c26c3fabc80e40d61cc88de4f61a | 48752b2b81dd040895c73e873bcb14f0305c5837229f043de9100fd555c0aec0 | d9f3c75abfa7e34c7b9bcfc18b70ff1dfbf49113a2148372e3d486823fca47e4 |
cat-searcher/leandojo-benchmark-4-random | test | 3,007 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [J'] using @this x.1 | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
this : J' ≤ ⊥
x : ↥↑I
hx : x ∈ ... | (:forall _ ((:c Membership.mem) ((:c Subtype) (:fv _uniq.14422) (:lambda x (:fv _uniq.14422) ((:c Membership.mem) (:fv _uniq.14422) ((:c Submodule) (:fv _uniq.14419) (:fv _uniq.14422) ((:c CommSemiring.toSemiring) (:fv _uniq.14419) ((:c CommRing.toCommSemiring) (:fv _uniq.14419) (:fv _uniq.14425))) ((:c AddCommGroup.to... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"simpa","sourceEnd":6686,"sourceStart":6681,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"chil... | [] | [{"source":"J'","source_end":6690,"source_start":6688,"syntax_kind":"ident"},{"source":"@this x.1\n -- We need to show that `J = ⊥`.\n -- Since `J` is an ideal of `L`, and `I` is an atom,\n -- it suffices to show that `J < I`.","source_end":6707,"source_start":6698,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 70 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 281e0dc243637f685378c6225447b84bb816f9e34e41eb7947d7f5f597b1f23d | d9f3c75abfa7e34c7b9bcfc18b70ff1dfbf49113a2148372e3d486823fca47e4 | e58fdcf1a36f7d0039794457e5ffc8a7b44ba5dfc3f0b213faa8464c720fce02 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,008 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro _ ⟨x, -, rfl⟩ | case a.left
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
⊢ J' ≤ I | case a.left.intro.intro
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
x : ↥↑I... | ((:c LE.le) ((:c LieIdeal) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) (:fv _uniq.14445)) ((:c Preorder.toLE) ((:c LieIdeal) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) (:fv _uniq.14445)) ((:c PartialOrder.toPreorder) ((:c LieIdeal) (:fv _uniq.14419) (:fv _uniq.14... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c LieIdeal) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rintro","sourceEnd":6975,"sourceStart":6969,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"_","sourceEnd":6977,"sourceStart":6976,"tag":"atom"}],"kind":"Lean.Parser.Tactic.rcasesPat.ignore","source":"_","sourceEnd":6977,"sourceStart":6976,"tag":"node"}],"kind":"Lean.Parser.Tacti... | [{"role":"fresh_name","source":"x","source_end":6982,"source_start":6981,"syntax_kind":"ident"}] | [{"source":"⟨x, -, rfl⟩","source_end":6993,"source_start":6978,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 80 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 44068918da270ea15f03e963ff46503214196cc542232cc2142a723fc4336b38 | 34e357323985dbabff19d29395aad90bfb0aa76566f1a01d1fbfbcfb3411cf00 | 371849a834b8e8e06786cbdc311b11507cb8b0d7ed37b69419716ab71fd9af5a | a2a7a2cf8b0a05384cfea6f78df58f925c268ada8484c7ccf7b3a986c1b4ee47 |
cat-searcher/leandojo-benchmark-4-random | test | 3,009 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact x.2 | case a.left.intro.intro
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
x : ↥↑I... | ((:c Membership.mem) (:fv _uniq.14422) ((:c LieSubmodule) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) ((:c LieRing.toAddCommGroup) (:fv _uniq.14422) (:fv _uniq.14428)) ((:c LieAlgebra.toModule) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) (:fv _un... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c LieSubmodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":7005,"sourceStart":7000,"tag":"atom"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"x","sourceEnd":7007,"sourceStart":7006,"tag":"identifier"},{"source":".","sourceEnd":7008,"sourceStart":7007,"tag":"atom"},{"children":[{"source":"2","sourceEnd":7009,"source... | [] | [{"source":"x.2\n -- So we need to show `J ≠ I` as ideals of `L`.\n -- This follows from our assumption that `J ≠ ⊤` as ideals of `I`.","source_end":7009,"source_start":7006,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 81 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fa26bfbb709548a5ab4f8bf76ea887741a9801cc882f69614546f58d40aef451 | a2a7a2cf8b0a05384cfea6f78df58f925c268ada8484c7ccf7b3a986c1b4ee47 | 65590340d0f0be6a163e102366f395b290c2f9c3a2838c92a082604784971efe | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,010 | Projectivization.Subspace.span_eq_sInf | Mathlib/LinearAlgebra/Projectivization/Subspace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext x | K : Type u_1
V : Type u_2
inst✝² : Field K
inst✝¹ : AddCommGroup V
inst✝ : Module K V
S : Set (ℙ K V)
⊢ span S = sInf {W | S ⊆ ↑W} | case carrier.h
K : Type u_1
V : Type u_2
inst✝² : Field K
inst✝¹ : AddCommGroup V
inst✝ : Module K V
S : Set (ℙ K V)
x : ℙ K V
⊢ x ∈ (span S).carrier ↔ x ∈ (sInf {W | S ⊆ ↑W}).carrier | ((:c Eq) ((:c Projectivization.Subspace) (:fv _uniq.44569) (:fv _uniq.44572) (:fv _uniq.44575) (:fv _uniq.44578) (:fv _uniq.45154)) ((:c Projectivization.Subspace.span) (:fv _uniq.44569) (:fv _uniq.44572) (:fv _uniq.44575) (:fv _uniq.44578) (:fv _uniq.45154) (:fv _uniq.45385)) ((:c InfSet.sInf) ((:c Projectivization.Su... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.44569))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.44572))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.44569) (:fv _uniq.44572) ((:c DivisionSemiring.toSemiring) (:fv _uni... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Projectivization.Subspace) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44569","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44572","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"ext","sourceEnd":9491,"sourceStart":9488,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":9493,"sourceStart":9492,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":9493,"sourceStart":9492,"tag":"nod... | [{"role":"fresh_name","source":"x","source_end":9493,"source_start":9492,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44569","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44572","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 51 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0718abe4de88188a6bb596da5de64e114dc43e536d0ed13961b00d0158998a61 | c58d7d76318da753658b60f90ffc2268883d0d52d88087b877f92ab7a9f9f882 | ee522618587c4a8062e9541e92fad69d5c6e7dbdf5366e9d82c63ebe3c1e08c5 | 824c8425a7b1b9f3da7f43575f3d3628d7dfcea00521b5b78cd469bccb729df2 |
cat-searcher/leandojo-benchmark-4-random | test | 3,011 | Projectivization.Subspace.span_eq_sInf | Mathlib/LinearAlgebra/Projectivization/Subspace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>Projectivization.Subspace.mem_carrier_iff</a>, <a>Projectivization.Subspace.mem_span</a> x] | case carrier.h
K : Type u_1
V : Type u_2
inst✝² : Field K
inst✝¹ : AddCommGroup V
inst✝ : Module K V
S : Set (ℙ K V)
x : ℙ K V
⊢ x ∈ (span S).carrier ↔ x ∈ (sInf {W | S ⊆ ↑W}).carrier | case carrier.h
K : Type u_1
V : Type u_2
inst✝² : Field K
inst✝¹ : AddCommGroup V
inst✝ : Module K V
S : Set (ℙ K V)
x : ℙ K V
⊢ (∀ (W : Subspace K V), S ⊆ ↑W → x ∈ W) ↔ x ∈ sInf {W | S ⊆ ↑W} | ((:c Iff) ((:c Membership.mem) ((:c Projectivization) (:fv _uniq.44569) (:fv _uniq.44572) ((:c Field.toDivisionRing) (:fv _uniq.44569) (:fv _uniq.44575)) (:fv _uniq.44578) (:fv _uniq.45154)) ((:c Set) ((:c Projectivization) (:fv _uniq.44569) (:fv _uniq.44572) ((:c Field.toDivisionRing) (:fv _uniq.44569) (:fv _uniq.4457... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.44569))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.44572))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.44569) (:fv _uniq.44572) ((:c DivisionSemiring.toSemiring) (:fv _uni... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Projectivization) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c DivisionRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44569","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44572","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"simp_rw","sourceEnd":9503,"sourceStart":9496,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9505,"sourceStart":9504,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Projectivizatio... | [] | [{"source":"mem_carrier_iff","source_end":9520,"source_start":9505,"syntax_kind":"ident"},{"source":"mem_span x","source_end":9532,"source_start":9522,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44569","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44572","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 51 | 5 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0fed244bc243e60b230d20ab40336406e675cb5310f2cf3487d294b62fd1e9b8 | 824c8425a7b1b9f3da7f43575f3d3628d7dfcea00521b5b78cd469bccb729df2 | 5e7b6a8fe7654a0c872a06e8d6333376431786766ac43d509cfc8c333a402ba0 | 95c9d9d3359de9038b675e23fb7174fc7759967527ea418f9954e0f9d53ea80b |
cat-searcher/leandojo-benchmark-4-random | test | 3,012 | Projectivization.Subspace.span_eq_sInf | Mathlib/LinearAlgebra/Projectivization/Subspace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨fun hx => ?_, fun hx W hW => ?_⟩ | case carrier.h
K : Type u_1
V : Type u_2
inst✝² : Field K
inst✝¹ : AddCommGroup V
inst✝ : Module K V
S : Set (ℙ K V)
x : ℙ K V
⊢ (∀ (W : Subspace K V), S ⊆ ↑W → x ∈ W) ↔ x ∈ sInf {W | S ⊆ ↑W} | case carrier.h.refine_1
K : Type u_1
V : Type u_2
inst✝² : Field K
inst✝¹ : AddCommGroup V
inst✝ : Module K V
S : Set (ℙ K V)
x : ℙ K V
hx : ∀ (W : Subspace K V), S ⊆ ↑W → x ∈ W
⊢ x ∈ sInf {W | S ⊆ ↑W}
case carrier.h.refine_2
K : Type u_1
V : Type u_2
inst✝² : Field K
inst✝¹ : AddCommGroup V
inst✝ : Module K V
S : Set ... | ((:c Iff) (:forall W ((:c Projectivization.Subspace) (:fv _uniq.44569) (:fv _uniq.44572) (:fv _uniq.44575) (:fv _uniq.44578) (:fv _uniq.45154)) (:forall _ ((:c HasSubset.Subset) ((:c Set) ((:c Projectivization) (:fv _uniq.44569) (:fv _uniq.44572) ((:c Field.toDivisionRing) (:fv _uniq.44569) (:fv _uniq.44575)) (:fv _uni... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.44569))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.44572))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.44569) (:fv _uniq.44572) ((:c DivisionSemiring.toSemiring) (:fv _uni... | (:app (:c Iff) (:arg :explicit 0 (:forall W :explicit (:app (:c Projectivization.Subspace) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44569","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44572","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"refine","sourceEnd":9542,"sourceStart":9536,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":9546,"sourceStart":9543,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":9549,"sourceStart":9546,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"hx... | [] | [{"source":"⟨fun hx => ?_, fun hx W hW => ?_⟩","source_end":9580,"source_start":9543,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44569","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44572","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 51 | 9 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 826b99d4380afb3bcdc9db5b133c7e72cdfa87133661865888166c515cab54ed | 95c9d9d3359de9038b675e23fb7174fc7759967527ea418f9954e0f9d53ea80b | c9f8439e8d20b87f8ed057bb21925ebd21328efccfd779acdd613ac07180f32b | 3e34f48fcb3b58225fb16702175314dcdbc78e659bf1e8fc7bce839c49e04891 |
cat-searcher/leandojo-benchmark-4-random | test | 3,013 | Projectivization.Subspace.span_eq_sInf | Mathlib/LinearAlgebra/Projectivization/Subspace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro W ⟨T, hT, rfl⟩ | case carrier.h.refine_1
K : Type u_1
V : Type u_2
inst✝² : Field K
inst✝¹ : AddCommGroup V
inst✝ : Module K V
S : Set (ℙ K V)
x : ℙ K V
hx : ∀ (W : Subspace K V), S ⊆ ↑W → x ∈ W
⊢ x ∈ sInf {W | S ⊆ ↑W} | case carrier.h.refine_1.intro.intro
K : Type u_1
V : Type u_2
inst✝² : Field K
inst✝¹ : AddCommGroup V
inst✝ : Module K V
S : Set (ℙ K V)
x : ℙ K V
hx : ∀ (W : Subspace K V), S ⊆ ↑W → x ∈ W
T : Subspace K V
hT : T ∈ {W | S ⊆ ↑W}
⊢ x ∈ ↑T | ((:c Membership.mem) ((:c Projectivization) (:fv _uniq.44569) (:fv _uniq.44572) ((:c Field.toDivisionRing) (:fv _uniq.44569) (:fv _uniq.44575)) (:fv _uniq.44578) (:fv _uniq.45154)) ((:c Projectivization.Subspace) (:fv _uniq.44569) (:fv _uniq.44572) (:fv _uniq.44575) (:fv _uniq.44578) (:fv _uniq.45154)) ((:c SetLike.ins... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.44569))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.44572))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.44569) (:fv _uniq.44572) ((:c DivisionSemiring.toSemiring) (:fv _uni... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Projectivization) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c DivisionRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :in... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44569","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44572","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rintro","sourceEnd":9592,"sourceStart":9586,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"W","sourceEnd":9594,"sourceStart":9593,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"W","sourceEnd":9594,"sourceStart":9593,"tag":"... | [{"role":"fresh_name","source":"T","source_end":9599,"source_start":9598,"syntax_kind":"ident"},{"role":"fresh_name","source":"hT","source_end":9603,"source_start":9601,"syntax_kind":"ident"}] | [{"source":"⟨T, hT, rfl⟩","source_end":9611,"source_start":9595,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44569","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44572","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 51 | 14 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5442ca8747f75b94c459f8b01095d895b9eb9a93c842f7081a135a8accefc7e8 | 44e5986acbb7f957db2a59564f2f5ca4a5a98112bfd782dfc98ed1b48d18cd45 | 602ca91db7aac84e1c16903c7ed0c634e37441270dda5f02d8877f2b02a32914 | 2fb4cfdd1aa6f4991afdda9be53e333bde521fc939e3e3da439b37b2cc28fb4d |
cat-searcher/leandojo-benchmark-4-random | test | 3,014 | Projectivization.Subspace.span_eq_sInf | Mathlib/LinearAlgebra/Projectivization/Subspace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hx T hT | case carrier.h.refine_1.intro.intro
K : Type u_1
V : Type u_2
inst✝² : Field K
inst✝¹ : AddCommGroup V
inst✝ : Module K V
S : Set (ℙ K V)
x : ℙ K V
hx : ∀ (W : Subspace K V), S ⊆ ↑W → x ∈ W
T : Subspace K V
hT : T ∈ {W | S ⊆ ↑W}
⊢ x ∈ ↑T | ((:c Membership.mem) ((:c Projectivization) (:fv _uniq.44569) (:fv _uniq.44572) ((:c Field.toDivisionRing) (:fv _uniq.44569) (:fv _uniq.44575)) (:fv _uniq.44578) (:fv _uniq.45154)) ((:c Set) ((:c Projectivization) (:fv _uniq.44569) (:fv _uniq.44572) ((:c Field.toDivisionRing) (:fv _uniq.44569) (:fv _uniq.44575)) (:fv _... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.44569))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.44572))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.44569) (:fv _uniq.44572) ((:c DivisionSemiring.toSemiring) (:fv _uni... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Projectivization) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c DivisionRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :in... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44569","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44572","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":9621,"sourceStart":9616,"tag":"atom"},{"children":[{"contextIndex":8,"semanticRole":"local","source":"hx","sourceEnd":9624,"sourceStart":9622,"tag":"identifier"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"T","sourceEnd":9626,"sourceStart":9625,"tag":"ident... | [] | [{"source":"hx T hT","source_end":9629,"source_start":9622,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44569","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44572","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 51 | 15 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7faa3f099f5e78bdcd8e5bbd8984de0613e60c24876d9359547f2ee7751318f1 | 2fb4cfdd1aa6f4991afdda9be53e333bde521fc939e3e3da439b37b2cc28fb4d | afb89b92d43122e4a45bb66d49109047cb5147379ade0b902438512214fc5d17 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,015 | Projectivization.Subspace.span_eq_sInf | Mathlib/LinearAlgebra/Projectivization/Subspace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (@<a>sInf_le</a> _ _ { W : <a>Projectivization.Subspace</a> K V | S ⊆ ↑W } W hW) hx | case carrier.h.refine_2
K : Type u_1
V : Type u_2
inst✝² : Field K
inst✝¹ : AddCommGroup V
inst✝ : Module K V
S : Set (ℙ K V)
x : ℙ K V
hx : x ∈ sInf {W | S ⊆ ↑W}
W : Subspace K V
hW : S ⊆ ↑W
⊢ x ∈ W | ((:c Membership.mem) ((:c Projectivization) (:fv _uniq.44569) (:fv _uniq.44572) ((:c Field.toDivisionRing) (:fv _uniq.44569) (:fv _uniq.44575)) (:fv _uniq.44578) (:fv _uniq.45154)) ((:c Projectivization.Subspace) (:fv _uniq.44569) (:fv _uniq.44572) (:fv _uniq.44575) (:fv _uniq.44578) (:fv _uniq.45154)) ((:c SetLike.ins... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.44569))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.44572))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.44569) (:fv _uniq.44572) ((:c DivisionSemiring.toSemiring) (:fv _uni... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Projectivization) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c DivisionRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :in... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44569","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44572","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":9640,"sourceStart":9635,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":9642,"sourceStart":9641,"tag":"atom"},{"children":[{"children":[{"source":"@","sourceEnd":9643,"sourceStart":9642,"tag":"atom"},{"name":"sInf_le","s... | [] | [{"source":"(@sInf_le _ _ { W : Subspace K V | S ⊆ ↑W } W hW) hx","source_end":9697,"source_start":9641,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44569","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.44572","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 51 | 18 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c42fa6511a9daa20205d3ac7b8be9741a304deb722f590133f4666b2b5624427 | 84ca32e68b6d2d7957111db9a232f0d9b1108ed2c9e20e9afe62126e7516ac7f | e1f60b85b5122f96159e4e0056f5945476c7f1b6cbca4e95c3caad335810ac7e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,016 | isConformalMap_complex_linear | Mathlib/Analysis/Complex/Conformal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have minor₁ : ‖map 1‖ ≠ 0 := by simpa only [<a>ContinuousLinearMap.ext_ring_iff</a>, <a>Ne</a>, <a>norm_eq_zero</a>] using nonzero | E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
⊢ IsConformalMap (restrictScalars ℝ map) | E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
⊢ IsConformalMap (restrictScalars ℝ map) | ((:c IsConformalMap) (:c Real) (:c Complex) (:fv _uniq.2325) (:c Real.normedField) ((:c NonUnitalSeminormedRing.toSeminormedAddCommGroup) (:c Complex) ((:c NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing) (:c Complex) ((:c SeminormedCommRing.toNonUnitalSeminormedCommRing) (:c Complex) ((:c NormedCommRing.toSemino... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.2325))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.2325) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328)))"},{"name":"inst✝","sexp":"((:c ... | (:app (:c IsConformalMap) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Complex)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c NormedField) (:arg :explicit 0 (:c Real))))) (:arg :instance 4 (:instance-of (:app (:c SeminormedAddCommGroup) (:arg :explicit 0 (:c Complex))))) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedAddCommGroup) (:arg... | {"children":[{"source":"have","sourceEnd":1988,"sourceStart":1984,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"minor₁","sourceEnd":1997,"sourceStart":1989,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"minor₁","sourceEnd":1997,"sourceStart":1989,"tag":"n... | [] | [{"source":"‖map 1‖ ≠ 0","source_end":2017,"source_start":2000,"syntax_kind":"«term_≠_»"},{"source":"ext_ring_iff","source_end":2048,"source_start":2036,"syntax_kind":"ident"},{"source":"Ne","source_end":2052,"source_start":2050,"syntax_kind":"ident"},{"source":"norm_eq_zero","source_end":2066,"source_start":2054,"synt... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":2,... | 8 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c9c5cb1230c88db22b9a0cb6c158005c9ba0215020f761d2c81b8ac41d0add37 | cc7f1c7628ca6ea6af1ddd453de3a63c3c6d08b5f7807fd4b531e0b6f494d440 | 564703160ab1f34eba7db4b0a2e429f6dc0e55ab1782b2fa9ec05ac428ae75e9 | 361c1e76a25bc0a38f2e23c93f34f9c445a77f8e0632146d1ba59c9f2af19366 |
cat-searcher/leandojo-benchmark-4-random | test | 3,017 | isConformalMap_complex_linear | Mathlib/Analysis/Complex/Conformal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨‖map 1‖, minor₁, ⟨‖map 1‖⁻¹ • ((map : ℂ →ₗ[ℂ] E) : ℂ →ₗ[ℝ] E), ?_⟩, ?_⟩ | E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
⊢ IsConformalMap (restrictScalars ℝ map) | case refine_1
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
⊢ ∀ (x : ℂ), ‖(‖map 1‖⁻¹ • ↑ℝ ↑map) x‖ = ‖x‖
case refine_2
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
in... | ((:c IsConformalMap) (:c Real) (:c Complex) (:fv _uniq.2325) (:c Real.normedField) ((:c NonUnitalSeminormedRing.toSeminormedAddCommGroup) (:c Complex) ((:c NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing) (:c Complex) ((:c SeminormedCommRing.toNonUnitalSeminormedCommRing) (:c Complex) ((:c NormedCommRing.toSemino... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.2325))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.2325) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328)))"},{"name":"inst✝","sexp":"((:c ... | (:app (:c IsConformalMap) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Complex)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c NormedField) (:arg :explicit 0 (:c Real))))) (:arg :instance 4 (:instance-of (:app (:c SeminormedAddCommGroup) (:arg :explicit 0 (:c Complex))))) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedAddCommGroup) (:arg... | {"children":[{"source":"refine","sourceEnd":2090,"sourceStart":2084,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":2094,"sourceStart":2091,"tag":"atom"},{"children":[{"children":[{"source":"‖","sourceEnd":2097,"sourceStart":2094,"tag":"atom"},{"children":[{"contextIndex":8,"semanticRole":"local","source":"map","s... | [] | [{"source":"⟨‖map 1‖, minor₁, ⟨‖map 1‖⁻¹ • ((map : ℂ →ₗ[ℂ] E) : ℂ →ₗ[ℝ] E), ?_⟩, ?_⟩","source_end":2202,"source_start":2091,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":2,... | 8 | 7 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3a4bf399dd3b201a9d6f5f710f618ce41fff1c9416b20095b5ae5f0ca6ac3fb2 | 361c1e76a25bc0a38f2e23c93f34f9c445a77f8e0632146d1ba59c9f2af19366 | c1e2c1c54989854a938ff96f934a898c82f61d849798dc50304d5bd4e0fbaa5a | d2e9b1b38f4e956737dc166eb5a57f3c6e0309768a77212fc653dc335288fa90 |
cat-searcher/leandojo-benchmark-4-random | test | 3,018 | isConformalMap_complex_linear | Mathlib/Analysis/Complex/Conformal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>ContinuousLinearMap.ext_ring_iff</a>, <a>Ne</a>, <a>norm_eq_zero</a>] using nonzero | E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
⊢ ‖map 1‖ ≠ 0 | ((:c Ne) (:c Real) ((:c Norm.norm) (:fv _uniq.2325) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.2325) (:fv _uniq.2328)) ((:c DFunLike.coe) ((:c ContinuousLinearMap) (:c Complex) (:c Complex) (:c Complex.instSemiring) (:c Complex.instSemiring) ((:c RingHom.id) (:c Complex) ((:c Semiring.toNonAssocSemiring) (:c Complex) (... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.2325))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.2325) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328)))"},{"name":"inst✝","sexp":"((:c ... | (:app (:c Ne) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedAddCommGroup) (:arg... | {"children":[{"source":"simpa","sourceEnd":2029,"sourceStart":2024,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"chil... | [] | [{"source":"ext_ring_iff","source_end":2048,"source_start":2036,"syntax_kind":"ident"},{"source":"Ne","source_end":2052,"source_start":2050,"syntax_kind":"ident"},{"source":"norm_eq_zero","source_end":2066,"source_start":2054,"syntax_kind":"ident"},{"source":"nonzero","source_end":2081,"source_start":2074,"syntax_kind"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":2,... | 8 | 6 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2f14289f7ffbfadb0f63ffa168cdd2650c1060ecbdf2ff544ae763b445949090 | 184932c73bcf2f25eac23a54dced3f6fb97a8ae9dcb0a5cf70cd0141b82bafba | 300741a25c2c80269bd8b4926be448634ecfd1f6752fa61d64ae8e138f336a67 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,019 | isConformalMap_complex_linear | Mathlib/Analysis/Complex/Conformal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro x | case refine_1
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
⊢ ∀ (x : ℂ), ‖(‖map 1‖⁻¹ • ↑ℝ ↑map) x‖ = ‖x‖ | case refine_1
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
x : ℂ
⊢ ‖(‖map 1‖⁻¹ • ↑ℝ ↑map) x‖ = ‖x‖ | (:forall x (:c Complex) ((:c Eq) (:c Real) ((:c Norm.norm) (:fv _uniq.2325) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.2325) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328))) ((:c DFunLike.coe) ((:c LinearMap) (:c Real) (:c Real) ((:c DivisionSemiring.toSemiring) (:c Real) ((:c S... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.2325))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.2325) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328)))"},{"name":"inst✝","sexp":"((:c ... | (:forall x :explicit (:c Complex) (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedAddCommGroup) (:arg... | {"children":[{"source":"intro","sourceEnd":2213,"sourceStart":2208,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":2215,"sourceStart":2214,"tag":"identifier"}],"kind":"null","source":"x","sourceEnd":2215,"sourceStart":2214,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source":"int... | [{"role":"fresh_name","source":"x","source_end":2215,"source_start":2214,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":2,... | 8 | 12 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e65027bbb8471c88a3bbaa7dcd7a7699d9022f12c8842ae3937c12d7a4b9d0a1 | b09aaffc24f0e9755cead28241ed53bf6356ed99180415360eb88f4db3d79dda | 727852cc0e84019aeee0e605b3833ee9bcd4d2abc203673e529dba747f5c5a0d | 1bf4a426f04560e848ee2cde2dfbdc8681aa14b3a23d5a82d89a9aceb5b3c047 |
cat-searcher/leandojo-benchmark-4-random | test | 3,020 | isConformalMap_complex_linear | Mathlib/Analysis/Complex/Conformal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>LinearMap.smul_apply</a>] | case refine_1
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
x : ℂ
⊢ ‖(‖map 1‖⁻¹ • ↑ℝ ↑map) x‖ = ‖x‖ | case refine_1
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
x : ℂ
⊢ ‖‖map 1‖⁻¹ • (↑ℝ ↑map) x‖ = ‖x‖ | ((:c Eq) (:c Real) ((:c Norm.norm) (:fv _uniq.2325) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.2325) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328))) ((:c DFunLike.coe) ((:c LinearMap) (:c Real) (:c Real) ((:c DivisionSemiring.toSemiring) (:c Real) ((:c Semifield.toDivisionSemir... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.2325))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.2325) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328)))"},{"name":"inst✝","sexp":"((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:c Real))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedAddCommGroup) (:arg... | {"children":[{"source":"simp","sourceEnd":2224,"sourceStart":2220,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":2229,"sourceStart":2225,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":2229,"s... | [] | [{"source":"LinearMap.smul_apply","source_end":2251,"source_start":2231,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":2,... | 8 | 13 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 88858d34597c6798c99a48dd813792ea62ee45f06f1669335cb7f5c7620fd665 | 1bf4a426f04560e848ee2cde2dfbdc8681aa14b3a23d5a82d89a9aceb5b3c047 | 7049175d482d1d82c1234fae5e441fcdf64bbc5985b8b5f65664ab2300fdce17 | 786773855fd71b81b8d6175b3f4dd461a1cef64c6c52b9b2f1a85294488abc47 |
cat-searcher/leandojo-benchmark-4-random | test | 3,021 | isConformalMap_complex_linear | Mathlib/Analysis/Complex/Conformal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : x = x • (1 : ℂ) := by rw [<a>smul_eq_mul</a>, <a>mul_one</a>] | case refine_1
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
x : ℂ
⊢ ‖‖map 1‖⁻¹ • (↑ℝ ↑map) x‖ = ‖x‖ | case refine_1
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
x : ℂ
this : x = x • 1
⊢ ‖‖map 1‖⁻¹ • (↑ℝ ↑map) x‖ = ‖x‖ | ((:c Eq) (:c Real) ((:c Norm.norm) (:fv _uniq.2325) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.2325) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328))) ((:c HSMul.hSMul) (:c Real) (:fv _uniq.2325) (:fv _uniq.2325) ((:c instHSMul) (:c Real) (:fv _uniq.2325) ((:c SMulZeroClass.toSMu... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.2325))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.2325) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328)))"},{"name":"inst✝","sexp":"((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :imp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedAddCommGroup) (:arg... | {"children":[{"source":"have","sourceEnd":2261,"sourceStart":2257,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":2262,"sourceStart":2262,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":2262,"sourceStart":2262,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"x = x • (1 : ℂ)","source_end":2283,"source_start":2264,"syntax_kind":"«term_=_»"},{"source":"smul_eq_mul","source_end":2305,"source_start":2294,"syntax_kind":"ident"},{"source":"mul_one","source_end":2314,"source_start":2307,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":2,... | 8 | 14 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | da2e11fe1dcb710a051012fc6f2c5c7d8d8f582df5eb6634f4e53ccf4ca444d5 | 786773855fd71b81b8d6175b3f4dd461a1cef64c6c52b9b2f1a85294488abc47 | e7e70dd56741a3666f2cbbf13f5d8578bc47de7559c6bd8fede7efd8f00bd5bd | fe651281b74eda6279639b8b1c95bf63350c108f78f9cdd0a757915c811d74fc |
cat-searcher/leandojo-benchmark-4-random | test | 3,022 | isConformalMap_complex_linear | Mathlib/Analysis/Complex/Conformal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | nth_rw 1 [this] | case refine_1
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
x : ℂ
this : x = x • 1
⊢ ‖‖map 1‖⁻¹ • (↑ℝ ↑map) x‖ = ‖x‖ | case refine_1
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
x : ℂ
this : x = x • 1
⊢ ‖‖map 1‖⁻¹ • (↑ℝ ↑map) (x • 1)‖ = ‖x‖ | ((:c Eq) (:c Real) ((:c Norm.norm) (:fv _uniq.2325) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.2325) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328))) ((:c HSMul.hSMul) (:c Real) (:fv _uniq.2325) (:fv _uniq.2325) ((:c instHSMul) (:c Real) (:fv _uniq.2325) ((:c SMulZeroClass.toSMu... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.2325))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.2325) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328)))"},{"name":"inst✝","sexp":"((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :imp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedAddCommGroup) (:arg... | {"children":[{"source":"nth_rw","sourceEnd":2326,"sourceStart":2320,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"source":"1","sourceEnd":2328,"sourceStart":2327,"tag":"atom"}],"kind":"num","source":"1","sourceEnd":2328,"sourc... | [] | [{"source":"this","source_end":2334,"source_start":2330,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":2,... | 8 | 20 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | baf88d191f361b229831c3746658e6230247d190a89ef4770a1ac78383adafbd | fe651281b74eda6279639b8b1c95bf63350c108f78f9cdd0a757915c811d74fc | 7a43666adf66c81229ef9a270bdf3cf3627e44dfae17a1f01afa870caed20881 | a8d4792dd4f8d8faba937b6ec4f086d18f22ea4f92130a5b405fafe69586fc69 |
cat-searcher/leandojo-benchmark-4-random | test | 3,023 | isConformalMap_complex_linear | Mathlib/Analysis/Complex/Conformal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>LinearMap.coe_restrictScalars</a>] | case refine_1
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
x : ℂ
this : x = x • 1
⊢ ‖‖map 1‖⁻¹ • (↑ℝ ↑map) (x • 1)‖ = ‖x‖ | case refine_1
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
x : ℂ
this : x = x • 1
⊢ ‖‖map 1‖⁻¹ • ↑map (x • 1)‖ = ‖x‖ | ((:c Eq) (:c Real) ((:c Norm.norm) (:fv _uniq.2325) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.2325) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328))) ((:c HSMul.hSMul) (:c Real) (:fv _uniq.2325) (:fv _uniq.2325) ((:c instHSMul) (:c Real) (:fv _uniq.2325) ((:c SMulZeroClass.toSMu... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.2325))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.2325) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328)))"},{"name":"inst✝","sexp":"((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :imp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedAddCommGroup) (:arg... | {"children":[{"source":"rw","sourceEnd":2342,"sourceStart":2340,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2344,"sourceStart":2343,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"LinearMap.coe_restri... | [] | [{"source":"LinearMap.coe_restrictScalars","source_end":2373,"source_start":2344,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":2,... | 8 | 23 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d3ae856bff7c83d1f6c6a9e98638204675c2e85989290bfde9368eb3a6b011b6 | a8d4792dd4f8d8faba937b6ec4f086d18f22ea4f92130a5b405fafe69586fc69 | c9678af439f071e83e7dbdcee8153c3b0563816e93a8b3c14173c8dfde8e815b | ba4f2a5b9838eeef62a3856bb7fa8f1176af5c34cc77dcfecb6edd4ba41c2d4f |
cat-searcher/leandojo-benchmark-4-random | test | 3,024 | isConformalMap_complex_linear | Mathlib/Analysis/Complex/Conformal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [map.coe_coe, map.map_smul, <a>norm_smul</a>, <a>norm_inv</a>, <a>norm_norm</a>] | case refine_1
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
x : ℂ
this : x = x • 1
⊢ ‖‖map 1‖⁻¹ • ↑map (x • 1)‖ = ‖x‖ | case refine_1
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
x : ℂ
this : x = x • 1
⊢ ‖map 1‖⁻¹ * (‖x‖ * ‖map 1‖) = ‖x‖ | ((:c Eq) (:c Real) ((:c Norm.norm) (:fv _uniq.2325) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.2325) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328))) ((:c HSMul.hSMul) (:c Real) (:fv _uniq.2325) (:fv _uniq.2325) ((:c instHSMul) (:c Real) (:fv _uniq.2325) ((:c SMulZeroClass.toSMu... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.2325))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.2325) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328)))"},{"name":"inst✝","sexp":"((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :imp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedAddCommGroup) (:arg... | {"children":[{"source":"simp","sourceEnd":2383,"sourceStart":2379,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":2388,"sourceStart":2384,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":2388,"s... | [] | [{"source":"map.coe_coe","source_end":2401,"source_start":2390,"syntax_kind":"ident"},{"source":"map.map_smul","source_end":2415,"source_start":2403,"syntax_kind":"ident"},{"source":"norm_smul","source_end":2426,"source_start":2417,"syntax_kind":"ident"},{"source":"norm_inv","source_end":2436,"source_start":2428,"synta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":2,... | 8 | 26 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 80c90e7a983f56ef3410aefc34ccf5e1d576030443c22ece40ef5430bd380080 | ba4f2a5b9838eeef62a3856bb7fa8f1176af5c34cc77dcfecb6edd4ba41c2d4f | 5168efc3330e56aea2799d236c470a8699269583bc3e750586218e55a4ab796d | 3abb4f8c05149b0c2785bb43c2380f1beadd073505269c97bb06dee79688a9d1 |
cat-searcher/leandojo-benchmark-4-random | test | 3,025 | isConformalMap_complex_linear | Mathlib/Analysis/Complex/Conformal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | field_simp only [<a>one_mul</a>] | case refine_1
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
x : ℂ
this : x = x • 1
⊢ ‖map 1‖⁻¹ * (‖x‖ * ‖map 1‖) = ‖x‖ | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c Inv.inv) (:c Real) (:c Real.instInv) ((:c Norm.norm) (:fv _uniq.2325) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.2325) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328)... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.2325))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.2325) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328)))"},{"name":"inst✝","sexp":"((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedAddCommGroup) (:arg... | {"children":[{"source":"field_simp","sourceEnd":2463,"sourceStart":2453,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":2468,"sourceStart":2464,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":2... | [] | [{"source":"one_mul","source_end":2477,"source_start":2470,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":2,... | 8 | 27 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dd88a4b548f6a97e575d836a66d0e8104b7de2004a67265ca0c32ce91413975b | 3abb4f8c05149b0c2785bb43c2380f1beadd073505269c97bb06dee79688a9d1 | 2ac2f0e7d58e70218fea3970ad287275f3e1d7c79900d56b03e27f178c6faa70 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,026 | isConformalMap_complex_linear | Mathlib/Analysis/Complex/Conformal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>smul_eq_mul</a>, <a>mul_one</a>] | E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
x : ℂ
⊢ x = x • 1 | ((:c Eq) (:c Complex) (:fv _uniq.15290) ((:c HSMul.hSMul) (:c Complex) (:c Complex) (:c Complex) ((:c instHSMul) (:c Complex) (:c Complex) ((:c Algebra.toSMul) (:c Complex) (:c Complex) (:c Complex.instCommSemiring) (:c Complex.instSemiring) ((:c Algebra.id) (:c Complex) (:c Complex.instCommSemiring)))) (:fv _uniq.1529... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.2325))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.2325) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328)))"},{"name":"inst✝","sexp":"((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:c Complex)) (:arg :implicit-type 1 (:c Complex)) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:instance-of (:app (:c HSMul) (:arg :explicit 0 (:c Complex)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedAddCommGroup) (:arg... | {"children":[{"source":"rw","sourceEnd":2292,"sourceStart":2290,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2294,"sourceStart":2293,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"smul_eq_mul","semant... | [] | [{"source":"smul_eq_mul","source_end":2305,"source_start":2294,"syntax_kind":"ident"},{"source":"mul_one","source_end":2314,"source_start":2307,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":2,... | 8 | 16 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dd56fd146903e3417f60a477b225ba289df977ce877c5d3628da7b373b4e6fb1 | 609ab5bd60da1b5cc5e8ec77f36c9c8dc6639919836f4c7a011e1b89723ce5d4 | a4080b04187058cdfe346872f8be1b6bb1901bf5dfd1147e2821622decd492f4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,027 | isConformalMap_complex_linear | Mathlib/Analysis/Complex/Conformal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext1 | case refine_2
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
⊢ restrictScalars ℝ map = ‖map 1‖ • { toLinearMap := ‖map 1‖⁻¹ • ↑ℝ ↑map, norm_map' := ⋯ }.toContinuousLinearMap | case refine_2.h
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
x✝ : ℂ
⊢ (restrictScalars ℝ map) x✝ =
(‖map 1‖ • { toLinearMap := ‖map 1‖⁻¹ • ↑ℝ ↑map, norm_map' := ⋯ }.toContinuousLinearM... | ((:c Eq) ((:c ContinuousLinearMap) (:c Real) (:c Real) ((:c DivisionSemiring.toSemiring) (:c Real) ((:c Semifield.toDivisionSemiring) (:c Real) ((:c Field.toSemifield) (:c Real) ((:c NormedField.toField) (:c Real) (:c Real.normedField))))) ((:c DivisionSemiring.toSemiring) (:c Real) ((:c Semifield.toDivisionSemiring) (... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.2325))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.2325) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328)))"},{"name":"inst✝","sexp":"((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Real))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedAddCommGroup) (:arg... | {"children":[{"source":"ext1","sourceEnd":2488,"sourceStart":2484,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.tacticExt1___","source":"ext1\n -- porting note (#10745): was `simp`; explicitly supplied simp lemma","sourceEnd":2488,"sourceStart":2484,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":2,... | 8 | 32 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 981a1c9df0b7db47d9686883e3cb806b5bc483b00436c05e2e479d1e15925573 | 598535170d1073c7a28a59f60760d476b12670920e3f6931196458a533a4e33f | e7fe907b3287888acfd1b4783f3ce5b528593e6c60d4d7f2923662da6d41fe8b | 9428f03bd89e006bed5310e5cefa4b765dd7905e97c870de4f6527d4623f12b9 |
cat-searcher/leandojo-benchmark-4-random | test | 3,028 | isConformalMap_complex_linear | Mathlib/Analysis/Complex/Conformal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>smul_inv_smul₀</a> minor₁] | case refine_2.h
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : NormedSpace ℂ E
z : ℂ
g : ℂ →L[ℝ] E
f : ℂ → E
map : ℂ →L[ℂ] E
nonzero : map ≠ 0
minor₁ : ‖map 1‖ ≠ 0
x✝ : ℂ
⊢ (restrictScalars ℝ map) x✝ =
(‖map 1‖ • { toLinearMap := ‖map 1‖⁻¹ • ↑ℝ ↑map, norm_map' := ⋯ }.toContinuousLinearM... | ((:c Eq) (:fv _uniq.2325) ((:c DFunLike.coe) ((:c ContinuousLinearMap) (:c Real) (:c Real) ((:c Ring.toSemiring) (:c Real) (:c Real.instRing)) ((:c Ring.toSemiring) (:c Real) (:c Real.instRing)) ((:c RingHom.id) (:c Real) ((:c Semiring.toNonAssocSemiring) (:c Real) ((:c Ring.toSemiring) (:c Real) (:c Real.instRing)))) ... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.2325))"},{"name":"inst✝¹","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.2325) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.2325) (:fv _uniq.2328)))"},{"name":"inst✝","sexp":"((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c NormedAddCommGroup) (:arg... | {"children":[{"source":"simp","sourceEnd":2570,"sourceStart":2566,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2572,"sourceStart":2571,"tag":"atom"... | [] | [{"source":"smul_inv_smul₀ minor₁","source_end":2597,"source_start":2572,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2325","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2328","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":2,... | 8 | 33 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | de53389d1233bed836057f60aef22bea83807da3d4fbc68c2775976e2c5bcf21 | 9428f03bd89e006bed5310e5cefa4b765dd7905e97c870de4f6527d4623f12b9 | 8b39bfd6881e5af47a9bc42c090db4a0e3669eb469f0f27e912f61994960ceea | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,029 | LucasLehmer.sMod_lt | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>LucasLehmer.sMod_mod</a>] | p : ℕ
hp : p ≠ 0
i : ℕ
⊢ sMod p i < 2 ^ p - 1 | p : ℕ
hp : p ≠ 0
i : ℕ
⊢ sMod p i % (2 ^ p - 1) < 2 ^ p - 1 | ((:c LT.lt) (:c Int) (:c Int.instLTInt) ((:c LucasLehmer.sMod) (:fv _uniq.12040) (:fv _uniq.12042)) ((:c HSub.hSub) (:c Int) (:c Int) (:c Int) ((:c instHSub) (:c Int) (:c Int.instSub)) ((:c HPow.hPow) (:c Int) (:c Nat) (:c Int) (:c Int.instHPowNat) ((:c OfNat.ofNat) (:c Int) (:lit 2) ((:c instOfNat) (:lit 2))) (:fv _un... | [{"name":"p","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Ne) (:c Nat) (:fv _uniq.12040) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"i","sexp":"(:c Nat)"}] | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:app (:c LucasLehmer.sMod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV3)))) (:arg :explicit 3 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:c Int)) (:arg :implicit... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.12040","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.12041","is_instance":false,"is_let":false,"name":"hp","sexp":"(:app (:c Ne) (:arg :implicit-type 0 (:c Nat)) (:... | {"children":[{"source":"rw","sourceEnd":4959,"sourceStart":4957,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4961,"sourceStart":4960,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":4964,"sourceStart":... | [] | [{"source":"sMod_mod","source_end":4973,"source_start":4965,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.12040","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.12041","is_instance":false,"is_let":false,"user_name":"hp"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 36 | 4 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2017d7318105dc4145b158317b164b8b43df6b95dc581a7bf70b840f1e7ef253 | 69ce6fb5e07b1df72d7d186a1ad8e9a0362edd9d043428298a12840bf523d70c | 1280299d742bd6ebe767e32f701d9c7336fea58312c80fb1ff6a27ec7a407fc1 | 9464d824a4712acf3cdf754f5141071ddc93c3e2b13f7ecea8a215af42f9b55d |
cat-searcher/leandojo-benchmark-4-random | test | 3,030 | LucasLehmer.sMod_lt | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (<a>Int.emod_lt</a> _ (<a>LucasLehmer.mersenne_int_ne_zero</a> p hp)).<a>LT.lt.trans_eq</a> ?_ | p : ℕ
hp : p ≠ 0
i : ℕ
⊢ sMod p i % (2 ^ p - 1) < 2 ^ p - 1 | p : ℕ
hp : p ≠ 0
i : ℕ
⊢ |2 ^ p - 1| = 2 ^ p - 1 | ((:c LT.lt) (:c Int) (:c Int.instLTInt) ((:c HMod.hMod) (:c Int) (:c Int) (:c Int) ((:c instHMod) (:c Int) (:c Int.instMod)) ((:c LucasLehmer.sMod) (:fv _uniq.12040) (:fv _uniq.12042)) ((:c HSub.hSub) (:c Int) (:c Int) (:c Int) ((:c instHSub) (:c Int) (:c Int.instSub)) ((:c HPow.hPow) (:c Int) (:c Nat) (:c Int) (:c Int... | [{"name":"p","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Ne) (:c Nat) (:fv _uniq.12040) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"i","sexp":"(:c Nat)"}] | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:app (:c HMod.hMod) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:c Int)) (:arg :implicit-type 2 (:c Int)) (:arg :instance 3 (:instance-of (:app (:c HMod) (:arg :... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.12040","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.12041","is_instance":false,"is_let":false,"name":"hp","sexp":"(:app (:c Ne) (:arg :implicit-type 0 (:c Nat)) (:... | {"children":[{"source":"refine","sourceEnd":4983,"sourceStart":4977,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":4985,"sourceStart":4984,"tag":"atom"},{"children":[{"name":"Int.emod_lt","semanticRole":"global","source":"Int.emod_lt","sourceEnd":4996,"sourceStart":4985,"tag":"identifier... | [] | [{"source":"(Int.emod_lt _ (mersenne_int_ne_zero p hp)).trans_eq ?_","source_end":5039,"source_start":4984,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.12040","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.12041","is_instance":false,"is_let":false,"user_name":"hp"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 36 | 7 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 023d8e8bc14da3cb0d724ed284e6215101680f9f4f50ed045167811f6b448dc9 | 9464d824a4712acf3cdf754f5141071ddc93c3e2b13f7ecea8a215af42f9b55d | a06a3ac8fae36a1146e45943c49d4979d7a256ede46b8d35a932f65f2a84e295 | ff4ca1777a986d9f11b1dd00ca0ce9c45e2f40e05f80945967b665e3fb4a5856 |
cat-searcher/leandojo-benchmark-4-random | test | 3,031 | LucasLehmer.sMod_lt | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>abs_of_nonneg</a> (<a>LucasLehmer.mersenne_int_pos</a> hp).<a>LT.lt.le</a> | p : ℕ
hp : p ≠ 0
i : ℕ
⊢ |2 ^ p - 1| = 2 ^ p - 1 | ((:c Eq) (:c Int) ((:c abs) (:c Int) (:c instLatticeInt) (:c Int.instAddGroup) ((:c HSub.hSub) (:c Int) (:c Int) (:c Int) ((:c instHSub) (:c Int) (:c Int.instSub)) ((:c HPow.hPow) (:c Int) (:c Nat) (:c Int) (:c Int.instHPowNat) ((:c OfNat.ofNat) (:c Int) (:lit 2) ((:c instOfNat) (:lit 2))) (:fv _uniq.12040)) ((:c OfNat... | [{"name":"p","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Ne) (:c Nat) (:fv _uniq.12040) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"i","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c abs) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c Lattice) (:arg :explicit 0 (:c Int))))) (:arg :instance 2 (:instance-of (:app (:c AddGroup) (:arg :explicit 0 (:c Int))))) (:arg :explicit 3 (:app (:c HSub.hSub) (:a... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.12040","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.12041","is_instance":false,"is_let":false,"name":"hp","sexp":"(:app (:c Ne) (:arg :implicit-type 0 (:c Nat)) (:... | {"children":[{"source":"exact","sourceEnd":5047,"sourceStart":5042,"tag":"atom"},{"children":[{"name":"abs_of_nonneg","semanticRole":"global","source":"abs_of_nonneg","sourceEnd":5061,"sourceStart":5048,"tag":"identifier"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":5063,"sourceStart":5062,"tag":"a... | [] | [{"source":"abs_of_nonneg (mersenne_int_pos hp).le","source_end":5086,"source_start":5048,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.12040","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.12041","is_instance":false,"is_let":false,"user_name":"hp"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 36 | 8 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ca77dfd5b6425b81f6b3c592c7488653636712d2fa414d16e07a24035eeaf231 | ff4ca1777a986d9f11b1dd00ca0ce9c45e2f40e05f80945967b665e3fb4a5856 | 68bfa7515045267c1d9b5ee989f5019b2dec7f8e47a7f8302e0221492cddb237 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,032 | ZFSet.toSet_sdiff | Mathlib/SetTheory/ZFC/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | change (<a>ZFSet.sep</a> (fun z => z ∉ y) x).<a>ZFSet.toSet</a> = _ | x y : ZFSet
⊢ (x \ y).toSet = x.toSet \ y.toSet | x y : ZFSet
⊢ (ZFSet.sep (fun z => z ∉ y) x).toSet = x.toSet \ y.toSet | ((:c Eq) ((:c Set) (:c ZFSet)) ((:c ZFSet.toSet) ((:c SDiff.sdiff) (:c ZFSet) (:c ZFSet.instSDiff) (:fv _uniq.69768) (:fv _uniq.69769))) ((:c SDiff.sdiff) ((:c Set) (:c ZFSet)) ((:c Set.instSDiff) (:c ZFSet)) ((:c ZFSet.toSet) (:fv _uniq.69768)) ((:c ZFSet.toSet) (:fv _uniq.69769)))) | [{"name":"x","sexp":"(:c ZFSet)"},{"name":"y","sexp":"(:c ZFSet)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:c ZFSet)))) (:arg :explicit 1 (:app (:c ZFSet.toSet) (:arg :explicit 0 (:app (:c SDiff.sdiff) (:arg :implicit-type 0 (:c ZFSet)) (:arg :instance 1 (:instance-of (:app (:c SDiff) (:arg :explicit 0 (:c ZFSet))))) (:arg :explicit 2 (:fv FV1)) (:arg :e... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.69768","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ZFSet)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69769","is_instance":false,"is_let":false,"name":"y","sexp":"(:c ZFSet)"}] | {"children":[{"source":"change","sourceEnd":38387,"sourceStart":38381,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":38389,"sourceStart":38388,"tag":"atom"},{"children":[{"name":"ZFSet.sep","semanticRole":"global","source":"ZFSet.sep","sourceEnd":38398,"sourceStart":38389,"tag":"identifi... | [] | [{"source":"(ZFSet.sep (fun z => z ∉ y) x).toSet = _","source_end":38430,"source_start":38388,"syntax_kind":"«term_=_»"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.69768","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69769","is_instance":false,"is_let":false,"user_name":"y"}] | 356 | 4 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d7491fe4e611a0b23ef07291a8391049e98c52bcd6ba3f1d211eda4221b96725 | ac0f879a096e271a99743df03939a05c76e3b7d3d53d6e9c979496530e1000be | 81f545359bdf7d0a097cc8182bea9e90b6dfa77e32dad93f4146714063f732ef | f5bda816b752b0f42c54f2746271ee957e7ce849b01d00a08be397b31bc8439b |
cat-searcher/leandojo-benchmark-4-random | test | 3,033 | ZFSet.toSet_sdiff | Mathlib/SetTheory/ZFC/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext | x y : ZFSet
⊢ (ZFSet.sep (fun z => z ∉ y) x).toSet = x.toSet \ y.toSet | case h
x y x✝ : ZFSet
⊢ x✝ ∈ (ZFSet.sep (fun z => z ∉ y) x).toSet ↔ x✝ ∈ x.toSet \ y.toSet | ((:c Eq) ((:c Set) (:c ZFSet)) ((:c ZFSet.toSet) ((:c ZFSet.sep) (:lambda z (:c ZFSet) ((:c Not) ((:c Membership.mem) (:c ZFSet) (:c ZFSet) (:c ZFSet.instMembership) 0 (:fv _uniq.69769)))) (:fv _uniq.69768))) ((:c SDiff.sdiff) ((:c Set) (:c ZFSet)) ((:c Set.instSDiff) (:c ZFSet)) ((:c ZFSet.toSet) (:fv _uniq.69768)) ((... | [{"name":"x","sexp":"(:c ZFSet)"},{"name":"y","sexp":"(:c ZFSet)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:c ZFSet)))) (:arg :explicit 1 (:app (:c ZFSet.toSet) (:arg :explicit 0 (:app (:c ZFSet.sep) (:arg :explicit 0 (:lambda z :explicit (:c ZFSet) (:app (:c Not) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:c ZFSet)) (:arg :impli... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.69768","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ZFSet)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69769","is_instance":false,"is_let":false,"name":"y","sexp":"(:c ZFSet)"}] | {"children":[{"source":"ext","sourceEnd":38436,"sourceStart":38433,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":38436,"sourceStart":38433,"tag":"node"} | [] | [] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.69768","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69769","is_instance":false,"is_let":false,"user_name":"y"}] | 356 | 5 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 681bbebcab6d392dd719aeda1ac80795c5d25c746d1a69d67f3ad4bcee302aed | f5bda816b752b0f42c54f2746271ee957e7ce849b01d00a08be397b31bc8439b | a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de | 41f9bbfb25a2a3f24ca96e7ab1f8b71929c9bc4f3028d0e2178087307325b0da |
cat-searcher/leandojo-benchmark-4-random | test | 3,034 | ZFSet.toSet_sdiff | Mathlib/SetTheory/ZFC/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case h
x y x✝ : ZFSet
⊢ x✝ ∈ (ZFSet.sep (fun z => z ∉ y) x).toSet ↔ x✝ ∈ x.toSet \ y.toSet | ((:c Iff) ((:c Membership.mem) (:c ZFSet) ((:c Set) (:c ZFSet)) ((:c Set.instMembership) (:c ZFSet)) (:fv _uniq.69841) ((:c ZFSet.toSet) ((:c ZFSet.sep) (:lambda z (:c ZFSet) ((:c Not) ((:c Membership.mem) (:c ZFSet) (:c ZFSet) (:c ZFSet.instMembership) 0 (:fv _uniq.69769)))) (:fv _uniq.69768)))) ((:c Membership.mem) (... | [{"name":"x","sexp":"(:c ZFSet)"},{"name":"y","sexp":"(:c ZFSet)"},{"name":"x✝","sexp":"(:c ZFSet)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:c ZFSet)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c ZFSet)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c ZFSet)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c ZFSet))))))) (:ar... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.69768","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ZFSet)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69769","is_instance":false,"is_let":false,"name":"y","sexp":"(:c ZFSet)"},{"binder_role":":explicit","context... | {"children":[{"source":"simp","sourceEnd":38443,"sourceStart":38439,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"ki... | [] | [] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.69768","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69769","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 356 | 6 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 241046d3477066474f6a995962e448e0572c7596ce03c7b443d854f8ed9be9d0 | 41f9bbfb25a2a3f24ca96e7ab1f8b71929c9bc4f3028d0e2178087307325b0da | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,035 | ContinuousLinearMap.zero_comp | Mathlib/Topology/Algebra/Module/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext | R₁ : Type u_1
R₂ : Type u_2
R₃ : Type u_3
inst✝¹⁷ : Semiring R₁
inst✝¹⁶ : Semiring R₂
inst✝¹⁵ : Semiring R₃
σ₁₂ : R₁ →+* R₂
σ₂₃ : R₂ →+* R₃
σ₁₃ : R₁ →+* R₃
M₁ : Type u_4
inst✝¹⁴ : TopologicalSpace M₁
inst✝¹³ : AddCommMonoid M₁
M'₁ : Type u_5
inst✝¹² : TopologicalSpace M'₁
inst✝¹¹ : AddCommMonoid M'₁
M₂ : Type u_6
inst✝... | case h
R₁ : Type u_1
R₂ : Type u_2
R₃ : Type u_3
inst✝¹⁷ : Semiring R₁
inst✝¹⁶ : Semiring R₂
inst✝¹⁵ : Semiring R₃
σ₁₂ : R₁ →+* R₂
σ₂₃ : R₂ →+* R₃
σ₁₃ : R₁ →+* R₃
M₁ : Type u_4
inst✝¹⁴ : TopologicalSpace M₁
inst✝¹³ : AddCommMonoid M₁
M'₁ : Type u_5
inst✝¹² : TopologicalSpace M'₁
inst✝¹¹ : AddCommMonoid M'₁
M₂ : Type u_... | ((:c Eq) ((:c ContinuousLinearMap) (:fv _uniq.359575) (:fv _uniq.359581) (:fv _uniq.359584) (:fv _uniq.359590) (:fv _uniq.359656) (:fv _uniq.359659) (:fv _uniq.359662) (:fv _uniq.359665) (:fv _uniq.359686) (:fv _uniq.359689) (:fv _uniq.359692) (:fv _uniq.359723) (:fv _uniq.359789)) ((:c ContinuousLinearMap.comp) (:fv _... | [{"name":"R₁","sexp":"(:sort (+ u_1 1))"},{"name":"R₂","sexp":"(:sort (+ u_2 1))"},{"name":"R₃","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹⁷","sexp":"((:c Semiring) (:fv _uniq.359575))"},{"name":"inst✝¹⁶","sexp":"((:c Semiring) (:fv _uniq.359578))"},{"name":"inst✝¹⁵","sexp":"((:c Semiring) (:fv _uniq.359581))"},{"name"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.359575","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.359578","is_instance":false,"is_let":false,"name":"R₂","sexp":"(:sort Type)"},{"binder_role":":implicit",... | {"children":[{"source":"ext","sourceEnd":38585,"sourceStart":38582,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":38585,"sourceStart":38582,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.359575","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.359578","is_instance":false,"is_let":false,"user_name":"R₂"},{"binder_role":":implicit","context_index":2,"internal_name":... | 256 | 4 | exact | true | 1 | 30 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 023284825829baeeed14dd5b13fe5e220797ef8e73e0db0cd8bdf6cccb501710 | 2f95f59259e70a0b14af5480c39751e655c8e2f14b9959cdb52e7de2db7d3aa5 | a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de | 2980a4f361e2075993fb288ad9c67b1e0103f4da950f2f51dfff461655da9684 |
cat-searcher/leandojo-benchmark-4-random | test | 3,036 | ContinuousLinearMap.zero_comp | Mathlib/Topology/Algebra/Module/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case h
R₁ : Type u_1
R₂ : Type u_2
R₃ : Type u_3
inst✝¹⁷ : Semiring R₁
inst✝¹⁶ : Semiring R₂
inst✝¹⁵ : Semiring R₃
σ₁₂ : R₁ →+* R₂
σ₂₃ : R₂ →+* R₃
σ₁₃ : R₁ →+* R₃
M₁ : Type u_4
inst✝¹⁴ : TopologicalSpace M₁
inst✝¹³ : AddCommMonoid M₁
M'₁ : Type u_5
inst✝¹² : TopologicalSpace M'₁
inst✝¹¹ : AddCommMonoid M'₁
M₂ : Type u_... | ((:c Eq) (:fv _uniq.359686) ((:c DFunLike.coe) ((:c ContinuousLinearMap) (:fv _uniq.359575) (:fv _uniq.359581) (:fv _uniq.359584) (:fv _uniq.359590) (:fv _uniq.359656) (:fv _uniq.359659) (:fv _uniq.359662) (:fv _uniq.359665) (:fv _uniq.359686) (:fv _uniq.359689) (:fv _uniq.359692) (:fv _uniq.359723) (:fv _uniq.359789))... | [{"name":"R₁","sexp":"(:sort (+ u_1 1))"},{"name":"R₂","sexp":"(:sort (+ u_2 1))"},{"name":"R₃","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹⁷","sexp":"((:c Semiring) (:fv _uniq.359575))"},{"name":"inst✝¹⁶","sexp":"((:c Semiring) (:fv _uniq.359578))"},{"name":"inst✝¹⁵","sexp":"((:c Semiring) (:fv _uniq.359581))"},{"name"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV18)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:ins... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.359575","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.359578","is_instance":false,"is_let":false,"name":"R₂","sexp":"(:sort Type)"},{"binder_role":":implicit",... | {"children":[{"source":"simp","sourceEnd":38592,"sourceStart":38588,"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.359575","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.359578","is_instance":false,"is_let":false,"user_name":"R₂"},{"binder_role":":implicit","context_index":2,"internal_name":... | 256 | 5 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ae429f91c2070a8e9312af141c17d0c096c42b1dacf98324e2bdd6414bb2b1a5 | 2980a4f361e2075993fb288ad9c67b1e0103f4da950f2f51dfff461655da9684 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,037 | Filter.eventually_prod_self_iff | Mathlib/Order/Filter/Bases.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.prod_subset_iff</a>, <a>Set.mem_setOf_eq</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
la : Filter α
pa : ι → Prop
sa : ι → Set α
lb : Filter β
pb : ι' → Prop
sb : ι' → Set β
f : α → β
r : α → α → Prop
⊢ (∃ t ∈ la, t ×ˢ t ⊆ {x | (fun x => r x.1 x.2) x}) ↔ ∃ t ∈ la, ∀ x ∈ t, ∀ y ∈ t, r x y | ((:c Iff) ((:c Exists) ((:c Set) (:fv _uniq.78891)) (:lambda t ((:c Set) (:fv _uniq.78891)) ((:c And) ((:c Membership.mem) ((:c Set) (:fv _uniq.78891)) ((:c Filter) (:fv _uniq.78891)) ((:c instMembershipSetFilter) (:fv _uniq.78891)) 0 (:fv _uniq.78906)) ((:c HasSubset.Subset) ((:c Set) ((:c Prod) (:fv _uniq.78891) (:fv... | [{"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":"la","sexp":"((:c Filter) (:fv _uniq.78891))"},{"name":"pa","sexp":"(:forall _ (:fv _uniq.78900) (:sort 0))"},{"name":"sa"... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.78891","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.78894","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":49294,"sourceStart":49290,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":49299,"sourceStart":49295,"tag":"atom"}],"kind"... | [] | [{"source":"prod_subset_iff","source_end":49316,"source_start":49301,"syntax_kind":"ident"},{"source":"mem_setOf_eq","source_end":49330,"source_start":49318,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.78891","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.78894","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 281 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b6c27abda479fbb9b34501d447efe54512c572ac4e1b51cf6591ae92fb084743 | 1630b81e2220af0c7965fbf118e315d578d05603516011f5371456b5f354cc5e | 343df0b60deffb4422d4bdf89a37ae3181c907417e49f46518a8eee1001507be | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,038 | PiTensorProduct.nonempty_lifts | Mathlib/LinearAlgebra/PiTensorProduct.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | existsi @<a>Quotient.out</a> _ (<a>addConGen</a> (<a>PiTensorProduct.Eqv</a> R s)).<a>AddCon.toSetoid</a> x | ι : Type u_1
ι₂ : Type u_2
ι₃ : Type u_3
R : Type u_4
inst✝⁷ : CommSemiring R
R₁ : Type u_5
R₂ : Type u_6
s : ι → Type u_7
inst✝⁶ : (i : ι) → AddCommMonoid (s i)
inst✝⁵ : (i : ι) → Module R (s i)
M : Type u_8
inst✝⁴ : AddCommMonoid M
inst✝³ : Module R M
E : Type u_9
inst✝² : AddCommMonoid E
inst✝¹ : Module R E
F : Type... | ι : Type u_1
ι₂ : Type u_2
ι₃ : Type u_3
R : Type u_4
inst✝⁷ : CommSemiring R
R₁ : Type u_5
R₂ : Type u_6
s : ι → Type u_7
inst✝⁶ : (i : ι) → AddCommMonoid (s i)
inst✝⁵ : (i : ι) → Module R (s i)
M : Type u_8
inst✝⁴ : AddCommMonoid M
inst✝³ : Module R M
E : Type u_9
inst✝² : AddCommMonoid E
inst✝¹ : Module R E
F : Type... | ((:c Set.Nonempty) ((:c FreeAddMonoid) ((:c Prod) (:fv _uniq.178166) (:forall i (:fv _uniq.178157) ((:fv _uniq.178180) 0)))) ((:c PiTensorProduct.lifts) (:fv _uniq.178157) (:fv _uniq.178166) (:fv _uniq.178169) (:fv _uniq.178180) (:fv _uniq.178188) (:fv _uniq.178368) (:fv _uniq.178937))) | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"ι₂","sexp":"(:sort (+ u_2 1))"},{"name":"ι₃","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁷","sexp":"((:c CommSemiring) (:fv _uniq.178166))"},{"name":"R₁","sexp":"(:sort (+ u_5 1))"},{"name":"R₂","sexp":"(:sort (+ u_6 1))"},{"name":"... | (:app (:c Set.Nonempty) (:arg :implicit-type 0 (:app (:c FreeAddMonoid) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:forall i :explicit (:fv FV0) (:app (:fv FV7) (:arg :explicit 0 0)))))))) (:arg :explicit 1 (:app (:c PiTensorProduct.lifts) (:arg :implicit-type 0 (:fv FV0)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.178157","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.178160","is_instance":false,"is_let":false,"name":"ι₂","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"existsi","sourceEnd":16462,"sourceStart":16455,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"@","sourceEnd":16464,"sourceStart":16463,"tag":"atom"},{"name":"Quotient.out","semanticRole":"global","source":"Quotient.out","sourceEnd":16476,"sourceStart":16464,"tag":"identifier"}],... | [] | [{"source":"@Quotient.out _ (addConGen (PiTensorProduct.Eqv R s)).toSetoid x","source_end":16527,"source_start":16463,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.178157","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.178160","is_instance":false,"is_let":false,"user_name":"ι₂"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 80 | 4 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1ec4d3c4d53e38e201724165aa2edbe5e07114409f52e68170a7e8bc4553360f | 74af6d95b5a5cc1f66077a06769575960bf6983aa2d097f4bd4f5f7082db2eb7 | 03772270c247f32e1c7d8a42404bdce7a29f583870bd5e0d068d2319163fb4a4 | 530a946b8dd0f410c152cb5bca17ee7171874dc1979f81d82f2b1785e95c1054 |
cat-searcher/leandojo-benchmark-4-random | test | 3,039 | PiTensorProduct.nonempty_lifts | Mathlib/LinearAlgebra/PiTensorProduct.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>PiTensorProduct.lifts</a>, <a>Set.mem_setOf_eq</a>] | ι : Type u_1
ι₂ : Type u_2
ι₃ : Type u_3
R : Type u_4
inst✝⁷ : CommSemiring R
R₁ : Type u_5
R₂ : Type u_6
s : ι → Type u_7
inst✝⁶ : (i : ι) → AddCommMonoid (s i)
inst✝⁵ : (i : ι) → Module R (s i)
M : Type u_8
inst✝⁴ : AddCommMonoid M
inst✝³ : Module R M
E : Type u_9
inst✝² : AddCommMonoid E
inst✝¹ : Module R E
F : Type... | ι : Type u_1
ι₂ : Type u_2
ι₃ : Type u_3
R : Type u_4
inst✝⁷ : CommSemiring R
R₁ : Type u_5
R₂ : Type u_6
s : ι → Type u_7
inst✝⁶ : (i : ι) → AddCommMonoid (s i)
inst✝⁵ : (i : ι) → Module R (s i)
M : Type u_8
inst✝⁴ : AddCommMonoid M
inst✝³ : Module R M
E : Type u_9
inst✝² : AddCommMonoid E
inst✝¹ : Module R E
F : Type... | ((:c Membership.mem) ((:c FreeAddMonoid) ((:c Prod) (:fv _uniq.178166) (:forall i (:fv _uniq.178157) ((:fv _uniq.178180) 0)))) ((:c Set) ((:c FreeAddMonoid) ((:c Prod) (:fv _uniq.178166) (:forall i (:fv _uniq.178157) ((:fv _uniq.178180) 0))))) ((:c Set.instMembership) ((:c FreeAddMonoid) ((:c Prod) (:fv _uniq.178166) (... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"ι₂","sexp":"(:sort (+ u_2 1))"},{"name":"ι₃","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁷","sexp":"((:c CommSemiring) (:fv _uniq.178166))"},{"name":"R₁","sexp":"(:sort (+ u_5 1))"},{"name":"R₂","sexp":"(:sort (+ u_6 1))"},{"name":"... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c FreeAddMonoid) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:forall i :explicit (:fv FV0) (:app (:fv FV7) (:arg :explicit 0 0)))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c FreeAddMonoid) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.178157","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.178160","is_instance":false,"is_let":false,"name":"ι₂","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"simp","sourceEnd":16534,"sourceStart":16530,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":16539,"sourceStart":16535,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":165... | [] | [{"source":"lifts","source_end":16546,"source_start":16541,"syntax_kind":"ident"},{"source":"Set.mem_setOf_eq","source_end":16564,"source_start":16548,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.178157","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.178160","is_instance":false,"is_let":false,"user_name":"ι₂"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 80 | 5 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 554b621f4020be80993ab580c3d76555752655df458d16e05106b9d3c17c60d6 | 530a946b8dd0f410c152cb5bca17ee7171874dc1979f81d82f2b1785e95c1054 | a761a8e1f0fd8d43bdc179ec9ecd99fcb8c348e9c6522130144d6d2ac89f87b7 | 648a41b69820bdf69e3a8119bec1854de45f3ce11a28e0ca65bf4beaea9dac9d |
cat-searcher/leandojo-benchmark-4-random | test | 3,040 | PiTensorProduct.nonempty_lifts | Mathlib/LinearAlgebra/PiTensorProduct.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>AddCon.quot_mk_eq_coe</a>] | ι : Type u_1
ι₂ : Type u_2
ι₃ : Type u_3
R : Type u_4
inst✝⁷ : CommSemiring R
R₁ : Type u_5
R₂ : Type u_6
s : ι → Type u_7
inst✝⁶ : (i : ι) → AddCommMonoid (s i)
inst✝⁵ : (i : ι) → Module R (s i)
M : Type u_8
inst✝⁴ : AddCommMonoid M
inst✝³ : Module R M
E : Type u_9
inst✝² : AddCommMonoid E
inst✝¹ : Module R E
F : Type... | ι : Type u_1
ι₂ : Type u_2
ι₃ : Type u_3
R : Type u_4
inst✝⁷ : CommSemiring R
R₁ : Type u_5
R₂ : Type u_6
s : ι → Type u_7
inst✝⁶ : (i : ι) → AddCommMonoid (s i)
inst✝⁵ : (i : ι) → Module R (s i)
M : Type u_8
inst✝⁴ : AddCommMonoid M
inst✝³ : Module R M
E : Type u_9
inst✝² : AddCommMonoid E
inst✝¹ : Module R E
F : Type... | ((:c Eq) ((:c AddCon.Quotient) ((:c FreeAddMonoid) ((:c Prod) (:fv _uniq.178166) (:forall i (:fv _uniq.178157) ((:fv _uniq.178180) 0)))) ((:c AddSemigroup.toAdd) ((:c FreeAddMonoid) ((:c Prod) (:fv _uniq.178166) (:forall i (:fv _uniq.178157) ((:fv _uniq.178180) 0)))) ((:c AddMonoid.toAddSemigroup) ((:c FreeAddMonoid) (... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"ι₂","sexp":"(:sort (+ u_2 1))"},{"name":"ι₃","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁷","sexp":"((:c CommSemiring) (:fv _uniq.178166))"},{"name":"R₁","sexp":"(:sort (+ u_5 1))"},{"name":"R₂","sexp":"(:sort (+ u_6 1))"},{"name":"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c AddCon.Quotient) (:arg :implicit-type 0 (:app (:c FreeAddMonoid) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:forall i :explicit (:fv FV0) (:app (:fv FV7) (:arg :explicit 0 0)))))))) (:arg :instance 1 (:instance-of (:app (:c Add) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.178157","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.178160","is_instance":false,"is_let":false,"name":"ι₂","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rw","sourceEnd":16570,"sourceStart":16568,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16572,"sourceStart":16571,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":16575,"sourceSt... | [] | [{"source":"AddCon.quot_mk_eq_coe","source_end":16597,"source_start":16576,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.178157","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.178160","is_instance":false,"is_let":false,"user_name":"ι₂"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 80 | 6 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 09f88e850da3c1205e2fbc4a02b6d9f9fdb45bacfe708bf83b178c77e672c08b | 648a41b69820bdf69e3a8119bec1854de45f3ce11a28e0ca65bf4beaea9dac9d | 00425365079eb6b8032068afd63038745e429e37c70f44adfe3d03fac5447b00 | e7ad55c32b2965d3bcf28f711510f4b686af5c61f6488aac59a25a5dbc92069d |
cat-searcher/leandojo-benchmark-4-random | test | 3,041 | PiTensorProduct.nonempty_lifts | Mathlib/LinearAlgebra/PiTensorProduct.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | erw [<a>Quot.out_eq</a>] | ι : Type u_1
ι₂ : Type u_2
ι₃ : Type u_3
R : Type u_4
inst✝⁷ : CommSemiring R
R₁ : Type u_5
R₂ : Type u_6
s : ι → Type u_7
inst✝⁶ : (i : ι) → AddCommMonoid (s i)
inst✝⁵ : (i : ι) → Module R (s i)
M : Type u_8
inst✝⁴ : AddCommMonoid M
inst✝³ : Module R M
E : Type u_9
inst✝² : AddCommMonoid E
inst✝¹ : Module R E
F : Type... | ((:c Eq) ((:c AddCon.Quotient) ((:c FreeAddMonoid) ((:c Prod) (:fv _uniq.178166) (:forall i (:fv _uniq.178157) ((:fv _uniq.178180) 0)))) ((:c AddSemigroup.toAdd) ((:c FreeAddMonoid) ((:c Prod) (:fv _uniq.178166) (:forall i (:fv _uniq.178157) ((:fv _uniq.178180) 0)))) ((:c AddMonoid.toAddSemigroup) ((:c FreeAddMonoid) (... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"ι₂","sexp":"(:sort (+ u_2 1))"},{"name":"ι₃","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁷","sexp":"((:c CommSemiring) (:fv _uniq.178166))"},{"name":"R₁","sexp":"(:sort (+ u_5 1))"},{"name":"R₂","sexp":"(:sort (+ u_6 1))"},{"name":"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c AddCon.Quotient) (:arg :implicit-type 0 (:app (:c FreeAddMonoid) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:forall i :explicit (:fv FV0) (:app (:fv FV7) (:arg :explicit 0 0)))))))) (:arg :instance 1 (:instance-of (:app (:c Add) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.178157","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.178160","is_instance":false,"is_let":false,"name":"ι₂","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"erw","sourceEnd":16604,"sourceStart":16601,"tag":"atom"},{"children":[{"source":"[","sourceEnd":16606,"sourceStart":16605,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Quot.out_eq","semanticRole":"global","source":"Quot.out_eq","sourceEnd... | [] | [{"source":"Quot.out_eq","source_end":16617,"source_start":16606,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.178157","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.178160","is_instance":false,"is_let":false,"user_name":"ι₂"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 80 | 9 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0001eb2123210a6e9ef14cf209b179ac58745f83df637796ed110de6ac8d38c4 | e7ad55c32b2965d3bcf28f711510f4b686af5c61f6488aac59a25a5dbc92069d | ea037840b7db8e177b98ab0818ae51d2f439adaf0504517310dcc634d8489248 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,042 | Complex.tan_mul_I | Mathlib/Data/Complex/Exponential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Complex.tan</a>, <a>Complex.sin_mul_I</a>, <a>Complex.cos_mul_I</a>, <a>mul_div_right_comm</a>, <a>Complex.tanh_eq_sinh_div_cosh</a>] | x y : ℂ
⊢ tan (x * I) = tanh x * I | ((:c Eq) (:c Complex) ((:c Complex.tan) ((:c HMul.hMul) (:c Complex) (:c Complex) (:c Complex) ((:c instHMul) (:c Complex) (:c Complex.instMul)) (:fv _uniq.95908) (:c Complex.I))) ((:c HMul.hMul) (:c Complex) (:c Complex) (:c Complex) ((:c instHMul) (:c Complex) (:c Complex.instMul)) ((:c Complex.tanh) (:fv _uniq.95908... | [{"name":"x","sexp":"(:c Complex)"},{"name":"y","sexp":"(:c Complex)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c Complex.tan) (:arg :explicit 0 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Complex)) (:arg :implicit-type 1 (:c Complex)) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Complex)... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.95908","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.95910","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Complex)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":19017,"sourceStart":19015,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":19019,"sourceStart":19018,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"tan","source_end":19022,"source_start":19019,"syntax_kind":"ident"},{"source":"sin_mul_I","source_end":19033,"source_start":19024,"syntax_kind":"ident"},{"source":"cos_mul_I","source_end":19044,"source_start":19035,"syntax_kind":"ident"},{"source":"mul_div_right_comm","source_end":19064,"source_start":19046... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.95908","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.95910","is_instance":false,"is_let":false,"user_name":"y"}] | 187 | 2 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c600d2372e29dd4baff1c00dcb2304fa100f1c477220a8c4879843a6c1af5033 | 04b219d84a6bfc5d9b5d492941ba9b5534dd78f5d766ad1c12f2735cd691073f | 96be39c633b4bca70e084747a8fb0ab1e87e4855ad448d934248b0c8f5700087 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,043 | IsBezout.gcd_dvd_left | Mathlib/RingTheory/PrincipalIdealDomain.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | R : Type u
M : Type v
inst✝¹ : CommRing R
x y z : R
inst✝ : IsPrincipal (Ideal.span {x, y})
⊢ x ∈ {x, y} | ((:c Membership.mem) (:fv _uniq.50319) ((:c Set) (:fv _uniq.50319)) ((:c Set.instMembership) (:fv _uniq.50319)) (:fv _uniq.50326) ((:c Insert.insert) (:fv _uniq.50319) ((:c Set) (:fv _uniq.50319)) ((:c Set.instInsert) (:fv _uniq.50319)) (:fv _uniq.50326) ((:c Singleton.singleton) (:fv _uniq.50319) ((:c Set) (:fv _uniq.... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.50319))"},{"name":"x","sexp":"(:fv _uniq.50319)"},{"name":"y","sexp":"(:fv _uniq.50319)"},{"name":"z","sexp":"(:fv _uniq.50319)"},{"name":"inst✝","sexp":"((:c Submodule.IsPrincipal) (:fv _uniq... | (: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 FV3)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.50319","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.50321","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":7401,"sourceStart":7397,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.50319","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.50321","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 62 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6b83aaa88f617949af1dfd024ffcb916273cd52bc4312a9b2e512855835812bf | dbe1fa78b879e35bf9cdc4dc4261ba01aa4807b64e6b5f5a5e6d7add16a0aadb | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,044 | Matrix.sub_mulVec | Mathlib/Data/Matrix/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>sub_eq_add_neg</a>, <a>Matrix.add_mulVec</a>, <a>Matrix.neg_mulVec</a>] | l : Type u_1
m : Type u_2
n : Type u_3
o : Type u_4
m' : o → Type u_5
n' : o → Type u_6
R : Type u_7
S : Type u_8
α : Type v
β : Type w
γ : Type u_9
inst✝¹ : NonUnitalNonAssocRing α
inst✝ : Fintype n
A B : Matrix m n α
x : n → α
⊢ (A - B) *ᵥ x = A *ᵥ x - B *ᵥ x | ((:c Eq) (:forall _ (:fv _uniq.537730) (:fv _uniq.537754)) ((:c Matrix.mulVec) (:fv _uniq.537730) (:fv _uniq.537733) (:fv _uniq.537754) ((:c NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring) (:fv _uniq.537754) (:fv _uniq.537762)) (:fv _uniq.538428) ((:c HSub.hSub) ((:c Matrix) (:fv _uniq.537730) (:fv _uniq.537733) (:f... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"o","sexp":"(:sort (+ u_4 1))"},{"name":"m'","sexp":"(:forall _ (:fv _uniq.537736) (:sort (+ u_5 1)))"},{"name":"n'","sexp":"(:forall _ (:fv _uniq.537736) (:sort (+ u_6 1)))"},{"name":"R","se... | (:app (:c Eq) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV1) (:fv FV8))) (:arg :explicit 1 (:app (:c Matrix.mulVec) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:fv FV8)) (:arg :instance 3 (:instance-of (:app (:c NonUnitalNonAssocSemiring) (:arg :explicit 0 (:fv FV8... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.537727","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.537730","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":69397,"sourceStart":69393,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"sub_eq_add_neg","source_end":69413,"source_start":69399,"syntax_kind":"ident"},{"source":"add_mulVec","source_end":69425,"source_start":69415,"syntax_kind":"ident"},{"source":"neg_mulVec","source_end":69437,"source_start":69427,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.537727","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.537730","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 665 | 2 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c1587ff3332496c571a856ef31db30ee3f44dc0a99f619ce5bdeab108fce4a0f | 973dba21369ba6e629a5deb77d1ed52207bb63b8ed5b0bcd4dbd132a0dfd835a | 5b16f948036bd1bf9b466f87bf9b82a66db7f98050e399992bbafb7983663274 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,045 | IsSelfAdjoint.neg_algebraMap_norm_le_self | Mathlib/Analysis/NormedSpace/Star/ContinuousFunctionalCalculus/Order.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : - a ≤ <a>algebraMap</a> ℝ A ‖a‖ := by rw [← <a>norm_neg</a>] exact <a>IsSelfAdjoint.le_algebraMap_norm_self</a> (<a>IsSelfAdjoint.neg</a> ha) | A : Type u_1
inst✝⁷ : NormedRing A
inst✝⁶ : StarRing A
inst✝⁵ : CstarRing A
inst✝⁴ : CompleteSpace A
inst✝³ : NormedAlgebra ℂ A
inst✝² : StarModule ℂ A
inst✝¹ : PartialOrder A
inst✝ : StarOrderedRing A
a : A
ha : autoParam (IsSelfAdjoint a) _auto✝
⊢ -(algebraMap ℝ A) ‖a‖ ≤ a | A : Type u_1
inst✝⁷ : NormedRing A
inst✝⁶ : StarRing A
inst✝⁵ : CstarRing A
inst✝⁴ : CompleteSpace A
inst✝³ : NormedAlgebra ℂ A
inst✝² : StarModule ℂ A
inst✝¹ : PartialOrder A
inst✝ : StarOrderedRing A
a : A
ha : autoParam (IsSelfAdjoint a) _auto✝
this : -a ≤ (algebraMap ℝ A) ‖a‖
⊢ -(algebraMap ℝ A) ‖a‖ ≤ a | ((:c LE.le) (:fv _uniq.8345) ((:c Preorder.toLE) (:fv _uniq.8345) ((:c PartialOrder.toPreorder) (:fv _uniq.8345) (:fv _uniq.9310))) ((:c Neg.neg) (:fv _uniq.8345) ((:c Ring.toNeg) (:fv _uniq.8345) ((:c NormedRing.toRing) (:fv _uniq.8345) (:fv _uniq.8348))) ((:c DFunLike.coe) ((:c RingHom) (:c Real) (:fv _uniq.8345) ((:... | [{"name":"A","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁷","sexp":"((:c NormedRing) (:fv _uniq.8345))"},{"name":"inst✝⁶","sexp":"((:c StarRing) (:fv _uniq.8345) ((:c NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring) (:fv _uniq.8345) ((:c NonAssocRing.toNonUnitalNonAssocRing) (:fv _uniq.8345) ((:c Ring.toNonAssocRing) (... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Neg.neg) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c DFunLike.coe)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8345","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.8348","is_instance":true,"is_let":false,"name":"inst✝⁷","sexp":"(:app (:c NormedRing) (:arg :explic... | {"children":[{"source":"have","sourceEnd":1666,"sourceStart":1662,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":1667,"sourceStart":1667,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":1667,"sourceStart":1667,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"- a ≤ algebraMap ℝ A ‖a‖","source_end":1701,"source_start":1669,"syntax_kind":"«term_≤_»"},{"source":"norm_neg","source_end":1728,"source_start":1720,"syntax_kind":"ident"},{"source":"IsSelfAdjoint.le_algebraMap_norm_self (neg ha)","source_end":1786,"source_start":1740,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8345","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.8348","is_instance":true,"is_let":false,"user_name":"inst✝⁷"},{"binder_role":":instance-implicit","context_index":2,... | 4 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 80825dc68d819f5c26de68e64961b024546d24eeffb64a5cf844be8805d893f6 | 2a48518a6bd82d2a4a67d804a39a2dbcb6f94f8e2b7a558cbb101e19403844f6 | 8b434a65aa860ed99cd8b3d147de9f969b60cbe101b456d74d266a817ab088da | 91aac29e3182d6b3c4c3678978cf41612161fedf898a7d698dbf954d1556fa90 |
cat-searcher/leandojo-benchmark-4-random | test | 3,046 | IsSelfAdjoint.neg_algebraMap_norm_le_self | Mathlib/Analysis/NormedSpace/Star/ContinuousFunctionalCalculus/Order.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact neg_le.mp this | A : Type u_1
inst✝⁷ : NormedRing A
inst✝⁶ : StarRing A
inst✝⁵ : CstarRing A
inst✝⁴ : CompleteSpace A
inst✝³ : NormedAlgebra ℂ A
inst✝² : StarModule ℂ A
inst✝¹ : PartialOrder A
inst✝ : StarOrderedRing A
a : A
ha : autoParam (IsSelfAdjoint a) _auto✝
this : -a ≤ (algebraMap ℝ A) ‖a‖
⊢ -(algebraMap ℝ A) ‖a‖ ≤ a | ((:c LE.le) (:fv _uniq.8345) ((:c Preorder.toLE) (:fv _uniq.8345) ((:c PartialOrder.toPreorder) (:fv _uniq.8345) (:fv _uniq.9310))) ((:c Neg.neg) (:fv _uniq.8345) ((:c Ring.toNeg) (:fv _uniq.8345) ((:c NormedRing.toRing) (:fv _uniq.8345) (:fv _uniq.8348))) ((:c DFunLike.coe) ((:c RingHom) (:c Real) (:fv _uniq.8345) ((:... | [{"name":"A","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁷","sexp":"((:c NormedRing) (:fv _uniq.8345))"},{"name":"inst✝⁶","sexp":"((:c StarRing) (:fv _uniq.8345) ((:c NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring) (:fv _uniq.8345) ((:c NonAssocRing.toNonUnitalNonAssocRing) (:fv _uniq.8345) ((:c Ring.toNonAssocRing) (... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Neg.neg) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c DFunLike.coe)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8345","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.8348","is_instance":true,"is_let":false,"name":"inst✝⁷","sexp":"(:app (:c NormedRing) (:arg :explic... | {"children":[{"source":"exact","sourceEnd":1794,"sourceStart":1789,"tag":"atom"},{"children":[{"source":"neg_le.mp","sourceEnd":1804,"sourceStart":1795,"tag":"identifier"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"this","sourceEnd":1809,"sourceStart":1805,"tag":"identifier"}],"kind":"null","sourc... | [] | [{"source":"neg_le.mp this","source_end":1809,"source_start":1795,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8345","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.8348","is_instance":true,"is_let":false,"user_name":"inst✝⁷"},{"binder_role":":instance-implicit","context_index":2,... | 4 | 10 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0839dae68d31e5fe52e38e0528c520f337a0f143e4ce5942f8b3d87bbf55af39 | 91aac29e3182d6b3c4c3678978cf41612161fedf898a7d698dbf954d1556fa90 | 2e6fc3d55b7b1df91a1fc8634cb1c728413ce4ab27dbf9dad84af7bba6491252 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,047 | IsSelfAdjoint.neg_algebraMap_norm_le_self | Mathlib/Analysis/NormedSpace/Star/ContinuousFunctionalCalculus/Order.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>norm_neg</a>] | A : Type u_1
inst✝⁷ : NormedRing A
inst✝⁶ : StarRing A
inst✝⁵ : CstarRing A
inst✝⁴ : CompleteSpace A
inst✝³ : NormedAlgebra ℂ A
inst✝² : StarModule ℂ A
inst✝¹ : PartialOrder A
inst✝ : StarOrderedRing A
a : A
ha : autoParam (IsSelfAdjoint a) _auto✝
⊢ -a ≤ (algebraMap ℝ A) ‖a‖ | A : Type u_1
inst✝⁷ : NormedRing A
inst✝⁶ : StarRing A
inst✝⁵ : CstarRing A
inst✝⁴ : CompleteSpace A
inst✝³ : NormedAlgebra ℂ A
inst✝² : StarModule ℂ A
inst✝¹ : PartialOrder A
inst✝ : StarOrderedRing A
a : A
ha : autoParam (IsSelfAdjoint a) _auto✝
⊢ -a ≤ (algebraMap ℝ A) ‖-a‖ | ((:c LE.le) (:fv _uniq.8345) ((:c Preorder.toLE) (:fv _uniq.8345) ((:c PartialOrder.toPreorder) (:fv _uniq.8345) (:fv _uniq.9310))) ((:c Neg.neg) (:fv _uniq.8345) ((:c Ring.toNeg) (:fv _uniq.8345) ((:c NormedRing.toRing) (:fv _uniq.8345) (:fv _uniq.8348))) (:fv _uniq.10471)) ((:c DFunLike.coe) ((:c RingHom) (:c Real) (... | [{"name":"A","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁷","sexp":"((:c NormedRing) (:fv _uniq.8345))"},{"name":"inst✝⁶","sexp":"((:c StarRing) (:fv _uniq.8345) ((:c NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring) (:fv _uniq.8345) ((:c NonAssocRing.toNonUnitalNonAssocRing) (:fv _uniq.8345) ((:c Ring.toNonAssocRing) (... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Neg.neg) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV10)))) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8345","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.8348","is_instance":true,"is_let":false,"name":"inst✝⁷","sexp":"(:app (:c NormedRing) (:arg :explic... | {"children":[{"source":"rw","sourceEnd":1714,"sourceStart":1712,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1716,"sourceStart":1715,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":1719,"sourceStart":... | [] | [{"source":"norm_neg","source_end":1728,"source_start":1720,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8345","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.8348","is_instance":true,"is_let":false,"user_name":"inst✝⁷"},{"binder_role":":instance-implicit","context_index":2,... | 4 | 6 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3097be449a06150de0bbb05a1dcf0307ae5eaeb8101208b427c69fba8077b252 | b387f53471e5eee84a6db90628bcc8a6ea5a3e4352291954a9db3dd4572e13f9 | b4c72945a78eaa5bae9cb107b46fd1bf17ca485e4a29dab6bf5ebe94afc15dee | 0d97cfcd2e2fa6e38d3406cadd61260d29b7dd01e19604d950b18c71d9b9dc76 |
cat-searcher/leandojo-benchmark-4-random | test | 3,048 | IsSelfAdjoint.neg_algebraMap_norm_le_self | Mathlib/Analysis/NormedSpace/Star/ContinuousFunctionalCalculus/Order.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>IsSelfAdjoint.le_algebraMap_norm_self</a> (<a>IsSelfAdjoint.neg</a> ha) | A : Type u_1
inst✝⁷ : NormedRing A
inst✝⁶ : StarRing A
inst✝⁵ : CstarRing A
inst✝⁴ : CompleteSpace A
inst✝³ : NormedAlgebra ℂ A
inst✝² : StarModule ℂ A
inst✝¹ : PartialOrder A
inst✝ : StarOrderedRing A
a : A
ha : autoParam (IsSelfAdjoint a) _auto✝
⊢ -a ≤ (algebraMap ℝ A) ‖-a‖ | ((:c LE.le) (:fv _uniq.8345) ((:c Preorder.toLE) (:fv _uniq.8345) ((:c PartialOrder.toPreorder) (:fv _uniq.8345) (:fv _uniq.9310))) ((:c Neg.neg) (:fv _uniq.8345) ((:c Ring.toNeg) (:fv _uniq.8345) ((:c NormedRing.toRing) (:fv _uniq.8345) (:fv _uniq.8348))) (:fv _uniq.10471)) ((:c DFunLike.coe) ((:c RingHom) (:c Real) (... | [{"name":"A","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁷","sexp":"((:c NormedRing) (:fv _uniq.8345))"},{"name":"inst✝⁶","sexp":"((:c StarRing) (:fv _uniq.8345) ((:c NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring) (:fv _uniq.8345) ((:c NonAssocRing.toNonUnitalNonAssocRing) (:fv _uniq.8345) ((:c Ring.toNonAssocRing) (... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Neg.neg) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV10)))) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8345","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.8348","is_instance":true,"is_let":false,"name":"inst✝⁷","sexp":"(:app (:c NormedRing) (:arg :explic... | {"children":[{"source":"exact","sourceEnd":1739,"sourceStart":1734,"tag":"atom"},{"children":[{"name":"IsSelfAdjoint.le_algebraMap_norm_self","semanticRole":"global","source":"IsSelfAdjoint.le_algebraMap_norm_self","sourceEnd":1777,"sourceStart":1740,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEn... | [] | [{"source":"IsSelfAdjoint.le_algebraMap_norm_self (neg ha)","source_end":1786,"source_start":1740,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8345","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.8348","is_instance":true,"is_let":false,"user_name":"inst✝⁷"},{"binder_role":":instance-implicit","context_index":2,... | 4 | 9 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1f9f9103e50021e522f343a7c0b7e006971a5abcd648c6cd8a7869d5ad8aafc3 | 0d97cfcd2e2fa6e38d3406cadd61260d29b7dd01e19604d950b18c71d9b9dc76 | 025e2e22bd99b678a4a04edb912a34eb537cc37bd15f20d3f79afebc5d9d35b2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,049 | MeasureTheory.Measure.compProd_apply_prod | Mathlib/Probability/Kernel/MeasureCompProd.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.Measure.compProd_apply</a> (hs.prod ht), ← <a>MeasureTheory.lintegral_indicator</a> _ hs] | α : Type u_1
β : Type u_2
mα : MeasurableSpace α
mβ : MeasurableSpace β
μ : Measure α
κ η : ↥(kernel α β)
inst✝¹ : SFinite μ
inst✝ : IsSFiniteKernel κ
s : Set α
t : Set β
hs : MeasurableSet s
ht : MeasurableSet t
⊢ (μ ⊗ₘ κ) (s ×ˢ t) = ∫⁻ (a : α) in s, (κ a) t ∂μ | α : Type u_1
β : Type u_2
mα : MeasurableSpace α
mβ : MeasurableSpace β
μ : Measure α
κ η : ↥(kernel α β)
inst✝¹ : SFinite μ
inst✝ : IsSFiniteKernel κ
s : Set α
t : Set β
hs : MeasurableSet s
ht : MeasurableSet t
⊢ ∫⁻ (a : α), (κ a) (Prod.mk a ⁻¹' s ×ˢ t) ∂μ = ∫⁻ (a : α), s.indicator (fun a => (κ a) t) a ∂μ | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) ((:c Prod) (:fv _uniq.10342) (:fv _uniq.10345)) ((:c Prod.instMeasurableSpace) (:fv _uniq.10342) (:fv _uniq.10345) (:fv _uniq.10348) (:fv _uniq.10351))) ((:c Set) ((:c Prod) (:fv _uniq.10342) (:fv _uniq.10345))) (:lambda _ ((:c Set) ((:c Prod) (:fv _u... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.10342))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.10345))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.10342) (:fv _uniq.10348))"},{"name":"κ","sexp":"((:c... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10342","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10345","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":2007,"sourceStart":2005,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2009,"sourceStart":2008,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Measure... | [] | [{"source":"compProd_apply (hs.prod ht)","source_end":2036,"source_start":2009,"syntax_kind":"Lean.Parser.Term.app"},{"source":"lintegral_indicator _ hs","source_end":2066,"source_start":2042,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10342","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10345","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 10 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 784ae705fb25bc423732b0b6d029ceae0407f6d7a43d5a78a4662bd2faab0464 | b9714c5ed0c3bfabd918d6daf1f20e69cf005fcb73b6d2383663e4e57f8e0821 | 5a11dea069287bce27e1bc0aecbf502c46b58af91e3e385be592c3492327545c | 2f552c18aa36fceba8b1d3b41624b4bce9d458e47e73e3b0ccf1b60a482cb037 |
cat-searcher/leandojo-benchmark-4-random | test | 3,050 | MeasureTheory.Measure.compProd_apply_prod | Mathlib/Probability/Kernel/MeasureCompProd.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr with a | α : Type u_1
β : Type u_2
mα : MeasurableSpace α
mβ : MeasurableSpace β
μ : Measure α
κ η : ↥(kernel α β)
inst✝¹ : SFinite μ
inst✝ : IsSFiniteKernel κ
s : Set α
t : Set β
hs : MeasurableSet s
ht : MeasurableSet t
⊢ ∫⁻ (a : α), (κ a) (Prod.mk a ⁻¹' s ×ˢ t) ∂μ = ∫⁻ (a : α), s.indicator (fun a => (κ a) t) a ∂μ | case e_f.h
α : Type u_1
β : Type u_2
mα : MeasurableSpace α
mβ : MeasurableSpace β
μ : Measure α
κ η : ↥(kernel α β)
inst✝¹ : SFinite μ
inst✝ : IsSFiniteKernel κ
s : Set α
t : Set β
hs : MeasurableSet s
ht : MeasurableSet t
a : α
⊢ (κ a) (Prod.mk a ⁻¹' s ×ˢ t) = s.indicator (fun a => (κ a) t) a | ((:c Eq) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.10342) (:fv _uniq.10348) (:fv _uniq.10360) (:lambda a (:fv _uniq.10342) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.10345) (:fv _uniq.10351)) ((:c Set) (:fv _uniq.10345)) (:lambda _ ((:c Set) (:fv _uniq.10345)) (:c ENNReal)) ((:c MeasureTheory... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.10342))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.10345))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.10342) (:fv _uniq.10348))"},{"name":"κ","sexp":"((:c... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV4)) (:arg :explicit 3 (:lambda a :explicit (:fv FV0) (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10342","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10345","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"congr","sourceEnd":2075,"sourceStart":2070,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":"with","sourceEnd":2080,"sourceStart":2076,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10342","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10345","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 10 | 8 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a3e0b8df40bbe6224cbabb1ab4124973d72f9adb950cadf9a59ca825bd9fcf91 | 2f552c18aa36fceba8b1d3b41624b4bce9d458e47e73e3b0ccf1b60a482cb037 | 5011123f861f9d949fd6e0a0e9aab90e2d65630d818d13307a95737d6d05b59a | 28bc2de6cb7edb02b8a0699c69e2cb0403e1ca2ca52feb1c95e840b8bd7dfe37 |
cat-searcher/leandojo-benchmark-4-random | test | 3,051 | MeasureTheory.Measure.compProd_apply_prod | Mathlib/Probability/Kernel/MeasureCompProd.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | classical rw [<a>Set.indicator_apply</a>] split_ifs with ha <;> simp [ha] | case e_f.h
α : Type u_1
β : Type u_2
mα : MeasurableSpace α
mβ : MeasurableSpace β
μ : Measure α
κ η : ↥(kernel α β)
inst✝¹ : SFinite μ
inst✝ : IsSFiniteKernel κ
s : Set α
t : Set β
hs : MeasurableSet s
ht : MeasurableSet t
a : α
⊢ (κ a) (Prod.mk a ⁻¹' s ×ˢ t) = s.indicator (fun a => (κ a) t) a | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.10345) (:fv _uniq.10351)) ((:c Set) (:fv _uniq.10345)) (:lambda _ ((:c Set) (:fv _uniq.10345)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.10345) (:fv _uniq.10351)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv _uniq... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.10342))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.10345))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.10342) (:fv _uniq.10348))"},{"name":"κ","sexp":"((:c... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV1))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10342","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10345","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"classical","sourceEnd":2094,"sourceStart":2085,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":2099,"sourceStart":2097,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2101,"sourceStart":2100,... | [] | [{"source":"Set.indicator_apply","source_end":2120,"source_start":2101,"syntax_kind":"ident"},{"source":"ha","source_end":2154,"source_start":2152,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10342","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10345","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 10 | 9 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ffa39a7823143bdac4507c751d4eeb53bb4fd9a3a9996ddb3ce3f7e273082e1e | 28bc2de6cb7edb02b8a0699c69e2cb0403e1ca2ca52feb1c95e840b8bd7dfe37 | 153358a3692e2c33fbf0ebb70c4f7291b2d7adca954e12c3a9a771b5e13a8559 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,052 | MeasureTheory.Measure.compProd_apply_prod | Mathlib/Probability/Kernel/MeasureCompProd.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.indicator_apply</a>] | case e_f.h
α : Type u_1
β : Type u_2
mα : MeasurableSpace α
mβ : MeasurableSpace β
μ : Measure α
κ η : ↥(kernel α β)
inst✝¹ : SFinite μ
inst✝ : IsSFiniteKernel κ
s : Set α
t : Set β
hs : MeasurableSet s
ht : MeasurableSet t
a : α
⊢ (κ a) (Prod.mk a ⁻¹' s ×ˢ t) = s.indicator (fun a => (κ a) t) a | case e_f.h
α : Type u_1
β : Type u_2
mα : MeasurableSpace α
mβ : MeasurableSpace β
μ : Measure α
κ η : ↥(kernel α β)
inst✝¹ : SFinite μ
inst✝ : IsSFiniteKernel κ
s : Set α
t : Set β
hs : MeasurableSet s
ht : MeasurableSet t
a : α
⊢ (κ a) (Prod.mk a ⁻¹' s ×ˢ t) = if a ∈ s then (κ a) t else 0 | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.10345) (:fv _uniq.10351)) ((:c Set) (:fv _uniq.10345)) (:lambda _ ((:c Set) (:fv _uniq.10345)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.10345) (:fv _uniq.10351)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv _uniq... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.10342))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.10345))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.10342) (:fv _uniq.10348))"},{"name":"κ","sexp":"((:c... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV1))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10342","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10345","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":2099,"sourceStart":2097,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2101,"sourceStart":2100,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.indicator_apply"... | [] | [{"source":"Set.indicator_apply","source_end":2120,"source_start":2101,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10342","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10345","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 10 | 12 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e094a6d0a7d918c71c44744b3463acce4af63b0f5ec2846cbfb502be51e25b23 | 28bc2de6cb7edb02b8a0699c69e2cb0403e1ca2ca52feb1c95e840b8bd7dfe37 | 4f688fcc4a794627ce90f0efb42db07ce455908bfe7aaae8a0918f6a3a7bf6ff | 9c96baf744681578142c06628e6fe984045d9e5cb8ab3f6bac9c958a48bb016e |
cat-searcher/leandojo-benchmark-4-random | test | 3,053 | MeasureTheory.Measure.compProd_apply_prod | Mathlib/Probability/Kernel/MeasureCompProd.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split_ifs with ha <;> simp [ha] | case e_f.h
α : Type u_1
β : Type u_2
mα : MeasurableSpace α
mβ : MeasurableSpace β
μ : Measure α
κ η : ↥(kernel α β)
inst✝¹ : SFinite μ
inst✝ : IsSFiniteKernel κ
s : Set α
t : Set β
hs : MeasurableSet s
ht : MeasurableSet t
a : α
⊢ (κ a) (Prod.mk a ⁻¹' s ×ˢ t) = if a ∈ s then (κ a) t else 0 | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.10345) (:fv _uniq.10351)) ((:c Set) (:fv _uniq.10345)) (:lambda _ ((:c Set) (:fv _uniq.10345)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.10345) (:fv _uniq.10351)) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv _uniq... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.10342))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.10345))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.10342) (:fv _uniq.10348))"},{"name":"κ","sexp":"((:c... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV1))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10342","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10345","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"source":"split_ifs","sourceEnd":2133,"sourceStart":2124,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"with","sourceEnd":2138,"sourceStart":2134,"tag":"atom"},{"children":[{"children":[{"source":"ha","sourceEnd":2141,"sourceStart":2139,"tag":"ide... | [] | [{"source":"ha","source_end":2154,"source_start":2152,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10342","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10345","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 10 | 15 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 589b9deaddc7921cc97f5cc3fe083ef763fb13ea41c3982c4b0bd28d0d37d41f | 9c96baf744681578142c06628e6fe984045d9e5cb8ab3f6bac9c958a48bb016e | cf6a5c1bd66ce98073fa263a2ef350ca452353c61164476caad19b8cdf55e362 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,054 | Rat.neg_normalize | .lake/packages/batteries/Batteries/Data/Rat/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Rat.normalize</a>] | n : Int
d : Nat
z : d ≠ 0
⊢ -normalize n d z = normalize (-n) d z | n : Int
d : Nat
z : d ≠ 0
⊢ -{ num := n.div ↑(n.natAbs.gcd d), den := d / n.natAbs.gcd d, den_nz := ⋯, reduced := ⋯ } =
{ num := -n.div ↑(n.natAbs.gcd d), den := d / n.natAbs.gcd d, den_nz := ⋯, reduced := ⋯ } | ((:c Eq) (:c Rat) ((:c Neg.neg) (:c Rat) (:c Rat.instNeg) ((:c Rat.normalize) (:fv _uniq.22912) (:fv _uniq.22913) (:fv _uniq.22914))) ((:c Rat.normalize) ((:c Neg.neg) (:c Int) (:c Int.instNegInt) (:fv _uniq.22912)) (:fv _uniq.22913) (:fv _uniq.22914))) | [{"name":"n","sexp":"(:c Int)"},{"name":"d","sexp":"(:c Nat)"},{"name":"z","sexp":"((:c Ne) ((:c optParam) (:c Nat) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) (:fv _uniq.22913) ((:c OfNat.ofNat) ((:c optParam) (:c Nat) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) (:lit 0) (... | (:app (:c Eq) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c Rat.normalize) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :proof 2 (:proof-o... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22912","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Int)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.22913","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":explicit","context_ind... | {"children":[{"source":"simp","sourceEnd":11336,"sourceStart":11332,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11338,"sourceStart":11337,"tag":"a... | [] | [{"source":"normalize","source_end":11347,"source_start":11338,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22912","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.22913","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 56 | 4 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5de3ebaa43c4fcb941e8b724aec8cc57cc18aabd4e8292a377aa35a90f2ac68a | a2cd6e3dd82372679a0b6b9cb6e90762ea4bed946b7edde788fdbf4835370b97 | cd6ebf427afeec6b36d186e98c15244eb1335556c0a4aba710a8ace28a964871 | 8492c5987ab3075370d7e97db77a26f53aa896a6e85a9da531d9b3aec5fc17f7 |
cat-searcher/leandojo-benchmark-4-random | test | 3,055 | Rat.neg_normalize | .lake/packages/batteries/Batteries/Data/Rat/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | n : Int
d : Nat
z : d ≠ 0
⊢ -{ num := n.div ↑(n.natAbs.gcd d), den := d / n.natAbs.gcd d, den_nz := ⋯, reduced := ⋯ } =
{ num := -n.div ↑(n.natAbs.gcd d), den := d / n.natAbs.gcd d, den_nz := ⋯, reduced := ⋯ } | ((:c Eq) (:c Rat) ((:c Neg.neg) (:c Rat) (:c Rat.instNeg) ((:c Rat.mk') ((:c Int.div) (:fv _uniq.22912) ((:c Nat.cast) (:c Int) (:c instNatCastInt) ((:c Nat.gcd) ((:c Int.natAbs) (:fv _uniq.22912)) (:fv _uniq.22913)))) ((:c HDiv.hDiv) (:c Nat) (:c Nat) (:c Nat) ((:c instHDiv) (:c Nat) (:c Nat.instDiv)) (:fv _uniq.22913... | [{"name":"n","sexp":"(:c Int)"},{"name":"d","sexp":"(:c Nat)"},{"name":"z","sexp":"((:c Ne) ((:c optParam) (:c Nat) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) (:fv _uniq.22913) ((:c OfNat.ofNat) ((:c optParam) (:c Nat) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) (:lit 0) (... | (:app (:c Eq) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c Rat.mk') (:arg :explicit 0 (:app (:c Int.div) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:ap... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22912","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Int)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.22913","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":explicit","context_ind... | {"children":[{"source":"rfl","sourceEnd":11353,"sourceStart":11350,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":11353,"sourceStart":11350,"tag":"node"} | [] | [] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22912","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.22913","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 56 | 6 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a01732b63fbd5d35bda749f1b35aad570a9192035a16cbcd8acb18ae2d13af4a | 8492c5987ab3075370d7e97db77a26f53aa896a6e85a9da531d9b3aec5fc17f7 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,056 | QPF.recF_eq_of_Wequiv | Mathlib/Data/QPF/Univariate/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro h | F : Type u → Type u
q : QPF F
α : Type u
u : F α → α
x y : (P F).W
⊢ Wequiv x y → recF u x = recF u y | F : Type u → Type u
q : QPF F
α : Type u
u : F α → α
x y : (P F).W
h : Wequiv x y
⊢ recF u x = recF u y | (:forall _ ((:c QPF.Wequiv) (:fv _uniq.4493) (:fv _uniq.4499) (:fv _uniq.4568) (:fv _uniq.4569)) ((:c Eq) (:fv _uniq.4566) ((:c QPF.recF) (:fv _uniq.4493) (:fv _uniq.4499) (:fv _uniq.4566) (:fv _uniq.4567) (:fv _uniq.4568)) ((:c QPF.recF) (:fv _uniq.4493) (:fv _uniq.4499) (:fv _uniq.4566) (:fv _uniq.4567) (:fv _uniq.45... | [{"name":"F","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c QPF) (:fv _uniq.4493))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"u","sexp":"(:forall _ ((:fv _uniq.4493) (:fv _uniq.4566)) (:fv _uniq.4566))"},{"name":"x","sexp":"((:c PFunctor.W) ((:c QPF.P) (:fv _uniq.4493) (:fv _uniq.4... | (:forall _ :explicit (:app (:c QPF.Wequiv) (:arg :implicit 0) (:arg :instance 1 (:instance-of (:app (:c QPF) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:fv FV6))) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c QPF.recF) (:arg :implicit 0) (:arg :instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4493","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.4499","is_instance":true,"is_let":false,"name":"q","sexp":"(:app... | {"children":[{"source":"intro","sourceEnd":6008,"sourceStart":6003,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":6010,"sourceStart":6009,"tag":"identifier"}],"kind":"null","source":"h","sourceEnd":6010,"sourceStart":6009,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source":"int... | [{"role":"fresh_name","source":"h","source_end":6010,"source_start":6009,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4493","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4499","is_instance":true,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":3,"internal_name... | 31 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | efc2b60a3c3aff06bbaca110d3f2d87225cc8366889b99871388d10cb0ba11c7 | 8712d44320ca4439b2d85b3bed91ca0adf7593b3cb740a88f634a89e3f544f88 | 5cf42e5c5e9faf9804f4b8005e32168f3a46b38347377087a457c72b727740cb | 6cfc84be726faa6ea88651f9bf28ee8640fb41072504941773e26f1e246b350d |
cat-searcher/leandojo-benchmark-4-random | test | 3,057 | QPF.recF_eq_of_Wequiv | Mathlib/Data/QPF/Univariate/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction h with | <a>QPF.Wequiv.ind</a> a f f' _ ih => simp only [<a>QPF.recF_eq'</a>, <a>PFunctor.map_eq</a>, <a>Function.comp</a>, ih] | <a>QPF.Wequiv.abs</a> a f a' f' h => simp only [<a>QPF.recF_eq'</a>, <a>QPF.abs_map</a>, h] | <a>QPF.Wequiv.trans</a> x y z _ _ ih₁ ih₂ => exact <a>Eq.trans</a> ih₁ ih₂ | F : Type u → Type u
q : QPF F
α : Type u
u : F α → α
x y : (P F).W
h : Wequiv x y
⊢ recF u x = recF u y | ((:c Eq) (:fv _uniq.4566) ((:c QPF.recF) (:fv _uniq.4493) (:fv _uniq.4499) (:fv _uniq.4566) (:fv _uniq.4567) (:fv _uniq.4568)) ((:c QPF.recF) (:fv _uniq.4493) (:fv _uniq.4499) (:fv _uniq.4566) (:fv _uniq.4567) (:fv _uniq.4569))) | [{"name":"F","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c QPF) (:fv _uniq.4493))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"u","sexp":"(:forall _ ((:fv _uniq.4493) (:fv _uniq.4566)) (:fv _uniq.4566))"},{"name":"x","sexp":"((:c PFunctor.W) ((:c QPF.P) (:fv _uniq.4493) (:fv _uniq.4... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c QPF.recF) (: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 (:fv FV4)) (:arg :explicit 4 (:fv FV5)))) (:arg :explicit 2 (:app (:c QPF.recF) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4493","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.4499","is_instance":true,"is_let":false,"name":"q","sexp":"(:app... | {"children":[{"source":"induction","sourceEnd":6022,"sourceStart":6013,"tag":"atom"},{"children":[{"contextIndex":7,"semanticRole":"local","source":"h","sourceEnd":6024,"sourceStart":6023,"tag":"identifier"}],"kind":"null","source":"h","sourceEnd":6024,"sourceStart":6023,"tag":"node"},{"children":[],"kind":"null","sour... | [] | [{"source":"h","source_end":6024,"source_start":6023,"syntax_kind":"ident"},{"source":"ind","source_end":6037,"source_start":6034,"syntax_kind":"ident"},{"source":"recF_eq'","source_end":6072,"source_start":6064,"syntax_kind":"ident"},{"source":"PFunctor.map_eq","source_end":6089,"source_start":6074,"syntax_kind":"iden... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4493","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4499","is_instance":true,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":3,"internal_name... | 31 | 5 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dcdf0255a4459c6eeb2c4036341a5c8cc2592060b5bd24c9726275e6c38a4c38 | 6cfc84be726faa6ea88651f9bf28ee8640fb41072504941773e26f1e246b350d | d7d3df3093ee76570fe7aa4e5cccc8c6e15c17a166a70e4cecace1692102a9e1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,058 | QPF.recF_eq_of_Wequiv | Mathlib/Data/QPF/Univariate/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>QPF.recF_eq'</a>, <a>PFunctor.map_eq</a>, <a>Function.comp</a>, ih] | case ind
F : Type u → Type u
q : QPF F
α : Type u
u : F α → α
x y : (P F).W
a : (P F).A
f f' : (P F).B a → (P F).W
a✝ : ∀ (x : (P F).B a), Wequiv (f x) (f' x)
ih : ∀ (x : (P F).B a), recF u (f x) = recF u (f' x)
⊢ recF u (WType.mk a f) = recF u (WType.mk a f') | ((:c Eq) (:fv _uniq.4566) ((:c QPF.recF) (:fv _uniq.4493) (:fv _uniq.4499) (:fv _uniq.4566) (:fv _uniq.4567) ((:c WType.mk) ((:c PFunctor.A) ((:c QPF.P) (:fv _uniq.4493) (:fv _uniq.4499))) ((:c PFunctor.B) ((:c QPF.P) (:fv _uniq.4493) (:fv _uniq.4499))) (:fv _uniq.4624) (:fv _uniq.4625))) ((:c QPF.recF) (:fv _uniq.4493... | [{"name":"F","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c QPF) (:fv _uniq.4493))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"u","sexp":"(:forall _ ((:fv _uniq.4493) (:fv _uniq.4566)) (:fv _uniq.4566))"},{"name":"x","sexp":"((:c PFunctor.W) ((:c QPF.P) (:fv _uniq.4493) (:fv _uniq.4... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c QPF.recF) (: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 (:fv FV4)) (:arg :explicit 4 (:app (:c WType.mk) (:arg :implicit-type 0 (:app (:c PF... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4493","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.4499","is_instance":true,"is_let":false,"name":"q","sexp":"(:app... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":6057,"sourceStart":6053,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":6062,"sourceStart":6058,"tag":"atom"}],"kind":"nu... | [] | [{"source":"recF_eq'","source_end":6072,"source_start":6064,"syntax_kind":"ident"},{"source":"PFunctor.map_eq","source_end":6089,"source_start":6074,"syntax_kind":"ident"},{"source":"Function.comp","source_end":6104,"source_start":6091,"syntax_kind":"ident"},{"source":"ih","source_end":6108,"source_start":6106,"syntax_... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4493","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4499","is_instance":true,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":3,"internal_name... | 31 | 8 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | daa6a7b393f4f442e9b256c5207fe3fc63f5aef1179704f99739169c3f66f741 | 0ae96e500e4af602a36d632f73fd2864abcc1892f27598fb935343f1d1ed4a42 | 75c97da89accf4b4a2e2f9fc2963605429d54e8d7829e58e325728eb0eef579c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,059 | QPF.recF_eq_of_Wequiv | Mathlib/Data/QPF/Univariate/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>QPF.recF_eq'</a>, <a>QPF.abs_map</a>, h] | case abs
F : Type u → Type u
q : QPF F
α : Type u
u : F α → α
x y : (P F).W
a : (P F).A
f : (P F).B a → (P F).W
a' : (P F).A
f' : (P F).B a' → (P F).W
h : abs ⟨a, f⟩ = abs ⟨a', f'⟩
⊢ recF u (WType.mk a f) = recF u (WType.mk a' f') | ((:c Eq) (:fv _uniq.4566) ((:c QPF.recF) (:fv _uniq.4493) (:fv _uniq.4499) (:fv _uniq.4566) (:fv _uniq.4567) ((:c WType.mk) ((:c PFunctor.A) ((:c QPF.P) (:fv _uniq.4493) (:fv _uniq.4499))) ((:c PFunctor.B) ((:c QPF.P) (:fv _uniq.4493) (:fv _uniq.4499))) (:fv _uniq.5007) (:fv _uniq.5008))) ((:c QPF.recF) (:fv _uniq.4493... | [{"name":"F","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c QPF) (:fv _uniq.4493))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"u","sexp":"(:forall _ ((:fv _uniq.4493) (:fv _uniq.4566)) (:fv _uniq.4566))"},{"name":"x","sexp":"((:c PFunctor.W) ((:c QPF.P) (:fv _uniq.4493) (:fv _uniq.4... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c QPF.recF) (: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 (:fv FV4)) (:arg :explicit 4 (:app (:c WType.mk) (:arg :implicit-type 0 (:app (:c PF... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4493","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.4499","is_instance":true,"is_let":false,"name":"q","sexp":"(:app... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":6137,"sourceStart":6133,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":6142,"sourceStart":6138,"tag":"atom"}],"kind":"nu... | [] | [{"source":"recF_eq'","source_end":6152,"source_start":6144,"syntax_kind":"ident"},{"source":"abs_map","source_end":6161,"source_start":6154,"syntax_kind":"ident"},{"source":"h","source_end":6164,"source_start":6163,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4493","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4499","is_instance":true,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":3,"internal_name... | 31 | 12 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 184124760f683ef952664a4ec8043260452073754e67d3bc93911181234f9972 | df3de276ec227843dc47adf12ae3ab2c8fbc74ad9b20964f00d0ccd95a7178f4 | fd255dfa077a18fbe0f86a1dc9701d916747257cef5d4bfd603151312be897ab | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,060 | QPF.recF_eq_of_Wequiv | Mathlib/Data/QPF/Univariate/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Eq.trans</a> ih₁ ih₂ | case trans
F : Type u → Type u
q : QPF F
α : Type u
u : F α → α
x✝ y✝ x y z : (P F).W
a✝¹ : Wequiv x y
a✝ : Wequiv y z
ih₁ : recF u x = recF u y
ih₂ : recF u y = recF u z
⊢ recF u x = recF u z | ((:c Eq) (:fv _uniq.4566) ((:c QPF.recF) (:fv _uniq.4493) (:fv _uniq.4499) (:fv _uniq.4566) (:fv _uniq.4567) (:fv _uniq.5166)) ((:c QPF.recF) (:fv _uniq.4493) (:fv _uniq.4499) (:fv _uniq.4566) (:fv _uniq.4567) (:fv _uniq.5168))) | [{"name":"F","sexp":"(:forall _ (:sort (+ u 1)) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c QPF) (:fv _uniq.4493))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"u","sexp":"(:forall _ ((:fv _uniq.4493) (:fv _uniq.4566)) (:fv _uniq.4566))"},{"name":"x✝","sexp":"((:c PFunctor.W) ((:c QPF.P) (:fv _uniq.4493) (:fv _uniq.... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c QPF.recF) (: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 (:fv FV4)) (:arg :explicit 4 (:fv FV7)))) (:arg :explicit 2 (:app (:c QPF.recF) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4493","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.4499","is_instance":true,"is_let":false,"name":"q","sexp":"(:app... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":6206,"sourceStart":6201,"tag":"atom"},{"children":[{"name":"Eq.trans","semanticRole":"global","source":"Eq.trans","sourceEnd":6215,"sourceStart":6207,"tag":"identifier"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"ih₁... | [] | [{"source":"Eq.trans ih₁ ih₂","source_end":6227,"source_start":6207,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4493","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4499","is_instance":true,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":3,"internal_name... | 31 | 16 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 187f089a13df2fb05809e87d6a79b77aea9bb62e81364c279858c23ae399d7f4 | 814c2b278dc8f23f09b45dc2e136c3aef1cd36b4efa02275a3ff52e6a17594ac | ffb1b969f8b01ebb04c93729da45b14c46dcecc6e2b490104db6f157fdef5ebd | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,061 | CategoryTheory.LocalizerMorphism.id_homMap | Mathlib/CategoryTheory/Localization/HomEquiv.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using (<a>CategoryTheory.LocalizerMorphism.id</a> W₁).<a>CategoryTheory.LocalizerMorphism.homMap_apply</a> L₁ L₁ (𝟭 D₁) (<a>CategoryTheory.Iso.refl</a> _) f | C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.24763, u_1} C
inst✝⁸ : Category.{u_9, u_2} C₁
inst✝⁷ : Category.{?u.24771, u_3} C₂
inst✝⁶ : Category.{?u.24775, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{?u.24783, u_6} D₂
inst✝³ : Cat... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.24754) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.24754) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.24754) (:fv _uniq.24780))) ((:c Prefunctor.obj) (:fv _uniq.24745) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.24745) ((:c CategoryTheory.Catego... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"C₁","sexp":"(:sort (+ u_2 1))"},{"name":"C₂","sexp":"(:sort (+ u_3 1))"},{"name":"C₃","sexp":"(:sort (+ u_4 1))"},{"name":"D₁","sexp":"(:sort (+ u_5 1))"},{"name":"D₂","sexp":"(:sort (+ u_6 1))"},{"name":"D₃","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁹","sexp":"((:c Cat... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV4)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24742","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24745","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":3485,"sourceStart":3480,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"(id W₁).homMap_apply L₁ L₁ (𝟭 D₁) (Iso.refl _) f","source_end":3551,"source_start":3492,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24742","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24745","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 11 | 2 | exact | true | 1 | 29 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5f697e4d400cbddba541674604920e6ccaa0a5777862c3b32933343f88372037 | 186f9447f71782ad1f3a52bb7d5b35dbb4a08c71ad050ace12a8d236a14c5253 | ce5c215fade69b7f41d3d92863ba7bec910567197a2b96f7c43329a53010d3bc | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,062 | Complex.tsum_exp_neg_mul_int_sq | Mathlib/Analysis/SpecialFunctions/Gaussian/PoissonSummation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>MulZeroClass.mul_zero</a>, <a>MulZeroClass.zero_mul</a>, <a>add_zero</a>] using <a>Complex.tsum_exp_neg_quadratic</a> ha 0 | E : Type u_1
inst✝ : NormedAddCommGroup E
a : ℂ
ha : 0 < a.re
⊢ ∑' (n : ℤ), cexp (-↑π * a * ↑n ^ 2) = 1 / a ^ (1 / 2) * ∑' (n : ℤ), cexp (-↑π / a * ↑n ^ 2) | ((:c Eq) (:c Complex) ((:c tsum) (:c Complex) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:c Complex) ((:c NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring) (:c Complex) ((:c NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring) (:c Complex) ((:c NonUnitalCommRing.toNonUnitalNonAssocCommRing) (:c Com... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.44978))"},{"name":"a","sexp":"(:c Complex)"},{"name":"ha","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Complex.re) (:fv _uni... | (:app (:c Eq) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c tsum) (:arg :implicit-type 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Complex))))) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Complex))))) (:arg :impl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44978","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.44981","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:ar... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":6276,"sourceStart":6271,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"mul_zero","source_end":6291,"source_start":6283,"syntax_kind":"ident"},{"source":"zero_mul","source_end":6301,"source_start":6293,"syntax_kind":"ident"},{"source":"add_zero","source_end":6311,"source_start":6303,"syntax_kind":"ident"},{"source":"Complex.tsum_exp_neg_quadratic ha 0","source_end":6354,"source... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.44978","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.44981","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna... | 16 | 2 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2e8fdb437c3363ad506366f7e91972bc9fb74c0c516af8ab9537b3bb6954fb1f | ac9f23cef654cd276f74744cecac8aa0facb62bcb50d807a08c74cee00d2dc08 | 6c69118c5de0342fcc5564c23a604db7b51ab7528071731ce0b34d3375d80d97 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,063 | Nat.gcd_add_mul_right_right | Mathlib/Data/Nat/GCD/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Nat.gcd_rec</a> m (n + k * m), <a>Nat.gcd_rec</a> m n] | m n k : ℕ
⊢ m.gcd (n + k * m) = m.gcd n | ((:c Eq) (:c Nat) ((:c Nat.gcd) (:fv _uniq.315) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.316) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.317) (:fv _uniq.315)))) ((:c Nat.gcd) (:fv _uniq.315) (:fv _uniq.316))) | [{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.gcd) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.315","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.316","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":1221,"sourceStart":1217,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"gcd_rec m (n + k * m)","source_end":1244,"source_start":1223,"syntax_kind":"Lean.Parser.Term.app"},{"source":"gcd_rec m n","source_end":1257,"source_start":1246,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.315","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.316","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.3... | 7 | 2 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d52f6f150fdd98597f22f92018a579bb4ebb55e68d1ec8e13cefcdfbaa156b72 | 948ec822af395f21cf6ef3ba8351337144b60bd292d0db24c38b045a4031f8ea | f897d3fa559f7b5342b3f8a447a4baeb187da19527c258615266dd1e8d771383 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,064 | affineSpan_singleton_union_vadd_eq_top_of_span_eq_top | Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert <a>AffineSubspace.ext_of_direction_eq</a> _ ⟨p, <a>mem_affineSpan</a> k (<a>Set.mem_union_left</a> _ (<a>Set.mem_singleton</a> _)), <a>AffineSubspace.mem_top</a> k V p⟩ | k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
s : Set V
p : P
h : Submodule.span k (range Subtype.val) = ⊤
⊢ affineSpan k ({p} ∪ (fun v => v +ᵥ p) '' s) = ⊤ | case convert_1
k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
s : Set V
p : P
h : Submodule.span k (range Subtype.val) = ⊤
⊢ (affineSpan k ({p} ∪ (fun v => v +ᵥ p) '' s)).direction = ⊤.direction | ((:c Eq) ((:c AffineSubspace) (:fv _uniq.323525) (:fv _uniq.323528) (:fv _uniq.323531) (:fv _uniq.323534) (:fv _uniq.323537) (:fv _uniq.324124) (:fv _uniq.324213)) ((:c affineSpan) (:fv _uniq.323525) (:fv _uniq.323528) (:fv _uniq.323531) (:fv _uniq.323534) (:fv _uniq.323537) (:fv _uniq.324124) (:fv _uniq.324213) ((:c U... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.323525))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.323528))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.323525) (:fv _uniq.323528)... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c AffineSubspace) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Ring) (: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.323525","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.323528","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"convert","sourceEnd":59053,"sourceStart":59046,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"AffineSubspace.ext_of_direction_eq","semanticRole":"global","source":"ext_of_direction_eq","sourceEnd":... | [] | [{"source":"ext_of_direction_eq _\n ⟨p, mem_affineSpan k (Set.mem_union_left _ (Set.mem_singleton _)), mem_top k V p⟩","source_end":59167,"source_start":59054,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.323525","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.323528","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 308 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a78446d0b54434da167f40921e460c6a827abdefa10cace360f613483e0f38f5 | 972106336fb228d125d6c9a97737da8d733e90995feb58a8f56160e863da1a35 | 9f791859e227467731fa295b7ad5683c13eae8d05878ae719834f077aa208773 | 312af60c0df9c65dcf30c4266dfde59f5ddd9a261d7db88a9e8cb1b8798695a0 |
cat-searcher/leandojo-benchmark-4-random | test | 3,065 | affineSpan_singleton_union_vadd_eq_top_of_span_eq_top | Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>direction_affineSpan</a>, <a>AffineSubspace.direction_top</a>, <a>vectorSpan_eq_span_vsub_set_right</a> k (<a>Set.mem_union_left</a> _ (<a>Set.mem_singleton</a> _) : p ∈ _), <a>eq_top_iff</a>, ← h] | case convert_1
k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
s : Set V
p : P
h : Submodule.span k (range Subtype.val) = ⊤
⊢ (affineSpan k ({p} ∪ (fun v => v +ᵥ p) '' s)).direction = ⊤.direction | case convert_1
k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
s : Set V
p : P
h : Submodule.span k (range Subtype.val) = ⊤
⊢ Submodule.span k (range Subtype.val) ≤ Submodule.span k ((fun x => x -ᵥ p) '' ({p} ∪ (fun v => v +ᵥ p) '' ... | ((:c Eq) ((:c Submodule) (:fv _uniq.323525) (:fv _uniq.323528) ((:c Ring.toSemiring) (:fv _uniq.323525) (:fv _uniq.323534)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.323528) (:fv _uniq.323537)) (:fv _uniq.324124)) ((:c AffineSubspace.direction) (:fv _uniq.323525) (:fv _uniq.323528) (:fv _uniq.323531) (:fv _uniq.323... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.323525))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.323528))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.323525) (:fv _uniq.323528)... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.323525","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.323528","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":59172,"sourceStart":59170,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":59174,"sourceStart":59173,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"direction_affine... | [] | [{"source":"direction_affineSpan","source_end":59194,"source_start":59174,"syntax_kind":"ident"},{"source":"direction_top","source_end":59209,"source_start":59196,"syntax_kind":"ident"},{"source":"vectorSpan_eq_span_vsub_set_right k (Set.mem_union_left _ (Set.mem_singleton _) : p ∈ _)","source_end":59305,"source_start"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.323525","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.323528","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 308 | 5 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d85a74b03150a6b1703812bb5443d3cfe7dc5d094eeb5160150d98c94422b272 | 312af60c0df9c65dcf30c4266dfde59f5ddd9a261d7db88a9e8cb1b8798695a0 | 5a66e94977a8dfe5e3c548b10b8c0ba6b36cd7142e7fa91c90dcc11ea27710f2 | fbb39e5af77af11725d4f173ddb854fc7fb802eb12a62a2354d00741fc490168 |
cat-searcher/leandojo-benchmark-4-random | test | 3,066 | affineSpan_singleton_union_vadd_eq_top_of_span_eq_top | Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Submodule.span_mono</a> | case convert_1
k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
s : Set V
p : P
h : Submodule.span k (range Subtype.val) = ⊤
⊢ Submodule.span k (range Subtype.val) ≤ Submodule.span k ((fun x => x -ᵥ p) '' ({p} ∪ (fun v => v +ᵥ p) '' ... | case convert_1.h
k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
s : Set V
p : P
h : Submodule.span k (range Subtype.val) = ⊤
⊢ range Subtype.val ⊆ (fun x => x -ᵥ p) '' ({p} ∪ (fun v => v +ᵥ p) '' s) | ((:c LE.le) ((:c Submodule) (:fv _uniq.323525) (:fv _uniq.323528) ((:c Ring.toSemiring) (:fv _uniq.323525) (:fv _uniq.323534)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.323528) (:fv _uniq.323537)) (:fv _uniq.324124)) ((:c Preorder.toLE) ((:c Submodule) (:fv _uniq.323525) (:fv _uniq.323528) ((:c Ring.toSemiring) (:f... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.323525))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.323528))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.323525) (:fv _uniq.323528)... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.323525","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.323528","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"apply","sourceEnd":59337,"sourceStart":59332,"tag":"atom"},{"name":"Submodule.span_mono","semanticRole":"global","source":"Submodule.span_mono","sourceEnd":59357,"sourceStart":59338,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Submodule.span_mono","sourceEnd":59357,"sou... | [] | [{"source":"Submodule.span_mono","source_end":59357,"source_start":59338,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.323525","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.323528","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 308 | 12 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6e710fa47ccad729d6f9b16947fd4932d29bb6867ac205ae7653c6b3a58b8378 | fbb39e5af77af11725d4f173ddb854fc7fb802eb12a62a2354d00741fc490168 | 532b2d1d60cd573b3d5957858ac9cb5c661d7f432840bf84c4a703a9c51b0dcc | 3ed931710b1f346af568a0e3dce9bd6693b016987cdf2e258cbf5cc71e3dd93c |
cat-searcher/leandojo-benchmark-4-random | test | 3,067 | affineSpan_singleton_union_vadd_eq_top_of_span_eq_top | Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro v ⟨v', rfl⟩ | case convert_1.h
k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
s : Set V
p : P
h : Submodule.span k (range Subtype.val) = ⊤
⊢ range Subtype.val ⊆ (fun x => x -ᵥ p) '' ({p} ∪ (fun v => v +ᵥ p) '' s) | case convert_1.h.intro
k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
s : Set V
p : P
h : Submodule.span k (range Subtype.val) = ⊤
v' : { x // x ∈ s }
⊢ ↑v' ∈ (fun x => x -ᵥ p) '' ({p} ∪ (fun v => v +ᵥ p) '' s) | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.323528)) ((:c Set.instHasSubset) (:fv _uniq.323528)) ((:c Set.range) (:fv _uniq.323528) ((:c Subtype) (:fv _uniq.323528) (:lambda x (:fv _uniq.323528) ((:c Membership.mem) (:fv _uniq.323528) ((:c Set) (:fv _uniq.323528)) ((:c Set.instMembership) (:fv _uniq.323528)) 0 (:fv _un... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.323525))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.323528))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.323525) (:fv _uniq.323528)... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 2 (:app (:c Set.range) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.323525","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.323528","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rintro","sourceEnd":59366,"sourceStart":59360,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"v","sourceEnd":59368,"sourceStart":59367,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"v","sourceEnd":59368,"sourceStart":59367,"... | [{"role":"fresh_name","source":"v'","source_end":59374,"source_start":59372,"syntax_kind":"ident"}] | [{"source":"⟨v', rfl⟩","source_end":59382,"source_start":59369,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.323525","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.323528","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 308 | 13 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9fd7d8c7a5fff7a0a091846d539683808831fd6ddf3365feec83336320fd2e79 | 3ed931710b1f346af568a0e3dce9bd6693b016987cdf2e258cbf5cc71e3dd93c | b526f0f17c70fc2a39bdbe9c077cd22c346936c80e36b6c53e1335041074c0f5 | 86374a3bc5ea32888d52780c882229df0741f595c80b43149c7ce16549f80c6c |
cat-searcher/leandojo-benchmark-4-random | test | 3,068 | affineSpan_singleton_union_vadd_eq_top_of_span_eq_top | Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | use (v' : V) +ᵥ p | case convert_1.h.intro
k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
s : Set V
p : P
h : Submodule.span k (range Subtype.val) = ⊤
v' : { x // x ∈ s }
⊢ ↑v' ∈ (fun x => x -ᵥ p) '' ({p} ∪ (fun v => v +ᵥ p) '' s) | case h
k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
s : Set V
p : P
h : Submodule.span k (range Subtype.val) = ⊤
v' : { x // x ∈ s }
⊢ ↑v' +ᵥ p ∈ {p} ∪ (fun v => v +ᵥ p) '' s ∧ (fun x => x -ᵥ p) (↑v' +ᵥ p) = ↑v' | ((:c Membership.mem) (:fv _uniq.323528) ((:c Set) (:fv _uniq.323528)) ((:c Set.instMembership) (:fv _uniq.323528)) ((:c Subtype.val) (:fv _uniq.323528) (:lambda x (:fv _uniq.323528) ((:c Membership.mem) (:fv _uniq.323528) ((:c Set) (:fv _uniq.323528)) ((:c Set.instMembership) (:fv _uniq.323528)) 0 (:fv _uniq.325803))) ... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.323525))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.323528))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.323525) (:fv _uniq.323528)... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:app (:c Subtype.val) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.323525","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.323528","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"use","sourceEnd":59388,"sourceStart":59385,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":59390,"sourceStart":59389,"tag":"atom"},{"contextIndex":12,"sem... | [] | [{"source":"(v' : V) +ᵥ p","source_end":59404,"source_start":59389,"syntax_kind":"«term_+ᵥ_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.323525","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.323528","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 308 | 14 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0c0c56814f9797dce4c1c50ebe945e3ccf46b729a24a2084c2cd5343997366f6 | 86374a3bc5ea32888d52780c882229df0741f595c80b43149c7ce16549f80c6c | 50c80d6426ffb954d5f90cd700fea400e5a546c10a9460d20040e8dd00ecd5d4 | ac75045bc58c88094b2824f7afae780b29cc9b6553eab705bdd60448db67822a |
cat-searcher/leandojo-benchmark-4-random | test | 3,069 | affineSpan_singleton_union_vadd_eq_top_of_span_eq_top | Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case h
k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
ι : Type u_4
s : Set V
p : P
h : Submodule.span k (range Subtype.val) = ⊤
v' : { x // x ∈ s }
⊢ ↑v' +ᵥ p ∈ {p} ∪ (fun v => v +ᵥ p) '' s ∧ (fun x => x -ᵥ p) (↑v' +ᵥ p) = ↑v' | ((:c And) ((:c Membership.mem) (:fv _uniq.323531) ((:c Set) (:fv _uniq.323531)) ((:c Set.instMembership) (:fv _uniq.323531)) ((:c HVAdd.hVAdd) (:fv _uniq.323528) (:fv _uniq.323531) (:fv _uniq.323531) ((:c instHVAdd) (:fv _uniq.323528) (:fv _uniq.323531) ((:c AddAction.toVAdd) (:fv _uniq.323528) (:fv _uniq.323531) ((:c ... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.323525))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.323528))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.323525) (:fv _uniq.323528)... | (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.323525","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.323528","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":59411,"sourceStart":59407,"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.323525","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.323528","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 308 | 15 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 08802727e190875e276e89c20ea689373c91d26700534cefd113270163c8edeb | ac75045bc58c88094b2824f7afae780b29cc9b6553eab705bdd60448db67822a | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,070 | MeasureTheory.pdf.lintegral_eq_measure_univ | Mathlib/Probability/Density.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>MeasureTheory.setLIntegral_univ</a>, ← <a>MeasureTheory.map_eq_setLIntegral_pdf</a> X ℙ μ <a>MeasurableSet.univ</a>, <a>MeasureTheory.Measure.map_apply_of_aemeasurable</a> (<a>MeasureTheory.HasPDF.aemeasurable</a> X ℙ μ) <a>MeasurableSet.univ</a>, <a>Set.preimage_univ</a>] | Ω : Type u_1
E : Type u_2
inst✝¹ : MeasurableSpace E
m : MeasurableSpace Ω
ℙ : Measure Ω
μ : Measure E
X : Ω → E
inst✝ : HasPDF X ℙ μ
⊢ ∫⁻ (x : E), pdf X ℙ μ x ∂μ = ℙ Set.univ | ((:c Eq) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.8225) (:fv _uniq.8228) (:fv _uniq.8249) (:lambda x (:fv _uniq.8225) ((:c MeasureTheory.pdf) (:fv _uniq.8222) (:fv _uniq.8225) (:fv _uniq.8228) (:fv _uniq.8231) (:fv _uniq.8420) (:fv _uniq.8240) (:fv _uniq.8249) 0))) ((:c DFunLike.coe) ((:c MeasureTheory.Mea... | [{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.8225))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.8222))"},{"name":"ℙ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.8222) (:fv _uniq.8231))"},{"name":"μ","sexp":"((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:lambda x :explicit (:fv FV1) (:app (:c MeasureTheory.pdf) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8222","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.8225","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":10288,"sourceStart":10286,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10290,"sourceStart":10289,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"setLIntegral_univ","source_end":10311,"source_start":10294,"syntax_kind":"ident"},{"source":"map_eq_setLIntegral_pdf X ℙ μ MeasurableSet.univ","source_end":10368,"source_start":10317,"syntax_kind":"Lean.Parser.Term.app"},{"source":"map_apply_of_aemeasurable (HasPDF.aemeasurable X ℙ μ) MeasurableSet.univ","s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8222","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.8225","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 50 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 323e95156dd46da1e69dd3d9df625e22c15eb2b08698334aa7f0987dfa8463dc | 07984b02eb0ea89df9d7d6773ad909df9b42c7d417c8e87ecb8ffdda1cd278a7 | c4cb458e70aa407e81982e0629a79b72824c564b7465501fd4fea402db4df4bf | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,071 | CochainComplex.HomComplex.Cochain.id_comp | Mathlib/Algebra/Homology/HomotopyCategory/HomComplex.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext p q hpq | C : Type u
inst✝³ : Category.{v, u} C
inst✝² : Preadditive C
R : Type u_1
inst✝¹ : Ring R
inst✝ : Linear R C
F G K L : CochainComplex C ℤ
n✝ m n : ℤ
z₂ : Cochain F G n
⊢ (ofHom (𝟙 F)).comp z₂ ⋯ = z₂ | case h
C : Type u
inst✝³ : Category.{v, u} C
inst✝² : Preadditive C
R : Type u_1
inst✝¹ : Ring R
inst✝ : Linear R C
F G K L : CochainComplex C ℤ
n✝ m n : ℤ
z₂ : Cochain F G n
p q : ℤ
hpq : p + n = q
⊢ ((ofHom (𝟙 F)).comp z₂ ⋯).v p q hpq = z₂.v p q hpq | ((:c Eq) ((:c CochainComplex.HomComplex.Cochain) (:fv _uniq.97877) (:fv _uniq.97880) (:fv _uniq.97895) (:fv _uniq.98204) (:fv _uniq.98222) (:fv _uniq.98663)) ((:c CochainComplex.HomComplex.Cochain.comp) (:fv _uniq.97877) (:fv _uniq.97880) (:fv _uniq.97895) (:fv _uniq.98204) (:fv _uniq.98204) (:fv _uniq.98222) ((:c OfNa... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.97877))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Preadditive) (:fv _uniq.97877) (:fv _uniq.97880))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.97898))"},{"name":"in... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CochainComplex.HomComplex.Cochain) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c CategoryTheory.Preadditive) (:arg :explicit 0 (:fv FV0)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.97877","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.97880","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"ext","sourceEnd":14033,"sourceStart":14030,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"p","sourceEnd":14035,"sourceStart":14034,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"p","sourceEnd":14035,"sourceStart":14034,"tag... | [{"role":"fresh_name","source":"p","source_end":14035,"source_start":14034,"syntax_kind":"ident"},{"role":"fresh_name","source":"q","source_end":14037,"source_start":14036,"syntax_kind":"ident"},{"role":"fresh_name","source":"hpq","source_end":14041,"source_start":14038,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.97877","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.97880","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":... | 63 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f30f86be1ae1d723c2a8ad803e022fb04605c5f896d15829e4770240525441ab | caac9b17277676a2f84978d91e4f0f59356a0060b787ecc6a7246210bd208a7d | 4b3e40fb12ab8bc2c1c809554097506a3191d9a2fe59a24ed76ccbb3c2eface9 | 07cde1a68a50cea926373e43c12385c9e23a16373260d8c86b047d2550fa9383 |
cat-searcher/leandojo-benchmark-4-random | test | 3,072 | CochainComplex.HomComplex.Cochain.id_comp | Mathlib/Algebra/Homology/HomotopyCategory/HomComplex.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>CochainComplex.HomComplex.Cochain.zero_cochain_comp_v</a>, <a>CochainComplex.HomComplex.Cochain.ofHom_v</a>, <a>HomologicalComplex.id_f</a>, <a>CategoryTheory.Category.id_comp</a>] | case h
C : Type u
inst✝³ : Category.{v, u} C
inst✝² : Preadditive C
R : Type u_1
inst✝¹ : Ring R
inst✝ : Linear R C
F G K L : CochainComplex C ℤ
n✝ m n : ℤ
z₂ : Cochain F G n
p q : ℤ
hpq : p + n = q
⊢ ((ofHom (𝟙 F)).comp z₂ ⋯).v p q hpq = z₂.v p q hpq | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.97877) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.97877) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.97877) (:fv _uniq.97880))) ((:c HomologicalComplex.X) (:c Int) (:fv _uniq.97877) (:fv _uniq.97880) ((:c CategoryTheory.Preadditive.preadditiveHasZeroMorphi... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.97877))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Preadditive) (:fv _uniq.97877) (:fv _uniq.97880))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.97898))"},{"name":"in... | (: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 HomologicalComplex.X) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.97877","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.97880","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"simp","sourceEnd":14048,"sourceStart":14044,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":14053,"sourceStart":14049,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":140... | [] | [{"source":"zero_cochain_comp_v","source_end":14074,"source_start":14055,"syntax_kind":"ident"},{"source":"ofHom_v","source_end":14083,"source_start":14076,"syntax_kind":"ident"},{"source":"HomologicalComplex.id_f","source_end":14108,"source_start":14085,"syntax_kind":"ident"},{"source":"id_comp","source_end":14117,"so... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.97877","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.97880","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":... | 63 | 5 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 189fef730d732f434dda739b3c0e1068df1c84d635e1b178a62d0487dd1f6000 | 07cde1a68a50cea926373e43c12385c9e23a16373260d8c86b047d2550fa9383 | ef5e1411dba8b2815b91629f3ecd1aba7b201b41d2b18a3161a7ededceeba015 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,073 | Finset.val_eq_singleton_iff | Mathlib/Data/Finset/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Finset.val_inj</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
s✝ : Finset α
a✝ b a : α
s : Finset α
⊢ s.val = {a} ↔ s = {a} | α : Type u_1
β : Type u_2
γ : Type u_3
s✝ : Finset α
a✝ b a : α
s : Finset α
⊢ s.val = {a} ↔ s.val = {a}.val | ((:c Iff) ((:c Eq) ((:c Multiset) (:fv _uniq.27760)) ((:c Finset.val) (:fv _uniq.27760) (:fv _uniq.27941)) ((:c Singleton.singleton) (:fv _uniq.27760) ((:c Multiset) (:fv _uniq.27760)) ((:c Multiset.instSingleton) (:fv _uniq.27760)) (:fv _uniq.27940))) ((:c Eq) ((:c Finset) (:fv _uniq.27760)) (:fv _uniq.27941) ((:c Sin... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"s✝","sexp":"((:c Finset) (:fv _uniq.27760))"},{"name":"a✝","sexp":"(:fv _uniq.27760)"},{"name":"b","sexp":"(:fv _uniq.27760)"},{"name":"a","sexp":"(:fv _uniq.27760)"},{"name":"s","sexp":"((:... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Finset.val) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV8)))) (:arg :explicit 2 (:app (:c Singleton.singleton) (:arg :implicit-type 0 (:fv FV0)) (:arg :impl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27760","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27763","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":26272,"sourceStart":26270,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":26274,"sourceStart":26273,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":26277,"sourceSt... | [] | [{"source":"val_inj","source_end":26285,"source_start":26278,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27760","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27763","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 243 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e30e5d2dcf9d1e87c4233164bd995447900ac56a0e6118b2848265f6f433b255 | fc101c02cbb9b0df410197b03f1a4b49ff15633596c7eecc649e7a34abed54cb | cb236a8ca25989460a1ea30bd2b628beb2a85570d204d9c9479c76de7340d94d | 0c9d78832e60f526761761b57d67444d0b9938b9913bcb94d109629154728256 |
cat-searcher/leandojo-benchmark-4-random | test | 3,074 | Finset.val_eq_singleton_iff | Mathlib/Data/Finset/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | α : Type u_1
β : Type u_2
γ : Type u_3
s✝ : Finset α
a✝ b a : α
s : Finset α
⊢ s.val = {a} ↔ s.val = {a}.val | ((:c Iff) ((:c Eq) ((:c Multiset) (:fv _uniq.27760)) ((:c Finset.val) (:fv _uniq.27760) (:fv _uniq.27941)) ((:c Singleton.singleton) (:fv _uniq.27760) ((:c Multiset) (:fv _uniq.27760)) ((:c Multiset.instSingleton) (:fv _uniq.27760)) (:fv _uniq.27940))) ((:c Eq) ((:c Multiset) (:fv _uniq.27760)) ((:c Finset.val) (:fv _u... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"s✝","sexp":"((:c Finset) (:fv _uniq.27760))"},{"name":"a✝","sexp":"(:fv _uniq.27760)"},{"name":"b","sexp":"(:fv _uniq.27760)"},{"name":"a","sexp":"(:fv _uniq.27760)"},{"name":"s","sexp":"((:... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Finset.val) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV8)))) (:arg :explicit 2 (:app (:c Singleton.singleton) (:arg :implicit-type 0 (:fv FV0)) (:arg :impl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27760","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27763","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rfl","sourceEnd":26292,"sourceStart":26289,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":26292,"sourceStart":26289,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27760","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27763","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 243 | 7 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 69efee64619a05f089a9ae3e76493635eeb101f4eebb797a8bb787d8b9d19198 | 0c9d78832e60f526761761b57d67444d0b9938b9913bcb94d109629154728256 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,075 | BooleanAlgebra.le_iff_atom_le_imp | Mathlib/Order/Atoms.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : x ⊓ yᶜ = ⊥ := <a>of_not_not</a> fun hbot => have ⟨a, ha, hle⟩ := (<a>IsAtomic.eq_bot_or_exists_atom_le</a> _).<a>Or.resolve_left</a> hbot have ⟨hx, hy'⟩ := <a>le_inf_iff</a>.1 hle have hy := h a ha hx have : a ≤ y ⊓ yᶜ := <a>le_inf_iff</a>.2 ⟨hy, hy'⟩ ha.1 (by simpa using this) | ι : Sort u_1
α✝ : Type u_2
β : Type u_3
inst✝² : PartialOrder α✝
α : Type u_4
inst✝¹ : BooleanAlgebra α
inst✝ : IsAtomic α
x y : α
h : ∀ (a : α), IsAtom a → a ≤ x → a ≤ y
⊢ x ≤ y | ι : Sort u_1
α✝ : Type u_2
β : Type u_3
inst✝² : PartialOrder α✝
α : Type u_4
inst✝¹ : BooleanAlgebra α
inst✝ : IsAtomic α
x y : α
h : ∀ (a : α), IsAtom a → a ≤ x → a ≤ y
this : x ⊓ yᶜ = ⊥
⊢ x ≤ y | ((:c LE.le) (:fv _uniq.20522) ((:c Preorder.toLE) (:fv _uniq.20522) ((:c PartialOrder.toPreorder) (:fv _uniq.20522) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.20522) ((:c Lattice.toSemilatticeInf) (:fv _uniq.20522) ((:c GeneralizedCoheytingAlgebra.toLattice) (:fv _uniq.20522) ((:c CoheytingAlgebra.toGeneralizedCohe... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α✝","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c PartialOrder) (:fv _uniq.20039))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c BooleanAlgebra) (:fv _uniq.20522))"},{"name":"inst✝","sexp":"((:c IsA... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV9))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20036","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20039","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"have","sourceEnd":14055,"sourceStart":14051,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":14056,"sourceStart":14056,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":14056,"sourceStart":14056,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"x ⊓ yᶜ = ⊥","source_end":14074,"source_start":14058,"syntax_kind":"«term_=_»"},{"source":"of_not_not fun hbot =>\n have ⟨a, ha, hle⟩ := (eq_bot_or_exists_atom_le _).resolve_left hbot\n have ⟨hx, hy'⟩ := le_inf_iff.1 hle\n have hy := h a ha hx\n have : a ≤ y ⊓ yᶜ := le_inf_iff.2 ⟨hy, hy'⟩\n ha... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20036","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20039","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 133 | 5 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b9dbf93362fe3b4d1c4e3e6b88f69445b2051018d0e45c470f6f16b8d726ab53 | 1bc463028dd41fae69c64c968b2147cc785ef00f96f6cb5d80f316d8ba82666b | 5b8e0ae8efc5d95afa43cd2d4080e5d17c7193e6f32659f243e60cf0aad3abfe | 6d525cdc7213eaaaa0b658b95b3c59202bbd8af892adaca9f123181a6ea88256 |
cat-searcher/leandojo-benchmark-4-random | test | 3,076 | BooleanAlgebra.le_iff_atom_le_imp | Mathlib/Order/Atoms.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>eq_compl_iff_isCompl</a>.1 (by simp)).<a>IsCompl.inf_right_eq_bot_iff</a>.1 this | ι : Sort u_1
α✝ : Type u_2
β : Type u_3
inst✝² : PartialOrder α✝
α : Type u_4
inst✝¹ : BooleanAlgebra α
inst✝ : IsAtomic α
x y : α
h : ∀ (a : α), IsAtom a → a ≤ x → a ≤ y
this : x ⊓ yᶜ = ⊥
⊢ x ≤ y | ((:c LE.le) (:fv _uniq.20522) ((:c Preorder.toLE) (:fv _uniq.20522) ((:c PartialOrder.toPreorder) (:fv _uniq.20522) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.20522) ((:c Lattice.toSemilatticeInf) (:fv _uniq.20522) ((:c GeneralizedCoheytingAlgebra.toLattice) (:fv _uniq.20522) ((:c CoheytingAlgebra.toGeneralizedCohe... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α✝","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c PartialOrder) (:fv _uniq.20039))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c BooleanAlgebra) (:fv _uniq.20522))"},{"name":"inst✝","sexp":"((:c IsA... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV9))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20036","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20039","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"exact","sourceEnd":14341,"sourceStart":14336,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"(","sourceEnd":14343,"sourceStart":14342,"tag":"atom"},{"children":[{"children":[{"name":"eq_compl_iff_isCompl","semanticRole":"global","source":"eq_compl_iff_isCompl","sourc... | [] | [{"source":"(eq_compl_iff_isCompl.1 (by simp)).inf_right_eq_bot_iff.1 this","source_end":14404,"source_start":14342,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20036","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20039","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 133 | 11 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6b10ca7dcdafb42214c9fb418520fbb2cf9fa5c68beb4d0d44340c3f1b04e54e | 6d525cdc7213eaaaa0b658b95b3c59202bbd8af892adaca9f123181a6ea88256 | ee54c2c394a4c7a6299174934fabfbef361980ae073b834c7bd007120138d782 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,077 | BooleanAlgebra.le_iff_atom_le_imp | Mathlib/Order/Atoms.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using this | ι : Sort u_1
α✝ : Type u_2
β : Type u_3
inst✝² : PartialOrder α✝
α : Type u_4
inst✝¹ : BooleanAlgebra α
inst✝ : IsAtomic α
x y : α
h : ∀ (a : α), IsAtom a → a ≤ x → a ≤ y
hbot : ¬x ⊓ yᶜ = ⊥
a : α
ha : IsAtom a
hle : a ≤ x ⊓ yᶜ
hx : a ≤ x
hy' : a ≤ yᶜ
hy : a ≤ y
this : a ≤ y ⊓ yᶜ
⊢ a = ⊥ | ((:c Eq) (:fv _uniq.20522) (:fv _uniq.21199) ((:c Bot.bot) (:fv _uniq.20522) ((:c OrderBot.toBot) (:fv _uniq.20522) ((:c Preorder.toLE) (:fv _uniq.20522) ((:c PartialOrder.toPreorder) (:fv _uniq.20522) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.20522) ((:c Lattice.toSemilatticeInf) (:fv _uniq.20522) ((:c Generalize... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α✝","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c PartialOrder) (:fv _uniq.20039))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c BooleanAlgebra) (:fv _uniq.20522))"},{"name":"inst✝","sexp":"((:c IsA... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:fv FV12)) (:arg :explicit 2 (:app (:c Bot.bot) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Bot) (:arg :explicit 0 (:fv FV5)))))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20036","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20039","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":14321,"sourceStart":14316,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"this","source_end":14332,"source_start":14328,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20036","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20039","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 133 | 8 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 37251a023eac8b09c7557d040bdaa8f38b420a14afd5d5bb6d4f9e82f53fb661 | 11fa0c2df97430f8fd562a18e13ac869e20a7552fcda290875b3040cf9ef0f92 | 0b3921c44845605e252e1bd356fd2f4a7a040ada5f0a7969881a98444ae0243c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,078 | BooleanAlgebra.le_iff_atom_le_imp | Mathlib/Order/Atoms.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | ι : Sort u_1
α✝ : Type u_2
β : Type u_3
inst✝² : PartialOrder α✝
α : Type u_4
inst✝¹ : BooleanAlgebra α
inst✝ : IsAtomic α
x y : α
h : ∀ (a : α), IsAtom a → a ≤ x → a ≤ y
this : x ⊓ yᶜ = ⊥
⊢ y = yᶜᶜ | ((:c Eq) (:fv _uniq.20522) (:fv _uniq.20526) ((:c HasCompl.compl) (:fv _uniq.20522) ((:c BooleanAlgebra.toHasCompl) (:fv _uniq.20522) (:fv _uniq.20523)) ((:c HasCompl.compl) (:fv _uniq.20522) ((:c BooleanAlgebra.toHasCompl) (:fv _uniq.20522) (:fv _uniq.20523)) (:fv _uniq.20526)))) | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α✝","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c PartialOrder) (:fv _uniq.20039))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹","sexp":"((:c BooleanAlgebra) (:fv _uniq.20522))"},{"name":"inst✝","sexp":"((:c IsA... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:fv FV9)) (:arg :explicit 2 (:app (:c HasCompl.compl) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c HasCompl) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c HasCompl.compl) (:arg :implicit-type 0 (:fv FV5)) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20036","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20039","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":14374,"sourceStart":14370,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","sour... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20036","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20039","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 133 | 14 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 23ede0c7f8bdcd799880dd919bed484983cefb15d92ac150eab0b9fc1467db95 | 6bfd9315ff46de9333ea656927e6901e0be16bb123fa5b9d23bf0bcc026c2050 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,079 | Zsqrtd.dmuld | Mathlib/NumberTheory/Zsqrtd/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext <;> simp | d : ℤ
⊢ sqrtd * sqrtd = ↑d | ((:c Eq) ((:c Zsqrtd) (:fv _uniq.38806)) ((:c HMul.hMul) ((:c Zsqrtd) (:fv _uniq.38806)) ((:c Zsqrtd) (:fv _uniq.38806)) ((:c Zsqrtd) (:fv _uniq.38806)) ((:c instHMul) ((:c Zsqrtd) (:fv _uniq.38806)) ((:c Zsqrtd.instMul) (:fv _uniq.38806))) ((:c Zsqrtd.sqrtd) (:fv _uniq.38806)) ((:c Zsqrtd.sqrtd) (:fv _uniq.38806))) ((... | [{"name":"d","sexp":"(:c Int)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Zsqrtd) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Zsqrtd) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Zsqrtd) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 2 (:app (:c Zsqrtd) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38806","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Int)"}] | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"ext","sourceEnd":8540,"sourceStart":8537,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":8540,"sourceStart... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38806","is_instance":false,"is_let":false,"user_name":"d"}] | 110 | 2 | exact | true | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 93979324dc0f825d0a47358864afb82bdd38b452c68706d610cd0827863ae8b1 | 6e4e4c873a641d7826af67060fd10a5208a94019abeb9150fcd0c37316e802de | 713034734afd1314a043e8a1a1465e1d87063abb19f50189203b0e64690a9a31 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,080 | round_neg_two_inv | Mathlib/Algebra/Order/Floor.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>round_eq</a>, ← <a>one_div</a>, <a>add_left_neg</a>, <a>Int.floor_zero</a>] | F : Type u_1
α : Type u_2
β : Type u_3
inst✝¹ : LinearOrderedField α
inst✝ : FloorRing α
⊢ round (-2⁻¹) = 0 | ((:c Eq) (:c Int) ((:c round) (:fv _uniq.301829) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.301829) ((:c LinearOrderedField.toLinearOrderedCommRing) (:fv _uniq.301829) (:fv _uniq.301835))) (:fv _uniq.301853) ((:c Neg.neg) (:fv _uniq.301829) ((:c Ring.toNeg) (:fv _uniq.301829) ((:c StrictOrderedRing.toRi... | [{"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 LinearOrderedField) (:fv _uniq.301829))"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.301829) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.301829) (... | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c round) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c FloorRing) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.301826","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.301829","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":57645,"sourceStart":57641,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":57650,"sourceStart":57646,"tag":"atom"}],"kind"... | [] | [{"source":"round_eq","source_end":57660,"source_start":57652,"syntax_kind":"ident"},{"source":"one_div","source_end":57673,"source_start":57666,"syntax_kind":"ident"},{"source":"add_left_neg","source_end":57687,"source_start":57675,"syntax_kind":"ident"},{"source":"floor_zero","source_end":57699,"source_start":57689,"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.301826","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.301829","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 511 | 2 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4c74e808be9610a35ca417d677c2247005870f4f9d6a90bf7dbbb137c17e7329 | 8b4e306c1275dfa60c4df1dfc87a1d51ab0435f219d3d2c11260b737da798970 | ef070d24dc1259e8599876922fdadeae278cccf2428ad0b7e0ca666ea0e0124a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,081 | TensorProduct.toDirectLimit_tmul_of | Mathlib/LinearAlgebra/TensorProduct/DirectLimit.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>TensorProduct.toDirectLimit</a>, <a>TensorProduct.lift.tmul</a>, <a>Module.DirectLimit.lift_of</a>] | R : Type u_1
inst✝⁶ : CommRing R
ι : Type u_2
inst✝⁵ : DecidableEq ι
inst✝⁴ : Preorder ι
G : ι → Type u_3
inst✝³ : (i : ι) → AddCommGroup (G i)
inst✝² : (i : ι) → Module R (G i)
f : (i j : ι) → i ≤ j → G i →ₗ[R] G j
M : Type u_4
inst✝¹ : AddCommGroup M
inst✝ : Module R M
i : ι
g : G i
m : M
⊢ (toDirectLimit f M) ((of R... | R : Type u_1
inst✝⁶ : CommRing R
ι : Type u_2
inst✝⁵ : DecidableEq ι
inst✝⁴ : Preorder ι
G : ι → Type u_3
inst✝³ : (i : ι) → AddCommGroup (G i)
inst✝² : (i : ι) → Module R (G i)
f : (i j : ι) → i ≤ j → G i →ₗ[R] G j
M : Type u_4
inst✝¹ : AddCommGroup M
inst✝ : Module R M
i : ι
g : G i
m : M
⊢ (((mk R (G i) M).compr₂ (o... | ((:c Eq) ((:c Module.DirectLimit) (:fv _uniq.98077) ((:c CommRing.toRing) (:fv _uniq.98077) (:fv _uniq.98080)) (:fv _uniq.98083) (:fv _uniq.98095) (:lambda _ (:fv _uniq.98083) ((:c TensorProduct) (:fv _uniq.98077) ((:c CommRing.toCommSemiring) (:fv _uniq.98077) (:fv _uniq.98080)) ((:fv _uniq.98100) 0) (:fv _uniq.99906)... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁶","sexp":"((:c CommRing) (:fv _uniq.98077))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁵","sexp":"((:c DecidableEq) (:fv _uniq.98083))"},{"name":"inst✝⁴","sexp":"((:c Preorder) (:fv _uniq.98083))"},{"name":"G","sexp":"(:forall _ (:fv _uniq.98083) (:so... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Module.DirectLimit) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 4 (:l... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98077","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.98080","is_instance":true,"is_let":false,"name":"inst✝⁶","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"rw","sourceEnd":2697,"sourceStart":2695,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2699,"sourceStart":2698,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"TensorProduct.toDire... | [] | [{"source":"toDirectLimit","source_end":2712,"source_start":2699,"syntax_kind":"ident"},{"source":"lift.tmul","source_end":2723,"source_start":2714,"syntax_kind":"ident"},{"source":"lift_of","source_end":2732,"source_start":2725,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98077","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.98080","is_instance":true,"is_let":false,"user_name":"inst✝⁶"},{"binder_role":":implicit","context_index":2,"intern... | 15 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a022013ce2f5fa20631f33a95dac13c8d8f8056916ab2d16c7e71af909bf9cd8 | b246a0dbbde47eb5a1943fabc11a70efa0d5c7e1a5801d66f8fff9ad68b7da69 | a0346f5684e8a933073b348b4df68d8d38549f333a522e6eaeb462e9006089c7 | 8aeb8bfbcca8d44a23f556d83c382478d509ef6c986170d1062763f064c07093 |
cat-searcher/leandojo-benchmark-4-random | test | 3,082 | TensorProduct.toDirectLimit_tmul_of | Mathlib/LinearAlgebra/TensorProduct/DirectLimit.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | R : Type u_1
inst✝⁶ : CommRing R
ι : Type u_2
inst✝⁵ : DecidableEq ι
inst✝⁴ : Preorder ι
G : ι → Type u_3
inst✝³ : (i : ι) → AddCommGroup (G i)
inst✝² : (i : ι) → Module R (G i)
f : (i j : ι) → i ≤ j → G i →ₗ[R] G j
M : Type u_4
inst✝¹ : AddCommGroup M
inst✝ : Module R M
i : ι
g : G i
m : M
⊢ (((mk R (G i) M).compr₂ (o... | ((:c Eq) ((:c Module.DirectLimit) (:fv _uniq.98077) ((:c CommRing.toRing) (:fv _uniq.98077) (:fv _uniq.98080)) (:fv _uniq.98083) (:fv _uniq.98095) (:lambda _ (:fv _uniq.98083) ((:c TensorProduct) (:fv _uniq.98077) ((:c CommRing.toCommSemiring) (:fv _uniq.98077) (:fv _uniq.98080)) ((:fv _uniq.98100) 0) (:fv _uniq.99906)... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁶","sexp":"((:c CommRing) (:fv _uniq.98077))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁵","sexp":"((:c DecidableEq) (:fv _uniq.98083))"},{"name":"inst✝⁴","sexp":"((:c Preorder) (:fv _uniq.98083))"},{"name":"G","sexp":"(:forall _ (:fv _uniq.98083) (:so... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Module.DirectLimit) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 4 (:l... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98077","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.98080","is_instance":true,"is_let":false,"name":"inst✝⁶","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"rfl","sourceEnd":2739,"sourceStart":2736,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":2739,"sourceStart":2736,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98077","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.98080","is_instance":true,"is_let":false,"user_name":"inst✝⁶"},{"binder_role":":implicit","context_index":2,"intern... | 15 | 9 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eec3515d6034d5b8209a9e3936dd4dad1c058278643673e8ae9e7760bae71c74 | 8aeb8bfbcca8d44a23f556d83c382478d509ef6c986170d1062763f064c07093 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,083 | CategoryTheory.Limits.ι_colimitConstInitial_hom | Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | aesop_cat | C✝ : Type u₁
inst✝³ : Category.{v₁, u₁} C✝
J : Type u_1
inst✝² : Category.{u_3, u_1} J
C : Type u_2
inst✝¹ : Category.{u_4, u_2} C
inst✝ : HasInitial C
j : J
⊢ colimit.ι ((Functor.const J).obj (⊥_ C)) j ≫ colimitConstInitial.hom = initial.to (⊥_ C) | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.108553) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.108553) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.108553) (:fv _uniq.108554))) ((:c Prefunctor.obj) (:fv _uniq.108551) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.108551) ((:c CategoryTheory.... | [{"name":"C✝","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.104352))"},{"name":"J","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.108551))"},{"name":"C","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.104352","is_instance":false,"is_let":false,"name":"C✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.104355","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c CategoryTheory.Categ... | {"children":[{"children":[{"children":[{"children":[{"source":"aesop_cat","sourceEnd":24944,"sourceStart":24935,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"CategoryTheory.aesop_cat","source":"aesop_cat","sourceEnd":24944,"sourceStart":24935,"tag":"node"}],"kind":"null","source":"aesop_... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.104352","is_instance":false,"is_let":false,"user_name":"C✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.104355","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":3,"int... | 153 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fa35dd4376fcebfe4253b41362338e0f76d35211d50872180589ca0fa3ca26a1 | 94c78490e724e84ac191aa9f9b59b6b4ff7c7c583c0bf4335af837f755b6fe9c | 5121c016cd001463f39ee8c4444b84a277d6f4c7f9897d838d825f1c14f96636 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 |
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