Datasets:
iCogLabs-Dev
/
Mathlib-Normalized-Sexpr

Dataset card Data Studio Files
xet
 Community
1
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
1,040
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
let O : <a>Finset</a> K := Finset.univ.image k ∪ {kx, ky}
case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...
case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...
((:c Eq) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c CategoryTheory.Funct...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.LargeCategory) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"let","sourceEnd":4236,"sourceStart":4233,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"O","sourceEnd":4238,"sourceStart":4237,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":4240,"so...
[]
[{"source":"Finset K","source_end":4249,"source_start":4241,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Finset.univ.image k ∪ {kx, ky}","source_end":4285,"source_start":4253,"syntax_kind":"«term_∪_»"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
21
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e1b10841c69b8c753443a30410cd3b13c032581a181d3c279f54b790d10ede3f
05f1ba678a1e02e3caad0a614a3a6916905d8da0aff538555916456cf57f19ef
e3d4063f47f1f3d79b3a39fb63f80f48a367f38ab2df024289fd0d32f7bb8202
0ac5bb4f9870e339cf5aa2369758cedc46a33bec22a7777b372dd2d211f2d13c
cat-searcher/leandojo-benchmark-4-random
test
1,041
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have kxO : kx ∈ O := Finset.mem_union.mpr (<a>Or.inr</a> (by simp))
case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...
case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...
((:c Eq) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c CategoryTheory.Funct...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.LargeCategory) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"have","sourceEnd":4294,"sourceStart":4290,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"kxO","sourceEnd":4298,"sourceStart":4295,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"kxO","sourceEnd":4298,"sourceStart":4295,"tag":"node"},...
[]
[{"source":"kx ∈ O","source_end":4309,"source_start":4301,"syntax_kind":"«term_∈_»"},{"source":"Finset.mem_union.mpr (Or.inr (by simp))","source_end":4352,"source_start":4313,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
22
exact
true
1
19
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e6107517afb340041714684852c39d50fe4d97cb7ddf7d3856dbbf679d531959
0ac5bb4f9870e339cf5aa2369758cedc46a33bec22a7777b372dd2d211f2d13c
a185c11619f184aeee38729e901cc990faa7202e924ee1e18b4f409797f9ac1e
d48b497a838cbbba07f876578bf5df0c3bae8d4fc88975d2dcfeadc1fb66e619
cat-searcher/leandojo-benchmark-4-random
test
1,042
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have kyO : ky ∈ O := Finset.mem_union.mpr (<a>Or.inr</a> (by simp))
case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...
case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...
((:c Eq) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c CategoryTheory.Funct...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.LargeCategory) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"have","sourceEnd":4361,"sourceStart":4357,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"kyO","sourceEnd":4365,"sourceStart":4362,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"kyO","sourceEnd":4365,"sourceStart":4362,"tag":"node"},...
[]
[{"source":"ky ∈ O","source_end":4376,"source_start":4368,"syntax_kind":"«term_∈_»"},{"source":"Finset.mem_union.mpr (Or.inr (by simp))","source_end":4419,"source_start":4380,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
28
exact
true
1
20
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3e0d6b5448e78ac3e745756a46858a8eca48ef18be344034de7b0b56c78aefca
d48b497a838cbbba07f876578bf5df0c3bae8d4fc88975d2dcfeadc1fb66e619
9f3e0c151b01fce8560a4f8ff7bd4a465293ab1ca826207543f03755ed3c4cc2
901779ffd5eb7387b31221aca7876402a545cb24d62b75fbcb0ca18719760acf
cat-searcher/leandojo-benchmark-4-random
test
1,043
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have kjO : ∀ j, k j ∈ O := fun j => Finset.mem_union.mpr (<a>Or.inl</a> (by simp))
case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...
case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...
((:c Eq) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c CategoryTheory.Funct...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.LargeCategory) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"have","sourceEnd":4428,"sourceStart":4424,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"kjO","sourceEnd":4432,"sourceStart":4429,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"kjO","sourceEnd":4432,"sourceStart":4429,"tag":"node"},...
[]
[{"source":"∀ j, k j ∈ O","source_end":4451,"source_start":4435,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"fun j => Finset.mem_union.mpr (Or.inl (by simp))","source_end":4503,"source_start":4455,"syntax_kind":"Lean.Parser.Term.fun"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
34
exact
true
1
21
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0fbc5e1a7fbca198a35478dc10cb14ca4fb21b3d9c3ee713e589e7d4e99c3c12
901779ffd5eb7387b31221aca7876402a545cb24d62b75fbcb0ca18719760acf
ddeecfdff4f9873af6acaa3d218d6f6d738922d21433ccbea0025cd4a1ba2c5d
70d67c7d51d7fb5b1542f04613b9ad1fb55633b47445777431d5d00d8761e2de
cat-searcher/leandojo-benchmark-4-random
test
1,044
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
let H : <a>Finset</a> (Σ' (X Y : K) (_ : X ∈ O) (_ : Y ∈ O), X ⟶ Y) := (Finset.univ.image fun j : J => ⟨kx, k j, kxO, Finset.mem_union.mpr (<a>Or.inl</a> (by simp)), f j⟩) ∪ Finset.univ.image fun j : J => ⟨ky, k j, kyO, Finset.mem_union.mpr (<a>Or.inl</a> (by simp)), g j⟩
case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...
case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...
((:c Eq) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c CategoryTheory.Funct...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.LargeCategory) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"let","sourceEnd":4511,"sourceStart":4508,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"H","sourceEnd":4513,"sourceStart":4512,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":4515,"so...
[]
[{"source":"Finset (Σ' (X Y : K) (_ : X ∈ O) (_ : Y ∈ O), X ⟶ Y)","source_end":4575,"source_start":4516,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(Finset.univ.image fun j : J =>\n ⟨kx, k j, kxO, Finset.mem_union.mpr (Or.inl (by simp)), f j⟩) ∪\n Finset.univ.image fun j : J => ⟨ky, k j, kyO, Finse...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
40
exact
true
1
22
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9fa861c8f230157f29c3543cb4ac1c223ef03e770e466e09def9a9caa3133da0
70d67c7d51d7fb5b1542f04613b9ad1fb55633b47445777431d5d00d8761e2de
3f6a62088e206be739cedbb417d35bb7d8ecf0221a7af20c5e2c3128da255857
3df650a91c6629bd09f0e7522abd52fb9400f4cd47d525b182626c21dd1e34ba
cat-searcher/leandojo-benchmark-4-random
test
1,045
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨S, T, W⟩ := <a>CategoryTheory.IsFiltered.sup_exists</a> O H
case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...
case intro.intro.intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J...
((:c Eq) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c CategoryTheory.Funct...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.LargeCategory) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"obtain","sourceEnd":4811,"sourceStart":4805,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":4815,"sourceStart":4812,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"S","sourceEnd":4...
[]
[{"source":"IsFiltered.sup_exists O H","source_end":4854,"source_start":4829,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨S, T, W⟩","source_end":4825,"source_start":4812,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
51
exact
true
1
23
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7d7a15361b2806c3bc9c5146b215c549395338440db0c7d59c9f969ff1e15877
3df650a91c6629bd09f0e7522abd52fb9400f4cd47d525b182626c21dd1e34ba
7c2c9ac83574da5727862965752adc2c8d690099cf4ca71de791b5eefd09f049
1db24f9b751e0bdf2b58e1f4a2f29bfca76020a75a8ea5bc265a22fec5b6da12
cat-searcher/leandojo-benchmark-4-random
test
1,046
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have fH : ∀ j, (⟨kx, k j, kxO, kjO j, f j⟩ : Σ' (X Y : K) (_ : X ∈ O) (_ : Y ∈ O), X ⟶ Y) ∈ H := fun j => Finset.mem_union.mpr (<a>Or.inl</a> (by simp only [<a>true_and_iff</a>, <a>Finset.mem_univ</a>, <a>eq_self_iff_true</a>, <a>exists_prop_of_true</a>, <a>Finset.mem_image</a>, <a>heq_iff_eq</a>] refine ⟨j, ?_⟩ simp o...
case intro.intro.intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J...
case intro.intro.intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J...
((:c Eq) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c CategoryTheory.Funct...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.LargeCategory) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"have","sourceEnd":4863,"sourceStart":4859,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"fH","sourceEnd":4866,"sourceStart":4864,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"fH","sourceEnd":4866,"sourceStart":4864,"tag":"node"},{"...
[]
[{"source":"∀ j, (⟨kx, k j, kxO, kjO j, f j⟩ : Σ' (X Y : K) (_ : X ∈ O) (_ : Y ∈ O), X ⟶ Y) ∈ H","source_end":4967,"source_start":4869,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"fun j =>\n Finset.mem_union.mpr\n (Or.inl\n (by\n simp only [true_and_iff, Finset.mem_univ, eq_self_i...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
52
exact
true
1
26
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
cae331d4ded5cd41672f4a9013beacbefdd5421223b1b9ff65d7e35b6d5f1b47
1db24f9b751e0bdf2b58e1f4a2f29bfca76020a75a8ea5bc265a22fec5b6da12
cf98c139e4aedff1a5531fd600fa78554489f9087a8ba7ef30d8f86f7f69c130
ca3e64e0155917a85908beb46c060538ab63d04e99e29d3755081e6fe055370e
cat-searcher/leandojo-benchmark-4-random
test
1,047
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have gH : ∀ j, (⟨ky, k j, kyO, kjO j, g j⟩ : Σ' (X Y : K) (_ : X ∈ O) (_ : Y ∈ O), X ⟶ Y) ∈ H := fun j => Finset.mem_union.mpr (<a>Or.inr</a> (by simp only [<a>true_and_iff</a>, <a>Finset.mem_univ</a>, <a>eq_self_iff_true</a>, <a>exists_prop_of_true</a>, <a>Finset.mem_image</a>, <a>heq_iff_eq</a>] refine ⟨j, ?_⟩ simp o...
case intro.intro.intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J...
case intro.intro.intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J...
((:c Eq) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c CategoryTheory.Funct...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.LargeCategory) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"have","sourceEnd":5257,"sourceStart":5253,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"gH","sourceEnd":5260,"sourceStart":5258,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"gH","sourceEnd":5260,"sourceStart":5258,"tag":"node"},{"...
[]
[{"source":"∀ j, (⟨ky, k j, kyO, kjO j, g j⟩ : Σ' (X Y : K) (_ : X ∈ O) (_ : Y ∈ O), X ⟶ Y) ∈ H","source_end":5367,"source_start":5269,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"fun j =>\n Finset.mem_union.mpr\n (Or.inr\n (by\n simp only [true_and_iff, Finset.mem_univ, eq_self_i...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
60
exact
true
1
27
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c7015af70a420845a928133613df997ae7abde4c7fcbcf8746b1defbf33aac5e
ca3e64e0155917a85908beb46c060538ab63d04e99e29d3755081e6fe055370e
9e74c44b80403be37f5e2fcaac0fda45851752b3713e02c47d17139eb8363e22
571f2d10ed01dbcc55f74ae52d31876e01f5e644492e08ec5a56c798e8483d5d
cat-searcher/leandojo-benchmark-4-random
test
1,048
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>CategoryTheory.Limits.Types.colimit_sound'</a> (T kxO) (T kyO)
case intro.intro.intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J...
case intro.intro.intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J...
((:c Eq) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c CategoryTheory.Funct...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.LargeCategory) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"apply","sourceEnd":5854,"sourceStart":5849,"tag":"atom"},{"children":[{"name":"CategoryTheory.Limits.Types.colimit_sound'","semanticRole":"global","source":"colimit_sound'","sourceEnd":5869,"sourceStart":5855,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":5871,"sourceSta...
[]
[{"source":"colimit_sound' (T kxO) (T kyO)\n -- We can check if two elements of a limit (in `Type`)\n -- are equal by comparing them componentwise.","source_end":5885,"source_start":5855,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
68
exact
true
1
28
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a5b1fe8ef30ad80acafb46aa6e8429ca529df9bd8aa28ed8d42add5745ded1f7
571f2d10ed01dbcc55f74ae52d31876e01f5e644492e08ec5a56c798e8483d5d
67ce35b4e383674f02f732ae288370bf36740408ec5f5d5bf9f5a46f72bf57ef
b6add10b8c13f83ffe6e8d4bec608779cf3c3651254e6824b38c6ffdef78b158
cat-searcher/leandojo-benchmark-4-random
test
1,049
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
ext j
case intro.intro.intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J...
case intro.intro.intro.intro.intro.intro.intro.w J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K...
((:c Eq) ((:c Prefunctor.obj) (:fv _uniq.1470) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.1470) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.1470) (:fv _uniq.1476))) (:sort (+ v 1)) ((:c CategoryTheory.CategoryStruct.toQuiver) (:sort (+ v 1)) ((:c CategoryTheory.Category.toCategoryStruct) (:so...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:sort Type))))) (:arg :explicit 4 (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"ext","sourceEnd":6002,"sourceStart":5999,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"j","sourceEnd":6004,"sourceStart":6003,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"j\n -- Now it's just a calculation using `W` a...
[{"role":"fresh_name","source":"j\n -- Now it's just a calculation using `W` and `w`.","source_end":6004,"source_start":6003,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
69
exact
true
1
28
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2f49f600d8246ca5387baf5ca0e162b68ffe129c86c371b887c9fc3fa7f9d284
b6add10b8c13f83ffe6e8d4bec608779cf3c3651254e6824b38c6ffdef78b158
541ea80d14360c000487eaabc2fb2dba269e64d03da1f54c11f36fec1cd0ca44
c3ac52e1c04860db2e5f1b2ab5ef76affd1d3f66debbbdc0cf84f5aa7db59f7f
cat-searcher/leandojo-benchmark-4-random
test
1,050
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>CategoryTheory.Functor.comp_map</a>, <a>CategoryTheory.Limits.Types.Limit.map_π_apply</a>, <a>CategoryTheory.curry_obj_map_app</a>, <a>CategoryTheory.Prod.swap_map</a>]
case intro.intro.intro.intro.intro.intro.intro.w J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K...
case intro.intro.intro.intro.intro.intro.intro.w J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K...
((:c Eq) ((:c Prefunctor.obj) (:fv _uniq.1468) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.1468) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.1468) (:fv _uniq.1473))) (:sort (+ v 1)) ((:c CategoryTheory.CategoryStruct.toQuiver) (:sort (+ v 1)) ((:c CategoryTheory.Category.toCategoryStruct) (:so...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:sort Type))))) (:arg :explicit 4 (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"simp","sourceEnd":6067,"sourceStart":6063,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":6072,"sourceStart":6068,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":6072,"s...
[]
[{"source":"Functor.comp_map","source_end":6090,"source_start":6074,"syntax_kind":"ident"},{"source":"Limit.map_π_apply","source_end":6110,"source_start":6092,"syntax_kind":"ident"},{"source":"curry_obj_map_app","source_end":6129,"source_start":6112,"syntax_kind":"ident"},{"source":"swap_map","source_end":6139,"source_...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
70
exact
true
1
29
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d13bacc897e46be498827e8b081f3cdf0fe5e4b333453c1d5890ea5c81414f49
c3ac52e1c04860db2e5f1b2ab5ef76affd1d3f66debbbdc0cf84f5aa7db59f7f
53c069e1424a0ed35ee58f08334ce55582c9d01fd534e22de7b566c84f7eac6a
3ccafc9d5febb44ed0941e79f82e0369ed60a68ee5d29a4b6102879ad5fa19bd
cat-searcher/leandojo-benchmark-4-random
test
1,051
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← W _ _ (fH j), ← W _ _ (gH j)]
case intro.intro.intro.intro.intro.intro.intro.w J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K...
case intro.intro.intro.intro.intro.intro.intro.w J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K...
((:c Eq) ((:c Prefunctor.obj) (:fv _uniq.1468) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.1468) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.1468) (:fv _uniq.1473))) (:sort (+ v 1)) ((:c CategoryTheory.CategoryStruct.toQuiver) (:sort (+ v 1)) ((:c CategoryTheory.Category.toCategoryStruct) (:so...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:sort Type))))) (:arg :explicit 4 (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"rw","sourceEnd":6147,"sourceStart":6145,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6149,"sourceStart":6148,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":6152,"sourceStart":...
[]
[{"source":"W _ _ (fH j)","source_end":6165,"source_start":6153,"syntax_kind":"Lean.Parser.Term.app"},{"source":"W _ _ (gH j)","source_end":6183,"source_start":6171,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
71
exact
true
1
29
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0452e513fc9f4d7ebb9a37afb9fd4ea0cd1ee3a7c40c7e2da5fea2c80bfc78d7
3ccafc9d5febb44ed0941e79f82e0369ed60a68ee5d29a4b6102879ad5fa19bd
51258ce2bf97df6886202e49c97b5bc8f27d1bc837c04151a661c5aa3c02d662
d8143dc69bf56ac3bef59030eb354063424c079bd400aad4eaf1e30846345f88
cat-searcher/leandojo-benchmark-4-random
test
1,052
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>CategoryTheory.Limits.Types.Limit.map_π_apply</a>, w]
case intro.intro.intro.intro.intro.intro.intro.w J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K...
((:c Eq) ((:c Prefunctor.obj) (:fv _uniq.1468) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.1468) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.1468) (:fv _uniq.1473))) (:sort (+ v 1)) ((:c CategoryTheory.CategoryStruct.toQuiver) (:sort (+ v 1)) ((:c CategoryTheory.Category.toCategoryStruct) (:so...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:sort Type))))) (:arg :explicit 4 (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"simp","sourceEnd":6314,"sourceStart":6310,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6316,"sourceStart":6315,"tag":"atom"...
[]
[{"source":"Limit.map_π_apply","source_end":6334,"source_start":6316,"syntax_kind":"ident"},{"source":"w","source_end":6337,"source_start":6336,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
75
exact
true
1
29
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c1d297bfdc6ef4a6351bea862aee79c41d0031c3dadb9e4c2090291a26df0bda
d8143dc69bf56ac3bef59030eb354063424c079bd400aad4eaf1e30846345f88
61de0dc1dc57f2bc811c590f579562fe457fbbed23276d0aa0d57f6361237636
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,053
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>CategoryTheory.Functor.comp_obj</a>, <a>CategoryTheory.Limits.colim_obj</a>, <a>CategoryTheory.Limits.ι_colimitLimitToLimitColimit_π_apply</a>, <a>CategoryTheory.Limits.Types.FilteredColimit.colimit_eq_iff</a>, <a>CategoryTheory.curry_obj_obj_obj</a>, <a>CategoryTheory.curry_obj_obj_map</a>] at h
case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...
case intro.intro.intro.intro.intro J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj k...
((:c Eq) ((:c CategoryTheory.Limits.colimit) (:fv _uniq.1470) (:fv _uniq.1476) (:sort (+ v 1)) (:c CategoryTheory.types) ((:c CategoryTheory.Functor.comp) (:fv _uniq.1470) (:fv _uniq.1476) ((:c CategoryTheory.Functor) (:fv _uniq.1468) (:fv _uniq.1473) (:sort (+ v 1)) (:c CategoryTheory.types)) ((:c CategoryTheory.Funct...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Limits.colimit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:sort Type)) (:arg :instance 3 (:instance-of (:app (:c CategoryTheory.LargeCategory) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":3400,"sourceStart":3396,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":3405,"sourceStart":3401,"tag":"atom"}],"kind":"nu...
[]
[{"source":"Functor.comp_obj","source_end":3423,"source_start":3407,"syntax_kind":"ident"},{"source":"colim_obj","source_end":3434,"source_start":3425,"syntax_kind":"ident"},{"source":"ι_colimitLimitToLimitColimit_π_apply","source_end":3474,"source_start":3436,"syntax_kind":"ident"},{"source":"colimit_eq_iff","source_e...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
14
exact
true
1
14
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ad6dc50d4b0aedad0e6646c712cc07b23a5fd5cfe17ff052bfaa8e9b54b4c231
6c8dd099f1aae6a0c5726e0bb434f74c96df2149d1fcea45bc493c251a94800f
79529b9189f467bbcc319c68a5cc5fca7ec848ea5abf5bd1865fb7b0b2bc0730
3d7361fed9a133ee9157bd98c9fa0de2c736021983648919ea704e00b5cfef8e
cat-searcher/leandojo-benchmark-4-random
test
1,054
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj ky) h : ∀ (j : J), ∃ k f g, ...
((:c Membership.mem) (:fv _uniq.1470) ((:c Finset) (:fv _uniq.1470)) ((:c Finset.instMembership) (:fv _uniq.1470)) (:fv _uniq.2756) ((:c Insert.insert) (:fv _uniq.1470) ((:c Finset) (:fv _uniq.1470)) ((:c Finset.instInsert) (:fv _uniq.1470) (:lambda a (:fv _uniq.1470) (:lambda b (:fv _uniq.1470) ((:c Classical.propDeci...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:fv FV10)) (:arg...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":4350,"sourceStart":4346,"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.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
25
exact
true
1
19
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2b6952403a7bf5d8972f46d27dd94ddf08306cfb7545794fd6e9fb1b125afba4
d37424d98d24c094b769bd35eac10793e392b026ea642b2ea44bbfffbbc4e7ef
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,055
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj ky) h : ∀ (j : J), ∃ k f g, ...
((:c Membership.mem) (:fv _uniq.1470) ((:c Finset) (:fv _uniq.1470)) ((:c Finset.instMembership) (:fv _uniq.1470)) (:fv _uniq.2832) ((:c Insert.insert) (:fv _uniq.1470) ((:c Finset) (:fv _uniq.1470)) ((:c Finset.instInsert) (:fv _uniq.1470) (:lambda a (:fv _uniq.1470) (:lambda b (:fv _uniq.1470) ((:c Classical.propDeci...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:fv FV12)) (:arg...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":4417,"sourceStart":4413,"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.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
31
exact
true
1
20
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9495d6b69fc57ccba748299bc0ef35bc6ae4a8eb3d27a9a0709128d96cf7b0bd
60cb50a69e6d95665c0aecfd3897e074ed9de3e07456af6d1be2ee788add12bb
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,056
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj ky) h : ∀ (j : J), ∃ k f g, ...
((:c Membership.mem) (:fv _uniq.1470) ((:c Finset) (:fv _uniq.1470)) ((:c Finset.instMembership) (:fv _uniq.1470)) ((:fv _uniq.7830) (:fv _uniq.13533)) ((:c Finset.image) (:fv _uniq.1468) (:fv _uniq.1470) (:lambda a (:fv _uniq.1470) (:lambda b (:fv _uniq.1470) ((:c Classical.propDecidable) ((:c Eq) (:fv _uniq.1470) 1 0...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:app (:fv FV15) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":4501,"sourceStart":4497,"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.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
37
exact
true
1
22
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
10bf7247101c7b1a7dd89cac9ea52e71e36f45fc1cbb4a3264fb860c40a76c21
d12decb43b0bb3386ecc2e30921e851f078695369e04f16d6ab904c69d4fe666
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,058
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>true_and_iff</a>, <a>Finset.mem_univ</a>, <a>eq_self_iff_true</a>, <a>exists_prop_of_true</a>, <a>Finset.mem_image</a>, <a>heq_iff_eq</a>]
J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj ky) h : ∀ (j : J), ∃ k f g, ...
J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj ky) h : ∀ (j : J), ∃ k f g, ...
((:c Membership.mem) ((:c PSigma) (:fv _uniq.1470) (:lambda X (:fv _uniq.1470) ((:c PSigma) (:fv _uniq.1470) (:lambda Y (:fv _uniq.1470) ((:c PSigma) ((:c Membership.mem) (:fv _uniq.1470) ((:c Finset) (:fv _uniq.1470)) ((:c Finset.instMembership) (:fv _uniq.1470)) 1 (:fv _uniq.13013)) (:lambda _ ((:c Membership.mem) (:...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c PSigma) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda X :explicit (:fv FV1) (:app (:c PSigma) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda Y :explicit (:fv FV1) (:app (:c PSigma) (:arg :implicit-type 0 (:app (:c Membership.mem) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"simp","sourceEnd":5059,"sourceStart":5055,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":5064,"sourceStart":5060,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":5064,"s...
[]
[{"source":"true_and_iff","source_end":5078,"source_start":5066,"syntax_kind":"ident"},{"source":"Finset.mem_univ","source_end":5095,"source_start":5080,"syntax_kind":"ident"},{"source":"eq_self_iff_true","source_end":5113,"source_start":5097,"syntax_kind":"ident"},{"source":"exists_prop_of_true","source_end":5134,"sou...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
57
exact
true
1
27
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1d4a2958ceca8c8974d2b823ac6ba9456d5b815c2e9d80d0199c697b6d13ade2
9f8e7929f2573c8c45a0668dfe486e68abcc238fc8f6547407895307e9de4b8f
4166f335df63f2a6dfcf29110c7e4c2be08c8cde0315c573b39c9dc295b71fd0
bcd4ab5c3866e52c67cce3137a9fc9df9b3cb26ac02758f32f363f265ed06d2f
cat-searcher/leandojo-benchmark-4-random
test
1,059
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨j, ?_⟩
J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj ky) h : ∀ (j : J), ∃ k f g, ...
J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj ky) h : ∀ (j : J), ∃ k f g, ...
((:c Exists) (:fv _uniq.1468) (:lambda a (:fv _uniq.1468) ((:c Eq) ((:c PSigma) (:fv _uniq.1470) (:lambda X (:fv _uniq.1470) ((:c PSigma) (:fv _uniq.1470) (:lambda Y (:fv _uniq.1470) ((:c PSigma) ((:c Membership.mem) (:fv _uniq.1470) ((:c Finset) (:fv _uniq.1470)) ((:c Finset.instMembership) (:fv _uniq.1470)) 1 (:fv _u...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda a :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c PSigma) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda X :explicit (:fv FV1) (:app (:c PSigma) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda Y ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"refine","sourceEnd":5198,"sourceStart":5192,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":5202,"sourceStart":5199,"tag":"atom"},{"children":[{"contextIndex":27,"semanticRole":"local","source":"j","sourceEnd":5203,"sourceStart":5202,"tag":"identifier"},{"source":",","sourceEnd":5204,"sourc...
[]
[{"source":"⟨j, ?_⟩","source_end":5210,"source_start":5199,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
58
exact
true
1
27
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a3f8ec865269547f549336457313bded5667fa408de28ffa8734372b707260b5
bcd4ab5c3866e52c67cce3137a9fc9df9b3cb26ac02758f32f363f265ed06d2f
bafb1d6aab8af5a273b2eb608dbe506490f21433e2e55d7b1c4276f1eae264a2
4a8a4303062b5ffaff34152ced6fc4cf8e3fddce9ba6edba5223303b289bbbf3
cat-searcher/leandojo-benchmark-4-random
test
1,060
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>heq_iff_eq</a>]
J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj ky) h : ∀ (j : J), ∃ k f g, ...
((:c Eq) ((:c PSigma) (:fv _uniq.1470) (:lambda X (:fv _uniq.1470) ((:c PSigma) (:fv _uniq.1470) (:lambda Y (:fv _uniq.1470) ((:c PSigma) ((:c Membership.mem) (:fv _uniq.1470) ((:c Finset) (:fv _uniq.1470)) ((:c Finset.instMembership) (:fv _uniq.1470)) 1 (:fv _uniq.13013)) (:lambda _ ((:c Membership.mem) (:fv _uniq.147...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c PSigma) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda X :explicit (:fv FV1) (:app (:c PSigma) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda Y :explicit (:fv FV1) (:app (:c PSigma) (:arg :implicit-type 0 (:app (:c Membership.mem) (:arg :implici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"simp","sourceEnd":5227,"sourceStart":5223,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":5232,"sourceStart":5228,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":5232,"s...
[]
[{"source":"heq_iff_eq","source_end":5244,"source_start":5234,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
59
exact
true
1
27
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4548696bafa4df083de3a5caf3546f8d7f896022edcb36d61f68c07cfb600377
4a8a4303062b5ffaff34152ced6fc4cf8e3fddce9ba6edba5223303b289bbbf3
4a854c607033084a0f73767c4f258130bc80a9ef22ba604ba5b8ff602a3b9c77
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,061
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>true_and_iff</a>, <a>Finset.mem_univ</a>, <a>eq_self_iff_true</a>, <a>exists_prop_of_true</a>, <a>Finset.mem_image</a>, <a>heq_iff_eq</a>]
J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj ky) h : ∀ (j : J), ∃ k f g, ...
J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj ky) h : ∀ (j : J), ∃ k f g, ...
((:c Membership.mem) ((:c PSigma) (:fv _uniq.1470) (:lambda X (:fv _uniq.1470) ((:c PSigma) (:fv _uniq.1470) (:lambda Y (:fv _uniq.1470) ((:c PSigma) ((:c Membership.mem) (:fv _uniq.1470) ((:c Finset) (:fv _uniq.1470)) ((:c Finset.instMembership) (:fv _uniq.1470)) 1 (:fv _uniq.13013)) (:lambda _ ((:c Membership.mem) (:...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c PSigma) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda X :explicit (:fv FV1) (:app (:c PSigma) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda Y :explicit (:fv FV1) (:app (:c PSigma) (:arg :implicit-type 0 (:app (:c Membership.mem) (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"simp","sourceEnd":5459,"sourceStart":5455,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":5464,"sourceStart":5460,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":5464,"s...
[]
[{"source":"true_and_iff","source_end":5478,"source_start":5466,"syntax_kind":"ident"},{"source":"Finset.mem_univ","source_end":5495,"source_start":5480,"syntax_kind":"ident"},{"source":"eq_self_iff_true","source_end":5513,"source_start":5497,"syntax_kind":"ident"},{"source":"exists_prop_of_true","source_end":5534,"sou...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
65
exact
true
1
28
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ac914cafd0323d5d18ab719bda6e8e94a0e485c5721fb736ac1a6dbee3224b10
c48c1e6d4442b132704b9bfa933c0507bf767c73aac9abd7dede89a287453607
4166f335df63f2a6dfcf29110c7e4c2be08c8cde0315c573b39c9dc295b71fd0
576cfc4476ab293587fad7bd8936a13b490748d77c1dd740c3ddff0e8bfce9cd
cat-searcher/leandojo-benchmark-4-random
test
1,062
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨j, ?_⟩
J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj ky) h : ∀ (j : J), ∃ k f g, ...
J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj ky) h : ∀ (j : J), ∃ k f g, ...
((:c Exists) (:fv _uniq.1468) (:lambda a (:fv _uniq.1468) ((:c Eq) ((:c PSigma) (:fv _uniq.1470) (:lambda X (:fv _uniq.1470) ((:c PSigma) (:fv _uniq.1470) (:lambda Y (:fv _uniq.1470) ((:c PSigma) ((:c Membership.mem) (:fv _uniq.1470) ((:c Finset) (:fv _uniq.1470)) ((:c Finset.instMembership) (:fv _uniq.1470)) 1 (:fv _u...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda a :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c PSigma) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda X :explicit (:fv FV1) (:app (:c PSigma) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda Y ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"refine","sourceEnd":5598,"sourceStart":5592,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":5602,"sourceStart":5599,"tag":"atom"},{"children":[{"contextIndex":28,"semanticRole":"local","source":"j","sourceEnd":5603,"sourceStart":5602,"tag":"identifier"},{"source":",","sourceEnd":5604,"sourc...
[]
[{"source":"⟨j, ?_⟩","source_end":5610,"source_start":5599,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
66
exact
true
1
28
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
6ed6e421e890113a39153f01b39cad2c521c900fc17c3e79c4e31fac85facb31
576cfc4476ab293587fad7bd8936a13b490748d77c1dd740c3ddff0e8bfce9cd
bafb1d6aab8af5a273b2eb608dbe506490f21433e2e55d7b1c4276f1eae264a2
b7fb4deaa08cd9ddbf422afee3d164fe319892217eeb59f868c2a8f28631eafb
cat-searcher/leandojo-benchmark-4-random
test
1,063
CategoryTheory.Limits.colimitLimitToLimitColimit_injective
Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>heq_iff_eq</a>]
J : Type u₁ K : Type u₂ inst✝⁴ : Category.{v₁, u₁} J inst✝³ : Category.{v₂, u₂} K inst✝² : Small.{v, u₂} K F : J × K ⥤ Type v inst✝¹ : IsFiltered K inst✝ : Finite J val✝ : Fintype J kx : K x : limit ((curry.obj (swap K J ⋙ F)).obj kx) ky : K y : limit ((curry.obj (swap K J ⋙ F)).obj ky) h : ∀ (j : J), ∃ k f g, ...
((:c Eq) ((:c PSigma) (:fv _uniq.1470) (:lambda X (:fv _uniq.1470) ((:c PSigma) (:fv _uniq.1470) (:lambda Y (:fv _uniq.1470) ((:c PSigma) ((:c Membership.mem) (:fv _uniq.1470) ((:c Finset) (:fv _uniq.1470)) ((:c Finset.instMembership) (:fv _uniq.1470)) 1 (:fv _uniq.13013)) (:lambda _ ((:c Membership.mem) (:fv _uniq.147...
[{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1468))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1470))"},{"name":"inst✝²","sexp":"((:c Small) (:fv _uniq.1470))"},{"name":"F","sexp":"((:c CategoryT...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c PSigma) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda X :explicit (:fv FV1) (:app (:c PSigma) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda Y :explicit (:fv FV1) (:app (:c PSigma) (:arg :implicit-type 0 (:app (:c Membership.mem) (:arg :implici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implici...
{"children":[{"source":"simp","sourceEnd":5627,"sourceStart":5623,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":5632,"sourceStart":5628,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":5632,"s...
[]
[{"source":"heq_iff_eq","source_end":5644,"source_start":5634,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1468","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1470","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_nam...
16
67
exact
true
1
28
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2ac88b866623dbcdbaa717669ad839694ffd63cedfa3173900e729535d8dee78
b7fb4deaa08cd9ddbf422afee3d164fe319892217eeb59f868c2a8f28631eafb
4a854c607033084a0f73767c4f258130bc80a9ef22ba604ba5b8ff602a3b9c77
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,064
PowerSeries.order_monomial
Mathlib/RingTheory/PowerSeries/Order.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
split_ifs with h
R : Type u_1 inst✝¹ : Semiring R φ : R⟦X⟧ n : ℕ a : R inst✝ : Decidable (a = 0) ⊢ ((monomial R n) a).order = if a = 0 then ⊤ else ↑n
case pos R : Type u_1 inst✝¹ : Semiring R φ : R⟦X⟧ n : ℕ a : R inst✝ : Decidable (a = 0) h : a = 0 ⊢ ((monomial R n) a).order = ⊤ case neg R : Type u_1 inst✝¹ : Semiring R φ : R⟦X⟧ n : ℕ a : R inst✝ : Decidable (a = 0) h : ¬a = 0 ⊢ ((monomial R n) a).order = ↑n
((:c Eq) (:c PartENat) ((:c PowerSeries.order) (:fv _uniq.67925) (:fv _uniq.67928) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.67925) (:fv _uniq.67925) (:fv _uniq.67928) (:fv _uniq.67928) ((:c RingHom.id) (:fv _uniq.67925) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.67925) (:fv _uniq.67928))) (:fv _uniq.67925) ((:c ...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.67925))"},{"name":"φ","sexp":"((:c PowerSeries) (:fv _uniq.67925))"},{"name":"n","sexp":"(:c Nat)"},{"name":"a","sexp":"(:fv _uniq.67925)"},{"name":"inst✝","sexp":"((:c Decidable) ((:c Eq) (:fv _uniq.67925) (:fv _uniq.68780) ((:...
(:app (:c Eq) (:arg :implicit-type 0 (:c PartENat)) (:arg :explicit 1 (:app (:c PowerSeries.order) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-t...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.67925","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.67928","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Semiring) (:arg :explic...
{"children":[{"source":"split_ifs","sourceEnd":8768,"sourceStart":8759,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"with","sourceEnd":8773,"sourceStart":8769,"tag":"atom"},{"children":[{"children":[{"source":"h","sourceEnd":8775,"sourceStart":8774,"tag":"identifier"}],"ki...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.67925","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.67928","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern...
42
4
exact
true
1
6
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
aafdffa11b74bf93776dc341c035c4eb056fc3871c440680c160053d1ad2582c
25653523d527ae93f2bace738c478827133c82dc0b3dd759232a09313b1b4b0d
4384516da9879e95125096635779b1b98675db82dd9560bb5f86d9ca5296b84d
c20011a5176fed4c124f058bee43f08fe2308a946b27badbd193d3f881229a78
cat-searcher/leandojo-benchmark-4-random
test
1,065
PowerSeries.order_monomial
Mathlib/RingTheory/PowerSeries/Order.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [h, <a>PowerSeries.order_eq_top</a>, <a>LinearMap.map_zero</a>]
case pos R : Type u_1 inst✝¹ : Semiring R φ : R⟦X⟧ n : ℕ a : R inst✝ : Decidable (a = 0) h : a = 0 ⊢ ((monomial R n) a).order = ⊤
((:c Eq) (:c PartENat) ((:c PowerSeries.order) (:fv _uniq.67925) (:fv _uniq.67928) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.67925) (:fv _uniq.67925) (:fv _uniq.67928) (:fv _uniq.67928) ((:c RingHom.id) (:fv _uniq.67925) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.67925) (:fv _uniq.67928))) (:fv _uniq.67925) ((:c ...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.67925))"},{"name":"φ","sexp":"((:c PowerSeries) (:fv _uniq.67925))"},{"name":"n","sexp":"(:c Nat)"},{"name":"a","sexp":"(:fv _uniq.67925)"},{"name":"inst✝","sexp":"((:c Decidable) ((:c Eq) (:fv _uniq.67925) (:fv _uniq.68780) ((:...
(:app (:c Eq) (:arg :implicit-type 0 (:c PartENat)) (:arg :explicit 1 (:app (:c PowerSeries.order) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-t...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.67925","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.67928","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Semiring) (:arg :explic...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":8783,"sourceStart":8781,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8785,"sourceStart":8784,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag...
[]
[{"source":"h","source_end":8786,"source_start":8785,"syntax_kind":"ident"},{"source":"order_eq_top","source_end":8800,"source_start":8788,"syntax_kind":"ident"},{"source":"LinearMap.map_zero","source_end":8820,"source_start":8802,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.67925","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.67928","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern...
42
7
exact
true
1
7
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
645c6657bb07cd5f906320097eaffec85036ebcb9cb54023067222cf8efd6a8c
932bdd7962b348c1ff56345449e92344e5462868fefff4cc1ac015615ae10a3b
eada2644e377e7dd14f771e7b0d39c839adb5c7484a8f71483d33e5d16bc679e
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,066
PowerSeries.order_monomial
Mathlib/RingTheory/PowerSeries/Order.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>PowerSeries.order_eq</a>]
case neg R : Type u_1 inst✝¹ : Semiring R φ : R⟦X⟧ n : ℕ a : R inst✝ : Decidable (a = 0) h : ¬a = 0 ⊢ ((monomial R n) a).order = ↑n
case neg R : Type u_1 inst✝¹ : Semiring R φ : R⟦X⟧ n : ℕ a : R inst✝ : Decidable (a = 0) h : ¬a = 0 ⊢ (∀ (i : ℕ), ↑i = ↑n → (coeff R i) ((monomial R n) a) ≠ 0) ∧ ∀ (i : ℕ), ↑i < ↑n → (coeff R i) ((monomial R n) a) = 0
((:c Eq) (:c PartENat) ((:c PowerSeries.order) (:fv _uniq.67925) (:fv _uniq.67928) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.67925) (:fv _uniq.67925) (:fv _uniq.67928) (:fv _uniq.67928) ((:c RingHom.id) (:fv _uniq.67925) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.67925) (:fv _uniq.67928))) (:fv _uniq.67925) ((:c ...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.67925))"},{"name":"φ","sexp":"((:c PowerSeries) (:fv _uniq.67925))"},{"name":"n","sexp":"(:c Nat)"},{"name":"a","sexp":"(:fv _uniq.67925)"},{"name":"inst✝","sexp":"((:c Decidable) ((:c Eq) (:fv _uniq.67925) (:fv _uniq.68780) ((:...
(:app (:c Eq) (:arg :implicit-type 0 (:c PartENat)) (:arg :explicit 1 (:app (:c PowerSeries.order) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-t...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.67925","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.67928","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Semiring) (:arg :explic...
{"children":[{"source":"rw","sourceEnd":8829,"sourceStart":8827,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8831,"sourceStart":8830,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"PowerSeries.order_eq...
[]
[{"source":"order_eq","source_end":8839,"source_start":8831,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.67925","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.67928","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern...
42
18
exact
true
1
7
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
71bd338c5c9f1ec1ecde4833d266f6055c878331b615271628b6333357292f3d
c5b51017c737468aea5846f8184c4e26da7aeed024103a9aa9454c6a86826ad4
0f13fc24137381270f81e2ed57d0d14edb49b9897afb561f668f7fb63d2bd8a8
e615f9de4849029237001f5c48ff58cac0e95ecf802a827327abe2594094b3de
cat-searcher/leandojo-benchmark-4-random
test
1,067
PowerSeries.order_monomial
Mathlib/RingTheory/PowerSeries/Order.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
constructor <;> intro i hi
case neg R : Type u_1 inst✝¹ : Semiring R φ : R⟦X⟧ n : ℕ a : R inst✝ : Decidable (a = 0) h : ¬a = 0 ⊢ (∀ (i : ℕ), ↑i = ↑n → (coeff R i) ((monomial R n) a) ≠ 0) ∧ ∀ (i : ℕ), ↑i < ↑n → (coeff R i) ((monomial R n) a) = 0
case neg.left R : Type u_1 inst✝¹ : Semiring R φ : R⟦X⟧ n : ℕ a : R inst✝ : Decidable (a = 0) h : ¬a = 0 i : ℕ hi : ↑i = ↑n ⊢ (coeff R i) ((monomial R n) a) ≠ 0 case neg.right R : Type u_1 inst✝¹ : Semiring R φ : R⟦X⟧ n : ℕ a : R inst✝ : Decidable (a = 0) h : ¬a = 0 i : ℕ hi : ↑i < ↑n ⊢ (coeff R i) ((monomial R n) a) =...
((:c And) (:forall i (:c Nat) (:forall _ ((:c Eq) (:c PartENat) ((:c Nat.cast) (:c PartENat) ((:c AddMonoidWithOne.toNatCast) (:c PartENat) ((:c AddCommMonoidWithOne.toAddMonoidWithOne) (:c PartENat) (:c PartENat.instAddCommMonoidWithOne))) 0) ((:c Nat.cast) (:c PartENat) ((:c AddMonoidWithOne.toNatCast) (:c PartENat) ...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.67925))"},{"name":"φ","sexp":"((:c PowerSeries) (:fv _uniq.67925))"},{"name":"n","sexp":"(:c Nat)"},{"name":"a","sexp":"(:fv _uniq.67925)"},{"name":"inst✝","sexp":"((:c Decidable) ((:c Eq) (:fv _uniq.67925) (:fv _uniq.68780) ((:...
(:app (:c And) (:arg :explicit 0 (:forall i :explicit (:c Nat) (:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:c PartENat)) (:arg :explicit 1 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c PartENat)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c PartENat))))) (:arg :explicit 2 0))...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.67925","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.67928","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Semiring) (:arg :explic...
{"children":[{"children":[{"source":"constructor","sourceEnd":8856,"sourceStart":8845,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":8856,"sourceStart":8845,"tag":"node"},{"source":"<;>","sourceEnd":8860,"sourceStart":8857,"tag":"atom"},{"children":[{"source":"intro","sourceEn...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.67925","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.67928","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern...
42
21
exact
true
1
7
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
31d64b15ae764491090ff6bb0cce5c47ab32ae0d10f8dd329f6dbfb760f8cdf8
e615f9de4849029237001f5c48ff58cac0e95ecf802a827327abe2594094b3de
a7eee8dab7a6eeef9fa0919a445905fd1c6407db1c13b513c00ac8438dde98a2
22d09f65e4818ed159a29d2f1bb4a32488c8aa6a8507b3d579357f7b0607a394
cat-searcher/leandojo-benchmark-4-random
test
1,068
PowerSeries.order_monomial
Mathlib/RingTheory/PowerSeries/Order.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>PartENat.natCast_inj</a>] at hi
case neg.left R : Type u_1 inst✝¹ : Semiring R φ : R⟦X⟧ n : ℕ a : R inst✝ : Decidable (a = 0) h : ¬a = 0 i : ℕ hi : ↑i = ↑n ⊢ (coeff R i) ((monomial R n) a) ≠ 0
case neg.left R : Type u_1 inst✝¹ : Semiring R φ : R⟦X⟧ n : ℕ a : R inst✝ : Decidable (a = 0) h : ¬a = 0 i : ℕ hi : i = n ⊢ (coeff R i) ((monomial R n) a) ≠ 0
((:c Ne) (:fv _uniq.67925) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.67925) (:fv _uniq.67925) (:fv _uniq.67928) (:fv _uniq.67928) ((:c RingHom.id) (:fv _uniq.67925) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.67925) (:fv _uniq.67928))) ((:c PowerSeries) (:fv _uniq.67925)) (:fv _uniq.67925) ((:c PowerSeries.instAdd...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.67925))"},{"name":"φ","sexp":"((:c PowerSeries) (:fv _uniq.67925))"},{"name":"n","sexp":"(:c Nat)"},{"name":"a","sexp":"(:fv _uniq.67925)"},{"name":"inst✝","sexp":"((:c Decidable) ((:c Eq) (:fv _uniq.67925) (:fv _uniq.68780) ((:...
(:app (:c Ne) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.67925","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.67928","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Semiring) (:arg :explic...
{"children":[{"source":"rw","sourceEnd":8881,"sourceStart":8879,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8883,"sourceStart":8882,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"PartENat.natCast_inj...
[]
[{"source":"PartENat.natCast_inj","source_end":8903,"source_start":8883,"syntax_kind":"ident"},{"source":"hi","source_end":8910,"source_start":8908,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.67925","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.67928","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern...
42
30
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9d74f57ccc118b9187581cc50171125aea459aae512d64cbef35fa9940cb41eb
decb738ec60823add4c02dad16a82d2f24d842a6050a7cd9e6e90b5840b70ae2
3139d316a1e12b2551e267fdaf50d26fd054a7737a2aace736a56254e2d8e9a2
9b2432ee54deb0f622636fd55881873eed9ef42a46859ae1656648a0dd9396da
cat-searcher/leandojo-benchmark-4-random
test
1,069
PowerSeries.order_monomial
Mathlib/RingTheory/PowerSeries/Order.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rwa [hi, <a>PowerSeries.coeff_monomial_same</a>]
case neg.left R : Type u_1 inst✝¹ : Semiring R φ : R⟦X⟧ n : ℕ a : R inst✝ : Decidable (a = 0) h : ¬a = 0 i : ℕ hi : i = n ⊢ (coeff R i) ((monomial R n) a) ≠ 0
((:c Ne) (:fv _uniq.67925) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.67925) (:fv _uniq.67925) (:fv _uniq.67928) (:fv _uniq.67928) ((:c RingHom.id) (:fv _uniq.67925) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.67925) (:fv _uniq.67928))) ((:c PowerSeries) (:fv _uniq.67925)) (:fv _uniq.67925) ((:c PowerSeries.instAdd...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.67925))"},{"name":"φ","sexp":"((:c PowerSeries) (:fv _uniq.67925))"},{"name":"n","sexp":"(:c Nat)"},{"name":"a","sexp":"(:fv _uniq.67925)"},{"name":"inst✝","sexp":"((:c Decidable) ((:c Eq) (:fv _uniq.67925) (:fv _uniq.68780) ((:...
(:app (:c Ne) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.67925","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.67928","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Semiring) (:arg :explic...
{"children":[{"source":"rwa","sourceEnd":8920,"sourceStart":8917,"tag":"atom"},{"children":[{"source":"[","sourceEnd":8922,"sourceStart":8921,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":9,"semanticRole":"local","source":"hi","sourceEnd":8924,"sourceStar...
[]
[{"source":"hi","source_end":8924,"source_start":8922,"syntax_kind":"ident"},{"source":"coeff_monomial_same","source_end":8945,"source_start":8926,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.67925","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.67928","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern...
42
33
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
811b0792d163db9751b4f7d11c4d18655948239a9c2ddde62542f7ad24c3bd03
9b2432ee54deb0f622636fd55881873eed9ef42a46859ae1656648a0dd9396da
662a2493942d06ddbdb2e1e75ed265cd4be1ed3df738e7bb3878ed3fd307bfb1
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,070
PowerSeries.order_monomial
Mathlib/RingTheory/PowerSeries/Order.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>PartENat.coe_lt_coe</a>] at hi
case neg.right R : Type u_1 inst✝¹ : Semiring R φ : R⟦X⟧ n : ℕ a : R inst✝ : Decidable (a = 0) h : ¬a = 0 i : ℕ hi : ↑i < ↑n ⊢ (coeff R i) ((monomial R n) a) = 0
case neg.right R : Type u_1 inst✝¹ : Semiring R φ : R⟦X⟧ n : ℕ a : R inst✝ : Decidable (a = 0) h : ¬a = 0 i : ℕ hi : i < n ⊢ (coeff R i) ((monomial R n) a) = 0
((:c Eq) (:fv _uniq.67925) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.67925) (:fv _uniq.67925) (:fv _uniq.67928) (:fv _uniq.67928) ((:c RingHom.id) (:fv _uniq.67925) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.67925) (:fv _uniq.67928))) ((:c PowerSeries) (:fv _uniq.67925)) (:fv _uniq.67925) ((:c PowerSeries.instAdd...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.67925))"},{"name":"φ","sexp":"((:c PowerSeries) (:fv _uniq.67925))"},{"name":"n","sexp":"(:c Nat)"},{"name":"a","sexp":"(:fv _uniq.67925)"},{"name":"inst✝","sexp":"((:c Decidable) ((:c Eq) (:fv _uniq.67925) (:fv _uniq.68780) ((:...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.67925","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.67928","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Semiring) (:arg :explic...
{"children":[{"source":"rw","sourceEnd":8956,"sourceStart":8954,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8958,"sourceStart":8957,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"PartENat.coe_lt_coe"...
[]
[{"source":"PartENat.coe_lt_coe","source_end":8977,"source_start":8958,"syntax_kind":"ident"},{"source":"hi","source_end":8984,"source_start":8982,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.67925","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.67928","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern...
42
41
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3a7307740bf7da8e12566f04558fff795ad127dd9b8fad62f659c6b3e3380abd
5fa8502f0d6f581ddd68cd977f987029002a4b2d6382e9a6d6772ab732408240
2c9237484dc94ca1667bf3a2b2328f6266e33e193bee52b9cc5ae7accf0a8268
5ec038fdd7e8daa4e66d6c75745fc055f831d2cded9ace70a484c3a0e84b32e1
cat-searcher/leandojo-benchmark-4-random
test
1,071
PowerSeries.order_monomial
Mathlib/RingTheory/PowerSeries/Order.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>PowerSeries.coeff_monomial</a>, <a>if_neg</a>]
case neg.right R : Type u_1 inst✝¹ : Semiring R φ : R⟦X⟧ n : ℕ a : R inst✝ : Decidable (a = 0) h : ¬a = 0 i : ℕ hi : i < n ⊢ (coeff R i) ((monomial R n) a) = 0
case neg.right.hnc R : Type u_1 inst✝¹ : Semiring R φ : R⟦X⟧ n : ℕ a : R inst✝ : Decidable (a = 0) h : ¬a = 0 i : ℕ hi : i < n ⊢ ¬i = n
((:c Eq) (:fv _uniq.67925) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.67925) (:fv _uniq.67925) (:fv _uniq.67928) (:fv _uniq.67928) ((:c RingHom.id) (:fv _uniq.67925) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.67925) (:fv _uniq.67928))) ((:c PowerSeries) (:fv _uniq.67925)) (:fv _uniq.67925) ((:c PowerSeries.instAdd...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.67925))"},{"name":"φ","sexp":"((:c PowerSeries) (:fv _uniq.67925))"},{"name":"n","sexp":"(:c Nat)"},{"name":"a","sexp":"(:fv _uniq.67925)"},{"name":"inst✝","sexp":"((:c Decidable) ((:c Eq) (:fv _uniq.67925) (:fv _uniq.68780) ((:...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.67925","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.67928","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Semiring) (:arg :explic...
{"children":[{"source":"rw","sourceEnd":8993,"sourceStart":8991,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8995,"sourceStart":8994,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"PowerSeries.coeff_mo...
[]
[{"source":"coeff_monomial","source_end":9009,"source_start":8995,"syntax_kind":"ident"},{"source":"if_neg","source_end":9017,"source_start":9011,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.67925","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.67928","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern...
42
44
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
55aee88e3f7e0ad27af4530bbaac33148f73afdee0fe4d7e541e0d89080fd861
5ec038fdd7e8daa4e66d6c75745fc055f831d2cded9ace70a484c3a0e84b32e1
2889c64db9e2a0a0025356bd40fae0b81ef2f1215e4c568bfb4ded8c7ee1f3f6
56a5c77d472154f4073cf212ec30731aa9dba4a8c624c7af9da6e281270865bd
cat-searcher/leandojo-benchmark-4-random
test
1,072
PowerSeries.order_monomial
Mathlib/RingTheory/PowerSeries/Order.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>ne_of_lt</a> hi
case neg.right.hnc R : Type u_1 inst✝¹ : Semiring R φ : R⟦X⟧ n : ℕ a : R inst✝ : Decidable (a = 0) h : ¬a = 0 i : ℕ hi : i < n ⊢ ¬i = n
((:c Not) ((:c Eq) (:c Nat) (:fv _uniq.70920) (:fv _uniq.68779)))
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.67925))"},{"name":"φ","sexp":"((:c PowerSeries) (:fv _uniq.67925))"},{"name":"n","sexp":"(:c Nat)"},{"name":"a","sexp":"(:fv _uniq.67925)"},{"name":"inst✝","sexp":"((:c Decidable) ((:c Eq) (:fv _uniq.67925) (:fv _uniq.68780) ((:...
(:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV8)) (:arg :explicit 2 (:fv FV4)))))
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.67925","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.67928","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Semiring) (:arg :explic...
{"children":[{"source":"exact","sourceEnd":9030,"sourceStart":9025,"tag":"atom"},{"children":[{"name":"ne_of_lt","semanticRole":"global","source":"ne_of_lt","sourceEnd":9039,"sourceStart":9031,"tag":"identifier"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"hi","sourceEnd":9042,"sourceStart":9040,"ta...
[]
[{"source":"ne_of_lt hi","source_end":9042,"source_start":9031,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.67925","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.67928","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern...
42
48
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
43932de44073a51314625ecb971887bb3fdbae72e67b421600791556d8172e2e
56a5c77d472154f4073cf212ec30731aa9dba4a8c624c7af9da6e281270865bd
e34cc19c0adbba1ef1d4cb61d371752570541e546e96d5d0a8a69bff31b56bfb
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,073
AlgEquiv.arrowCongr_comp
Mathlib/Algebra/Algebra/Equiv.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
ext
R : Type uR A₁ : Type uA₁ A₂ : Type uA₂ A₃ : Type uA₃ A₁' : Type uA₁' A₂' : Type uA₂' A₃' : Type uA₃' inst✝¹² : CommSemiring R inst✝¹¹ : Semiring A₁ inst✝¹⁰ : Semiring A₂ inst✝⁹ : Semiring A₃ inst✝⁸ : Semiring A₁' inst✝⁷ : Semiring A₂' inst✝⁶ : Semiring A₃' inst✝⁵ : Algebra R A₁ inst✝⁴ : Algebra R A₂ inst✝³ : Algebra R...
case H R : Type uR A₁ : Type uA₁ A₂ : Type uA₂ A₃ : Type uA₃ A₁' : Type uA₁' A₂' : Type uA₂' A₃' : Type uA₃' inst✝¹² : CommSemiring R inst✝¹¹ : Semiring A₁ inst✝¹⁰ : Semiring A₂ inst✝⁹ : Semiring A₃ inst✝⁸ : Semiring A₁' inst✝⁷ : Semiring A₂' inst✝⁶ : Semiring A₃' inst✝⁵ : Algebra R A₁ inst✝⁴ : Algebra R A₂ inst✝³ : Al...
((:c Eq) ((:c AlgHom) (:fv _uniq.82015) (:fv _uniq.82023) (:fv _uniq.82027) (:fv _uniq.82030) (:fv _uniq.82042) (:fv _uniq.82048) (:fv _uniq.82134) (:fv _uniq.82176)) ((:c DFunLike.coe) ((:c Equiv) ((:c AlgHom) (:fv _uniq.82015) (:fv _uniq.82017) (:fv _uniq.82021) (:fv _uniq.82030) (:fv _uniq.82033) (:fv _uniq.82039) (...
[{"name":"R","sexp":"(:sort (+ uR 1))"},{"name":"A₁","sexp":"(:sort (+ uA₁ 1))"},{"name":"A₂","sexp":"(:sort (+ uA₂ 1))"},{"name":"A₃","sexp":"(:sort (+ uA₃ 1))"},{"name":"A₁'","sexp":"(:sort (+ uA₁' 1))"},{"name":"A₂'","sexp":"(:sort (+ uA₂' 1))"},{"name":"A₃'","sexp":"(:sort (+ uA₃' 1))"},{"name":"inst✝¹²","sexp":"((...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c AlgHom) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV4)) (:arg :explicit 2 (:fv FV6)) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV4))))) (:arg ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.82015","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.82017","is_instance":false,"is_let":false,"name":"A₁","sexp":"(:sort Type)"},{"binder_role":":implicit","co...
{"children":[{"source":"ext","sourceEnd":17919,"sourceStart":17916,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":17919,"sourceStart":17916,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.82015","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.82017","is_instance":false,"is_let":false,"user_name":"A₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
157
4
exact
true
1
26
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8166dcf16794f88809947c3fc10103e93897882603277a13a7cdeddc1284afc6
e3029c2d90f69464ea462e3f59f98747ffbfad4ca3f0cf511d54d8a2f7bf6c6e
a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de
94769c16c9ace75c3fe001109a6e09d171776a98285fcee7d97bdb953503da36
cat-searcher/leandojo-benchmark-4-random
test
1,074
AlgEquiv.arrowCongr_comp
Mathlib/Algebra/Algebra/Equiv.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>AlgEquiv.arrowCongr</a>, <a>Equiv.coe_fn_mk</a>, <a>AlgHom.comp_apply</a>]
case H R : Type uR A₁ : Type uA₁ A₂ : Type uA₂ A₃ : Type uA₃ A₁' : Type uA₁' A₂' : Type uA₂' A₃' : Type uA₃' inst✝¹² : CommSemiring R inst✝¹¹ : Semiring A₁ inst✝¹⁰ : Semiring A₂ inst✝⁹ : Semiring A₃ inst✝⁸ : Semiring A₁' inst✝⁷ : Semiring A₂' inst✝⁶ : Semiring A₃' inst✝⁵ : Algebra R A₁ inst✝⁴ : Algebra R A₂ inst✝³ : Al...
case H R : Type uR A₁ : Type uA₁ A₂ : Type uA₂ A₃ : Type uA₃ A₁' : Type uA₁' A₂' : Type uA₂' A₃' : Type uA₃' inst✝¹² : CommSemiring R inst✝¹¹ : Semiring A₁ inst✝¹⁰ : Semiring A₂ inst✝⁹ : Semiring A₃ inst✝⁸ : Semiring A₁' inst✝⁷ : Semiring A₂' inst✝⁶ : Semiring A₃' inst✝⁵ : Algebra R A₁ inst✝⁴ : Algebra R A₂ inst✝³ : Al...
((:c Eq) (:fv _uniq.82027) ((:c DFunLike.coe) ((:c AlgHom) (:fv _uniq.82015) (:fv _uniq.82023) (:fv _uniq.82027) (:fv _uniq.82030) (:fv _uniq.82042) (:fv _uniq.82048) (:fv _uniq.82134) (:fv _uniq.82176)) (:fv _uniq.82023) (:lambda _ (:fv _uniq.82023) (:fv _uniq.82027)) ((:c AlgHom.funLike) (:fv _uniq.82015) (:fv _uniq....
[{"name":"R","sexp":"(:sort (+ uR 1))"},{"name":"A₁","sexp":"(:sort (+ uA₁ 1))"},{"name":"A₂","sexp":"(:sort (+ uA₂ 1))"},{"name":"A₃","sexp":"(:sort (+ uA₃ 1))"},{"name":"A₁'","sexp":"(:sort (+ uA₁' 1))"},{"name":"A₂'","sexp":"(:sort (+ uA₂' 1))"},{"name":"A₃'","sexp":"(:sort (+ uA₃' 1))"},{"name":"inst✝¹²","sexp":"((...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AlgHom) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV4)) (:arg :explicit 2 (:fv FV6)) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instanc...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.82015","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.82017","is_instance":false,"is_let":false,"name":"A₁","sexp":"(:sort Type)"},{"binder_role":":implicit","co...
{"children":[{"source":"simp","sourceEnd":17926,"sourceStart":17922,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":17931,"sourceStart":17927,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":179...
[]
[{"source":"arrowCongr","source_end":17943,"source_start":17933,"syntax_kind":"ident"},{"source":"Equiv.coe_fn_mk","source_end":17960,"source_start":17945,"syntax_kind":"ident"},{"source":"AlgHom.comp_apply","source_end":17979,"source_start":17962,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.82015","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.82017","is_instance":false,"is_let":false,"user_name":"A₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
157
5
exact
true
1
27
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d0f2f02c4f449b8d66a39938065b2593b185dccbfebae7121900e538d9d7d55b
94769c16c9ace75c3fe001109a6e09d171776a98285fcee7d97bdb953503da36
800fd8ca56e4a0567b6cd77aa158f034d98ef062979745f156b24a932f13c303
2385a797701ede2938331156c6adadb1c577313a5aac46173e2ecb94ab33d2ed
cat-searcher/leandojo-benchmark-4-random
test
1,075
AlgEquiv.arrowCongr_comp
Mathlib/Algebra/Algebra/Equiv.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
congr
case H R : Type uR A₁ : Type uA₁ A₂ : Type uA₂ A₃ : Type uA₃ A₁' : Type uA₁' A₂' : Type uA₂' A₃' : Type uA₃' inst✝¹² : CommSemiring R inst✝¹¹ : Semiring A₁ inst✝¹⁰ : Semiring A₂ inst✝⁹ : Semiring A₃ inst✝⁸ : Semiring A₁' inst✝⁷ : Semiring A₂' inst✝⁶ : Semiring A₃' inst✝⁵ : Algebra R A₁ inst✝⁴ : Algebra R A₂ inst✝³ : Al...
case H.h.e_6.h.h.e_6.h R : Type uR A₁ : Type uA₁ A₂ : Type uA₂ A₃ : Type uA₃ A₁' : Type uA₁' A₂' : Type uA₂' A₃' : Type uA₃' inst✝¹² : CommSemiring R inst✝¹¹ : Semiring A₁ inst✝¹⁰ : Semiring A₂ inst✝⁹ : Semiring A₃ inst✝⁸ : Semiring A₁' inst✝⁷ : Semiring A₂' inst✝⁶ : Semiring A₃' inst✝⁵ : Algebra R A₁ inst✝⁴ : Algebra ...
((:c Eq) (:fv _uniq.82027) ((:c DFunLike.coe) ((:c AlgHom) (:fv _uniq.82015) (:fv _uniq.82021) (:fv _uniq.82027) (:fv _uniq.82030) (:fv _uniq.82039) (:fv _uniq.82048) (:fv _uniq.82113) (:fv _uniq.82176)) (:fv _uniq.82021) (:lambda _ (:fv _uniq.82021) (:fv _uniq.82027)) ((:c AlgHom.funLike) (:fv _uniq.82015) (:fv _uniq....
[{"name":"R","sexp":"(:sort (+ uR 1))"},{"name":"A₁","sexp":"(:sort (+ uA₁ 1))"},{"name":"A₂","sexp":"(:sort (+ uA₂ 1))"},{"name":"A₃","sexp":"(:sort (+ uA₃ 1))"},{"name":"A₁'","sexp":"(:sort (+ uA₁' 1))"},{"name":"A₂'","sexp":"(:sort (+ uA₂' 1))"},{"name":"A₃'","sexp":"(:sort (+ uA₃' 1))"},{"name":"inst✝¹²","sexp":"((...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AlgHom) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV6)) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instanc...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.82015","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.82017","is_instance":false,"is_let":false,"name":"A₁","sexp":"(:sort Type)"},{"binder_role":":implicit","co...
{"children":[{"source":"congr","sourceEnd":17988,"sourceStart":17983,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.congr","source":"congr","sourceEnd":17988,"sourceStart":17983,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.82015","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.82017","is_instance":false,"is_let":false,"user_name":"A₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
157
6
exact
true
1
27
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0016914b09124ffe32d4f634c489e568c51d9aac51efdfab1717c61f9698b6f7
2385a797701ede2938331156c6adadb1c577313a5aac46173e2ecb94ab33d2ed
092b163cac48997cb6cc327c63cda260e694055f56ff3698a70cdfda80ffbb2b
0f37d056047336a24bfa20a29bc9d8b356e6bd6b14789011f65f1c76194893cb
cat-searcher/leandojo-benchmark-4-random
test
1,076
AlgEquiv.arrowCongr_comp
Mathlib/Algebra/Algebra/Equiv.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact (e₂.symm_apply_apply _).<a>Eq.symm</a>
case H.h.e_6.h.h.e_6.h R : Type uR A₁ : Type uA₁ A₂ : Type uA₂ A₃ : Type uA₃ A₁' : Type uA₁' A₂' : Type uA₂' A₃' : Type uA₃' inst✝¹² : CommSemiring R inst✝¹¹ : Semiring A₁ inst✝¹⁰ : Semiring A₂ inst✝⁹ : Semiring A₃ inst✝⁸ : Semiring A₁' inst✝⁷ : Semiring A₂' inst✝⁶ : Semiring A₃' inst✝⁵ : Algebra R A₁ inst✝⁴ : Algebra ...
((:c Eq) (:fv _uniq.82019) ((:c DFunLike.coe) ((:c AlgHom) (:fv _uniq.82015) (:fv _uniq.82017) (:fv _uniq.82019) (:fv _uniq.82030) (:fv _uniq.82033) (:fv _uniq.82036) (:fv _uniq.82071) (:fv _uniq.82092)) (:fv _uniq.82017) (:lambda _ (:fv _uniq.82017) (:fv _uniq.82019)) ((:c AlgHom.funLike) (:fv _uniq.82015) (:fv _uniq....
[{"name":"R","sexp":"(:sort (+ uR 1))"},{"name":"A₁","sexp":"(:sort (+ uA₁ 1))"},{"name":"A₂","sexp":"(:sort (+ uA₂ 1))"},{"name":"A₃","sexp":"(:sort (+ uA₃ 1))"},{"name":"A₁'","sexp":"(:sort (+ uA₁' 1))"},{"name":"A₂'","sexp":"(:sort (+ uA₂' 1))"},{"name":"A₃'","sexp":"(:sort (+ uA₃' 1))"},{"name":"inst✝¹²","sexp":"((...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AlgHom) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instanc...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.82015","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.82017","is_instance":false,"is_let":false,"name":"A₁","sexp":"(:sort Type)"},{"binder_role":":implicit","co...
{"children":[{"source":"exact","sourceEnd":17996,"sourceStart":17991,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":17998,"sourceStart":17997,"tag":"atom"},{"children":[{"source":"e₂.symm_apply_apply","sourceEnd":18019,"sourceStart":17998,"tag":"identifier"},{"children":[{"children":[{"source":"_","s...
[]
[{"source":"(e₂.symm_apply_apply _).symm","source_end":18027,"source_start":17997,"syntax_kind":"Lean.Parser.Term.proj"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.82015","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.82017","is_instance":false,"is_let":false,"user_name":"A₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_u...
157
7
exact
true
1
27
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
880dba4b8a62c5a9268ba4540f94c6176c5a177c5fcd0d17cc816ff377c6e636
0f37d056047336a24bfa20a29bc9d8b356e6bd6b14789011f65f1c76194893cb
f342249e9ff5f53f66f5786ac2dea270d423639c8402436084f1bf80612d9cb9
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,077
ProbabilityTheory.measure_ge_le_exp_mul_mgf
Mathlib/Probability/Moments.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rcases ht.eq_or_lt with ht_zero_eq | ht_pos
Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ⊢ (μ {ω | ε ≤ X ω}).toReal ≤ rexp (-t * ε) * mgf X μ t
case inl Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_zero_eq : 0 = t ⊢ (μ {ω | ε ≤ X ω}).toReal ≤ rexp (-t * ε) * mgf X μ t case inr Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω ...
((:c LE.le) (:c Real) (:c Real.instLE) ((:c ENNReal.toReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)) ((:c Set) (:fv _uniq.33656)) (:lambda _ ((:c Set) (:fv _uniq.33656)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.33656) (:fv _uniq.33662)) (:fv _uniq.33677...
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.33656))"},{"name":"X","sexp":"(:forall _ (:fv _uniq.33656) (:c Real))"},{"name":"p","sexp":"(:c Nat)"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c ENNReal.toReal) (:arg :explicit 0 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"rcases","sourceEnd":16321,"sourceStart":16315,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"LE.le.eq_or_lt","semanticRole":"global","source":"ht.eq_or_lt","sourceEnd":16333,"sourceStart":16322,"tag":"identifier"}],"kind":"Lean.Parser.Tact...
[]
[{"source":"ht.eq_or_lt","source_end":16333,"source_start":16322,"syntax_kind":"ident"},{"source":"ht_zero_eq | ht_pos","source_end":16358,"source_start":16339,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
85
4
exact
true
1
11
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
303f80a70712dc0fb652847862ac3d87a589d9ee1b752fdf623df0de22b446a0
50ca984300ef9841ba5f9dbb126b6ff9482f7f4ac7c9cf7fee9ee842b76c079a
a255dd919ba72f1fc2e5a420b1ed666cc37524b2b52f68be29976c2b67a65d00
d7203a160e51f85fc7b0ffbc428a47caaa9295a6980c506ca34cd332635dddae
cat-searcher/leandojo-benchmark-4-random
test
1,078
ProbabilityTheory.measure_ge_le_exp_mul_mgf
Mathlib/Probability/Moments.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
calc (μ {ω | ε ≤ X ω}).<a>ENNReal.toReal</a> = (μ {ω | <a>Real.exp</a> (t * ε) ≤ <a>Real.exp</a> (t * X ω)}).<a>ENNReal.toReal</a> := by congr with ω simp only [<a>Set.mem_setOf_eq</a>, <a>Real.exp_le_exp</a>, <a>gt_iff_lt</a>] exact ⟨fun h => <a>mul_le_mul_of_nonneg_left</a> h ht_pos.le, fun h => <a>le_of_mul_le_mul_l...
case inr Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_pos : 0 < t ⊢ (μ {ω | ε ≤ X ω}).toReal ≤ rexp (-t * ε) * mgf X μ t
((:c LE.le) (:c Real) (:c Real.instLE) ((:c ENNReal.toReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)) ((:c Set) (:fv _uniq.33656)) (:lambda _ ((:c Set) (:fv _uniq.33656)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.33656) (:fv _uniq.33662)) (:fv _uniq.33677...
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.33656))"},{"name":"X","sexp":"(:forall _ (:fv _uniq.33656) (:c Real))"},{"name":"p","sexp":"(:c Nat)"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c ENNReal.toReal) (:arg :explicit 0 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"calc","sourceEnd":16577,"sourceStart":16573,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"(","sourceEnd":16583,"sourceStart":16582,"tag":"atom"},{"children":[{"contextIndex":5,"semanticRole":"local","source":"μ","sourceEnd":16585,"sourceStart":16583,"t...
[]
[{"source":"(μ {ω | ε ≤ X ω}).toReal = (μ {ω | exp (t * ε) ≤ exp (t * X ω)}).toReal","source_end":16665,"source_start":16582,"syntax_kind":"«term_=_»"},{"source":"Set.mem_setOf_eq","source_end":16725,"source_start":16709,"syntax_kind":"ident"},{"source":"exp_le_exp","source_end":16737,"source_start":16727,"syntax_kind"...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
85
17
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3ef67d1b41dbcf6fb80767f0f15a9051394f56eef2db694ad18c0af8be9e1b16
970a67645db00525bca682c79cb7a596704138e21eb3c4da088e57193d2adb1f
acc994d51247bb52d9ea149183103572a26ed59bf54d1424aaa67efd2d670861
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,079
ProbabilityTheory.measure_ge_le_exp_mul_mgf
Mathlib/Probability/Moments.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [ht_zero_eq.symm]
case inl Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_zero_eq : 0 = t ⊢ (μ {ω | ε ≤ X ω}).toReal ≤ rexp (-t * ε) * mgf X μ t
case inl Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_zero_eq : 0 = t ⊢ (μ {ω | ε ≤ X ω}).toReal ≤ rexp (-0 * ε) * mgf X μ 0
((:c LE.le) (:c Real) (:c Real.instLE) ((:c ENNReal.toReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)) ((:c Set) (:fv _uniq.33656)) (:lambda _ ((:c Set) (:fv _uniq.33656)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.33656) (:fv _uniq.33662)) (:fv _uniq.33677...
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.33656))"},{"name":"X","sexp":"(:forall _ (:fv _uniq.33656) (:c Real))"},{"name":"p","sexp":"(:c Nat)"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c ENNReal.toReal) (:arg :explicit 0 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"rw","sourceEnd":16366,"sourceStart":16364,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16368,"sourceStart":16367,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Eq.symm","semant...
[]
[{"source":"ht_zero_eq.symm","source_end":16383,"source_start":16368,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
85
9
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d7af004fcddf74d11a1694e2842ab1205beb35c04e2723897566d47e3260141d
39cae4b40cda57c64dd1f62df034407edac8880532c03b99e753457c7f465b3a
8dc66694d44c042c7831908e111939200cf3abbefb047c8aa8a5c0a0b57bbd36
22c8a06fa5656e7a5ad8da88f368f0b01f1211ce17c125fe9bb362e613cdbb35
cat-searcher/leandojo-benchmark-4-random
test
1,080
ProbabilityTheory.measure_ge_le_exp_mul_mgf
Mathlib/Probability/Moments.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>neg_zero</a>, <a>MulZeroClass.zero_mul</a>, <a>Real.exp_zero</a>, <a>ProbabilityTheory.mgf_zero'</a>, <a>one_mul</a>]
case inl Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_zero_eq : 0 = t ⊢ (μ {ω | ε ≤ X ω}).toReal ≤ rexp (-0 * ε) * mgf X μ 0
case inl Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_zero_eq : 0 = t ⊢ (μ {ω | ε ≤ X ω}).toReal ≤ (μ Set.univ).toReal
((:c LE.le) (:c Real) (:c Real.instLE) ((:c ENNReal.toReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)) ((:c Set) (:fv _uniq.33656)) (:lambda _ ((:c Set) (:fv _uniq.33656)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.33656) (:fv _uniq.33662)) (:fv _uniq.33677...
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.33656))"},{"name":"X","sexp":"(:forall _ (:fv _uniq.33656) (:c Real))"},{"name":"p","sexp":"(:c Nat)"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c ENNReal.toReal) (:arg :explicit 0 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"simp","sourceEnd":16393,"sourceStart":16389,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":16398,"sourceStart":16394,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":163...
[]
[{"source":"neg_zero","source_end":16408,"source_start":16400,"syntax_kind":"ident"},{"source":"zero_mul","source_end":16418,"source_start":16410,"syntax_kind":"ident"},{"source":"exp_zero","source_end":16428,"source_start":16420,"syntax_kind":"ident"},{"source":"mgf_zero'","source_end":16439,"source_start":16430,"synt...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
85
12
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8f025fe0cf8942e0949e6c5b806de20c5a816ab470f8b1f4e5e439f6248d143d
22c8a06fa5656e7a5ad8da88f368f0b01f1211ce17c125fe9bb362e613cdbb35
52b9690b3a4452889a8b25ffd771557acc37d76043db65ee0dd6d31866fe569a
f0459c9bb50b5f6696204ddd624b6fb2cb09bf502764d5d79b64eebdde575495
cat-searcher/leandojo-benchmark-4-random
test
1,081
ProbabilityTheory.measure_ge_le_exp_mul_mgf
Mathlib/Probability/Moments.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>ENNReal.toReal_le_toReal</a> (<a>MeasureTheory.measure_ne_top</a> μ _) (<a>MeasureTheory.measure_ne_top</a> μ _)]
case inl Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_zero_eq : 0 = t ⊢ (μ {ω | ε ≤ X ω}).toReal ≤ (μ Set.univ).toReal
case inl Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_zero_eq : 0 = t ⊢ μ {ω | ε ≤ X ω} ≤ μ Set.univ
((:c LE.le) (:c Real) (:c Real.instLE) ((:c ENNReal.toReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)) ((:c Set) (:fv _uniq.33656)) (:lambda _ ((:c Set) (:fv _uniq.33656)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.33656) (:fv _uniq.33662)) (:fv _uniq.33677...
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.33656))"},{"name":"X","sexp":"(:forall _ (:fv _uniq.33656) (:c Real))"},{"name":"p","sexp":"(:c Nat)"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c ENNReal.toReal) (:arg :explicit 0 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"rw","sourceEnd":16456,"sourceStart":16454,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16458,"sourceStart":16457,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"ENN...
[]
[{"source":"ENNReal.toReal_le_toReal (measure_ne_top μ _) (measure_ne_top μ _)","source_end":16526,"source_start":16458,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
85
13
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ee2516139b92cdc2961520aa0cbf8826f0b8ce24d44cb33bb0269cd0d175cad5
f0459c9bb50b5f6696204ddd624b6fb2cb09bf502764d5d79b64eebdde575495
1b87685b12d69006cdef1a3a21961229602ef72576f87776f8fa31c2453c47f9
ee79160b49f7dafa6258290ca60b1e085af48e1594cbf69ce675bc624e295c20
cat-searcher/leandojo-benchmark-4-random
test
1,082
ProbabilityTheory.measure_ge_le_exp_mul_mgf
Mathlib/Probability/Moments.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>MeasureTheory.measure_mono</a> (<a>Set.subset_univ</a> _)
case inl Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_zero_eq : 0 = t ⊢ μ {ω | ε ≤ X ω} ≤ μ Set.univ
((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.toPartialOrder) (:c ENNReal) ((:c OrderedCommSemiring.toOrderedSemiring) (:c ENNReal) ((:c CanonicallyOrderedCommSemiring.toOrderedCommSemiring) (:c ENNReal) (:c ENNReal.instCanonicallyOrderedCommSe...
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.33656))"},{"name":"X","sexp":"(:forall _ (:fv _uniq.33656) (:c Real))"},{"name":"p","sexp":"(:c Nat)"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)...
(:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace)...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"exact","sourceEnd":16537,"sourceStart":16532,"tag":"atom"},{"children":[{"name":"MeasureTheory.measure_mono","semanticRole":"global","source":"measure_mono","sourceEnd":16550,"sourceStart":16538,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":16552,"sourceStart":16551,"ta...
[]
[{"source":"measure_mono (Set.subset_univ _)","source_end":16570,"source_start":16538,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
85
16
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5f9a99a6d14995bff4b4ced98472140d8a1ac4202f59d2df385c50e81320d192
ee79160b49f7dafa6258290ca60b1e085af48e1594cbf69ce675bc624e295c20
fff61e4405290f76f4132dcc6819ca839e18b71942560e03410d11883fc0715f
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,083
ProbabilityTheory.measure_ge_le_exp_mul_mgf
Mathlib/Probability/Moments.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
congr with ω
Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_pos : 0 < t ⊢ (μ {ω | ε ≤ X ω}).toReal = (μ {ω | rexp (t * ε) ≤ rexp (t * X ω)}).toReal
case e_a.h.e_6.h.h Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_pos : 0 < t ω : Ω ⊢ ω ∈ {ω | ε ≤ X ω} ↔ ω ∈ {ω | rexp (t * ε) ≤ rexp (t * X ω)}
((:c Eq) (:c Real) ((:c ENNReal.toReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)) ((:c Set) (:fv _uniq.33656)) (:lambda _ ((:c Set) (:fv _uniq.33656)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.33656) (:fv _uniq.33662)) (:fv _uniq.33677) ((:c setOf) (:fv _...
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.33656))"},{"name":"X","sexp":"(:forall _ (:fv _uniq.33656) (:c Real))"},{"name":"p","sexp":"(:c Nat)"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)...
(:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c ENNReal.toReal) (:arg :explicit 0 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))))) (:arg :i...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"congr","sourceEnd":16683,"sourceStart":16678,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":"with","sourceEnd":16688,"sourceStart":16684,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"sc...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
85
22
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
12137bcb3d66e5dd49ff4dde1972dccf78fc542d7fb19debab3bf4f6ba8ee002
be71e072f2f8faf6ebf200e3a3cc6058e88376f67cfc86aba513b1ebf0918054
c3cec9e4434154414b17e8f94cfaa5f52ad2ad34ff9bab008cf5b6e459b16f05
b4e5c66cdf94d34519eb8dc603dbe9ff6cf7b53dd348325e8d307e03ada54952
cat-searcher/leandojo-benchmark-4-random
test
1,084
ProbabilityTheory.measure_ge_le_exp_mul_mgf
Mathlib/Probability/Moments.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>Set.mem_setOf_eq</a>, <a>Real.exp_le_exp</a>, <a>gt_iff_lt</a>]
case e_a.h.e_6.h.h Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_pos : 0 < t ω : Ω ⊢ ω ∈ {ω | ε ≤ X ω} ↔ ω ∈ {ω | rexp (t * ε) ≤ rexp (t * X ω)}
case e_a.h.e_6.h.h Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_pos : 0 < t ω : Ω ⊢ ε ≤ X ω ↔ t * ε ≤ t * X ω
((:c Iff) ((:c Membership.mem) (:fv _uniq.33656) ((:c Set) (:fv _uniq.33656)) ((:c Set.instMembership) (:fv _uniq.33656)) (:fv _uniq.36559) ((:c setOf) (:fv _uniq.33656) (:lambda ω (:fv _uniq.33656) ((:c LE.le) (:c Real) (:c Real.instLE) (:fv _uniq.34016) ((:fv _uniq.33666) 0))))) ((:c Membership.mem) (:fv _uniq.33656)...
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.33656))"},{"name":"X","sexp":"(:forall _ (:fv _uniq.33656) (:c Real))"},{"name":"p","sexp":"(:c Nat)"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :e...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"simp","sourceEnd":16702,"sourceStart":16698,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":16707,"sourceStart":16703,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":167...
[]
[{"source":"Set.mem_setOf_eq","source_end":16725,"source_start":16709,"syntax_kind":"ident"},{"source":"exp_le_exp","source_end":16737,"source_start":16727,"syntax_kind":"ident"},{"source":"gt_iff_lt","source_end":16748,"source_start":16739,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
85
23
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7054eb6d49549736682709ea94faeef81d19d1879bc7c0b2590bd2515f55a848
b4e5c66cdf94d34519eb8dc603dbe9ff6cf7b53dd348325e8d307e03ada54952
8deae09a3085dfbd38485a4a4844b03c6bd8cc537ef78d2c5123debcc7db9ee8
99c0a89c908f65732dcebbb269583cfe3875e43d0b3f980c3503d47fcee7340f
cat-searcher/leandojo-benchmark-4-random
test
1,085
ProbabilityTheory.measure_ge_le_exp_mul_mgf
Mathlib/Probability/Moments.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact ⟨fun h => <a>mul_le_mul_of_nonneg_left</a> h ht_pos.le, fun h => <a>le_of_mul_le_mul_left</a> h ht_pos⟩
case e_a.h.e_6.h.h Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_pos : 0 < t ω : Ω ⊢ ε ≤ X ω ↔ t * ε ≤ t * X ω
((:c Iff) ((:c LE.le) (:c Real) (:c Real.instLE) (:fv _uniq.34016) ((:fv _uniq.33666) (:fv _uniq.36559))) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.33679) (:fv _uniq.34016)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((...
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.33656))"},{"name":"X","sexp":"(:forall _ (:fv _uniq.33656) (:c Real))"},{"name":"p","sexp":"(:c Nat)"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)...
(:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV9)) (:arg :explicit 3 (:app (:fv FV3) (:arg :explicit 0 (:fv FV13)))))) (:arg :explicit 1 (:app (:c LE.le) (:arg :implicit-type 0 (:c...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"exact","sourceEnd":16761,"sourceStart":16756,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":16765,"sourceStart":16762,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":16768,"sourceStart":16765,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source...
[]
[{"source":"⟨fun h => mul_le_mul_of_nonneg_left h ht_pos.le,\n fun h => le_of_mul_le_mul_left h ht_pos⟩","source_end":16863,"source_start":16762,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
85
24
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7bf67412f9ebdc45d0b45012221013dc19a0caa9d3a4ddeeec74e73463ada332
99c0a89c908f65732dcebbb269583cfe3875e43d0b3f980c3503d47fcee7340f
b177016eeb2fffbd31f90f2d945e9bab20325904450391f293a9044dbbb8a67b
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,086
ProbabilityTheory.measure_ge_le_exp_mul_mgf
Mathlib/Probability/Moments.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have : <a>Real.exp</a> (t * ε) * (μ {ω | <a>Real.exp</a> (t * ε) ≤ <a>Real.exp</a> (t * X ω)}).<a>ENNReal.toReal</a> ≤ μ[fun ω => <a>Real.exp</a> (t * X ω)] := <a>MeasureTheory.mul_meas_ge_le_integral_of_nonneg</a> (<a>MeasureTheory.ae_of_all</a> _ fun x => (<a>Real.exp_pos</a> _).<a>LT.lt.le</a>) h_int _
Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_pos : 0 < t ⊢ (μ {ω | rexp (t * ε) ≤ rexp (t * X ω)}).toReal ≤ (rexp (t * ε))⁻¹ * ∫ (x : Ω), (fun ω => rexp (t * X ω)) x ∂μ
Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_pos : 0 < t this : rexp (t * ε) * (μ {ω | rexp (t * ε) ≤ rexp (t * X ω)}).toReal ≤ ∫ (x : Ω), (fun ω => rexp (t * X ω)) x ∂μ ⊢ (μ {ω | rexp (t ...
((:c LE.le) (:c Real) (:c Real.instLE) ((:c ENNReal.toReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)) ((:c Set) (:fv _uniq.33656)) (:lambda _ ((:c Set) (:fv _uniq.33656)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.33656) (:fv _uniq.33662)) (:fv _uniq.33677...
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.33656))"},{"name":"X","sexp":"(:forall _ (:fv _uniq.33656) (:c Real))"},{"name":"p","sexp":"(:c Nat)"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c ENNReal.toReal) (:arg :explicit 0 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"have","sourceEnd":16941,"sourceStart":16937,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":16942,"sourceStart":16942,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":16942,"sourceStart":16942,"tag":"node"}],"kind":"Lean.Parser.Term.hav...
[]
[{"source":"exp (t * ε) * (μ {ω | exp (t * ε) ≤ exp (t * X ω)}).toReal ≤\n μ[fun ω => exp (t * X ω)]","source_end":17052,"source_start":16944,"syntax_kind":"«term_≤_»"},{"source":"mul_meas_ge_le_integral_of_nonneg (ae_of_all _ fun x => (exp_pos _).le) h_int _","source_end":17143,"source_start":17064,"syntax_ki...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
85
29
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
254565e8a8e2d655198d6a8e4bca16c9bd430fe689839038ec541644f167c068
04670312d17730155b6c4cffe8db8dfab2d8559bec7ea5be103044c9d8ea9cfa
20d812eb02c9431cbcf5d75c528f7b3bdb4255c8d064e22c65825844a6887853
2608e2b82b3ff13db6da85db4be2be4571f130d3c8934dcdf63d9162a370d693
cat-searcher/leandojo-benchmark-4-random
test
1,087
ProbabilityTheory.measure_ge_le_exp_mul_mgf
Mathlib/Probability/Moments.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rwa [<a>mul_comm</a> (<a>Real.exp</a> (t * ε))⁻¹, ← <a>div_eq_mul_inv</a>, <a>le_div_iff'</a> (<a>Real.exp_pos</a> _)]
Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_pos : 0 < t this : rexp (t * ε) * (μ {ω | rexp (t * ε) ≤ rexp (t * X ω)}).toReal ≤ ∫ (x : Ω), (fun ω => rexp (t * X ω)) x ∂μ ⊢ (μ {ω | rexp (t ...
((:c LE.le) (:c Real) (:c Real.instLE) ((:c ENNReal.toReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)) ((:c Set) (:fv _uniq.33656)) (:lambda _ ((:c Set) (:fv _uniq.33656)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.33656) (:fv _uniq.33662)) (:fv _uniq.33677...
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.33656))"},{"name":"X","sexp":"(:forall _ (:fv _uniq.33656) (:c Real))"},{"name":"p","sexp":"(:c Nat)"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)...
(:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c ENNReal.toReal) (:arg :explicit 0 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"rwa","sourceEnd":17153,"sourceStart":17150,"tag":"atom"},{"children":[{"source":"[","sourceEnd":17155,"sourceStart":17154,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"mul_comm","semanticRole":"global","source":"mul_comm","so...
[]
[{"source":"mul_comm (exp (t * ε))⁻¹","source_end":17183,"source_start":17155,"syntax_kind":"Lean.Parser.Term.app"},{"source":"div_eq_mul_inv","source_end":17203,"source_start":17189,"syntax_kind":"ident"},{"source":"le_div_iff' (exp_pos _)","source_end":17228,"source_start":17205,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
85
30
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7c91bd6b2b2d2289648f018c3866e4832cb592aec1f7e7700757bb7785653a03
2608e2b82b3ff13db6da85db4be2be4571f130d3c8934dcdf63d9162a370d693
40c730fdc98e752cf50a188d49515fb1bc9add2bea22513d50895ddf10a593d3
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,088
ProbabilityTheory.measure_ge_le_exp_mul_mgf
Mathlib/Probability/Moments.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>neg_mul</a>, <a>Real.exp_neg</a>]
Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_pos : 0 < t ⊢ (rexp (t * ε))⁻¹ * ∫ (x : Ω), (fun ω => rexp (t * X ω)) x ∂μ = rexp (-t * ε) * mgf X μ t
Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_pos : 0 < t ⊢ (rexp (t * ε))⁻¹ * ∫ (x : Ω), (fun ω => rexp (t * X ω)) x ∂μ = (rexp (t * ε))⁻¹ * mgf X μ t
((: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 Real.exp) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.33679) (:fv _uniq.34016)))) ((:c MeasureTheory.integr...
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.33656))"},{"name":"X","sexp":"(:forall _ (:fv _uniq.33656) (:c Real))"},{"name":"p","sexp":"(:c Nat)"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)...
(: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.33656","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"rw","sourceEnd":17273,"sourceStart":17271,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":17275,"sourceStart":17274,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"neg_mul","semant...
[]
[{"source":"neg_mul","source_end":17282,"source_start":17275,"syntax_kind":"ident"},{"source":"exp_neg","source_end":17291,"source_start":17284,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
85
39
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
111ed047deb365afd71d09ac1b1302bf62ee5351c0144483111ecf488264166e
2c1ce8a43fe32b39cbd9187c54150342f8eb138c96ed4dd6937c0753e73a8f0a
9b6e273dcdd241d8036d890137433b688269c39ec9aa1f6a4a90fab4a9b514cb
07998a3f4cef09d279f7830f2e1dc21640976c28b71df8c04fc0bf45f4a85a0d
cat-searcher/leandojo-benchmark-4-random
test
1,089
ProbabilityTheory.measure_ge_le_exp_mul_mgf
Mathlib/Probability/Moments.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rfl
Ω : Type u_1 ι : Type u_2 m : MeasurableSpace Ω X : Ω → ℝ p : ℕ μ : Measure Ω t : ℝ inst✝ : IsFiniteMeasure μ ε : ℝ ht : 0 ≤ t h_int : Integrable (fun ω => rexp (t * X ω)) μ ht_pos : 0 < t ⊢ (rexp (t * ε))⁻¹ * ∫ (x : Ω), (fun ω => rexp (t * X ω)) x ∂μ = (rexp (t * ε))⁻¹ * mgf X μ t
((: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 Real.exp) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.33679) (:fv _uniq.34016)))) ((:c MeasureTheory.integr...
[{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.33656))"},{"name":"X","sexp":"(:forall _ (:fv _uniq.33656) (:c Real))"},{"name":"p","sexp":"(:c Nat)"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.33656) (:fv _uniq.33662)...
(: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.33656","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"rfl","sourceEnd":17297,"sourceStart":17294,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":17297,"sourceStart":17294,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33656","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33659","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
85
44
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a6d6e7a09c105717eb4b4b3ef2624452706e70fb83b24f5422e10261562bebd8
07998a3f4cef09d279f7830f2e1dc21640976c28b71df8c04fc0bf45f4a85a0d
5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,090
FirstOrder.Language.realize_noTopOrder_iff
Mathlib/ModelTheory/Order.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>FirstOrder.Language.noTopOrderSentence</a>, <a>FirstOrder.Language.Sentence.Realize</a>, <a>FirstOrder.Language.Formula.Realize</a>, <a>FirstOrder.Language.BoundedFormula.realize_all</a>, <a>FirstOrder.Language.BoundedFormula.realize_ex</a>, <a>FirstOrder.Language.BoundedFormula.realize_not</a>, <a>FirstO...
L : Language α : Type w M : Type w' n : ℕ inst✝ : LE M ⊢ M ⊨ Language.order.noTopOrderSentence ↔ NoTopOrder M
L : Language α : Type w M : Type w' n : ℕ inst✝ : LE M ⊢ (∀ (a : M), ∃ a_1, ¬Fin.snoc (Fin.snoc default a) a_1 1 ≤ Fin.snoc (Fin.snoc default a) a_1 0) ↔ NoTopOrder M
((:c Iff) ((:c FirstOrder.Language.Sentence.Realize) (:c FirstOrder.Language.order) (:fv _uniq.12514) ((:c FirstOrder.Language.orderStructure) (:fv _uniq.12514) (:fv _uniq.12519)) ((:c FirstOrder.Language.noTopOrderSentence) (:c FirstOrder.Language.order) (:c FirstOrder.Language.instIsOrderedOrder))) ((:c NoTopOrder) (...
[{"name":"L","sexp":"(:c FirstOrder.Language)"},{"name":"α","sexp":"(:sort (+ w 1))"},{"name":"M","sexp":"(:sort (+ w' 1))"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c LE) (:fv _uniq.12514))"}]
(:app (:c Iff) (:arg :explicit 0 (:app (:c FirstOrder.Language.Sentence.Realize) (:arg :implicit 0) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c FirstOrder.Language.Structure) (:arg :explicit 0 (:c FirstOrder.Language.order)) (:arg :explicit 1 (:fv FV2))))) (:arg :explicit 3 (:app (:c FirstOrd...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12510","is_instance":false,"is_let":false,"name":"L","sexp":"(:c FirstOrder.Language)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12512","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":im...
{"children":[{"source":"simp","sourceEnd":9508,"sourceStart":9504,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":9513,"sourceStart":9509,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":9513,"s...
[]
[{"source":"noTopOrderSentence","source_end":9533,"source_start":9515,"syntax_kind":"ident"},{"source":"Sentence.Realize","source_end":9551,"source_start":9535,"syntax_kind":"ident"},{"source":"Formula.Realize","source_end":9568,"source_start":9553,"syntax_kind":"ident"},{"source":"BoundedFormula.realize_all","source_e...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12510","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12512","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
80
4
exact
true
1
5
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a0fd0bd16061d29669af4b926ca9ba1a215479d55bf7576c7c343b184b880437
0c810861a82d53fa777b6ba23d62d2dfbd1c5248f963d58f66f5f59e64c15e24
eb5313542c9e6c0df4d1d0034cf80d080dc5e23a8d6b4de041dfe2326d0f9ac2
ab5fe10dca42da5ff4e2e35591a7571a443d7600962f7bf31c392e430ae719e2
cat-searcher/leandojo-benchmark-4-random
test
1,091
FirstOrder.Language.realize_noTopOrder_iff
Mathlib/ModelTheory/Order.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨fun h => ⟨fun a => h a⟩, ?_⟩
L : Language α : Type w M : Type w' n : ℕ inst✝ : LE M ⊢ (∀ (a : M), ∃ a_1, ¬Fin.snoc (Fin.snoc default a) a_1 1 ≤ Fin.snoc (Fin.snoc default a) a_1 0) ↔ NoTopOrder M
L : Language α : Type w M : Type w' n : ℕ inst✝ : LE M ⊢ NoTopOrder M → ∀ (a : M), ∃ a_1, ¬Fin.snoc (Fin.snoc default a) a_1 1 ≤ Fin.snoc (Fin.snoc default a) a_1 0
((:c Iff) (:forall a (:fv _uniq.12514) ((:c Exists) (:fv _uniq.12514) (:lambda a (:fv _uniq.12514) ((:c Not) ((:c LE.le) (:fv _uniq.12514) (:fv _uniq.12519) ((:c Fin.snoc) ((:c Nat.succ) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) (:lambda _ ((:c Fin) ((:c Nat.succ) ((:c Nat.succ) ((:c OfNat.ofNa...
[{"name":"L","sexp":"(:c FirstOrder.Language)"},{"name":"α","sexp":"(:sort (+ w 1))"},{"name":"M","sexp":"(:sort (+ w' 1))"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c LE) (:fv _uniq.12514))"}]
(:app (:c Iff) (:arg :explicit 0 (:forall a :explicit (:fv FV2) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda a :explicit (:fv FV2) (:app (:c Not) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12510","is_instance":false,"is_let":false,"name":"L","sexp":"(:c FirstOrder.Language)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12512","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":im...
{"children":[{"source":"refine","sourceEnd":9714,"sourceStart":9708,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":9718,"sourceStart":9715,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":9721,"sourceStart":9718,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"h"...
[]
[{"source":"⟨fun h => ⟨fun a => h a⟩, ?_⟩","source_end":9752,"source_start":9715,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12510","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12512","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
80
5
exact
true
1
5
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
62510722368c3de9070ad94c56f87d7bf0c2e32c4510bea24caba4b926dc772c
ab5fe10dca42da5ff4e2e35591a7571a443d7600962f7bf31c392e430ae719e2
03bd8154cd633df8832ed47d796bfc89eb3d19feb3c471a1f59e7e0720d90316
ddee962bdfbabc016d991786c9402e0310f47279888d18b03265d15855aef20a
cat-searcher/leandojo-benchmark-4-random
test
1,092
FirstOrder.Language.realize_noTopOrder_iff
Mathlib/ModelTheory/Order.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro h a
L : Language α : Type w M : Type w' n : ℕ inst✝ : LE M ⊢ NoTopOrder M → ∀ (a : M), ∃ a_1, ¬Fin.snoc (Fin.snoc default a) a_1 1 ≤ Fin.snoc (Fin.snoc default a) a_1 0
L : Language α : Type w M : Type w' n : ℕ inst✝ : LE M h : NoTopOrder M a : M ⊢ ∃ a_1, ¬Fin.snoc (Fin.snoc default a) a_1 1 ≤ Fin.snoc (Fin.snoc default a) a_1 0
(:forall _ ((:c NoTopOrder) (:fv _uniq.12514) (:fv _uniq.12519)) (:forall a (:fv _uniq.12514) ((:c Exists) (:fv _uniq.12514) (:lambda a (:fv _uniq.12514) ((:c Not) ((:c LE.le) (:fv _uniq.12514) (:fv _uniq.12519) ((:c Fin.snoc) ((:c Nat.succ) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) (:lambda _ ...
[{"name":"L","sexp":"(:c FirstOrder.Language)"},{"name":"α","sexp":"(:sort (+ w 1))"},{"name":"M","sexp":"(:sort (+ w' 1))"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c LE) (:fv _uniq.12514))"}]
(:forall _ :explicit (:app (:c NoTopOrder) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV2)))))) (:forall a :explicit (:fv FV2) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda a :explicit (:fv FV2) (:app (:c Not) (:arg :explicit 0 (:ap...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12510","is_instance":false,"is_let":false,"name":"L","sexp":"(:c FirstOrder.Language)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12512","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":im...
{"children":[{"source":"intro","sourceEnd":9760,"sourceStart":9755,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":9762,"sourceStart":9761,"tag":"identifier"},{"semanticRole":"scoped_local","source":"a","sourceEnd":9764,"sourceStart":9763,"tag":"identifier"}],"kind":"null","source":"h...
[{"role":"fresh_name","source":"h","source_end":9762,"source_start":9761,"syntax_kind":"ident"},{"role":"fresh_name","source":"a","source_end":9764,"source_start":9763,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12510","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12512","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
80
6
exact
true
1
5
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1b1c387beddc3c49d6fdedd94989c0f971282c6661addfb003197a93c6662024
ddee962bdfbabc016d991786c9402e0310f47279888d18b03265d15855aef20a
f02ea869e0155586cbed052a18797e2ea19f0568cd2da5216c3da639ea62644b
0f4b80ed6c379fdd8f6782168fa0eac78125b6fd7983c3a172377a16b9077bdb
cat-searcher/leandojo-benchmark-4-random
test
1,093
FirstOrder.Language.realize_noTopOrder_iff
Mathlib/ModelTheory/Order.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>NoTopOrder.exists_not_le</a> a
L : Language α : Type w M : Type w' n : ℕ inst✝ : LE M h : NoTopOrder M a : M ⊢ ∃ a_1, ¬Fin.snoc (Fin.snoc default a) a_1 1 ≤ Fin.snoc (Fin.snoc default a) a_1 0
((:c Exists) (:fv _uniq.12514) (:lambda a (:fv _uniq.12514) ((:c Not) ((:c LE.le) (:fv _uniq.12514) (:fv _uniq.12519) ((:c Fin.snoc) ((:c Nat.succ) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) (:lambda _ ((:c Fin) ((:c Nat.succ) ((:c Nat.succ) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat)...
[{"name":"L","sexp":"(:c FirstOrder.Language)"},{"name":"α","sexp":"(:sort (+ w 1))"},{"name":"M","sexp":"(:sort (+ w' 1))"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c LE) (:fv _uniq.12514))"},{"name":"h","sexp":"((:c NoTopOrder) (:fv _uniq.12514) (:fv _uniq.12519))"},{"name":"a","sexp":"(:fv _uniq.125...
(:app (:c Exists) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda a :explicit (:fv FV2) (:app (:c Not) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 (:app (:c Fin.snoc) (:arg :implicit 0) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12510","is_instance":false,"is_let":false,"name":"L","sexp":"(:c FirstOrder.Language)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12512","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":im...
{"children":[{"source":"exact","sourceEnd":9772,"sourceStart":9767,"tag":"atom"},{"children":[{"name":"NoTopOrder.exists_not_le","semanticRole":"global","source":"exists_not_le","sourceEnd":9786,"sourceStart":9773,"tag":"identifier"},{"children":[{"contextIndex":7,"semanticRole":"local","source":"a","sourceEnd":9788,"s...
[]
[{"source":"exists_not_le a","source_end":9788,"source_start":9773,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12510","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12512","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
80
7
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
cde2379f5a3bd3d061ca1e1faa564e5e23321f4f7a9fe2b25d4af59a370f4b58
0f4b80ed6c379fdd8f6782168fa0eac78125b6fd7983c3a172377a16b9077bdb
90625576a35b5b8531e6f4ae50531f87520aa9e2f735e73000401e89af2deeb9
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,094
CategoryTheory.GrothendieckTopology.W_adj_unit_app
Mathlib/CategoryTheory/Sites/Localization.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>CategoryTheory.GrothendieckTopology.W_eq_W_range_sheafToPresheaf_obj</a>]
C : Type u_1 inst✝¹ : Category.{u_3, u_1} C J : GrothendieckTopology C A : Type u_2 inst✝ : Category.{u_4, u_2} A G : (Cᵒᵖ ⥤ A) ⥤ Sheaf J A adj : G ⊣ sheafToPresheaf J A P : Cᵒᵖ ⥤ A ⊢ J.W (adj.unit.app P)
C : Type u_1 inst✝¹ : Category.{u_3, u_1} C J : GrothendieckTopology C A : Type u_2 inst✝ : Category.{u_4, u_2} A G : (Cᵒᵖ ⥤ A) ⥤ Sheaf J A adj : G ⊣ sheafToPresheaf J A P : Cᵒᵖ ⥤ A ⊢ LeftBousfield.W (fun x => x ∈ Set.range (sheafToPresheaf J A).obj) (adj.unit.app P)
((:c CategoryTheory.GrothendieckTopology.W) (:fv _uniq.4381) (:fv _uniq.4385) (:fv _uniq.4400) (:fv _uniq.4403) (:fv _uniq.4407) ((:c Prefunctor.obj) ((:c CategoryTheory.Functor) ((:c Opposite) (:fv _uniq.4381)) ((:c CategoryTheory.Category.opposite) (:fv _uniq.4381) (:fv _uniq.4385)) (:fv _uniq.4403) (:fv _uniq.4407))...
[{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.4381))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.4381) (:fv _uniq.4385))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq....
(:app (:c CategoryTheory.GrothendieckTopology.W) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :implicit-type 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c CategoryTheory.Category) (:arg :e...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4381","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4385","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category) ...
{"children":[{"source":"rw","sourceEnd":1638,"sourceStart":1636,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1640,"sourceStart":1639,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"CategoryTheory.Groth...
[]
[{"source":"W_eq_W_range_sheafToPresheaf_obj","source_end":1672,"source_start":1640,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4381","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4385","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"internal...
10
4
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
375128c97b793129bf085be246419f9b2e43bcd52853b204dd7082a966a1d6fa
1ce1617bfbe44e4caaf1dbdef930e87eea46efec416f72ec74b5d1d4ee59e11e
e1c4d45f42d753621ad458cb2fe86111cea3ce0d38c5cb6115e5061549d2bce7
af51f121b9eb18e97548549d750466459601c397c3d0115b9989ea83564460d1
cat-searcher/leandojo-benchmark-4-random
test
1,095
CategoryTheory.GrothendieckTopology.W_adj_unit_app
Mathlib/CategoryTheory/Sites/Localization.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>CategoryTheory.Localization.LeftBousfield.W_adj_unit_app</a> adj P
C : Type u_1 inst✝¹ : Category.{u_3, u_1} C J : GrothendieckTopology C A : Type u_2 inst✝ : Category.{u_4, u_2} A G : (Cᵒᵖ ⥤ A) ⥤ Sheaf J A adj : G ⊣ sheafToPresheaf J A P : Cᵒᵖ ⥤ A ⊢ LeftBousfield.W (fun x => x ∈ Set.range (sheafToPresheaf J A).obj) (adj.unit.app P)
((:c CategoryTheory.Localization.LeftBousfield.W) ((:c CategoryTheory.Functor) ((:c Opposite) (:fv _uniq.4381)) ((:c CategoryTheory.Category.opposite) (:fv _uniq.4381) (:fv _uniq.4385)) (:fv _uniq.4403) (:fv _uniq.4407)) ((:c CategoryTheory.Functor.category) ((:c Opposite) (:fv _uniq.4381)) ((:c CategoryTheory.Category...
[{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.4381))"},{"name":"J","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.4381) (:fv _uniq.4385))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq....
(:app (:c CategoryTheory.Localization.LeftBousfield.W) (:arg :implicit-type 0 (:app (:c CategoryTheory.Functor) (:arg :explicit 0 (:app (:c Opposite) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:app (:c Opposite) (:arg :explicit 0 (:fv FV0))))))) ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4381","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4385","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category) ...
{"children":[{"source":"exact","sourceEnd":1681,"sourceStart":1676,"tag":"atom"},{"children":[{"name":"CategoryTheory.Localization.LeftBousfield.W_adj_unit_app","semanticRole":"global","source":"LeftBousfield.W_adj_unit_app","sourceEnd":1710,"sourceStart":1682,"tag":"identifier"},{"children":[{"contextIndex":6,"semanti...
[]
[{"source":"LeftBousfield.W_adj_unit_app adj P","source_end":1716,"source_start":1682,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4381","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.4385","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"internal...
10
7
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5b8fdd629e15253a2c1a6c37d04ed8adf463583e5b3a569cb5f5d85540134eba
af51f121b9eb18e97548549d750466459601c397c3d0115b9989ea83564460d1
c11f83882c8f310451da19261cbe8dd37c1f2c7078305a589a931823720e637a
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,096
Vector.tendsto_cons
Mathlib/Topology/List.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>tendsto_subtype_rng</a>, <a>Vector.cons_val</a>]
α : Type u_1 β : Type u_2 inst✝¹ : TopologicalSpace α inst✝ : TopologicalSpace β n : ℕ a : α l : Vector α n ⊢ Tendsto (fun p => p.1 ::ᵥ p.2) (𝓝 a ×ˢ 𝓝 l) (𝓝 (a ::ᵥ l))
α : Type u_1 β : Type u_2 inst✝¹ : TopologicalSpace α inst✝ : TopologicalSpace β n : ℕ a : α l : Vector α n ⊢ Tendsto (fun x => ↑(x.1 ::ᵥ x.2)) (𝓝 a ×ˢ 𝓝 l) (𝓝 (a :: ↑l))
((:c Filter.Tendsto) ((:c Prod) (:fv _uniq.46072) ((:c Vector) (:fv _uniq.46072) (:fv _uniq.46279))) ((:c Vector) (:fv _uniq.46072) ((:c Nat.succ) (:fv _uniq.46279))) (:lambda p ((:c Prod) (:fv _uniq.46072) ((:c Vector) (:fv _uniq.46072) (:fv _uniq.46279))) ((:c Vector.cons) (:fv _uniq.46072) (:fv _uniq.46279) ((:c Pro...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.46072))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.46075))"},{"name":"n","sexp":"(:c Nat)"},{"name":"a","sexp":"(:fv _uniq.46072)"},{"name":"l","sexp":"((:c Vector...
(:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Vector) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)))))) (:arg :implicit-type 1 (:app (:c Vector) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Nat.succ) (:arg :explicit 0 (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.46072","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.46075","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"rw","sourceEnd":8589,"sourceStart":8587,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8591,"sourceStart":8590,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"tendsto_subtype_rng"...
[]
[{"source":"tendsto_subtype_rng","source_end":8610,"source_start":8591,"syntax_kind":"ident"},{"source":"cons_val","source_end":8620,"source_start":8612,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.46072","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.46075","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
48
4
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
efa0e343aff6bed40a417caa5e34fa8f2ad9bfb654cacb12bc26562850439e14
a7a24586a0cc56144847b825bea254e7dfd926b2834b3887b672f3ff7b87548a
cb6a56c998f1311ae63888639287692712f0a839a783d03d6214b71078548b9f
12637cca5e657c1adabcbcd0704004a59ad2ee5f0fc1002accd2ea1549862d79
cat-searcher/leandojo-benchmark-4-random
test
1,097
Vector.tendsto_cons
Mathlib/Topology/List.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact tendsto_fst.cons (<a>Filter.Tendsto.comp</a> <a>continuousAt_subtype_val</a> <a>Filter.tendsto_snd</a>)
α : Type u_1 β : Type u_2 inst✝¹ : TopologicalSpace α inst✝ : TopologicalSpace β n : ℕ a : α l : Vector α n ⊢ Tendsto (fun x => ↑(x.1 ::ᵥ x.2)) (𝓝 a ×ˢ 𝓝 l) (𝓝 (a :: ↑l))
((:c Filter.Tendsto) ((:c Prod) (:fv _uniq.46072) ((:c Vector) (:fv _uniq.46072) (:fv _uniq.46279))) ((:c List) (:fv _uniq.46072)) (:lambda x ((:c Prod) (:fv _uniq.46072) ((:c Vector) (:fv _uniq.46072) (:fv _uniq.46279))) ((:c Subtype.val) ((:c List) (:fv _uniq.46072)) (:lambda l ((:c List) (:fv _uniq.46072)) ((:c Eq) ...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.46072))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.46075))"},{"name":"n","sexp":"(:c Nat)"},{"name":"a","sexp":"(:fv _uniq.46072)"},{"name":"l","sexp":"((:c Vector...
(:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Vector) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)))))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 2 (:lambda x :explicit (:app (:c Prod) (:a...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.46072","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.46075","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"exact","sourceEnd":8629,"sourceStart":8624,"tag":"atom"},{"children":[{"source":"tendsto_fst.cons","sourceEnd":8646,"sourceStart":8630,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":8648,"sourceStart":8647,"tag":"atom"},{"children":[{"name":"Filter.Tendsto.comp","semanti...
[]
[{"source":"tendsto_fst.cons (Tendsto.comp continuousAt_subtype_val tendsto_snd)","source_end":8698,"source_start":8630,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.46072","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.46075","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
48
8
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2cd9321527d9c58f3f70fdde57cae00a29a080739e9246de4b6545759ea86fec
12637cca5e657c1adabcbcd0704004a59ad2ee5f0fc1002accd2ea1549862d79
b1ae0a179b7259661fc7dd40152316547f3054f8a2893420126a191eef95a2d6
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,098
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>Submodule.carrier_inj</a>]
R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B ⊢ Submodule.restrictScalars R (map includeRight I) = LinearMap.range (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype)
R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B ⊢ (Submodule.restrictScalars R (map includeRight I)).carrier = (LinearMap.range (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype)).carrier
((:c Eq) ((:c Submodule) (:fv _uniq.758422) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uni...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"rw","sourceEnd":24506,"sourceStart":24504,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":24508,"sourceStart":24507,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":24511,"sourceSt...
[]
[{"source":"Submodule.carrier_inj","source_end":24533,"source_start":24512,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
4
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
693935b1c002405ad86fcb5cb6a35a71bb5935b1ce2698251cd16c0e3d3a3e99
f00f75212bcb64ff12b924d5a75d2d37fd550802aaf62050d6887efd36a26c21
8b9990218206b6b474f087301a30c2859ab8dbcde9acad95df0b8159920e3af6
e82daa85b97333bef2727f38cfa3bd22bc4c83fd79b44090bfaa9d44ecad4518
cat-searcher/leandojo-benchmark-4-random
test
1,099
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>le_antisymm</a>
R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B ⊢ (Submodule.restrictScalars R (map includeRight I)).carrier = (LinearMap.range (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype)).carrier
case a R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B ⊢ (Submodule.restrictScalars R (map includeRight I)).carrier ≤ (LinearMap.range (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype)).carrier ca...
((:c Eq) ((:c Set) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.7584...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommM...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"apply","sourceEnd":24542,"sourceStart":24537,"tag":"atom"},{"name":"le_antisymm","semanticRole":"global","source":"le_antisymm","sourceEnd":24554,"sourceStart":24543,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply le_antisymm","sourceEnd":24554,"sourceStart":24537,"tag":"n...
[]
[{"source":"le_antisymm","source_end":24554,"source_start":24543,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
7
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a27aca092473461fe660a33ba2a28a83476528192fd49e47eff40947a97280d4
e82daa85b97333bef2727f38cfa3bd22bc4c83fd79b44090bfaa9d44ecad4518
0abfddcb77ef175f592e63086534058d51fe8d6b63ac2fff9f69f045bc0962dc
92eec732b67b1aa53022dd13a6d9acce4efb9563e11e46b8cd129236a1df129b
cat-searcher/leandojo-benchmark-4-random
test
1,100
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro x
case a R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B ⊢ (Submodule.restrictScalars R (map includeRight I)).carrier ≤ (LinearMap.range (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype)).carrier
case a R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B ⊢ x ∈ (Submodule.restrictScalars R (map includeRight I)).carrier → x ∈ (LinearMap.range (LinearMap.lTensor A (Submodule.restrictScalars R I)...
((:c LE.le) ((:c Set) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.7...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCo...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"intro","sourceEnd":24565,"sourceStart":24560,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":24567,"sourceStart":24566,"tag":"identifier"}],"kind":"null","source":"x","sourceEnd":24567,"sourceStart":24566,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source...
[{"role":"fresh_name","source":"x","source_end":24567,"source_start":24566,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
12
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8eeee7b5424d2679c5febde4c02aa6db4592fa130ffa03ff17f530b158aa1666
8e9607dc2d3b587281b22260ac0d4335c4b3d127ae5cc6c8ae93f3feda771f91
727852cc0e84019aeee0e605b3833ee9bcd4d2abc203673e529dba747f5c5a0d
6b6f39489632c2d22973817c1a06691f3232333963a611feff80b838d9dd04df
cat-searcher/leandojo-benchmark-4-random
test
1,101
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>AddSubsemigroup.mem_carrier</a>, <a>AddSubmonoid.mem_toSubsemigroup</a>, <a>Submodule.mem_toAddSubmonoid</a>, <a>Submodule.restrictScalars_mem</a>, <a>LinearMap.mem_range</a>]
case a R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B ⊢ x ∈ (Submodule.restrictScalars R (map includeRight I)).carrier → x ∈ (LinearMap.range (LinearMap.lTensor A (Submodule.restrictScalars R I)...
case a R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B ⊢ x ∈ map includeRight I → ∃ y, (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype) y = x
(:forall _ ((:c Membership.mem) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommM...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"simp","sourceEnd":24576,"sourceStart":24572,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":24581,"sourceStart":24577,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":245...
[]
[{"source":"AddSubsemigroup.mem_carrier","source_end":24610,"source_start":24583,"syntax_kind":"ident"},{"source":"AddSubmonoid.mem_toSubsemigroup","source_end":24643,"source_start":24612,"syntax_kind":"ident"},{"source":"Submodule.mem_toAddSubmonoid","source_end":24679,"source_start":24651,"syntax_kind":"ident"},{"sou...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
13
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9520daf7bb2602ef0b2c87006724e9d3bcff44ccb0bca621bb0de70d19bd98c5
6b6f39489632c2d22973817c1a06691f3232333963a611feff80b838d9dd04df
bf433e74a1dada918ab5e651f7e1bfb255741dcc42bd69448e3a598f00b0371f
7036d577c1a4374c60be04dedc792992261778c58d97837879aecdf6079abc9b
cat-searcher/leandojo-benchmark-4-random
test
1,102
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro hx
case a R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B ⊢ x ∈ map includeRight I → ∃ y, (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype) y = x
case a R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B hx : x ∈ map includeRight I ⊢ ∃ y, (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype) y = x
(:forall _ ((:c Membership.mem) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommM...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"intro","sourceEnd":24742,"sourceStart":24737,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hx","sourceEnd":24745,"sourceStart":24743,"tag":"identifier"}],"kind":"null","source":"hx","sourceEnd":24745,"sourceStart":24743,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","sour...
[{"role":"fresh_name","source":"hx","source_end":24745,"source_start":24743,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
14
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
34ae862d0593602002dcb6cdd8a16d8b92087f1a2bdd21436dc3f761d0164ea7
7036d577c1a4374c60be04dedc792992261778c58d97837879aecdf6079abc9b
a055c7ae8fb78bdde993424353a6909ceea94b437aa5556765bc3d467a0076ba
dd2156ee4c335a8041b3e0ff0d5e092e3abeef73b20a1f9af0949549c94dd7a5
cat-searcher/leandojo-benchmark-4-random
test
1,103
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Ideal.map</a>, ← <a>Ideal.submodule_span_eq</a>] at hx
case a R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B hx : x ∈ map includeRight I ⊢ ∃ y, (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype) y = x
case a R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B hx : x ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) ⊢ ∃ y, (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype) y = x
((:c Exists) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) ((:c Subtype) (:fv _uniq.758431) (:lambda x (:fv _uniq.758431) ((:c Membership.mem) (:fv _uniq.758431) ((:c Submodule) (:fv _uniq.758422) (:fv _uniq.758431) ((:c CommSemiring.toSemiring) (:fv _uniq.758422) (:fv _uniq.758425)) ((:c...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"rw","sourceEnd":24752,"sourceStart":24750,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":24754,"sourceStart":24753,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Ideal.map","sema...
[]
[{"source":"Ideal.map","source_end":24763,"source_start":24754,"syntax_kind":"ident"},{"source":"hx","source_end":24793,"source_start":24791,"syntax_kind":"ident"},{"source":"submodule_span_eq","source_end":24786,"source_start":24769,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
15
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2f6d389aba8d899d93fc5a6cdd82b995b3594f2e7174d6d1035d54d04f3dcf27
dd2156ee4c335a8041b3e0ff0d5e092e3abeef73b20a1f9af0949549c94dd7a5
9d6ff581bfde3741fbfa7684523b5a3759712212f304320cad4381595eb1abaf
36ae7ac4e536cedf9fc4bf53d3d5108c95c0d6decc7df9c34dcbdec93dd29c71
cat-searcher/leandojo-benchmark-4-random
test
1,104
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine <a>Submodule.span_induction</a> hx ?_ ?_ ?_ ?_
case a R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B hx : x ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) ⊢ ∃ y, (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype) y = x
case a.refine_1 R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B hx : x ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) ⊢ ∀ x ∈ ⇑includeRight '' ↑I, ∃ y, (LinearMap.lTensor A (Submodule.restrictScal...
((:c Exists) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) ((:c Subtype) (:fv _uniq.758431) (:lambda x (:fv _uniq.758431) ((:c Membership.mem) (:fv _uniq.758431) ((:c Submodule) (:fv _uniq.758422) (:fv _uniq.758431) ((:c CommSemiring.toSemiring) (:fv _uniq.758422) (:fv _uniq.758425)) ((:c...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"refine","sourceEnd":24804,"sourceStart":24798,"tag":"atom"},{"children":[{"name":"Submodule.span_induction","semanticRole":"global","source":"Submodule.span_induction","sourceEnd":24829,"sourceStart":24805,"tag":"identifier"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"hx","...
[]
[{"source":"Submodule.span_induction hx ?_ ?_ ?_ ?_","source_end":24844,"source_start":24805,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
19
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
707ddfaa5f94caafe9a3ceef0c02211312509d405bb56d7e6da0dd3bd73fc5f8
36ae7ac4e536cedf9fc4bf53d3d5108c95c0d6decc7df9c34dcbdec93dd29c71
53591cf15f374acc1bfe8b35faa52f69d9fdf20131f015b10f359090ceadfa7f
a753a9f1704d4a801102562dc629b12a7f05ee3ce518d78249afeee4a3dba6aa
cat-searcher/leandojo-benchmark-4-random
test
1,105
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro x
case a.refine_1 R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B hx : x ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) ⊢ ∀ x ∈ ⇑includeRight '' ↑I, ∃ y, (LinearMap.lTensor A (Submodule.restrictScal...
case a.refine_1 R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) x : A ⊗[R] B ⊢ x ∈ ⇑includeRight '' ↑I → ∃ y, (LinearMap.lTensor A (Submodul...
(:forall x ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.758434)))) (...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:forall x :explicit (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV2))))) (:arg :ins...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"intro","sourceEnd":24857,"sourceStart":24852,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":24859,"sourceStart":24858,"tag":"identifier"}],"kind":"null","source":"x","sourceEnd":24859,"sourceStart":24858,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source...
[{"role":"fresh_name","source":"x","source_end":24859,"source_start":24858,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
24
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d58c310d94fa2c8376f63a2ac5d5d0e96f6eec0cda4e1b0fb385003feada31d4
fe78820c80d1dcaf15912ee0982d9f5000c2cedd769e8f4af8e991961e6beec9
727852cc0e84019aeee0e605b3833ee9bcd4d2abc203673e529dba747f5c5a0d
6f3a06b865e54611229a5bb28577505cabfed75e9fab585bbc97412a22eedf42
cat-searcher/leandojo-benchmark-4-random
test
1,106
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>Algebra.TensorProduct.includeRight_apply</a>, <a>Set.mem_image</a>, <a>SetLike.mem_coe</a>]
case a.refine_1 R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) x : A ⊗[R] B ⊢ x ∈ ⇑includeRight '' ↑I → ∃ y, (LinearMap.lTensor A (Submodul...
case a.refine_1 R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) x : A ⊗[R] B ⊢ (∃ x_1 ∈ I, 1 ⊗ₜ[R] x_1 = x) → ∃ y, (LinearMap.lTensor A (Sub...
(:forall _ ((:c Membership.mem) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommM...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"simp","sourceEnd":24870,"sourceStart":24866,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":24875,"sourceStart":24871,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":248...
[]
[{"source":"includeRight_apply","source_end":24895,"source_start":24877,"syntax_kind":"ident"},{"source":"Set.mem_image","source_end":24910,"source_start":24897,"syntax_kind":"ident"},{"source":"SetLike.mem_coe","source_end":24927,"source_start":24912,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
25
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
01d30855a9526b6f3323595cc536d70f0216533340fd06aa9e88adf0b245acea
6f3a06b865e54611229a5bb28577505cabfed75e9fab585bbc97412a22eedf42
4d3ceb8bf0ab1ba1f6ea4dde4bdf04a3a4c9504c58b990ecbc634ffce414a105
4851552ae2e86ec1bc9c02d6101ede2a7ade933fdcfec4ed4e33a6cc0e4f29d9
cat-searcher/leandojo-benchmark-4-random
test
1,107
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro ⟨y, hy, rfl⟩
case a.refine_1 R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) x : A ⊗[R] B ⊢ (∃ x_1 ∈ I, 1 ⊗ₜ[R] x_1 = x) → ∃ y, (LinearMap.lTensor A (Sub...
case a.refine_1.intro.intro R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B hx : x ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) y : B hy : y ∈ I ⊢ ∃ y_1, (LinearMap.lTensor A (Submodule.restrict...
(:forall _ ((:c Exists) (:fv _uniq.758431) (:lambda x (:fv _uniq.758431) ((:c And) ((:c Membership.mem) (:fv _uniq.758431) ((:c Ideal) (:fv _uniq.758431) (:fv _uniq.758437)) ((:c SetLike.instMembership) ((:c Ideal) (:fv _uniq.758431) (:fv _uniq.758437)) (:fv _uniq.758431) ((:c Submodule.setLike) (:fv _uniq.758431) (:fv...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:forall _ :explicit (:app (:c Exists) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explicit (:fv FV3) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c Ideal) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:ap...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"rintro","sourceEnd":24941,"sourceStart":24935,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":24945,"sourceStart":24942,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":24946,"sou...
[{"role":"fresh_name","source":"y","source_end":24946,"source_start":24945,"syntax_kind":"ident"},{"role":"fresh_name","source":"hy","source_end":24950,"source_start":24948,"syntax_kind":"ident"}]
[{"source":"⟨y, hy, rfl⟩","source_end":24958,"source_start":24942,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
26
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b698da143516d6a954577b9a357c241d70278bc789c01412947ca3214f47e88b
4851552ae2e86ec1bc9c02d6101ede2a7ade933fdcfec4ed4e33a6cc0e4f29d9
7475662c9aa90519d533b33e1b7d34c1434526be9eaa7aab4a67b65646373a83
36602826ce17b434da64a96bb27eb373eacd5d15780f325655b5e61eb9ae7129
cat-searcher/leandojo-benchmark-4-random
test
1,108
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
use 1 ⊗ₜ[R] ⟨y, hy⟩
case a.refine_1.intro.intro R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B hx : x ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) y : B hy : y ∈ I ⊢ ∃ y_1, (LinearMap.lTensor A (Submodule.restrict...
case h R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B hx : x ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) y : B hy : y ∈ I ⊢ (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype) (1 ⊗ₜ[...
((:c Exists) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) ((:c Subtype) (:fv _uniq.758431) (:lambda x (:fv _uniq.758431) ((:c Membership.mem) (:fv _uniq.758431) ((:c Submodule) (:fv _uniq.758422) (:fv _uniq.758431) ((:c CommSemiring.toSemiring) (:fv _uniq.758422) (:fv _uniq.758425)) ((:c...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"use","sourceEnd":24968,"sourceStart":24965,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"children":[{"children":[{"source":"1","sourceEnd":24970,"sourceStart":24969,"tag":"atom"}],"kind":"num","source":...
[]
[{"source":"1 ⊗ₜ[R] ⟨y, hy⟩","source_end":24992,"source_start":24969,"syntax_kind":"TensorProduct.«term_⊗ₜ[_]_»"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
27
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d3a070dec6aa87121cadc63fe887b1dbbb61b923a365da25c70d77ad0157185a
36602826ce17b434da64a96bb27eb373eacd5d15780f325655b5e61eb9ae7129
f98138e873b676fc413f7229ff54be994d573a49d659dc8ac81df7d2f3c3ccf7
222984bdf3ae1232f38bf47a6474ccb794e1742ba36011344fb03943def7447f
cat-searcher/leandojo-benchmark-4-random
test
1,109
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rfl
case h R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B hx : x ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) y : B hy : y ∈ I ⊢ (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype) (1 ⊗ₜ[...
((:c Eq) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.758434)))) ((:...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV2...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"rfl","sourceEnd":25002,"sourceStart":24999,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":25002,"sourceStart":24999,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
28
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
69edfc5d40c886e3df07fef40496fb0a4a2c2f9c4fab991607c520badb15dffc
222984bdf3ae1232f38bf47a6474ccb794e1742ba36011344fb03943def7447f
5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,110
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
use 0
case a.refine_2 R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B hx : x ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) ⊢ ∃ y, (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype) y = 0
case h R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B hx : x ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) ⊢ (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype) 0 = 0
((:c Exists) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) ((:c Subtype) (:fv _uniq.758431) (:lambda x (:fv _uniq.758431) ((:c Membership.mem) (:fv _uniq.758431) ((:c Submodule) (:fv _uniq.758422) (:fv _uniq.758431) ((:c CommSemiring.toSemiring) (:fv _uniq.758422) (:fv _uniq.758425)) ((:c...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"use","sourceEnd":25013,"sourceStart":25010,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"children":[{"source":"0","sourceEnd":25015,"sourceStart":25014,"tag":"atom"}],"kind":"num","source":"0","sourceEn...
[]
[{"source":"0","source_end":25015,"source_start":25014,"syntax_kind":"num"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
33
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7994d09519f5d135483e1ee101843841c9eece0c1dd9b34afe3e77e1674b70ce
16f0070365eb77adb3b60890f731b3e815f0855c68fd508bef7bc6d2d44fa839
fc0898278c6585051f8c3b82b7959b2c694cc728f85ae93e887872ebb848972d
a49ff3a0d95e7e111bcfeaaeb6e996642636fc9e9458c9418910ba1a13abfd54
cat-searcher/leandojo-benchmark-4-random
test
1,111
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>map_zero</a>]
case h R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B hx : x ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) ⊢ (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype) 0 = 0
((:c Eq) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.758434)))) ((:...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV2...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"simp","sourceEnd":25026,"sourceStart":25022,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":25031,"sourceStart":25027,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":250...
[]
[{"source":"map_zero","source_end":25041,"source_start":25033,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
34
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4a483928260e1f1ecdb8280cb9e1fabe27b1520d1c8e4fa5aadeda7c6a0eaa79
a49ff3a0d95e7e111bcfeaaeb6e996642636fc9e9458c9418910ba1a13abfd54
8d318a70b529134c41495f0d3d4070d4366ffab1eddc10d45828eefa9b203336
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,112
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro x y ⟨x, hx, rfl⟩ ⟨y, hy, rfl⟩
case a.refine_3 R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B hx : x ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) ⊢ ∀ (x y : A ⊗[R] B), (∃ y, (LinearMap.lTensor A (Submodule.restrictScalar...
case a.refine_3.intro.refl.intro.refl R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) x y : A ⊗[R] ↥(Submodule.restrictScalars R I) ⊢ ∃ y_1,...
(:forall x ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.758434)))) (...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:forall x :explicit (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV2))))) (:arg :ins...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"rintro","sourceEnd":25056,"sourceStart":25050,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":25058,"sourceStart":25057,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":25058,"sourceStart":25057,"...
[{"role":"fresh_name","source":"x","source_end":25058,"source_start":25057,"syntax_kind":"ident"},{"role":"fresh_name","source":"y","source_end":25060,"source_start":25059,"syntax_kind":"ident"},{"role":"fresh_name","source":"x","source_end":25065,"source_start":25064,"syntax_kind":"ident"},{"role":"fresh_name","source...
[{"source":"⟨x, hx, rfl⟩","source_end":25077,"source_start":25061,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"},{"source":"⟨y, hy, rfl⟩","source_end":25094,"source_start":25078,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
39
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
09011403093c523e622060d8da14a8d7c455a559c04204a79a50e4e4bb27696f
e91dabb35f7c7943578e8373398eadfe9c2056d43697c1f8a1796b7c4196b93f
6e106d0b9e6072ad22f4c882550be0dbb4decff38368d4d4c67b497a559d7207
24229c5feb15e6be7e3bdb3430b6aded9e57c1ecb0f1e21ca606077766815836
cat-searcher/leandojo-benchmark-4-random
test
1,113
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
use x + y
case a.refine_3.intro.refl.intro.refl R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) x y : A ⊗[R] ↥(Submodule.restrictScalars R I) ⊢ ∃ y_1,...
case h R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) x y : A ⊗[R] ↥(Submodule.restrictScalars R I) ⊢ (LinearMap.lTensor A (Submodule.restr...
((:c Exists) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) ((:c Subtype) (:fv _uniq.758431) (:lambda x (:fv _uniq.758431) ((:c Membership.mem) (:fv _uniq.758431) ((:c Submodule) (:fv _uniq.758422) (:fv _uniq.758431) ((:c CommSemiring.toSemiring) (:fv _uniq.758422) (:fv _uniq.758425)) ((:c...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"use","sourceEnd":25104,"sourceStart":25101,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"children":[{"contextIndex":12,"semanticRole":"local","source":"x","sourceEnd":25106,"sourceStart":25105,"tag":"id...
[]
[{"source":"x + y","source_end":25110,"source_start":25105,"syntax_kind":"«term_+_»"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
40
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7554cc9f01d9ce672c6672d304769572fd2cd268e66b28bab4c28a653fd4cb30
24229c5feb15e6be7e3bdb3430b6aded9e57c1ecb0f1e21ca606077766815836
dcfed21a55c5be050f6ca0b21c5bd81453d5520fe9ec92af1807b555fa082876
5f48c328ad593063d41b4f3cd91ab2edd6b8e2f78714ef1b84c6361d5bb7f4cf
cat-searcher/leandojo-benchmark-4-random
test
1,114
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>map_add</a>]
case h R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) x y : A ⊗[R] ↥(Submodule.restrictScalars R I) ⊢ (LinearMap.lTensor A (Submodule.restr...
((:c Eq) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.758434)))) ((:...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV2...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"simp","sourceEnd":25121,"sourceStart":25117,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":25126,"sourceStart":25122,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":251...
[]
[{"source":"map_add","source_end":25135,"source_start":25128,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
41
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
926e4efb0f2e77857cd4fc9514d296a47c69ad5420b04bd1378eb2770761be3c
5f48c328ad593063d41b4f3cd91ab2edd6b8e2f78714ef1b84c6361d5bb7f4cf
690a44a07341fe5482e118a061593fd3a4a9a38831e6d0179a2c13903c42de0f
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,115
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro a x ⟨x, hx, rfl⟩
case a.refine_4 R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B hx : x ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) ⊢ ∀ (a x : A ⊗[R] B), (∃ y, (LinearMap.lTensor A (Submodule.restrictScalar...
case a.refine_4.intro.refl R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) a : A ⊗[R] B x : A ⊗[R] ↥(Submodule.restrictScalars R I) ⊢ ∃ y, ...
(:forall a ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.758434)))) (...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:forall a :explicit (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV2))))) (:arg :ins...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"rintro","sourceEnd":25150,"sourceStart":25144,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":25152,"sourceStart":25151,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"a","sourceEnd":25152,"sourceStart":25151,"...
[{"role":"fresh_name","source":"a","source_end":25152,"source_start":25151,"syntax_kind":"ident"},{"role":"fresh_name","source":"x","source_end":25154,"source_start":25153,"syntax_kind":"ident"},{"role":"fresh_name","source":"x","source_end":25159,"source_start":25158,"syntax_kind":"ident"}]
[{"source":"⟨x, hx, rfl⟩","source_end":25171,"source_start":25155,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
46
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ce6db6370b338687e8761479f299c650db10aece98257bb3f8036e5363e62166
89369e3e511a939d8dd375f222dd67f19292a2ad3f5365b0110b2d9aa0434b44
48bdd3dfdb75404f9a60100e6ff684acbf1c8fd78b2fb1cb21b3a09c5736d13c
1856b87b2948bc505cf9e6750db0b605dcc576fdfe6f4d7dfd208b8b0ec4819a
cat-searcher/leandojo-benchmark-4-random
test
1,116
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
induction a with | zero => use 0 simp only [<a>map_zero</a>, <a>smul_eq_mul</a>, <a>MulZeroClass.zero_mul</a>] | tmul a b => induction x with | zero => use 0 simp only [<a>map_zero</a>, <a>smul_eq_mul</a>, <a>MulZeroClass.mul_zero</a>] | tmul x y => use (a * x) ⊗ₜ[R] (b •y) simp only [<a>LinearMap.lTensor_tmul</a>, <a>...
case a.refine_4.intro.refl R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) a : A ⊗[R] B x : A ⊗[R] ↥(Submodule.restrictScalars R I) ⊢ ∃ y, ...
((:c Exists) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) ((:c Subtype) (:fv _uniq.758431) (:lambda x (:fv _uniq.758431) ((:c Membership.mem) (:fv _uniq.758431) ((:c Submodule) (:fv _uniq.758422) (:fv _uniq.758431) ((:c CommSemiring.toSemiring) (:fv _uniq.758422) (:fv _uniq.758425)) ((:c...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"induction","sourceEnd":25187,"sourceStart":25178,"tag":"atom"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"a","sourceEnd":25189,"sourceStart":25188,"tag":"identifier"}],"kind":"null","source":"a","sourceEnd":25189,"sourceStart":25188,"tag":"node"},{"children":[],"kind":"null...
[]
[{"source":"a","source_end":25189,"source_start":25188,"syntax_kind":"ident"},{"source":"0","source_end":25224,"source_start":25223,"syntax_kind":"num"},{"source":"map_zero","source_end":25252,"source_start":25244,"syntax_kind":"ident"},{"source":"smul_eq_mul","source_end":25265,"source_start":25254,"syntax_kind":"iden...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
47
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5ec5cf46b1c2fc7a8e245e97948deb5a718be4d2a54f463d822df3e427c09b90
1856b87b2948bc505cf9e6750db0b605dcc576fdfe6f4d7dfd208b8b0ec4819a
60268d9cad9c2ffec283dea550b7a9b160eebf5a3f04e963b7500d0bb758e359
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,117
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
use 0
case a.refine_4.intro.refl.zero R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) x : A ⊗[R] ↥(Submodule.restrictScalars R I) ⊢ ∃ y, (Line...
case h R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) x : A ⊗[R] ↥(Submodule.restrictScalars R I) ⊢ (LinearMap.lTensor A (Submodule.restric...
((:c Exists) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) ((:c Subtype) (:fv _uniq.758431) (:lambda x (:fv _uniq.758431) ((:c Membership.mem) (:fv _uniq.758431) ((:c Submodule) (:fv _uniq.758422) (:fv _uniq.758431) ((:c CommSemiring.toSemiring) (:fv _uniq.758422) (:fv _uniq.758425)) ((:c...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"use","sourceEnd":25222,"sourceStart":25219,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"children":[{"source":"0","sourceEnd":25224,"sourceStart":25223,"tag":"atom"}],"kind":"num","source":"0","sourceEn...
[]
[{"source":"0","source_end":25224,"source_start":25223,"syntax_kind":"num"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
52
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
85b4225082264f3a29b067758a02d518323a3f48204060216d3141e0904dd821
e1b09df1fd644c8a10332bda7df5b74424bdd5c454386cb6044ad1c32f60bec2
fc0898278c6585051f8c3b82b7959b2c694cc728f85ae93e887872ebb848972d
42d6fe1ff952a80a4c4020d6bea8ad9e8d413a21ba57e883802d6addf59e86f8
cat-searcher/leandojo-benchmark-4-random
test
1,118
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>map_zero</a>, <a>smul_eq_mul</a>, <a>MulZeroClass.zero_mul</a>]
case h R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) x : A ⊗[R] ↥(Submodule.restrictScalars R I) ⊢ (LinearMap.lTensor A (Submodule.restric...
((:c Eq) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.758434)))) ((:...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV2...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"simp","sourceEnd":25237,"sourceStart":25233,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":25242,"sourceStart":25238,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":252...
[]
[{"source":"map_zero","source_end":25252,"source_start":25244,"syntax_kind":"ident"},{"source":"smul_eq_mul","source_end":25265,"source_start":25254,"syntax_kind":"ident"},{"source":"zero_mul","source_end":25275,"source_start":25267,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
53
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
35a6e13f582be2b2a125c970b6fc98889b77ffa509a82ed6774ee56fabf1bb9a
42d6fe1ff952a80a4c4020d6bea8ad9e8d413a21ba57e883802d6addf59e86f8
7b649cd1dfc8910faf83c8aba515731f95491dd3ba77c5501ed5fa711c94c1f9
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,119
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
induction x with | zero => use 0 simp only [<a>map_zero</a>, <a>smul_eq_mul</a>, <a>MulZeroClass.mul_zero</a>] | tmul x y => use (a * x) ⊗ₜ[R] (b •y) simp only [<a>LinearMap.lTensor_tmul</a>, <a>Submodule.coeSubtype</a>, <a>smul_eq_mul</a>, <a>Algebra.TensorProduct.tmul_mul_tmul</a>] rfl | add x y hx hy => obtain ⟨x', ...
case a.refine_4.intro.refl.tmul R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) x : A ⊗[R] ↥(Submodule.restrictScalars R I) a : A b : B ⊢ ∃ ...
((:c Exists) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) ((:c Subtype) (:fv _uniq.758431) (:lambda x (:fv _uniq.758431) ((:c Membership.mem) (:fv _uniq.758431) ((:c Submodule) (:fv _uniq.758422) (:fv _uniq.758431) ((:c CommSemiring.toSemiring) (:fv _uniq.758422) (:fv _uniq.758425)) ((:c...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"children":[{"children":[{"children":[{"source":"induction","sourceEnd":25314,"sourceStart":25305,"tag":"atom"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"x","sourceEnd":25316,"sourceStart":25315,"tag":"identifier"}],"kind":"null","source":"x","sourceEnd":25316,"sourceStart":25315,"t...
[]
[{"source":"x","source_end":25316,"source_start":25315,"syntax_kind":"ident"},{"source":"0","source_end":25355,"source_start":25354,"syntax_kind":"num"},{"source":"map_zero","source_end":25385,"source_start":25377,"syntax_kind":"ident"},{"source":"smul_eq_mul","source_end":25398,"source_start":25387,"syntax_kind":"iden...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
55
exact
true
1
14
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e02b78f6c3e645e46690d4fa86de62be59428859f8329309e2b5ceb2bdcc3e2c
d81f0d1f46f7d385b30946d96b39a80fd1197dce263fa2c3e19f9119582deca8
ab3de3e78595176e70b0a6d7c95ec9b361280c887c875c70725eb9f1e8f683d0
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,120
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
use 0
case a.refine_4.intro.refl.tmul.zero R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B hx : x ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) a : A b : B ⊢ ∃ y, (LinearMap.lTensor A (Submodule.re...
case h R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B hx : x ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) a : A b : B ⊢ (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype) 0 = a ⊗...
((:c Exists) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) ((:c Subtype) (:fv _uniq.758431) (:lambda x (:fv _uniq.758431) ((:c Membership.mem) (:fv _uniq.758431) ((:c Submodule) (:fv _uniq.758422) (:fv _uniq.758431) ((:c CommSemiring.toSemiring) (:fv _uniq.758422) (:fv _uniq.758425)) ((:c...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"use","sourceEnd":25353,"sourceStart":25350,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"children":[{"source":"0","sourceEnd":25355,"sourceStart":25354,"tag":"atom"}],"kind":"num","source":"0","sourceEn...
[]
[{"source":"0","source_end":25355,"source_start":25354,"syntax_kind":"num"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
62
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
894acafece7b5d848dcc4da05d08b341b8367b88b7a03454f9eb5fe8262fc386
4e7c7a39498d292c9db90646f2dc98bc4a42e7a1ba070183cdc624fe598d435c
fc0898278c6585051f8c3b82b7959b2c694cc728f85ae93e887872ebb848972d
9b5bb5b320f4467b97d1409a418ebcf463148f47a58b7aa2ca5a6a7d34c4a7af
cat-searcher/leandojo-benchmark-4-random
test
1,121
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>map_zero</a>, <a>smul_eq_mul</a>, <a>MulZeroClass.mul_zero</a>]
case h R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x : A ⊗[R] B hx : x ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) a : A b : B ⊢ (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype) 0 = a ⊗...
((:c Eq) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.758434)))) ((:...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV2...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"simp","sourceEnd":25370,"sourceStart":25366,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":25375,"sourceStart":25371,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":253...
[]
[{"source":"map_zero","source_end":25385,"source_start":25377,"syntax_kind":"ident"},{"source":"smul_eq_mul","source_end":25398,"source_start":25387,"syntax_kind":"ident"},{"source":"mul_zero","source_end":25408,"source_start":25400,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
63
exact
true
1
13
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
57571d432bc0bd3b207c5ceb5f8ea600980a397720d99dc9bac22f70c8a544b7
9b5bb5b320f4467b97d1409a418ebcf463148f47a58b7aa2ca5a6a7d34c4a7af
dc4e98443d0aa6c9ece3a5dccc32424b084ac5003598eef29c87e77fddd6c119
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,122
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
use (a * x) ⊗ₜ[R] (b •y)
case a.refine_4.intro.refl.tmul.tmul R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) a : A b : B x : A y : ↥(Submodule.restrictScalars R I) ...
case h R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) a : A b : B x : A y : ↥(Submodule.restrictScalars R I) ⊢ (LinearMap.lTensor A (Submod...
((:c Exists) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) ((:c Subtype) (:fv _uniq.758431) (:lambda x (:fv _uniq.758431) ((:c Membership.mem) (:fv _uniq.758431) ((:c Submodule) (:fv _uniq.758422) (:fv _uniq.758431) ((:c CommSemiring.toSemiring) (:fv _uniq.758422) (:fv _uniq.758425)) ((:c...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"use","sourceEnd":25445,"sourceStart":25442,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":25447,"sourceStart":25446,"tag":"atom"},{"children":[{"contextI...
[]
[{"source":"(a * x) ⊗ₜ[R] (b •y)","source_end":25472,"source_start":25446,"syntax_kind":"TensorProduct.«term_⊗ₜ[_]_»"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
67
exact
true
1
15
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
eb1ce19c62cb8f06299251acc3347373d9e34e1f4336a50df0b710a1d82376b5
d4c306daa980668866161fce86b235258bb0ceb4047154341404787de19e23c3
0a10881a5b0e03837b545188c760c354744ddff37bb26cdf63705ef8b490385f
073f92f6f1137d2d6378c3875b22d63138d68f1517afaf8078a0e0b4fafd0817
cat-searcher/leandojo-benchmark-4-random
test
1,123
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>LinearMap.lTensor_tmul</a>, <a>Submodule.coeSubtype</a>, <a>smul_eq_mul</a>, <a>Algebra.TensorProduct.tmul_mul_tmul</a>]
case h R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) a : A b : B x : A y : ↥(Submodule.restrictScalars R I) ⊢ (LinearMap.lTensor A (Submod...
case h R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) a : A b : B x : A y : ↥(Submodule.restrictScalars R I) ⊢ (a * x) ⊗ₜ[R] ↑(b • y) = (a ...
((:c Eq) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.758434)))) ((:...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV2...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"simp","sourceEnd":25487,"sourceStart":25483,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":25492,"sourceStart":25488,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":254...
[]
[{"source":"LinearMap.lTensor_tmul","source_end":25516,"source_start":25494,"syntax_kind":"ident"},{"source":"Submodule.coeSubtype","source_end":25538,"source_start":25518,"syntax_kind":"ident"},{"source":"smul_eq_mul","source_end":25551,"source_start":25540,"syntax_kind":"ident"},{"source":"tmul_mul_tmul","source_end"...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
68
exact
true
1
15
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7cae5b175fe9adc86b62b00eb84be25c9538f398b0b48d10530e35441775010c
073f92f6f1137d2d6378c3875b22d63138d68f1517afaf8078a0e0b4fafd0817
6859255c9264524653cd8c911de734ac95c7a69cba1fcef5fbf8f9fda1cc416e
902c28b3e9a0c6011ecaf35a7e31a39c26868a53147645833010a7eb2810e72f
cat-searcher/leandojo-benchmark-4-random
test
1,124
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rfl
case h R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) a : A b : B x : A y : ↥(Submodule.restrictScalars R I) ⊢ (a * x) ⊗ₜ[R] ↑(b • y) = (a ...
((:c Eq) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.758434)))) ((:...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV2...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"rfl","sourceEnd":25581,"sourceStart":25578,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":25581,"sourceStart":25578,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
69
exact
true
1
15
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2e0288a39c1fd99ff3326c49e0c6935882e3fdae160c357a3881cdaff2d68573
902c28b3e9a0c6011ecaf35a7e31a39c26868a53147645833010a7eb2810e72f
5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,125
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨x', hx'⟩ := hx
case a.refine_4.intro.refl.tmul.add R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx✝ : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) a : A b : B x y : A ⊗[R] ↥(Submodule.restrictScalars R ...
case a.refine_4.intro.refl.tmul.add.intro R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) a : A b : B x y : A ⊗[R] ↥(Submodule.restrictScala...
((:c Exists) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) ((:c Subtype) (:fv _uniq.758431) (:lambda x (:fv _uniq.758431) ((:c Membership.mem) (:fv _uniq.758431) ((:c Submodule) (:fv _uniq.758422) (:fv _uniq.758431) ((:c CommSemiring.toSemiring) (:fv _uniq.758422) (:fv _uniq.758425)) ((:c...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"obtain","sourceEnd":25625,"sourceStart":25619,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":25629,"sourceStart":25626,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x'","sourceE...
[]
[{"source":"hx","source_end":25645,"source_start":25643,"syntax_kind":"ident"},{"source":"⟨x', hx'⟩","source_end":25639,"source_start":25626,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
73
exact
true
1
17
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
bf4f6d6dc843d5c39fa678bd06c23960477b8ecbecf087804baaed2e78b02cc4
66cbe1205c8e2c12a039b5b48d77091a4026ddd3385ecbfd9f9275e1028fb8d7
0bce9ab8616bee43b1ab2161383c6a5b95cb9152f6c8e7820fc330d936a22127
62a50be65680172625ef10ee83ebbe5b149c420bc6af77a122f519b2cb5071db
cat-searcher/leandojo-benchmark-4-random
test
1,126
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨y', hy'⟩ := hy
case a.refine_4.intro.refl.tmul.add.intro R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) a : A b : B x y : A ⊗[R] ↥(Submodule.restrictScala...
case a.refine_4.intro.refl.tmul.add.intro.intro R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) a : A b : B x y x' : A ⊗[R] ↥(Submodule.rest...
((:c Exists) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) ((:c Subtype) (:fv _uniq.758431) (:lambda x (:fv _uniq.758431) ((:c Membership.mem) (:fv _uniq.758431) ((:c Submodule) (:fv _uniq.758422) (:fv _uniq.758431) ((:c CommSemiring.toSemiring) (:fv _uniq.758422) (:fv _uniq.758425)) ((:c...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"obtain","sourceEnd":25662,"sourceStart":25656,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":25666,"sourceStart":25663,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"y'","sourceE...
[]
[{"source":"hy","source_end":25682,"source_start":25680,"syntax_kind":"ident"},{"source":"⟨y', hy'⟩","source_end":25676,"source_start":25663,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
74
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ad7c702d4a55f401432eafaf84117e00054988251ecf40692a0f2acf32361c61
62a50be65680172625ef10ee83ebbe5b149c420bc6af77a122f519b2cb5071db
a602a4462e805333f227f2d7d6de012c26ab3d853796a9654e40f6228206e627
138c9e731b56d895486a0ce7a52bf276e6396f89792097482b737be383796422
cat-searcher/leandojo-benchmark-4-random
test
1,127
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
use x' + y'
case a.refine_4.intro.refl.tmul.add.intro.intro R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) a : A b : B x y x' : A ⊗[R] ↥(Submodule.rest...
case h R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) a : A b : B x y x' : A ⊗[R] ↥(Submodule.restrictScalars R I) hx' : (LinearMap.lTens...
((:c Exists) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) ((:c Subtype) (:fv _uniq.758431) (:lambda x (:fv _uniq.758431) ((:c Membership.mem) (:fv _uniq.758431) ((:c Submodule) (:fv _uniq.758422) (:fv _uniq.758431) ((:c CommSemiring.toSemiring) (:fv _uniq.758422) (:fv _uniq.758425)) ((:c...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"use","sourceEnd":25696,"sourceStart":25693,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"children":[{"contextIndex":16,"semanticRole":"local","source":"x'","sourceEnd":25699,"sourceStart":25697,"tag":"i...
[]
[{"source":"x' + y'","source_end":25704,"source_start":25697,"syntax_kind":"«term_+_»"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
75
exact
true
1
19
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
884eff851652752cbcd8dc51eed0bcfc0268617cc0beafd4b9d0c8863ea6fe4d
138c9e731b56d895486a0ce7a52bf276e6396f89792097482b737be383796422
9051e88b65a7a5c2df3fa68229a35a5fcbf4aa26a4f0aba7824c3cf97fd80b41
3dc30ae457c389f6f4691f4123e93c32a7bf88a558446d3a4087032a8a1fe97f
cat-searcher/leandojo-benchmark-4-random
test
1,128
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>map_add</a>, hx', <a>smul_add</a>, hy']
case h R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) a : A b : B x y x' : A ⊗[R] ↥(Submodule.restrictScalars R I) hx' : (LinearMap.lTens...
((:c Eq) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.758434)))) ((:...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV2...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"simp","sourceEnd":25719,"sourceStart":25715,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":25724,"sourceStart":25720,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":257...
[]
[{"source":"map_add","source_end":25733,"source_start":25726,"syntax_kind":"ident"},{"source":"hx'","source_end":25738,"source_start":25735,"syntax_kind":"ident"},{"source":"smul_add","source_end":25748,"source_start":25740,"syntax_kind":"ident"},{"source":"hy'","source_end":25753,"source_start":25750,"syntax_kind":"id...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
76
exact
true
1
19
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9dd74af7dc2775a51ac024465fec93fe675739ab87ce96f8e0754cbf650a0c10
3dc30ae457c389f6f4691f4123e93c32a7bf88a558446d3a4087032a8a1fe97f
efbb684d838633415b5656c00fdd9d80e440c7362250ed0d44cb6c42a0e2a51e
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,129
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨x', ha'⟩ := ha
case a.refine_4.intro.refl.add R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) x : A ⊗[R] ↥(Submodule.restrictScalars R I) a b : A ⊗[R] B ha...
case a.refine_4.intro.refl.add.intro R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) x : A ⊗[R] ↥(Submodule.restrictScalars R I) a b : A ⊗[R...
((:c Exists) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) ((:c Subtype) (:fv _uniq.758431) (:lambda x (:fv _uniq.758431) ((:c Membership.mem) (:fv _uniq.758431) ((:c Submodule) (:fv _uniq.758422) (:fv _uniq.758431) ((:c CommSemiring.toSemiring) (:fv _uniq.758422) (:fv _uniq.758425)) ((:c...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"obtain","sourceEnd":25794,"sourceStart":25788,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":25798,"sourceStart":25795,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x'","sourceE...
[]
[{"source":"ha","source_end":25814,"source_start":25812,"syntax_kind":"ident"},{"source":"⟨x', ha'⟩","source_end":25808,"source_start":25795,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
80
exact
true
1
16
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
6ab5138f520788abd5a9fa12851180b511379b8f7b550c9f19858299e183c259
9eeaeed2bb46ba9b3d865944136062af106ed696835723331b7bf811db36314a
77249b224ae8390a0e43434c7afe1653ee8e455bd6b3be75b56101f4d7589951
46d4a7b8ceb4eb17cbfd3f92c86d4759bfbb647adcedc001ebc6532a65ef3b7d
cat-searcher/leandojo-benchmark-4-random
test
1,130
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨y', hb'⟩ := hb
case a.refine_4.intro.refl.add.intro R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) x : A ⊗[R] ↥(Submodule.restrictScalars R I) a b : A ⊗[R...
case a.refine_4.intro.refl.add.intro.intro R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) x : A ⊗[R] ↥(Submodule.restrictScalars R I) a b :...
((:c Exists) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) ((:c Subtype) (:fv _uniq.758431) (:lambda x (:fv _uniq.758431) ((:c Membership.mem) (:fv _uniq.758431) ((:c Submodule) (:fv _uniq.758422) (:fv _uniq.758431) ((:c CommSemiring.toSemiring) (:fv _uniq.758422) (:fv _uniq.758425)) ((:c...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"obtain","sourceEnd":25829,"sourceStart":25823,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":25833,"sourceStart":25830,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"y'","sourceE...
[]
[{"source":"hb","source_end":25849,"source_start":25847,"syntax_kind":"ident"},{"source":"⟨y', hb'⟩","source_end":25843,"source_start":25830,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
81
exact
true
1
17
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
4266a58cc194abf9186b83dc23d94cd69d8b3ddce80da3131cb11cb840a5ed6a
46d4a7b8ceb4eb17cbfd3f92c86d4759bfbb647adcedc001ebc6532a65ef3b7d
83c62972d59da9c3e85e77e515b282b48dce8138a18f64039376cd811313184a
510121b02f7ade8c516345f23c5d6f38ddb379525297bc2fbd2fb34c13707ca0
cat-searcher/leandojo-benchmark-4-random
test
1,131
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
use x' + y'
case a.refine_4.intro.refl.add.intro.intro R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) x : A ⊗[R] ↥(Submodule.restrictScalars R I) a b :...
case h R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) x : A ⊗[R] ↥(Submodule.restrictScalars R I) a b : A ⊗[R] B x' : A ⊗[R] ↥(Submodule.re...
((:c Exists) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) ((:c Subtype) (:fv _uniq.758431) (:lambda x (:fv _uniq.758431) ((:c Membership.mem) (:fv _uniq.758431) ((:c Submodule) (:fv _uniq.758422) (:fv _uniq.758431) ((:c CommSemiring.toSemiring) (:fv _uniq.758422) (:fv _uniq.758425)) ((:c...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"use","sourceEnd":25861,"sourceStart":25858,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"children":[{"contextIndex":15,"semanticRole":"local","source":"x'","sourceEnd":25864,"sourceStart":25862,"tag":"i...
[]
[{"source":"x' + y'","source_end":25869,"source_start":25862,"syntax_kind":"«term_+_»"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
82
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
74668522714ec158d6e06d1fd3f4df00c797cc600e5fc329dd2715d20a736b5e
510121b02f7ade8c516345f23c5d6f38ddb379525297bc2fbd2fb34c13707ca0
9051e88b65a7a5c2df3fa68229a35a5fcbf4aa26a4f0aba7824c3cf97fd80b41
c8119f0223ea73005976f3e6911e80f73f97eb9a0d94894f3806bf5a75bfd52c
cat-searcher/leandojo-benchmark-4-random
test
1,132
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>map_add</a>, ha', <a>add_smul</a>, hb']
case h R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B x✝ : A ⊗[R] B hx : x✝ ∈ Submodule.span (A ⊗[R] B) (⇑includeRight '' ↑I) x : A ⊗[R] ↥(Submodule.restrictScalars R I) a b : A ⊗[R] B x' : A ⊗[R] ↥(Submodule.re...
((:c Eq) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.758434)))) ((:...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV2...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"simp","sourceEnd":25882,"sourceStart":25878,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":25887,"sourceStart":25883,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":258...
[]
[{"source":"map_add","source_end":25896,"source_start":25889,"syntax_kind":"ident"},{"source":"ha'","source_end":25901,"source_start":25898,"syntax_kind":"ident"},{"source":"add_smul","source_end":25911,"source_start":25903,"syntax_kind":"ident"},{"source":"hb'","source_end":25916,"source_start":25913,"syntax_kind":"id...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
83
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
355aa0981d8e8fe724fbfca64a4c1fa66bdcaab4892acae58af96a66aa6b40a5
c8119f0223ea73005976f3e6911e80f73f97eb9a0d94894f3806bf5a75bfd52c
59e950fb992ff8948f172a23391f262a4a008610c5aef5f2f29c56a008bb842e
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,133
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro x ⟨y, rfl⟩
case a R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B ⊢ (LinearMap.range (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype)).carrier ≤ (Submodule.restrictScalars R (map includeRight I)).carrier
case a.intro R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B y : A ⊗[R] ↥(Submodule.restrictScalars R I) ⊢ (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype) y ∈ (Submodule.restrictScalars R (map i...
((:c LE.le) ((:c Set) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.7...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCo...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"rintro","sourceEnd":25930,"sourceStart":25924,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":25932,"sourceStart":25931,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":25932,"sourceStart":25931,"...
[{"role":"fresh_name","source":"y","source_end":25937,"source_start":25936,"syntax_kind":"ident"}]
[{"source":"⟨y, rfl⟩","source_end":25945,"source_start":25933,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
88
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b29df86e7105eed7a424115404e1a134c4225b649ea88ae57d2449f1e3060c3d
ece5cad72bc097548048902790b9293413a5e852abfa3a07b7df37b53cc4c960
7fca1d1946e9233c604341b7f674f123a59fdd8a8ec0063a04271a21e2314782
86614a4bebc752bf0743d079a668ee653eb6a3be50b73ebb056ca7a0745a3929
cat-searcher/leandojo-benchmark-4-random
test
1,135
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>map_zero</a>]
case a.intro.zero R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B ⊢ (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype) 0 ∈ (Submodule.restrictScalars R (map includeRight I)).carrier
case a.intro.zero R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B ⊢ 0 ∈ (Submodule.restrictScalars R (map includeRight I)).carrier
((:c Membership.mem) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.75...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"rw","sourceEnd":25991,"sourceStart":25989,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":25993,"sourceStart":25992,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"map_zero","seman...
[]
[{"source":"map_zero","source_end":26001,"source_start":25993,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
94
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ca7128dd122a54dd72b31bf06f75019a3d3bd176841c526ad17a746a8fe8f8d1
a88aac137291b4351c00d13e7dde1fe6d65457e13002c4404c0636c08bf6a506
d4cdfc996f0d39b50b77cedec4ef61665ad7423a3eb1292fa3dc3d5ac4d0bce6
a4f66d27f9f6ef0d3a8a9746792c23e7cfec85b418e3400310687fb7384655eb
cat-searcher/leandojo-benchmark-4-random
test
1,136
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>ZeroMemClass.zero_mem</a>
case a.intro.zero R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B ⊢ 0 ∈ (Submodule.restrictScalars R (map includeRight I)).carrier
((:c Membership.mem) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.75...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"apply","sourceEnd":26016,"sourceStart":26011,"tag":"atom"},{"name":"ZeroMemClass.zero_mem","semanticRole":"global","source":"zero_mem","sourceEnd":26025,"sourceStart":26017,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply zero_mem","sourceEnd":26025,"sourceStart":26011,"tag...
[]
[{"source":"zero_mem","source_end":26025,"source_start":26017,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
97
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
46f2cf1dc4d712f152e53dd22cb96553ec06234e1ae0b54271bd3718a1bdcc41
a4f66d27f9f6ef0d3a8a9746792c23e7cfec85b418e3400310687fb7384655eb
0062a762cd47379c6309effc8a1741cfef1edc02ace3528a1aa75445a91ced57
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,137
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>LinearMap.lTensor_tmul</a>, <a>Submodule.coeSubtype</a>]
case a.intro.tmul R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B a : A b : ↥(Submodule.restrictScalars R I) ⊢ (LinearMap.lTensor A (Submodule.restrictScalars R I).subtype) (a ⊗ₜ[R] b) ∈ (Submodule.restrictSc...
case a.intro.tmul R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B a : A b : ↥(Submodule.restrictScalars R I) ⊢ a ⊗ₜ[R] ↑b ∈ (Submodule.restrictScalars R (map includeRight I)).carrier
((:c Membership.mem) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.75...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"simp","sourceEnd":26056,"sourceStart":26052,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":26061,"sourceStart":26057,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":260...
[]
[{"source":"LinearMap.lTensor_tmul","source_end":26085,"source_start":26063,"syntax_kind":"ident"},{"source":"Submodule.coeSubtype","source_end":26107,"source_start":26087,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
101
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
be68557d6f427855986ca871efb86c7233acd63f9719aa98e0b89c3d4ccd45a7
b383eb6bdaf4642f7d0632f2e094a25de5ed2b62c0fa998bffc49d965545512d
0cfdea76afe6dbd23eadd5de047f4499adef913c56c5c79e8acf814eba52911c
21e0d864841464fc74006616039d4f7e08a00ddb89a11b8c21d65f693e421969
cat-searcher/leandojo-benchmark-4-random
test
1,139
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>Submodule.coe_restrictScalars</a>, <a>Algebra.TensorProduct.tmul_mul_tmul</a>, <a>mul_one</a>, <a>one_mul</a>]
case a.intro.tmul R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B a : A b : ↥(Submodule.restrictScalars R I) ⊢ a ⊗ₜ[R] ↑b = a ⊗ₜ[R] 1 * 1 ⊗ₜ[R] ↑b
((:c Eq) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.758434)))) ((:...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV2...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"simp","sourceEnd":26585,"sourceStart":26581,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":26590,"sourceStart":26586,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":265...
[]
[{"source":"Submodule.coe_restrictScalars","source_end":26621,"source_start":26592,"syntax_kind":"ident"},{"source":"Algebra.TensorProduct.tmul_mul_tmul","source_end":26658,"source_start":26623,"syntax_kind":"ident"},{"source":"mul_one","source_end":26677,"source_start":26670,"syntax_kind":"ident"},{"source":"one_mul",...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
112
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
cdb4285ab0b4bd2889d0f1c7d54f7dad296b503362e955dc1028b055f8e7b014
cdeac5cffebefb94cea4a77ffd4d45fe36316f128fc6688cd28c793b5cf5b91e
1ea685bc5215c3027396727ca29dc878594668bfcc1a3d0fc8481e10b7fbb76b
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,140
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [this]
R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B a : A b : ↥(Submodule.restrictScalars R I) this : a ⊗ₜ[R] ↑b = a ⊗ₜ[R] 1 * 1 ⊗ₜ[R] ↑b ⊢ a ⊗ₜ[R] ↑b ∈ (Submodule.restrictScalars R (map includeRight I)).carrier
R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B a : A b : ↥(Submodule.restrictScalars R I) this : a ⊗ₜ[R] ↑b = a ⊗ₜ[R] 1 * 1 ⊗ₜ[R] ↑b ⊢ a ⊗ₜ[R] 1 * 1 ⊗ₜ[R] ↑b ∈ (Submodule.restrictScalars R (map includeRight I))....
((:c Membership.mem) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.75...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"rw","sourceEnd":26215,"sourceStart":26213,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":26217,"sourceStart":26216,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":12,"seman...
[]
[{"source":"this","source_end":26221,"source_start":26217,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
105
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
de16958cdba29cf8afaa3c001d8dbff7c3e6bf52cc216b07665441c8dae3036b
d5f6fdcb75bb70a29dbe4d28840f96c49dfc5c703a978b008c609877fc674f69
65e47f2d4a9bfabc21e1664a0b073b87e8fee657aeade999395c39aa954c5bad
2f7da6cc413098a53662a8c08e59c402b78ae8f285d9990a2efce14fdc5b9131
cat-searcher/leandojo-benchmark-4-random
test
1,141
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [<a>AddSubsemigroup.mem_carrier</a>, <a>AddSubmonoid.mem_toSubsemigroup</a>, <a>Submodule.mem_toAddSubmonoid</a>, <a>Submodule.restrictScalars_mem</a>]
R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B a : A b : ↥(Submodule.restrictScalars R I) this : a ⊗ₜ[R] ↑b = a ⊗ₜ[R] 1 * 1 ⊗ₜ[R] ↑b ⊢ a ⊗ₜ[R] 1 * 1 ⊗ₜ[R] ↑b ∈ (Submodule.restrictScalars R (map includeRight I))....
R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B a : A b : ↥(Submodule.restrictScalars R I) this : a ⊗ₜ[R] ↑b = a ⊗ₜ[R] 1 * 1 ⊗ₜ[R] ↑b ⊢ a ⊗ₜ[R] 1 * 1 ⊗ₜ[R] ↑b ∈ map includeRight I
((:c Membership.mem) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.75...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"simp","sourceEnd":26237,"sourceStart":26233,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":26242,"sourceStart":26238,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":262...
[]
[{"source":"AddSubsemigroup.mem_carrier","source_end":26271,"source_start":26244,"syntax_kind":"ident"},{"source":"AddSubmonoid.mem_toSubsemigroup","source_end":26304,"source_start":26273,"syntax_kind":"ident"},{"source":"Submodule.mem_toAddSubmonoid","source_end":26346,"source_start":26318,"syntax_kind":"ident"},{"sou...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
108
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
df446c47c57809a80de19a75796f50416e96627b2bc3c186359547f5a47a15b8
2f7da6cc413098a53662a8c08e59c402b78ae8f285d9990a2efce14fdc5b9131
1bd6299b6b062cefbfc50db5c7da31cec1ccafd5000b344c4551c591141c519d
d15f59cc52d1410be85663b2c0d645ecc347a65382e98682a5673338b015a5fe
cat-searcher/leandojo-benchmark-4-random
test
1,142
Ideal.map_includeRight_eq
Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>Ideal.mul_mem_left</a>
R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B a : A b : ↥(Submodule.restrictScalars R I) this : a ⊗ₜ[R] ↑b = a ⊗ₜ[R] 1 * 1 ⊗ₜ[R] ↑b ⊢ a ⊗ₜ[R] 1 * 1 ⊗ₜ[R] ↑b ∈ map includeRight I
case a R : Type u_1 inst✝⁴ : CommSemiring R A : Type u_2 B : Type u_3 inst✝³ : Semiring A inst✝² : Semiring B inst✝¹ : Algebra R A inst✝ : Algebra R B I : Ideal B a : A b : ↥(Submodule.restrictScalars R I) this : a ⊗ₜ[R] ↑b = a ⊗ₜ[R] 1 * 1 ⊗ₜ[R] ↑b ⊢ 1 ⊗ₜ[R] ↑b ∈ map includeRight I
((:c Membership.mem) ((:c TensorProduct) (:fv _uniq.758422) (:fv _uniq.758425) (:fv _uniq.758428) (:fv _uniq.758431) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.758428) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.758428) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.758428) (:fv _uniq.75...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommSemiring) (:fv _uniq.758422))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"B","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Semiring) (:fv _uniq.758428))"},{"name":"inst✝²","sexp":"((:c Semiring) (:fv _uniq.758431))"},{"name":"...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c TensorProduct) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV3)) (:arg :instance 4 (:instance-of (:app (:c AddCommMonoid) (:arg :explici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommSemiring) (:arg :...
{"children":[{"source":"apply","sourceEnd":26394,"sourceStart":26389,"tag":"atom"},{"name":"Ideal.mul_mem_left","semanticRole":"global","source":"Ideal.mul_mem_left","sourceEnd":26413,"sourceStart":26395,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Ideal.mul_mem_left\n -- Note: adding...
[]
[{"source":"Ideal.mul_mem_left\n -- Note: adding `includeRight` as a hint fixes a timeout #8386","source_end":26413,"source_start":26395,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.758422","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.758425","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"inte...
64
109
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8753266e0a3ba8e7e5c757663fdbe79bf8172d290c0030050dccbf1d8016e6c5
d15f59cc52d1410be85663b2c0d645ecc347a65382e98682a5673338b015a5fe
a2bb59b54dbfbe44c900772cb8840c023b459e2eb4df783a5e63ad0fb69eab78
b3a14cf49864f30eb7982c19dc2e050ab59d62f783e0207b980afede37e0a710