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
1,659
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
dsimp only [<a>Function.comp_def</a>]
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
((:c Eq) (:fv _uniq.48554) ((:c PartialHomeomorph.toFun') (:fv _uniq.48953) (:fv _uniq.48554) (:fv _uniq.48956) (:fv _uniq.48557) (:fv _uniq.50977) (:fv _uniq.50672)) ((:c Function.comp) (:fv _uniq.48554) (:fv _uniq.48953) (:fv _uniq.48554) ((:c PartialHomeomorph.toFun') (:fv _uniq.48953) (:fv _uniq.48554) (:fv _uniq.4...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:app (:c PartialHomeomorph.toFun') (:arg :implicit-type 0 (:fv FV18)) (:arg :implicit-type 1 (:fv FV5)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV18))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpa...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"dsimp","sourceEnd":9956,"sourceStart":9951,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":9961,"sourceStart":9957,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":9961,"...
[]
[{"source":"Function.comp_def","source_end":9980,"source_start":9963,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
59
exact
true
1
43
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
23e419a306619ab6bf80211e5fb78111ae6affb254c401057fa4696cabb69cfe
36f5593df5467a75e02f56a2173b4af2afdc161bd51c4dd2639d04f076d21240
6dc510c49059abd3d6f79510c3e898adbf521cefff556cd9caf1bf9404a12ca7
6a223acfc702a693e6e843280891470b5e5c8359bf5e1abb374cc3cc5acbb11f
cat-searcher/leandojo-benchmark-4-random
test
1,660
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have hfX : f.symm X ∈ c.source := by simp only [c, hX, mfld_simps]
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
((:c Eq) (:fv _uniq.48554) ((:c PartialHomeomorph.toFun') (:fv _uniq.48953) (:fv _uniq.48554) (:fv _uniq.48956) (:fv _uniq.48557) (:fv _uniq.50977) (:fv _uniq.50672)) ((:c PartialHomeomorph.toFun') (:fv _uniq.48953) (:fv _uniq.48554) (:fv _uniq.48956) (:fv _uniq.48557) (:fv _uniq.50977) ((:c PartialHomeomorph.toFun') (...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:app (:c PartialHomeomorph.toFun') (:arg :implicit-type 0 (:fv FV18)) (:arg :implicit-type 1 (:fv FV5)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV18))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpa...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"have","sourceEnd":9992,"sourceStart":9988,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hfX","sourceEnd":9996,"sourceStart":9993,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hfX","sourceEnd":9996,"sourceStart":9993,"tag":"node"},...
[]
[{"source":"f.symm X ∈ c.source","source_end":10020,"source_start":9999,"syntax_kind":"«term_∈_»"},{"source":"c","source_end":10039,"source_start":10038,"syntax_kind":"ident"},{"source":"hX","source_end":10043,"source_start":10041,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
60
exact
true
1
43
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1069dbb447a2cb12a1288dd4639a1989a1349ce685d6b26da96886dc9a16efcd
6a223acfc702a693e6e843280891470b5e5c8359bf5e1abb374cc3cc5acbb11f
359a6ead2be217763a50feefb1846b8fba5b76951bf3b2ba0e9accd0609cb439
c7651324479b2cf5cdf01c6f116d0677268b4609bcc7d66f0a64c3e6b69c8a70
cat-searcher/leandojo-benchmark-4-random
test
1,661
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [c.left_inv hfX, f.right_inv hX]
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
((:c Eq) (:fv _uniq.48554) ((:c PartialHomeomorph.toFun') (:fv _uniq.48953) (:fv _uniq.48554) (:fv _uniq.48956) (:fv _uniq.48557) (:fv _uniq.50977) (:fv _uniq.50672)) ((:c PartialHomeomorph.toFun') (:fv _uniq.48953) (:fv _uniq.48554) (:fv _uniq.48956) (:fv _uniq.48557) (:fv _uniq.50977) ((:c PartialHomeomorph.toFun') (...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:app (:c PartialHomeomorph.toFun') (:arg :implicit-type 0 (:fv FV18)) (:arg :implicit-type 1 (:fv FV5)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV18))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpa...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"rw","sourceEnd":10065,"sourceStart":10063,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10067,"sourceStart":10066,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"c...
[]
[{"source":"c.left_inv hfX","source_end":10081,"source_start":10067,"syntax_kind":"Lean.Parser.Term.app"},{"source":"f.right_inv hX","source_end":10097,"source_start":10083,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
63
exact
true
1
44
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0b7edbb757de10814542abdd315c4ab503a3e5df172cc0bf5dfbc7afb6dd08c6
c7651324479b2cf5cdf01c6f116d0677268b4609bcc7d66f0a64c3e6b69c8a70
1d46451dc47b85001a4d536ce52655a0ea1a058076231088b94799b9d5111680
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,662
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [c, hX, mfld_simps]
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
((:c Membership.mem) (:fv _uniq.48592) ((:c Set) (:fv _uniq.48592)) ((:c Set.instMembership) (:fv _uniq.48592)) ((:c PartialHomeomorph.toFun') (:fv _uniq.48953) (:fv _uniq.48592) (:fv _uniq.48956) (:fv _uniq.48595) ((:c PartialHomeomorph.symm) (:fv _uniq.48592) (:fv _uniq.48953) (:fv _uniq.48595) (:fv _uniq.48956) (:fv...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV8)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV8)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV8)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV8))))))) (:arg :explicit 3 (:app (:c PartialHomeom...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"simp","sourceEnd":10031,"sourceStart":10027,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":10036,"sourceStart":10032,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":100...
[]
[{"source":"c","source_end":10039,"source_start":10038,"syntax_kind":"ident"},{"source":"hX","source_end":10043,"source_start":10041,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
62
exact
true
1
43
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
fd0a28f81d7e3037dd9f1a63ada86fe362e360918703dac4ba4f3312711ecb4b
f940bea721da4e9e7dcffb585f42fd040ef1bf57d2aaad97f2372904f9fb7162
650350ed956f195b2c4b2c22abf006fd0971bce795ab7cecfebc26d2076a6840
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,663
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have h2 : e.target ⊆ (c.symm ≫ₕ f ≫ₕ c').<a>PartialEquiv.target</a> := by intro x hx; rw [← e.right_inv hx, ← hef (e.symm.mapsTo hx)] exact <a>PartialHomeomorph.mapsTo</a> _ (h2e <| e.symm.mapsTo hx)
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
((:c Set.EqOn) (:fv _uniq.48554) (:fv _uniq.48554) ((:c Function.comp) (:fv _uniq.48554) (:fv _uniq.48592) (:fv _uniq.48554) ((:c PartialHomeomorph.toFun') (:fv _uniq.48592) (:fv _uniq.48554) (:fv _uniq.48595) (:fv _uniq.48557) (:fv _uniq.50893)) ((:c Function.comp) (:fv _uniq.48554) (:fv _uniq.48953) (:fv _uniq.48592)...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Set.EqOn) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV5)) (:arg :explicit 2 (:app (:c Function.comp) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV8)) (:arg :implicit-type 2 (:fv FV5)) (:arg :explicit 3 (:app (:c PartialHomeomorph.toFun') (:arg :implicit-type 0 (:fv FV8))...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"have","sourceEnd":10492,"sourceStart":10488,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h2","sourceEnd":10495,"sourceStart":10493,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h2","sourceEnd":10495,"sourceStart":10493,"tag":"nod...
[]
[{"source":"e.target ⊆ (c.symm ≫ₕ f ≫ₕ c').target","source_end":10545,"source_start":10498,"syntax_kind":"«term_⊆_»"},{"source":"e.right_inv hx","source_end":10594,"source_start":10580,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hef (e.symm.mapsTo hx)","source_end":10622,"source_start":10600,"syntax_kind":"Lean.Pa...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
90
exact
true
1
45
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
55d3b96e6555af5a7fc399a2f6cb3946e6500f5f95d7f4fbf36c24da98af1d0e
edff0236d32c14ee869f893e998bc287f6be96873a05d9f25c32b1269e4166f8
29458e71f0945106bf3a5b198e1fb26b41e2ffe4b8d7339afb53df9184d4bc51
278e0eff044504d7c9ab6fda04699b564fe49c35eaf46e5345094b6e9f866268
cat-searcher/leandojo-benchmark-4-random
test
1,664
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Set.inter_self</a>] at h1
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
((:c Set.EqOn) (:fv _uniq.48554) (:fv _uniq.48554) ((:c Function.comp) (:fv _uniq.48554) (:fv _uniq.48592) (:fv _uniq.48554) ((:c PartialHomeomorph.toFun') (:fv _uniq.48592) (:fv _uniq.48554) (:fv _uniq.48595) (:fv _uniq.48557) (:fv _uniq.50893)) ((:c Function.comp) (:fv _uniq.48554) (:fv _uniq.48953) (:fv _uniq.48592)...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Set.EqOn) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV5)) (:arg :explicit 2 (:app (:c Function.comp) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV8)) (:arg :implicit-type 2 (:fv FV5)) (:arg :explicit 3 (:app (:c PartialHomeomorph.toFun') (:arg :implicit-type 0 (:fv FV8))...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"rw","sourceEnd":10699,"sourceStart":10697,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10701,"sourceStart":10700,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.inter_self",...
[]
[{"source":"inter_self","source_end":10711,"source_start":10701,"syntax_kind":"ident"},{"source":"h1","source_end":10718,"source_start":10716,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
99
exact
true
1
46
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2d6f40aa3a2d7b9d571c3ad47691c7d7c7cc5387db99adf3c8802bb9a97c967c
278e0eff044504d7c9ab6fda04699b564fe49c35eaf46e5345094b6e9f866268
0d9c143f7c12f8d34fb468c9ba4be703e4e7b2492e95867e657743b9299223f0
4b0b5e46660aba7f9e132cfb4ca90617663117da7bb919d2cb61c79843cf65bf
cat-searcher/leandojo-benchmark-4-random
test
1,665
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rwa [inter_eq_right.mpr]
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
((:c Set.EqOn) (:fv _uniq.48554) (:fv _uniq.48554) ((:c Function.comp) (:fv _uniq.48554) (:fv _uniq.48592) (:fv _uniq.48554) ((:c PartialHomeomorph.toFun') (:fv _uniq.48592) (:fv _uniq.48554) (:fv _uniq.48595) (:fv _uniq.48557) (:fv _uniq.50893)) ((:c Function.comp) (:fv _uniq.48554) (:fv _uniq.48953) (:fv _uniq.48592)...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Set.EqOn) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV5)) (:arg :explicit 2 (:app (:c Function.comp) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV8)) (:arg :implicit-type 2 (:fv FV5)) (:arg :explicit 3 (:app (:c PartialHomeomorph.toFun') (:arg :implicit-type 0 (:fv FV8))...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"rwa","sourceEnd":10728,"sourceStart":10725,"tag":"atom"},{"children":[{"source":"[","sourceEnd":10730,"sourceStart":10729,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Iff.mpr","semanticRole":"global","source":"inter_eq_right.mpr","source...
[]
[{"source":"inter_eq_right.mpr","source_end":10748,"source_start":10730,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
102
exact
true
1
46
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
672a4095ad4ea97b8b5946ce4926e12439ce0045127710dfdc536562e4d3deaf
4b0b5e46660aba7f9e132cfb4ca90617663117da7bb919d2cb61c79843cf65bf
a70f53015f13bd712a4da5bbebc0b8891ed48350610273cc5444071500db5fa3
56e19aa767f62d4715603f5abb95cb28de31c0ce03d6395bf2126465e0934750
cat-searcher/leandojo-benchmark-4-random
test
1,666
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine h2.trans ?_
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
((:c HasSubset.Subset) ((:c Set) (:fv _uniq.48554)) ((:c Set.instHasSubset) (:fv _uniq.48554)) ((:c PartialEquiv.target) (:fv _uniq.48554) (:fv _uniq.48554) ((:c PartialHomeomorph.toPartialEquiv) (:fv _uniq.48554) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48557) (:fv _uniq.54771))) ((:c Set.preimage) (:fv _uniq.48...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV5))))))) (:arg :explicit 2 (:app (:c PartialEquiv.target) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"refine","sourceEnd":10762,"sourceStart":10756,"tag":"atom"},{"children":[{"source":"h2.trans","sourceEnd":10771,"sourceStart":10763,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":10773,"sourceStart":10772,"tag":"atom"},{"children":[{"source":"_","sourceEnd":10774,"source...
[]
[{"source":"h2.trans ?_","source_end":10774,"source_start":10763,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
105
exact
true
1
46
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9cdaa2a9e6599c844dac284c830a80acbc03417e3686c6f46ed6c85a82ed8f46
56e19aa767f62d4715603f5abb95cb28de31c0ce03d6395bf2126465e0934750
9f8e2cbea243da9f724d0c71f4dd7e6e9e8d2499299478a1e6c16745adaa64f8
dde593ba98f763d4b6460cb1b34f98d9f5fe046579655c8e06c9241ccda556d5
cat-searcher/leandojo-benchmark-4-random
test
1,667
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
mfld_set_tac
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
((:c HasSubset.Subset) ((:c Set) (:fv _uniq.48554)) ((:c Set.instHasSubset) (:fv _uniq.48554)) ((:c PartialEquiv.target) (:fv _uniq.48554) (:fv _uniq.48554) ((:c PartialHomeomorph.toPartialEquiv) (:fv _uniq.48554) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48557) ((:c PartialHomeomorph.trans) (:fv _uniq.48554) (:fv...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV5))))))) (:arg :explicit 2 (:app (:c PartialEquiv.target) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"mfld_set_tac","sourceEnd":10793,"sourceStart":10781,"tag":"atom"}],"kind":"Tactic.MfldSetTac.mfldSetTac","source":"mfld_set_tac","sourceEnd":10793,"sourceStart":10781,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
106
exact
true
1
46
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2a7793c01a697b7a981fbd20b1d0618f8534090fc222aade19a484e82329185d
dde593ba98f763d4b6460cb1b34f98d9f5fe046579655c8e06c9241ccda556d5
35baa4b4c1735a9b88ed94b0eeab328a8a537a3a069cc4f5274c84edee865427
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,668
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>Set.EqOn.symm</a>
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
case h 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 i...
((:c Set.EqOn) (:fv _uniq.48554) (:fv _uniq.48554) ((:c PartialHomeomorph.toFun') (:fv _uniq.48554) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48557) ((:c PartialHomeomorph.symm) (:fv _uniq.48554) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48557) ((:c PartialHomeomorph.trans) (:fv _uniq.48554) (:fv _uniq.48592)...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Set.EqOn) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV5)) (:arg :explicit 2 (:app (:c PartialHomeomorph.toFun') (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV5)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 3 ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"apply","sourceEnd":10302,"sourceStart":10297,"tag":"atom"},{"name":"Set.EqOn.symm","semanticRole":"global","source":"EqOn.symm","sourceEnd":10312,"sourceStart":10303,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply EqOn.symm","sourceEnd":10312,"sourceStart":10297,"tag":"nod...
[]
[{"source":"EqOn.symm","source_end":10312,"source_start":10303,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
71
exact
true
1
44
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
58c9ed3b4aa21b69ac0ae4b410786fcadb514058518e2f7128d19285b959afb3
8ae03da08a94db983a22619ecc10611fcd51ca8368ab1d153e2ba3f2287e7fd3
58902addebc1a11764d454a8e7027418ca7f48c522e6ad140bbabb3d9dae891a
f2a45bb8e5e478067e66425a73fc51a9667c5d1c9dde8a93f697f052caa87fd1
cat-searcher/leandojo-benchmark-4-random
test
1,669
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine e.isImage_source_target.symm_eqOn_of_inter_eq_of_eqOn ?_ ?_
case h 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 i...
case h.refine_1 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : T...
((:c Set.EqOn) (:fv _uniq.48554) (:fv _uniq.48554) ((:c PartialHomeomorph.toFun') (:fv _uniq.48554) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48557) ((:c PartialHomeomorph.symm) (:fv _uniq.48554) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48557) (:fv _uniq.54771))) ((:c PartialHomeomorph.toFun') (:fv _uniq.485...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Set.EqOn) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV5)) (:arg :explicit 2 (:app (:c PartialHomeomorph.toFun') (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV5)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 3 ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"refine","sourceEnd":10327,"sourceStart":10321,"tag":"atom"},{"children":[{"source":"e.isImage_source_target.symm_eqOn_of_inter_eq_of_eqOn","sourceEnd":10381,"sourceStart":10328,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":10383,"sourceStart":10382,"tag":"atom"},{"child...
[]
[{"source":"e.isImage_source_target.symm_eqOn_of_inter_eq_of_eqOn ?_ ?_","source_end":10387,"source_start":10328,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
72
exact
true
1
44
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
92bee451bdfd8cf431bb82d619b96bf46e7eb4dfcfb6ac5e540f999e4d981ad0
f2a45bb8e5e478067e66425a73fc51a9667c5d1c9dde8a93f697f052caa87fd1
3e38ff5a13c58ba60c1c93544d962de41a5666b5146c6c3a7753df316d11f51e
ce2556b9ac7dd8e0e7de75b4dbfb8d08d5d27743f6ac42849c9773bdf47f8935
cat-searcher/leandojo-benchmark-4-random
test
1,670
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Set.inter_self</a>, inter_eq_right.mpr h2e]
case h.refine_1 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : T...
((:c Eq) ((:c Set) (:fv _uniq.48554)) ((:c Inter.inter) ((:c Set) (:fv _uniq.48554)) ((:c Set.instInter) (:fv _uniq.48554)) ((:c PartialEquiv.source) (:fv _uniq.48554) (:fv _uniq.48554) ((:c PartialHomeomorph.toPartialEquiv) (:fv _uniq.48554) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48557) (:fv _uniq.54771))) ((:...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :explicit 1 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :instance 1 (:instance-of (:app (:c Inter) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV5))))))) (:arg :expl...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":10401,"sourceStart":10399,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10403,"sourceStart":10402,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",...
[]
[{"source":"inter_self","source_end":10413,"source_start":10403,"syntax_kind":"ident"},{"source":"inter_eq_right.mpr h2e","source_end":10437,"source_start":10415,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
75
exact
true
1
44
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e7a0487c4cb5cadff7c0ef3e92e6abdc65aa66853cb023f6dbaf76692b8e9b10
e72a75406a80c0b46fc7aa02239c4b1bfcfd251848ac52c3067b1da40be9f152
7166ed91b1abf6c3e5de6e5e5982368272676c0484da64d999610684c4f16ba3
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,671
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Set.inter_self</a>]
case h.refine_2 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : T...
case h.refine_2 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : T...
((:c Set.EqOn) (:fv _uniq.48554) (:fv _uniq.48554) ((:c PartialHomeomorph.toFun') (:fv _uniq.48554) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48557) (:fv _uniq.54771)) ((:c PartialHomeomorph.toFun') (:fv _uniq.48554) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48557) ((:c PartialHomeomorph.trans) (:fv _uniq.485...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Set.EqOn) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV5)) (:arg :explicit 2 (:app (:c PartialHomeomorph.toFun') (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV5)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 3 ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"rw","sourceEnd":10452,"sourceStart":10450,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10454,"sourceStart":10453,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.inter_self",...
[]
[{"source":"inter_self","source_end":10464,"source_start":10454,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
85
exact
true
1
44
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8878a5f6b802a97f9673c58269cbceb2a74b685bccd2229d0c937f0a489f51bd
4e8a777d30deabb1adbc14b4ec4b97e93f6567fcd9df8e8c6c22588a0961ce91
d9b8276c891e9eaa85dfab180f85f7634b2661bda79e6be93dfee78fae0050a3
a1fb6f51e71150dd49a0efdd94195a5dc6445f64609373a1097a2e15775098e9
cat-searcher/leandojo-benchmark-4-random
test
1,672
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact hef.symm
case h.refine_2 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : T...
((:c Set.EqOn) (:fv _uniq.48554) (:fv _uniq.48554) ((:c PartialHomeomorph.toFun') (:fv _uniq.48554) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48557) (:fv _uniq.54771)) ((:c PartialHomeomorph.toFun') (:fv _uniq.48554) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48557) ((:c PartialHomeomorph.trans) (:fv _uniq.485...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Set.EqOn) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV5)) (:arg :explicit 2 (:app (:c PartialHomeomorph.toFun') (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV5)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 3 ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"exact","sourceEnd":10472,"sourceStart":10467,"tag":"atom"},{"name":"Set.EqOn.symm","semanticRole":"global","source":"hef.symm","sourceEnd":10481,"sourceStart":10473,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact hef.symm","sourceEnd":10481,"sourceStart":10467,"tag":"node"...
[]
[{"source":"hef.symm","source_end":10481,"source_start":10473,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
89
exact
true
1
44
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
16eff63016c8d37fde7a4594819cc7bec3eab67b24b4c08d2092e12dc09dc1e9
a1fb6f51e71150dd49a0efdd94195a5dc6445f64609373a1097a2e15775098e9
9002430ca4bfe82f7a73c5524850ef0fae7a755d657be377bbf1c392a5af8976
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,673
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro x hx
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
((:c HasSubset.Subset) ((:c Set) (:fv _uniq.48554)) ((:c Set.instHasSubset) (:fv _uniq.48554)) ((:c PartialEquiv.target) (:fv _uniq.48554) (:fv _uniq.48554) ((:c PartialHomeomorph.toPartialEquiv) (:fv _uniq.48554) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48557) (:fv _uniq.54771))) ((:c PartialEquiv.target) (:fv _...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV5))))))) (:arg :explicit 2 (:app (:c PartialEquiv.target) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"intro","sourceEnd":10565,"sourceStart":10560,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":10567,"sourceStart":10566,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hx","sourceEnd":10570,"sourceStart":10568,"tag":"identifier"}],"kind":"null","sou...
[{"role":"fresh_name","source":"x","source_end":10567,"source_start":10566,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":10570,"source_start":10568,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
92
exact
true
1
45
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
bcc985222d38d1c3dc668c5fd3e0036fc1aad1fc80e78de5f05d83545d1c5b58
795fa66a649b660859aecd26714daad1ba5f58f533640804dcb329503fbc6f46
65777af1f444837568ec00c3040db2bdc96178d91d8bf83037116b747be939ac
98a481ed7a8d10bf2451c11fb98dea4b35507156edfbe019ae280ddc618864d4
cat-searcher/leandojo-benchmark-4-random
test
1,674
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← e.right_inv hx, ← hef (e.symm.mapsTo hx)]
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
((:c Membership.mem) (:fv _uniq.48554) ((:c Set) (:fv _uniq.48554)) ((:c Set.instMembership) (:fv _uniq.48554)) (:fv _uniq.56305) ((:c PartialEquiv.target) (:fv _uniq.48554) (:fv _uniq.48554) ((:c PartialHomeomorph.toPartialEquiv) (:fv _uniq.48554) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48557) ((:c PartialHomeo...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV5))))))) (:arg :explicit 3 (:fv FV46)) (:arg :expl...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"rw","sourceEnd":10574,"sourceStart":10572,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10576,"sourceStart":10575,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":10579,"sourceSt...
[]
[{"source":"e.right_inv hx","source_end":10594,"source_start":10580,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hef (e.symm.mapsTo hx)","source_end":10622,"source_start":10600,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
94
exact
true
1
47
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
73dfacbde71051504b36548371022e424ffadbbe2197aa5431903f5491766a60
98a481ed7a8d10bf2451c11fb98dea4b35507156edfbe019ae280ddc618864d4
01bc863e9e9a31390e90edebbc458b318c942bf63d3e3b40b72678364c3fff84
467413587c2faf2616542805a37b34ab060c692a8fb5e6b16d368cfd40dca779
cat-searcher/leandojo-benchmark-4-random
test
1,675
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>PartialHomeomorph.mapsTo</a> _ (h2e <| e.symm.mapsTo hx)
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
((:c Membership.mem) (:fv _uniq.48554) ((:c Set) (:fv _uniq.48554)) ((:c Set.instMembership) (:fv _uniq.48554)) ((:c Function.comp) (:fv _uniq.48554) (:fv _uniq.48953) (:fv _uniq.48554) ((:c PartialHomeomorph.toFun') (:fv _uniq.48953) (:fv _uniq.48554) (:fv _uniq.48956) (:fv _uniq.48557) (:fv _uniq.50977)) ((:c Functio...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV5))))))) (:arg :explicit 3 (:app (:c Function.comp...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"exact","sourceEnd":10637,"sourceStart":10632,"tag":"atom"},{"children":[{"name":"PartialHomeomorph.mapsTo","semanticRole":"global","source":"PartialHomeomorph.mapsTo","sourceEnd":10662,"sourceStart":10638,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":10664,"sourceStart"...
[]
[{"source":"PartialHomeomorph.mapsTo _ (h2e <| e.symm.mapsTo hx)","source_end":10690,"source_start":10638,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
98
exact
true
1
47
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8b257b77d2f36040c7ab155852b68cf74f0d42f7a173186ad2ea8d736ea116c2
467413587c2faf2616542805a37b34ab060c692a8fb5e6b16d368cfd40dca779
4458649b6dd2dcf866e0017c0b321cd558a24a2c57593f7b92c0252eabf982c2
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,676
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro ⟨h₁, h₂⟩ x hx
case mpr 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5...
case mpr.intro 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Ty...
(:forall _ ((:c And) ((:c SmoothOn) (:fv _uniq.48429) (:fv _uniq.48432) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48589) (:fv _uniq.48592) (:fv _uniq.48595) (:fv _uniq.48607) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48554) (:fv _uniq.485...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:forall _ :explicit (:app (:c And) (:arg :explicit 0 (:app (:c SmoothOn) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"rintro","sourceEnd":11183,"sourceStart":11177,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":11187,"sourceStart":11184,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h₁","sourceEnd":11191,"so...
[{"role":"fresh_name","source":"h₁","source_end":11191,"source_start":11187,"syntax_kind":"ident"},{"role":"fresh_name","source":"h₂","source_end":11197,"source_start":11193,"syntax_kind":"ident"},{"role":"fresh_name","source":"x","source_end":11202,"source_start":11201,"syntax_kind":"ident"},{"role":"fresh_name","sour...
[{"source":"⟨h₁, h₂⟩","source_end":11200,"source_start":11184,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
117
exact
true
1
29
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f18cdf637b81296089a7d878cee9afc32cb1b7beec5a087455d0fb4de57aa04d
724f1de2f36adfa0d12f5fb9530ed7d42a734a36eff52f5b0e511ac6b1b1216c
e1a4b72ffb95ccb9261dcdc554f32916d9906d607b7debb81d0c2bec55fee5ce
56d047eae34b1948e5e99a500284508fb484892a47de8b540558ac40d473fbce
cat-searcher/leandojo-benchmark-4-random
test
1,677
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨(h₁ x hx).<a>ContMDiffWithinAt.continuousWithinAt</a>, ?_⟩
case mpr.intro 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Ty...
case mpr.intro 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Ty...
((:c ChartedSpace.LiftPropWithinAt) (:fv _uniq.48554) (:fv _uniq.48592) (:fv _uniq.48554) (:fv _uniq.48953) (:fv _uniq.48557) (:fv _uniq.48595) (:fv _uniq.48607) (:fv _uniq.48557) (:fv _uniq.48956) (:fv _uniq.49183) ((:c StructureGroupoid.IsLocalStructomorphWithinAt) (:fv _uniq.48554) (:fv _uniq.48557) ((:c contDiffGro...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c ChartedSpace.LiftPropWithinAt) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV8)) (:arg :implicit-type 2 (:fv FV5)) (:arg :implicit-type 3 (:fv FV18)) (:arg :instance 4 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 5 (:instance-of (:app (:c Topologi...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"refine","sourceEnd":11216,"sourceStart":11210,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":11220,"sourceStart":11217,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":11221,"sourceStart":11220,"tag":"atom"},{"children":[{"contextIndex":30,"semanticRole":"loca...
[]
[{"source":"⟨(h₁ x hx).continuousWithinAt, ?_⟩","source_end":11257,"source_start":11217,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
118
exact
true
1
33
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d7acb0cc4ad541037d78b271e893ffd0cc4a85b01e63766bdd04020f26f27d57
56d047eae34b1948e5e99a500284508fb484892a47de8b540558ac40d473fbce
5d0a009d3c2797bb3617c8f969e71877d3743b007b4b27d2b89baf73bda47846
e0ac724a71bddb18df272f3ef08701f63e965132a806634eee96778c14c042ad
cat-searcher/leandojo-benchmark-4-random
test
1,678
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
let c := <a>chartAt</a> H x
case mpr.intro 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Ty...
case mpr.intro 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Ty...
((:c StructureGroupoid.IsLocalStructomorphWithinAt) (:fv _uniq.48554) (:fv _uniq.48557) ((:c contDiffGroupoid) ((:c Top.top) (:c ENat) (:c instENatTop)) (:fv _uniq.48429) (:fv _uniq.48432) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48589)) ((:c Function.comp) (:...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c StructureGroupoid.IsLocalStructomorphWithinAt) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c contDiffGroupoid) (:arg :explicit 0 (:app (:c Top.top) (:arg :implicit-type 0 (:c ENat)) (:arg :instance 1 (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"let","sourceEnd":11265,"sourceStart":11262,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"c","sourceEnd":11267,"sourceStart":11266,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{...
[]
[{"source":"chartAt H x","source_end":11282,"source_start":11271,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
119
exact
true
1
33
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
30092f287a4b719213632bbcd7a562ce50871bf9d9af1a3911a1238b85916597
e0ac724a71bddb18df272f3ef08701f63e965132a806634eee96778c14c042ad
d2e9ec06c490ce6d1b546694570624b62a8ec4c37c9e99c4da82500d9e6a3997
a1e7b972cdec92f8f9b0ca76a499c21ba58c4c71d3f6b3cf1ab83f7a68881499
cat-searcher/leandojo-benchmark-4-random
test
1,679
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
let c' := <a>chartAt</a> H (f x)
case mpr.intro 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Ty...
case mpr.intro 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Ty...
((:c StructureGroupoid.IsLocalStructomorphWithinAt) (:fv _uniq.48554) (:fv _uniq.48557) ((:c contDiffGroupoid) ((:c Top.top) (:c ENat) (:c instENatTop)) (:fv _uniq.48429) (:fv _uniq.48432) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48589)) ((:c Function.comp) (:...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c StructureGroupoid.IsLocalStructomorphWithinAt) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c contDiffGroupoid) (:arg :explicit 0 (:app (:c Top.top) (:arg :implicit-type 0 (:c ENat)) (:arg :instance 1 (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"let","sourceEnd":11290,"sourceStart":11287,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"c'","sourceEnd":11293,"sourceStart":11291,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},...
[]
[{"source":"chartAt H (f x)","source_end":11312,"source_start":11297,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
120
exact
true
1
34
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
980ad510417583c5778aa4e63d633622d5fcb2a599e0b434e2a0b38821f18269
a1e7b972cdec92f8f9b0ca76a499c21ba58c4c71d3f6b3cf1ab83f7a68881499
c2f19c096a8b14db3fd25f6a23654d7154bb82c0afb39e58b6d1dbedd8f7362c
8fda91510ce76d4ed5304216a038788e8c675a6b73b6d63fb17ab3b5fad1066b
cat-searcher/leandojo-benchmark-4-random
test
1,680
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro (hx' : c x ∈ c.symm ⁻¹' f.source)
case mpr.intro 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Ty...
case mpr.intro 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Ty...
((:c StructureGroupoid.IsLocalStructomorphWithinAt) (:fv _uniq.48554) (:fv _uniq.48557) ((:c contDiffGroupoid) ((:c Top.top) (:c ENat) (:c instENatTop)) (:fv _uniq.48429) (:fv _uniq.48432) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48589)) ((:c Function.comp) (:...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c StructureGroupoid.IsLocalStructomorphWithinAt) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c contDiffGroupoid) (:arg :explicit 0 (:app (:c Top.top) (:arg :implicit-type 0 (:c ENat)) (:arg :instance 1 (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"rintro","sourceEnd":11323,"sourceStart":11317,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":11325,"sourceStart":11324,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hx'","sourceEnd":11328,"sourceStart":11325,"tag":"identifier"}],...
[{"role":"fresh_name","source":"hx'","source_end":11328,"source_start":11325,"syntax_kind":"ident"}]
[{"source":"(hx' : c x ∈ c.symm ⁻¹' f.source)\n -- propose `(c.symm.trans f).trans c'` as a candidate for a local structomorphism of `H`","source_end":11362,"source_start":11324,"syntax_kind":"Lean.Parser.Tactic.rintroPat.binder"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
121
exact
true
1
35
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
07b7294ea647df5c4e192aa1cbc7364ced893a8fec314503417500f9f557bbf3
8fda91510ce76d4ed5304216a038788e8c675a6b73b6d63fb17ab3b5fad1066b
cf0d18ac8d5fcd119325379be8a5e4c52055388628830534fdb64abae4a0e076
cb138e3a1f606c44aafedb9667d819802557f3cf539dd1db819751588038dd57
cat-searcher/leandojo-benchmark-4-random
test
1,681
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨(c.symm.trans f).<a>PartialHomeomorph.trans</a> c', ⟨?_, ?_⟩, (?_ : <a>Set.EqOn</a> (c' ∘ f ∘ c.symm) _ _), ?_⟩
case mpr.intro 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Ty...
case mpr.intro.refine_1 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I ...
((:c Exists) ((:c PartialHomeomorph) (:fv _uniq.48554) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48557)) (:lambda e ((:c PartialHomeomorph) (:fv _uniq.48554) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48557)) ((:c And) ((:c Membership.mem) ((:c PartialHomeomorph) (:fv _uniq.48554) (:fv _uniq.48554) (:fv _uniq....
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c PartialHomeomorph) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:fv FV5)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV5))))))) (:arg ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"refine","sourceEnd":11466,"sourceStart":11460,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":11470,"sourceStart":11467,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"(","sourceEnd":11471,"sourceStart":11470,"tag":"atom"},{"children":[{"source":"c.symm.trans","...
[]
[{"source":"⟨(c.symm.trans f).trans c', ⟨?_, ?_⟩, (?_ : EqOn (c' ∘ f ∘ c.symm) _ _), ?_⟩","source_end":11555,"source_start":11467,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
122
exact
true
1
36
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
fe7f2bd736c5812bc428d245b246700c3a98bd7b28df81c3f68f5d3dd6e931c2
cb138e3a1f606c44aafedb9667d819802557f3cf539dd1db819751588038dd57
78bd4632abb934efa9fb3956f43b1e2004b95fabddb68a59663473b1963ef2c0
fb6bbefb21926d7a503ce6985a3cb64f2ba27ba094e02f8641a29fee393df28c
cat-searcher/leandojo-benchmark-4-random
test
1,682
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro y hy
case mpr.intro.refine_1 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I ...
case mpr.intro.refine_1 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I ...
((:c Pregroupoid.property) (:fv _uniq.48554) (:fv _uniq.48557) ((:c contDiffPregroupoid) ((:c Top.top) (:c ENat) (:c instENatTop)) (:fv _uniq.48429) (:fv _uniq.48432) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48589)) ((:c PartialHomeomorph.toFun') (:fv _uniq.48...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Pregroupoid.property) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c contDiffPregroupoid) (:arg :explicit 0 (:app (:c Top.top) (:arg :implicit-type 0 (:c ENat)) (:arg :instance 1 (:instance-of (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"intro","sourceEnd":11652,"sourceStart":11647,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":11654,"sourceStart":11653,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hy","sourceEnd":11657,"sourceStart":11655,"tag":"identifier"}],"kind":"null","sou...
[{"role":"fresh_name","source":"y","source_end":11654,"source_start":11653,"syntax_kind":"ident"},{"role":"fresh_name","source":"hy","source_end":11657,"source_start":11655,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
127
exact
true
1
36
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9d7bd5e3bb137f403969752314511cc59909f7a645a66e65af40102dc4d629f5
f175b8e3f219d4f75ff41afa8b6148ad9485d287f054c4bd1e25989ca3b548d5
69ac7ac9f4300ee3290568559761b10f79f65930316d628484707cb4cb9d79dc
4dbc30b5f3f0b22b237ad40f36e4c7d8a4cf0b064ed3b4898a718ca8a1486503
cat-searcher/leandojo-benchmark-4-random
test
1,683
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [mfld_simps] at hy
case mpr.intro.refine_1 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I ...
case mpr.intro.refine_1 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I ...
((:c ContDiffWithinAt) (:fv _uniq.48429) (:fv _uniq.48432) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) ((:c Top.top) (:c ENat) (:c instENatTop)) ((:c Function.comp) (:fv _uniq.48435) (:fv _uniq.48554) (:fv _uniq.48435) ((:c ModelWithCorners.toFun') (:fv _u...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c ContDiffWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:ap...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"simp","sourceEnd":11668,"sourceStart":11664,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":11673,"sourceStart":11669,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":116...
[]
[{"source":"hy","source_end":11692,"source_start":11690,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
128
exact
true
1
38
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
78a24fb105367df13fbd7cf0bc448b27c80145689751fbe030c4b7b239fc6ef7
4dbc30b5f3f0b22b237ad40f36e4c7d8a4cf0b064ed3b4898a718ca8a1486503
055efa59a55ca2c71a28d9bdcca97fef6d01f426f5e0026b7e96a240d7054f83
da5775ca3e27247608630927035c7c298602c0fe90aad0b4b9e5f60b3e7b9cd7
cat-searcher/leandojo-benchmark-4-random
test
1,684
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have hy' : (<a>extChartAt</a> I x).<a>PartialEquiv.symm</a> y ∈ c.source := by simp only [hy, mfld_simps]
case mpr.intro.refine_1 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorner...
case mpr.intro.refine_1 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorner...
((:c ContDiffWithinAt) (:fv _uniq.48429) (:fv _uniq.48432) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) ((:c Top.top) (:c ENat) (:c instENatTop)) ((:c Function.comp) (:fv _uniq.48435) (:fv _uniq.48554) (:fv _uniq.48435) ((:c ModelWithCorners.toFun') (:fv _u...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c ContDiffWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:ap...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"have","sourceEnd":11920,"sourceStart":11916,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hy'","sourceEnd":11924,"sourceStart":11921,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hy'","sourceEnd":11924,"sourceStart":11921,"tag":"n...
[]
[{"source":"(extChartAt I x).symm y ∈ c.source","source_end":11963,"source_start":11927,"syntax_kind":"«term_∈_»"},{"source":"hy","source_end":11983,"source_start":11981,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
142
exact
true
1
39
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8bc32ebd66fb61e56a98e944f24cd981b85a4a4c1c955335e656bc19a9a203c0
01eab5dfcca8ee92728ab86ca62f0d6e9fa76e1886c36b588283bcf12281f9b1
6cd1f4bc23488805eb4afc52eca8129be60584b0c52a46e06852559758bf2b6b
e59c889002eaccef62159c8106c3cbb0d89dade68e4a55d9aaec26fa82a58343
cat-searcher/leandojo-benchmark-4-random
test
1,685
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have hy'' : f ((<a>extChartAt</a> I x).<a>PartialEquiv.symm</a> y) ∈ c'.source := by simp only [hy, mfld_simps]
case mpr.intro.refine_1 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorner...
case mpr.intro.refine_1 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorner...
((:c ContDiffWithinAt) (:fv _uniq.48429) (:fv _uniq.48432) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) ((:c Top.top) (:c ENat) (:c instENatTop)) ((:c Function.comp) (:fv _uniq.48435) (:fv _uniq.48554) (:fv _uniq.48435) ((:c ModelWithCorners.toFun') (:fv _u...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c ContDiffWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:ap...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"have","sourceEnd":12007,"sourceStart":12003,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hy''","sourceEnd":12012,"sourceStart":12008,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hy''","sourceEnd":12012,"sourceStart":12008,"tag":...
[]
[{"source":"f ((extChartAt I x).symm y) ∈ c'.source","source_end":12056,"source_start":12015,"syntax_kind":"«term_∈_»"},{"source":"hy","source_end":12076,"source_start":12074,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
145
exact
true
1
40
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d3ea85ed76159b5fdf84eef11db6b2e382008a572a96ac8171339fefce135503
e59c889002eaccef62159c8106c3cbb0d89dade68e4a55d9aaec26fa82a58343
03422510ecb7ead09e8ca7f5e72666814888c5e0cfa069946a79bd4ba6862a25
8107ad98892859e4d34a85d5a61019c52572dd272a64e1849e317e57f47ea00a
cat-searcher/leandojo-benchmark-4-random
test
1,686
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>contMDiffWithinAt_iff_of_mem_source</a> hy' hy''] at H
case mpr.intro.refine_1 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorner...
case mpr.intro.refine_1 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorner...
((:c ContDiffWithinAt) (:fv _uniq.48429) (:fv _uniq.48432) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) ((:c Top.top) (:c ENat) (:c instENatTop)) ((:c Function.comp) (:fv _uniq.48435) (:fv _uniq.48554) (:fv _uniq.48435) ((:c ModelWithCorners.toFun') (:fv _u...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c ContDiffWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:ap...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"rw","sourceEnd":12098,"sourceStart":12096,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12100,"sourceStart":12099,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"con...
[]
[{"source":"H","source_end":12150,"source_start":12149,"syntax_kind":"ident"},{"source":"contMDiffWithinAt_iff_of_mem_source hy' hy''","source_end":12144,"source_start":12100,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
148
exact
true
1
41
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
60d18f8278e57600ecfca344b4be8fed74b6c6696873f14e4ddd70af6cd3864b
8107ad98892859e4d34a85d5a61019c52572dd272a64e1849e317e57f47ea00a
b6cf15f1b774ac3309e12bdfe60d8e026bb7f0809616606f2080b27a28d32792
a1092c3fd47dfbad4ec789a12e1d0424c1f11f324dfdf29cfaf351b81bee0075
cat-searcher/leandojo-benchmark-4-random
test
1,687
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
convert H.2.<a>ContDiffWithinAt.mono</a> _
case mpr.intro.refine_1 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorner...
case h.e'_12 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorners I M E' : ...
((:c ContDiffWithinAt) (:fv _uniq.48429) (:fv _uniq.48432) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) ((:c Top.top) (:c ENat) (:c instENatTop)) ((:c Function.comp) (:fv _uniq.48435) (:fv _uniq.48554) (:fv _uniq.48435) ((:c ModelWithCorners.toFun') (:fv _u...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c ContDiffWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:ap...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"convert","sourceEnd":12164,"sourceStart":12157,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"children":[{"contextIndex":39,"semanticRole":"local","source":"H","sourceEnd":12166,"sourceStart"...
[]
[{"source":"H.2.mono _","source_end":12175,"source_start":12165,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
151
exact
true
1
41
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7077d4179cbde4fa976d7d8776470e626f49ceb28911dc4f9019ae41875c0017
a1092c3fd47dfbad4ec789a12e1d0424c1f11f324dfdf29cfaf351b81bee0075
1a730b635ed526b6a7a3b1019233628a99898c8257f0a0e42efe8f51a93da320
5b98d91e9f97bec50d2eab910d30e86346b591a60bd42609676c6ea16797e3fc
cat-searcher/leandojo-benchmark-4-random
test
1,688
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine (h₁ ((<a>extChartAt</a> I x).<a>PartialEquiv.symm</a> y) ?_).<a>ContMDiffWithinAt.mono</a> ?_
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
case refine_1 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Typ...
((:c ContMDiffWithinAt) (:fv _uniq.48429) (:fv _uniq.48432) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48589) (:fv _uniq.48592) (:fv _uniq.48595) (:fv _uniq.48607) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _un...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c ContMDiffWithinAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-o...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"refine","sourceEnd":11803,"sourceStart":11797,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":11805,"sourceStart":11804,"tag":"atom"},{"children":[{"contextIndex":30,"semanticRole":"local","source":"h₁","sourceEnd":11809,"sourceStart":11805,"tag":"identifier"},{"ch...
[]
[{"source":"(h₁ ((extChartAt I x).symm y) ?_).mono ?_","source_end":11847,"source_start":11804,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
131
exact
true
1
38
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a54783910aa020ce56cd56e138868076e331d3597e5c5e76babcfd5154ea40c5
07d4ff0e662501a6ae90d0d1ec3312c418cba6e8012e66ec66d1c73ec44be019
8448b4017c82adf7a1a7b1f882a3bc4afcc7cebbad472af0d3ae4e2ee1cc8501
b98e8b2adda72c035bf27ab0206267397dd24eecadfac09603ef29d3e022519b
cat-searcher/leandojo-benchmark-4-random
test
1,689
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [hy, mfld_simps]
case refine_1 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Typ...
((:c Membership.mem) (:fv _uniq.48592) ((:c Set) (:fv _uniq.48592)) ((:c Set.instMembership) (:fv _uniq.48592)) ((:c PartialEquiv.toFun) (:fv _uniq.48435) (:fv _uniq.48592) ((:c PartialEquiv.symm) (:fv _uniq.48592) (:fv _uniq.48435) ((:c extChartAt) (:fv _uniq.48429) (:fv _uniq.48435) (:fv _uniq.48592) (:fv _uniq.48554...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV8)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV8)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV8)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV8))))))) (:arg :explicit 3 (:app (:c PartialEquiv....
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":11863,"sourceStart":11859,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":11868,"sourceStart":11864,"tag":"atom"}],"kind"...
[]
[{"source":"hy","source_end":11872,"source_start":11870,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
134
exact
true
1
38
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
afdc434221e4c0a8c047c826c22c6710bd33a9d093de0ec11f42e186a0afa118
bb0f4759eadf649cb61f33eef230d6a630fd96180eb01045fd46aee1aacfec04
7ed2c825ae122109ac44de3e83f2536eadd7555c131a9ab3f241ca2abd3f81b7
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,690
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
mfld_set_tac
case refine_2 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Typ...
((:c HasSubset.Subset) ((:c Set) (:fv _uniq.48592)) ((:c Set.instHasSubset) (:fv _uniq.48592)) ((:c PartialEquiv.source) (:fv _uniq.48592) (:fv _uniq.48554) ((:c PartialHomeomorph.toPartialEquiv) (:fv _uniq.48592) (:fv _uniq.48554) (:fv _uniq.48595) (:fv _uniq.48557) ((:c PartialHomeomorph.trans) (:fv _uniq.48592) (:fv...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV8)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV8))))))) (:arg :explicit 2 (:app (:c PartialEquiv.source) (:arg :implicit-type 0 (:fv FV8)) (:arg :implicit-type...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"children":[{"children":[{"children":[{"source":"mfld_set_tac","sourceEnd":11909,"sourceStart":11897,"tag":"atom"}],"kind":"Tactic.MfldSetTac.mfldSetTac","source":"mfld_set_tac","sourceEnd":11909,"sourceStart":11897,"tag":"node"}],"kind":"null","source":"mfld_set_tac","sourceEnd":11909,"sourceStart":11897...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
139
exact
true
1
38
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e131d019dd679c48760cd6964bc7fd3c390b65683c27b14a76eaf40083002143
62ce2144b3fe14aa7d6bcd14220ae6805e8646ab024d36ab5c9fe37b2cd46ffe
35baa4b4c1735a9b88ed94b0eeab328a8a537a3a069cc4f5274c84edee865427
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,691
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [hy, mfld_simps]
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst...
((:c Membership.mem) (:fv _uniq.48592) ((:c Set) (:fv _uniq.48592)) ((:c Set.instMembership) (:fv _uniq.48592)) ((:c PartialEquiv.toFun) (:fv _uniq.48435) (:fv _uniq.48592) ((:c PartialEquiv.symm) (:fv _uniq.48592) (:fv _uniq.48435) ((:c extChartAt) (:fv _uniq.48429) (:fv _uniq.48435) (:fv _uniq.48592) (:fv _uniq.48554...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV8)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV8)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV8)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV8))))))) (:arg :explicit 3 (:app (:c PartialEquiv....
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"simp","sourceEnd":11974,"sourceStart":11970,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":11979,"sourceStart":11975,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":119...
[]
[{"source":"hy","source_end":11983,"source_start":11981,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
144
exact
true
1
39
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f20c96964600a9ca286c9a4f4b115d03bba76e23b40485c01de2887b376e86d4
35aab0c0ca3f1a544e32c04b4f51bfe2be40de4c869238b67380b53071946463
7ed2c825ae122109ac44de3e83f2536eadd7555c131a9ab3f241ca2abd3f81b7
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,692
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [hy, mfld_simps]
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst...
((:c Membership.mem) (:fv _uniq.48953) ((:c Set) (:fv _uniq.48953)) ((:c Set.instMembership) (:fv _uniq.48953)) ((:c PartialHomeomorph.toFun') (:fv _uniq.48592) (:fv _uniq.48953) (:fv _uniq.48595) (:fv _uniq.48956) (:fv _uniq.49776) ((:c PartialEquiv.toFun) (:fv _uniq.48435) (:fv _uniq.48592) ((:c PartialEquiv.symm) (:...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV18)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV18)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV18)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV18))))))) (:arg :explicit 3 (:app (:c PartialHo...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"simp","sourceEnd":12067,"sourceStart":12063,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":12072,"sourceStart":12068,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":120...
[]
[{"source":"hy","source_end":12076,"source_start":12074,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
147
exact
true
1
40
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c0695fcc7c970fd5b035ca28ab121f9b49cfa448bd6ffa25deb350b48d8841ae
4bd247460962e282ae41052529e17fd3a78bcce9ec3001cdda92fe48d61c0c8e
7ed2c825ae122109ac44de3e83f2536eadd7555c131a9ab3f241ca2abd3f81b7
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,693
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [hy, mfld_simps]
case h.e'_12 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorners I M E' : ...
((:c Eq) (:fv _uniq.48435) (:fv _uniq.58423) ((:c PartialEquiv.toFun) (:fv _uniq.48592) (:fv _uniq.48435) ((:c extChartAt) (:fv _uniq.48429) (:fv _uniq.48435) (:fv _uniq.48592) (:fv _uniq.48554) (:fv _uniq.48432) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48557) (:fv _uniq.48595) (:fv _uniq.48589) (:fv _uniq.48607)...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:fv FV37)) (:arg :explicit 2 (:app (:c PartialEquiv.toFun) (:arg :implicit-type 0 (:fv FV8)) (:arg :implicit-type 1 (:fv FV2)) (:arg :explicit 2 (:app (:c extChartAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-ty...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":12189,"sourceStart":12185,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":12194,"sourceStart":12190,"tag":"atom"}],"kind"...
[]
[{"source":"hy","source_end":12198,"source_start":12196,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
154
exact
true
1
41
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ce1b289637fb97cae0ee27cf14ef520f0cb0456d060b5c229cfcc5a083793ea5
1c53a52dd8e069bba81787d053ef0c736807017ecb0a63bafd39818930aaae1d
7ed2c825ae122109ac44de3e83f2536eadd7555c131a9ab3f241ca2abd3f81b7
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,694
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
mfld_set_tac
case mpr.intro.refine_1.convert_2 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifold...
((:c HasSubset.Subset) ((:c Set) (:fv _uniq.48435)) ((:c Set.instHasSubset) (:fv _uniq.48435)) ((:c Inter.inter) ((:c Set) (:fv _uniq.48435)) ((:c Set.instInter) (:fv _uniq.48435)) ((:c Set.preimage) (:fv _uniq.48435) (:fv _uniq.48554) ((:c PartialEquiv.toFun) (:fv _uniq.48435) (:fv _uniq.48554) ((:c ModelWithCorners.s...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 2 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv F...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"children":[{"children":[{"children":[{"source":"mfld_set_tac","sourceEnd":12233,"sourceStart":12221,"tag":"atom"}],"kind":"Tactic.MfldSetTac.mfldSetTac","source":"mfld_set_tac","sourceEnd":12233,"sourceStart":12221,"tag":"node"}],"kind":"null","source":"mfld_set_tac","sourceEnd":12233,"sourceStart":12221...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
159
exact
true
1
41
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
85d1d939048e6e002df9263a853b1ec762ecdf0a1896fa050bb23d319660d875
66804b32860e6fddb109d23a64e5fd78a12864579d69b2b1eef4c78d171782e0
35baa4b4c1735a9b88ed94b0eeab328a8a537a3a069cc4f5274c84edee865427
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,695
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro y hy
case mpr.intro.refine_2 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I ...
case mpr.intro.refine_2 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I ...
((:c Pregroupoid.property) (:fv _uniq.48554) (:fv _uniq.48557) ((:c contDiffPregroupoid) ((:c Top.top) (:c ENat) (:c instENatTop)) (:fv _uniq.48429) (:fv _uniq.48432) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48589)) ((:c PartialHomeomorph.toFun') (:fv _uniq.48...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Pregroupoid.property) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c contDiffPregroupoid) (:arg :explicit 0 (:app (:c Top.top) (:arg :implicit-type 0 (:c ENat)) (:arg :instance 1 (:instance-of (:app (:c ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"intro","sourceEnd":12330,"sourceStart":12325,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":12332,"sourceStart":12331,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hy","sourceEnd":12335,"sourceStart":12333,"tag":"identifier"}],"kind":"null","sou...
[{"role":"fresh_name","source":"y","source_end":12332,"source_start":12331,"syntax_kind":"ident"},{"role":"fresh_name","source":"hy","source_end":12335,"source_start":12333,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
166
exact
true
1
36
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
bdb06c920262ef58911a23659f6e2476614630a04bc5a288536d85a44ad9f19d
4b52796be68c87a71bf00ce5b2d5514903988c360afabd3cea55c4bdb35d1041
69ac7ac9f4300ee3290568559761b10f79f65930316d628484707cb4cb9d79dc
e7a596836349bb69c02635757d73e6b4d263868b84d2ee5c10ec48bd380d3c64
cat-searcher/leandojo-benchmark-4-random
test
1,696
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [mfld_simps] at hy
case mpr.intro.refine_2 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I ...
case mpr.intro.refine_2 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I ...
((:c ContDiffWithinAt) (:fv _uniq.48429) (:fv _uniq.48432) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) ((:c Top.top) (:c ENat) (:c instENatTop)) ((:c Function.comp) (:fv _uniq.48435) (:fv _uniq.48554) (:fv _uniq.48435) ((:c ModelWithCorners.toFun') (:fv _u...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c ContDiffWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:ap...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"simp","sourceEnd":12346,"sourceStart":12342,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":12351,"sourceStart":12347,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":123...
[]
[{"source":"hy","source_end":12370,"source_start":12368,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
167
exact
true
1
38
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3f8d8c06461121c2426ba16c9edd741a86597c6155a6de19a136d868c1716377
e7a596836349bb69c02635757d73e6b4d263868b84d2ee5c10ec48bd380d3c64
055efa59a55ca2c71a28d9bdcca97fef6d01f426f5e0026b7e96a240d7054f83
d7dd8c0b275490e47e470651b741280b0741542bcbf780178534be3417bee83e
cat-searcher/leandojo-benchmark-4-random
test
1,697
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have hy' : (<a>extChartAt</a> I (f x)).<a>PartialEquiv.symm</a> y ∈ c'.source := by simp only [hy, mfld_simps]
case mpr.intro.refine_2 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorner...
case mpr.intro.refine_2 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorner...
((:c ContDiffWithinAt) (:fv _uniq.48429) (:fv _uniq.48432) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) ((:c Top.top) (:c ENat) (:c instENatTop)) ((:c Function.comp) (:fv _uniq.48435) (:fv _uniq.48554) (:fv _uniq.48435) ((:c ModelWithCorners.toFun') (:fv _u...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c ContDiffWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:ap...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"have","sourceEnd":12625,"sourceStart":12621,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hy'","sourceEnd":12629,"sourceStart":12626,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hy'","sourceEnd":12629,"sourceStart":12626,"tag":"n...
[]
[{"source":"(extChartAt I (f x)).symm y ∈ c'.source","source_end":12673,"source_start":12632,"syntax_kind":"«term_∈_»"},{"source":"hy","source_end":12693,"source_start":12691,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
181
exact
true
1
39
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
df7b76a2ed15111c50942648d59245d98a385bb78c4225160a74b404a439c3a4
3752d8d99373c5e76d32acb51d8cb825d1341911cddc2b72d039e6480ed066bb
c3dc83ea6ae661f2332a0e6c6b4a9e74b665e81dee3795f79f6d1311713320e9
410e500bd68b3a41d41a573de56e258cb4f8e5c99fe14f39ea227d2b1cce301b
cat-searcher/leandojo-benchmark-4-random
test
1,698
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have hy'' : f.symm ((<a>extChartAt</a> I (f x)).<a>PartialEquiv.symm</a> y) ∈ c.source := by simp only [hy, mfld_simps]
case mpr.intro.refine_2 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorner...
case mpr.intro.refine_2 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorner...
((:c ContDiffWithinAt) (:fv _uniq.48429) (:fv _uniq.48432) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) ((:c Top.top) (:c ENat) (:c instENatTop)) ((:c Function.comp) (:fv _uniq.48435) (:fv _uniq.48554) (:fv _uniq.48435) ((:c ModelWithCorners.toFun') (:fv _u...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c ContDiffWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:ap...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"have","sourceEnd":12717,"sourceStart":12713,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hy''","sourceEnd":12722,"sourceStart":12718,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hy''","sourceEnd":12722,"sourceStart":12718,"tag":...
[]
[{"source":"f.symm ((extChartAt I (f x)).symm y) ∈ c.source","source_end":12774,"source_start":12725,"syntax_kind":"«term_∈_»"},{"source":"hy","source_end":12794,"source_start":12792,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
184
exact
true
1
40
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1d0e928d75be9f9443ee55985fcb19006e3f06b023de6812e717d04ea4d94114
410e500bd68b3a41d41a573de56e258cb4f8e5c99fe14f39ea227d2b1cce301b
d2cd1f79d9f0ed60bdf42643e74d5f1c7aa8b0b8dca720aca81885a4f4e22b43
e468e472df0e24808934d29793654b4279931ae15b9316630ff7c759d167303f
cat-searcher/leandojo-benchmark-4-random
test
1,699
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>contMDiffWithinAt_iff_of_mem_source</a> hy' hy''] at H
case mpr.intro.refine_2 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorner...
case mpr.intro.refine_2 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorner...
((:c ContDiffWithinAt) (:fv _uniq.48429) (:fv _uniq.48432) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) ((:c Top.top) (:c ENat) (:c instENatTop)) ((:c Function.comp) (:fv _uniq.48435) (:fv _uniq.48554) (:fv _uniq.48435) ((:c ModelWithCorners.toFun') (:fv _u...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c ContDiffWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:ap...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"rw","sourceEnd":12816,"sourceStart":12814,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12818,"sourceStart":12817,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"con...
[]
[{"source":"H","source_end":12868,"source_start":12867,"syntax_kind":"ident"},{"source":"contMDiffWithinAt_iff_of_mem_source hy' hy''","source_end":12862,"source_start":12818,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
187
exact
true
1
41
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f6a94acb1635005a19f964f8b730bccda9a9563f48aadf85f4051e16b2f14cdf
e468e472df0e24808934d29793654b4279931ae15b9316630ff7c759d167303f
b6cf15f1b774ac3309e12bdfe60d8e026bb7f0809616606f2080b27a28d32792
a4427dfc384d55bb252358110b54a2078fba1362be61d4e07259c644f3661c9d
cat-searcher/leandojo-benchmark-4-random
test
1,700
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
convert H.2.<a>ContDiffWithinAt.mono</a> _
case mpr.intro.refine_2 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorner...
case h.e'_12 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorners I M E' : ...
((:c ContDiffWithinAt) (:fv _uniq.48429) (:fv _uniq.48432) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) ((:c Top.top) (:c ENat) (:c instENatTop)) ((:c Function.comp) (:fv _uniq.48435) (:fv _uniq.48554) (:fv _uniq.48435) ((:c ModelWithCorners.toFun') (:fv _u...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c ContDiffWithinAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:ap...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"convert","sourceEnd":12882,"sourceStart":12875,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"children":[{"contextIndex":39,"semanticRole":"local","source":"H","sourceEnd":12884,"sourceStart"...
[]
[{"source":"H.2.mono _","source_end":12893,"source_start":12883,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
190
exact
true
1
41
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
f0fb12f3e5ee7108b7828bc68e7943b62e047a02fe81f76778269af7aa9f678b
a4427dfc384d55bb252358110b54a2078fba1362be61d4e07259c644f3661c9d
1a730b635ed526b6a7a3b1019233628a99898c8257f0a0e42efe8f51a93da320
d608c4ace33598112fa29b809b4105585f67d465fbe34744872116807897bb72
cat-searcher/leandojo-benchmark-4-random
test
1,701
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine (h₂ ((<a>extChartAt</a> I (f x)).<a>PartialEquiv.symm</a> y) ?_).<a>ContMDiffWithinAt.mono</a> ?_
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst✝⁶ :...
case refine_1 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Typ...
((:c ContMDiffWithinAt) (:fv _uniq.48429) (:fv _uniq.48432) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48589) (:fv _uniq.48953) (:fv _uniq.48956) (:fv _uniq.49183) (:fv _uniq.48435) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _un...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c ContMDiffWithinAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-o...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"refine","sourceEnd":12504,"sourceStart":12498,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":12506,"sourceStart":12505,"tag":"atom"},{"children":[{"contextIndex":31,"semanticRole":"local","source":"h₂","sourceEnd":12510,"sourceStart":12506,"tag":"identifier"},{"ch...
[]
[{"source":"(h₂ ((extChartAt I (f x)).symm y) ?_).mono ?_","source_end":12552,"source_start":12505,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
170
exact
true
1
38
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
6c527f8864d04dcf5ec3b2367ba7e7fc69a29f2b09eb855b8457a78abdfd92ed
720d0ad015ac13cac7706925ce7712e3104f650c74b859cdcc71baeb6f5c115e
19737e2abe2a7814d2e5fb1fbb705b4bf0efe7a05be14cb1d7e1a68346b71bb8
f3388a072b5924e570489cec04a5ebe2d307555ea83ce3f56a1ce3807ff6e632
cat-searcher/leandojo-benchmark-4-random
test
1,702
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [hy, mfld_simps]
case refine_1 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Typ...
((:c Membership.mem) (:fv _uniq.48953) ((:c Set) (:fv _uniq.48953)) ((:c Set.instMembership) (:fv _uniq.48953)) ((:c PartialEquiv.toFun) (:fv _uniq.48435) (:fv _uniq.48953) ((:c PartialEquiv.symm) (:fv _uniq.48953) (:fv _uniq.48435) ((:c extChartAt) (:fv _uniq.48429) (:fv _uniq.48435) (:fv _uniq.48953) (:fv _uniq.48554...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV18)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV18)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV18)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV18))))))) (:arg :explicit 3 (:app (:c PartialEq...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":12568,"sourceStart":12564,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":12573,"sourceStart":12569,"tag":"atom"}],"kind"...
[]
[{"source":"hy","source_end":12577,"source_start":12575,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
173
exact
true
1
38
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
cd51d612a49c126db4b1a2aa48c4df648be13bb6ebd7c55c1ed09d13c4c9cb16
46625534bb35b4c27dd62d639471924870b951509e26eb756468e5e49a3f30a1
7ed2c825ae122109ac44de3e83f2536eadd7555c131a9ab3f241ca2abd3f81b7
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,703
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
mfld_set_tac
case refine_2 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I M E' : Typ...
((:c HasSubset.Subset) ((:c Set) (:fv _uniq.48953)) ((:c Set.instHasSubset) (:fv _uniq.48953)) ((:c PartialEquiv.source) (:fv _uniq.48953) (:fv _uniq.48554) ((:c PartialHomeomorph.toPartialEquiv) (:fv _uniq.48953) (:fv _uniq.48554) (:fv _uniq.48956) (:fv _uniq.48557) ((:c PartialHomeomorph.trans) (:fv _uniq.48953) (:fv...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV18)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV18))))))) (:arg :explicit 2 (:app (:c PartialEquiv.source) (:arg :implicit-type 0 (:fv FV18)) (:arg :implicit-t...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"children":[{"children":[{"children":[{"source":"mfld_set_tac","sourceEnd":12614,"sourceStart":12602,"tag":"atom"}],"kind":"Tactic.MfldSetTac.mfldSetTac","source":"mfld_set_tac","sourceEnd":12614,"sourceStart":12602,"tag":"node"}],"kind":"null","source":"mfld_set_tac","sourceEnd":12614,"sourceStart":12602...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
178
exact
true
1
38
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c65a0f1b599f1542a01a3290251bf8b776e0d94ace4d8adffde0b84ece5b5cc3
6adcf3b362e4174dd7c96c66aa5786fa91aa25a4cc21e1ac03e4cd5e6f29676a
35baa4b4c1735a9b88ed94b0eeab328a8a537a3a069cc4f5274c84edee865427
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,704
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [hy, mfld_simps]
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst...
((:c Membership.mem) (:fv _uniq.48953) ((:c Set) (:fv _uniq.48953)) ((:c Set.instMembership) (:fv _uniq.48953)) ((:c PartialEquiv.toFun) (:fv _uniq.48435) (:fv _uniq.48953) ((:c PartialEquiv.symm) (:fv _uniq.48953) (:fv _uniq.48435) ((:c extChartAt) (:fv _uniq.48429) (:fv _uniq.48435) (:fv _uniq.48953) (:fv _uniq.48554...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV18)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV18)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV18)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV18))))))) (:arg :explicit 3 (:app (:c PartialEq...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"simp","sourceEnd":12684,"sourceStart":12680,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":12689,"sourceStart":12685,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":126...
[]
[{"source":"hy","source_end":12693,"source_start":12691,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
183
exact
true
1
39
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3c87a5e28fdb08e11896afb2f08eb5102209f041c195dc695dae1e6310c2a386
c0c00ec5b5db1d8cd732307185a1c56d111a30d7d14e03d08142b4e74b0b9a94
7ed2c825ae122109ac44de3e83f2536eadd7555c131a9ab3f241ca2abd3f81b7
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,705
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [hy, mfld_simps]
𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorners I M E' : Type u_5 inst...
((:c Membership.mem) (:fv _uniq.48592) ((:c Set) (:fv _uniq.48592)) ((:c Set.instMembership) (:fv _uniq.48592)) ((:c PartialHomeomorph.toFun') (:fv _uniq.48953) (:fv _uniq.48592) (:fv _uniq.48956) (:fv _uniq.48595) ((:c PartialHomeomorph.symm) (:fv _uniq.48592) (:fv _uniq.48953) (:fv _uniq.48595) (:fv _uniq.48956) (:fv...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV8)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV8)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV8)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV8))))))) (:arg :explicit 3 (:app (:c PartialHomeom...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"simp","sourceEnd":12785,"sourceStart":12781,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":12790,"sourceStart":12786,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":127...
[]
[{"source":"hy","source_end":12794,"source_start":12792,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
186
exact
true
1
40
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0a6ef3bdeb5afbe21d33d4a620af70bd972e2d066b63890731b5a63ed0ebdae4
d1e46cee44e6ddbf4a283133315a0aba0d6f96cc7f58357355f9dce4d5295cee
7ed2c825ae122109ac44de3e83f2536eadd7555c131a9ab3f241ca2abd3f81b7
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,706
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [hy, mfld_simps]
case h.e'_12 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifoldWithCorners I M E' : ...
((:c Eq) (:fv _uniq.48435) (:fv _uniq.63953) ((:c PartialEquiv.toFun) (:fv _uniq.48953) (:fv _uniq.48435) ((:c extChartAt) (:fv _uniq.48429) (:fv _uniq.48435) (:fv _uniq.48953) (:fv _uniq.48554) (:fv _uniq.48432) (:fv _uniq.48438) (:fv _uniq.48551) (:fv _uniq.48557) (:fv _uniq.48956) (:fv _uniq.48589) (:fv _uniq.49183)...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:fv FV37)) (:arg :explicit 2 (:app (:c PartialEquiv.toFun) (:arg :implicit-type 0 (:fv FV18)) (:arg :implicit-type 1 (:fv FV2)) (:arg :explicit 2 (:app (:c extChartAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-t...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":12907,"sourceStart":12903,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":12912,"sourceStart":12908,"tag":"atom"}],"kind"...
[]
[{"source":"hy","source_end":12916,"source_start":12914,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
193
exact
true
1
41
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
548b502d332b3c2b3966d3d1df9461a0b7a43c8af05ea613f1d7955912681d48
b0771e4996ac38c60f58a9bf49035ddf50027495ade83f207d08534bdd22ed8b
7ed2c825ae122109ac44de3e83f2536eadd7555c131a9ab3f241ca2abd3f81b7
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,707
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
mfld_set_tac
case mpr.intro.refine_2.convert_2 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H✝ : Type u_3 inst✝¹⁰ : TopologicalSpace H✝ I : ModelWithCorners 𝕜 E H✝ M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H✝ M inst✝⁷ : SmoothManifold...
((:c HasSubset.Subset) ((:c Set) (:fv _uniq.48435)) ((:c Set.instHasSubset) (:fv _uniq.48435)) ((:c Inter.inter) ((:c Set) (:fv _uniq.48435)) ((:c Set.instInter) (:fv _uniq.48435)) ((:c Set.preimage) (:fv _uniq.48435) (:fv _uniq.48554) ((:c PartialEquiv.toFun) (:fv _uniq.48435) (:fv _uniq.48554) ((:c ModelWithCorners.s...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 2 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv F...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"children":[{"children":[{"children":[{"source":"mfld_set_tac","sourceEnd":12951,"sourceStart":12939,"tag":"atom"}],"kind":"Tactic.MfldSetTac.mfldSetTac","source":"mfld_set_tac\n -- now check the candidate local structomorphism agrees with `f` where it is supposed to","sourceEnd":12951,"sourceStart":12...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
198
exact
true
1
41
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
dbbd4749525c76929d75ebb170dd58e1216db5f8db68cb6f0f8c374a4447ce27
1555a5294eee35f6eeebbd080b21553a57a62a641fce2bce0c8c38e577b13cd1
35baa4b4c1735a9b88ed94b0eeab328a8a537a3a069cc4f5274c84edee865427
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,708
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [mfld_simps]
case mpr.intro.refine_3 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I ...
case mpr.intro.refine_3 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I ...
((:c Set.EqOn) (:fv _uniq.48554) (:fv _uniq.48554) ((:c Function.comp) (:fv _uniq.48554) (:fv _uniq.48953) (:fv _uniq.48554) ((:c PartialHomeomorph.toFun') (:fv _uniq.48953) (:fv _uniq.48554) (:fv _uniq.48956) (:fv _uniq.48557) (:fv _uniq.58049)) ((:c Function.comp) (:fv _uniq.48554) (:fv _uniq.48592) (:fv _uniq.48953)...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Set.EqOn) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV5)) (:arg :explicit 2 (:app (:c Function.comp) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV18)) (:arg :implicit-type 2 (:fv FV5)) (:arg :explicit 3 (:app (:c PartialHomeomorph.toFun') (:arg :implicit-type 0 (:fv FV18...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"simp","sourceEnd":13056,"sourceStart":13052,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":13061,"sourceStart":13057,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":130...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
205
exact
true
1
36
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
06e8d37dcc3997eec8695e24a4ea55ae2c94095de57670f00357d99de029fa9b
bd1d12bc5a0222868164b2b9a410d20b0067d3ecd3bafb15483a8bf19d1760ef
b446a4221aa6b1388f9c2e382e93c42c01fdbc35140ca04db8cb07c90046ad2e
774fc4daaf13034ef7aa937d48db755968269c65d4a9492bab208d2d199ce8f5
cat-searcher/leandojo-benchmark-4-random
test
1,709
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
apply <a>Set.eqOn_refl</a>
case mpr.intro.refine_3 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I ...
((:c Set.EqOn) (:fv _uniq.48554) (:fv _uniq.48554) ((:c Function.comp) (:fv _uniq.48554) (:fv _uniq.48953) (:fv _uniq.48554) ((:c PartialHomeomorph.toFun') (:fv _uniq.48953) (:fv _uniq.48554) (:fv _uniq.48956) (:fv _uniq.48557) (:fv _uniq.58049)) ((:c Function.comp) (:fv _uniq.48554) (:fv _uniq.48592) (:fv _uniq.48953)...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Set.EqOn) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV5)) (:arg :explicit 2 (:app (:c Function.comp) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:fv FV18)) (:arg :implicit-type 2 (:fv FV5)) (:arg :explicit 3 (:app (:c PartialHomeomorph.toFun') (:arg :implicit-type 0 (:fv FV18...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"source":"apply","sourceEnd":13081,"sourceStart":13076,"tag":"atom"},{"name":"Set.eqOn_refl","semanticRole":"global","source":"eqOn_refl","sourceEnd":13091,"sourceStart":13082,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply eqOn_refl","sourceEnd":13091,"sourceStart":13076,"tag":"nod...
[]
[{"source":"eqOn_refl","source_end":13091,"source_start":13082,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
207
exact
true
1
36
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
28e08a3c7c3369265ebf6d4fdda89abac404be6a237516019e611315144cd56b
774fc4daaf13034ef7aa937d48db755968269c65d4a9492bab208d2d199ce8f5
d229fa2be867be0d81f024bbcd4899787450e147f1bbce29e5ed4130e2022878
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,710
isLocalStructomorphOn_contDiffGroupoid_iff
Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp only [c, c', hx', mfld_simps]
case mpr.intro.refine_4 𝕜 : Type u_1 inst✝¹³ : NontriviallyNormedField 𝕜 E : Type u_2 inst✝¹² : NormedAddCommGroup E inst✝¹¹ : NormedSpace 𝕜 E H : Type u_3 inst✝¹⁰ : TopologicalSpace H I : ModelWithCorners 𝕜 E H M : Type u_4 inst✝⁹ : TopologicalSpace M inst✝⁸ : ChartedSpace H M inst✝⁷ : SmoothManifoldWithCorners I ...
((:c Membership.mem) (:fv _uniq.48554) ((:c Set) (:fv _uniq.48554)) ((:c Set.instMembership) (:fv _uniq.48554)) ((:c PartialHomeomorph.toFun') (:fv _uniq.48592) (:fv _uniq.48554) (:fv _uniq.48595) (:fv _uniq.48557) ((:c chartAt) (:fv _uniq.48554) (:fv _uniq.48557) (:fv _uniq.48592) (:fv _uniq.48595) (:fv _uniq.48607) (...
[{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹³","sexp":"((:c NontriviallyNormedField) (:fv _uniq.48429))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.48435))"},{"name":"inst✝¹¹","sexp":"((:c NormedSpace) (:fv _uniq.48429) (:fv _uniq.48435) ((:c Nont...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV5)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV5))))))) (:arg :explicit 3 (:app (:c PartialHomeom...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"name":"inst✝¹³","sexp":"(:app (:c NontriviallyNormedFie...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":13103,"sourceStart":13099,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":13108,"sourceStart":13104,"tag":"atom"}],"kind"...
[]
[{"source":"c","source_end":13111,"source_start":13110,"syntax_kind":"ident"},{"source":"c'","source_end":13115,"source_start":13113,"syntax_kind":"ident"},{"source":"hx'","source_end":13120,"source_start":13117,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48429","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.48432","is_instance":true,"is_let":false,"user_name":"inst✝¹³"},{"binder_role":":implicit","context_index":2,"inte...
42
210
exact
true
1
36
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
39e3dc80464305c6c1970acdda804c83795a537b41e61cfb422f022cf7874c54
86ff357cedc1476c3f11428f1b41ae00d4a1ce82098c637f8f3d2a2a7bbdd2b5
e05bbf2ad2542ccb0858de071c99b65095004dfd2e2de1b8fb0f380fd3ee25a0
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,711
Nat.ceil_eq_zero
Mathlib/Algebra/Order/Floor.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>Nat.le_zero</a>, <a>Nat.ceil_le</a>, <a>Nat.cast_zero</a>]
F : Type u_1 α : Type u_2 β : Type u_3 inst✝¹ : LinearOrderedSemiring α inst✝ : FloorSemiring α a : α n : ℕ ⊢ ⌈a⌉₊ = 0 ↔ a ≤ 0
((:c Iff) ((:c Eq) (:c Nat) ((:c Nat.ceil) (:fv _uniq.50055) ((:c StrictOrderedSemiring.toOrderedSemiring) (:fv _uniq.50055) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.50055) (:fv _uniq.50061))) (:fv _uniq.50142) (:fv _uniq.50144)) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) (...
[{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedSemiring) (:fv _uniq.50055))"},{"name":"inst✝","sexp":"((:c FloorSemiring) (:fv _uniq.50055) ((:c StrictOrderedSemiring.toOrderedSemiring) (:fv _uniq.50055)...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.ceil) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c OrderedSemiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c FloorSemiring) (:arg :explicit 0 (:...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.50052","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.50055","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":11888,"sourceStart":11886,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11890,"sourceStart":11889,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"...
[]
[{"source":"Nat.le_zero","source_end":11905,"source_start":11894,"syntax_kind":"ident"},{"source":"ceil_le","source_end":11914,"source_start":11907,"syntax_kind":"ident"},{"source":"Nat.cast_zero","source_end":11929,"source_start":11916,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.50052","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.50055","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
112
2
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
435bcd32271372a3ab886479d53a0698b0bf7a60309a2b2672f993c54c775c84
a5c8220530155acd8fd03bcb1662faadcb513efc7c4b45f6fa08de4ca919a711
bcbf5b6e7da7fddf6f368a5920ef2af99060aeae7cac68575b0a903fae2feb8b
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,712
pow_two
Mathlib/Algebra/Group/Defs.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>pow_succ</a>, <a>pow_one</a>]
G : Type u_1 M : Type u_2 inst✝ : Monoid M a✝ b c : M m n : ℕ a : M ⊢ a ^ 2 = a * a
((:c Eq) (:fv _uniq.16260) ((:c HPow.hPow) (:fv _uniq.16260) (:c Nat) (:fv _uniq.16260) ((:c instHPow) (:fv _uniq.16260) (:c Nat) ((:c Monoid.toNatPow) (:fv _uniq.16260) (:fv _uniq.16263))) (:fv _uniq.16452) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c HMul.hMul) (:fv _uniq.16260) (:fv _uniq....
[{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c Monoid) (:fv _uniq.16260))"},{"name":"a✝","sexp":"(:fv _uniq.16260)"},{"name":"b","sexp":"(:fv _uniq.16260)"},{"name":"c","sexp":"(:fv _uniq.16260)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:fv FV1)...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16257","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16260","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":30067,"sourceStart":30065,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":30069,"sourceStart":30068,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",...
[]
[{"source":"pow_succ","source_end":30077,"source_start":30069,"syntax_kind":"ident"},{"source":"pow_one","source_end":30086,"source_start":30079,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16257","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16260","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
217
2
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b390ee41a421801dae06766b2ce612a4ec8227b93adabba1785ca5dc02bbebc6
6c4fac5c5671e2d0246b17373f869f938f34221150d88af950dad0e2b95a39ea
13f5b3ad3a830e527e3330751b79cf560a24c2e0627a73576f4a90a3269be0ea
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,713
smul_ceilDiv
Mathlib/Algebra/Order/Floor/Div.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>smul_le_smul_iff_of_pos_left</a>, ha]
ι : Type u_1 α : Type u_2 β : Type u_3 inst✝⁵ : OrderedSemiring α inst✝⁴ : OrderedAddCommMonoid β inst✝³ : MulActionWithZero α β inst✝² : CeilDiv α β a : α inst✝¹ : PosSMulMono α β inst✝ : PosSMulReflectLE α β ha : 0 < a b : β ⊢ ∀ (c : β), a • b ⌈/⌉ a ≤ c ↔ b ≤ c
(:forall c (:fv _uniq.77895) ((:c Iff) ((:c LE.le) (:fv _uniq.77895) ((:c Preorder.toLE) (:fv _uniq.77895) ((:c PartialOrder.toPreorder) (:fv _uniq.77895) ((:c OrderedAddCommMonoid.toPartialOrder) (:fv _uniq.77895) (:fv _uniq.77901)))) ((:c CeilDiv.ceilDiv) (:fv _uniq.77892) (:fv _uniq.77895) ((:c OrderedSemiring.toOrd...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁵","sexp":"((:c OrderedSemiring) (:fv _uniq.77892))"},{"name":"inst✝⁴","sexp":"((:c OrderedAddCommMonoid) (:fv _uniq.77895))"},{"name":"inst✝³","sexp":"((:c MulActionWithZero) (:fv _uni...
(:forall c :explicit (:fv FV2) (:app (:c Iff) (: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 CeilDiv.ceilDiv) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instanc...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77889","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.77892","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":6189,"sourceStart":6185,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn...
[]
[{"source":"smul_le_smul_iff_of_pos_left","source_end":6219,"source_start":6191,"syntax_kind":"ident"},{"source":"ha","source_end":6223,"source_start":6221,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77889","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.77892","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
42
2
exact
true
1
12
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
54b6fcd16bc65cb2053dd46d239f5df165913fe4b99aaedc30b90adc3ab87fce
a071b5c0d12fdae631c477782693e5039fda0461d1e0c6e0408999f34d9be113
8f33042b8bdd8f16180112baaadfbbaa93bfd3079959bb19df1fee648c5854a6
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,714
Ideal.IsHomogeneous.sSup
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>sSup_eq_iSup</a>]
ι : Type u_1 σ : Type u_2 R : Type u_3 A : Type u_4 inst✝⁵ : Semiring A inst✝⁴ : DecidableEq ι inst✝³ : AddMonoid ι inst✝² : SetLike σ A inst✝¹ : AddSubmonoidClass σ A 𝒜 : ι → σ inst✝ : GradedRing 𝒜 ℐ : Set (Ideal A) h : ∀ I ∈ ℐ, IsHomogeneous 𝒜 I ⊢ IsHomogeneous 𝒜 (SupSet.sSup ℐ)
ι : Type u_1 σ : Type u_2 R : Type u_3 A : Type u_4 inst✝⁵ : Semiring A inst✝⁴ : DecidableEq ι inst✝³ : AddMonoid ι inst✝² : SetLike σ A inst✝¹ : AddSubmonoidClass σ A 𝒜 : ι → σ inst✝ : GradedRing 𝒜 ℐ : Set (Ideal A) h : ∀ I ∈ ℐ, IsHomogeneous 𝒜 I ⊢ IsHomogeneous 𝒜 (⨆ a ∈ ℐ, a)
((:c Ideal.IsHomogeneous) (:fv _uniq.64719) (:fv _uniq.64722) (:fv _uniq.64728) (:fv _uniq.64731) (:fv _uniq.64747) (:fv _uniq.64914) (:fv _uniq.64918) (:fv _uniq.64738) (:fv _uniq.64743) (:fv _uniq.65256) ((:c SupSet.sSup) ((:c Ideal) (:fv _uniq.64728) (:fv _uniq.64731)) ((:c ConditionallyCompleteLattice.toSupSet) ((:...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"σ","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"A","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁵","sexp":"((:c Semiring) (:fv _uniq.64728))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.64719))"},{"name":"inst✝³","sexp":"((:c AddM...
(:app (:c Ideal.IsHomogeneous) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV3))))) (:arg :instance 4 (:instance-of (:app (:c SetLike) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.64719","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.64722","is_instance":false,"is_let":false,"name":"σ","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"rw","sourceEnd":12581,"sourceStart":12579,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12583,"sourceStart":12582,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"sSup_eq_iSup","s...
[]
[{"source":"sSup_eq_iSup","source_end":12595,"source_start":12583,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.64719","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.64722","is_instance":false,"is_let":false,"user_name":"σ"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
96
4
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5395f2829caacf049a596bb599cf014260b4365bab9baaef459b7d24f1834fb4
ee466a88a9f0e76f521a9ee1999a93ed74f3ee94e7bf1c0a9ab84aca35de3de0
4b3b708fde372f9aa45ee5ec591297314fea8839240d8dce7b4f204da657a0d1
9305577cff29492c750fd029cb2bc3c497c16ddc3f4b864368b6e7a0a1004024
cat-searcher/leandojo-benchmark-4-random
test
1,715
Ideal.IsHomogeneous.sSup
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact <a>Ideal.IsHomogeneous.iSup₂</a> h
ι : Type u_1 σ : Type u_2 R : Type u_3 A : Type u_4 inst✝⁵ : Semiring A inst✝⁴ : DecidableEq ι inst✝³ : AddMonoid ι inst✝² : SetLike σ A inst✝¹ : AddSubmonoidClass σ A 𝒜 : ι → σ inst✝ : GradedRing 𝒜 ℐ : Set (Ideal A) h : ∀ I ∈ ℐ, IsHomogeneous 𝒜 I ⊢ IsHomogeneous 𝒜 (⨆ a ∈ ℐ, a)
((:c Ideal.IsHomogeneous) (:fv _uniq.64719) (:fv _uniq.64722) (:fv _uniq.64728) (:fv _uniq.64731) (:fv _uniq.64747) (:fv _uniq.64914) (:fv _uniq.64918) (:fv _uniq.64738) (:fv _uniq.64743) (:fv _uniq.65256) ((:c iSup) ((:c Ideal) (:fv _uniq.64728) (:fv _uniq.64731)) ((:c Ideal) (:fv _uniq.64728) (:fv _uniq.64731)) ((:c ...
[{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"σ","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"A","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁵","sexp":"((:c Semiring) (:fv _uniq.64728))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.64719))"},{"name":"inst✝³","sexp":"((:c AddM...
(:app (:c Ideal.IsHomogeneous) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV3))))) (:arg :instance 4 (:instance-of (:app (:c SetLike) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.64719","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.64722","is_instance":false,"is_let":false,"name":"σ","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"exact","sourceEnd":12604,"sourceStart":12599,"tag":"atom"},{"children":[{"name":"Ideal.IsHomogeneous.iSup₂","semanticRole":"global","source":"iSup₂","sourceEnd":12612,"sourceStart":12605,"tag":"identifier"},{"children":[{"contextIndex":13,"semanticRole":"local","source":"h","sourceEnd":12614,"so...
[]
[{"source":"iSup₂ h","source_end":12614,"source_start":12605,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.64719","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.64722","is_instance":false,"is_let":false,"user_name":"σ"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
96
7
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ce7e7942b1e7c8664e61ae064305ac46342c175b4178e325720b290f4b5e5a8e
9305577cff29492c750fd029cb2bc3c497c16ddc3f4b864368b6e7a0a1004024
42a3e07312a58a8f3a5c2d82cf5089dff33f79895c4ccd3422b68b2e6cb0624a
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,716
LieAlgebra.IsKilling.eq_neg_or_eq_of_eq_smul
Mathlib/Algebra/Lie/Weights/RootSystem.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
by_cases hα : α.IsZero
K : Type u_1 L : Type u_2 inst✝⁷ : Field K inst✝⁶ : CharZero K inst✝⁵ : LieRing L inst✝⁴ : LieAlgebra K L inst✝³ : IsKilling K L inst✝² : FiniteDimensional K L H : LieSubalgebra K L inst✝¹ : H.IsCartanSubalgebra inst✝ : IsTriangularizable K (↥H) L α β : Weight K (↥H) L hα : α.IsNonZero hβ : β.IsNonZero k : K h : ⇑β = k...
case pos K : Type u_1 L : Type u_2 inst✝⁷ : Field K inst✝⁶ : CharZero K inst✝⁵ : LieRing L inst✝⁴ : LieAlgebra K L inst✝³ : IsKilling K L inst✝² : FiniteDimensional K L H : LieSubalgebra K L inst✝¹ : H.IsCartanSubalgebra inst✝ : IsTriangularizable K (↥H) L α β : Weight K (↥H) L hα✝ : α.IsNonZero hβ : β.IsNonZero k : K ...
((:c Or) ((:c Eq) ((:c LieModule.Weight) (:fv _uniq.463183) ((:c Subtype) (:fv _uniq.463186) (:lambda x (:fv _uniq.463186) ((:c Membership.mem) (:fv _uniq.463186) ((:c LieSubalgebra) (:fv _uniq.463183) (:fv _uniq.463186) ((:c EuclideanDomain.toCommRing) (:fv _uniq.463183) ((:c Field.toEuclideanDomain) (:fv _uniq.463183...
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.463183))"},{"name":"inst✝⁶","sexp":"((:c CharZero) (:fv _uniq.463183) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.463183) ((:c Ring.toAddGroupWithOne) (:fv _uniq.463183) ((:c Division...
(:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LieModule.Weight) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"by_cases","sourceEnd":17673,"sourceStart":17665,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hα","sourceEnd":17677,"sourceStart":17674,"tag":"identifier"},{"source":":","sourceEnd":17679,"sourceStart":17678,"tag":"atom"}],"kind":"null","source":"hα :","sourceEnd":17679,"so...
[]
[{"source":"α.IsZero","source_end":17689,"source_start":17680,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...
33
4
exact
true
1
17
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
e9f3ac09785dd3e44c555586ff63e0c5eca5c8970f623ae15dbbe7de5f667e21
f2d9d3e0b45be86215e69a912dabfcc7087beefc16ec1d3eeab94252db182240
355ebe10681f58e8031e20ad7efdf692626d6a3869b60dcf69a8942f6f10cdd7
4c46dc5156ea7b6fd8c18a901c1a36f0b3c6ae190f0c7c474092dcff253f6500
cat-searcher/leandojo-benchmark-4-random
test
1,717
LieAlgebra.IsKilling.eq_neg_or_eq_of_eq_smul
Mathlib/Algebra/Lie/Weights/RootSystem.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rcases <a>LieAlgebra.IsKilling.eq_neg_one_or_eq_zero_or_eq_one_of_eq_smul</a> α β hα k h with (rfl | rfl | rfl)
case neg K : Type u_1 L : Type u_2 inst✝⁷ : Field K inst✝⁶ : CharZero K inst✝⁵ : LieRing L inst✝⁴ : LieAlgebra K L inst✝³ : IsKilling K L inst✝² : FiniteDimensional K L H : LieSubalgebra K L inst✝¹ : H.IsCartanSubalgebra inst✝ : IsTriangularizable K (↥H) L α β : Weight K (↥H) L hα✝ : α.IsNonZero hβ : β.IsNonZero k : K ...
case neg.inl K : Type u_1 L : Type u_2 inst✝⁷ : Field K inst✝⁶ : CharZero K inst✝⁵ : LieRing L inst✝⁴ : LieAlgebra K L inst✝³ : IsKilling K L inst✝² : FiniteDimensional K L H : LieSubalgebra K L inst✝¹ : H.IsCartanSubalgebra inst✝ : IsTriangularizable K (↥H) L α β : Weight K (↥H) L hα✝ : α.IsNonZero hβ : β.IsNonZero hα...
((:c Or) ((:c Eq) ((:c LieModule.Weight) (:fv _uniq.463183) ((:c Subtype) (:fv _uniq.463186) (:lambda x (:fv _uniq.463186) ((:c Membership.mem) (:fv _uniq.463186) ((:c LieSubalgebra) (:fv _uniq.463183) (:fv _uniq.463186) ((:c EuclideanDomain.toCommRing) (:fv _uniq.463183) ((:c Field.toEuclideanDomain) (:fv _uniq.463183...
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.463183))"},{"name":"inst✝⁶","sexp":"((:c CharZero) (:fv _uniq.463183) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.463183) ((:c Ring.toAddGroupWithOne) (:fv _uniq.463183) ((:c Division...
(:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LieModule.Weight) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"rcases","sourceEnd":17741,"sourceStart":17735,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"LieAlgebra.IsKilling.eq_neg_one_or_eq_zero_or_eq_one_of_eq_smul","semanticRole":"global","source":"eq_neg_one_or_eq_zero_or_eq_one_of...
[]
[{"source":"eq_neg_one_or_eq_zero_or_eq_one_of_eq_smul α β hα k h","source_end":17798,"source_start":17742,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(rfl | rfl | rfl)","source_end":17821,"source_start":17804,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...
33
15
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
c148b37c207f41abdee17079eb362f2e0b9b6c4603240155f2ac1c27c573fa21
9f3b22f7de68c8014ba7b54442cd4ee1bd88e668b8f0d9ae8e82b528c9881231
9d54d88731bda4be845d07988adfffd2722df80eabbcd5236daf52f4193b554a
2563a5818f334ed763da42fab16b25df003fc507a361fe149d70740fbab96d67
cat-searcher/leandojo-benchmark-4-random
test
1,718
LieAlgebra.IsKilling.eq_neg_or_eq_of_eq_smul
Mathlib/Algebra/Lie/Weights/RootSystem.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [hα, <a>smul_zero</a>] at h
case pos K : Type u_1 L : Type u_2 inst✝⁷ : Field K inst✝⁶ : CharZero K inst✝⁵ : LieRing L inst✝⁴ : LieAlgebra K L inst✝³ : IsKilling K L inst✝² : FiniteDimensional K L H : LieSubalgebra K L inst✝¹ : H.IsCartanSubalgebra inst✝ : IsTriangularizable K (↥H) L α β : Weight K (↥H) L hα✝ : α.IsNonZero hβ : β.IsNonZero k : K ...
case pos K : Type u_1 L : Type u_2 inst✝⁷ : Field K inst✝⁶ : CharZero K inst✝⁵ : LieRing L inst✝⁴ : LieAlgebra K L inst✝³ : IsKilling K L inst✝² : FiniteDimensional K L H : LieSubalgebra K L inst✝¹ : H.IsCartanSubalgebra inst✝ : IsTriangularizable K (↥H) L α β : Weight K (↥H) L hα✝ : α.IsNonZero hβ : β.IsNonZero k : K ...
((:c Or) ((:c Eq) ((:c LieModule.Weight) (:fv _uniq.463183) ((:c Subtype) (:fv _uniq.463186) (:lambda x (:fv _uniq.463186) ((:c Membership.mem) (:fv _uniq.463186) ((:c LieSubalgebra) (:fv _uniq.463183) (:fv _uniq.463186) ((:c EuclideanDomain.toCommRing) (:fv _uniq.463183) ((:c Field.toEuclideanDomain) (:fv _uniq.463183...
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.463183))"},{"name":"inst✝⁶","sexp":"((:c CharZero) (:fv _uniq.463183) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.463183) ((:c Ring.toAddGroupWithOne) (:fv _uniq.463183) ((:c Division...
(:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LieModule.Weight) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"rw","sourceEnd":17697,"sourceStart":17695,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":17699,"sourceStart":17698,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":18,"seman...
[]
[{"source":"hα","source_end":17702,"source_start":17699,"syntax_kind":"ident"},{"source":"h","source_end":17719,"source_start":17718,"syntax_kind":"ident"},{"source":"smul_zero","source_end":17713,"source_start":17704,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...
33
9
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
293897c81b2eaa6388211e2fe5428ada6a63cd7cd4f829b7355792351acca59f
10ee4042554857478a96691ad5f53a38989385523f9f026fc04d8e4006a336e8
b8df5b1af4409a334f8aa2af2b8ee6e56f3765ff58c3a4c96cc66dd909b60d34
b2039308eccd87a775b6e9b5851e38ce6d6d7b491639e82a6896e86fbf029fbe
cat-searcher/leandojo-benchmark-4-random
test
1,719
LieAlgebra.IsKilling.eq_neg_or_eq_of_eq_smul
Mathlib/Algebra/Lie/Weights/RootSystem.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
cases hβ h
case pos K : Type u_1 L : Type u_2 inst✝⁷ : Field K inst✝⁶ : CharZero K inst✝⁵ : LieRing L inst✝⁴ : LieAlgebra K L inst✝³ : IsKilling K L inst✝² : FiniteDimensional K L H : LieSubalgebra K L inst✝¹ : H.IsCartanSubalgebra inst✝ : IsTriangularizable K (↥H) L α β : Weight K (↥H) L hα✝ : α.IsNonZero hβ : β.IsNonZero k : K ...
((:c Or) ((:c Eq) ((:c LieModule.Weight) (:fv _uniq.463183) ((:c Subtype) (:fv _uniq.463186) (:lambda x (:fv _uniq.463186) ((:c Membership.mem) (:fv _uniq.463186) ((:c LieSubalgebra) (:fv _uniq.463183) (:fv _uniq.463186) ((:c EuclideanDomain.toCommRing) (:fv _uniq.463183) ((:c Field.toEuclideanDomain) (:fv _uniq.463183...
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.463183))"},{"name":"inst✝⁶","sexp":"((:c CharZero) (:fv _uniq.463183) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.463183) ((:c Ring.toAddGroupWithOne) (:fv _uniq.463183) ((:c Division...
(:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LieModule.Weight) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"cases","sourceEnd":17726,"sourceStart":17721,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"hβ","sourceEnd":17730,"sourceStart":17727,"tag":"identifier"},{"children":[{"contextIndex":...
[]
[{"source":"hβ h","source_end":17732,"source_start":17727,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...
33
14
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
3650e3fbcab7298a304a3294517fcff4308a70e5d0fac5117b4244d1ad617c05
b2039308eccd87a775b6e9b5851e38ce6d6d7b491639e82a6896e86fbf029fbe
c59611028914b4a834463bce8c024208c22dbb873c3733144c65acc94d12eb43
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,720
LieAlgebra.IsKilling.eq_neg_or_eq_of_eq_smul
Mathlib/Algebra/Lie/Weights/RootSystem.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact .inl (by ext; rw [h, <a>neg_one_smul</a>]; rfl)
case neg.inl K : Type u_1 L : Type u_2 inst✝⁷ : Field K inst✝⁶ : CharZero K inst✝⁵ : LieRing L inst✝⁴ : LieAlgebra K L inst✝³ : IsKilling K L inst✝² : FiniteDimensional K L H : LieSubalgebra K L inst✝¹ : H.IsCartanSubalgebra inst✝ : IsTriangularizable K (↥H) L α β : Weight K (↥H) L hα✝ : α.IsNonZero hβ : β.IsNonZero hα...
((:c Or) ((:c Eq) ((:c LieModule.Weight) (:fv _uniq.463183) ((:c Subtype) (:fv _uniq.463186) (:lambda x (:fv _uniq.463186) ((:c Membership.mem) (:fv _uniq.463186) ((:c LieSubalgebra) (:fv _uniq.463183) (:fv _uniq.463186) ((:c EuclideanDomain.toCommRing) (:fv _uniq.463183) ((:c Field.toEuclideanDomain) (:fv _uniq.463183...
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.463183))"},{"name":"inst✝⁶","sexp":"((:c CharZero) (:fv _uniq.463183) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.463183) ((:c Ring.toAddGroupWithOne) (:fv _uniq.463183) ((:c Division...
(:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LieModule.Weight) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":17832,"sourceStart":17827,"tag":"atom"},{"children":[{"children":[{"source":".","sourceEnd":17834,"sourceStart":17833,"tag":"atom"},{"source":"inl","sourceEnd":17837,"sourceStart":17834,"tag":"identifier"}],"kind":"Lean.Parser.Term.dotIde...
[]
[{"source":".inl (by ext; rw [h, neg_one_smul]; rfl)","source_end":17873,"source_start":17833,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...
33
18
exact
true
1
17
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a0cb09a3a1dbb6178d6b7411a6cb1f336c27a0467680ced84a304fc9f3c3aa59
c66dac9cc7d23bda3dc88ac630c395aac1885efce8dd1d0822dabea5fe2fbc15
a154669a768c3b6988aaeb54fa6030aff136d005fa06830104a028a3d94d1b45
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,721
LieAlgebra.IsKilling.eq_neg_or_eq_of_eq_smul
Mathlib/Algebra/Lie/Weights/RootSystem.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
ext
K : Type u_1 L : Type u_2 inst✝⁷ : Field K inst✝⁶ : CharZero K inst✝⁵ : LieRing L inst✝⁴ : LieAlgebra K L inst✝³ : IsKilling K L inst✝² : FiniteDimensional K L H : LieSubalgebra K L inst✝¹ : H.IsCartanSubalgebra inst✝ : IsTriangularizable K (↥H) L α β : Weight K (↥H) L hα✝ : α.IsNonZero hβ : β.IsNonZero hα : ¬α.IsZero ...
case h K : Type u_1 L : Type u_2 inst✝⁷ : Field K inst✝⁶ : CharZero K inst✝⁵ : LieRing L inst✝⁴ : LieAlgebra K L inst✝³ : IsKilling K L inst✝² : FiniteDimensional K L H : LieSubalgebra K L inst✝¹ : H.IsCartanSubalgebra inst✝ : IsTriangularizable K (↥H) L α β : Weight K (↥H) L hα✝ : α.IsNonZero hβ : β.IsNonZero hα : ¬α....
((:c Eq) ((:c LieModule.Weight) (:fv _uniq.463183) ((:c Subtype) (:fv _uniq.463186) (:lambda x (:fv _uniq.463186) ((:c Membership.mem) (:fv _uniq.463186) ((:c LieSubalgebra) (:fv _uniq.463183) (:fv _uniq.463186) ((:c EuclideanDomain.toCommRing) (:fv _uniq.463183) ((:c Field.toEuclideanDomain) (:fv _uniq.463183) (:fv _u...
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.463183))"},{"name":"inst✝⁶","sexp":"((:c CharZero) (:fv _uniq.463183) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.463183) ((:c Ring.toAddGroupWithOne) (:fv _uniq.463183) ((:c Division...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c LieModule.Weight) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c LieSubalgebra...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"ext","sourceEnd":17845,"sourceStart":17842,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":17845,"sourceStart":17842,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...
33
25
exact
true
1
17
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b318d323624884f3dac565b2b1320aca95913f7438d671ab3cd1b06ff4167f5f
732d8e36155dc42b92452036df53ecab6e3460b7195b5ecfe7ccd5d3d31372ee
a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de
d0cfc6d5f2c409af718447fa1f9256507b253da8fdc5a6fcb0b99c1af2294927
cat-searcher/leandojo-benchmark-4-random
test
1,722
LieAlgebra.IsKilling.eq_neg_or_eq_of_eq_smul
Mathlib/Algebra/Lie/Weights/RootSystem.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [h, <a>neg_one_smul</a>]
case h K : Type u_1 L : Type u_2 inst✝⁷ : Field K inst✝⁶ : CharZero K inst✝⁵ : LieRing L inst✝⁴ : LieAlgebra K L inst✝³ : IsKilling K L inst✝² : FiniteDimensional K L H : LieSubalgebra K L inst✝¹ : H.IsCartanSubalgebra inst✝ : IsTriangularizable K (↥H) L α β : Weight K (↥H) L hα✝ : α.IsNonZero hβ : β.IsNonZero hα : ¬α....
case h K : Type u_1 L : Type u_2 inst✝⁷ : Field K inst✝⁶ : CharZero K inst✝⁵ : LieRing L inst✝⁴ : LieAlgebra K L inst✝³ : IsKilling K L inst✝² : FiniteDimensional K L H : LieSubalgebra K L inst✝¹ : H.IsCartanSubalgebra inst✝ : IsTriangularizable K (↥H) L α β : Weight K (↥H) L hα✝ : α.IsNonZero hβ : β.IsNonZero hα : ¬α....
((:c Eq) (:fv _uniq.463183) ((:c DFunLike.coe) ((:c LieModule.Weight) (:fv _uniq.463183) ((:c Subtype) (:fv _uniq.463186) (:lambda x (:fv _uniq.463186) ((:c Membership.mem) (:fv _uniq.463186) ((:c LieSubalgebra) (:fv _uniq.463183) (:fv _uniq.463186) ((:c EuclideanDomain.toCommRing) (:fv _uniq.463183) ((:c Field.toEucli...
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.463183))"},{"name":"inst✝⁶","sexp":"((:c CharZero) (:fv _uniq.463183) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.463183) ((:c Ring.toAddGroupWithOne) (:fv _uniq.463183) ((:c Division...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LieModule.Weight) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:ar...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"rw","sourceEnd":17849,"sourceStart":17847,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":17851,"sourceStart":17850,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":17,"seman...
[]
[{"source":"h","source_end":17852,"source_start":17851,"syntax_kind":"ident"},{"source":"neg_one_smul","source_end":17866,"source_start":17854,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...
33
27
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
23ecc1c61b4bc617ef552e5e9b6efa0cdc9f29285da59152346ea9420b120fee
d0cfc6d5f2c409af718447fa1f9256507b253da8fdc5a6fcb0b99c1af2294927
72265dc1e549eac8b47250184509d7fd9bdd581ce76267fafb8c19b35200ae48
bbcefac1bf0a9b1be8e225110a7c86c4e17b01eecb71fffde030d5b4327c537a
cat-searcher/leandojo-benchmark-4-random
test
1,723
LieAlgebra.IsKilling.eq_neg_or_eq_of_eq_smul
Mathlib/Algebra/Lie/Weights/RootSystem.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rfl
case h K : Type u_1 L : Type u_2 inst✝⁷ : Field K inst✝⁶ : CharZero K inst✝⁵ : LieRing L inst✝⁴ : LieAlgebra K L inst✝³ : IsKilling K L inst✝² : FiniteDimensional K L H : LieSubalgebra K L inst✝¹ : H.IsCartanSubalgebra inst✝ : IsTriangularizable K (↥H) L α β : Weight K (↥H) L hα✝ : α.IsNonZero hβ : β.IsNonZero hα : ¬α....
((:c Eq) (:fv _uniq.463183) ((:c Neg.neg) (:forall a ((:c Subtype) (:fv _uniq.463186) (:lambda x (:fv _uniq.463186) ((:c Membership.mem) (:fv _uniq.463186) ((:c LieSubalgebra) (:fv _uniq.463183) (:fv _uniq.463186) ((:c EuclideanDomain.toCommRing) (:fv _uniq.463183) ((:c Field.toEuclideanDomain) (:fv _uniq.463183) (:fv ...
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.463183))"},{"name":"inst✝⁶","sexp":"((:c CharZero) (:fv _uniq.463183) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.463183) ((:c Ring.toAddGroupWithOne) (:fv _uniq.463183) ((:c Division...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Neg.neg) (:arg :implicit-type 0 (:forall a :explicit (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"rfl","sourceEnd":17872,"sourceStart":17869,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":17872,"sourceStart":17869,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...
33
32
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9015a4c8d6d932f38d78dcbddbd8d67cf3f0be677497e3c656027cefdbf56b96
bbcefac1bf0a9b1be8e225110a7c86c4e17b01eecb71fffde030d5b4327c537a
5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,724
LieAlgebra.IsKilling.eq_neg_or_eq_of_eq_smul
Mathlib/Algebra/Lie/Weights/RootSystem.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
cases hβ (by rwa [<a>zero_smul</a>] at h)
case neg.inr.inl K : Type u_1 L : Type u_2 inst✝⁷ : Field K inst✝⁶ : CharZero K inst✝⁵ : LieRing L inst✝⁴ : LieAlgebra K L inst✝³ : IsKilling K L inst✝² : FiniteDimensional K L H : LieSubalgebra K L inst✝¹ : H.IsCartanSubalgebra inst✝ : IsTriangularizable K (↥H) L α β : Weight K (↥H) L hα✝ : α.IsNonZero hβ : β.IsNonZer...
((:c Or) ((:c Eq) ((:c LieModule.Weight) (:fv _uniq.463183) ((:c Subtype) (:fv _uniq.463186) (:lambda x (:fv _uniq.463186) ((:c Membership.mem) (:fv _uniq.463186) ((:c LieSubalgebra) (:fv _uniq.463183) (:fv _uniq.463186) ((:c EuclideanDomain.toCommRing) (:fv _uniq.463183) ((:c Field.toEuclideanDomain) (:fv _uniq.463183...
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.463183))"},{"name":"inst✝⁶","sexp":"((:c CharZero) (:fv _uniq.463183) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.463183) ((:c Ring.toAddGroupWithOne) (:fv _uniq.463183) ((:c Division...
(:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LieModule.Weight) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"children":[{"children":[{"children":[{"source":"cases","sourceEnd":17884,"sourceStart":17879,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"hβ","sourceEnd":17888,"sourceStart":17885,"tag":"ide...
[]
[{"source":"hβ (by rwa [zero_smul] at h)","source_end":17914,"source_start":17885,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...
33
35
exact
true
1
17
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
470c63fa3d43e51d8c6135a9b10b39436c2859789c0573aaabd1ba25fb6319a8
2e192d29b620b271a2e941ff5e5e0945ee3ac90e2b8df1f16c6c81aa29ec43d4
9b942ad4c01c025c582983d332b67601efa1ee4065075d9357fa98f47c3e087e
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,725
LieAlgebra.IsKilling.eq_neg_or_eq_of_eq_smul
Mathlib/Algebra/Lie/Weights/RootSystem.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rwa [<a>zero_smul</a>] at h
K : Type u_1 L : Type u_2 inst✝⁷ : Field K inst✝⁶ : CharZero K inst✝⁵ : LieRing L inst✝⁴ : LieAlgebra K L inst✝³ : IsKilling K L inst✝² : FiniteDimensional K L H : LieSubalgebra K L inst✝¹ : H.IsCartanSubalgebra inst✝ : IsTriangularizable K (↥H) L α β : Weight K (↥H) L hα✝ : α.IsNonZero hβ : β.IsNonZero hα : ¬α.IsZero ...
((:c LieModule.Weight.IsZero) (:fv _uniq.463183) ((:c Subtype) (:fv _uniq.463186) (:lambda x (:fv _uniq.463186) ((:c Membership.mem) (:fv _uniq.463186) ((:c LieSubalgebra) (:fv _uniq.463183) (:fv _uniq.463186) ((:c EuclideanDomain.toCommRing) (:fv _uniq.463183) ((:c Field.toEuclideanDomain) (:fv _uniq.463183) (:fv _uni...
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.463183))"},{"name":"inst✝⁶","sexp":"((:c CharZero) (:fv _uniq.463183) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.463183) ((:c Ring.toAddGroupWithOne) (:fv _uniq.463183) ((:c Division...
(:app (:c LieModule.Weight.IsZero) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c LieSubalgebra) (:arg :explicit 0 ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":17896,"sourceStart":17893,"tag":"atom"},{"children":[{"source":"[","sourceEnd":17898,"sourceStart":17897,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"zero_smul","semanticRole":"glob...
[]
[{"source":"zero_smul","source_end":17907,"source_start":17898,"syntax_kind":"ident"},{"source":"h","source_end":17913,"source_start":17912,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...
33
40
exact
true
1
17
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
159aded9e18ae13ec7020720902324545d5e1a520e25bf6927354a1bfdd4c378
1d42af9970c1a31268706b5afe7840ce30b4a73235dc3a31a1848e7d6ad3f63b
9dafb62d00d06b54860f66a21590ed2b48b1289ef00acd0892c92882ac3de773
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,726
LieAlgebra.IsKilling.eq_neg_or_eq_of_eq_smul
Mathlib/Algebra/Lie/Weights/RootSystem.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact .inr (by ext; rw [h, <a>one_smul</a>])
case neg.inr.inr K : Type u_1 L : Type u_2 inst✝⁷ : Field K inst✝⁶ : CharZero K inst✝⁵ : LieRing L inst✝⁴ : LieAlgebra K L inst✝³ : IsKilling K L inst✝² : FiniteDimensional K L H : LieSubalgebra K L inst✝¹ : H.IsCartanSubalgebra inst✝ : IsTriangularizable K (↥H) L α β : Weight K (↥H) L hα✝ : α.IsNonZero hβ : β.IsNonZer...
((:c Or) ((:c Eq) ((:c LieModule.Weight) (:fv _uniq.463183) ((:c Subtype) (:fv _uniq.463186) (:lambda x (:fv _uniq.463186) ((:c Membership.mem) (:fv _uniq.463186) ((:c LieSubalgebra) (:fv _uniq.463183) (:fv _uniq.463186) ((:c EuclideanDomain.toCommRing) (:fv _uniq.463183) ((:c Field.toEuclideanDomain) (:fv _uniq.463183...
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.463183))"},{"name":"inst✝⁶","sexp":"((:c CharZero) (:fv _uniq.463183) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.463183) ((:c Ring.toAddGroupWithOne) (:fv _uniq.463183) ((:c Division...
(:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LieModule.Weight) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implici...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":17925,"sourceStart":17920,"tag":"atom"},{"children":[{"children":[{"source":".","sourceEnd":17927,"sourceStart":17926,"tag":"atom"},{"source":"inr","sourceEnd":17930,"sourceStart":17927,"tag":"identifier"}],"kind":"Lean.Parser.Term.dotIde...
[]
[{"source":".inr (by ext; rw [h, one_smul])","source_end":17957,"source_start":17926,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...
33
47
exact
true
1
17
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
be4a5a7f8b16ef1e686b9fa010a36e58f0e131264146956fe1021b48b4da6268
276bb7752a95030fa2dc2a01f464e9f892b0192e1ef8470838581157ac8dfdc8
0d9aa029f2038054ba4a06a4fd590caf1ec2626544a16ae5bd48d5c9ce3cbe85
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,727
LieAlgebra.IsKilling.eq_neg_or_eq_of_eq_smul
Mathlib/Algebra/Lie/Weights/RootSystem.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
ext
K : Type u_1 L : Type u_2 inst✝⁷ : Field K inst✝⁶ : CharZero K inst✝⁵ : LieRing L inst✝⁴ : LieAlgebra K L inst✝³ : IsKilling K L inst✝² : FiniteDimensional K L H : LieSubalgebra K L inst✝¹ : H.IsCartanSubalgebra inst✝ : IsTriangularizable K (↥H) L α β : Weight K (↥H) L hα✝ : α.IsNonZero hβ : β.IsNonZero hα : ¬α.IsZero ...
case h K : Type u_1 L : Type u_2 inst✝⁷ : Field K inst✝⁶ : CharZero K inst✝⁵ : LieRing L inst✝⁴ : LieAlgebra K L inst✝³ : IsKilling K L inst✝² : FiniteDimensional K L H : LieSubalgebra K L inst✝¹ : H.IsCartanSubalgebra inst✝ : IsTriangularizable K (↥H) L α β : Weight K (↥H) L hα✝ : α.IsNonZero hβ : β.IsNonZero hα : ¬α....
((:c Eq) ((:c LieModule.Weight) (:fv _uniq.463183) ((:c Subtype) (:fv _uniq.463186) (:lambda x (:fv _uniq.463186) ((:c Membership.mem) (:fv _uniq.463186) ((:c LieSubalgebra) (:fv _uniq.463183) (:fv _uniq.463186) ((:c EuclideanDomain.toCommRing) (:fv _uniq.463183) ((:c Field.toEuclideanDomain) (:fv _uniq.463183) (:fv _u...
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.463183))"},{"name":"inst✝⁶","sexp":"((:c CharZero) (:fv _uniq.463183) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.463183) ((:c Ring.toAddGroupWithOne) (:fv _uniq.463183) ((:c Division...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c LieModule.Weight) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c LieSubalgebra...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"ext","sourceEnd":17938,"sourceStart":17935,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":17938,"sourceStart":17935,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...
33
54
exact
true
1
17
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
7f3b854c94aa287f623ca78b1d13711b6abfe00dfbb56d4b10bc42434fe917bf
1d23b50eff6cf0dcc04efa590e7f4bde62800251ed9fabebafcbef5aef9a33d6
a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de
9417fbbb4d42ff531809356d50823832ca3e239510bfb3b90b0810e93d7976ec
cat-searcher/leandojo-benchmark-4-random
test
1,728
LieAlgebra.IsKilling.eq_neg_or_eq_of_eq_smul
Mathlib/Algebra/Lie/Weights/RootSystem.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [h, <a>one_smul</a>]
case h K : Type u_1 L : Type u_2 inst✝⁷ : Field K inst✝⁶ : CharZero K inst✝⁵ : LieRing L inst✝⁴ : LieAlgebra K L inst✝³ : IsKilling K L inst✝² : FiniteDimensional K L H : LieSubalgebra K L inst✝¹ : H.IsCartanSubalgebra inst✝ : IsTriangularizable K (↥H) L α β : Weight K (↥H) L hα✝ : α.IsNonZero hβ : β.IsNonZero hα : ¬α....
((:c Eq) (:fv _uniq.463183) ((:c DFunLike.coe) ((:c LieModule.Weight) (:fv _uniq.463183) ((:c Subtype) (:fv _uniq.463186) (:lambda x (:fv _uniq.463186) ((:c Membership.mem) (:fv _uniq.463186) ((:c LieSubalgebra) (:fv _uniq.463183) (:fv _uniq.463186) ((:c EuclideanDomain.toCommRing) (:fv _uniq.463183) ((:c Field.toEucli...
[{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.463183))"},{"name":"inst✝⁶","sexp":"((:c CharZero) (:fv _uniq.463183) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.463183) ((:c Ring.toAddGroupWithOne) (:fv _uniq.463183) ((:c Division...
(:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LieModule.Weight) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:ar...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-imp...
{"children":[{"source":"rw","sourceEnd":17942,"sourceStart":17940,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":17944,"sourceStart":17943,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":17,"seman...
[]
[{"source":"h","source_end":17945,"source_start":17944,"syntax_kind":"ident"},{"source":"one_smul","source_end":17955,"source_start":17947,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.463183","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.463186","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal...
33
56
exact
true
1
18
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
fd8eca57065430b6d58453f85f3f6f9c618afb7aaecfafa63c6964ad304f2646
9417fbbb4d42ff531809356d50823832ca3e239510bfb3b90b0810e93d7976ec
316f092a37f818c188bdd7b8d56b6f2efa4cf2736920d6939cdb6afeed6e1178
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,729
MeasureTheory.measure_union_lt_top_iff
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨fun h => ⟨?_, ?_⟩, fun h => <a>MeasureTheory.measure_union_lt_top</a> h.1 h.2⟩
α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 ι : Sort u_5 inst✝ : MeasurableSpace α μ μ₁ μ₂ : Measure α s s₁ s₂ t : Set α ⊢ μ (s ∪ t) < ⊤ ↔ μ s < ⊤ ∧ μ t < ⊤
case refine_1 α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 ι : Sort u_5 inst✝ : MeasurableSpace α μ μ₁ μ₂ : Measure α s s₁ s₂ t : Set α h : μ (s ∪ t) < ⊤ ⊢ μ s < ⊤ case refine_2 α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 ι : Sort u_5 inst✝ : MeasurableSpace α μ μ₁ μ₂ : Measure α s s₁ s₂ t : Set α h : μ ...
((:c Iff) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrd...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort u_5)"},{"name":"inst✝","sexp":"((:c MeasurableSpace) (:fv _uniq.18018))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq...
(:app (:c Iff) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:insta...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18018","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18021","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"refine","sourceEnd":12211,"sourceStart":12205,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":12215,"sourceStart":12212,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":12218,"sourceStart":12215,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","sourc...
[]
[{"source":"⟨fun h => ⟨?_, ?_⟩, fun h => measure_union_lt_top h.1 h.2⟩","source_end":12278,"source_start":12212,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18018","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18021","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
72
4
exact
true
1
13
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
9f61326d5bc85d23980c02fd206fba7a9f9cb5b63833a767def8f45b78c66b56
828412539ecfd59c342d46f9a3f52aa02e5f5598020b0d48cd74855290c2a264
3d5b8122fb268b69ea82373db88d2ac3a2946a9b53673e723ce9c52b5d9cdf31
573d2f6239f79f2e21e01b410883af30a8d079a8e7278cefa6420d6be2e463f5
cat-searcher/leandojo-benchmark-4-random
test
1,730
MeasureTheory.measure_union_lt_top_iff
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact (<a>MeasureTheory.measure_mono</a> <a>Set.subset_union_left</a>).<a>LE.le.trans_lt</a> h
case refine_1 α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 ι : Sort u_5 inst✝ : MeasurableSpace α μ μ₁ μ₂ : Measure α s s₁ s₂ t : Set α h : μ (s ∪ t) < ⊤ ⊢ μ s < ⊤
((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort u_5)"},{"name":"inst✝","sexp":"((:c MeasurableSpace) (:fv _uniq.18018))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq...
(:app (:c LT.lt) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c 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.18018","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18021","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":12289,"sourceStart":12284,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":12291,"sourceStart":12290,"tag":"atom"},{"children":[{"name":"MeasureTheory.measure_mono","semanticRole":"global","source":"measure_m...
[]
[{"source":"(measure_mono Set.subset_union_left).trans_lt h","source_end":12337,"source_start":12290,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18018","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18021","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
72
7
exact
true
1
14
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5a64e8b0bf147e8755b03c09e245d0ef4876598ce5833c1c7a9fccc813b0cb20
364ab8e89728954c318c68fe6d7e2d429171036c8806480510918b41568e3aff
299f0dc08b5cc5fb8c63dee4d5a8efe9c0655c28cd8d02845e74b38731ff5b27
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,731
MeasureTheory.measure_union_lt_top_iff
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact (<a>MeasureTheory.measure_mono</a> <a>Set.subset_union_right</a>).<a>LE.le.trans_lt</a> h
case refine_2 α : Type u_1 β : Type u_2 γ : Type u_3 δ : Type u_4 ι : Sort u_5 inst✝ : MeasurableSpace α μ μ₁ μ₂ : Measure α s s₁ s₂ t : Set α h : μ (s ∪ t) < ⊤ ⊢ μ t < ⊤
((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl...
[{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort u_5)"},{"name":"inst✝","sexp":"((:c MeasurableSpace) (:fv _uniq.18018))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq...
(:app (:c LT.lt) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c 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.18018","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18021","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":12348,"sourceStart":12343,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":12350,"sourceStart":12349,"tag":"atom"},{"children":[{"name":"MeasureTheory.measure_mono","semanticRole":"global","source":"measure_m...
[]
[{"source":"(measure_mono Set.subset_union_right).trans_lt h","source_end":12397,"source_start":12349,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18018","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18021","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
72
12
exact
true
1
14
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d4f3a555d15e5d0c5882a5b37b79e2d60c72fa83eecc94d4aea00a296189f00e
62da6c22084baf10c63c3563dd24b0e580372e8f66eab666375150dd7f195352
c9ab406b1923187e32d43b3413bc1b25f9c09113c8cff460e75db05cd0d3c5e4
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,732
IsPreconnected.intermediate_value₂_eventually₂
Mathlib/Topology/Order/IntermediateValue.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>continuousOn_iff_continuous_restrict</a>] at hf hg
X : Type u α : Type v inst✝⁵ : TopologicalSpace X inst✝⁴ : LinearOrder α inst✝³ : TopologicalSpace α inst✝² : OrderClosedTopology α s : Set X hs : IsPreconnected s l₁ l₂ : Filter X inst✝¹ : l₁.NeBot inst✝ : l₂.NeBot hl₁ : l₁ ≤ 𝓟 s hl₂ : l₂ ≤ 𝓟 s f g : X → α hf : ContinuousOn f s hg : ContinuousOn g s he₁ : f ≤ᶠ[l₁] g...
X : Type u α : Type v inst✝⁵ : TopologicalSpace X inst✝⁴ : LinearOrder α inst✝³ : TopologicalSpace α inst✝² : OrderClosedTopology α s : Set X hs : IsPreconnected s l₁ l₂ : Filter X inst✝¹ : l₁.NeBot inst✝ : l₂.NeBot hl₁ : l₁ ≤ 𝓟 s hl₂ : l₂ ≤ 𝓟 s f g : X → α hf : Continuous (s.restrict f) hg : Continuous (s.restrict g...
((:c Exists) (:fv _uniq.10600) (:lambda x (:fv _uniq.10600) ((:c And) ((:c Membership.mem) (:fv _uniq.10600) ((:c Set) (:fv _uniq.10600)) ((:c Set.instMembership) (:fv _uniq.10600)) 0 (:fv _uniq.11908)) ((:c Eq) (:fv _uniq.10602) ((:fv _uniq.11916) 0) ((:fv _uniq.11917) 0)))))
[{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"α","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁵","sexp":"((:c TopologicalSpace) (:fv _uniq.10600))"},{"name":"inst✝⁴","sexp":"((:c LinearOrder) (:fv _uniq.10602))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.10602))"},{"name":"inst✝²","sexp":"((:c OrderClosed...
(:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10600","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10602","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"rw","sourceEnd":6129,"sourceStart":6127,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6131,"sourceStart":6130,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"continuousOn_iff_con...
[]
[{"source":"continuousOn_iff_continuous_restrict","source_end":6167,"source_start":6131,"syntax_kind":"ident"},{"source":"hf","source_end":6174,"source_start":6172,"syntax_kind":"ident"},{"source":"hg","source_end":6177,"source_start":6175,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10600","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10602","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
18
4
exact
true
1
20
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
843f35dcd20a1f469c02a00cbece92e068e87255a63eaaffda2410152b3ea675
74098e2c9770b000de7006a23f028f227ebbc0969bf973b499fbb4bfcf3368f5
da3fd01aa795285f44317cd8449868eea1e3c553c04394cdfc9d811c8ff77421
729378091c879011d7883988e7fcb855592b1193ee7854533fd894ba3c5e55e3
cat-searcher/leandojo-benchmark-4-random
test
1,733
IsPreconnected.intermediate_value₂_eventually₂
Mathlib/Topology/Order/IntermediateValue.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
obtain ⟨b, h⟩ := @<a>intermediate_value_univ₂_eventually₂</a> _ _ _ _ _ _ (<a>Subtype.preconnectedSpace</a> hs) _ _ (<a>Filter.comap_coe_neBot_of_le_principal</a> hl₁) (<a>Filter.comap_coe_neBot_of_le_principal</a> hl₂) _ _ hf hg (he₁.comap _) (he₂.comap _)
X : Type u α : Type v inst✝⁵ : TopologicalSpace X inst✝⁴ : LinearOrder α inst✝³ : TopologicalSpace α inst✝² : OrderClosedTopology α s : Set X hs : IsPreconnected s l₁ l₂ : Filter X inst✝¹ : l₁.NeBot inst✝ : l₂.NeBot hl₁ : l₁ ≤ 𝓟 s hl₂ : l₂ ≤ 𝓟 s f g : X → α hf : Continuous (s.restrict f) hg : Continuous (s.restrict g...
case intro X : Type u α : Type v inst✝⁵ : TopologicalSpace X inst✝⁴ : LinearOrder α inst✝³ : TopologicalSpace α inst✝² : OrderClosedTopology α s : Set X hs : IsPreconnected s l₁ l₂ : Filter X inst✝¹ : l₁.NeBot inst✝ : l₂.NeBot hl₁ : l₁ ≤ 𝓟 s hl₂ : l₂ ≤ 𝓟 s f g : X → α hf : Continuous (s.restrict f) hg : Continuous (s...
((:c Exists) (:fv _uniq.10600) (:lambda x (:fv _uniq.10600) ((:c And) ((:c Membership.mem) (:fv _uniq.10600) ((:c Set) (:fv _uniq.10600)) ((:c Set.instMembership) (:fv _uniq.10600)) 0 (:fv _uniq.11908)) ((:c Eq) (:fv _uniq.10602) ((:fv _uniq.11916) 0) ((:fv _uniq.11917) 0)))))
[{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"α","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁵","sexp":"((:c TopologicalSpace) (:fv _uniq.10600))"},{"name":"inst✝⁴","sexp":"((:c LinearOrder) (:fv _uniq.10602))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.10602))"},{"name":"inst✝²","sexp":"((:c OrderClosed...
(:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10600","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10602","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"obtain","sourceEnd":6186,"sourceStart":6180,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":6190,"sourceStart":6187,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"b","sourceEnd":6...
[]
[{"source":"@intermediate_value_univ₂_eventually₂ _ _ _ _ _ _ (Subtype.preconnectedSpace hs) _ _\n (comap_coe_neBot_of_le_principal hl₁) (comap_coe_neBot_of_le_principal hl₂) _ _ hf hg\n (he₁.comap _) (he₂.comap _)","source_end":6427,"source_start":6205,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨b, h⟩"...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10600","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10602","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
18
7
exact
true
1
20
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5f89afdb861e3260d07706f844c602ecbcded8baaf516ca8eebe1f5f9a62fab6
729378091c879011d7883988e7fcb855592b1193ee7854533fd894ba3c5e55e3
5ec3fc607c3f43cf8d25eae2ae4a19d8bae9a9a5f354d765f630415dda7e6e1b
2a5d08150c761cd915848d05fe61815d8fb05df70889679913efd863b4674cd2
cat-searcher/leandojo-benchmark-4-random
test
1,734
IsPreconnected.intermediate_value₂_eventually₂
Mathlib/Topology/Order/IntermediateValue.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
exact ⟨b, b.prop, h⟩
case intro X : Type u α : Type v inst✝⁵ : TopologicalSpace X inst✝⁴ : LinearOrder α inst✝³ : TopologicalSpace α inst✝² : OrderClosedTopology α s : Set X hs : IsPreconnected s l₁ l₂ : Filter X inst✝¹ : l₁.NeBot inst✝ : l₂.NeBot hl₁ : l₁ ≤ 𝓟 s hl₂ : l₂ ≤ 𝓟 s f g : X → α hf : Continuous (s.restrict f) hg : Continuous (s...
((:c Exists) (:fv _uniq.10600) (:lambda x (:fv _uniq.10600) ((:c And) ((:c Membership.mem) (:fv _uniq.10600) ((:c Set) (:fv _uniq.10600)) ((:c Set.instMembership) (:fv _uniq.10600)) 0 (:fv _uniq.11908)) ((:c Eq) (:fv _uniq.10602) ((:fv _uniq.11916) 0) ((:fv _uniq.11917) 0)))))
[{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"α","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁵","sexp":"((:c TopologicalSpace) (:fv _uniq.10600))"},{"name":"inst✝⁴","sexp":"((:c LinearOrder) (:fv _uniq.10602))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.10602))"},{"name":"inst✝²","sexp":"((:c OrderClosed...
(:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10600","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10602","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli...
{"children":[{"source":"exact","sourceEnd":6435,"sourceStart":6430,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":6439,"sourceStart":6436,"tag":"atom"},{"children":[{"contextIndex":21,"semanticRole":"local","source":"b","sourceEnd":6440,"sourceStart":6439,"tag":"identifier"},{"source":",","sourceEnd":6441,"source...
[]
[{"source":"⟨b, b.prop, h⟩","source_end":6454,"source_start":6436,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.10600","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.10602","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n...
18
8
exact
true
1
22
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5bc6f29b4a0bce980a7e01ee7653d05252dff8858b221203552d97b76f25278e
2a5d08150c761cd915848d05fe61815d8fb05df70889679913efd863b4674cd2
f3cdb38a42bfedb2a82ec762f9aafbd276f6319e02d8f53cd9c413fe45f1a543
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,735
Nat.gcd_add_self_left
Mathlib/Data/Nat/GCD/Basic.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [<a>Nat.gcd_comm</a>, <a>Nat.gcd_add_self_right</a>, <a>Nat.gcd_comm</a>]
m n : ℕ ⊢ (m + n).gcd n = m.gcd n
((:c Eq) (:c Nat) ((:c Nat.gcd) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.2160) (:fv _uniq.2161)) (:fv _uniq.2161)) ((:c Nat.gcd) (:fv _uniq.2160) (:fv _uniq.2161)))
[{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"}]
(:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.gcd) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c ...
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.2160","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2161","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"}]
{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":3007,"sourceStart":3005,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3009,"sourceStart":3008,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag...
[]
[{"source":"gcd_comm","source_end":3017,"source_start":3009,"syntax_kind":"ident"},{"source":"gcd_add_self_right","source_end":3037,"source_start":3019,"syntax_kind":"ident"},{"source":"gcd_comm","source_end":3047,"source_start":3039,"syntax_kind":"ident"}]
[{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.2160","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2161","is_instance":false,"is_let":false,"user_name":"n"}]
26
2
exact
true
1
2
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8752ac2fadb10e7b9daeec16079dbc3ac7df94fa90ff35c2b38768138eb3cfd6
a90a19dd29aef545758b5fa58c9c8366450d62c5940bc31b004400a1af7659eb
fbb57b599b111c0947f6d62f791ea0abc30a3517a9bee7b63175edbfec17c7f0
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,736
List.mem_zip_inits_tails
Mathlib/Data/List/Zip.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
induction' l with hd tl ih generalizing init tail <;> simp_rw [<a>List.tails</a>, <a>List.inits</a>, <a>List.zip_cons_cons</a>]
α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 l init tail : List α ⊢ (init, tail) ∈ l.inits.zip l.tails ↔ init ++ tail = l
case nil α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 init tail : List α ⊢ (init, tail) ∈ ([], []) :: [].zip [] ↔ init ++ tail = [] case cons α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 hd : α tl : List α ih : ∀ {init tail : List α}, (init, tail) ∈ tl.inits.zip tl.tails ↔ init ++ ta...
((:c Iff) ((:c Membership.mem) ((:c Prod) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428))) ((:c List) ((:c Prod) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)))) ((:c List.instMembership) ((:c Prod) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)))) ((:c Prod.mk) ((:c List) (:fv _uni...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u_1 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"ε","sexp":"(:sort (+ u_4 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.65428))"},{"name":"init","sexp":"((:c List) (:fv _uniq.65428))"},{"name":"tail"...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c List) (:arg :explicit 0 (:fv FV0)))))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"source":"induction'","sourceEnd":14841,"sourceStart":14831,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":6,"semanticRole":"local","source":"l","sourceEnd":14843,"sourceStart":14842,"tag":"identifier"}],"kind":"Lean.Parser.Tacti...
[]
[{"source":"l","source_end":14843,"source_start":14842,"syntax_kind":"ident"},{"source":"init","source_end":14875,"source_start":14871,"syntax_kind":"ident"},{"source":"tail","source_end":14880,"source_start":14876,"syntax_kind":"ident"},{"source":"tails","source_end":14899,"source_start":14894,"syntax_kind":"ident"},{...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
113
4
exact
true
1
8
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
870840fec2bb6404321d324fb6811311248f2fe7d18446662fd3b58cec01b208
36016b37243dee90057f6e6bd5a0aae5abea83f5bd05810677a98107ffe557d5
b5b495c0641824eccb643ab5ea73bdca67531435c805db2d9c148c0dd5ec362d
348f1399bc18ff2a788b82f223225ad6e34e50608f177c2866ec903fdd3f7ebd
cat-searcher/leandojo-benchmark-4-random
test
1,737
List.mem_zip_inits_tails
Mathlib/Data/List/Zip.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
case nil α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 init tail : List α ⊢ (init, tail) ∈ ([], []) :: [].zip [] ↔ init ++ tail = []
((:c Iff) ((:c Membership.mem) ((:c Prod) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428))) ((:c List) ((:c Prod) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)))) ((:c List.instMembership) ((:c Prod) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)))) ((:c Prod.mk) ((:c List) (:fv _uni...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u_1 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"ε","sexp":"(:sort (+ u_4 1))"},{"name":"init","sexp":"((:c List) (:fv _uniq.65428))"},{"name":"tail","sexp":"((:c List) (:fv _uniq.65428))"}]
(:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c List) (:arg :explicit 0 (:fv FV0)))))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":14932,"sourceStart":14928,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","sour...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
113
19
exact
true
1
7
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
5ec693951e928394c5467c0843fe3869bb1e841e14c5181af6a8f7a4f5f471b9
6f76b4dbffcc65cd4781518cbad34682c89ff522320aec4da9f97a69e6bd1330
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,738
List.mem_zip_inits_tails
Mathlib/Data/List/Zip.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
constructor <;> rw [<a>List.mem_cons</a>, <a>List.zip_map_left</a>, <a>List.mem_map</a>, <a>Prod.exists</a>]
case cons α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 hd : α tl : List α ih : ∀ {init tail : List α}, (init, tail) ∈ tl.inits.zip tl.tails ↔ init ++ tail = tl init tail : List α ⊢ (init, tail) ∈ ([], hd :: tl) :: (map (fun t => hd :: t) tl.inits).zip tl.tails ↔ init ++ tail = hd :: tl
case cons.mp α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 hd : α tl : List α ih : ∀ {init tail : List α}, (init, tail) ∈ tl.inits.zip tl.tails ↔ init ++ tail = tl init tail : List α ⊢ ((init, tail) = ([], hd :: tl) ∨ ∃ a b, (a, b) ∈ tl.inits.zip tl.tails ∧ Prod.map (fun t => hd :: t) id (a, b) =...
((:c Iff) ((:c Membership.mem) ((:c Prod) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428))) ((:c List) ((:c Prod) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)))) ((:c List.instMembership) ((:c Prod) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)))) ((:c Prod.mk) ((:c List) (:fv _uni...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u_1 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"ε","sexp":"(:sort (+ u_4 1))"},{"name":"hd","sexp":"(:fv _uniq.65428)"},{"name":"tl","sexp":"((:c List) (:fv _uniq.65428))"},{"name":"ih","sexp":"(:fora...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c List) (:arg :explicit 0 (:fv FV0)))))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"source":"constructor","sourceEnd":14949,"sourceStart":14938,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":14949,"sourceStart":14938,"tag":"node"},{"source":"<;>","sourceEnd":14953,"sourceStart":14950,"tag":"atom"},{"children":[{"source":"rw","sourc...
[]
[{"source":"mem_cons","source_end":14966,"source_start":14958,"syntax_kind":"ident"},{"source":"zip_map_left","source_end":14980,"source_start":14968,"syntax_kind":"ident"},{"source":"mem_map","source_end":14989,"source_start":14982,"syntax_kind":"ident"},{"source":"Prod.exists","source_end":15002,"source_start":14991,...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
113
26
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d8b8a75c7f4d0758c5e805e9c4aaf4c03a03aa9795db36a448813b69c94efdeb
813f3940382a14f5ec63e3697bda820a5310833f6ceeb697a47a189891fb4a70
42a654bbcbec19223b845047b0af18be19095da91f1bb161b3e528010de51968
ac167b8fd6e3192dfd0cb7f5bf533e1b0950545089ea3ceba85085cf51264644
cat-searcher/leandojo-benchmark-4-random
test
1,739
List.mem_zip_inits_tails
Mathlib/Data/List/Zip.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro (⟨rfl, rfl⟩ | ⟨_, _, h, rfl, rfl⟩)
case cons.mp α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 hd : α tl : List α ih : ∀ {init tail : List α}, (init, tail) ∈ tl.inits.zip tl.tails ↔ init ++ tail = tl init tail : List α ⊢ ((init, tail) = ([], hd :: tl) ∨ ∃ a b, (a, b) ∈ tl.inits.zip tl.tails ∧ Prod.map (fun t => hd :: t) id (a, b) =...
case cons.mp.inl.refl α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 hd : α tl : List α ih : ∀ {init tail : List α}, (init, tail) ∈ tl.inits.zip tl.tails ↔ init ++ tail = tl ⊢ [] ++ hd :: tl = hd :: tl case cons.mp.inr.intro.intro.intro.refl α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4...
(:forall _ ((:c Or) ((:c Eq) ((:c Prod) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428))) ((:c Prod.mk) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)) (:fv _uniq.65565) (:fv _uniq.65566)) ((:c Prod.mk) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)) ((:c List.nil) (:fv _uniq.65428)) ...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u_1 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"ε","sexp":"(:sort (+ u_4 1))"},{"name":"hd","sexp":"(:fv _uniq.65428)"},{"name":"tl","sexp":"((:c List) (:fv _uniq.65428))"},{"name":"ih","sexp":"(:fora...
(:forall _ :explicit (:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c List) (:arg :explicit 0 (:fv FV0)))))) (:arg :explicit 1 (:app (:c Prod.mk) (:arg :implicit-type 0 (:app (:c List) (:arg ...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"rintro","sourceEnd":15017,"sourceStart":15011,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":15019,"sourceStart":15018,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":15022,"sourceStart":15019,"tag":"atom"},{"children":[...
[{"role":"fresh_name","source":"h","source_end":15046,"source_start":15045,"syntax_kind":"ident"}]
[{"source":"(⟨rfl, rfl⟩ | ⟨_, _, h, rfl, rfl⟩)","source_end":15060,"source_start":15018,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
113
45
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1e6925c18634ae9de7e19a7a47d1bc785475bfd92bb5abe73dc0c7e1e985e8b8
c14d873bdc0b0715ff52f57fdc1c13b058b98fc87b09dd4c22ae804a780de9b9
c1a96e34bb7ea8fd0421137fa603da659649c3fffa2e4d2cbba5237e35deb796
3599b6f068cc858707bb869a7e4f357ca3633e88928f171fd6d40b75296d059b
cat-searcher/leandojo-benchmark-4-random
test
1,740
List.mem_zip_inits_tails
Mathlib/Data/List/Zip.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
case cons.mp.inl.refl α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 hd : α tl : List α ih : ∀ {init tail : List α}, (init, tail) ∈ tl.inits.zip tl.tails ↔ init ++ tail = tl ⊢ [] ++ hd :: tl = hd :: tl
((:c Eq) ((:c List) (:fv _uniq.65428)) ((:c HAppend.hAppend) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)) ((:c instHAppendOfAppend) ((:c List) (:fv _uniq.65428)) ((:c List.instAppend) (:fv _uniq.65428))) ((:c List.nil) (:fv _uniq.65428)) ((:c List.cons) (:fv _uniq.65428) (:f...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u_1 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"ε","sexp":"(:sort (+ u_4 1))"},{"name":"hd","sexp":"(:fv _uniq.65428)"},{"name":"tl","sexp":"((:c List) (:fv _uniq.65428))"},{"name":"ih","sexp":"(:fora...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c HAppend.hAppend) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 2 (:app (:c List) (:arg :expli...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":15074,"sourceStart":15070,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","sour...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
113
48
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a6fcba7930793bcd66ebe4622548834eef334fada2979f256c4cfbcd7c8e1e50
e367a3c8d2dcfe3710111af35aa133fdaa6c0a4cf44b744a331d2240bd7e2374
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,741
List.mem_zip_inits_tails
Mathlib/Data/List/Zip.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [ih.mp h]
case cons.mp.inr.intro.intro.intro.refl α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 hd : α tl : List α ih : ∀ {init tail : List α}, (init, tail) ∈ tl.inits.zip tl.tails ↔ init ++ tail = tl w✝¹ w✝ : List α h : (w✝¹, w✝) ∈ tl.inits.zip tl.tails ⊢ (fun t => hd :: t) w✝¹ ++ id w✝ = hd :: tl
((:c Eq) ((:c List) (:fv _uniq.65428)) ((:c HAppend.hAppend) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)) ((:c instHAppendOfAppend) ((:c List) (:fv _uniq.65428)) ((:c List.instAppend) (:fv _uniq.65428))) ((:lambda t ((:c List) (:fv _uniq.65428)) ((:c List.cons) (:fv _uniq.65...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u_1 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"ε","sexp":"(:sort (+ u_4 1))"},{"name":"hd","sexp":"(:fv _uniq.65428)"},{"name":"tl","sexp":"((:c List) (:fv _uniq.65428))"},{"name":"ih","sexp":"(:fora...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c HAppend.hAppend) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 2 (:app (:c List) (:arg :expli...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":15088,"sourceStart":15084,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...
[]
[{"source":"ih.mp h","source_end":15097,"source_start":15090,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
113
53
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
700d3f69bc83a3784ea58078d4ea4bf0f2189471f2c99291bb611e8bd1e28ab3
cc56ffde4b4feb442420bd338e3f6a4b7bc4835a04136bd2528af722046a9b65
20254711651ee09982a8ebc8a6cdcfadddbcce44731413a9e2909cde67c68222
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,742
List.mem_zip_inits_tails
Mathlib/Data/List/Zip.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
cases' init with hd' tl'
case cons.mpr α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 hd : α tl : List α ih : ∀ {init tail : List α}, (init, tail) ∈ tl.inits.zip tl.tails ↔ init ++ tail = tl init tail : List α ⊢ init ++ tail = hd :: tl → (init, tail) = ([], hd :: tl) ∨ ∃ a b, (a, b) ∈ tl.inits.zip tl.tails ∧ Prod.map ...
case cons.mpr.nil α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 hd : α tl : List α ih : ∀ {init tail : List α}, (init, tail) ∈ tl.inits.zip tl.tails ↔ init ++ tail = tl tail : List α ⊢ [] ++ tail = hd :: tl → ([], tail) = ([], hd :: tl) ∨ ∃ a b, (a, b) ∈ tl.inits.zip tl.tails ∧ Prod.map (fun ...
(:forall _ ((:c Eq) ((:c List) (:fv _uniq.65428)) ((:c HAppend.hAppend) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)) ((:c instHAppendOfAppend) ((:c List) (:fv _uniq.65428)) ((:c List.instAppend) (:fv _uniq.65428))) (:fv _uniq.65565) (:fv _uniq.65566)) ((:c List.cons) (:fv _u...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u_1 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"ε","sexp":"(:sort (+ u_4 1))"},{"name":"hd","sexp":"(:fv _uniq.65428)"},{"name":"tl","sexp":"((:c List) (:fv _uniq.65428))"},{"name":"ih","sexp":"(:fora...
(:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c HAppend.hAppend) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 2 (:app (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"cases'","sourceEnd":15112,"sourceStart":15106,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":9,"semanticRole":"local","source":"init","sourceEnd":15117,"sourceStart":15113,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget"...
[]
[{"source":"init","source_end":15117,"source_start":15113,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
113
60
exact
true
1
10
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
854ddd47c340d390d220714e2482fbc66b5be6595f01e9b6c2fe4c835149dfd6
0d86e116cdf984a61704bd4aa249b9c6be1542f72b3ceaced36933776d76f9b5
f9328ddfe19b1dfa69fc827de6bd2370ad5103589bebc0a6259aa0d7c40c4c8f
0ce660fc3569fb4591073a7ad589c4adaa3110e87f4e492f8b1119150de7fcdf
cat-searcher/leandojo-benchmark-4-random
test
1,743
List.mem_zip_inits_tails
Mathlib/Data/List/Zip.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro rfl
case cons.mpr.nil α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 hd : α tl : List α ih : ∀ {init tail : List α}, (init, tail) ∈ tl.inits.zip tl.tails ↔ init ++ tail = tl tail : List α ⊢ [] ++ tail = hd :: tl → ([], tail) = ([], hd :: tl) ∨ ∃ a b, (a, b) ∈ tl.inits.zip tl.tails ∧ Prod.map (fun ...
case cons.mpr.nil α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 hd : α tl : List α ih : ∀ {init tail : List α}, (init, tail) ∈ tl.inits.zip tl.tails ↔ init ++ tail = tl ⊢ ([], hd :: tl) = ([], hd :: tl) ∨ ∃ a b, (a, b) ∈ tl.inits.zip tl.tails ∧ Prod.map (fun t => hd :: t) id (a, b) = ([], hd :: tl)
(:forall _ ((:c Eq) ((:c List) (:fv _uniq.65428)) ((:c HAppend.hAppend) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)) ((:c instHAppendOfAppend) ((:c List) (:fv _uniq.65428)) ((:c List.instAppend) (:fv _uniq.65428))) ((:c List.nil) (:fv _uniq.65428)) (:fv _uniq.65566)) ((:c Li...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u_1 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"ε","sexp":"(:sort (+ u_4 1))"},{"name":"hd","sexp":"(:fv _uniq.65428)"},{"name":"tl","sexp":"((:c List) (:fv _uniq.65428))"},{"name":"ih","sexp":"(:fora...
(:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c HAppend.hAppend) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 2 (:app (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"rintro","sourceEnd":15146,"sourceStart":15140,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":15150,"sourceStart":15147,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl","sourceEnd":15150,"sourceStart":151...
[]
[{"source":"rfl","source_end":15150,"source_start":15147,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
113
65
exact
true
1
9
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
2e494c3c42b35c938e4632c1026ecb11269d959529db1a2628deb68c3a7ead50
852ab9c9ef07bf1995219cc28739dd4d8c19da42b27d6a0d3a67b2a218a9a182
09e128cd6787f35d3c063b643315aff1382388dafa4e55b6546fbf9dcecb02da
974075bb9be9d7557b9f3d8c34194ea57753e091237e319b84abdde8c7758877
cat-searcher/leandojo-benchmark-4-random
test
1,744
List.mem_zip_inits_tails
Mathlib/Data/List/Zip.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp
case cons.mpr.nil α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 hd : α tl : List α ih : ∀ {init tail : List α}, (init, tail) ∈ tl.inits.zip tl.tails ↔ init ++ tail = tl ⊢ ([], hd :: tl) = ([], hd :: tl) ∨ ∃ a b, (a, b) ∈ tl.inits.zip tl.tails ∧ Prod.map (fun t => hd :: t) id (a, b) = ([], hd :: tl)
((:c Or) ((:c Eq) ((:c Prod) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428))) ((:c Prod.mk) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)) ((:c List.nil) (:fv _uniq.65428)) ((:c List.cons) (:fv _uniq.65428) (:fv _uniq.65558) (:fv _uniq.65559))) ((:c Prod.mk) ((:c List) (:fv _uniq.65428)) ((:c L...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u_1 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"ε","sexp":"(:sort (+ u_4 1))"},{"name":"hd","sexp":"(:fv _uniq.65428)"},{"name":"tl","sexp":"((:c List) (:fv _uniq.65428))"},{"name":"ih","sexp":"(:fora...
(:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c List) (:arg :explicit 0 (:fv FV0)))))) (:arg :explicit 1 (:app (:c Prod.mk) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"simp","sourceEnd":15163,"sourceStart":15159,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"ki...
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
113
66
exact
true
1
8
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
94b156ab0366e8f556d6d089842e2d916c21ea79005f8a7e19c6faaeb1beb5e9
974075bb9be9d7557b9f3d8c34194ea57753e091237e319b84abdde8c7758877
8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,745
List.mem_zip_inits_tails
Mathlib/Data/List/Zip.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro h
case cons.mpr.cons α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 hd : α tl : List α ih : ∀ {init tail : List α}, (init, tail) ∈ tl.inits.zip tl.tails ↔ init ++ tail = tl tail : List α hd' : α tl' : List α ⊢ hd' :: tl' ++ tail = hd :: tl → (hd' :: tl', tail) = ([], hd :: tl) ∨ ∃ a b, (a, b) ∈ ...
case cons.mpr.cons α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 hd : α tl : List α ih : ∀ {init tail : List α}, (init, tail) ∈ tl.inits.zip tl.tails ↔ init ++ tail = tl tail : List α hd' : α tl' : List α h : hd' :: tl' ++ tail = hd :: tl ⊢ (hd' :: tl', tail) = ([], hd :: tl) ∨ ∃ a b, (a, b) ∈ tl.i...
(:forall _ ((:c Eq) ((:c List) (:fv _uniq.65428)) ((:c HAppend.hAppend) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)) ((:c instHAppendOfAppend) ((:c List) (:fv _uniq.65428)) ((:c List.instAppend) (:fv _uniq.65428))) ((:c List.cons) (:fv _uniq.65428) (:fv _uniq.66738) (:fv _un...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u_1 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"ε","sexp":"(:sort (+ u_4 1))"},{"name":"hd","sexp":"(:fv _uniq.65428)"},{"name":"tl","sexp":"((:c List) (:fv _uniq.65428))"},{"name":"ih","sexp":"(:fora...
(:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c HAppend.hAppend) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 2 (:app (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"intro","sourceEnd":15178,"sourceStart":15173,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":15180,"sourceStart":15179,"tag":"identifier"}],"kind":"null","source":"h","sourceEnd":15180,"sourceStart":15179,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source...
[{"role":"fresh_name","source":"h","source_end":15180,"source_start":15179,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
113
71
exact
true
1
11
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
134c7890ca541073f64eec240bd09a56a59a48179b272f00d3824bc8a6a6d35d
aec73702a511adea2b6f48e8741130d3442c386b3a42cd4087ebfc3e3d29e3e1
5cf42e5c5e9faf9804f4b8005e32168f3a46b38347377087a457c72b727740cb
d0e95eda24b293dfd133747fc248f0002f8e7435cbfe30e3ad91f768395ef504
cat-searcher/leandojo-benchmark-4-random
test
1,746
List.mem_zip_inits_tails
Mathlib/Data/List/Zip.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
right
case cons.mpr.cons α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 hd : α tl : List α ih : ∀ {init tail : List α}, (init, tail) ∈ tl.inits.zip tl.tails ↔ init ++ tail = tl tail : List α hd' : α tl' : List α h : hd' :: tl' ++ tail = hd :: tl ⊢ (hd' :: tl', tail) = ([], hd :: tl) ∨ ∃ a b, (a, b) ∈ tl.i...
case cons.mpr.cons.h α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 hd : α tl : List α ih : ∀ {init tail : List α}, (init, tail) ∈ tl.inits.zip tl.tails ↔ init ++ tail = tl tail : List α hd' : α tl' : List α h : hd' :: tl' ++ tail = hd :: tl ⊢ ∃ a b, (a, b) ∈ tl.inits.zip tl.tails ∧ Prod.map (fun t => h...
((:c Or) ((:c Eq) ((:c Prod) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428))) ((:c Prod.mk) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)) ((:c List.cons) (:fv _uniq.65428) (:fv _uniq.66738) (:fv _uniq.66739)) (:fv _uniq.65566)) ((:c Prod.mk) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq....
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u_1 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"ε","sexp":"(:sort (+ u_4 1))"},{"name":"hd","sexp":"(:fv _uniq.65428)"},{"name":"tl","sexp":"((:c List) (:fv _uniq.65428))"},{"name":"ih","sexp":"(:fora...
(:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c List) (:arg :explicit 0 (:fv FV0)))))) (:arg :explicit 1 (:app (:c Prod.mk) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"right","sourceEnd":15194,"sourceStart":15189,"tag":"atom"}],"kind":"Lean.Parser.Tactic.right","source":"right","sourceEnd":15194,"sourceStart":15189,"tag":"node"}
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
113
72
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d1a7abeb4dbf373a1140adde1aa9b9e0b03f9ca6e607213a9d02acbcecd492b9
d0e95eda24b293dfd133747fc248f0002f8e7435cbfe30e3ad91f768395ef504
27042f4e6eca7d0b2a7ee4026df2ecfa51d3339e6d122aa099118ecd8563bad9
245bbe8fb21051170b1897e88f53a92683e92e361b49f0e8258d718c2dd1fc8f
cat-searcher/leandojo-benchmark-4-random
test
1,747
List.mem_zip_inits_tails
Mathlib/Data/List/Zip.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
use tl', tail
case cons.mpr.cons.h α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 hd : α tl : List α ih : ∀ {init tail : List α}, (init, tail) ∈ tl.inits.zip tl.tails ↔ init ++ tail = tl tail : List α hd' : α tl' : List α h : hd' :: tl' ++ tail = hd :: tl ⊢ ∃ a b, (a, b) ∈ tl.inits.zip tl.tails ∧ Prod.map (fun t => h...
case h α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 hd : α tl : List α ih : ∀ {init tail : List α}, (init, tail) ∈ tl.inits.zip tl.tails ↔ init ++ tail = tl tail : List α hd' : α tl' : List α h : hd' :: tl' ++ tail = hd :: tl ⊢ (tl', tail) ∈ tl.inits.zip tl.tails ∧ Prod.map (fun t => hd :: t) id (tl',...
((:c Exists) ((:c List) (:fv _uniq.65428)) (:lambda a ((:c List) (:fv _uniq.65428)) ((:c Exists) ((:c List) (:fv _uniq.65428)) (:lambda b ((:c List) (:fv _uniq.65428)) ((:c And) ((:c Membership.mem) ((:c Prod) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428))) ((:c List) ((:c Prod) ((:c List) (:fv _uniq.65428...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u_1 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"ε","sexp":"(:sort (+ u_4 1))"},{"name":"hd","sexp":"(:fv _uniq.65428)"},{"name":"tl","sexp":"((:c List) (:fv _uniq.65428))"},{"name":"ih","sexp":"(:fora...
(:app (:c Exists) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda a :explicit (:app (:c List) (:arg :explicit 0 (:fv FV0))) (:app (:c Exists) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda b :explicit (:app (:c List) (:ar...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"use","sourceEnd":15206,"sourceStart":15203,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"tl'","sourceEnd":15210,"sourceStart":15207,"tag":"identifier"},...
[]
[{"source":"tl'","source_end":15210,"source_start":15207,"syntax_kind":"ident"},{"source":"tail","source_end":15216,"source_start":15212,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
113
73
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
6fdb48f7fe8a6310c4af9b2ffc7ef1a68576779d467be49a78ef0757cca241e1
245bbe8fb21051170b1897e88f53a92683e92e361b49f0e8258d718c2dd1fc8f
a20162406be5e8d9da5e5ccf8b09495b538e63f99a727baa4e2f11f6f0dbbca9
c29ba37209a608dd4de15a2d6612fc6a35f2a165296d405c6618f37f4e079333
cat-searcher/leandojo-benchmark-4-random
test
1,748
List.mem_zip_inits_tails
Mathlib/Data/List/Zip.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp_all
case h α : Type u β : Type u_1 γ : Type u_2 δ : Type u_3 ε : Type u_4 hd : α tl : List α ih : ∀ {init tail : List α}, (init, tail) ∈ tl.inits.zip tl.tails ↔ init ++ tail = tl tail : List α hd' : α tl' : List α h : hd' :: tl' ++ tail = hd :: tl ⊢ (tl', tail) ∈ tl.inits.zip tl.tails ∧ Prod.map (fun t => hd :: t) id (tl',...
((:c And) ((:c Membership.mem) ((:c Prod) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428))) ((:c List) ((:c Prod) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)))) ((:c List.instMembership) ((:c Prod) ((:c List) (:fv _uniq.65428)) ((:c List) (:fv _uniq.65428)))) ((:c Prod.mk) ((:c List) (:fv _uni...
[{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u_1 1))"},{"name":"γ","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"ε","sexp":"(:sort (+ u_4 1))"},{"name":"hd","sexp":"(:fv _uniq.65428)"},{"name":"tl","sexp":"((:c List) (:fv _uniq.65428))"},{"name":"ih","sexp":"(:fora...
(:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c List) (:arg :explicit 0 (:fv FV0)))))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con...
{"children":[{"source":"simp_all","sourceEnd":15233,"sourceStart":15225,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean....
[]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65428","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65431","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
113
74
exact
true
1
12
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ae44b3c84043ce3776e5da10f4ac7a3102cb1752e61c94b3726d85c771785650
c29ba37209a608dd4de15a2d6612fc6a35f2a165296d405c6618f37f4e079333
770a776fdf57bd2930634d5176197b90f459fb4a0a757471ffc33c700413d7a2
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,749
Turing.PartrecToTM2.supports_singleton
Mathlib/Computability/TMToPartrec.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>Turing.PartrecToTM2.Supports</a>]
S : Finset Λ' q : Λ' ⊢ Supports {q} S ↔ TM2.SupportsStmt S (tr q)
((:c Iff) ((:c Turing.PartrecToTM2.Supports) ((:c Singleton.singleton) (:c Turing.PartrecToTM2.Λ') ((:c Finset) (:c Turing.PartrecToTM2.Λ')) ((:c Finset.instSingleton) (:c Turing.PartrecToTM2.Λ')) (:fv _uniq.343909)) (:fv _uniq.343908)) ((:c Turing.TM2.SupportsStmt) (:c Turing.PartrecToTM2.K') (:lambda _ (:c Turing.Par...
[{"name":"S","sexp":"((:c Finset) (:c Turing.PartrecToTM2.Λ'))"},{"name":"q","sexp":"(:c Turing.PartrecToTM2.Λ')"}]
(:app (:c Iff) (:arg :explicit 0 (:app (:c Turing.PartrecToTM2.Supports) (:arg :explicit 0 (:app (:c Singleton.singleton) (:arg :implicit-type 0 (:c Turing.PartrecToTM2.Λ')) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:c Turing.PartrecToTM2.Λ')))) (:arg :instance 2 (:instance-of (:app (:c Singleton) (:a...
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.343908","is_instance":false,"is_let":false,"name":"S","sexp":"(:app (:c Finset) (:arg :explicit 0 (:c Turing.PartrecToTM2.Λ')))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.343909","is_instance":false,"is_let":false,"name":"q"...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":92022,"sourceStart":92018,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...
[]
[{"source":"Supports","source_end":92032,"source_start":92024,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.343908","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.343909","is_instance":false,"is_let":false,"user_name":"q"}]
312
2
exact
true
1
2
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
1986d6ded3fc0936be62d17af546fa6312e38e6282ab7ef1a336befccaecc8a7
103b9b9b61887b29d53e61e7a301f597291b070b980d4da0de101bcb1f957501
b699c84f5199581538187aeffeab9170551c32bc0015f26eaf500bbf5cce2ecf
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,750
LiouvilleWith.int_sub_iff
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp [<a>sub_eq_add_neg</a>]
p q x y : ℝ r : ℚ m : ℤ n : ℕ ⊢ LiouvilleWith p (↑m - x) ↔ LiouvilleWith p x
((:c Iff) ((:c LiouvilleWith) (:fv _uniq.65689) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c Int.cast) (:c Real) (:c Real.instIntCast) (:fv _uniq.65699)) (:fv _uniq.65693))) ((:c LiouvilleWith) (:fv _uniq.65689) (:fv _uniq.65693)))
[{"name":"p","sexp":"(:c Real)"},{"name":"q","sexp":"(:c Real)"},{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"r","sexp":"(:c Rat)"},{"name":"m","sexp":"(:c Int)"},{"name":"n","sexp":"(:c Nat)"}]
(:app (:c Iff) (:arg :explicit 0 (:app (:c LiouvilleWith) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HSub.hSub) (: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 HSub) (:arg :explicit 0 (:c Real)) (:arg :explicit...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65689","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65691","is_instance":false,"is_let":false,"name":"q","sexp":"(:c Real)"},{"binder_role":":implicit","context_i...
{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":12952,"sourceStart":12948,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source...
[]
[{"source":"sub_eq_add_neg","source_end":12968,"source_start":12954,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.65689","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.65691","is_instance":false,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":2,"internal_name":"_un...
84
2
exact
true
1
7
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
b80f94527cd4e0929186db0de4c7fbd85b7777415c166d8102894f7cdf058159
5857df48905ac4188286a0ba1cf1f84b8f29e038715278f6513f1816385e44cf
6c65ecc57a4eae091051517e6a0bda752e7e82d097dfbcda6aabf3b5a963d716
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,751
Ideal.irreducible_of_irreducible_absNorm
Mathlib/RingTheory/Ideal/Norm.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simpa only [<a>Ideal.isUnit_iff</a>, <a>Nat.isUnit_iff</a>, <a>Ideal.absNorm_eq_one_iff</a>] using h
S : Type u_1 inst✝⁵ : CommRing S inst✝⁴ : IsDomain S inst✝³ : Nontrivial S inst✝² : IsDedekindDomain S inst✝¹ : Module.Free ℤ S inst✝ : Module.Finite ℤ S I : Ideal S hI : Irreducible (absNorm I) h : IsUnit I ⊢ IsUnit (absNorm I)
((:c IsUnit) (:c Nat) (:c Nat.instMonoid) ((:c DFunLike.coe) ((:c MonoidWithZeroHom) ((:c Ideal) (:fv _uniq.198160) ((:c CommSemiring.toSemiring) (:fv _uniq.198160) ((:c CommRing.toCommSemiring) (:fv _uniq.198160) (:fv _uniq.198163)))) (:c Nat) ((:c NonAssocSemiring.toMulZeroOneClass) ((:c Ideal) (:fv _uniq.198160) ((:...
[{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.198160))"},{"name":"inst✝⁴","sexp":"((:c IsDomain) (:fv _uniq.198160) ((:c CommSemiring.toSemiring) (:fv _uniq.198160) ((:c CommRing.toCommSemiring) (:fv _uniq.198160) (:fv _uniq.198163))))"},{"name":"inst✝³","sexp":"((:c Nontri...
(:app (:c IsUnit) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MonoidWithZeroHom) (:arg :explicit 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-o...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.198160","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.198163","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :expl...
{"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":19528,"sourceStart":19523,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind...
[]
[{"source":"Ideal.isUnit_iff","source_end":19551,"source_start":19535,"syntax_kind":"ident"},{"source":"Nat.isUnit_iff","source_end":19567,"source_start":19553,"syntax_kind":"ident"},{"source":"absNorm_eq_one_iff","source_end":19587,"source_start":19569,"syntax_kind":"ident"},{"source":"h","source_end":19596,"source_st...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.198160","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.198163","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":instance-implicit","context_index...
69
2
exact
true
1
10
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
438d27c1e1add7fccae3c1c52dd3f5758b9918524eaa033feb9dae63b9dcd298
050ba38b615eab13d7df8b669217ceade4159f0606775f6ed004ac28f2d96c04
c874d2bdffa4359995b8b4dae1c545d9fcc3d85d4743b26244509bffd4d415b3
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,752
Ideal.irreducible_of_irreducible_absNorm
Mathlib/RingTheory/Ideal/Norm.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rintro a b rfl
S : Type u_1 inst✝⁵ : CommRing S inst✝⁴ : IsDomain S inst✝³ : Nontrivial S inst✝² : IsDedekindDomain S inst✝¹ : Module.Free ℤ S inst✝ : Module.Finite ℤ S I : Ideal S hI : Irreducible (absNorm I) ⊢ ∀ (a b : Ideal S), I = a * b → IsUnit a ∨ IsUnit b
S : Type u_1 inst✝⁵ : CommRing S inst✝⁴ : IsDomain S inst✝³ : Nontrivial S inst✝² : IsDedekindDomain S inst✝¹ : Module.Free ℤ S inst✝ : Module.Finite ℤ S a b : Ideal S hI : Irreducible (absNorm (a * b)) ⊢ IsUnit a ∨ IsUnit b
(:forall a ((:c Ideal) (:fv _uniq.198160) ((:c CommSemiring.toSemiring) (:fv _uniq.198160) ((:c CommRing.toCommSemiring) (:fv _uniq.198160) (:fv _uniq.198163)))) (:forall b ((:c Ideal) (:fv _uniq.198160) ((:c CommSemiring.toSemiring) (:fv _uniq.198160) ((:c CommRing.toCommSemiring) (:fv _uniq.198160) (:fv _uniq.198163)...
[{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.198160))"},{"name":"inst✝⁴","sexp":"((:c IsDomain) (:fv _uniq.198160) ((:c CommSemiring.toSemiring) (:fv _uniq.198160) ((:c CommRing.toCommSemiring) (:fv _uniq.198160) (:fv _uniq.198163))))"},{"name":"inst✝³","sexp":"((:c Nontri...
(:forall a :explicit (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0)))))) (:forall b :explicit (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0)))))) (:forall _ :expl...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.198160","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.198163","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :expl...
{"children":[{"source":"rintro","sourceEnd":19620,"sourceStart":19614,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":19622,"sourceStart":19621,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"a","sourceEnd":19622,"sourceStart":19621,"...
[{"role":"fresh_name","source":"a","source_end":19622,"source_start":19621,"syntax_kind":"ident"},{"role":"fresh_name","source":"b","source_end":19624,"source_start":19623,"syntax_kind":"ident"}]
[{"source":"rfl","source_end":19628,"source_start":19625,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.198160","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.198163","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":instance-implicit","context_index...
69
9
exact
true
1
9
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
008acc0de2bbdf35a937fa573c873378c73a44a712771c26501bca9957010535
92c5b9e951f6767ebb4cdd6840e945bcf7119b66bc1e7f9f32e8c2bc993b64c5
bc105ec7128b0ef3ae06b78570b551eec78bccb05437c96e6a4efd5d399be33f
cfe78c320f0ffbfe39ac73ae09807119f0a5ec12f7aaa354dbf2b8939f09bd85
cat-searcher/leandojo-benchmark-4-random
test
1,753
Ideal.irreducible_of_irreducible_absNorm
Mathlib/RingTheory/Ideal/Norm.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simpa only [<a>Ideal.isUnit_iff</a>, <a>Nat.isUnit_iff</a>, <a>Ideal.absNorm_eq_one_iff</a>] using hI.isUnit_or_isUnit (<a>map_mul</a> <a>Ideal.absNorm</a> a b)
S : Type u_1 inst✝⁵ : CommRing S inst✝⁴ : IsDomain S inst✝³ : Nontrivial S inst✝² : IsDedekindDomain S inst✝¹ : Module.Free ℤ S inst✝ : Module.Finite ℤ S a b : Ideal S hI : Irreducible (absNorm (a * b)) ⊢ IsUnit a ∨ IsUnit b
((:c Or) ((:c IsUnit) ((:c Ideal) (:fv _uniq.198160) ((:c CommSemiring.toSemiring) (:fv _uniq.198160) ((:c CommRing.toCommSemiring) (:fv _uniq.198160) (:fv _uniq.198163)))) ((:c MonoidWithZero.toMonoid) ((:c Ideal) (:fv _uniq.198160) ((:c CommSemiring.toSemiring) (:fv _uniq.198160) ((:c CommRing.toCommSemiring) (:fv _u...
[{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁵","sexp":"((:c CommRing) (:fv _uniq.198160))"},{"name":"inst✝⁴","sexp":"((:c IsDomain) (:fv _uniq.198160) ((:c CommSemiring.toSemiring) (:fv _uniq.198160) ((:c CommRing.toCommSemiring) (:fv _uniq.198160) (:fv _uniq.198163))))"},{"name":"inst✝³","sexp":"((:c Nontri...
(:app (:c Or) (:arg :explicit 0 (:app (:c IsUnit) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV0)) (...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.198160","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.198163","is_instance":true,"is_let":false,"name":"inst✝⁵","sexp":"(:app (:c CommRing) (:arg :expl...
{"children":[{"source":"simpa","sourceEnd":19640,"sourceStart":19635,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"ch...
[]
[{"source":"Ideal.isUnit_iff","source_end":19663,"source_start":19647,"syntax_kind":"ident"},{"source":"Nat.isUnit_iff","source_end":19679,"source_start":19665,"syntax_kind":"ident"},{"source":"absNorm_eq_one_iff","source_end":19699,"source_start":19681,"syntax_kind":"ident"},{"source":"hI.isUnit_or_isUnit (_root_.map_...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.198160","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.198163","is_instance":true,"is_let":false,"user_name":"inst✝⁵"},{"binder_role":":instance-implicit","context_index...
69
10
exact
true
1
10
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
974a3277206ed5d35c64a8bdb7822a1442d8cccbf94779853da0c885d45bc2d0
cfe78c320f0ffbfe39ac73ae09807119f0a5ec12f7aaa354dbf2b8939f09bd85
97f67225b595442ba1e9b789190c758d7406dd615c9680d6b5eb273898980034
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,754
vectorSpan_insert_eq_vectorSpan
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
simp_rw [← <a>direction_affineSpan</a>, <a>affineSpan_insert_eq_affineSpan</a> _ h]
k : Type u_1 V : Type u_2 P : Type u_3 inst✝³ : Ring k inst✝² : AddCommGroup V inst✝¹ : Module k V inst✝ : AffineSpace V P ι : Type u_4 p : P ps : Set P h : p ∈ affineSpan k ps ⊢ vectorSpan k (insert p ps) = vectorSpan k ps
((:c Eq) ((:c Submodule) (:fv _uniq.389546) (:fv _uniq.389549) ((:c Ring.toSemiring) (:fv _uniq.389546) (:fv _uniq.389555)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.389549) (:fv _uniq.389558)) (:fv _uniq.390145)) ((:c vectorSpan) (:fv _uniq.389546) (:fv _uniq.389549) (:fv _uniq.389552) (:fv _uniq.389555) (:fv _uni...
[{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.389546))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.389549))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.389546) (:fv _uniq.389549)...
(:app (:c Eq) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.389546","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.389549","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c...
{"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":68302,"sourceStart":68295,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":68304,"sourceStart":68303,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children...
[]
[{"source":"direction_affineSpan","source_end":68328,"source_start":68308,"syntax_kind":"ident"},{"source":"affineSpan_insert_eq_affineSpan _ h","source_end":68365,"source_start":68330,"syntax_kind":"Lean.Parser.Term.app"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.389546","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.389549","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_...
361
2
exact
true
1
11
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
a4eb9433963e0b92ff7b693e6f5d8d4b54dcac43b4166d4a9573c3579b193be9
9a2680eb88a8a9496a17b7e1ad3c74a3b2fb35c57bca8c9ff7c40ef2b3d1ab62
921cc1d538264be0f5ef8839e36e745188031e95fce90e179a3aa64d16cd3cf5
d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981
cat-searcher/leandojo-benchmark-4-random
test
1,755
LinearMap.injective_domRestrict_iff
Mathlib/Algebra/Module/Submodule/Ker.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
rw [← <a>LinearMap.ker_eq_bot</a>]
R : Type u_1 R₁ : Type u_2 R₂ : Type u_3 R₃ : Type u_4 K : Type u_5 M : Type u_6 M₁ : Type u_7 M₂ : Type u_8 M₃ : Type u_9 V : Type u_10 V₂ : Type u_11 inst✝¹¹ : Ring R inst✝¹⁰ : Ring R₂ inst✝⁹ : Ring R₃ inst✝⁸ : AddCommGroup M inst✝⁷ : AddCommGroup M₂ inst✝⁶ : AddCommGroup M₃ inst✝⁵ : Module R M inst✝⁴ : Module R₂ M₂ ...
R : Type u_1 R₁ : Type u_2 R₂ : Type u_3 R₃ : Type u_4 K : Type u_5 M : Type u_6 M₁ : Type u_7 M₂ : Type u_8 M₃ : Type u_9 V : Type u_10 V₂ : Type u_11 inst✝¹¹ : Ring R inst✝¹⁰ : Ring R₂ inst✝⁹ : Ring R₃ inst✝⁸ : AddCommGroup M inst✝⁷ : AddCommGroup M₂ inst✝⁶ : AddCommGroup M₃ inst✝⁵ : Module R M inst✝⁴ : Module R₂ M₂ ...
((:c Iff) ((:c Function.Injective) ((:c Subtype) (:fv _uniq.141918) (:lambda x (:fv _uniq.141918) ((:c Membership.mem) (:fv _uniq.141918) ((:c Submodule) (:fv _uniq.141903) (:fv _uniq.141918) ((:c Ring.toSemiring) (:fv _uniq.141903) (:fv _uniq.141936)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.141918) (:fv _uniq.14...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₁","sexp":"(:sort (+ u_2 1))"},{"name":"R₂","sexp":"(:sort (+ u_3 1))"},{"name":"R₃","sexp":"(:sort (+ u_4 1))"},{"name":"K","sexp":"(:sort (+ u_5 1))"},{"name":"M","sexp":"(:sort (+ u_6 1))"},{"name":"M₁","sexp":"(:sort (+ u_7 1))"},{"name":"M₂","sexp":"(:sort (+ u_8 ...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Function.Injective) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:lambda x :explicit (:fv FV5) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0))...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"rw","sourceEnd":8696,"sourceStart":8694,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8698,"sourceStart":8697,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":8701,"sourceStart":...
[]
[{"source":"LinearMap.ker_eq_bot","source_end":8722,"source_start":8702,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":2,"internal_name":"...
83
4
exact
true
1
30
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
ad71837d39740fa1b751c21846a5066c24ae0f56394d50b060187207c8cf656f
ec8f0f0e57a35a45453e2decb4cbabd519ee192d52248b13cade8943c852d060
58ea53f8932ae2a3f7b2dc999464125912e9182c88e42b77fa8574a4b60733db
c336f19b38b4901ace0d211765464f1565332afdd9f6091b95d21c68f17997e2
cat-searcher/leandojo-benchmark-4-random
test
1,756
LinearMap.injective_domRestrict_iff
Mathlib/Algebra/Module/Submodule/Ker.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
refine ⟨fun h ↦ <a>le_bot_iff</a>.1 ?_, fun h ↦ <a>le_bot_iff</a>.1 ?_⟩
R : Type u_1 R₁ : Type u_2 R₂ : Type u_3 R₃ : Type u_4 K : Type u_5 M : Type u_6 M₁ : Type u_7 M₂ : Type u_8 M₃ : Type u_9 V : Type u_10 V₂ : Type u_11 inst✝¹¹ : Ring R inst✝¹⁰ : Ring R₂ inst✝⁹ : Ring R₃ inst✝⁸ : AddCommGroup M inst✝⁷ : AddCommGroup M₂ inst✝⁶ : AddCommGroup M₃ inst✝⁵ : Module R M inst✝⁴ : Module R₂ M₂ ...
case refine_1 R : Type u_1 R₁ : Type u_2 R₂ : Type u_3 R₃ : Type u_4 K : Type u_5 M : Type u_6 M₁ : Type u_7 M₂ : Type u_8 M₃ : Type u_9 V : Type u_10 V₂ : Type u_11 inst✝¹¹ : Ring R inst✝¹⁰ : Ring R₂ inst✝⁹ : Ring R₃ inst✝⁸ : AddCommGroup M inst✝⁷ : AddCommGroup M₂ inst✝⁶ : AddCommGroup M₃ inst✝⁵ : Module R M inst✝⁴ :...
((:c Iff) ((:c Eq) ((:c Submodule) (:fv _uniq.141903) ((:c Subtype) (:fv _uniq.141918) (:lambda x (:fv _uniq.141918) ((:c Membership.mem) (:fv _uniq.141918) ((:c Submodule) (:fv _uniq.141903) (:fv _uniq.141918) ((:c Ring.toSemiring) (:fv _uniq.141903) (:fv _uniq.141936)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.14...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₁","sexp":"(:sort (+ u_2 1))"},{"name":"R₂","sexp":"(:sort (+ u_3 1))"},{"name":"R₃","sexp":"(:sort (+ u_4 1))"},{"name":"K","sexp":"(:sort (+ u_5 1))"},{"name":"M","sexp":"(:sort (+ u_6 1))"},{"name":"M₁","sexp":"(:sort (+ u_7 1))"},{"name":"M₂","sexp":"(:sort (+ u_8 ...
(:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:lambda x :explicit (:fv FV5) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"refine","sourceEnd":8732,"sourceStart":8726,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":8736,"sourceStart":8733,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":8739,"sourceStart":8736,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"h"...
[]
[{"source":"⟨fun h ↦ le_bot_iff.1 ?_, fun h ↦ le_bot_iff.1 ?_⟩","source_end":8791,"source_start":8733,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":2,"internal_name":"...
83
7
exact
true
1
30
true
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
d56bd1a5f2ca598462aa9f6bcede8d93b9b8f06d9adfb52446831ecd5b83dca8
c336f19b38b4901ace0d211765464f1565332afdd9f6091b95d21c68f17997e2
74bc0218e073384d529283aafa72f4a42aa4d35cb090bc7589cf1c0f2456a48c
262c237eda17576f4b8ebe64a6f6c30d55ccb25230b5a98f5ba628a86533cde8
cat-searcher/leandojo-benchmark-4-random
test
1,757
LinearMap.injective_domRestrict_iff
Mathlib/Algebra/Module/Submodule/Ker.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
intro x ⟨hx, h'x⟩
case refine_1 R : Type u_1 R₁ : Type u_2 R₂ : Type u_3 R₃ : Type u_4 K : Type u_5 M : Type u_6 M₁ : Type u_7 M₂ : Type u_8 M₃ : Type u_9 V : Type u_10 V₂ : Type u_11 inst✝¹¹ : Ring R inst✝¹⁰ : Ring R₂ inst✝⁹ : Ring R₃ inst✝⁸ : AddCommGroup M inst✝⁷ : AddCommGroup M₂ inst✝⁶ : AddCommGroup M₃ inst✝⁵ : Module R M inst✝⁴ :...
case refine_1 R : Type u_1 R₁ : Type u_2 R₂ : Type u_3 R₃ : Type u_4 K : Type u_5 M : Type u_6 M₁ : Type u_7 M₂ : Type u_8 M₃ : Type u_9 V : Type u_10 V₂ : Type u_11 inst✝¹¹ : Ring R inst✝¹⁰ : Ring R₂ inst✝⁹ : Ring R₃ inst✝⁸ : AddCommGroup M inst✝⁷ : AddCommGroup M₂ inst✝⁶ : AddCommGroup M₃ inst✝⁵ : Module R M inst✝⁴ :...
((:c LE.le) ((:c Submodule) (:fv _uniq.141903) (:fv _uniq.141918) ((:c Ring.toSemiring) (:fv _uniq.141903) (:fv _uniq.141936)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.141918) (:fv _uniq.141945)) (:fv _uniq.142475)) ((:c Preorder.toLE) ((:c Submodule) (:fv _uniq.141903) (:fv _uniq.141918) ((:c Ring.toSemiring) (:f...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₁","sexp":"(:sort (+ u_2 1))"},{"name":"R₂","sexp":"(:sort (+ u_3 1))"},{"name":"R₃","sexp":"(:sort (+ u_4 1))"},{"name":"K","sexp":"(:sort (+ u_5 1))"},{"name":"M","sexp":"(:sort (+ u_6 1))"},{"name":"M₁","sexp":"(:sort (+ u_7 1))"},{"name":"M₂","sexp":"(:sort (+ u_8 ...
(:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV5))))) (:arg :instance 4 (:instance...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"intro","sourceEnd":8802,"sourceStart":8797,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":8804,"sourceStart":8803,"tag":"identifier"},{"children":[{"source":"⟨","sourceEnd":8808,"sourceStart":8805,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","sour...
[{"role":"fresh_name","source":"x","source_end":8804,"source_start":8803,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":8810,"source_start":8808,"syntax_kind":"ident"},{"role":"fresh_name","source":"h'x","source_end":8815,"source_start":8812,"syntax_kind":"ident"}]
[]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":2,"internal_name":"...
83
12
exact
true
1
31
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
0463da24dd7920cc2329100b6013c8ac5b44febf81d0791b2b73df24cbdf56f9
f3aa7ab4a680860169d1a2b4beb9b56aba651c77e26d977bb8e168ede907c188
03da3aa93cc4e81e5f3f3103a1e8244f2fad45c23c1ed1a38eec9478ea471f7d
99002bcbcb6f54fded954407334696bcc8c8b2ead037d2973a480e25449bfb70
cat-searcher/leandojo-benchmark-4-random
test
1,758
LinearMap.injective_domRestrict_iff
Mathlib/Algebra/Module/Submodule/Ker.lean
https://github.com/leanprover-community/mathlib4
29dcec074de168ac2bf835a77ef68bbe069194c5
have : ⟨x, hx⟩ ∈ <a>LinearMap.ker</a> (<a>LinearMap.domRestrict</a> f S) := by simpa using h'x
case refine_1 R : Type u_1 R₁ : Type u_2 R₂ : Type u_3 R₃ : Type u_4 K : Type u_5 M : Type u_6 M₁ : Type u_7 M₂ : Type u_8 M₃ : Type u_9 V : Type u_10 V₂ : Type u_11 inst✝¹¹ : Ring R inst✝¹⁰ : Ring R₂ inst✝⁹ : Ring R₃ inst✝⁸ : AddCommGroup M inst✝⁷ : AddCommGroup M₂ inst✝⁶ : AddCommGroup M₃ inst✝⁵ : Module R M inst✝⁴ :...
case refine_1 R : Type u_1 R₁ : Type u_2 R₂ : Type u_3 R₃ : Type u_4 K : Type u_5 M : Type u_6 M₁ : Type u_7 M₂ : Type u_8 M₃ : Type u_9 V : Type u_10 V₂ : Type u_11 inst✝¹¹ : Ring R inst✝¹⁰ : Ring R₂ inst✝⁹ : Ring R₃ inst✝⁸ : AddCommGroup M inst✝⁷ : AddCommGroup M₂ inst✝⁶ : AddCommGroup M₃ inst✝⁵ : Module R M inst✝⁴ :...
((:c Membership.mem) (:fv _uniq.141918) ((:c Submodule) (:fv _uniq.141903) (:fv _uniq.141918) ((:c Ring.toSemiring) (:fv _uniq.141903) (:fv _uniq.141936)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.141918) (:fv _uniq.141945)) (:fv _uniq.142475)) ((:c SetLike.instMembership) ((:c Submodule) (:fv _uniq.141903) (:fv _u...
[{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₁","sexp":"(:sort (+ u_2 1))"},{"name":"R₂","sexp":"(:sort (+ u_3 1))"},{"name":"R₃","sexp":"(:sort (+ u_4 1))"},{"name":"K","sexp":"(:sort (+ u_5 1))"},{"name":"M","sexp":"(:sort (+ u_6 1))"},{"name":"M₁","sexp":"(:sort (+ u_7 1))"},{"name":"M₂","sexp":"(:sort (+ u_8 ...
(:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0...
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","...
{"children":[{"source":"have","sourceEnd":8827,"sourceStart":8823,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":8828,"sourceStart":8828,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":8828,"sourceStart":8828,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","...
[]
[{"source":"⟨x, hx⟩ ∈ LinearMap.ker (LinearMap.domRestrict f S)","source_end":8887,"source_start":8830,"syntax_kind":"«term_∈_»"},{"source":"h'x","source_end":8909,"source_start":8906,"syntax_kind":"ident"}]
[{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141903","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141906","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":2,"internal_name":"...
83
13
exact
true
1
34
false
4
source-invocation-v4
2
lean-model-sexp-v2
3
lean-action-trace-v3
73781c2d58456e4bf369dadd4a501e1b78a0b177
73781c2d58456e4bf369dadd4a501e1b78a0b177
8b903ebf2220acc6f2be7a7ad5dd789e1c7464a85d86001fbfc688e116298df1
99002bcbcb6f54fded954407334696bcc8c8b2ead037d2973a480e25449bfb70
18f0f10719889939184f61e601a14de1e0bc7cd711d8e46804db9acbd6305f51
353d2983cea27bace3da0deac34232472558faf153ad04495100efaffbcb8ff5