url
stringclasses 147
values | commit
stringclasses 147
values | file_path
stringlengths 7
101
| full_name
stringlengths 1
94
| start
stringlengths 6
10
| end
stringlengths 6
11
| tactic
stringlengths 1
11.2k
| state_before
stringlengths 3
2.09M
| state_after
stringlengths 6
2.09M
|
|---|---|---|---|---|---|---|---|---|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds
|
[201, 1]
|
[225, 42]
|
rw [β hg]
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
β’ AnalyticAt β g (β(extChartAt π(β, β) z) z)
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
β’ AnalyticAt β (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) (β(extChartAt π(β, β) z) z)
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds
|
[201, 1]
|
[225, 42]
|
exact n.holomorphicAt.2
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
β’ AnalyticAt β (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) (β(extChartAt π(β, β) z) z)
|
no goals
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds
|
[201, 1]
|
[225, 42]
|
contrapose h
|
case inl
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h : βαΆ (z_1 : β) in π (β(extChartAt π(β, β) z) z), g z_1 = g (β(extChartAt π(β, β) z) z)
β’ π (f z) β€ Filter.map f (π z)
|
case inl
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h : Β¬π (f z) β€ Filter.map f (π z)
β’ Β¬βαΆ (z_1 : β) in π (β(extChartAt π(β, β) z) z), g z_1 = g (β(extChartAt π(β, β) z) z)
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds
|
[201, 1]
|
[225, 42]
|
clear h
|
case inl
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h : Β¬π (f z) β€ Filter.map f (π z)
β’ Β¬βαΆ (z_1 : β) in π (β(extChartAt π(β, β) z) z), g z_1 = g (β(extChartAt π(β, β) z) z)
|
case inl
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
β’ Β¬βαΆ (z_1 : β) in π (β(extChartAt π(β, β) z) z), g z_1 = g (β(extChartAt π(β, β) z) z)
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds
|
[201, 1]
|
[225, 42]
|
simp only [Filter.not_eventually]
|
case inl
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
β’ Β¬βαΆ (z_1 : β) in π (β(extChartAt π(β, β) z) z), g z_1 = g (β(extChartAt π(β, β) z) z)
|
case inl
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
β’ βαΆ (x : β) in π (β(extChartAt π(β, β) z) z), Β¬g x = g (β(extChartAt π(β, β) z) z)
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds
|
[201, 1]
|
[225, 42]
|
apply n.inCharts.nonconst.mp
|
case inl
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
β’ βαΆ (x : β) in π (β(extChartAt π(β, β) z) z), Β¬g x = g (β(extChartAt π(β, β) z) z)
|
case inl
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
β’ βαΆ (x : β) in π (β(extChartAt π(β, β) z) z),
β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x)) β
β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) z))) β
Β¬g x = g (β(extChartAt π(β, β) z) z)
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds
|
[201, 1]
|
[225, 42]
|
simp only [β hg, Ne, imp_self, Filter.eventually_true]
|
case inl
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
β’ βαΆ (x : β) in π (β(extChartAt π(β, β) z) z),
β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x)) β
β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) z))) β
Β¬g x = g (β(extChartAt π(β, β) z) z)
|
no goals
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds
|
[201, 1]
|
[225, 42]
|
simp only [β extChartAt_map_nhds' I z, Filter.map_map] at h
|
case inr
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h : π (g (β(extChartAt π(β, β) z) z)) β€ Filter.map g (π (β(extChartAt π(β, β) z) z))
β’ π (f z) β€ Filter.map f (π z)
|
case inr
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h : π (g (β(extChartAt π(β, β) z) z)) β€ Filter.map (g β β(extChartAt π(β, β) z)) (π z)
β’ π (f z) β€ Filter.map f (π z)
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds
|
[201, 1]
|
[225, 42]
|
replace h := @Filter.map_mono _ _ (extChartAt I (f z)).symm _ _ h
|
case inr
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h : π (g (β(extChartAt π(β, β) z) z)) β€ Filter.map (g β β(extChartAt π(β, β) z)) (π z)
β’ π (f z) β€ Filter.map f (π z)
|
case inr
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h :
Filter.map (β(extChartAt π(β, β) (f z)).symm) (π (g (β(extChartAt π(β, β) z) z))) β€
Filter.map (β(extChartAt π(β, β) (f z)).symm) (Filter.map (g β β(extChartAt π(β, β) z)) (π z))
β’ π (f z) β€ Filter.map f (π z)
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds
|
[201, 1]
|
[225, 42]
|
simp only [β hg] at h
|
case inr
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h :
Filter.map (β(extChartAt π(β, β) (f z)).symm) (π (g (β(extChartAt π(β, β) z) z))) β€
Filter.map (β(extChartAt π(β, β) (f z)).symm) (Filter.map (g β β(extChartAt π(β, β) z)) (π z))
β’ π (f z) β€ Filter.map f (π z)
|
case inr
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h :
Filter.map (β(extChartAt π(β, β) (f z)).symm)
(π (β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) z))))) β€
Filter.map (β(extChartAt π(β, β) (f z)).symm)
(Filter.map
((fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) β β(extChartAt π(β, β) z)) (π z))
β’ π (f z) β€ Filter.map f (π z)
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds
|
[201, 1]
|
[225, 42]
|
rw [PartialEquiv.left_inv _ (mem_extChartAt_source I z)] at h
|
case inr
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h :
Filter.map (β(extChartAt π(β, β) (f z)).symm)
(π (β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) z))))) β€
Filter.map (β(extChartAt π(β, β) (f z)).symm)
(Filter.map
((fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) β β(extChartAt π(β, β) z)) (π z))
β’ π (f z) β€ Filter.map f (π z)
|
case inr
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h :
Filter.map (β(extChartAt π(β, β) (f z)).symm) (π (β(extChartAt π(β, β) (f z)) (f z))) β€
Filter.map (β(extChartAt π(β, β) (f z)).symm)
(Filter.map
((fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) β β(extChartAt π(β, β) z)) (π z))
β’ π (f z) β€ Filter.map f (π z)
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds
|
[201, 1]
|
[225, 42]
|
simp only [extChartAt_symm_map_nhds' I (f z), Filter.map_map, Function.comp] at h
|
case inr
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h :
Filter.map (β(extChartAt π(β, β) (f z)).symm) (π (β(extChartAt π(β, β) (f z)) (f z))) β€
Filter.map (β(extChartAt π(β, β) (f z)).symm)
(Filter.map
((fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) β β(extChartAt π(β, β) z)) (π z))
β’ π (f z) β€ Filter.map f (π z)
|
case inr
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h :
π (f z) β€
Filter.map
(fun x =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x)))))
(π z)
β’ π (f z) β€ Filter.map f (π z)
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds
|
[201, 1]
|
[225, 42]
|
have e : (fun w β¦ (extChartAt I (f z)).symm
(extChartAt I (f z) (f ((extChartAt I z).symm (extChartAt I z w))))) =αΆ [π z] f := by
apply ((isOpen_extChartAt_source I z).eventually_mem (mem_extChartAt_source I z)).mp
apply (n.holomorphicAt.continuousAt.eventually_mem (extChartAt_source_mem_nhds I (f z))).mp
refine eventually_of_forall fun w fm m β¦ ?_
simp only [PartialEquiv.left_inv _ m, PartialEquiv.left_inv _ fm]
|
case inr
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h :
π (f z) β€
Filter.map
(fun x =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x)))))
(π z)
β’ π (f z) β€ Filter.map f (π z)
|
case inr
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h :
π (f z) β€
Filter.map
(fun x =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x)))))
(π z)
e :
(π z).EventuallyEq
(fun w =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) w)))))
f
β’ π (f z) β€ Filter.map f (π z)
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds
|
[201, 1]
|
[225, 42]
|
rw [Filter.map_congr e] at h
|
case inr
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h :
π (f z) β€
Filter.map
(fun x =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x)))))
(π z)
e :
(π z).EventuallyEq
(fun w =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) w)))))
f
β’ π (f z) β€ Filter.map f (π z)
|
case inr
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h : π (f z) β€ Filter.map f (π z)
e :
(π z).EventuallyEq
(fun w =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) w)))))
f
β’ π (f z) β€ Filter.map f (π z)
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds
|
[201, 1]
|
[225, 42]
|
exact h
|
case inr
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h : π (f z) β€ Filter.map f (π z)
e :
(π z).EventuallyEq
(fun w =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) w)))))
f
β’ π (f z) β€ Filter.map f (π z)
|
no goals
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds
|
[201, 1]
|
[225, 42]
|
apply ((isOpen_extChartAt_source I z).eventually_mem (mem_extChartAt_source I z)).mp
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h :
π (f z) β€
Filter.map
(fun x =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x)))))
(π z)
β’ (π z).EventuallyEq
(fun w =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) w)))))
f
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h :
π (f z) β€
Filter.map
(fun x =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x)))))
(π z)
β’ βαΆ (x : S) in π z,
x β (extChartAt π(β, β) z).source β
(fun w =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) w)))))
x =
f x
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds
|
[201, 1]
|
[225, 42]
|
apply (n.holomorphicAt.continuousAt.eventually_mem (extChartAt_source_mem_nhds I (f z))).mp
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h :
π (f z) β€
Filter.map
(fun x =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x)))))
(π z)
β’ βαΆ (x : S) in π z,
x β (extChartAt π(β, β) z).source β
(fun w =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) w)))))
x =
f x
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h :
π (f z) β€
Filter.map
(fun x =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x)))))
(π z)
β’ βαΆ (x : S) in π z,
f x β (extChartAt π(β, β) (f z)).source β
x β (extChartAt π(β, β) z).source β
(fun w =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) w)))))
x =
f x
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds
|
[201, 1]
|
[225, 42]
|
refine eventually_of_forall fun w fm m β¦ ?_
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h :
π (f z) β€
Filter.map
(fun x =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x)))))
(π z)
β’ βαΆ (x : S) in π z,
f x β (extChartAt π(β, β) (f z)).source β
x β (extChartAt π(β, β) z).source β
(fun w =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) w)))))
x =
f x
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h :
π (f z) β€
Filter.map
(fun x =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x)))))
(π z)
w : S
fm : f w β (extChartAt π(β, β) (f z)).source
m : w β (extChartAt π(β, β) z).source
β’ (fun w =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) w)))))
w =
f w
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds
|
[201, 1]
|
[225, 42]
|
simp only [PartialEquiv.left_inv _ m, PartialEquiv.left_inv _ fm]
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : S β T
z : S
n : NontrivialHolomorphicAt f z
g : β β β
hg : (fun x => β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β g (β(extChartAt π(β, β) z) z)
h :
π (f z) β€
Filter.map
(fun x =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x)))))
(π z)
w : S
fm : f w β (extChartAt π(β, β) (f z)).source
m : w β (extChartAt π(β, β) z).source
β’ (fun w =>
β(extChartAt π(β, β) (f z)).symm
(β(extChartAt π(β, β) (f z)) (f (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) w)))))
w =
f w
|
no goals
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
refine le_antisymm ?_ (continuousAt_fst.prod fa.continuousAt)
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
β’ π (c, f c z) = Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
generalize hg : (fun e x β¦ extChartAt I (f c z) (f e ((extChartAt I z).symm x))) = g
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
have ga : AnalyticAt β (uncurry g) (c, extChartAt I z z) := by
rw [β hg]; exact (holomorphicAt_iff.mp fa).2
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
have gn : NontrivialHolomorphicAt (g c) (extChartAt I z z) := by rw [β hg]; exact n.inCharts
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
have h := gn.nhds_le_map_nhds_param' ga
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
h : π (c, g c (β(extChartAt π(β, β) z) z)) β€ Filter.map (fun p => (p.1, g p.1 p.2)) (π (c, β(extChartAt π(β, β) z) z))
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
simp only [nhds_prod_eq, β extChartAt_map_nhds' I z, Filter.map_map, Filter.prod_map_id_map_eq,
Function.comp] at h
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
h : π (c, g c (β(extChartAt π(β, β) z) z)) β€ Filter.map (fun p => (p.1, g p.1 p.2)) (π (c, β(extChartAt π(β, β) z) z))
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
h :
π c ΓΛ’ π (g c (β(extChartAt π(β, β) z) z)) β€
Filter.map (fun x => (x.1, g x.1 (β(extChartAt π(β, β) z) x.2))) (π c ΓΛ’ π z)
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
replace h := @Filter.map_mono _ _ (fun p : β Γ β β¦ (p.1, (extChartAt I (f c z)).symm p.2)) _ _ h
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
h :
π c ΓΛ’ π (g c (β(extChartAt π(β, β) z) z)) β€
Filter.map (fun x => (x.1, g x.1 (β(extChartAt π(β, β) z) x.2))) (π c ΓΛ’ π z)
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
h :
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2)) (π c ΓΛ’ π (g c (β(extChartAt π(β, β) z) z))) β€
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(Filter.map (fun x => (x.1, g x.1 (β(extChartAt π(β, β) z) x.2))) (π c ΓΛ’ π z))
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
simp only [β hg] at h
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
h :
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2)) (π c ΓΛ’ π (g c (β(extChartAt π(β, β) z) z))) β€
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(Filter.map (fun x => (x.1, g x.1 (β(extChartAt π(β, β) z) x.2))) (π c ΓΛ’ π z))
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
h :
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(π c ΓΛ’ π (β(extChartAt π(β, β) (f c z)) (f c (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) z))))) β€
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(Filter.map
(fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(π c ΓΛ’ π z))
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
rw [PartialEquiv.left_inv _ (mem_extChartAt_source I z)] at h
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
h :
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(π c ΓΛ’ π (β(extChartAt π(β, β) (f c z)) (f c (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) z))))) β€
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(Filter.map
(fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(π c ΓΛ’ π z))
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
h :
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(π c ΓΛ’ π (β(extChartAt π(β, β) (f c z)) (f c z))) β€
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(Filter.map
(fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(π c ΓΛ’ π z))
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
have pe := Filter.prod_map_id_map_eq (f := π c) (g := π (extChartAt I (f c z) (f c z)))
(m := fun x β¦ (extChartAt I (f c z)).symm x)
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
h :
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(π c ΓΛ’ π (β(extChartAt π(β, β) (f c z)) (f c z))) β€
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(Filter.map
(fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(π c ΓΛ’ π z))
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
h :
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(π c ΓΛ’ π (β(extChartAt π(β, β) (f c z)) (f c z))) β€
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(Filter.map
(fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(π c ΓΛ’ π z))
pe :
π c ΓΛ’ Filter.map (fun x => β(extChartAt π(β, β) (f c z)).symm x) (π (β(extChartAt π(β, β) (f c z)) (f c z))) =
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(π c ΓΛ’ π (β(extChartAt π(β, β) (f c z)) (f c z)))
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
rw [extChartAt_symm_map_nhds', βnhds_prod_eq] at pe
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
h :
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(π c ΓΛ’ π (β(extChartAt π(β, β) (f c z)) (f c z))) β€
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(Filter.map
(fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(π c ΓΛ’ π z))
pe :
π c ΓΛ’ Filter.map (fun x => β(extChartAt π(β, β) (f c z)).symm x) (π (β(extChartAt π(β, β) (f c z)) (f c z))) =
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(π c ΓΛ’ π (β(extChartAt π(β, β) (f c z)) (f c z)))
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
h :
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(π c ΓΛ’ π (β(extChartAt π(β, β) (f c z)) (f c z))) β€
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(Filter.map
(fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(π c ΓΛ’ π z))
pe :
π (c, f c z) =
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(π c ΓΛ’ π (β(extChartAt π(β, β) (f c z)) (f c z)))
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
refine _root_.trans (le_of_eq pe) (_root_.trans h (le_of_eq ?_))
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
h :
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(π c ΓΛ’ π (β(extChartAt π(β, β) (f c z)) (f c z))) β€
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(Filter.map
(fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(π c ΓΛ’ π z))
pe :
π (c, f c z) =
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(π c ΓΛ’ π (β(extChartAt π(β, β) (f c z)) (f c z)))
β’ π (c, f c z) β€ Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
h :
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(π c ΓΛ’ π (β(extChartAt π(β, β) (f c z)) (f c z))) β€
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(Filter.map
(fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(π c ΓΛ’ π z))
pe :
π (c, f c z) =
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(π c ΓΛ’ π (β(extChartAt π(β, β) (f c z)) (f c z)))
β’ Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(Filter.map
(fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(π c ΓΛ’ π z)) =
Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
clear h pe
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
h :
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(π c ΓΛ’ π (β(extChartAt π(β, β) (f c z)) (f c z))) β€
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(Filter.map
(fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(π c ΓΛ’ π z))
pe :
π (c, f c z) =
Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(π c ΓΛ’ π (β(extChartAt π(β, β) (f c z)) (f c z)))
β’ Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(Filter.map
(fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(π c ΓΛ’ π z)) =
Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
β’ Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(Filter.map
(fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(π c ΓΛ’ π z)) =
Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
rw [βnhds_prod_eq, Filter.map_map]
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
β’ Filter.map (fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2))
(Filter.map
(fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(π c ΓΛ’ π z)) =
Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
β’ Filter.map
((fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2)) β fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(π (c, z)) =
Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
apply Filter.map_congr
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
β’ Filter.map
((fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2)) β fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(π (c, z)) =
Filter.map (fun p => (p.1, f p.1 p.2)) (π (c, z))
|
case h
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
β’ (π (c, z)).EventuallyEq
((fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2)) β fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
fun p => (p.1, f p.1 p.2)
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
apply ((isOpen_extChartAt_source II (c, z)).eventually_mem (mem_extChartAt_source II (c, z))).mp
|
case h
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
β’ (π (c, z)).EventuallyEq
((fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2)) β fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
fun p => (p.1, f p.1 p.2)
|
case h
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
β’ βαΆ (x : β Γ S) in π (c, z),
x β (extChartAt (π(β, β).prod π(β, β)) (c, z)).source β
((fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2)) β fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
x =
(fun p => (p.1, f p.1 p.2)) x
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
apply (fa.continuousAt.eventually_mem (extChartAt_source_mem_nhds I (f c z))).mp
|
case h
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
β’ βαΆ (x : β Γ S) in π (c, z),
x β (extChartAt (π(β, β).prod π(β, β)) (c, z)).source β
((fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2)) β fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
x =
(fun p => (p.1, f p.1 p.2)) x
|
case h
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
β’ βαΆ (x : β Γ S) in π (c, z),
uncurry f x β (extChartAt π(β, β) (f c z)).source β
x β (extChartAt (π(β, β).prod π(β, β)) (c, z)).source β
((fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2)) β fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
x =
(fun p => (p.1, f p.1 p.2)) x
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
apply eventually_of_forall
|
case h
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
β’ βαΆ (x : β Γ S) in π (c, z),
uncurry f x β (extChartAt π(β, β) (f c z)).source β
x β (extChartAt (π(β, β).prod π(β, β)) (c, z)).source β
((fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2)) β fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
x =
(fun p => (p.1, f p.1 p.2)) x
|
case h.hp
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
β’ β (x : β Γ S),
uncurry f x β (extChartAt π(β, β) (f c z)).source β
x β (extChartAt (π(β, β).prod π(β, β)) (c, z)).source β
((fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2)) β fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
x =
(fun p => (p.1, f p.1 p.2)) x
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
intro β¨e, wβ© fm m
|
case h.hp
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
β’ β (x : β Γ S),
uncurry f x β (extChartAt π(β, β) (f c z)).source β
x β (extChartAt (π(β, β).prod π(β, β)) (c, z)).source β
((fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2)) β fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
x =
(fun p => (p.1, f p.1 p.2)) x
|
case h.hp
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
e : β
w : S
fm : uncurry f (e, w) β (extChartAt π(β, β) (f c z)).source
m : (e, w) β (extChartAt (π(β, β).prod π(β, β)) (c, z)).source
β’ ((fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2)) β fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(e, w) =
(fun p => (p.1, f p.1 p.2)) (e, w)
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
simp only [Function.comp, uncurry, extChartAt_prod, PartialEquiv.prod_source, mem_prod_eq] at fm m
|
case h.hp
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
e : β
w : S
fm : uncurry f (e, w) β (extChartAt π(β, β) (f c z)).source
m : (e, w) β (extChartAt (π(β, β).prod π(β, β)) (c, z)).source
β’ ((fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2)) β fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(e, w) =
(fun p => (p.1, f p.1 p.2)) (e, w)
|
case h.hp
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
e : β
w : S
fm : f e w β (extChartAt π(β, β) (f c z)).source
m : e β (extChartAt π(β, β) c).source β§ w β (extChartAt π(β, β) z).source
β’ ((fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2)) β fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(e, w) =
(fun p => (p.1, f p.1 p.2)) (e, w)
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
simp only [Function.comp, PartialEquiv.left_inv _ m.2, PartialEquiv.left_inv _ fm]
|
case h.hp
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
gn : NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
e : β
w : S
fm : f e w β (extChartAt π(β, β) (f c z)).source
m : e β (extChartAt π(β, β) c).source β§ w β (extChartAt π(β, β) z).source
β’ ((fun p => (p.1, β(extChartAt π(β, β) (f c z)).symm p.2)) β fun x =>
(x.1, β(extChartAt π(β, β) (f c z)) (f x.1 (β(extChartAt π(β, β) z).symm (β(extChartAt π(β, β) z) x.2)))))
(e, w) =
(fun p => (p.1, f p.1 p.2)) (e, w)
|
no goals
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
rw [β hg]
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
β’ AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
β’ AnalyticAt β (uncurry fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x)))
(c, β(extChartAt π(β, β) z) z)
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
exact (holomorphicAt_iff.mp fa).2
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
β’ AnalyticAt β (uncurry fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x)))
(c, β(extChartAt π(β, β) z) z)
|
no goals
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
rw [β hg]
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
β’ NontrivialHolomorphicAt (g c) (β(extChartAt π(β, β) z) z)
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
β’ NontrivialHolomorphicAt ((fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) c)
(β(extChartAt π(β, β) z) z)
|
https://github.com/girving/ray.git
|
0be790285dd0fce78913b0cb9bddaffa94bd25f9
|
Ray/AnalyticManifold/OpenMapping.lean
|
NontrivialHolomorphicAt.nhds_eq_map_nhds_param
|
[234, 1]
|
[258, 85]
|
exact n.inCharts
|
X : Type
instββΆ : TopologicalSpace X
S : Type
instββ΅ : TopologicalSpace S
instββ΄ : ChartedSpace β S
cms : AnalyticManifold π(β, β) S
T : Type
instβΒ³ : TopologicalSpace T
instβΒ² : ChartedSpace β T
cmt : AnalyticManifold π(β, β) T
U : Type
instβΒΉ : TopologicalSpace U
instβ : ChartedSpace β U
cmu : AnalyticManifold π(β, β) U
f : β β S β T
c : β
z : S
n : NontrivialHolomorphicAt (f c) z
fa : HolomorphicAt (π(β, β).prod π(β, β)) π(β, β) (uncurry f) (c, z)
g : β β β β β
hg : (fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) = g
ga : AnalyticAt β (uncurry g) (c, β(extChartAt π(β, β) z) z)
β’ NontrivialHolomorphicAt ((fun e x => β(extChartAt π(β, β) (f c z)) (f e (β(extChartAt π(β, β) z).symm x))) c)
(β(extChartAt π(β, β) z) z)
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Option.bind_const_none
|
[23, 1]
|
[24, 22]
|
cases x <;> simp
|
Ξ± : Type u_1
Ξ² : Type u_2
x : Option Ξ±
β’ (Option.bind x fun x => none) = none
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Option.isNone_false_iff_isSome
|
[28, 1]
|
[29, 22]
|
cases x <;> simp
|
Ξ± : Type u_1
x : Option Ξ±
β’ isNone x = false β isSome x = true
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Fin.tuple_sequenceβ
|
[56, 1]
|
[58, 41]
|
simp [Fin.tupleSequence, functor_norm]
|
m : Type u β Type v
instβΒΉ : Monad m
instβ : LawfulMonad m
Ξ± : Fin 1 β Type u
x : (i : Fin 1) β m (Ξ± i)
β’ tupleSequence x = do
let rβ β x 0
pure (cons rβ default)
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Fin.tuple_sequenceβ
|
[62, 1]
|
[66, 6]
|
simp [Fin.tupleSequence, functor_norm]
|
m : Type u β Type v
instβΒΉ : Monad m
instβ : LawfulMonad m
Ξ± : Fin 2 β Type u
x : (i : Fin 2) β m (Ξ± i)
β’ tupleSequence x = do
let rβ β x 0
let rβ β x 1
pure (cons rβ (cons rβ default))
|
m : Type u β Type v
instβΒΉ : Monad m
instβ : LawfulMonad m
Ξ± : Fin 2 β Type u
x : (i : Fin 2) β m (Ξ± i)
β’ (do
let r β x 0
let x β tail x 0
pure (cons r (cons x default))) =
do
let rβ β x 0
let rβ β x 1
pure (cons rβ (cons rβ default))
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Fin.tuple_sequenceβ
|
[62, 1]
|
[66, 6]
|
rfl
|
m : Type u β Type v
instβΒΉ : Monad m
instβ : LawfulMonad m
Ξ± : Fin 2 β Type u
x : (i : Fin 2) β m (Ξ± i)
β’ (do
let r β x 0
let x β tail x 0
pure (cons r (cons x default))) =
do
let rβ β x 0
let rβ β x 1
pure (cons rβ (cons rβ default))
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Option.bind_isSome
|
[74, 1]
|
[75, 84]
|
cases x <;> simp
|
m : Type u β Type v
instβ : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
x : Option Ξ±
y : Ξ± β Option Ξ²
β’ isSome (Option.bind x y) = true β β (h : isSome x = true), isSome (y (get x h)) = true
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Option.map_isSome
|
[79, 1]
|
[80, 19]
|
cases x <;> simp
|
m : Type u β Type v
instβ : Monad m
Ξ± Ξ² : Type u_1
x : Option Ξ±
y : Ξ± β Ξ²
β’ isSome (y <$> x) = isSome x
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Option.not_isSome'
|
[84, 1]
|
[84, 92]
|
cases x <;> simp
|
m : Type u β Type v
instβ : Monad m
Ξ± : Type u_1
x : Option Ξ±
β’ (!decide (isSome x = isNone x)) = true
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Option.guardProp_isSome
|
[92, 1]
|
[95, 22]
|
dsimp only [Option.guardProp]
|
m : Type u β Type v
instβΒΉ : Monad m
Ξ± : Type u_1
p : Prop
instβ : Decidable p
x : Ξ±
β’ isSome (guardProp p x) = true β p
|
m : Type u β Type v
instβΒΉ : Monad m
Ξ± : Type u_1
p : Prop
instβ : Decidable p
x : Ξ±
β’ isSome (if p then some x else none) = true β p
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Option.guardProp_isSome
|
[92, 1]
|
[95, 22]
|
split_ifs <;> simpa
|
m : Type u β Type v
instβΒΉ : Monad m
Ξ± : Type u_1
p : Prop
instβ : Decidable p
x : Ξ±
β’ isSome (if p then some x else none) = true β p
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Option.coe_part_dom
|
[99, 1]
|
[99, 100]
|
cases x <;> simp
|
m : Type u β Type v
instβ : Monad m
Ξ± : Type u_1
x : Option Ξ±
β’ (βx).Dom β isSome x = true
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Option.coe_part_eq_some
|
[103, 1]
|
[104, 74]
|
simp [Part.eq_some_iff]
|
m : Type u β Type v
instβ : Monad m
Ξ± : Type u_1
x : Option Ξ±
y : Ξ±
β’ βx = Part.some y β x = some y
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
List.get?_isSome_iff
|
[108, 1]
|
[110, 35]
|
rw [β not_iff_not]
|
m : Type u β Type v
instβ : Monad m
Ξ± : Type u_1
x : List Ξ±
n : β
β’ Option.isSome (get? x n) = true β n < length x
|
m : Type u β Type v
instβ : Monad m
Ξ± : Type u_1
x : List Ξ±
n : β
β’ Β¬Option.isSome (get? x n) = true β Β¬n < length x
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
List.get?_isSome_iff
|
[108, 1]
|
[110, 35]
|
simp [Option.isNone_iff_eq_none]
|
m : Type u β Type v
instβ : Monad m
Ξ± : Type u_1
x : List Ξ±
n : β
β’ Β¬Option.isSome (get? x n) = true β Β¬n < length x
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Option.map_is_some'
|
[114, 1]
|
[115, 19]
|
cases x <;> simp
|
m : Type u β Type v
instβ : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
x : Option Ξ±
f : Ξ± β Ξ²
β’ isSome (Option.map f x) = isSome x
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
List.zipWith_fst
|
[118, 1]
|
[121, 11]
|
erw [β List.map_uncurry_zip_eq_zipWith, List.map_fst_zip]
|
m : Type u β Type v
instβ : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
lβ : List Ξ±
lβ : List Ξ²
hl : length lβ β€ length lβ
β’ zipWith (fun a b => a) lβ lβ = lβ
|
case a
m : Type u β Type v
instβ : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
lβ : List Ξ±
lβ : List Ξ²
hl : length lβ β€ length lβ
β’ length lβ β€ length lβ
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
List.zipWith_fst
|
[118, 1]
|
[121, 11]
|
exact hl
|
case a
m : Type u β Type v
instβ : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
lβ : List Ξ±
lβ : List Ξ²
hl : length lβ β€ length lβ
β’ length lβ β€ length lβ
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
List.zipWith_snd
|
[124, 1]
|
[127, 11]
|
erw [β List.map_uncurry_zip_eq_zipWith, List.map_snd_zip]
|
m : Type u β Type v
instβ : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
lβ : List Ξ±
lβ : List Ξ²
hl : length lβ β€ length lβ
β’ zipWith (fun a b => b) lβ lβ = lβ
|
case a
m : Type u β Type v
instβ : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
lβ : List Ξ±
lβ : List Ξ²
hl : length lβ β€ length lβ
β’ length lβ β€ length lβ
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
List.zipWith_snd
|
[124, 1]
|
[127, 11]
|
exact hl
|
case a
m : Type u β Type v
instβ : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
lβ : List Ξ±
lβ : List Ξ²
hl : length lβ β€ length lβ
β’ length lβ β€ length lβ
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Multiset.map_get
|
[134, 1]
|
[136, 36]
|
simp [Finset.univ, Fintype.elems]
|
m : Type u β Type v
instβ : Monad m
Ξ± : Type u_1
l : List Ξ±
β’ map (List.get l) Finset.univ.val = βl
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Multiset.get_zero
|
[142, 1]
|
[142, 88]
|
simp [Multiset.get]
|
m : Type u β Type v
instβ : Monad m
Ξ± : Type u_1
β’ get 0 = none
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Multiset.get_singleton
|
[144, 1]
|
[144, 105]
|
simp [Multiset.get]
|
m : Type u β Type v
instβ : Monad m
Ξ± : Type u_1
a : Ξ±
β’ get {a} = some a
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
le_false_iff
|
[147, 1]
|
[147, 72]
|
decide
|
m : Type u β Type v
instβ : Monad m
β’ β {b : Bool}, b β€ false β b = false
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
lt_true_iff
|
[151, 1]
|
[151, 70]
|
decide
|
m : Type u β Type v
instβ : Monad m
β’ β {b : Bool}, b < true β b = false
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
false_lt_iff
|
[155, 1]
|
[155, 71]
|
decide
|
m : Type u β Type v
instβ : Monad m
β’ β {b : Bool}, false < b β b = true
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
ne_min_of_ne_and_ne
|
[158, 1]
|
[159, 81]
|
rcases min_choice x y with h | h <;> rw [h] <;> assumption
|
m : Type u β Type v
instβΒΉ : Monad m
ΞΉ : Type u_1
instβ : LinearOrder ΞΉ
a x y : ΞΉ
hx : a β x
hy : a β y
β’ a β min x y
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
max_ne_self_iff
|
[163, 1]
|
[167, 31]
|
rw [max_def]
|
m : Type u β Type v
instβΒΉ : Monad m
ΞΉ : Type u_1
instβ : LinearOrder ΞΉ
a b : ΞΉ
β’ Β¬a = max a b β a < b
|
m : Type u β Type v
instβΒΉ : Monad m
ΞΉ : Type u_1
instβ : LinearOrder ΞΉ
a b : ΞΉ
β’ (Β¬a = if a β€ b then b else a) β a < b
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
max_ne_self_iff
|
[163, 1]
|
[167, 31]
|
split_ifs with h
|
m : Type u β Type v
instβΒΉ : Monad m
ΞΉ : Type u_1
instβ : LinearOrder ΞΉ
a b : ΞΉ
β’ (Β¬a = if a β€ b then b else a) β a < b
|
case pos
m : Type u β Type v
instβΒΉ : Monad m
ΞΉ : Type u_1
instβ : LinearOrder ΞΉ
a b : ΞΉ
h : a β€ b
β’ Β¬a = b β a < b
case neg
m : Type u β Type v
instβΒΉ : Monad m
ΞΉ : Type u_1
instβ : LinearOrder ΞΉ
a b : ΞΉ
h : Β¬a β€ b
β’ Β¬a = a β a < b
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
max_ne_self_iff
|
[163, 1]
|
[167, 31]
|
simpa using h
|
case pos
m : Type u β Type v
instβΒΉ : Monad m
ΞΉ : Type u_1
instβ : LinearOrder ΞΉ
a b : ΞΉ
h : a β€ b
β’ Β¬a = b β a < b
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
max_ne_self_iff
|
[163, 1]
|
[167, 31]
|
simpa using le_of_not_ge h
|
case neg
m : Type u β Type v
instβΒΉ : Monad m
ΞΉ : Type u_1
instβ : LinearOrder ΞΉ
a b : ΞΉ
h : Β¬a β€ b
β’ Β¬a = a β a < b
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
max_ne_self_iff'
|
[171, 1]
|
[172, 22]
|
rw [max_comm]
|
m : Type u β Type v
instβΒΉ : Monad m
ΞΉ : Type u_1
instβ : LinearOrder ΞΉ
a b : ΞΉ
β’ Β¬b = max a b β b < a
|
m : Type u β Type v
instβΒΉ : Monad m
ΞΉ : Type u_1
instβ : LinearOrder ΞΉ
a b : ΞΉ
β’ Β¬b = max b a β b < a
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
max_ne_self_iff'
|
[171, 1]
|
[172, 22]
|
simp
|
m : Type u β Type v
instβΒΉ : Monad m
ΞΉ : Type u_1
instβ : LinearOrder ΞΉ
a b : ΞΉ
β’ Β¬b = max b a β b < a
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
WithTop.isSome_iff_lt_top
|
[180, 1]
|
[183, 6]
|
rw [β not_iff_not, Bool.eq_false_eq_not_eq_true, Option.not_isSome, Option.isNone_iff_eq_none,
lt_top_iff_ne_top, Ne, Classical.not_not]
|
m : Type u β Type v
instβΒΉ : Monad m
ΞΉ : Type
instβ : PartialOrder ΞΉ
x : WithTop ΞΉ
β’ Option.isSome x = true β x < β€
|
m : Type u β Type v
instβΒΉ : Monad m
ΞΉ : Type
instβ : PartialOrder ΞΉ
x : WithTop ΞΉ
β’ x = none β x = β€
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
WithTop.isSome_iff_lt_top
|
[180, 1]
|
[183, 6]
|
rfl
|
m : Type u β Type v
instβΒΉ : Monad m
ΞΉ : Type
instβ : PartialOrder ΞΉ
x : WithTop ΞΉ
β’ x = none β x = β€
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.le_iff''
|
[233, 1]
|
[237, 8]
|
rw [Prod.Lex.le_iff', le_iff_lt_or_eq]
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : PartialOrder Ξ±
instβ : Preorder Ξ²
x y : Lex (Ξ± Γ Ξ²)
β’ x β€ y β x.1 β€ y.1 β§ (x.1 = y.1 β x.2 β€ y.2)
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : PartialOrder Ξ±
instβ : Preorder Ξ²
x y : Lex (Ξ± Γ Ξ²)
β’ x.1 < y.1 β¨ x.1 = y.1 β§ x.2 β€ y.2 β (x.1 < y.1 β¨ x.1 = y.1) β§ (x.1 = y.1 β x.2 β€ y.2)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.le_iff''
|
[233, 1]
|
[237, 8]
|
have := @ne_of_lt _ _ x.1 y.1
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : PartialOrder Ξ±
instβ : Preorder Ξ²
x y : Lex (Ξ± Γ Ξ²)
β’ x.1 < y.1 β¨ x.1 = y.1 β§ x.2 β€ y.2 β (x.1 < y.1 β¨ x.1 = y.1) β§ (x.1 = y.1 β x.2 β€ y.2)
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : PartialOrder Ξ±
instβ : Preorder Ξ²
x y : Lex (Ξ± Γ Ξ²)
this : x.1 < y.1 β x.1 β y.1
β’ x.1 < y.1 β¨ x.1 = y.1 β§ x.2 β€ y.2 β (x.1 < y.1 β¨ x.1 = y.1) β§ (x.1 = y.1 β x.2 β€ y.2)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.le_iff''
|
[233, 1]
|
[237, 8]
|
tauto
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : PartialOrder Ξ±
instβ : Preorder Ξ²
x y : Lex (Ξ± Γ Ξ²)
this : x.1 < y.1 β x.1 β y.1
β’ x.1 < y.1 β¨ x.1 = y.1 β§ x.2 β€ y.2 β (x.1 < y.1 β¨ x.1 = y.1) β§ (x.1 = y.1 β x.2 β€ y.2)
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.lt_iff''
|
[244, 1]
|
[248, 8]
|
rw [lt_iff', le_iff_lt_or_eq]
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : PartialOrder Ξ±
instβ : Preorder Ξ²
x y : Lex (Ξ± Γ Ξ²)
β’ x < y β x.1 β€ y.1 β§ (x.1 = y.1 β x.2 < y.2)
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : PartialOrder Ξ±
instβ : Preorder Ξ²
x y : Lex (Ξ± Γ Ξ²)
β’ x.1 < y.1 β¨ x.1 = y.1 β§ x.2 < y.2 β (x.1 < y.1 β¨ x.1 = y.1) β§ (x.1 = y.1 β x.2 < y.2)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.lt_iff''
|
[244, 1]
|
[248, 8]
|
have : x.1 < y.1 β Β¬x.1 = y.1 := ne_of_lt
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : PartialOrder Ξ±
instβ : Preorder Ξ²
x y : Lex (Ξ± Γ Ξ²)
β’ x.1 < y.1 β¨ x.1 = y.1 β§ x.2 < y.2 β (x.1 < y.1 β¨ x.1 = y.1) β§ (x.1 = y.1 β x.2 < y.2)
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : PartialOrder Ξ±
instβ : Preorder Ξ²
x y : Lex (Ξ± Γ Ξ²)
this : x.1 < y.1 β Β¬x.1 = y.1
β’ x.1 < y.1 β¨ x.1 = y.1 β§ x.2 < y.2 β (x.1 < y.1 β¨ x.1 = y.1) β§ (x.1 = y.1 β x.2 < y.2)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.lt_iff''
|
[244, 1]
|
[248, 8]
|
tauto
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : PartialOrder Ξ±
instβ : Preorder Ξ²
x y : Lex (Ξ± Γ Ξ²)
this : x.1 < y.1 β Β¬x.1 = y.1
β’ x.1 < y.1 β¨ x.1 = y.1 β§ x.2 < y.2 β (x.1 < y.1 β¨ x.1 = y.1) β§ (x.1 = y.1 β x.2 < y.2)
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.fst_le_of_le
|
[251, 1]
|
[255, 26]
|
rw [Prod.Lex.le_iff'] at h
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : Preorder Ξ±
instβ : Preorder Ξ²
x y : Lex (Ξ± Γ Ξ²)
h : x β€ y
β’ x.1 β€ y.1
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : Preorder Ξ±
instβ : Preorder Ξ²
x y : Lex (Ξ± Γ Ξ²)
h : x.1 < y.1 β¨ x.1 = y.1 β§ x.2 β€ y.2
β’ x.1 β€ y.1
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.fst_le_of_le
|
[251, 1]
|
[255, 26]
|
cases h with
| inl h => exact h.le
| inr h => exact h.1.le
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : Preorder Ξ±
instβ : Preorder Ξ²
x y : Lex (Ξ± Γ Ξ²)
h : x.1 < y.1 β¨ x.1 = y.1 β§ x.2 β€ y.2
β’ x.1 β€ y.1
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.fst_le_of_le
|
[251, 1]
|
[255, 26]
|
exact h.le
|
case inl
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : Preorder Ξ±
instβ : Preorder Ξ²
x y : Lex (Ξ± Γ Ξ²)
h : x.1 < y.1
β’ x.1 β€ y.1
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.fst_le_of_le
|
[251, 1]
|
[255, 26]
|
exact h.1.le
|
case inr
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : Preorder Ξ±
instβ : Preorder Ξ²
x y : Lex (Ξ± Γ Ξ²)
h : x.1 = y.1 β§ x.2 β€ y.2
β’ x.1 β€ y.1
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.fst_lt_of_lt_of_le
|
[258, 1]
|
[263, 33]
|
rw [Prod.Lex.lt_iff'] at h
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : Preorder Ξ±
instβ : PartialOrder Ξ²
x y : Lex (Ξ± Γ Ξ²)
h : x < y
h' : y.2 β€ x.2
β’ x.1 < y.1
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : Preorder Ξ±
instβ : PartialOrder Ξ²
x y : Lex (Ξ± Γ Ξ²)
h : x.1 < y.1 β¨ x.1 = y.1 β§ x.2 < y.2
h' : y.2 β€ x.2
β’ x.1 < y.1
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.fst_lt_of_lt_of_le
|
[258, 1]
|
[263, 33]
|
cases h with
| inl h => exact h
| inr h => cases h.2.not_le h'
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : Preorder Ξ±
instβ : PartialOrder Ξ²
x y : Lex (Ξ± Γ Ξ²)
h : x.1 < y.1 β¨ x.1 = y.1 β§ x.2 < y.2
h' : y.2 β€ x.2
β’ x.1 < y.1
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.fst_lt_of_lt_of_le
|
[258, 1]
|
[263, 33]
|
exact h
|
case inl
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : Preorder Ξ±
instβ : PartialOrder Ξ²
x y : Lex (Ξ± Γ Ξ²)
h' : y.2 β€ x.2
h : x.1 < y.1
β’ x.1 < y.1
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.fst_lt_of_lt_of_le
|
[258, 1]
|
[263, 33]
|
cases h.2.not_le h'
|
case inr
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : Preorder Ξ±
instβ : PartialOrder Ξ²
x y : Lex (Ξ± Γ Ξ²)
h' : y.2 β€ x.2
h : x.1 = y.1 β§ x.2 < y.2
β’ x.1 < y.1
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.mk_fst_mono_iff
|
[275, 1]
|
[276, 56]
|
simp [le_iff']
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : Preorder Ξ±
instβ : Preorder Ξ²
x : Ξ±
yβ yβ : Ξ²
β’ (x, yβ) β€ (x, yβ) β yβ β€ yβ
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.mk_fst_mono_lt_iff
|
[280, 1]
|
[281, 56]
|
simp [lt_iff']
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : Preorder Ξ±
instβ : Preorder Ξ²
x : Ξ±
yβ yβ : Ξ²
β’ (x, yβ) < (x, yβ) β yβ < yβ
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.mk_snd_mono_le_iff
|
[285, 1]
|
[286, 57]
|
simp [le_iff'']
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : PartialOrder Ξ±
instβ : Preorder Ξ²
xβ xβ : Ξ±
y : Ξ²
β’ (xβ, y) β€ (xβ, y) β xβ β€ xβ
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.mk_snd_mono_lt_iff
|
[290, 1]
|
[291, 56]
|
simp [lt_iff']
|
m : Type u β Type v
instβΒ² : Monad m
Ξ± : Type u_1
Ξ² : Type u_2
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβΒΉ : Preorder Ξ±
instβ : Preorder Ξ²
xβ xβ : Ξ±
y : Ξ²
β’ (xβ, y) < (xβ, y) β xβ < xβ
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.mk_false_lt_mk_true_iff
|
[295, 1]
|
[296, 96]
|
simp [lt_iff', le_iff_lt_or_eq]
|
m : Type u β Type v
instβΒΉ : Monad m
Ξ± : Type u_1
Ξ² : Type ?u.49210
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβ : PartialOrder Ξ±
xβ xβ : Ξ±
β’ (xβ, false) < (xβ, true) β xβ β€ xβ
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.mk_true_le_mk_false_iff_lt
|
[300, 1]
|
[301, 75]
|
simp [le_iff']
|
m : Type u β Type v
instβΒΉ : Monad m
Ξ± : Type u_1
Ξ² : Type ?u.50081
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβ : PartialOrder Ξ±
x y : Ξ±
β’ (x, true) β€ (y, false) β x < y
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.mk_true_lt_iff_lt
|
[305, 1]
|
[306, 68]
|
simp [lt_iff']
|
m : Type u β Type v
instβΒΉ : Monad m
Ξ± : Type u_1
Ξ² : Type ?u.51649
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβ : PartialOrder Ξ±
x : Ξ±
y : Lex (Ξ± Γ Bool)
β’ (x, true) < y β x < y.1
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/Misc.lean
|
Prod.Lex.lt_mk_true_iff
|
[308, 1]
|
[310, 26]
|
simp [lt_iff', le_iff']
|
m : Type u β Type v
instβΒΉ : Monad m
Ξ± : Type u_1
Ξ² : Type ?u.53384
rβ : Ξ± β Ξ± β Prop
rβ : Ξ² β Ξ² β Prop
instβ : PartialOrder Ξ±
x : Lex (Ξ± Γ Bool)
y : Ξ±
β’ x < (y, true) β x β€ (y, false)
|
no goals
|
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