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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