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/Dynamics/BottcherNear.lean | SuperAtC.ga_of_fa | [527, 1] | [537, 73] | exact m | case refine_2
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
t : Set (ℂ × ℂ)
o : IsOpen t
fa : AnalyticOn ℂ (uncurry f) t
tc : ∀ {p : ℂ × ℂ}, p ∈ t → p.1 ∈ u
c z : ℂ
m : (c, z) ∈ t
⊢ (c, id z) ∈ t | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | set tu := ⋃ i, t i | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
⊢ SuperNearC f d (⋃ i, u i) (⋃ i, t i) | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
⊢ SuperNearC f d (⋃ i, u i) tu |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | have o : IsOpen tu := isOpen_iUnion fun i ↦ (s i).o | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
⊢ SuperNearC f d (⋃ i, u i) tu | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
⊢ SuperNearC f d (⋃ i, u i) tu |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | exact
{ o
tc := by
intro p m; rcases Set.mem_iUnion.mp m with ⟨i, m⟩
exact Set.subset_iUnion _ i ((s i).tc m)
fa := by intro p m; rcases Set.mem_iUnion.mp m with ⟨i, m⟩; exact (s i).fa _ m
s := by
intro c m; rcases Set.mem_iUnion.mp m with ⟨i, m⟩; have s := (s i).s m
exact
... | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
⊢ SuperNearC f d (⋃ i, u i) tu | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | intro c z m | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
⊢ ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
c z : ℂ
m : (c, z) ∈ tu
⊢ ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | rcases Set.mem_iUnion.mp m with ⟨i, m⟩ | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
c z : ℂ
m : (c, z) ∈ tu
⊢ ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u | case intro
f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
c z : ℂ
m✝ : (c, z) ∈ tu
i : I
m : (c, z) ∈ t i
⊢ ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | use{z | (c, z) ∈ t i} | case intro
f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
c z : ℂ
m✝ : (c, z) ∈ tu
i : I
m : (c, z) ∈ t i
⊢ ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u | case h
f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
c z : ℂ
m✝ : (c, z) ∈ tu
i : I
m : (c, z) ∈ t i
⊢ z ∈ {z | (c, z) ∈ t i} ∧ {z | (c, z) ∈ t i} ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d {z ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | simp only [Set.mem_setOf_eq, m, Set.mem_iUnion, Set.setOf_subset_setOf, true_and, tu] | case h
f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
c z : ℂ
m✝ : (c, z) ∈ tu
i : I
m : (c, z) ∈ t i
⊢ z ∈ {z | (c, z) ∈ t i} ∧ {z | (c, z) ∈ t i} ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d {z ... | case h
f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
c z : ℂ
m✝ : (c, z) ∈ tu
i : I
m : (c, z) ∈ t i
⊢ (∀ (a : ℂ), (c, a) ∈ t i → ∃ i, (c, a) ∈ t i) ∧ SuperNear (f c) d {z | (c, z) ∈ t i} |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | constructor | case h
f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
c z : ℂ
m✝ : (c, z) ∈ tu
i : I
m : (c, z) ∈ t i
⊢ (∀ (a : ℂ), (c, a) ∈ t i → ∃ i, (c, a) ∈ t i) ∧ SuperNear (f c) d {z | (c, z) ∈ t i} | case h.left
f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
c z : ℂ
m✝ : (c, z) ∈ tu
i : I
m : (c, z) ∈ t i
⊢ ∀ (a : ℂ), (c, a) ∈ t i → ∃ i, (c, a) ∈ t i
case h.right
f : ℂ → ℂ → ℂ
d : ℕ
u✝ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | exact fun z m ↦ ⟨i, m⟩ | case h.left
f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
c z : ℂ
m✝ : (c, z) ∈ tu
i : I
m : (c, z) ∈ t i
⊢ ∀ (a : ℂ), (c, a) ∈ t i → ∃ i, (c, a) ∈ t i | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | exact (s i).s ((s i).tc m) | case h.right
f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
c z : ℂ
m✝ : (c, z) ∈ tu
i : I
m : (c, z) ∈ t i
⊢ SuperNear (f c) d {z | (c, z) ∈ t i} | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | intro p m | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
⊢ ∀ {p : ℂ × ℂ}, p ∈ tu → p.1 ∈ ⋃ i, u i | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
p : ℂ × ℂ
m : p ∈ tu
⊢ p.1 ∈ ⋃ i, u i |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | rcases Set.mem_iUnion.mp m with ⟨i, m⟩ | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
p : ℂ × ℂ
m : p ∈ tu
⊢ p.1 ∈ ⋃ i, u i | case intro
f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
p : ℂ × ℂ
m✝ : p ∈ tu
i : I
m : p ∈ t i
⊢ p.... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | exact Set.subset_iUnion _ i ((s i).tc m) | case intro
f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
p : ℂ × ℂ
m✝ : p ∈ tu
i : I
m : p ∈ t i
⊢ p.... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | intro p m | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
⊢ AnalyticOn ℂ (uncurry f) tu | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
p : ℂ × ℂ
m : p ∈ tu
⊢ AnalyticAt ℂ (uncurry f) p |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | rcases Set.mem_iUnion.mp m with ⟨i, m⟩ | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
p : ℂ × ℂ
m : p ∈ tu
⊢ AnalyticAt ℂ (uncurry f) p | case intro
f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
p : ℂ × ℂ
m✝ : p ∈ tu
i : I
m : p ∈ t i
⊢ An... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | exact (s i).fa _ m | case intro
f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
p : ℂ × ℂ
m✝ : p ∈ tu
i : I
m : p ∈ t i
⊢ An... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | intro c m | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
⊢ ∀ {c : ℂ}, c ∈ ⋃ i, u i → SuperNear (f c) d {z | (c, ... | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m : c ∈ ⋃ i, u i
⊢ SuperNear (f c) d {z | (c, z) ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | rcases Set.mem_iUnion.mp m with ⟨i, m⟩ | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m : c ∈ ⋃ i, u i
⊢ SuperNear (f c) d {z | (c, z) ... | case intro
f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝ : c ∈ ⋃ i, u i
i : I
m : c ∈ u i
⊢ ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | have s := (s i).s m | case intro
f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝ : c ∈ ⋃ i, u i
i : I
m : c ∈ u i
⊢ ... | case intro
f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝ : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝ : c ∈ ⋃ i, u i
i : I
m : c ∈ u i
s... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | exact
{ d2 := s.d2
fa0 := s.fa0
fd := s.fd
fc := s.fc
o := o.snd_preimage c
t0 := Set.subset_iUnion _ i s.t0
t2 := by intro z m; rcases sm m with ⟨u, m, _, s⟩; exact s.t2 m
fa := by intro z m; rcases sm m with ⟨u, m, _, s⟩; exact s.fa _ m
ft := by intro z m; rcases sm m with ⟨u, m, us,... | case intro
f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝ : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝ : c ∈ ⋃ i, u i
i : I
m : c ∈ u i
s... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | intro z m | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝ : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝ : c ∈ ⋃ i, u i
i : I
m : c ∈ u i
s : SuperNea... | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝ : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝¹ : c ∈ ⋃ i, u i
i : I
m✝ : c ∈ u i
s : SuperN... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | rcases sm m with ⟨u, m, _, s⟩ | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝ : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝¹ : c ∈ ⋃ i, u i
i : I
m✝ : c ∈ u i
s : SuperN... | case intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u✝¹ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u✝ : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝¹ : ∀ (i : I), SuperNearC f d (u✝ i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝² : c ∈ ⋃ i, u✝ i
i... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | exact s.t2 m | case intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u✝¹ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u✝ : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝¹ : ∀ (i : I), SuperNearC f d (u✝ i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝² : c ∈ ⋃ i, u✝ i
i... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | intro z m | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝ : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝ : c ∈ ⋃ i, u i
i : I
m : c ∈ u i
s : SuperNea... | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝ : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝¹ : c ∈ ⋃ i, u i
i : I
m✝ : c ∈ u i
s : SuperN... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | rcases sm m with ⟨u, m, _, s⟩ | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝ : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝¹ : c ∈ ⋃ i, u i
i : I
m✝ : c ∈ u i
s : SuperN... | case intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u✝¹ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u✝ : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝¹ : ∀ (i : I), SuperNearC f d (u✝ i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝² : c ∈ ⋃ i, u✝ i
i... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | exact s.fa _ m | case intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u✝¹ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u✝ : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝¹ : ∀ (i : I), SuperNearC f d (u✝ i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝² : c ∈ ⋃ i, u✝ i
i... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | intro z m | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝ : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝ : c ∈ ⋃ i, u i
i : I
m : c ∈ u i
s : SuperNea... | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝ : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝¹ : c ∈ ⋃ i, u i
i : I
m✝ : c ∈ u i
s : SuperN... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | rcases sm m with ⟨u, m, us, s⟩ | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝ : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝¹ : c ∈ ⋃ i, u i
i : I
m✝ : c ∈ u i
s : SuperN... | case intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u✝¹ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u✝ : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝¹ : ∀ (i : I), SuperNearC f d (u✝ i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝² : c ∈ ⋃ i, u✝ i
i... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | exact us (s.ft m) | case intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u✝¹ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u✝ : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝¹ : ∀ (i : I), SuperNearC f d (u✝ i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝² : c ∈ ⋃ i, u✝ i
i... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | intro z z0 m | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝ : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝ : c ∈ ⋃ i, u i
i : I
m : c ∈ u i
s : SuperNea... | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝ : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝¹ : c ∈ ⋃ i, u i
i : I
m✝ : c ∈ u i
s : SuperN... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | rcases sm m with ⟨u, m, _, s⟩ | f : ℂ → ℂ → ℂ
d : ℕ
u✝ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝ : ∀ (i : I), SuperNearC f d (u i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝¹ : c ∈ ⋃ i, u i
i : I
m✝ : c ∈ u i
s : SuperN... | case intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u✝¹ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u✝ : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝¹ : ∀ (i : I), SuperNearC f d (u✝ i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝² : c ∈ ⋃ i, u✝ i
i... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperNearC.union | [544, 1] | [573, 88] | exact s.gs' z0 m | case intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u✝¹ : Set ℂ
t✝ : Set (ℂ × ℂ)
I : Type
u✝ : I → Set ℂ
t : I → Set (ℂ × ℂ)
s✝¹ : ∀ (i : I), SuperNearC f d (u✝ i) (t i)
tu : Set (ℂ × ℂ) := ⋃ i, t i
o : IsOpen tu
sm : ∀ {c z : ℂ}, (c, z) ∈ tu → ∃ u, z ∈ u ∧ u ⊆ {z | (c, z) ∈ tu} ∧ SuperNear (f c) d u
c : ℂ
m✝² : c ∈ ⋃ i, u✝ i
i... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | set r := fun c : u ↦ choose (h _ c.mem) | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
⊢ ∃ t ⊆ w, SuperNearC f d u t | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
⊢ ∃ t ⊆ w, SuperNearC f d u t |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | set v := fun c : u ↦ ball (c : ℂ) (r c) | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
⊢ ∃ t ⊆ w, SuperNearC f d u t | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
⊢ ∃ t ⊆ w, SuperNearC f d ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | set t := fun c : u ↦ ball ((c : ℂ), (0 : ℂ)) (r c) | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
⊢ ∃ t ⊆ w, SuperNearC f d ... | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ℂ) := f... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | use⋃ c : u, t c | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ℂ) := f... | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | have tw : (⋃ c : u, t c) ⊆ w := by
apply Set.iUnion_subset; intro i; rcases choose_spec (h _ i.mem) with ⟨_, _, rw, _⟩; exact rw | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ... | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | have si : ∀ c : u, SuperNearC f d (v c) (t c) := by
intro i; rcases choose_spec (h _ i.mem) with ⟨_, _, _, s⟩; exact s | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ... | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | have s := SuperNearC.union si | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ... | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s✝ : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ ×... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | rw [← e] at s | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s✝ : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ ×... | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s✝ : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ ×... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | exact ⟨tw, s⟩ | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s✝ : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ ×... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | intro c m | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
⊢ ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r) | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
⊢ ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r) |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | rcases(s.fa m).exists_ball_analyticOn with ⟨r0, r0p, fa⟩ | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
⊢ ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r) | case intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
⊢ ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r) |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | rcases Metric.isOpen_iff.mp s.o c m with ⟨r1, r1p, rc⟩ | case intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
⊢ ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r) | case intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc : ball c r1 ⊆ u
⊢ ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ Sup... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | set r2 := min r0 r1 | case intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc : ball c r1 ⊆ u
⊢ ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ Sup... | case intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
⊢ ∃ r > 0, ball c r ⊆ u ∧ bal... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | have fa := fa.mono (Metric.ball_subset_ball (min_le_left r0 r1)) | case intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
⊢ ∃ r > 0, ball c r ⊆ u ∧ bal... | case intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | have rc : ball c r2 ⊆ u := le_trans (Metric.ball_subset_ball (by bound)) rc | case intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f... | case intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | have ga := s.ga_of_fa isOpen_ball fa
(by intro p m; simp only [← ball_prod_same, Set.mem_prod] at m; exact rc m.1) | case intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry ... | case intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | rcases Metric.isOpen_iff.mp wo (c, 0) (wc c m) with ⟨r3, r3p, rw⟩ | case intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry ... | case intro.intro.intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | rcases Metric.continuousAt_iff.mp (ga (c, 0) (mem_ball_self (by bound))).continuousAt
(1 / 4) (by norm_num) with ⟨r4, r4p, gs⟩ | case intro.intro.intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn... | case intro.intro.intro.intro.intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | set r := min (min r2 r3) (min r4 (1 / 2)) | case intro.intro.intro.intro.intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa ... | case intro.intro.intro.intro.intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | have rp : 0 < r := by bound | case intro.intro.intro.intro.intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa ... | case intro.intro.intro.intro.intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | have rh : r ≤ 1 / 2 := le_trans (min_le_right _ _) (min_le_right _ _) | case intro.intro.intro.intro.intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa ... | case intro.intro.intro.intro.intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | have rr4 : r ≤ r4 := le_trans (min_le_right _ _) (min_le_left r4 _) | case intro.intro.intro.intro.intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa ... | case intro.intro.intro.intro.intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | have rc : ball c r ⊆ u := le_trans (Metric.ball_subset_ball (by bound)) rc | case intro.intro.intro.intro.intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa ... | case intro.intro.intro.intro.intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | have rw : ball (c, 0) r ⊆ w :=
_root_.trans (Metric.ball_subset_ball (le_trans (min_le_left _ _) (min_le_right _ _))) rw | case intro.intro.intro.intro.intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa... | case intro.intro.intro.intro.intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | use r, rp, rc, rw | case intro.intro.intro.intro.intro.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa... | case right
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | bound | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1))
⊢... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | intro p m | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1))
... | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1))... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | simp only [← ball_prod_same, Set.mem_prod] at m | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1))... | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1))... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | exact rc m.1 | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1))... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | bound | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1))
... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | norm_num | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1))
... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | bound | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1))
... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | bound | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1))
... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | intro p m | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1))... | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1)... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | simp only [← ball_prod_same, Set.mem_prod] at m | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1)... | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1)... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | exact Metric.ball_subset_ball (by linarith) m.1 | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1)... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | linarith | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1)... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | intro c' m | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1))... | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1)... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | simp only [← ball_prod_same, Set.mem_prod, m, true_and_iff] | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1)... | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1)... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | apply (s.s (rc m)).super_on_ball rp rh | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1)... | case fa
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (mi... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | apply fa.comp₂ analyticOn_const (analyticOn_id _) | case fa
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (mi... | case fa
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (mi... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | intro z zm | case fa
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (mi... | case fa
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (mi... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | apply Metric.ball_subset_ball (by bound : r ≤ r2) | case fa
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (mi... | case fa.a
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | simp only [← ball_prod_same, Set.mem_prod, m, true_and_iff] | case fa.a
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (... | case fa.a
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | exact zm | case fa.a
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | bound | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (min r0 r1)... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | simp only [Complex.dist_eq, Prod.dist_eq, sub_zero, max_lt_iff, and_imp, g2, g0] at gs | case gs
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (mi... | case gs
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (mi... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | simp only [Metric.mem_ball, Complex.dist_eq] at m | case gs
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (mi... | case gs
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (mi... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | intro z zr | case gs
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (mi... | case gs
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (mi... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | exact @gs ⟨c', z⟩ (lt_of_lt_of_le m rr4) (lt_of_lt_of_le zr rr4) | case gs
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
c : ℂ
m✝ : c ∈ u
r0 : ℝ
r0p : 0 < r0
fa✝ : AnalyticOn ℂ (uncurry f) (ball (c, 0) r0)
r1 : ℝ
r1p : r1 > 0
rc✝¹ : ball c r1 ⊆ u
r2 : ℝ := min r0 r1
fa : AnalyticOn ℂ (uncurry f) (ball (c, 0) (mi... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | apply Set.ext | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ℂ) := f... | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | intro c | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ... | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | rw [Set.mem_iUnion] | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ... | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | constructor | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ... | case h.mp
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | intro m | case h.mp
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ... | case h.mp
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | use⟨c, m⟩ | case h.mp
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ... | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | rcases choose_spec (h c m) with ⟨rp, _, _⟩ | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ... | case h.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | exact mem_ball_self rp | case h.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | intro m | case h.mpr
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (... | case h.mpr
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | rcases m with ⟨i, m⟩ | case h.mpr
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (... | case h.mpr.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u →... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | rcases choose_spec (h _ i.mem) with ⟨_, us, _⟩ | case h.mpr.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u →... | case h.mpr.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | exact us m | case h.mpr.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | apply Set.iUnion_subset | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ℂ) := f... | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | intro i | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ... | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | rcases choose_spec (h _ i.mem) with ⟨_, _, rw, _⟩ | case h
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ... | case h.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | exact rw | case h.intro.intro.intro
f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNear.lean | SuperAtC.superNearC' | [576, 1] | [630, 16] | intro i | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ℂ) := f... | f : ℂ → ℂ → ℂ
d : ℕ
u : Set ℂ
t✝ : Set (ℂ × ℂ)
s : SuperAtC f d u
w : Set (ℂ × ℂ)
wo : IsOpen w
wc : ∀ c ∈ u, (c, 0) ∈ w
h : ∀ c ∈ u, ∃ r > 0, ball c r ⊆ u ∧ ball (c, 0) r ⊆ w ∧ SuperNearC f d (ball c r) (ball (c, 0) r)
r : ↑u → ℝ := fun c => choose ⋯
v : ↑u → Set ℂ := fun c => ball (↑c) (r c)
t : ↑u → Set (ℂ × ℂ) := f... |
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