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 | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | use m, e | case h.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x✝ : ℂ
m✝ : c' = c ∧ Complex.abs x... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreim... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | use uncurry r | case neg
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex.abs x ≤ p
c... | case h
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex.abs x ≤ p
ct ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | simp only [not_not] at x0 | case h
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex.abs x ≤ p
ct ... | case h
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex.abs x ≤ p
ct ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | simp only [m.1, x0, eq_self_iff_true, and_true_iff] at ct ⊢ | case h
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex.abs x ≤ p
ct ... | case h
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex.abs x ≤ p
x0 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | constructor | case h
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex.abs x ≤ p
x0 ... | case h.left
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex.abs x ≤ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | refine
(g.eqn.filter_mono (nhds_le_nhdsSet ?_)).eventually_nhds.mp
(eventually_of_forall fun y e ↦ ?_) | case h.left
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex.abs x ≤ ... | case h.left.refine_1
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.left
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreima... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | use rfl, mem_ball_self g.pos | case h.left.refine_1
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex... | case h.left.refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.left.refine_1
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | simp only [Function.curry_uncurry] | case h.left.refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex... | case h.left.refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.left.refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | exact
{ eqn := e
start := by
simp only [Filter.EventuallyEq.refl, imp_true_iff, Filter.eventually_true] } | case h.left.refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.left.refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | simp only [Filter.EventuallyEq.refl, imp_true_iff, Filter.eventually_true] | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex.abs x ≤ p
x0 : x = 0... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | refine ct.frequently (Filter.Eventually.frequently ?_) | case h.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex.abs x ≤... | case h.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex.abs x ≤... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreim... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | simp only [mem_prod_eq, mem_singleton_iff, eq_self_iff_true, true_and_iff] | case h.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex.abs x ≤... | case h.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex.abs x ≤... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreim... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | exact isOpen_ball.eventually_mem (mem_ball_self g.pos) | case h.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
c' x : ℂ
m : c' = c ∧ Complex.abs x ≤... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreim... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | intro r0 r1 t _ pre e0 e1 r01 | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
⊢ ∀ {f0 f1 : ℂ × ℂ → S} {t : Set (ℂ × ℂ)},
IsO... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
r0 r1 : ℂ × ℂ → S
t : Set (ℂ × ℂ)
a✝ : IsOpen t
pr... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | have u := eqns_unique pre e0 e1 ?_ | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
r0 r1 : ℂ × ℂ → S
t : Set (ℂ × ℂ)
a✝ : IsOpen t
pr... | case refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
r0 r1 : ℂ × ℂ → S
t : Set (ℂ × ℂ)
a✝... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | simp only [Function.uncurry_curry] at u | case refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
r0 r1 : ℂ × ℂ → S
t : Set (ℂ × ℂ)
a✝... | case refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
r0 r1 : ℂ × ℂ → S
t : Set (ℂ × ℂ)
a✝... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePrei... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | exact u | case refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
r0 r1 : ℂ × ℂ → S
t : Set (ℂ × ℂ)
a✝... | case refine_1
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
r0 r1 : ℂ × ℂ → S
t : Set (ℂ × ℂ)
a✝... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePrei... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | simp only [Function.uncurry_curry] | case refine_1
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
r0 r1 : ℂ × ℂ → S
t : Set (ℂ × ℂ)
a✝... | case refine_1
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
r0 r1 : ℂ × ℂ → S
t : Set (ℂ × ℂ)
a✝... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePrei... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | exact r01 | case refine_1
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
r0 r1 : ℂ × ℂ → S
t : Set (ℂ × ℂ)
a✝... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePrei... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | simp only [mem_prod_eq, mem_singleton_iff, eq_self_iff_true, true_and_iff, mem_ball_self g.pos] | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
b : Base (fun f_1 x => Eqns s n r (curry f_1) x) (... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | rw [curry, b.uf.self_of_nhdsSet m0, uncurry, g.zero] | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
b : Base (fun f_1 x => Eqns s n r (curry f_1) x) (... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | refine g.start.mp ((b.uf.filter_mono (nhds_le_nhdsSet m0)).mp (eventually_of_forall ?_)) | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
b : Base (fun f_1 x => Eqns s n r (curry f_1) x) (... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
b : Base (fun f_1 x => Eqns s n r (curry f_1) x) (... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | intro x e b | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
b : Base (fun f_1 x => Eqns s n r (curry f_1) x) (... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
b✝ : Base (fun f_1 x => Eqns s n r (curry f_1) x) ... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | simp only [curry, uncurry, Prod.mk.eta] at e ⊢ | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
b✝ : Base (fun f_1 x => Eqns s n r (curry f_1) x) ... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
b✝ : Base (fun f_1 x => Eqns s n r (curry f_1) x) ... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | rw [e] | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
b✝ : Base (fun f_1 x => Eqns s n r (curry f_1) x) ... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
b✝ : Base (fun f_1 x => Eqns s n r (curry f_1) x) ... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | exact b | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
b✝ : Base (fun f_1 x => Eqns s n r (curry f_1) x) ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | have fp := b.up | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
b : Base (fun f_1 x => Eqns s n r (curry f_1) x) (... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
b : Base (fun f_1 x => Eqns s n r (curry f_1) x) (... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | simp only [closure_prod_eq, closure_singleton, closure_ball _ g.pos.ne'] at fp | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
b : Base (fun f_1 x => Eqns s n r (curry f_1) x) (... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
b : Base (fun f_1 x => Eqns s n r (curry f_1) x) (... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | GrowOpen.grow | [436, 1] | [498, 74] | exact fp.mp (eventually_of_forall fun x e ↦ e.eqn.self_of_nhds) | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ := s.np c p
b : Base (fun f_1 x => Eqns s n r (curry f_1) x) (... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p : ℝ
s : Super f d a
r : ℂ → ℂ → S
g : GrowOpen s c p r
inst✝ : OnePreimage s
n : ℕ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | have above : ∀ k, p k ≤ ps := fun k ↦ mono.ge_of_tendsto tend k | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r k)
mono :... | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r k)
mono :... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | generalize hrs : (fun e x : ℂ ↦
if h : abs x < ps then r (Nat.find (tend.exists_lt h)) e x else a) = rs | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r k)
mono :... | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r k)
mono :... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | use rs | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r k)
mono :... | case h
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r k)... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | intro k x xk | case h
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r k)... | case h
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r k)... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | rcases eventually_nhds_iff.mp (loc k) with ⟨u, eq, uo, uc⟩ | case h
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r k)... | case h.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | have m : u ×ˢ ball (0 : ℂ) (p k) ∈ 𝓝 (c, x) := by
refine prod_mem_nhds (uo.mem_nhds uc) (isOpen_ball.mem_nhds ?_)
simp only [mem_ball, Complex.dist_eq, sub_zero, xk] | case h.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c... | case h.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ →... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | apply Filter.eventually_of_mem m | case h.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c... | case h.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ →... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | intro ⟨e, y⟩ ⟨m0, m1⟩ | case h.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c... | case h.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ →... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | simp only [mem_ball, Complex.dist_eq, sub_zero] at m1 | case h.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c... | case h.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ →... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | exact eq _ m0 _ m1 | case h.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ →... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | intro k | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r k)
mono :... | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r k)
mono :... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | induction' k with k h | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r k)
mono :... | case zero
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | apply eventually_of_forall | case zero
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r... | case zero.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k)... | Please generate a tactic in lean4 to solve the state.
STATE:
case zero
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | intro e x x0 | case zero.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k)... | case zero.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k)... | Please generate a tactic in lean4 to solve the state.
STATE:
case zero.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | have xe : ∃ k, abs x < p k := ⟨0, x0⟩ | case zero.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k)... | case zero.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k)... | Please generate a tactic in lean4 to solve the state.
STATE:
case zero.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | simp only [← hrs, lt_of_lt_of_le x0 (above _), dif_pos, (Nat.find_eq_zero xe).mpr x0] | case zero.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case zero.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | have eq := (g k).unique (g (k + 1)) (mono (Nat.lt_succ_self _).le) | case succ
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r... | case succ
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r... | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | simp only [isCompact_singleton.nhdsSet_prod_eq (isCompact_closedBall _ _)] at eq | case succ
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r... | case succ
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r... | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | apply h.mp | case succ
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r... | case succ
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r... | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | rcases Filter.mem_prod_iff.mp eq with ⟨u0, n0, u1, n1, eq⟩ | case succ
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r... | case succ.intro.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ),... | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | simp only [nhdsSet_singleton] at n0 | case succ.intro.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ),... | case succ.intro.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ),... | Please generate a tactic in lean4 to solve the state.
STATE:
case succ.intro.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | refine Filter.eventually_of_mem n0 fun e eu h x xk1 ↦ ?_ | case succ.intro.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ),... | case succ.intro.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ),... | Please generate a tactic in lean4 to solve the state.
STATE:
case succ.intro.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | by_cases xk0 : abs x < p k | case succ.intro.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ),... | case pos
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r ... | Please generate a tactic in lean4 to solve the state.
STATE:
case succ.intro.intro.intro.intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | have m : (e, x) ∈ u0 ×ˢ u1 := by
refine mk_mem_prod eu (subset_of_mem_nhdsSet n1 ?_)
simp only [mem_closedBall, Complex.dist_eq, sub_zero, xk0.le] | case pos
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r ... | case pos
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | specialize eq m | case pos
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r ... | case pos
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | simp only [mem_setOf, uncurry] at eq | case pos
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r ... | case pos
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | rw [h _ xk0, eq] | case pos
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | refine mk_mem_prod eu (subset_of_mem_nhdsSet n1 ?_) | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r k)
mono :... | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r k)
mono :... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | simp only [mem_closedBall, Complex.dist_eq, sub_zero, xk0.le] | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r k)
mono :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | have xe : ∃ k, abs x < p k := ⟨k + 1, xk1⟩ | case neg
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r ... | case neg
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | have n := (Nat.find_eq_iff xe).mpr ⟨xk1, ?_⟩ | case neg
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r ... | case neg.refine_2
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝¹ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n✝ : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | simp only [← hrs, lt_of_lt_of_le xk1 (above _), dif_pos, n] | case neg.refine_2
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝¹ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n✝ : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k... | case neg.refine_1
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.refine_2
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝¹ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n✝ ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | intro j jk | case neg.refine_1
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) ... | case neg.refine_1
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.refine_1
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | simp only [not_lt, Nat.lt_succ_iff] at jk xk0 ⊢ | case neg.refine_1
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) ... | case neg.refine_1
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.refine_1
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | exact _root_.trans (mono jk) xk0 | case neg.refine_1
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.refine_1
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | refine prod_mem_nhds (uo.mem_nhds uc) (isOpen_ball.mem_nhds ?_) | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r k)
mono :... | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r k)
mono :... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | join_r | [502, 1] | [541, 21] | simp only [mem_ball, Complex.dist_eq, sub_zero, xk] | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ → ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (n k) (r k)
mono :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n✝ : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
n : ℕ → ℕ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | rcases tend.exists_lt pos with ⟨k, pos⟩ | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.np c ps) (r... | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | have e := (loc k 0 (by simp only [Complex.abs.map_zero, pos])).self_of_nhds | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | simp only [uncurry] at e | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | simp only [e, (g k).zero] | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | simp only [Complex.abs.map_zero, pos] | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.np c ps) (r... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | rcases tend.exists_lt pos with ⟨k, pos⟩ | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.np c ps) (r... | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | apply (g k).start.mp | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | apply (loc k 0 (by simp only [Complex.abs.map_zero, pos])).mp | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | apply eventually_of_forall | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | case intro.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | intro ⟨e, x⟩ loc start | case intro.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) ... | case intro.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | simp only [uncurry] at loc start ⊢ | case intro.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) ... | case intro.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | simp only [start, loc] | case intro.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | apply mem_nhdsSet_iff_forall.mpr | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.np c ps) (r... | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.np c ps) (r... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | intro ⟨c', x⟩ lt | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.np c ps) (r... | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.np c ps) (r... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | simp only [mem_prod_eq, mem_singleton_iff, mem_ball, Complex.dist_eq, sub_zero] at lt | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.np c ps) (r... | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.np c ps) (r... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | simp only [lt.1, eq_self_iff_true, true_and_iff, ← Filter.eventually_iff] at lt ⊢ | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.np c ps) (r... | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.np c ps) (r... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | clear c' | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.np c ps) (r... | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.np c ps) (r... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | rcases tend.exists_lt lt with ⟨k, ltp⟩ | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.np c ps) (r... | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | have m : (c, x) ∈ {c} ×ˢ closedBall (0 : ℂ) (p k) := by
simp only [mem_prod_eq, mem_singleton_iff, Metric.mem_closedBall, eq_self_iff_true,
true_and_iff, Complex.dist_eq, sub_zero, ltp.le] | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | have lt' : ∀ᶠ y : ℂ × ℂ in 𝓝 (c, x), abs y.2 < ps :=
(Complex.continuous_abs.continuousAt.comp continuousAt_snd).eventually_lt
continuousAt_const lt | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | apply ((g k).eqn.filter_mono (nhds_le_nhdsSet m)).mp | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | apply (loc _ _ ltp).eventually_nhds.mp | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | apply lt'.mp | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | apply eventually_of_forall | case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.... | case intro.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | intro ⟨e, y⟩ _ loc eq | case intro.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) ... | case intro.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | exact eq.congr (Filter.EventuallyEq.symm loc) | case intro.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.hp
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | joined_growOpen | [544, 1] | [576, 54] | simp only [mem_prod_eq, mem_singleton_iff, Metric.mem_closedBall, eq_self_iff_true,
true_and_iff, Complex.dist_eq, sub_zero, ltp.le] | S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → S
rs : ℂ → ℂ → S
g : ∀ (k : ℕ), Grow s c (p k) (s.np c ps) (r... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁴ : TopologicalSpace S
inst✝³ : CompactSpace S
inst✝² : T3Space S
inst✝¹ : ChartedSpace ℂ S
inst✝ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p✝ : ℝ
s✝ : Super f d a
r✝ : ℂ → ℂ → S
s : Super f d a
p : ℕ → ℝ
ps : ℝ
r : ℕ → ℂ → ℂ → ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | Super.grow | [579, 1] | [618, 23] | set t : Set ℝ := {p | 0 ≤ p ∧ ∀ q, 0 ≤ q → q ≤ p → ∃ r, Grow s c q (s.np c q) r} | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : OnePreimage s
⊢ ∀ (p : ℝ), 0 ≤ p → p < s.p c → ∃ r, Grow s c p (s.np c p) r | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : OnePreimage s
t : Set ℝ := {p | 0 ≤ p ∧ ∀ (q : ℝ), 0 ≤ q → q ≤ p → ∃ r, Grow s c q (s.n... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : OnePreimage s
⊢ ∀ (p : ℝ),... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | Super.grow | [579, 1] | [618, 23] | have self : ∀ {p}, p ∈ t → ∃ r, Grow s c p (s.np c p) r := fun {p} m ↦ m.2 _ m.1 (le_refl _) | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : OnePreimage s
t : Set ℝ := {p | 0 ≤ p ∧ ∀ (q : ℝ), 0 ≤ q → q ≤ p → ∃ r, Grow s c q (s.n... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : OnePreimage s
t : Set ℝ := {p | 0 ≤ p ∧ ∀ (q : ℝ), 0 ≤ q → q ≤ p → ∃ r, Grow s c q (s.n... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : OnePreimage s
t : Set ℝ :=... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | Super.grow | [579, 1] | [618, 23] | have t1 : ∀ p : ℝ, p ∈ t → p < 1 := by intro p m; rcases self m with ⟨r, g⟩; exact g.p1 | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : OnePreimage s
t : Set ℝ := {p | 0 ≤ p ∧ ∀ (q : ℝ), 0 ≤ q → q ≤ p → ∃ r, Grow s c q (s.n... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : OnePreimage s
t : Set ℝ := {p | 0 ≤ p ∧ ∀ (q : ℝ), 0 ≤ q → q ≤ p → ∃ r, Grow s c q (s.n... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : OnePreimage s
t : Set ℝ :=... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | Super.grow | [579, 1] | [618, 23] | have above : BddAbove t := bddAbove_def.mpr ⟨1, fun p m ↦ (t1 p m).le⟩ | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : OnePreimage s
t : Set ℝ := {p | 0 ≤ p ∧ ∀ (q : ℝ), 0 ≤ q → q ≤ p → ∃ r, Grow s c q (s.n... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : OnePreimage s
t : Set ℝ := {p | 0 ≤ p ∧ ∀ (q : ℝ), 0 ≤ q → q ≤ p → ∃ r, Grow s c q (s.n... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : OnePreimage s
t : Set ℝ :=... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | Super.grow | [579, 1] | [618, 23] | rcases s.grow_start c with ⟨p0, r0, pos0, g0⟩ | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : OnePreimage s
t : Set ℝ := {p | 0 ≤ p ∧ ∀ (q : ℝ), 0 ≤ q → q ≤ p → ∃ r, Grow s c q (s.n... | case intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : OnePreimage s
t : Set ℝ := {p | 0 ≤ p ∧ ∀ (q : ℝ), 0 ≤ q → q ≤ p... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : OnePreimage s
t : Set ℝ :=... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | Super.grow | [579, 1] | [618, 23] | have start : p0 ∈ t := by
use g0.nonneg; intro q q0 qp; use r0; exact (g0.anti q0 qp).mono (Nat.zero_le _) | case intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : OnePreimage s
t : Set ℝ := {p | 0 ≤ p ∧ ∀ (q : ℝ), 0 ≤ q → q ≤ p... | case intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : OnePreimage s
t : Set ℝ := {p | 0 ≤ p ∧ ∀ (q : ℝ), 0 ≤ q → q ≤ p... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : One... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Grow.lean | Super.grow | [579, 1] | [618, 23] | have ne : t.Nonempty := ⟨p0, start⟩ | case intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : OnePreimage s
t : Set ℝ := {p | 0 ≤ p ∧ ∀ (q : ℝ), 0 ≤ q → q ≤ p... | case intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : OnePreimage s
t : Set ℝ := {p | 0 ≤ p ∧ ∀ (q : ℝ), 0 ≤ q → q ≤ p... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : CompactSpace S
inst✝³ : T3Space S
inst✝² : ChartedSpace ℂ S
inst✝¹ : AnalyticManifold I S
f : ℂ → S → S
c : ℂ
a z : S
d n : ℕ
p : ℝ
s✝ : Super f d a
r : ℂ → ℂ → S
s : Super f d a
inst✝ : One... |
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