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Update analyticAt.lean

This commit is contained in:
Stefan Kebekus 2024-09-12 06:58:43 +02:00
parent dbeb631178
commit f83f772506
1 changed files with 19 additions and 7 deletions
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Nevanlinna/analyticAt.lean
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@ -165,26 +165,38 @@ theorem AnalyticAt.order_comp_CLE
obtain ⟨g, h₁g, h₂g, h₃g⟩ := hn obtain ⟨g, h₁g, h₂g, h₃g⟩ := hn
have A := eventually_nhds_comp_composition h₃g ℓ.continuous have A := eventually_nhds_comp_composition h₃g ℓ.continuous
have t₁ : AnalyticAt ℂ (fun z => ℓ z - ℓ z₀) z₀ := by
apply AnalyticAt.sub
exact ContinuousLinearEquiv.analyticAt ℓ z₀
exact analyticAt_const
have t₀ : AnalyticAt ℂ (fun z => (ℓ z - ℓ z₀) ^ n) z₀ := by
exact pow t₁ n
have : AnalyticAt ℂ (fun z ↦ (ℓ z - ℓ z₀) ^ n • g (ℓ z) : ℂ → ℂ) z₀ := by have : AnalyticAt ℂ (fun z ↦ (ℓ z - ℓ z₀) ^ n • g (ℓ z) : ℂ → ℂ) z₀ := by
sorry apply AnalyticAt.mul
exact t₀
apply AnalyticAt.comp h₁g
exact ContinuousLinearEquiv.analyticAt ℓ z₀
rw [AnalyticAt.order_congr (hf.comp (ℓ.analyticAt z₀)) this A] rw [AnalyticAt.order_congr (hf.comp (ℓ.analyticAt z₀)) this A]
simp simp
have t₀ : AnalyticAt ℂ (fun z => (ℓ z - ℓ z₀) ^ n) z₀ := by
sorry
rw [AnalyticAt.order_mul t₀ ((h₁g.comp (ℓ.analyticAt z₀)))] rw [AnalyticAt.order_mul t₀ ((h₁g.comp (ℓ.analyticAt z₀)))]
have t₁ : AnalyticAt ℂ (fun z => ℓ z - ℓ z₀) z₀ := by
sorry
have : t₁.order = (1 : ℕ) := by have : t₁.order = (1 : ℕ) := by
rw [AnalyticAt.order_eq_nat_iff] rw [AnalyticAt.order_eq_nat_iff]
use (fun z ↦ ℓ 1) use (fun _ ↦ ℓ 1)
simp simp
constructor constructor
· exact analyticAt_const · exact analyticAt_const
· apply Filter.Eventually.of_forall · apply Filter.Eventually.of_forall
intro x intro x
sorry calc ℓ x - ℓ z₀
_ = ℓ (x - z₀) := by
exact Eq.symm (ContinuousLinearEquiv.map_sub ℓ x z₀)
_ = ℓ ((x - z₀) * 1) := by
simp
_ = (x - z₀) * ℓ 1 := by
rw [← smul_eq_mul, ← smul_eq_mul]
exact ContinuousLinearEquiv.map_smul ℓ (x - z₀) 1
have : t₀.order = n := by have : t₀.order = n := by
rw [AnalyticAt.order_pow t₁, this] rw [AnalyticAt.order_pow t₁, this]