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Update analyticAt.lean

This commit is contained in:
Stefan Kebekus 2024-09-12 07:04:00 +02:00
parent f83f772506
commit dbea68061b
1 changed files with 8 additions and 7 deletions
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Nevanlinna/analyticAt.lean
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@ -123,7 +123,7 @@ theorem eventually_nhds_comp_composition
exact h₁t (ℓ y) hy exact h₁t (ℓ y) hy
· constructor · constructor
· apply IsOpen.preimage · apply IsOpen.preimage
exact ContinuousLinearEquiv.continuous ℓ exact hℓ
exact h₂t exact h₂t
· exact h₃t · exact h₃t
@ -132,9 +132,10 @@ theorem AnalyticAt.order_congr
{f₁ f₂ : ℂ → ℂ} {f₁ f₂ : ℂ → ℂ}
{z₀ : ℂ} {z₀ : ℂ}
(hf₁ : AnalyticAt ℂ f₁ z₀) (hf₁ : AnalyticAt ℂ f₁ z₀)
(hf₂ : AnalyticAt ℂ f₂ z₀) (hf : f₁ =ᶠ[nhds z₀] f₂) :
(hf : ∀ᶠ (z : ℂ) in nhds z₀, f₁ z = f₂ z) : hf₁.order = (hf₁.congr hf).order := by
hf₁.order = hf₂.order := by
sorry sorry
@ -151,9 +152,9 @@ theorem AnalyticAt.order_comp_CLE
rw [AnalyticAt.order_eq_top_iff] at h₁f rw [AnalyticAt.order_eq_top_iff] at h₁f
let A := eventually_nhds_comp_composition h₁f ℓ.continuous let A := eventually_nhds_comp_composition h₁f ℓ.continuous
simp at A simp at A
have : AnalyticAt ℂ (0 : ℂ → ℂ) z₀ := by apply analyticAt_const rw [AnalyticAt.order_congr (hf.comp (ℓ.analyticAt z₀)) A]
rw [AnalyticAt.order_congr (hf.comp (ℓ.analyticAt z₀)) this A]
have : AnalyticAt ℂ (0 : ℂ → ℂ) z₀ := by apply analyticAt_const
have : this.order = ⊤ := by have : this.order = ⊤ := by
rw [AnalyticAt.order_eq_top_iff] rw [AnalyticAt.order_eq_top_iff]
simp simp
@ -176,7 +177,7 @@ theorem AnalyticAt.order_comp_CLE
exact t₀ exact t₀
apply AnalyticAt.comp h₁g apply AnalyticAt.comp h₁g
exact ContinuousLinearEquiv.analyticAt ℓ z₀ 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)) A]
simp simp
rw [AnalyticAt.order_mul t₀ ((h₁g.comp (ℓ.analyticAt z₀)))] rw [AnalyticAt.order_mul t₀ ((h₁g.comp (ℓ.analyticAt z₀)))]