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Cleanup

This commit is contained in:
Stefan Kebekus 2024-08-20 12:54:30 +02:00
parent 688347a837
commit e8fa4b646d
2 changed files with 15 additions and 15 deletions
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29
Nevanlinna/analyticOn_zeroSet.lean
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@ -1,11 +1,6 @@
import Mathlib.Analysis.Analytic.Linear
import Init.Classical
import Mathlib.Analysis.Analytic.Meromorphic
import Mathlib.Topology.ContinuousOn
import Mathlib.Analysis.Analytic.IsolatedZeros
import Mathlib.Analysis.Analytic.Constructions import Mathlib.Analysis.Analytic.Constructions
import Nevanlinna.holomorphic import Mathlib.Analysis.Analytic.IsolatedZeros
import Mathlib.Analysis.Complex.Basic
theorem AnalyticOn.order_eq_nat_iff theorem AnalyticOn.order_eq_nat_iff
@ -97,7 +92,7 @@ theorem AnalyticOn.order_eq_nat_iff
exact ⟨h₁g z₀ hz₀, ⟨h₂g, Filter.eventually_of_forall h₃g⟩⟩ exact ⟨h₁g z₀ hz₀, ⟨h₂g, Filter.eventually_of_forall h₃g⟩⟩
theorem AnalyticOn.order_of_mul theorem AnalyticAt.order_mul
{f₁ f₂ : ℂ → ℂ} {f₁ f₂ : ℂ → ℂ}
{z₀ : ℂ} {z₀ : ℂ}
(hf₁ : AnalyticAt ℂ f₁ z₀) (hf₁ : AnalyticAt ℂ f₁ z₀)
@ -183,10 +178,11 @@ theorem AnalyticOn.eliminateZeros
have h₁φ : AnalyticAt ℂ φ b₀ := by have h₁φ : AnalyticAt ℂ φ b₀ := by
dsimp [φ] dsimp [φ]
apply Finset.analyticAt_prod apply Finset.analyticAt_prod
intro b hb intro b _
apply AnalyticAt.pow apply AnalyticAt.pow
apply AnalyticAt.sub apply AnalyticAt.sub
apply analyticAt_id apply analyticAt_id ℂ
exact analyticAt_const
have h₂φ : h₁φ.order = (0 : ℕ) := by have h₂φ : h₁φ.order = (0 : ℕ) := by
rw [AnalyticAt.order_eq_nat_iff h₁φ 0] rw [AnalyticAt.order_eq_nat_iff h₁φ 0]
@ -198,13 +194,16 @@ theorem AnalyticOn.eliminateZeros
push_neg push_neg
rw [Finset.prod_ne_zero_iff] rw [Finset.prod_ne_zero_iff]
intro a ha intro a ha
have AA : b₀.1 - a ≠ 0 := by simp
sorry have : ¬ (b₀.1 - a.1 = 0) := by
simp [AA] by_contra C
rw [sub_eq_zero] at C
rw [SetCoe.ext C] at hb
tauto
tauto
· simp · simp
rw [AnalyticOn.order_of_mul h₁φ (h₁g₀ b₀ b₀.2)] rw [AnalyticAt.order_mul h₁φ (h₁g₀ b₀ b₀.2)]
rw [h₂φ] rw [h₂φ]
simp simp

1
Nevanlinna/holomorphic_zero.lean
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@ -3,6 +3,7 @@ import Mathlib.Analysis.Analytic.Meromorphic
import Mathlib.Topology.ContinuousOn import Mathlib.Topology.ContinuousOn
import Mathlib.Analysis.Analytic.IsolatedZeros import Mathlib.Analysis.Analytic.IsolatedZeros
import Nevanlinna.holomorphic import Nevanlinna.holomorphic
import Nevanlinna.analyticOn_zeroSet
noncomputable def zeroDivisor noncomputable def zeroDivisor