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Update analyticOn_zeroSet.lean

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Stefan Kebekus 2024-08-20 17:27:42 +02:00
parent 867b88bf5a
commit 6d0870d533
1 changed files with 27 additions and 8 deletions
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Nevanlinna/analyticOn_zeroSet.lean
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@ -380,14 +380,33 @@ theorem AnalyticOnCompact.eliminateZeros
obtain ⟨g, h₁g, h₂g, h₃g⟩ := AnalyticOn.eliminateZeros (A := A) h₁f n hn obtain ⟨g, h₁g, h₂g, h₃g⟩ := AnalyticOn.eliminateZeros (A := A) h₁f n hn
use g use g
use A use A
constructor
· exact h₁g have inter : ∀ (z : ℂ), f z = (∏ a ∈ A, (z - ↑a) ^ (h₁f (↑a) a.property).order.toNat) • g z := by
· constructor intro z
· sorry
· intro z
rw [h₃g z] rw [h₃g z]
congr congr
funext a funext a
congr congr
dsimp [n] dsimp [n]
simp [a.2] simp [a.2]
constructor
· exact h₁g
· constructor
· intro z h₁z
by_cases h₂z : ⟨z, h₁z⟩ ∈ ↑A.toSet
· exact h₂g ⟨z, h₁z⟩ h₂z
· have : f z ≠ 0 := by
by_contra C
have : ⟨z, h₁z⟩ ∈ ↑A₁ := by
dsimp [A₁, ι]
simp
exact C
have : ⟨z, h₁z⟩ ∈ ↑A.toSet := by
dsimp [A]
simp
exact this
tauto
rw [inter z] at this
exact right_ne_zero_of_smul this
· exact inter