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Update stronglyMeromorphicOn_eliminate.lean

This commit is contained in:
Stefan Kebekus 2024-11-20 12:01:52 +01:00
parent b3eefceb39
commit 6294e3c4ea
1 changed files with 25 additions and 2 deletions
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27
Nevanlinna/stronglyMeromorphicOn_eliminate.lean
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@ -337,9 +337,32 @@ theorem MeromorphicOn.decompose₃
obtain ⟨g, h₁g, h₂g, h₃g, h₄g⟩ := MeromorphicOn.decompose₂ h₁f (P := P) hP obtain ⟨g, h₁g, h₂g, h₃g, h₄g⟩ := MeromorphicOn.decompose₂ h₁f (P := P) hP
let h := ∏ p ∈ P, fun z => (z - p.1) ^ h₁f.meromorphicOn.divisor p.1 let h := ∏ p ∈ P, fun z => (z - p.1) ^ h₁f.meromorphicOn.divisor p.1
have h₁h : MeromorphicOn h U := by
sorry
have h₂h : StronglyMeromorphicOn h U := by have h₂h : StronglyMeromorphicOn h U := by
-- WARNING: This is a general lemma we should add!
intro u hu
right
by_cases h₁u : ⟨u, hu⟩ ∈ P
· sorry
· use 0
use h
simp only [zpow_zero, smul_eq_mul, one_mul, eventually_true, and_true]
constructor
·
sorry
· unfold h
simp only [Finset.prod_apply]
rw [Finset.prod_ne_zero_iff]
intro p hp
apply zpow_ne_zero
rw [sub_ne_zero]
by_contra hCon
have : ⟨u, hu⟩ = p := by
exact SetCoe.ext hCon
rw [← this] at hp
tauto
have h₁h : MeromorphicOn h U := by
sorry sorry
have h₃h : h₁h.divisor = h₁f.meromorphicOn.divisor := by have h₃h : h₁h.divisor = h₁f.meromorphicOn.divisor := by
sorry sorry