Update stronglyMeromorphic.lean

This commit is contained in:
Stefan Kebekus 2024-10-14 13:25:49 +02:00
parent 24139d9d00
commit 405b68924d
1 changed files with 6 additions and 16 deletions

View File

@ -63,28 +63,17 @@ theorem StronglyMeromorphicAt.analytic
exact h₁g exact h₁g
/- Make strongly MeromorphicAt -/ /- Make strongly MeromorphicAt -/
noncomputable def MeromorphicAt.makeStronglyMeromorphicAt
def MeromorphicAt.makeStronglyMeromorphicAt
{f : } {f : }
{z₀ : } {z₀ : }
(hf : MeromorphicAt f z₀) : (hf : MeromorphicAt f z₀) :
:= by := by
by_cases h₂f : hf.order = by_cases h₂f : hf.order = 0
· have : (0 : WithTop ) = (0 : ) := rfl
rw [this, hf.order_eq_int_iff] at h₂f
exact Classical.choose h₂f
· exact 0 · exact 0
· have : ∃ n : , hf.order = n := by
exact Option.ne_none_iff_exists'.mp h₂f
let o := hf.order.untop h₂f
have : hf.order = o := by
exact Eq.symm (WithTop.coe_untop hf.order h₂f)
rw [MeromorphicAt.order_eq_int_iff] at this
obtain ⟨g, hg⟩ := this
exact fun z ↦ (z - z₀) ^ o • g z
sorry
theorem StronglyMeromorphicAt_of_makeStronglyMeromorphic theorem StronglyMeromorphicAt_of_makeStronglyMeromorphic
@ -92,6 +81,7 @@ theorem StronglyMeromorphicAt_of_makeStronglyMeromorphic
{z₀ : } {z₀ : }
(hf : MeromorphicAt f z₀) : (hf : MeromorphicAt f z₀) :
StronglyMeromorphicAt hf.makeStronglyMeromorphic z₀ := by StronglyMeromorphicAt hf.makeStronglyMeromorphic z₀ := by
sorry sorry