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Nevanlinna/stronglyMeromorphic.lean

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+import Mathlib.Analysis.Analytic.Meromorphic
+import Nevanlinna.analyticAt
+
+def StronglyMeromorphicAt
+  (f : ℂ → ℂ)
+  (z₀ : ℂ) :=
+  (∀ᶠ (z : ℂ) in nhds z₀, f z = 0) ∨ (∃ (n : ℕ), ∃ g : ℂ → ℂ, (AnalyticAt ℂ g z₀) ∧ (g z₀ ≠ 0) ∧ (∀ᶠ (z : ℂ) in nhds z₀, f z = (z - z₀) ^ n • g z))
+
+def MeromorphicAt.makeStronglyMeromorphic
+  {f : ℂ → ℂ}
+  {z₀ : ℂ}
+  (hf : MeromorphicAt f z₀) :
+  ℂ → ℂ := by
+  exact 0
+
+theorem makeStronglyMeromorphic
+  {f : ℂ → ℂ}
+  {z₀ : ℂ}
+  (hf : MeromorphicAt f z₀) :
+  StronglyMeromorphicAt hf.makeStronglyMeromorphic z₀ := by
+  sorry