working

Nevanlinna/meromorphicOn.lean

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+import Mathlib.Analysis.Analytic.Meromorphic
+import Nevanlinna.analyticAt
+import Nevanlinna.divisor
+import Nevanlinna.meromorphicAt
+import Nevanlinna.meromorphicOn_divisor
+import Nevanlinna.stronglyMeromorphicOn
+import Nevanlinna.mathlibAddOn
+
+open scoped Interval Topology
+open Real Filter MeasureTheory intervalIntegral
+
+theorem MeromorphicOn.order_ne_top
+  {f : ℂ → ℂ}
+  {U : Set ℂ}
+  (h₁U : IsConnected U)
+  (h₁f : MeromorphicOn f U) :
+  (∃ z₀ : U, (h₁f z₀.1 z₀.2).order ≠ ⊤) ↔ (∀ z : U, (h₁f z.1 z.2).order ≠ ⊤) := by
+
+  constructor
+  · intro h
+    obtain ⟨h₁z₀, h₂z₀⟩ := h
+    intro hz
+
+    sorry
+
+  · intro h
+    obtain ⟨w, hw⟩ := h₁U.nonempty
+    use ⟨w, hw⟩
+    exact h ⟨w, hw⟩