Update meromorphicOn.lean

Nevanlinna/meromorphicOn.lean

@@ -9,6 +9,31 @@ import Nevanlinna.mathlibAddOn
 open scoped Interval Topology
 open Real Filter MeasureTheory intervalIntegral
 
+theorem MeromorphicOn.open_of_order_eq_top
+  {f : ℂ → ℂ}
+  {U : Set ℂ}
+  (h₁f : MeromorphicOn f U) :
+  IsOpen { u : U | (h₁f u.1 u.2).order = ⊤ } := by
+
+  apply isOpen_iff_forall_mem_open.mpr
+  intro z hz
+  simp at hz
+  rw [MeromorphicAt.order_eq_top_iff] at hz
+  rw [eventually_nhdsWithin_iff] at hz
+  rw [eventually_nhds_iff] at hz
+  obtain ⟨t', h₁t', h₂t', h₃t'⟩ := hz
+  let t :=
+  have : t ⊆ { u : U | (h₁f u.1 u.2).order = ⊤} := by
+    sorry
+
+
+
+  rw [← eventually_eventually_nhds] at hz
+
+
+  sorry
+
+
 theorem MeromorphicOn.order_ne_top
   {f : ℂ → ℂ}
   {U : Set ℂ}