Working

Nevanlinna/meromorphicOn_integrability.lean

@@ -12,6 +12,22 @@ open scoped Interval Topology
 open Real Filter MeasureTheory intervalIntegral
 
 
+lemma a
+  (S : Set ℂ)
+  (hS : S ∈ Filter.codiscreteWithin ⊤) :
+  DiscreteTopology (Sᶜ : Set ℂ) := by
+
+  rw [mem_codiscreteWithin] at hS
+  simp at hS
+  have : (Set.univ \ S)ᶜ = S := by ext z; simp
+  rw [this] at hS
+
+  rw [discreteTopology_subtype_iff]
+  intro x hx
+  rw [← mem_iff_inf_principal_compl]
+  exact (hS x)
+
+
 theorem integrability_congr_changeDiscrete
   {f₁ f₂ : ℂ → ℂ}
   {r : ℝ}
@@ -28,6 +44,7 @@ theorem integrability_congr_changeDiscrete
       exact rfl
     rw [this]
     apply Set.Countable.preimage_circleMap
+
     sorry
     sorry
   · sorry