diff --git a/Nevanlinna/divisor.lean b/Nevanlinna/divisor.lean
index e498d42..8e74b25 100644
--- a/Nevanlinna/divisor.lean
+++ b/Nevanlinna/divisor.lean
@@ -87,5 +87,7 @@ theorem Divisor.finiteSupport
   (hU : IsCompact U)
   (D : Divisor U) :
   Set.Finite D.toFun.support := by
-
-  sorry
+  apply IsCompact.finite
+  · apply IsCompact.of_isClosed_subset hU (D.closedSupport hU.isClosed)
+    exact D.supportInU
+  · exact D.discreteSupport hU.isClosed