diff --git a/theories/fin_map_dom.v b/theories/fin_map_dom.v
index cff6fd424914db4b49202165b3d74af22ccb70eb..486ce52970ebf15b93f5af63f9b8b6b5212be9c8 100644
--- a/theories/fin_map_dom.v
+++ b/theories/fin_map_dom.v
@@ -90,6 +90,7 @@ Proof.
   destruct (decide (i = j)); set_solver.
 Qed.
 Lemma dom_insert_lookup {A} (m : M A) i x :
+  is_Some (m !! i) → dom D (<[i:=x]>m) ≡ dom D m.
 Proof. intros Hindom%elem_of_dom. rewrite dom_insert. set_solver. Qed.
 Lemma dom_insert_subseteq {A} (m : M A) i x : dom D m ⊆ dom D (<[i:=x]>m).
 Proof. rewrite (dom_insert _). set_solver. Qed.