Add option_local_update_None

iris/algebra/local_updates.v

@@ -172,6 +172,16 @@ Proof.
   split; first done. destruct mz as [?|]; constructor; auto.
 Qed.
 
+Lemma option_local_update_None {A: ucmra} (x x' y': A):
+  (x, ε) ~l~> (x', y') -> (Some x, None) ~l~> (Some x', Some y').
+Proof.
+  intros HUp. apply local_update_unital. intros ? ?.
+  rewrite ucmra_unit_left_id => HValid HEq. rewrite -HEq.
+  destruct (HUp n (Some x)); rewrite /= //.
+  - by rewrite ucmra_unit_left_id.
+  - simpl in *. split; try done. rewrite -Some_op. by constructor.
+Qed.
+
 Lemma alloc_option_local_update {A : cmra} (x : A) y :
   ✓ x →
   (None, y) ~l~> (Some x, Some x).