Proof using.
intros.
unfold update_elections_data_client_request in *.
repeat break_match; subst; simpl in *; auto.
Qed.

Lemma prefix_within_term_union :
forall l1 l1' l1'' l2,
prefix_within_term l1' l2 ->
prefix_within_term l1'' l2 ->
(forall e, In e l1 -> In e l1' \/ In e l1'') ->
prefix_within_term l1 l2.