Proof using.
unfold prefix_within_term. intros.
find_apply_lem_hyp findGtIndex_in. eauto.
Qed.

Lemma update_elections_data_client_request_leaderLogs :
forall h st client id c,
leaderLogs (update_elections_data_client_request h st client id c) =
leaderLogs (fst st).