Ltac start :=
    red; unfold leaders_have_leaderLogs_strong; intros;
    subst; simpl in *; find_higher_order_rewrite;
    update_destruct; subst; rewrite_update; eauto; simpl in *.

Lemma update_elections_data_appendEntries_leaderLogs : forall h st t h' pli plt es ci, leaderLogs (update_elections_data_appendEntries h st t h' pli plt es ci) = leaderLogs (fst st).