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 doLeader_type : forall st h os st' ms, doLeader st h = (os, st', ms) -> type st' = type st /\ currentTerm st' = currentTerm st /\ log st' = log st.