Proof using.
intros. unfold handleAppendEntries in *.
break_if; [find_inversion; subst; eauto|].
break_if;
[do_bool; break_if; find_inversion; subst;
try find_apply_lem_hyp haveNewEntries_true;
simpl in *; intuition eauto using advanceCurrentTerm_log, advanceCurrentTerm_commitIndex, some_none, advanceCurrentTerm_term|].
simpl in *. intuition eauto using advanceCurrentTerm_log, advanceCurrentTerm_commitIndex.
break_match; [|find_inversion; subst; eauto].
break_if; [find_inversion; subst; eauto|].
break_if; [|find_inversion; subst; eauto using advanceCurrentTerm_log, advanceCurrentTerm_commitIndex].
find_inversion; subst; simpl in *.
right. right.
find_apply_lem_hyp findAtIndex_elim.
intuition; do_bool; find_apply_lem_hyp haveNewEntries_true;
intuition eauto using advanceCurrentTerm_term; congruence.
Qed.

(* Specifications: *)
Lemma advanceCurrentTerm_currentTerm_leaderId :
forall st t,
currentTerm st < currentTerm (advanceCurrentTerm st t) \/
leaderId (advanceCurrentTerm st t) = leaderId st.