Proof using.
intros. unfold handleAppendEntriesReply, advanceCurrentTerm in *.
repeat break_match; find_inversion; auto.
Qed.

(* Specifications: *)
Lemma handleRequestVote_type :
forall st h h' t lli llt st' m,
handleRequestVote h st t h' lli llt = (st', m) ->
(type st' = type st /\ currentTerm st' = currentTerm st /\ log st' = log st) \/
type st' = Follower.
Lemma handleAppendEntriesReply_type_term :
forall h st h' t es r st' ms,
handleAppendEntriesReply h st h' t es r = (st', ms) ->
(type st' = type st /\ currentTerm st' = currentTerm st) \/
(type st' = Follower /\ currentTerm st' >= currentTerm st).