Proof using.
intros.
unfold handleAppendEntriesReply in *.
repeat (break_match; repeat (find_inversion; simpl in *)); intuition.
Qed.

Lemma handleAppendEntries_doesn't_send_AE :
forall n st t i l t' l' l'' st' m,
handleAppendEntries n st t i l t' l' l'' = (st', m) ->
~ is_append_entries m.