Proof using.
unfold raft_net_invariant_append_entries_reply. unfold logs_sorted.
intuition; simpl in *.
- unfold logs_sorted_host in *. simpl in *. intros.
find_apply_lem_hyp handleAppendEntriesReply_log.
repeat find_higher_order_rewrite. break_match; try find_rewrite; eauto.
- find_apply_lem_hyp handleAppendEntriesReply_packets. subst. simpl in *.
eapply logs_sorted_nw_packets_unchanged; eauto.
intros. find_apply_hyp_hyp. find_rewrite. in_crush.
- find_apply_lem_hyp handleAppendEntriesReply_packets. subst. simpl in *.
eapply packets_gt_prevIndex_packets_unchanged; eauto.
intros. find_apply_hyp_hyp. find_rewrite. in_crush.
- find_apply_lem_hyp handleAppendEntriesReply_packets. subst. simpl in *.
eapply packets_ge_prevTerm_packets_unchanged; eauto.
intros. find_apply_hyp_hyp. find_rewrite. in_crush.
Qed.

Lemma handleRequestVote_packets :
forall h st t candidate lli llt st' m,
handleRequestVote h st t candidate lli llt = (st', m) ->
~ is_append_entries m.