Proof using.
unfold packets_gt_prevIndex. intros. simpl in *.
find_apply_hyp_hyp. intuition eauto.
Qed.

Theorem packets_gt_prevIndex_no_append_entries :
forall net ps' l st',
packets_gt_prevIndex net ->
(forall p, In p ps' -> In p (nwPackets net) \/ In p l) ->
(forall p, In p l -> ~ is_append_entries (pBody p)) ->
packets_gt_prevIndex (mkNetwork ps' st').