Proof using.
intros. eapply packets_gt_prevIndex_only_new_packets_matter; eauto.
unfold packets_gt_prevIndex. intros. simpl in *. find_apply_hyp_hyp.
exfalso. match goal with H : _ |- _ => apply H end.
repeat eexists; eauto.
Qed.

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