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

Theorem packets_ge_prevTerm_only_new_packets_matter :
forall net ps' l st',
packets_ge_prevTerm net ->
(forall p, In p ps' -> In p (nwPackets net) \/ In p l) ->
packets_ge_prevTerm (mkNetwork l st') ->
packets_ge_prevTerm (mkNetwork ps' st').