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

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