Proof using.
intros.
unfold log_matching_hosts in *.
intuition; repeat rewrite <- H0 in *; eauto.
Qed.
Ltac log_matching_hosts_easy_case :=
repeat find_inversion; intros;
eapply log_matching_hosts_ignores_packets; eauto;
intros; simpl; repeat break_if; try congruence.

Lemma log_matching_state_same_packet_subset :
forall net net',
log_matching net ->
(forall h, log (nwState net h) = log (nwState net' h)) ->
(forall p, is_append_entries (pBody p) -> In p (nwPackets net') -> In p (nwPackets net)) ->
log_matching net'.