Ltac log_matching_hosts_easy_case :=
    repeat find_inversion; intros;
    eapply log_matching_hosts_ignores_packets; eauto;
    intros; simpl; repeat break_if; try congruence.

(* Specifications: *)
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'.