Proof using.
unfold leaderLogs_entries_match_nw.
intros.
eapply_prop_hyp In nwPackets; [|eauto 10].
match goal with
| [ H : _ |- _ ] =>
solve [eapply H; eauto;
repeat find_higher_order_rewrite;
eauto]
end.
Qed.

Lemma leaderLogs_entries_match_host_state_same :
forall net net',
leaderLogs_entries_match_host net ->
(forall h, leaderLogs (fst (nwState net' h)) = leaderLogs (fst (nwState net h))) ->
(forall h, log (snd (nwState net' h)) = log (snd (nwState net h))) ->
leaderLogs_entries_match_host net'.