Proof using.
unfold leader_sublog_host_invariant in *. intros.
specialize (H leader e h).
forward H; [apply H1; auto|].
intuition.
rewrite H0 in *. specialize (H1 leader). intuition.
rewrite H7 in *; auto.
rewrite H0 in *. auto.
Qed.

Lemma leader_sublog_invariant_subset :
forall net net',
leader_sublog_invariant net ->
(forall p, is_append_entries (pBody p) -> In p (nwPackets net') -> In p (nwPackets net)) ->
(forall h, log (nwState net h) = log (nwState net' h)) ->
(forall h, type (nwState net' h) = Leader ->
type (nwState net h) = Leader /\
currentTerm (nwState net h) = currentTerm (nwState net' h)) ->
leader_sublog_invariant net'.