Proof using.
unfold committed.
intros.
break_exists_exists.
intuition.
eapply directly_committed_allEntries_preserved; eauto.
Qed.

Lemma lifted_committed_log_allEntries_preserved :
forall net net' e t,
lifted_committed net e t ->
(forall h e',
In e' (log (snd (nwState net h))) ->
In e' (log (snd (nwState net' h)))) ->
(forall h e' t',
In (t', e') (allEntries (fst (nwState net h))) ->
In (t', e') (allEntries (fst (nwState net' h)))) ->
lifted_committed net' e t.