Proof using rri.
unfold commit_recorded.
intros.
rewrite deghost_spec.
auto.
Qed.

Lemma msg_commit_recorded_lift_intro :
forall (net : ghost_log_network) h e,
In e (log (snd (nwState net h))) ->
(eIndex e <= lastApplied (snd (nwState net h)) \/
eIndex e <= commitIndex (snd (nwState net h))) ->
commit_recorded (deghost (mgv_deghost net)) h e.