Proof using rmri rri.
intros.
eapply lifted_sms_nw.
- eauto.
- eauto using in_mgv_ghost_packet.
- rewrite pBody_mgv_deghost_packet. eauto.
- rewrite msg_deghost_spec with (net0 := net). eauto.
- auto.
Qed.

(* Specifications: *)
Lemma commit_recorded_lift_intro :
forall (net : network (params := raft_refined_multi_params)) 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 net) h e.