Proof using rmri.
intros.
find_apply_lem_hyp lifted_committed_committed.
find_eapply_lem_hyp committed_log_allEntries_preserved; eauto.
apply committed_lifted_committed.
eapply committed_log_allEntries_preserved; eauto;
intros;
repeat find_rewrite_lem msg_deghost_spec;
rewrite msg_deghost_spec; auto.
Qed.

(* Specifications: *)
Lemma lift_max_index_sanity :
forall (net : ghost_log_network) h,
msg_refined_raft_intermediate_reachable net ->
maxIndex_sanity (deghost (mgv_deghost net)) ->
lastApplied (snd (nwState net h)) <= maxIndex (log (snd (nwState net h))) /\
commitIndex (snd (nwState net h)) <= maxIndex (log (snd (nwState net h))).