Proof using lmi rri.
intros.
pose proof (lift_prop _ log_matching_invariant).
find_insterU. conclude_using eauto.
auto.
Qed.

(* Specifications: *)
Lemma lifted_log_matching_host :
forall net,
refined_raft_intermediate_reachable net ->
(forall h h',
entries_match (log (snd (nwState net h))) (log (snd (nwState net h')))) /\
(forall h i,
1 <= i <= maxIndex (log (snd (nwState net h))) ->
exists e, eIndex e = i /\ In e (log (snd (nwState net h)))) /\
(forall h e,
In e (log (snd (nwState net h))) -> eIndex e > 0).