Proof using rmri lsi rri.
intros.
pose proof msg_lift_prop _ (lift_prop _ leader_sublog_invariant_invariant) _ ltac:(eauto).
simpl in *.
unfold leader_sublog_invariant, leader_sublog_host_invariant, msg_lifted_leader_sublog_host in *.
intuition.
match goal with
| [ H : _ |- _ ] =>
specialize (H leader e h)
end.
repeat find_rewrite_lem deghost_spec.
repeat find_rewrite_lem msg_deghost_spec.
auto.
Qed.

(* Specifications: *)
Lemma lifted_entries_match_invariant :
forall net h h',
msg_refined_raft_intermediate_reachable net ->
entries_match (log (snd (nwState net h))) (log (snd (nwState net h'))).