Proof using si rri.
intros.
pose proof (lift_prop _ logs_sorted_invariant).
find_insterU. conclude_using eauto.
unfold logs_sorted, logs_sorted_host in *. break_and.
unfold deghost in *. simpl in *. break_match. eauto.
Qed.

Lemma msg_lifted_sorted_host :
forall net h,
msg_refined_raft_intermediate_reachable net ->
sorted (log (snd (nwState net h))).