Proof using si rri.
intros.
pose proof (lift_prop _ logs_sorted_invariant).
find_insterU. conclude_using eauto.
unfold logs_sorted in *. break_and.
unfold logs_sorted_nw in *.
eapply H3.
- unfold deghost. simpl.
apply in_map_iff. eauto.
- simpl. eauto.
Qed.

(* Specifications: *)
Lemma lifted_logs_sorted_host :
forall net h ,
refined_raft_intermediate_reachable net ->
sorted (log (snd (nwState net h))).