Definition msg_lifted_leader_sublog_host (net : ghost_log_network) : Prop :=
    forall leader e h,
      type (snd (nwState net leader)) = Leader ->
      In e (log (snd (nwState net h))) ->
      eTerm e = currentTerm (snd (nwState net leader)) ->
      In e (log (snd (nwState net leader))).

Lemma lifted_terms_and_indices_from_one_log : forall net h, refined_raft_intermediate_reachable net -> terms_and_indices_from_one (log (snd (nwState net h))).