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_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'))).