Definition lifted_no_entries_past_current_term_host net :=
    forall (h : name) e,
      In e (log (snd (nwState net h))) ->
      eTerm e <= currentTerm (snd (nwState net h)).

Lemma all_the_way_deghost_spec : forall (net : ghost_log_network) h, snd (nwState net h) = nwState (deghost (mgv_deghost net)) h.