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 lifted_sms_nw : forall (net : network (params := raft_refined_multi_params)) h p t leaderId prevLogIndex prevLogTerm entries leaderCommit e, state_machine_safety (deghost net) -> In p (nwPackets net) -> pBody p = AppendEntries t leaderId prevLogIndex prevLogTerm entries leaderCommit -> t >= currentTerm (snd (nwState net h)) -> commit_recorded (deghost net) h e -> (prevLogIndex > eIndex e \/ (prevLogIndex = eIndex e /\ prevLogTerm = eTerm e) \/ eIndex e > maxIndex entries \/ In e entries).