Definition lifted_state_machine_safety_nw' net :=
    forall p t leaderId prevLogIndex prevLogTerm entries leaderCommit e t',
      In p (nwPackets net) ->
      snd (pBody p) = AppendEntries t leaderId prevLogIndex prevLogTerm
                              entries leaderCommit ->
      lifted_committed net e t' ->
      t >= t' ->
      (prevLogIndex > eIndex e \/
       (prevLogIndex = eIndex e /\ prevLogTerm = eTerm e) \/
       eIndex e > maxIndex entries \/
       In e entries).

Lemma lifted_transitive_commit_invariant : forall net h e e' t, msg_refined_raft_intermediate_reachable net -> In e (log (snd (nwState net h))) -> In e' (log (snd (nwState net h))) -> eIndex e <= eIndex e' -> lifted_committed net e' t -> lifted_committed net e t.