Definition leader_sublog (net : network) :=
    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))).

(* Specifications: *)
Lemma lifted_leader_sublog_invariant : forall net, refined_raft_intermediate_reachable net -> leader_sublog net.
Lemma lifted_leader_sublog_nw_invariant : forall net p t n pli plt es ci h e, refined_raft_intermediate_reachable net -> In p (nwPackets net) -> pBody p = AppendEntries t n pli plt es ci -> type (snd (nwState net h)) = Leader -> eTerm e = currentTerm (snd (nwState net h)) -> In e es -> In e (log (snd (nwState net h))).
Lemma invalid_index : forall net h e, refined_raft_intermediate_reachable net -> In e (log (snd (nwState net h))) -> eIndex e = S (maxIndex (log (snd (nwState net h)))) -> False.