Definition match_index_all_entries_nw (net : network) : Prop :=
    forall p t es e,
      In p (nwPackets net) ->
      pBody p = AppendEntriesReply t es true ->
      currentTerm (snd (nwState net (pDst p))) = t ->
      In e (log (snd (nwState net (pDst p)))) ->
      eTerm e = t ->
      eIndex e <= maxIndex es ->
      type (snd (nwState net (pDst p))) = Leader ->
      In (t, e) (allEntries (fst (nwState net (pSrc p)))).Definition match_index_all_entries_inv (net : network) : Prop :=
    match_index_all_entries net /\ match_index_all_entries_nw net.

Lemma not_empty_false_elim : forall A (l : list A), not_empty l = false -> l = nil.