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 lifted_append_entries_reply_sublog : forall net p t es h e, refined_raft_intermediate_reachable net -> In p (nwPackets net) -> pBody p = AppendEntriesReply t es true -> currentTerm (snd (nwState net h)) = t -> type (snd (nwState net h)) = Leader -> In e es -> In e (log (snd (nwState net h))).