Definition lifted_entries_gt_0 (net : ghost_log_network) : Prop :=
    forall h e,
      In e (log (snd (nwState net h))) -> eIndex e > 0.

Lemma lifted_maxIndex_sanity_append_entries : forall xs (p : ghost_log_packet) ys (net : ghost_log_network) st' ps' gd d m t n pli plt es ci, handleAppendEntries (pDst p) (snd (nwState net (pDst p))) t n pli plt es ci = (d, m) -> gd = update_elections_data_appendEntries (pDst p) (nwState net (pDst p)) t n pli plt es ci -> snd (pBody p) = AppendEntries t n pli plt es ci -> lifted_maxIndex_sanity net -> state_machine_safety (deghost (mgv_deghost net)) -> msg_refined_raft_intermediate_reachable net -> nwPackets net = xs ++ p :: ys -> (forall h, st' h = update name_eq_dec (nwState net) (pDst p) (gd, d) h) -> (forall (p' : ghost_log_packet), In p' ps' -> In p' (xs ++ ys) \/ mgv_deghost_packet p' = mkPacket (params := raft_refined_multi_params) (pDst p) (pSrc p) m) -> lifted_maxIndex_sanity (mkNetwork ps' st').