Definition ghost_log_network : Type := @network _ raft_msg_refined_multi_params.Definition ghost_log_packet : Type := @packet _ raft_msg_refined_multi_params.Definition lifted_maxIndex_sanity (net : ghost_log_network) : Prop :=
    (forall h,
      lastApplied (snd (nwState net h)) <= maxIndex (log (snd (nwState net h)))) /\
    (forall h, commitIndex (snd (nwState net h)) <= maxIndex (log (snd (nwState net h)))).

Lemma msg_lifted_sorted_host : forall net h, msg_refined_raft_intermediate_reachable net -> sorted (log (snd (nwState net h))).