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

Lemma doGenericServer_lastApplied : forall h st out st' ms, doGenericServer h st = (out, st', ms) -> lastApplied st' = lastApplied st \/ (lastApplied st < commitIndex st /\ lastApplied st' = commitIndex st).