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

Lemma doLeader_same_lastApplied : forall st n os st' ms, doLeader st n = (os, st', ms) -> lastApplied st' = lastApplied st.