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_commitIndex : forall st n os st' ms, doLeader st n = (os, st', ms) -> sorted (log st) -> commitIndex st <= maxIndex (log st) -> commitIndex st' <= maxIndex (log st').