Definition nextIndex_preserved st st' :=
    (type st' = Leader ->
     type st = Leader /\
     maxIndex (log st) <= maxIndex (log st') /\
     nextIndex st' = nextIndex st).

Lemma nextIndex_safety_preserved : forall st st', (forall h', type st = Leader -> Nat.pred (getNextIndex st h') <= maxIndex (log st)) -> nextIndex_preserved st st' -> (forall h', type st' = Leader -> Nat.pred (getNextIndex st' h') <= maxIndex (log st')).