Definition safe s k := forall s2 k2,
  star s k s2 k2 -> exists s', exists k', step s2 k2 s' k'.Definition safeN s k := forall s2 k2 n,
  stepN n s k s2 k2 -> exists s', exists k', step s2 k2 s' k'.

Lemma safe_safeN s k : safe s k <-> safeN s k.