Fixpoint safeN (n : nat) (c : C) (m : M) : Prop :=
  match n with
    | O => True
    | S n' =>
      match halted sem c with
        | None =>
          exists c', exists m',
            corestep sem ge c m c' m' /\
            safeN n' c' m'
        | Some i => True
      end
  end.

Lemma safe_corestep_backward c m c' m' n : corestep sem ge c m c' m' -> safeN (n - 1) c' m' -> safeN n c m.