- intros a x px; eauto.
- intros a (x, px); apply (a x px).
Qed.

(* Specifications: *)
Lemma safeN_S n x : safeN (S n) x -> safeN n x.
Lemma safeN_le n n' x : n <= n' -> safeN n' x -> safeN n x.
Lemma konigsafe x : (forall P, P \/ ~P) -> (forall x, finite (R x)) -> (forall n, safeN n x) -> safe x.
End Safety.