theorem le_n_O_to_eq : \forall n:nat. n \leq O \to O=n.
intro.elim n.reflexivity.
apply False_ind.
-apply not_le_Sn_O.
-goal 17. apply H1.
+apply not_le_Sn_O;
+[2: apply H1 | skip].
qed.
theorem le_n_O_elim: \forall n:nat.n \leq O \to \forall P: nat \to Prop.