proposition: Lemma ord_le_S: forall alpha:Ordinal, alpha <= ordS alpha.
proof: Proof. induction alpha. apply ord_le_respects_succ; trivial. apply ord_sup_minimal. intro. apply ord_le_trans with (ordS (o i)). apply H. apply ord_le_respects_succ. apply ord_le_sup. Qed.
imports: Classical