proposition: Lemma sup_members_disj (alpha : Ord) : alpha = sup (members alpha) -> alpha = zero \/ is_limit alpha.
proof: Proof. intro H; unfold is_limit. case (classic (alpha=zero)). - auto. - right;repeat split;auto. red; destruct 1 as [x Hx]. case (sup_members_not_succ x H Hx). Qed.
imports: Coq(Relations Classical Classical_sets) ZornsLemma(CountableTypes) hydras(Well_Orders Lub Countable)