proposition: Lemma succ_mono (alpha beta : Ord): alpha < beta -> succ alpha < succ beta.
proof: Proof. Proof with eauto with schutte. intros; eapply le_lt_trans with beta ... - eapply lt_succ_le ... Qed.
imports: Coq(Relations Classical Classical_sets) ZornsLemma(CountableTypes) hydras(Well_Orders Lub Countable)