proposition: Lemma trichotomy : forall a b : Ord , a < b \/ a = b \/ b < a.
proof: Proof. Proof (Lt_connect AX1). Ltac tricho t u Hname := case (@trichotomy t u); [ intro Hname | intros [Hname|Hname]]. Lemma lt_or_ge : forall a b: Ord, a < b \/ b <= a. Proof. intros a b ; tricho a b H;auto with schutte. Qed.
imports: Coq(Relations Classical Classical_sets) ZornsLemma(CountableTypes) hydras(Well_Orders Lub Countable)