proposition: Lemma le_antisym : forall a b, a <= b -> b <= a -> a = b.
proof: Proof. Proof (Le_antisym AX1). Lemma le_eq_or_lt : forall a b, a <= b -> a = b \/ a < b. Proof. intros a b [H |H];auto. Qed.
imports: Coq(Relations Classical Classical_sets) ZornsLemma(CountableTypes) hydras(Well_Orders Lub Countable)