proposition: Lemma plus_mono_weak_l : forall alpha beta gamma, alpha <= beta -> alpha + gamma <= beta + gamma.
proof: Proof. intros alpha beta gamma H0; assert (H1 : ordinal alpha) by ( eauto with schutte). assert (H2 :ordinal beta) by ( eauto with schutte). case (minus_exists H0); intros khi ekhi; subst beta. rewrite <- plus_assoc. apply plus_mono_r_weak. apply le_plus_r. Qed.
imports: Coq(Arith Logic.Epsilon Ensembles) ZornsLemma(CountableTypes)