proposition: Lemma phi0_mono_R_weak (alpha beta: Ord): phi0 alpha <= phi0 beta -> alpha <= beta.
proof: Proof. pattern phi0; apply phi0_elim. intros f Hf; eapply ordering_function_mono_weakR;eauto. all : split. Qed.
imports: Coq(Arith Logic.Epsilon Ensembles Lia) ZornsLemma(CountableTypes)