proposition: Lemma pred_of_limit : forall alpha, is_limit alpha -> nf alpha -> pred alpha = None.
proof: Proof. induction 1. - rewrite (pred_of_cons' n H); trivial. - rewrite (pred_of_cons (a :=alpha)(b:=beta) n). + rewrite IHis_limit; auto. eapply nf_c;eauto. + apply is_limit_ab with n gamma; constructor;auto. Qed.
imports: Coq(Arith List Lia Compare_dec Relations Wellfounded RelationClasses) hydras(Epsilon0) hydras(More_Arith Restriction) hydras(ON_Generic) hydras(rpo.term rpo.rpo) hydras(T2) hydras(Compat815)