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). auto. 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: EPSILON0 Arith List Omega Compare_dec Relations Wellfounded Max Tools More_nat AccP not_decreasing EPSILON0 More_nat Gamma0_prelude Gamma0_length term rpo