proposition: Lemma is_succ_not_lim : forall alpha, is_successor alpha -> ~ is_limit alpha.
proof: Proof. induction alpha. intro;apply zero_not_lim. inversion_clear 1. apply (F_not_lim (S n)). red;inversion 1. subst alpha3;inversion H1. case IHalpha3;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