proposition: Lemma succ_as_plus : forall alpha, nf alpha -> alpha + one = succ alpha.
proof: Proof. intro alpha;elim alpha. simpl;auto with T2. unfold one;simpl. intros. case t; case t0. simpl. rewrite plus_0_r;auto with T2. simpl. rewrite <- H1. simpl;auto with T2. inversion H2;auto with T2. simpl. rewrite <- H1. simpl;auto with T2. inversion H2;auto with T2. simpl. rewrite <- H1. simpl;auto with T2. inversion H2;auto with T2. 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