proposition: Lemma pred_of_succ : forall alpha, nf alpha -> pred (succ alpha) = Some alpha.
proof: Proof. induction alpha;simpl. auto with T2. case alpha1;case alpha2. simpl. inversion_clear 1;auto with T2. inversion H0. inversion H5. inversion H4. inversion H12. inversion H4. inversion H4. simpl. intros;rewrite IHalpha3. auto with T2. inversion H;auto with T2. simpl. intros;rewrite IHalpha3. auto with T2. inversion H;auto with T2. simpl. intros;rewrite IHalpha3. auto with T2. inversion H;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