proposition: Lemma lt_omega_is_finite : forall alpha, nf alpha -> alpha < omega -> is_finite alpha.
proof: Proof. intros alpha N_alpha H; case (lt_omega_inv N_alpha H). destruct x; intro e;rewrite e; simpl; constructor. 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