proposition: Lemma lt_omega_inv : forall alpha, nf alpha -> alpha < omega -> {n:nat | alpha = finite n}.
proof: Proof. intros a; case a. exists 0;simpl. auto with T2. intros. case (lt_cons_omega_inv H0);auto with T2. destruct 2;intros. exists (S n);auto with T2. simpl. subst t;subst t1;subst t0; 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