proposition: Lemma lt_epsilon0_okR: forall alpha, nf alpha -> alpha < epsilon0 -> lt_epsilon0 alpha.
proof: Proof. induction alpha. constructor. unfold epsilon0;intros. inversion H0. rewrite (lt_one_inv H3). right. apply IHalpha2. inversion H;auto with T2. compute;auto with T2. apply IHalpha3. inversion H;auto with T2. compute;auto with T2. apply transitivity with (cons alpha1 alpha2 n alpha3). apply lt_tail. auto with T2. auto with T2. inversion H2. inversion H10. inversion H2. inversion H2. 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