proposition: Lemma phi_to_psi_1 : forall beta1 beta2 n, alpha < beta1 -> [alpha, (cons beta1 beta2 0 (F n))] = phi alpha (cons beta1 beta2 0 (F (S n))).
proof: Proof. intros. generalize (phi_of_psi_succ alpha beta1 beta2 n). case (lt_ge_dec alpha beta1). auto with T2. intro. absurd (alpha < alpha). apply lt_irr. eapply lt_le_trans;eauto 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