proposition: Lemma phi_to_psi_6 : forall beta, nf beta -> phi alpha beta = beta -> [alpha, beta] =phi alpha (succ beta).
proof: Proof. intros. case (phi_fix _ H0 ). intros beta1 (beta2,(H2,H3)). subst beta. generalize (phi_to_psi_1 beta2 0 H3). simpl (succ (cons beta1 beta2 0 zero)). generalize H3 ; case beta1. inversion 1. 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