proposition: Theorem phi_spec1 : forall alpha beta gamma, nf alpha -> nf beta -> nf gamma -> gamma < alpha -> phi gamma (phi alpha beta) = phi alpha beta.
proof: Proof. intros. case (phi_le_ge H H0 ). intros alpha' (beta', (H'1,(H'2,H'3))). rewrite H'1. simpl. rewrite (compare_rw_lt);auto with T2. apply lt_le_trans with alpha;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