proposition: Theorem phi_nf : forall alpha beta, nf alpha -> nf beta -> nf (phi alpha beta).
proof: Proof. intros t1 t2 v1 v2; case (phi_cases t1 v2). destruct 1. rewrite e;auto with T2. rewrite e;unfold psi;constructor;auto with T2. destruct 1 as (b', (V,(H,H0))). rewrite H. unfold psi;constructor;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