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 as [e|e]. + rewrite e;auto with T2. + rewrite e;unfold psi;constructor;auto with T2. - destruct 1 as (b', (H,(H0,H1))). rewrite H0; unfold psi;constructor;auto with T2. Qed.
imports: Coq(Arith List Lia Compare_dec Relations Wellfounded RelationClasses) hydras(Epsilon0) hydras(More_Arith Restriction) hydras(ON_Generic) hydras(rpo.term rpo.rpo) hydras(T2) hydras(Compat815)