proposition: Lemma phi_principal : forall alpha beta, ap (phi alpha beta).
proof: Proof. intros alpha beta; case (phi_to_psi alpha beta);intros x (y,e); rewrite e;try constructor. 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)