proposition: Lemma phi_to_psi_1 : forall beta1 beta2 n, alpha t2< beta1 -> [alpha, (gcons beta1 beta2 0 (fin n))] = phi alpha (gcons beta1 beta2 0 (fin (S n))).
proof: Proof. intros; generalize (phi_of_psi_succ alpha beta1 beta2 n). case (lt_ge_dec alpha beta1). - auto with T2. - intro; absurd (alpha t2< alpha). apply lt_irr. eapply lt_le_trans;eauto 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)