proposition: Lemma phi_to_psi_2 : forall beta1 beta2 n, beta1 t2<= alpha -> [alpha, (gcons beta1 beta2 0 (fin n))] = phi alpha (gcons beta1 beta2 0 (fin n)).
proof: Proof. intros; case n. - simpl (fin 0); generalize (phi_of_psi alpha beta1 beta2). case (lt_ge_dec alpha beta1). intro; (absurd (alpha t2< alpha)). + apply lt_irr. + eapply lt_le_trans;eauto with T2. + auto with T2. - intro n0;generalize (phi_of_psi_succ alpha beta1 beta2 n0). case (lt_ge_dec alpha beta1). + intro; absurd (alpha t2< alpha). apply lt_irr. eapply lt_le_trans;eauto with T2. + 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)