Instance agB : ageable B := (ag_bij _ _ ag bijAB).

Lemma age_twin {A} {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A}{AG: ageable A}{XA: Age_alg A}: forall phi1 phi2 n phi1', level phi1 = level phi2 -> ageN n phi1 = Some phi1' -> exists phi2', ageN n phi2 = Some phi2' /\ level phi1' = level phi2'.