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

Lemma age1_join_eq {A} {JA: Join A}{PA: Perm_alg A}{agA: ageable A}{AgeA: Age_alg A} : forall phi1 phi2 phi3, join phi1 phi2 phi3 -> forall phi1', age1 phi1 = Some phi1' -> forall phi2', age1 phi2 = Some phi2' -> forall phi3', age1 phi3 = Some phi3' -> join phi1' phi2' phi3'.