Definition age1_list {A} `{ageable A} := list_forall2 age.

Lemma join_unage {A} {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A}{agA: ageable A}{AgeA: Age_alg A}: forall (phi3 phi1' phi2' phi3': A), age1 phi3 = Some phi3' -> join phi1' phi2' phi3' -> exists phi1, exists phi2, join phi1 phi2 phi3 /\ age1 phi1 = Some phi1' /\ age1 phi2 = Some phi2'.