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

Lemma age1_list_join2 {A} {JA: Join A}{PA: Perm_alg A}{agA: ageable A}{AgeA: Age_alg A}: forall (l: list A) phi phi2 phi2', age1 phi2 = Some phi2' -> list_join phi l phi2 -> exists l', exists phi', age1 phi = Some phi' /\ age1_list l l' /\ list_join phi' l' phi2'.