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

Lemma ageN_join {A} {JA: Join A}{PA: Perm_alg A}{agA: ageable A}{AgeA: Age_alg A}: forall n (w1 w2 w3 w1': A), join w1 w2 w3 -> ageN n w1 = Some w1' -> exists w2', exists w3', ageN n w2 = Some w2' /\ ageN n w3 = Some w3' /\ join w1' w2' w3'.