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

Lemma ageN_join2 {A} {JA: Join A}{PA: Perm_alg A}{agA: ageable A}{AgeA: Age_alg A}: forall n (w1 w2 w3 w3': A), join w1 w2 w3 -> ageN n w3 = Some w3' -> exists w1', exists w2', ageN n w1 = Some w1' /\ ageN n w2 = Some w2' /\ join w1' w2' w3'.