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

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