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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'.