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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'.