Section PROD'.
Variable A : Type.
Variable J_A: Join A.
Variable saA : Perm_alg A.
Variable B: Type.
Variable J_B: Join B.
Variable saB : Perm_alg B.
Variable agB : ageable B.
Variable asb : Age_alg B.

Lemma age_twin {A}  {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A}{AG: ageable A}{XA: Age_alg A}:
forall phi1 phi2 n phi1',
level phi1 = level phi2 ->
ageN n phi1 = Some phi1' ->
exists phi2', ageN n phi2 = Some phi2' /\ level phi1' = level phi2'.