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.
End PROD'.

Lemma age1_join_eq {A}  {JA: Join A}{PA: Perm_alg A}{agA: ageable A}{AgeA: Age_alg A} : forall phi1 phi2 phi3,
join phi1 phi2 phi3 ->
forall phi1', age1 phi1 = Some phi1' ->
forall phi2', age1 phi2 = Some phi2' ->
forall phi3', age1 phi3 = Some phi3' ->
join phi1' phi2' phi3'.