Section PROD.
Variable A : Type.
Variable J_A: Join A.
Variable saA : Perm_alg A.
Variable agA : ageable A.
Variable B: Type.
Variable J_B: Join B.
Variable saB : Perm_alg B.
Variable asa : Age_alg A.

Theorem asa_prod : @Age_alg (prod A B) _ (ag_prod A B agA).