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_identity {A} `{asaA: Age_alg A}: forall phi phi', age phi phi'->
identity phi -> identity phi'.