Instance Cross_prod : forall A B saA saB,
@Cross_alg A saA ->
@Cross_alg B saB ->
@Cross_alg (A * B) (Join_prod _ saA _ saB).

Lemma sa_distributive_bij : forall A B JA bij,
@sa_distributive A JA ->
@sa_distributive B (Join_bij A JA B bij).