Instance cross_split_fun: forall A (JOIN: Join A) (key: Type),
Cross_alg A -> Cross_alg (key -> A).

(* Specifications: *)
Lemma sa_distributive_prod : forall A B saA saB,
@sa_distributive A saA ->
@sa_distributive B saB ->
@sa_distributive (A * B) (Join_prod A _ B _).