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 _).