Definition S_op_together := Build_Map2 S_together_l S_together_r.

(* Specifications: *)
Lemma Eq1_Sprod : Eq1_prod_law (Proj1_SPROD A B) S_op_together.
Lemma Eq2_Sprod : Eq2_prod_law (Proj2_SPROD A B) S_op_together.
Lemma Unique_S_together : Unique_together_law (Proj1_SPROD A B) (Proj2_SPROD A B) S_op_together.