Section set_together_def.
Variables (f : Map C A) (g : Map C B).
Definition S_together_fun (c : C) := Build_Sprod (f c) (g c).
Definition S_together := Build_Map S_together_map_law.
End set_together_def.
(* ve'rification des lois *)
Definition S_op_together := Build_Map2 S_together_l S_together_r.
End set_op_together_def.

Lemma Eq2_Sprod : Eq2_prod_law (Proj2_SPROD A B) S_op_together.