Definition proj1_map : MAP (cart E F) E := Build_Map proj1_comp.Definition proj2_map : MAP (cart E F) F := Build_Map proj2_comp.Definition couple (x : E) (y : F) : cart E F := Build_cart_type x y.

(* Specifications: *)
Lemma couple_comp : forall (x x' : E) (y y' : F), Equal x x' -> Equal y y' -> Equal (couple x y) (couple x' y').
Lemma coupl_proj : forall x : cart E F, Equal (couple (proj1 x) (proj2 x)) x.