Section Def.
Variable E F : Setoid.
Comments "The type of elements of a cartesian product:".
Record cart_type : Type :=  {cart_l : E; cart_r : F}.
Comments "Equality of couples:".
Definition cart_eq (x y : cart_type) :=
Equal (cart_l x) (cart_l y) /\ Equal (cart_r x) (cart_r y).

Lemma cart_eq_equiv : equivalence cart_eq.