Section Projections.
Variable E F : Setoid.
Definition proj1 (x : cart E F) : E := cart_l x.
Definition proj2 (x : cart E F) : F := cart_r x.
Comments "We note" (proj1 x) "and" (proj2 x) "the components of a couple" x
"in " (cart E F).
red in |- *.
simpl in |- *.
unfold app_rel, cart_eq in |- *; intuition.
Qed.

Lemma proj2_comp :
forall x y : cart E F, Equal x y -> Equal (proj2 x) (proj2 y).