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).

Lemma proj1_comp :
forall x y : cart E F, Equal x y -> Equal (proj1 x) (proj1 y).