Section cartesian_is_relation_proof.
Variable A B : Ens.
Variable U : Ens.
Variable i : IN U (Cartesian A B).
Let step1 : in_cartesian A B U.
Proof Cartesian_pr2 A B U i.
Proof in_cartesian_pair A B U step1.
End cartesian_is_relation_proof.
Proof cartesian_is_relation_Out.

Theorem cartesian_subs_are_relations :
forall (A B R : Ens) (s : SUB R (Cartesian A B)), is_a_relation R.