Proof relations_in_cartesian_Out.
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.

Lemma cartesian_is_relation_Out : is_a_pair U.
Proof in_cartesian_pair A B U step1.