Definition COMP (F G : Ens) := REPLACEMENT (Comp_prop F G).
(******* note that this is the full composition of relations, like composition of correspondences in algebraic geometry ************)

Theorem COMP_th1 : forall F G : Ens, is_a_relation (COMP F G).
Proof
fun (F G X : Ens) (i : IN X (COMP F G)) =>
Comp_pair F G X (COMP_pr2 F G X i).