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_pr1 : forall F G X : Ens, Comp_prop F G X -> IN X (COMP F G).
Proof
fun F G X : Ens =>
REPLACEMENT_pr1 (Comp_prop F G) (composition_bounded F G) X.