Definition COMP (F G : Ens) := REPLACEMENT (Comp_prop F G).

(* Specifications: *)
Theorem COMP_pr1 : forall F G X : Ens, Comp_prop F G X -> IN X (COMP F G).
Theorem COMP_pr2 : forall F G X : Ens, IN X (COMP F G) -> Comp_prop F G X.
Theorem COMP_th1 : forall F G : Ens, is_a_relation (COMP F G).
Theorem COMP_th2 : forall F G : Ens, SUB (COMP F G) (Cartesian (Domain F) (Range G)).
Theorem COMP_th3 : forall (F G X : Ens) (i : IN X (COMP F G)), IN (PAIR (PR1 X) (Comp_INTER F G X)) F.
Theorem COMP_th4 : forall (F G X : Ens) (i : IN X (COMP F G)), IN (PAIR (Comp_INTER F G X) (PR2 X)) G.