Proof Domain_th1_Out.
(***** same thing for Range *********)
Definition Range (R : Ens) := REPLACEMENT (Range_prop R).

(* Specifications: *)
Theorem Range_pr1 : forall (R X : Ens) (p : Range_prop R X), IN X (Range R).
Proof fun R : Ens => REPLACEMENT_pr1 (Range_prop R) (Range_prop_bounded R).
Theorem Range_pr2 : forall (R X : Ens) (i : IN X (Range R)), Range_prop R X.
Proof fun R : Ens => REPLACEMENT_pr2 (Range_prop R) (Range_prop_bounded R).
Theorem inverse_EV_th1 :
forall (R Y : Ens) (i : IN Y (Range R)), IN (PAIR (inverse_EV R Y) Y) R.