Definition inverse_EV (R Y : Ens) := CHOICE (fun X : Ens => IN (PAIR X Y) R).

(* Specifications: *)
Theorem inverse_EV_pr : forall (R Y : Ens) (p : Range_prop R Y), IN (PAIR (inverse_EV R Y) Y) R.
Lemma Domain_prop_bounded_proof_1_Out : IN X T.
Lemma Domain_prop_bounded_Out : Bounded (Domain_prop R).
Theorem Domain_prop_bounded : forall R : Ens, Bounded (Domain_prop R).
Lemma Range_prop_bounded_proof_1_Out : IN Y T.
Lemma Range_prop_bounded_Out : Bounded (Range_prop R).
Theorem Range_prop_bounded : forall R : Ens, Bounded (Range_prop R).