simple induction E'; intros A' f' r' i.
exists (fun a : A => IN (f a) (sup A' f')).
simpl in |- *.
split.
intros.
elim (i (f' x)); auto with zfc.
intros a e.
cut (EQ (f a) (f' x)); auto with zfc.
intros e1.
exists
(dep_i A (fun a : A => EXType A' (fun y : A' => EQ (f a) (f' y))) a
(EXTypei A' (fun y : A' => EQ (f a) (f' y)) x e1)).
simpl in |- *.
auto with zfc.
auto with zfc.
simpl in |- *.
exists x; auto with zfc.
simple induction y; simpl in |- *.
simple induction 1; intros.
exists x0; auto with zfc.
Qed.

(* Specifications: *)
Theorem Power_mon : forall E E' : Ens, INC E E' -> INC (Power E) (Power E').
intros.
Theorem Power_mon : forall E E' : Ens, INC E E' -> INC (Power E) (Power E').
intros.