simple induction 1; intros HR1 HR2; split.
intros a1; elim (HR1 a1); intros a2 Ha2; exists a2; auto with zfc.
intros a2; elim (HR2 a2); intros a1 Ha1; exists a1; auto with zfc.
Qed.
Definition Power' (E : Ens') : Ens' :=
match E with
| sup' A f =>
sup' _
(fun P : A -> Prop =>
sup' _
(fun c : depprod'' A (fun a : A => P a) =>
match c with
| dep_i'' a p => f a
end))
end.

(* Specifications: *)
Theorem Power_sound_inj :
forall E : Ens', EQ (inj (Power' E)) (Power (inj E)).
Theorem Power_sound_inj :
forall E : Ens', EQ (inj (Power' E)) (Power (inj E)).