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)).