Proof power2_Out.
Section power3.
Variable A X Y : Ens.
Hypothesis x : IN X A.
Hypothesis y : IN Y A.
Let step1 : IN (Singleton X) (Powerset A).
Proof Powerset_th4 A X x.
Let step2 : IN (Singleton Y) (Powerset A).
Proof Powerset_th4 A Y y.

(* Specifications: *)
Lemma power3_Out : IN (Doubleton X Y) (Powerset A).
Proof Powerset_th2 A (Singleton X) (Singleton Y) step1 step2.