Proof power3_Out.
Section power4.
Variable A X : Ens.
Hypothesis x : IN X A.
Let sX := Singleton X.
Let P := Powerset A.
Let step1 : IN Zero P.
Proof Powerset_th1 A.
Let step2 : IN sX P.
Proof Powerset_th4 A X x.

Lemma power4_Out : IN (Second X) (Powerset P).
Proof Powerset_th5 P Zero sX step1 step2.