Section powerplus2.
Variable A B X Y : Ens.
Hypothesis x : IN X A.
Hypothesis y : IN Y B.
Let U := union A B.
Let step1 : SUB A U.
Proof union_pr1 A B.
Let step2 : SUB B U.
Proof union_pr2 A B.
Let step3 : IN X U.
Proof step1 X x.
Let step4 : IN Y U.
Proof step2 Y y.
Proof PowerTotal_th1 U X Y step3 step4.
End powerplus2.

Theorem PowerTotal_th2 :
forall (A B X Y : Ens) (x : IN X A) (y : IN Y B),
IN (PAIR X Y) (PowerTotal (union A B)).