Section power1.
Variable A X Y : Ens.
Hypothesis x : IN X (Powerset A).
Hypothesis y : IN Y (Powerset A).
Let step1 : SUB X A.
Proof Powerset_pr2 A X x.
Let step2 : SUB Y A.
Proof Powerset_pr2 A Y y.
Let step3 : SUB (union X Y) A.
Proof union_pr3 X Y A step1 step2.

(* Specifications: *)
Lemma power1_Out1 : IN (union X Y) (Powerset A).
Proof Powerset_pr1 A (union X Y) step3.