reserve U for Universe;
reserve x for Element of U;

theorem
  for x being Set of FinSETS holds x is finite
  proof
    let x be Set of FinSETS;
    x is FinSETS-set by Def10;
    then card x in card FinSETS by CLASSES4:30;
    then card x in omega by CLASSES4:19,CARD_3:def 15;
    hence thesis;
  end;
