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

theorem
  for x being object holds x is Set of FinSETS iff x is FinSet
  proof
    let x be object;
    hereby
      assume x is Set of FinSETS;
      then x is FinSETS-set by Def10;
      hence x is FinSet;
    end;
    assume x is FinSet;
    then x is FinSETS-set;
    hence thesis by Def10;
  end;
