theorem
  for T being TopSpace, FX being Subset-Family of T holds clf FX is closed
proof
  let T be TopSpace, FX be Subset-Family of T;
  for V being Subset of T st V in clf FX holds V is closed
  proof
    let V be Subset of T;
    assume V in clf FX;
    then ex W being Subset of T st V = Cl W & W in FX by Def2;
    hence thesis;
  end;
  hence thesis by TOPS_2:def 2;
end;
