reserve
  X for non empty set,
  FX for Filter of X,
  SFX for Subset-Family of X;

theorem
  for A be Element of BoolePoset X holds
  {B where B is Element of BoolePoset X:A c= B} is Filter of BoolePoset X
  proof
    let A be Element of BoolePoset X;
    reconsider A as Subset of X by WAYBEL_8:26;
    {B where B is Element of BoolePoset X:A c=B}=
    {B where B is Subset of X: A c= B} by Th29;
    hence thesis by Th30Thm70;
  end;
