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

theorem
  for X be set, A be Subset of X holds
  {B where B is Element of BoolePoset X: A c= B} =
  uparrow PLO2bis A
  proof
    let X be set,A be Subset of X;
    reconsider Z=PLO2bis A as Element of BoolePoset X;
    set S1={Y where Y is Subset of X : Z c=Y};
    set S2={B where B is Subset of X: A c= B};
    {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 WAYBEL15:2;
  end;
