reserve X for set,
  F for Filter of BoolePoset X,
  x for Element of BoolePoset X ,
  z for Element of X;

theorem Th9:
  FixedUltraFilters X c= Filt BoolePoset X
proof
  let F be object;
  assume F in FixedUltraFilters X;
  then
  ex x being Element of BoolePoset X st F = uparrow x & ex y being Element
  of X st x = {y};
  hence thesis;
end;
