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

theorem Th16:
  FixedUltraFilters X is_FreeGen_set_of InclPoset Filt BoolePoset X
proof
  set FUF = FixedUltraFilters X;
  set IP = InclPoset Filt BoolePoset X;
  let L be continuous complete non empty Poset;
  let f be Function of FUF, the carrier of L;
  reconsider F = f-extension_to_hom as CLHomomorphism of IP, L by
WAYBEL16:def 1;
  take F;
  thus F|FUF = f by Th14;
  let h9 be CLHomomorphism of IP, L;
  assume h9|FUF = f;
  hence thesis by Th15;
end;
