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

theorem :: Theorem 4.17, p. 90-91
  for L being continuous complete LATTICE, G being set st G
  is_FreeGen_set_of L & card G = card X holds L, InclPoset Filt BoolePoset X
  are_isomorphic
proof
A1: FixedUltraFilters X is_FreeGen_set_of InclPoset Filt BoolePoset X & card
  X = card FixedUltraFilters X by Th10,Th16;
  let L be continuous complete LATTICE, G be set;
  assume G is_FreeGen_set_of L & card G = card X;
  hence thesis by A1,Th17;
end;
