
theorem Th34:
  for S being complete LATTICE holds UPS(S, BoolePoset{0}),
  InclPoset sigma S are_isomorphic
proof
  let S be complete LATTICE;
  consider F being Function of UPS(S, BoolePoset{0}), InclPoset sigma S such
  that
A1: F is isomorphic and
  for f being directed-sups-preserving Function of S, BoolePoset{0} holds F
  .f = f"{1} by Th33;
  take F;
  thus thesis by A1;
end;
