reserve L for complete Scott TopLattice,
  x for Element of L,
  X, Y for Subset of L,
  V, W for Element of InclPoset sigma L,
  VV for Subset of InclPoset sigma L;

theorem :: Theorem 1.14 (5) iff (6) p. 107
  (for V ex VV st V = sup VV & for W st W in VV holds W is co-prime) &
  InclPoset sigma L is continuous iff InclPoset sigma L is
  completely-distributive
proof
  InclPoset sigma L = InclPoset the topology of L by Th23;
  hence thesis by WAYBEL_6:38;
end;
