
theorem
  for L being complete LATTICE holds InclPoset sigma L is continuous iff
for S being complete LATTICE holds Sigma [:S, L:] = Omega [:Sigma S, Sigma L:]
proof
  let L be complete LATTICE;
  InclPoset sigma L is continuous iff for S being complete LATTICE holds
  sigma [:S, L:] = the topology of [:Sigma S, Sigma L:] by Th30;
  hence thesis by Th32;
end;
