
theorem
  for N being continuous Lawson complete TopLattice holds N is compact
  Hausdorff topological_semilattice with_open_semilattices
proof
  let N be continuous Lawson complete TopLattice;
  thus N is compact Hausdorff;
  InclPoset sigma N is continuous;
  hence N is topological_semilattice by Th22;
  thus thesis;
end;
