
theorem Th10:
  for N being Lawson complete TopLattice holds sigma N c= lambda N
proof
  let N be Lawson complete TopLattice;
  set Z = {W\uparrow F where W, F is Subset of N: W in sigma N & F is finite};
  Z is Basis of N by WAYBEL19:32;
  then Z c= the topology of N by TOPS_2:64;
  then
A1: Z c= lambda N by Th9;
  sigma N c= Z by Th8;
  hence thesis by A1;
end;
