
theorem Th23:
  for L being upper-bounded Semilattice, V being Subset of L holds
  {x where x is Element of L : V "/\" {x} c= V} is non empty
proof
  let L be upper-bounded Semilattice, V be Subset of L;
  set G = {x where x is Element of L : V "/\" {x} c= V};
  V "/\" {Top L} = V by Th14;
  then Top L in G;
  hence thesis;
end;
