
theorem
  for L being non empty LattStr, X being Subset of L st X is directed
  holds X is non empty
proof
  let L be non empty LattStr, X be Subset of L;
  assume for Y being finite Subset of X ex x being Element of L st "\/"(Y, L)
  [= x & x in X;
  then ex x being Element of L st "\/"({}X, L) [= x & x in X;
  hence thesis;
end;
