
theorem
  for L being complete antisymmetric non empty RelStr, X being upper
  Subset of L st inf X in X holds X = uparrow inf X
proof
  let L be complete antisymmetric non empty RelStr, X be upper Subset of L
  such that
A1: inf X in X;
  X is_>=_than inf X by YELLOW_0:33;
  hence X c= uparrow inf X by YELLOW_2:2;
  thus thesis by A1,WAYBEL11:42;
end;
