
theorem Th9:
  for L being upper-bounded antisymmetric non empty RelStr for X
  being non empty Subset of L holds Top L in uparrow X
proof
  let L be upper-bounded antisymmetric non empty RelStr, X be non empty Subset
  of L;
  consider y being object such that
A1: y in X by XBOOLE_0:def 1;
  reconsider y as Element of X by A1;
  uparrow X = {x where x is Element of L: ex y being Element of L st x >=
  y & y in X} & Top L >= y by WAYBEL_0:15,YELLOW_0:45;
  hence thesis;
end;
