
theorem
  for L being lower-bounded antisymmetric non empty RelStr for X being
  non empty lower Subset of L holds Bottom L in X
proof
  let L be lower-bounded antisymmetric non empty RelStr, X be non empty lower
  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;
  Bottom L <= y by YELLOW_0:44;
  hence thesis by WAYBEL_0:def 19;
end;
