
theorem Th19:
  for L be lower-bounded non empty antisymmetric RelStr for a be
  Element of L holds a <= Bottom L implies a = Bottom L
proof
  let L be lower-bounded non empty antisymmetric RelStr;
  let a be Element of L;
A1: Bottom L <= a by YELLOW_0:44;
  assume a <= Bottom L;
  hence thesis by A1,YELLOW_0:def 3;
end;
