
theorem
  for L be lower-bounded antisymmetric with_suprema RelStr for a,b be
  Element of L holds a"\/"b = Bottom L implies a = Bottom L & b = Bottom L
proof
  let L be lower-bounded antisymmetric with_suprema RelStr;
  let a,b be Element of L;
  assume a"\/"b = Bottom L;
  then a <= Bottom L & b <= Bottom L by YELLOW_0:22;
  hence thesis by Th19;
end;
