
theorem
  for L being bounded antisymmetric non empty RelStr holds L is
  trivial iff Top L = Bottom L
proof
  let L be bounded antisymmetric non empty RelStr;
  thus L is trivial implies Top L = Bottom L;
  assume
A1: Top L = Bottom L;
  let x,y be Element of L;
  reconsider x, y as Element of L;
  x >= Bottom L & x <= Bottom L by A1,YELLOW_0:44,45;
  then
A2: x = Bottom L by ORDERS_2:2;
  y >= Bottom L & y <= Bottom L by A1,YELLOW_0:44,45;
  hence thesis by A2,ORDERS_2:2;
end;
