
theorem
  for L being non empty reflexive antisymmetric RelStr, x,y being Element of L
  st x << y & x >> y holds x = y
proof
  let L be non empty reflexive antisymmetric RelStr, x,y be Element of L;
  assume that
A1: x << y and
A2: x >> y;
A3: x <= y by A1,Th1;
  y <= x by A2,Th1;
  hence thesis by A3,ORDERS_2:2;
end;
