
theorem Th2:
  for x,y be R_eal holds y-x <= |.x-y.|
proof
  let x,y be R_eal;
  -|.x-y.| <= (x-y) by EXTREAL1:20;
  then -(x-y) <= |.x-y.| by XXREAL_3:60;
  hence thesis by XXREAL_3:26;
end;
