reserve x,y,z for Element of REAL+;

theorem Th11:
  x -' y <=' x
proof
  per cases;
  suppose
    y <=' x;
    then x -' y + y = x by Def1;
    hence thesis by ARYTM_2:19;
  end;
  suppose
    not y <=' x;
    then x -' y = {} by Def1;
    hence thesis by Th6;
  end;
end;
