reserve a,b for object, I,J for set;

theorem Lem2:
  for R being asymmetric non empty RelStr
  for x,y being Element of R holds x <= y iff x < y
  proof
    let R be asymmetric non empty RelStr;
    let x,y be Element of R;
    hereby
      assume Z0: x <= y;
      then x <> y;
      hence x < y by Z0,ORDERS_2:def 6;
    end;
    assume x < y;
    hence x <= y by ORDERS_2:def 6;
  end;
