reserve T for non empty RelStr,
  a for Element of T;

theorem
  for DP be discrete non empty RelStr, x,y be Element of DP holds x <= y
  iff x = y
proof
  let DP be discrete non empty RelStr, x,y be Element of DP;
  hereby
    assume x <= y;
    then [x,y] in the InternalRel of DP by ORDERS_2:def 5;
    then [x,y] in id (the carrier of DP) by Def1;
    hence x = y by RELAT_1:def 10;
  end;
  assume x = y;
  then [x,y] in id (the carrier of DP) by RELAT_1:def 10;
  then [x,y] in the InternalRel of DP by Def1;
  hence thesis by ORDERS_2:def 5;
end;
