But a > b, c > d b+d is not right.

That is to say, if A+C > B+D holds, A > B and C > D may not be obtained.

For example, a=2, b = 3；; C=4, d= 1, then A+C = 2+4 = 6 > B+D = 3+ 1 = 4.

But a > b doesn't hold.

So the double arrow is wrong.