At a minimum, eq.33 shows that the corresponding even and odd sums, for A and B respectively, must have the same value. Consider equation 33 by splitting it into 2 cases. Let case 1 be the sums having a shared value of 0, and let case 2 be sharing any value other than 0. It is now shown by way of contradiction that it must be case one, that the shared value is 0, and furthermore, that it leads to the requirement that all the sums must individually be 0 at the same time.