Since both 
and 
are both probability distributions, then by the information inequality (see chapter 2) we find
but the left hand side is also 
. Thus the result 
. Also, then, the last three terms on the right side of equation 4.12 sum to a non-positive number, i.e.
This result is also general, in fact by considering 
and 
resursively we can easily show 
.