For all,whereHere is the entropy function and .

Let , where and ThenChas the property that for any binary word of lengthkthere is a unique with a prefix of . Now for any with length where the sum is over all of lengthkfor which is a prefix of . Hence From (2.16) this implies that where denotes the number of vectors in . The already proved first part of Theorem A shows that so that to prove (2.17) it suffices to bound from above.Now the definition (2.15) of an inflating vector implies that

so that The right side of (2.19) is just the tail of the binomial distribution. It is easily checked using Stirling's formula that for any constant and any the bound holds for all sufficiently largek. With more work one can obtain the more precise estimate (Ash [8], Lemma 4.7.2) that for any which used in (2.19) implies (2.17).