Proof of these two lemma in analytical number theory

Question

in publication On Gaps Between Primitive Roots in the Hamming Metric by Dietmann, Sharplinski & Elsholtz, there are 2 lemmas:

H is a binary entropy function.

Unfortunately these lemmas are not proved in that publication. They are proved in publications from bibliography, but they are both paid (one is a book over 50 $). I need proofs of these lemmas.

Do You know a place where these lemmas are proved for free?

Thanks for help.