Equivalence of Two Proof Techniques for Non-Shannon-type Inequalities

We compare two different techniques for proving non-Shannon-type information inequalities. The first one is the original Zhang-Yeung's method, commonly referred to as the copy/pasting lemma/trick. The copy lemma was used to derive the first conditional and unconditional non-Shannon-type inequalities. The second technique first appeared in Makarychev et al paper [7] and is based on a coding lemma from Ahlswede and K\"orner works. We first emphasize the importance of balanced inequalities and provide a simpler proof of a theorem of Chan's for the case of Shannon-type inequalities. We compare the power of various proof systems based on a single technique.