How to Use Undiscovered Information Inequalities: Direct Applications of the Copy Lemma

We discuss linear programming techniques that help to deduce corollaries of non-classical inequalities for Shannon's entropy. We focus on direct applications of the copy lemma. These applications involve implicitly some (known or unknown) non-classical universal inequalities for Shannon's entropy, though we do not derive these inequalities explicitly. To reduce the computational complexity of these problems, we extensively use symmetry considerations. We present two examples of use of these techniques: we provide a reduced size formal inference of the best known bound for the Ingleton score (originally proven by Dougherty et al. with explicitly derived non-Shannon type inequalities), and improve the lower bound for the optimal information ratio of the secret sharing scheme for an access structure based on the Vámos matroid.