proposition: Lemma mutual_info0P : mutual_info PQ = 0 <-> PQ = P `x Q.
proof: Proof. split; last by rewrite /mutual_info => <-; rewrite div0P //; exact: dominatesxx. by rewrite /mutual_info div0P //; exact: Prod_dominates_Joint. Qed.
imports: mathcomp(all_ssreflect all_algebra fingroup perm matrix) Reals mathcomp(Rstruct) ssrR Reals_ext realType_ext ssr_ext ssralg_ext bigop_ext logb ln_facts fdist jfdist_cond proba binary_entropy_function divergence