proposition: Lemma mutual_infoE0 : mutual_info PQ = \sum_(a in A) \sum_(b in B) PQ (a, b) * log (PQ (a, b) / (P a * Q b)).
proof: Proof. rewrite /mutual_info /div pair_big /=; apply eq_bigr; case => a b _ /=. have [->|H0] := eqVneq (PQ (a, b)) 0; first by rewrite !mul0R. by rewrite fdist_prodE. 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