proposition: Lemma mutual_infoE3 : mutual_info PQ = `H P + `H Q - `H PQ.
proof: Proof. rewrite mutual_infoE; have := chain_rule QP. rewrite addRC -subR_eq -(fdistXI PQ) -/QP => <-. by rewrite -addR_opp oppRB fdistX1 -/Q addRA joint_entropyC. 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