proposition: Lemma entropyB : `H P - cond_entropy PQ = `H Q - cond_entropy QP.
proof: Proof. rewrite subR_eq addRAC -subR_eq subR_opp -chain_rule joint_entropyC. by rewrite -/(joint_entropy (fdistX PQ)) chain_rule fdistX1 -/Q fdistXI. 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