proposition: Lemma f1 : \sum_(x in {: 'I_4 * 'I_4}) f x = 1.
proof: Proof. rewrite (eq_bigr (fun x => f (x.1, x.2))); last by case. rewrite -(pair_bigA _ (fun x1 x2 => f (x1, x2))) /=. rewrite !big_ord_recl !big_ord0 /f /= !ffunE /=; field. Qed.
imports: mathcomp(all_ssreflect ssralg ssrnum fingroup finalg matrix) Reals Lra mathcomp(Rstruct) ssrR Reals_ext realType_ext logb ssr_ext ssralg_ext bigop_ext fdist proba jfdist_cond entropy