proposition: Lemma pr_in_pairA E F G : `Pr[ [% X, [% Y, Z]] \in E `* (F `* G) ] = `Pr[ [% [% X, Y], Z] \in (E `* F) `* G].
proof: Proof. by rewrite !pr_eq_setE; apply eq_bigl => u; rewrite !inE /= andbA. Qed.
imports: mathcomp(all_ssreflect ssralg ssrnum matrix) mathcomp(Rstruct reals) Reals Lra ssrR Reals_ext realType_ext logb ssr_ext ssralg_ext bigop_ext fdist