proposition: Lemma pr_in_pairCA E F G : `Pr[ [% X, [%Y, Z]] \in E `* (F `* G) ] = `Pr[ [% Y, [%X, Z]] \in F `* (E `* G)].
proof: Proof. by rewrite !pr_eq_setE; apply eq_bigl => u; rewrite !inE /= andbCA. 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