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