proposition: Lemma Pr_domin_setX (A B : finType) (P : {fdist A * B}) E F : Pr P`1 E = 0 -> Pr P (E `* F) = 0.
proof: Proof. move/Pr_set0P => H; apply/Pr_set0P => -[? ?]. by rewrite inE /= => /andP[/H /dom_by_fdist_fst ->]. 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