proposition: Lemma Pr_fdist_proj23_domin (A B C : finType) (P : {fdist A * B * C})E F G : Pr (fdist_proj23 P) (F `* G) = 0 -> Pr P (E `* F `* G) = 0.
proof: Proof. move/Pr_set0P => H; apply/Pr_set0P => -[[? ?] ?]. rewrite !inE /= -andbA => /and3P[aE bF cG]. by apply/fdist_proj23_domin/H; rewrite inE /= bF cG. 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