proposition: Lemma cPr_eq0 E F : `Pr_[E | F] = 0 <-> Pr d (E :&: F) = 0.
proof: Proof. split; rewrite /cPr; last by move=> ->; rewrite div0R. rewrite /cPr /Rdiv mulR_eq0 => -[//|/invR_eq0]. by rewrite setIC; exact: Pr_domin_setI. 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