proposition: Lemma cPr_cplt E F : Pr d E != 0 -> `Pr_[ ~: F | E] = 1 - `Pr_[F | E].
proof: Proof. move=> PE0; rewrite /cPr -(divRR _ PE0) -divRBl; congr (_ / _). apply/esym; rewrite subR_eq addRC. rewrite -{1}(@setIT _ E) -(setUCr F) setIC setIUl Pr_union_disj //. by rewrite -setI_eq0 setIACA setICr set0I. 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