proposition: Lemma Bayes (E F : {set A}) : `Pr_[E | F] = `Pr_[F | E] * Pr d E / Pr d F.
proof: Proof. have [PE0|PE0] := eqVneq (Pr d E) 0. by rewrite /cPr [in RHS]setIC !(Pr_domin_setI F PE0) !(div0R,mul0R). by rewrite /cPr -mulRA mulVR // mulR1 setIC. 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