proposition: Lemma jBayes E F : \Pr_PQ[E | F] = \Pr_QP [F | E] * Pr P E / Pr Q F.
proof: Proof. rewrite 2!jcPrE Bayes /Rdiv -2!mulRA. rewrite EsetT Pr_XsetT setTE Pr_setTX /cPr; congr ((_ / _) * (_ / _)). by rewrite EsetT setTE [in RHS]setIX Pr_fdistX setIX. by rewrite setTE Pr_fdistX. Qed.
imports: mathcomp(all_ssreflect ssralg matrix) mathcomp(Rstruct) Reals ssrR realType_ext Reals_ext logb ssr_ext ssralg_ext bigop_ext fdist proba