proposition: Lemma jcPr_diff E1 E2 F : \Pr_[E1 :\: E2 | F] = \Pr_[E1 | F] - \Pr_[E1 :&: E2 | F].
proof: Proof. rewrite jcPrE DsetT cPr_diff jcPrE; congr (_ - _). by rewrite 2!EsetT setIX setTI -EsetT jcPrE. Qed.
imports: mathcomp(all_ssreflect ssralg matrix) mathcomp(Rstruct) Reals ssrR realType_ext Reals_ext logb ssr_ext ssralg_ext bigop_ext fdist proba