proposition: Lemma Pr_union_eq E1 E2 : Pr (E1 :|: E2) = Pr E1 + Pr E2 - Pr (E1 :&: E2).
proof: Proof. rewrite addRC -addR_opp -addRA addR_opp -Pr_diff -Pr_union_disj -?setU_setUD //. by rewrite -setI_eq0 setIDA setDIl setDv 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