proposition: Lemma Pr_cplt E : Pr E + Pr (~: E) = 1.
proof: Proof. rewrite /Pr -bigU /=; last by rewrite -subsets_disjoint. rewrite (_ : 1 = GRing.one _)//. by rewrite -(FDist.f1 P); apply eq_bigl => /= a; rewrite !inE /= orbN. 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