proposition: Lemma E_Ind (P : {fdist A}) s : `E (Ind s : {RV P -> R}) = Pr P s.
proof: Proof. rewrite /Ex /Ind /Pr (bigID (mem s)) /=. rewrite [X in _ + X = _]big1; last by move=> i /negbTE ->; rewrite mul0R. by rewrite addR0; apply: eq_bigr => i ->; rewrite mul1R. 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