proposition: Lemma f1 : \sum_(a <- finsupp f) f a = 1.
proof: Proof. rewrite -DsuppE /D big_imfset /=; last by move=> i j _ _; exact: s_inj. rewrite (eq_bigr P) ?FSDist.f1 // => i _; rewrite /f fsfunE /D H. apply/eqP; case: ifPn => //; apply: contraNT => Pi0. by apply/imfsetP => /=; exists i => //; rewrite mem_finsupp eq_sym. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrnum) mathcomp(finmap) Reals mathcomp(mathcomp_extra) mathcomp(classical_sets boolp cardinality Rstruct reals) mathcomp(ereal topology esum measure probability) ssrR realType_ext Reals_ext ssr_ext ssralg_ext bigop_ext fdist convex