proposition: Lemma ssum_scaled_set n (P : pred 'I_n) (X : {convex_set T}) (d : {fdist 'I_n}) (g : 'I_n -> T) : (forall j, P j -> g j \in X) -> \ssum_(i | P i) scalept (d i) (S1 (g i)) \in scaled_set X.
proof: Proof. move=> PX; apply big_ind. - by rewrite in_setE. - exact: addpt_scaled_set. - by move=> i /PX => giX; exact: scalept_scaled_set. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg fingroup perm matrix) mathcomp(mathcomp_extra boolp classical_sets Rstruct) mathcomp(ssrnum ereal) mathcomp(lra Rstruct reals) Reals ssrR Reals_ext Ranalysis_ext ssr_ext ssralg_ext logb realType_ext fdist