proposition: Lemma fsdistbindE x : fsdistbind x = \sum_(a <- finsupp p) p a * (g a) x.
proof: Proof. rewrite fsdistbindEcond. case: ifPn => // aD. apply/eqP; move: aD; apply: contraLR. rewrite eq_sym negbK sumR_neq0; last by move=> ?; exact: mulR_ge0. case => i [] suppi pg0. apply/bigfcupP; exists (g i). - by rewrite in_imfset. - by rewrite mem_finsupp; apply/gtR_eqF/(pmulR_rgt0' pg0). 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