proposition: Lemma gt0 (d : t) a : a \in finsupp d -> 0 < d a.
proof: Proof. by rewrite mem_finsupp => da; apply/RltP; rewrite lt0r da; exact/RleP/ge0. 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