proposition: Lemma Rpos_convex : is_convex_set (fun x => 0 < x)%coqR.
proof: Proof. apply/asboolP => x y t Hx Hy. have [->|Ht0] := eqVneq t 0%:pr; first by rewrite conv0. apply addR_gt0wl; first by apply mulR_gt0 => //; exact/RltP/prob_gt0. apply mulR_ge0 => //; exact: ltRW. 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