proposition: Lemma convmm_cset (p : {prob R}) (X : {convex_set A}) : X :<| p |>: X = X.
proof: Proof. rewrite eqEsubset; split=> [x /conv_in_conv_set'[] | x ?]. - by move=> x0 [] x1 [] ? [] ? ->; move/asboolP : (convex_setP X); apply. - by rewrite -(convmm p x); apply conv_in_conv_set. Qed.
imports: HB(structures) Reals mathcomp(all_ssreflect ssralg ssrnum) mathcomp(mathcomp_extra boolp classical_sets Rstruct reals) mathcomp(finmap) Reals_ext realType_ext classical_sets_ext ssrR fdist fsdist convex