proposition: Lemma conv_pt_cset_is_convex (p : {prob R}) (x : A) (Y : {convex_set A}) : is_convex_set (conv_pt_set p x Y).
proof: Proof. apply/asboolP=> u v q. rewrite conv_pt_setE /= => -[y0 Yy0 <-] [y1 Yy1 <-]. rewrite -convDr; apply/imageP. by move/asboolP: (convex_setP Y); apply. 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