proposition: Lemma conv_set_monotone (p : {prob R}) (X Y Y' : set A) : Y `<=` Y' -> X :<| p |>: Y `<=` X :<| p |>: Y'.
proof: Proof. by move/conv_pt_set_monotone=> YY' u [] x Xx /YY' HY'; exists x. 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