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