proposition: Lemma convC_set p (X Y : set A) : X :<| p |>: Y = Y :<| (Prob.p p).~%:pr |>: X.
proof: Proof. by rewrite eqEsubset; split=> u; case=> x Xx; rewrite conv_pt_setE => -[] y Yy <-; exists y => //; rewrite conv_pt_setE; exists x => //; rewrite -convC. 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