proposition: Lemma conv1_set X (Y : neset A) : X :<| 1%:pr |>: Y = X.
proof: Proof. transitivity (\bigcup_(x in X) [set x]); last by rewrite bigcup_imset1 image_id. by apply :eq_bigcupr => x; rewrite conv1_pt_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