proposition: Lemma biglub_oplus_conv_setE (X Y : neset L) : |_| (oplus_conv_set X Y)%:ne = |_| ((fun p => |_| X <|p|> |_| Y) @` probset)%:ne.
proof: Proof. transitivity (|_| (\bigcup_(p in probset_neset) (X :<| p |>: Y))%:ne). by congr (|_| _%:ne); apply/neset_ext. rewrite biglub_bigcup //; congr (|_| _%:ne); apply/neset_ext => /=. rewrite image_comp; congr image; apply funext => p /=. by rewrite biglub_conv_setD. 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