proposition: Lemma F1join0'_convex X : is_convex_set (F1join0' X).
proof: Proof. apply/asboolP=> x y p [] dx Xdx <-{x} [] dy Xdy <-{y}. exists (dx <|p|>dy); first by move/asboolP: (convex_setP X); apply. by rewrite Convn_of_fsdist_affine. 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