proposition: Lemma is_convex_setI (C D : {convex_set E}) : is_convex_set (C `&` D).
proof: Proof. apply/asboolP =>x y p [Cx Dx] [Cy Dy]; split. by move/asboolP: (convex_setP C); apply. by move/asboolP: (convex_setP D); apply. Qed.
imports: mathcomp(all_ssreflect all_algebra vector reals ereal classical_sets boolp Rstruct) infotheo(convex Reals_ext) preliminaries Reals