proposition: Lemma radius_scale_ball (A : set R) (k : R) : 0 <= k -> is_ball A -> (radius (k *` A))%:num = k * (radius A)%:num.
proof: Proof. move=> k0 ballA. by rewrite [in LHS](ballE ballA) (scale_ballE _ _ k0)// radius_ball// mulr_ge0. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrint ssrnum finmap matrix) mathcomp(rat interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality set_interval Rstruct) ereal reals signed topology prodnormedzmodule