proposition: Lemma cpoint_scale_ball A (k : R) : 0 < k -> is_ball A -> 0 < (radius A)%:num -> cpoint (k *` A) = cpoint A :> R.
proof: Proof. move=> k0 ballA r0. rewrite [in LHS](ballE ballA) (scale_ballE _ _ (ltW k0))// cpoint_ball//. by rewrite mulr_gt0. 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