proposition: Lemma radius_ball_num x r : 0 <= r -> (radius (ball x r))%:num = r.
proof: Proof. rewrite le_eqVlt => /orP[/eqP <-|r0]; first by rewrite (ball0 _ _).2// radius0. rewrite /radius; case: xgetP => [y _ /(ball_inj r0)[]//|]. by move=> /(_ (NngNum (ltW r0)))/=; rewrite cpoint_ball. 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