∀ {A : Type u_1} [inst : NormedAddCommGroup A] [CompactSpace A] [PreconnectedSpace A] [inst_3 : MeasurableSpace A]
  [BorelSpace A] {μ : MeasureTheory.Measure A} [μ.IsAddHaarMeasure] (ξ : A) {n : ℕ},
  0 < n → ∀ (δ : ℝ), μ Set.univ ≤ (n + 1) • μ (Metric.closedBall 0 (δ / 2)) → ∃ j ∈ Set.Icc 1 n, ‖j • ξ‖ ≤ δ