∀ {β : Type u_1} {α : Type u_2} {A : List β → Set α} [inst : PseudoMetricSpace α],
  CantorScheme.VanishingDiam A →
    ∀ (ε : ℝ), 0 < ε → ∀ (x : ℕ → β), ∃ n, ∀ y ∈ A (PiNat.res x n), ∀ z ∈ A (PiNat.res x n), dist y z < ε