∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type v} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [CompleteSpace 𝕜] {c : 𝕜},
  1 < ‖c‖ →
    ∀ {R : ℝ}, ‖c‖ < R → ¬FiniteDimensional 𝕜 E → ∃ f, (∀ (n : ℕ), ‖f n‖ ≤ R) ∧ Pairwise fun m n => 1 ≤ ‖f m - f n‖