Identifying the leading coefficient of a power-saving count

theorem NairTenenbaum.tendsto_div_of_power_error {A : ℝ → ℝ} {V C θ : ℝ} (hθ : θ < 1) (hA : ∀ (x : ℝ), 1 ≤ x → |A x - V * x| ≤ C * x ^ θ) : Filter.Tendsto (fun (x : ℝ) => A x / x) Filter.atTop (nhds V)

theorem NairTenenbaum.leading_coefficient_eq_of_power_error {A : ℝ → ℝ} {V C θ L : ℝ} (hθ : θ < 1) (hA : ∀ (x : ℝ), 1 ≤ x → |A x - V * x| ≤ C * x ^ θ) (hmean : Filter.Tendsto (fun (x : ℝ) => A x / x) Filter.atTop (nhds L)) : V = L