refine AECover.integral_eq_of_tendsto h_cover _
  (.sub (integrable_fourierIntegrand _ ξ) ((integrable_fourierIntegrand f ξ).smul' _)) ?_
F : Type u_1
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedSpace ℂ F
inst✝ : CompleteSpace F
f : 𝓢(ℝ, F)
ξ : ℝ
h_cover : AECover volume Filter.atTop fun i => Set.Ioc (-↑i) ↑i
⊢ ∫ (a : ℝ),
      ↑(Real.fourierChar (Multiplicative.ofAdd (-(a * ξ)))) • ((derivCLM ℝ) f) a -
        (2 * ↑π * I * ↑ξ) • ↑(Real.fourierChar (Multiplicative.ofAdd (-(a * ξ)))) • f a =
    0
F : Type u_1
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedSpace ℂ F
inst✝ : CompleteSpace F
f : 𝓢(ℝ, F)
ξ : ℝ
h_cover : AECover volume Filter.atTop fun i => Set.Ioc (-↑i) ↑i
⊢ Filter.Tendsto
    (fun n =>
      ∫ (x : ℝ) in Set.Ioc (-↑n) ↑n,
        ↑(Real.fourierChar (Multiplicative.ofAdd (-(x * ξ)))) • ((derivCLM ℝ) f) x -
          (2 * ↑π * I * ↑ξ) • ↑(Real.fourierChar (Multiplicative.ofAdd (-(x * ξ)))) • f x)
    Filter.atTop (nhds 0)