refine Filter.Tendsto.comp ?_ tendsto_nat_cast_atTop_atTop
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 x =>
        ↑(Real.fourierChar (Multiplicative.ofAdd (-(x * ξ)))) • f x -
          ↑(Real.fourierChar (Multiplicative.ofAdd (-(-x * ξ)))) • f (-x)) ∘
      fun n => ↑n)
    Filter.atTop (nhds 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 x =>
      ↑(Real.fourierChar (Multiplicative.ofAdd (-(x * ξ)))) • f x -
        ↑(Real.fourierChar (Multiplicative.ofAdd (-(-x * ξ)))) • f (-x))
    Filter.atTop (nhds 0)