have h_cover : AECover volume Filter.atTop (fun i => Set.Ioc (-i) i : ℕ → Set ℝ)
F : Type u_1
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedSpace ℂ F
inst✝ : CompleteSpace F
f : 𝓢(ℝ, F)
ξ : ℝ
⊢ ∫ (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
case h_cover
F : Type u_1
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedSpace ℂ F
inst✝ : CompleteSpace F
f : 𝓢(ℝ, F)
ξ : ℝ
⊢ AECover volume Filter.atTop fun i => Set.Ioc (-↑i) ↑i

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