dsimp [SmoothedChebyshev, SmoothedChebyshevIntegrand, VerticalIntegral', VerticalIntegral]
ψ : ℝ → ℝ
diffΨ : ContDiff ℝ 1 ψ
ψpos : ∀ (x : ℝ), 0 ≤ ψ x
suppΨ : support ψ ⊆ Icc (1 / 2) 2
mass_one : ∫ (x : ℝ) in Ioi 0, ψ x / x = 1
X : ℝ
X_pos : 0 < X
ε : ℝ
εpos : 0 < ε
⊢ SmoothedChebyshev ψ ε X = ↑(∑' (n : ℕ), Λ n * Smooth1 ψ ε (↑n / X))
ψ : ℝ → ℝ
diffΨ : ContDiff ℝ 1 ψ
ψpos : ∀ (x : ℝ), 0 ≤ ψ x
suppΨ : support ψ ⊆ Icc (1 / 2) 2
mass_one : ∫ (x : ℝ) in Ioi 0, ψ x / x = 1
X : ℝ
X_pos : 0 < X
ε : ℝ
εpos : 0 < ε
⊢ 1 / (2 * ↑π * I) *
      (I *
        ∫ (t : ℝ),
          -deriv riemannZeta (2 + ↑t * I) / riemannZeta (2 + ↑t * I) * 𝓜 (fun x => ↑(Smooth1 ψ ε x)) (2 + ↑t * I) *
            ↑X ^ (2 + ↑t * I)) =
    ↑(∑' (n : ℕ), Λ n * Smooth1 ψ ε (↑n / X))