∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f : ℂ → E} {z : ℂ} {a b l u : ℝ},
  l < u →
    z ∈ Complex.HadamardThreeLines.verticalClosedStrip l u →
      DiffContOnCl ℂ f (Complex.HadamardThreeLines.verticalStrip l u) →
        BddAbove (norm ∘ f '' Complex.HadamardThreeLines.verticalClosedStrip l u) →
          (∀ z ∈ Complex.re ⁻¹' {l}, ‖f z‖ ≤ a) →
            (∀ z ∈ Complex.re ⁻¹' {u}, ‖f z‖ ≤ b) → ‖f z‖ ≤ a ^ (1 - (z.re - l) / (u - l)) * b ^ ((z.re - l) / (u - l))