∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {C : ℝ} {f : ℂ → E} {z : ℂ},
  DiffContOnCl ℂ f (Set.Ioi 0 ×ℂ Set.Iio 0) →
    (∃ c < 2,
        ∃ B, f =O[Bornology.cobounded ℂ ⊓ Filter.principal (Set.Ioi 0 ×ℂ Set.Iio 0)] fun z => Real.exp (B * ‖z‖ ^ c)) →
      (∀ (x : ℝ), 0 ≤ x → ‖f ↑x‖ ≤ C) → (∀ x ≤ 0, ‖f (↑x * Complex.I)‖ ≤ C) → 0 ≤ z.re → z.im ≤ 0 → ‖f z‖ ≤ C