∀ {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : ℝ → E} {a b t : ℝ} (x : ℝ) {n : ℕ},
  a < b →
    t ∈ Set.Icc a b →
      ContDiffOn ℝ (↑n) f (Set.Icc a b) →
        DifferentiableOn ℝ (iteratedDerivWithin n f (Set.Icc a b)) (Set.Icc a b) →
          HasDerivWithinAt (fun y => taylorWithinEval f n (Set.Icc a b) y x)
            (((↑n.factorial)⁻¹ * (x - t) ^ n) • iteratedDerivWithin (n + 1) f (Set.Icc a b) t) (Set.Icc a b) t