∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {s : Set ℝ} {e : E} {a : ℝ} {f : ℝ → E},
  DifferentiableOn ℝ f s →
    ContinuousWithinAt f s a →
      s ∈ nhdsWithin a (Set.Iio a) →
        Filter.Tendsto (fun x => deriv f x) (nhdsWithin a (Set.Iio a)) (nhds e) → HasDerivWithinAt f e (Set.Iic a) a