refine' ⟨y, hy, _⟩
case intro.intro
f : ℝ → ℝ
x x₀ a b : ℝ
n : ℕ
hab : a < b
hx : x ∈ Icc a b
hx₀ : x₀ ∈ Icc a b
hf : ContDiffOn ℝ (↑n) f (Icc a b)
hf' : DifferentiableOn ℝ (iteratedDerivWithin n f (Icc a b)) (Ioo a b)
y : ℝ
hy : y ∈ Ioo a b
h :
  f x - taylorWithinEval f n (Icc a b) x₀ x =
    ((x - y) ^ n / ↑n ! * (id x - id x₀) / 1) • iteratedDerivWithin (n + 1) f (Icc a b) y
⊢ ∃ x',
    ∃ (_ : x' ∈ Ioo a b),
      f x - taylorWithinEval f n (Icc a b) x₀ x =
        iteratedDerivWithin (n + 1) f (Icc a b) x' * (x - x') ^ n / ↑n ! * (x - x₀)
case intro.intro
f : ℝ → ℝ
x x₀ a b : ℝ
n : ℕ
hab : a < b
hx : x ∈ Icc a b
hx₀ : x₀ ∈ Icc a b
hf : ContDiffOn ℝ (↑n) f (Icc a b)
hf' : DifferentiableOn ℝ (iteratedDerivWithin n f (Icc a b)) (Ioo a b)
y : ℝ
hy : y ∈ Ioo a b
h :
  f x - taylorWithinEval f n (Icc a b) x₀ x =
    ((x - y) ^ n / ↑n ! * (id x - id x₀) / 1) • iteratedDerivWithin (n + 1) f (Icc a b) y
⊢ f x - taylorWithinEval f n (Icc a b) x₀ x = iteratedDerivWithin (n + 1) f (Icc a b) y * (x - y) ^ n / ↑n ! * (x - x₀)