simp_rw [this, Finset.sum_singleton, Int.cast_add, Int.cast_one, add_comm]
φ : ℝ → ℂ
a b : ℝ
k : ℤ
b_eq_kpOne : b = ↑k + 1
φDiff : ∀ x ∈ [[a, b]], HasDerivAt φ (deriv φ x) x
derivφCont : ContinuousOn (deriv φ) [[a, b]]
flb_eq_k : ⌊b⌋ = k + 1
this : Finset.Ioc k (1 + k) = {k + 1}
⊢ ∑ x ∈ Finset.Ioc k (1 + k), φ ↑x = φ (1 + ↑k)
no goals