∀ {α : Type u_1} {M : Type u_2} [inst : AddCommMonoid M] {a b : α} [inst_1 : LinearOrder α]
  [inst_2 : LocallyFiniteOrder α] [inst_3 : AddMonoidWithOne α] [SuccAddOrder α] [NoMaxOrder α],
  a ≤ b → ∀ (f : α → M), ∑ x ∈ Finset.Ico a b, f x + f b = ∑ x ∈ Finset.Ico a (b + 1), f x