{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {D : Type u₁} →
      [inst_1 : CategoryTheory.Category.{v₁, u₁} D] →
        {α : Type w} →
          [inst_2 : CategoryTheory.Limits.HasLimitsOfShape (CategoryTheory.Discrete α) C] →
            (f : α → CategoryTheory.Functor D C) → (d : D) → (∏ᶜ f).obj d ≅ ∏ᶜ fun s => (f s).obj d