(A : Type u₁) →
  [inst : CategoryTheory.Category.{v₁, u₁} A] →
    (B : Type u₂) →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} B] →
        (C : Type u₃) →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} C] →
            CategoryTheory.Functor.id (CategoryTheory.Functor A B × CategoryTheory.Functor A C) ≅
              (CategoryTheory.prodFunctorToFunctorProd A B C).comp (CategoryTheory.functorProdToProdFunctor A B C)