∀ {C : Type u_3} [inst : CategoryTheory.Category.{u_2, u_3} C] {R : CategoryTheory.Functor Cᵒᵖ RingCat} {X Y Z : Cᵒᵖ}
  (f : X ⟶ Y) (g : Y ⟶ Z) (x y : ↑(R.obj X)),
  ((RingCat.Hom.hom (R.map g)).toNonUnitalRingHom.comp (RingCat.Hom.hom (R.map f)).toNonUnitalRingHom).toFun (x + y) =
    ((RingCat.Hom.hom (R.map g)).toNonUnitalRingHom.comp (RingCat.Hom.hom (R.map f)).toNonUnitalRingHom).toFun x +
      ((RingCat.Hom.hom (R.map g)).toNonUnitalRingHom.comp (RingCat.Hom.hom (R.map f)).toNonUnitalRingHom).toFun y