∀ (R : CommRingCat) ⦃X Y : Type u_1⦄ (f : X ⟶ Y),
  (CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.id (Type u_1)).map f) fun i =>
      CommRingCat.ofHom (Pi.evalRingHom (fun a => ↑R) i)) =
    CategoryTheory.CategoryStruct.comp (fun i => CommRingCat.ofHom (Pi.evalRingHom (fun a => ↑R) i))
      (((CommRingCat.coyoneda.flip.obj R).rightOp.comp (CategoryTheory.yoneda.obj R)).map f)