∀ (R : Type u_2) [inst : CommRing R] {X Y Z : CommAlgCat R} (f : X ⟶ Y) (g : Y ⟶ Z),
  CommAlgCat.ofHom
      ((↑ULift.algEquiv.symm).comp
        ((CommAlgCat.Hom.hom (CategoryTheory.CategoryStruct.comp f g)).comp ↑ULift.algEquiv)) =
    CategoryTheory.CategoryStruct.comp
      (CommAlgCat.ofHom ((↑ULift.algEquiv.symm).comp ((CommAlgCat.Hom.hom f).comp ↑ULift.algEquiv)))
      (CommAlgCat.ofHom ((↑ULift.algEquiv.symm).comp ((CommAlgCat.Hom.hom g).comp ↑ULift.algEquiv)))