∀ {X Y Z : UniformSpaceCat} (f : X ⟶ Y) (g : Y ⟶ Z),
  ⇑(CategoryTheory.ConcreteCategory.hom
        (CategoryTheory.ConcreteCategory.ofHom
            ⟨UniformSpace.Completion.map ⇑(CategoryTheory.CategoryStruct.comp f g).hom', ⋯⟩).hom) =
    ⇑(CategoryTheory.ConcreteCategory.hom
        (CategoryTheory.CategoryStruct.comp
            (CategoryTheory.ConcreteCategory.ofHom ⟨UniformSpace.Completion.map ⇑f.hom', ⋯⟩)
            (CategoryTheory.ConcreteCategory.ofHom ⟨UniformSpace.Completion.map ⇑g.hom', ⋯⟩)).hom)