∀ (x : SemiNormedGrp),
  SemiNormedGrp.ofHom (SemiNormedGrp.Hom.hom (CategoryTheory.CategoryStruct.id x)).completion =
    CategoryTheory.CategoryStruct.id
      { carrier := UniformSpace.Completion x.carrier, str := NormedAddCommGroup.toSeminormedAddCommGroup }