∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.CartesianMonoidalCategory C] [inst_3 : CategoryTheory.BraidedCategory C] (X : C),
  CategoryTheory.CategoryStruct.comp
      ((CategoryTheory.Preadditive.toCommGrp C).map ((CategoryTheory.Iso.refl (CategoryTheory.Functor.id C)).hom.app X))
      (CategoryTheory.Preadditive.commGrpEquivalenceAux.hom.app ((CategoryTheory.Preadditive.toCommGrp C).obj X)) =
    CategoryTheory.CategoryStruct.id ((CategoryTheory.Preadditive.toCommGrp C).obj X)