∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_2, u_1} C] (F : CategoryTheory.Functor C CategoryTheory.Cat)
  (X : CategoryTheory.Grothendieck (F.comp CategoryTheory.Cat.asSmallFunctor)),
  CategoryTheory.CategoryStruct.comp
      ((CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceFunctor F).map
        ((CategoryTheory.Iso.refl
                (CategoryTheory.Functor.id
                  (CategoryTheory.Grothendieck (F.comp CategoryTheory.Cat.asSmallFunctor)))).hom.app
          X))
      ((CategoryTheory.Iso.refl
              ((CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceInverse F).comp
                (CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceFunctor F))).hom.app
        ((CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceFunctor F).obj X)) =
    CategoryTheory.CategoryStruct.id ((CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceFunctor F).obj X)