∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {F : CategoryTheory.Functor C CategoryTheory.Cat}
  {X Y : CategoryTheory.Grothendieck F} (e₁ : X.base ≅ Y.base) (e₂ : (F.map e₁.hom).toFunctor.obj X.fiber ≅ Y.fiber),
  (CategoryTheory.CategoryStruct.comp { base := e₁.hom, fiber := e₂.hom }
        { base := e₁.inv,
          fiber :=
            CategoryTheory.CategoryStruct.comp ((F.map e₁.inv).toFunctor.map e₂.inv)
              (CategoryTheory.eqToHom ⋯) }).base =
    (CategoryTheory.CategoryStruct.id X).base