∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {F : CategoryTheory.Functor C C}
  {A₀ A₁ : CategoryTheory.Endofunctor.Algebra F} (h : A₀.a ≅ A₁.a),
  CategoryTheory.CategoryStruct.comp (F.map h.hom) A₁.str = CategoryTheory.CategoryStruct.comp A₀.str h.hom →
    CategoryTheory.CategoryStruct.comp (F.map h.inv) A₀.str = CategoryTheory.CategoryStruct.comp A₁.str h.inv