{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {α : Type t} →
      {A B : α → C} →
        {g : (a : α) → A a ⟶ B a} →
          {X₁ X₂ : C} →
            {f : X₁ ⟶ X₂} →
              HomotopicalAlgebra.AttachCells g f →
                {Y₁ Y₂ : C} →
                  {f' : Y₁ ⟶ Y₂} →
                    (CategoryTheory.Arrow.mk f ≅ CategoryTheory.Arrow.mk f') → HomotopicalAlgebra.AttachCells g f'