∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {F₁ F₂ : CategoryTheory.Functor C (Type w)}
  {A : CategoryTheory.Subfunctor F₁} (f g : A.toFunctor ⟶ F₂) {G : CategoryTheory.Functor C (Type w)}
  (φ : G ⟶ A.toFunctor) (w : CategoryTheory.CategoryStruct.comp φ f = CategoryTheory.CategoryStruct.comp φ g),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Subfunctor.equalizer.lift f g φ w)
      (CategoryTheory.Subfunctor.equalizer f g).ι =
    CategoryTheory.CategoryStruct.comp φ A.ι