∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {X Y : C} [inst_1 : CategoryTheory.Limits.HasPullbacks C]
  {U V₁ V₂ : C} (f : X ⟶ Y) (i : U ⟶ Y) (i₁ : V₁ ⟶ CategoryTheory.Limits.pullback f i)
  (i₂ : V₂ ⟶ CategoryTheory.Limits.pullback f i) [inst_2 : CategoryTheory.Limits.HasPullback i₁ i₂],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullbackDiagonalMapIso.inv f i i₁ i₂)
      (CategoryTheory.Limits.pullbackDiagonalMapIso.hom f i i₁ i₂) =
    CategoryTheory.CategoryStruct.id (CategoryTheory.Limits.pullback i₁ i₂)