∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {X Y Z : C} {f : X ⟶ Z} {g : Y ⟶ Z}
  {t : CategoryTheory.Limits.PullbackCone f g} (ht : CategoryTheory.Limits.IsLimit t) {W : C} (h : W ⟶ X) (k : W ⟶ Y)
  (w : CategoryTheory.CategoryStruct.comp h f = CategoryTheory.CategoryStruct.comp k g),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.PullbackCone.IsLimit.lift ht h k w) t.fst = h ∧
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.PullbackCone.IsLimit.lift ht h k w) t.snd = k