∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {X Y : C} (f : X ⟶ Y) (Z : C)
  [inst_1 : CategoryTheory.Limits.HasBinaryProduct Z Y] [inst_2 : CategoryTheory.Limits.HasBinaryProduct Z X]
  [inst_3 : CategoryTheory.Limits.HasPullback CategoryTheory.Limits.prod.snd f],
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Limits.prod.lift
        (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.fst CategoryTheory.Limits.prod.snd f)
          CategoryTheory.Limits.prod.fst)
        (CategoryTheory.Limits.pullback.snd CategoryTheory.Limits.prod.snd f))
      (CategoryTheory.Limits.pullback.lift (CategoryTheory.Limits.prod.map (CategoryTheory.CategoryStruct.id Z) f)
        CategoryTheory.Limits.prod.snd ⋯) =
    CategoryTheory.CategoryStruct.id (CategoryTheory.Limits.pullback CategoryTheory.Limits.prod.snd f)