∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {X Y : C} (f : X ⟶ Y)
  [inst_1 : CategoryTheory.Limits.HasPullbacksAlong f] {X_1 Y_1 Z : CategoryTheory.Over Y} (f_1 : X_1 ⟶ Y_1)
  (g : Y_1 ⟶ Z),
  CategoryTheory.Over.homMk
      (CategoryTheory.Limits.pullback.lift
        (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.fst X_1.hom f)
          (CategoryTheory.CategoryStruct.comp f_1 g).left)
        (CategoryTheory.Limits.pullback.snd X_1.hom f) ⋯)
      ⋯ =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Over.homMk
        (CategoryTheory.Limits.pullback.lift
          (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.fst X_1.hom f) f_1.left)
          (CategoryTheory.Limits.pullback.snd X_1.hom f) ⋯)
        ⋯)
      (CategoryTheory.Over.homMk
        (CategoryTheory.Limits.pullback.lift
          (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.fst Y_1.hom f) g.left)
          (CategoryTheory.Limits.pullback.snd Y_1.hom f) ⋯)
        ⋯)