∀ {T : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} T] {P Q : CategoryTheory.MorphismProperty T}
  [inst_1 : Q.IsMultiplicative] {X Y Z : T} (f : X ⟶ Y) (g : Y ⟶ Z) [inst_2 : P.IsStableUnderBaseChangeAlong f]
  [inst_3 : P.IsStableUnderBaseChangeAlong g] [inst_4 : P.HasPullbacksAlong f] [inst_5 : P.HasPullbacksAlong g]
  [inst_6 : Q.IsStableUnderBaseChange] (fg : X ⟶ Z) (hfg : fg = CategoryTheory.CategoryStruct.comp f g)
  (X_1 : P.Over Q Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Limits.pullback.congrHom ⋯ hfg ≪≫
          (CategoryTheory.Limits.pullbackLeftPullbackSndIso X_1.hom g f).symm).hom
      (((CategoryTheory.MorphismProperty.Over.pullback P Q g).comp
              (CategoryTheory.MorphismProperty.Over.pullback P Q f)).obj
          X_1).hom =
    ((CategoryTheory.MorphismProperty.Over.pullback P Q fg).obj X_1).hom