∀ {A : Type u₁} {B : Type u₂} {C : Type u₃} [inst : CategoryTheory.Category.{v₁, u₁} A]
  [inst_1 : CategoryTheory.Category.{v₂, u₂} B] [inst_2 : CategoryTheory.Category.{v₃, u₃} C]
  (F : CategoryTheory.Functor A B) (G : CategoryTheory.Functor C B) {X : Type u₄} {Y : Type u₅} {Z : Type u₆}
  [inst_3 : CategoryTheory.Category.{v₄, u₄} X] [inst_4 : CategoryTheory.Category.{v₅, u₅} Y]
  [inst_5 : CategoryTheory.Category.{v₆, u₆} Z] {T : Type u₇} [inst_6 : CategoryTheory.Category.{v₇, u₇} T]
  (U : CategoryTheory.Functor X Y) (V : CategoryTheory.Functor Y Z) (W : CategoryTheory.Functor Z T),
  (CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose F G).map (U.associator V W).hom =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp F G (U.comp V) W).hom
      (CategoryTheory.CategoryStruct.comp
        (((CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose F G).obj W).whiskerLeft
          (CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp F G U V).hom)
        (CategoryTheory.CategoryStruct.comp
          (((CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose F G).obj W).associator
              ((CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose F G).obj V)
              ((CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose F G).obj U)).inv
          (CategoryTheory.CategoryStruct.comp
            (CategoryTheory.Functor.whiskerRight
              (CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp F G V W).inv
              ((CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose F G).obj U))
            (CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp F G U (V.comp W)).inv)))