∀ (A : Type u_1) {B : Type u_2} {C : Type u_3} {D : Type u_4} [inst : CategoryTheory.Category.{v_1, u_1} A]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} B] [inst_2 : CategoryTheory.Category.{v_3, u_3} C]
  [inst_3 : CategoryTheory.Category.{v_4, u_4} D] {F G : CategoryTheory.Functor B C} (η : F ⟶ G)
  (H : CategoryTheory.Functor C D),
  CategoryTheory.Join.mapWhiskerLeft (CategoryTheory.Functor.id A) (CategoryTheory.Functor.whiskerRight η H) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Join.mapCompRight A F H).hom
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Functor.whiskerRight (CategoryTheory.Join.mapWhiskerLeft (CategoryTheory.Functor.id A) η)
          (CategoryTheory.Join.mapPair (CategoryTheory.Functor.id A) H))
        (CategoryTheory.Join.mapCompRight A G H).inv)