∀ (C : Type u_2) [inst : CategoryTheory.Category.{u_1, u_2} C] (D : Type u_4)
  [inst_1 : CategoryTheory.Category.{u_3, u_4} D] (F : CategoryTheory.Functor C D)
  (X : CategoryTheory.CosimplicialObject.Augmented C),
  { left := F.map (CategoryTheory.CategoryStruct.id X).left,
      right := CategoryTheory.Functor.whiskerRight (CategoryTheory.CategoryStruct.id X).right F, w := ⋯ } =
    CategoryTheory.CategoryStruct.id
      { left := F.obj (CategoryTheory.CosimplicialObject.Augmented.point.obj X),
        right :=
          ((CategoryTheory.CosimplicialObject.whiskering C D).obj F).obj
            (CategoryTheory.CosimplicialObject.Augmented.drop.obj X),
        hom :=
          CategoryTheory.CategoryStruct.comp
            (CategoryTheory.Functor.constComp SimplexCategory (CategoryTheory.CosimplicialObject.Augmented.point.obj X)
                F).inv
            (CategoryTheory.Functor.whiskerRight X.hom F) }