∀ (C : Type u_1) [inst : CategoryTheory.Category.{u_2, u_1} C] (X : (CategoryTheory.SimplicialObject.Augmented C)ᵒᵖ),
  CategoryTheory.CategoryStruct.comp
      ((CategoryTheory.simplicialToCosimplicialAugmented C).map
        ((CategoryTheory.NatIso.ofComponents (fun X => (Opposite.unop X).rightOpLeftOpIso.op) ⋯).hom.app X))
      ((CategoryTheory.NatIso.ofComponents (fun X => X.leftOpRightOpIso) ⋯).hom.app
        ((CategoryTheory.simplicialToCosimplicialAugmented C).obj X)) =
    CategoryTheory.CategoryStruct.id ((CategoryTheory.simplicialToCosimplicialAugmented C).obj X)