∀ {C₁ : Type u_4} {C₂ : Type u_7} {C₃ : Type u_8} {C₄ : Type u_5} {C₂₃ : Type u_2}
  [inst : CategoryTheory.Category.{u_1, u_4} C₁] [inst_1 : CategoryTheory.Category.{u_9, u_7} C₂]
  [inst_2 : CategoryTheory.Category.{u_10, u_8} C₃] [inst_3 : CategoryTheory.Category.{u_3, u_5} C₄]
  [inst_4 : CategoryTheory.Category.{u_6, u_2} C₂₃] (X : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂₃ C₄)),
  CategoryTheory.bifunctorComp₂₃FunctorMap (CategoryTheory.CategoryStruct.id X) =
    CategoryTheory.CategoryStruct.id (CategoryTheory.bifunctorComp₂₃FunctorObj X)