∀ (C : Type u_4) (D : Type u_2) [inst : CategoryTheory.Category.{u_3, u_4} C]
  [inst_1 : CategoryTheory.Category.{u_1, u_2} D] (F : CategoryTheory.Functor C (CategoryTheory.Idempotents.Karoubi D))
  (X : C),
  CategoryTheory.CategoryStruct.comp { f := (F.obj X).p, comm := ⋯ } { f := (F.obj X).p, comm := ⋯ } =
    CategoryTheory.CategoryStruct.id
      (((CategoryTheory.Functor.id (CategoryTheory.Functor C (CategoryTheory.Idempotents.Karoubi D))).obj F).obj X)