∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {X Y : C} (f : X ⟶ Y) [inst_2 : CategoryTheory.Limits.HasKernel f] {X' Y' : C} (f' : X' ⟶ Y')
  [inst_3 : CategoryTheory.Limits.HasKernel f'] (p : X ≅ X') (q : Y ≅ Y')
  (w : CategoryTheory.CategoryStruct.comp f q.hom = CategoryTheory.CategoryStruct.comp p.hom f'),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.kernel.map f f' p.hom q.hom w)
      (CategoryTheory.Limits.kernel.map f' f p.inv q.inv ⋯) =
    CategoryTheory.CategoryStruct.id (CategoryTheory.Limits.kernel f)