∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {f : X ⟶ Y} [inst_2 : CategoryTheory.Limits.HasKernel f],
  CategoryTheory.Limits.kernelSubobjectMap (CategoryTheory.CategoryStruct.id (CategoryTheory.Arrow.mk f)) =
    CategoryTheory.CategoryStruct.id (CategoryTheory.Subobject.underlying.obj (CategoryTheory.Limits.kernelSubobject f))