∀ {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] {X' Y' : C} {f' : X' ⟶ Y'}
  [inst_3 : CategoryTheory.Limits.HasKernel f'] (sq : CategoryTheory.Arrow.mk f ⟶ CategoryTheory.Arrow.mk f'),
  CategoryTheory.Limits.kernelSubobjectMap sq =
    (CategoryTheory.Limits.kernelSubobject f').factorThru
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.kernelSubobject f).arrow sq.left) ⋯