{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y : C} →
      [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
        {X' : C} →
          (f : X' ⟶ X) →
            [inst_2 : CategoryTheory.IsIso f] →
              (g : X ⟶ Y) →
                [inst_3 : CategoryTheory.Limits.HasKernel g] →
                  CategoryTheory.Subobject.underlying.obj
                      (CategoryTheory.Limits.kernelSubobject (CategoryTheory.CategoryStruct.comp f g)) ≅
                    CategoryTheory.Subobject.underlying.obj (CategoryTheory.Limits.kernelSubobject g)