∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Abelian C]
  (S : CategoryTheory.ShortComplex C) {W' : C} (k : W' ⟶ CategoryTheory.Limits.kernel S.g)
  (hk :
    CategoryTheory.CategoryStruct.comp k
        (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.kernel.ι S.g)
          (CategoryTheory.Limits.cokernel.π S.f)) =
      0)
  (b : W' ⟶ CategoryTheory.Abelian.image S.f),
  CategoryTheory.CategoryStruct.comp b S.abelianImageToKernel = k →
    b =
      (fun {W'} k hk =>
          CategoryTheory.Limits.kernel.lift (CategoryTheory.Limits.cokernel.π S.f)
            (CategoryTheory.CategoryStruct.comp k (CategoryTheory.Limits.kernel.ι S.g)) ⋯)
        k hk