∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {X Y : C}
  (f : X ⟶ Y) [inst_2 : CategoryTheory.Limits.HasKernel f] [inst_3 : CategoryTheory.Limits.HasImage f]
  [inst_4 : CategoryTheory.Limits.HasKernel (CategoryTheory.Limits.factorThruImage f)] {Z : C} (h : X ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.kernelFactorThruImage f).hom
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.kernel.ι f) h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.kernel.ι (CategoryTheory.Limits.factorThruImage f)) h