∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {D : Type u₂} [inst_2 : CategoryTheory.Category.{v₂, u₂} D] [inst_3 : CategoryTheory.Limits.HasZeroMorphisms D]
  (F : CategoryTheory.Functor C D) [inst_4 : F.PreservesZeroMorphisms] {X Y : C} (f : X ⟶ Y)
  [inst_5 : CategoryTheory.Limits.HasKernel f] [inst_6 : CategoryTheory.Limits.HasCokernel f]
  [inst_7 : CategoryTheory.Limits.HasKernel (CategoryTheory.Limits.cokernel.π f)]
  [inst_8 : CategoryTheory.Limits.HasCokernel (CategoryTheory.Limits.kernel.ι f)]
  [inst_9 : CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.parallelPair f 0) F]
  [inst_10 : CategoryTheory.Limits.PreservesColimit (CategoryTheory.Limits.parallelPair f 0) F]
  [inst_11 :
    CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.parallelPair (CategoryTheory.Limits.cokernel.π f) 0) F]
  [inst_12 :
    CategoryTheory.Limits.PreservesColimit (CategoryTheory.Limits.parallelPair (CategoryTheory.Limits.kernel.ι f) 0) F]
  [inst_13 : CategoryTheory.Limits.HasKernel (CategoryTheory.Limits.cokernel.π (F.map f))]
  [inst_14 : CategoryTheory.Limits.HasCokernel (CategoryTheory.Limits.kernel.ι (F.map f))],
  (CategoryTheory.Abelian.PreservesCoimageImageComparison.iso F f).inv.left =
    (CategoryTheory.Abelian.PreservesCoimage.iso F f).inv