∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} {f : X ⟶ Y}
  [inst_1 : CategoryTheory.Limits.HasImage f] {Z : C} (h : Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Limits.image.lift
        { I := CategoryTheory.Limits.image f, m := CategoryTheory.Limits.image.ι f, m_mono := ⋯,
          e := CategoryTheory.Limits.factorThruImage f, fac := ⋯ })
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.image.ι f) h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.image.ι f) h