∀ (C : Type u_2) [inst : CategoryTheory.Category.{u_1, u_2} C]
  [inst_1 : CategoryTheory.Limits.HasStrongEpiMonoFactorisations C] ⦃X Y : CategoryTheory.Arrow C⦄ (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.im.map f) (CategoryTheory.Limits.image.ι Y.hom) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.image.ι X.hom) (CategoryTheory.Arrow.rightFunc.map f)