{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y : C} →
      {f : X ⟶ Y} →
        {F : CategoryTheory.Limits.MonoFactorisation f} →
          {motive : CategoryTheory.Limits.IsImage F → Sort u_1} →
            ((lift : (F' : CategoryTheory.Limits.MonoFactorisation f) → F.I ⟶ F'.I) →
                (lift_fac :
                    ∀ (F' : CategoryTheory.Limits.MonoFactorisation f),
                      CategoryTheory.CategoryStruct.comp (lift F') F'.m = F.m) →
                  motive { lift := lift, lift_fac := lift_fac }) →
              (t : CategoryTheory.Limits.IsImage F) → motive t