∀ {J : Type u} [inst : CategoryTheory.Category.{v, u} J] {C : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} C]
  {F : CategoryTheory.Functor Jᵒᵖ (CategoryTheory.Functor J C)} [inst_2 : CategoryTheory.Limits.HasCoend F] {X : C}
  {f g : CategoryTheory.Limits.coend F ⟶ X},
  f = g ↔
    ∀ (j : J),
      CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.coend.ι F j) f =
        CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.coend.ι F j) g