∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_3, u_2} C] {X Y : CategoryTheory.Limits.FormalCoproduct C}
  (f : X.Hom Y),
  { f := f.f ∘ { f := id, φ := fun x => CategoryTheory.CategoryStruct.id (X.obj x) }.f,
      φ := fun x =>
        CategoryTheory.CategoryStruct.comp ({ f := id, φ := fun x => CategoryTheory.CategoryStruct.id (X.obj x) }.φ x)
          (f.φ ({ f := id, φ := fun x => CategoryTheory.CategoryStruct.id (X.obj x) }.f x)) } =
    f