∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (F G : CategoryTheory.Functor C (Type w)) {X Y : C} (f : X ⟶ Y)
  (x : F.obj X ⊕ G.obj X),
  (CategoryTheory.FunctorToTypes.binaryCoproductCocone F G).pt.map f x =
    Sum.rec (motive := fun t => x = t → F.obj Y ⊕ G.obj Y) (fun val h => Sum.inl (F.map f val))
      (fun val h => Sum.inr (G.map f val)) x ⋯