∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_3, u_4} C] {J : CategoryTheory.Limits.MultispanShape}
  (I : CategoryTheory.Limits.MultispanIndex J C) {c : CategoryTheory.Limits.Cofan I.left}
  (hc : CategoryTheory.Limits.IsColimit c) {d : CategoryTheory.Limits.Cofan I.right}
  (hd : CategoryTheory.Limits.IsColimit d) {X Y : CategoryTheory.Limits.Multicofork I} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.id (CategoryTheory.Limits.Multicofork I)).map f)
      ((fun K =>
            CategoryTheory.Limits.Cocones.ext
              (CategoryTheory.Iso.refl ((CategoryTheory.Functor.id (CategoryTheory.Limits.Multicofork I)).obj K).pt) ⋯)
          Y).hom =
    CategoryTheory.CategoryStruct.comp
      ((fun K =>
            CategoryTheory.Limits.Cocones.ext
              (CategoryTheory.Iso.refl ((CategoryTheory.Functor.id (CategoryTheory.Limits.Multicofork I)).obj K).pt) ⋯)
          X).hom
      (((I.toSigmaCoforkFunctor hc hd).comp (I.ofSigmaCoforkFunctor hc)).map f)