∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_2, u_4} C] {J : Type u_3}
  [inst_1 : CategoryTheory.Category.{u_1, u_3} J] {X : C} {K : CategoryTheory.Functor J (CategoryTheory.Under X)}
  (X_1 : CategoryTheory.Limits.Cocone (CategoryTheory.WithInitial.liftFromUnder.obj K)),
  { hom := CategoryTheory.Under.homMk (CategoryTheory.CategoryStruct.id X_1).hom ⋯, w := ⋯ } =
    CategoryTheory.CategoryStruct.id
      { pt := CategoryTheory.Under.mk (X_1.ι.app CategoryTheory.WithInitial.star),
        ι :=
          {
            app := fun a =>
              { left := CategoryTheory.CategoryStruct.id (K.obj a).left,
                right := X_1.ι.app (CategoryTheory.WithInitial.of a), w := ⋯ },
            naturality := ⋯ } }