∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {J : Type w} [inst_1 : CategoryTheory.Category.{w', w} J]
  {X : C} {K : CategoryTheory.Functor J (CategoryTheory.Under X)} {t₁ t₂ : CategoryTheory.Limits.Cocone K}
  (f : t₁ ⟶ t₂), (CategoryTheory.WithInitial.coconeEquiv.functor.map f).hom = f.hom.right