∀ (C : Type u_3) [inst : CategoryTheory.Category.{u_2, u_3} C]
  {F₁ : CategoryTheory.Functor (CategoryTheory.Discrete PEmpty.{u_1 + 1}) C}
  {F₂ : CategoryTheory.Functor (CategoryTheory.Discrete PEmpty.{u_4 + 1}) C} (c : CategoryTheory.Limits.Cocone F₂)
  ⦃X Y : CategoryTheory.Discrete PEmpty.{u_1 + 1}⦄ (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp (F₁.map f) (id (CategoryTheory.Discrete.casesOn Y fun as => ⋯.elim)) =
    CategoryTheory.CategoryStruct.comp (id (CategoryTheory.Discrete.casesOn X fun as => ⋯.elim))
      (((CategoryTheory.Functor.const (CategoryTheory.Discrete PEmpty.{u_1 + 1})).obj c.pt).map f)