∀ {F : CategoryTheory.Functor ℕᵒᵖ (Type u_1)},
  (∀ (n : ℕ), Function.Surjective (F.map (CategoryTheory.homOfLE ⋯).op)) →
    ∀ (n : ℕ) (x : Nat.below n.succ), ∃ a, F.map (CategoryTheory.homOfLE ⋯).op a = x.1