∀ {β : Type u_1} [inst : LinearOrder β] {t : Set β} (motive : ℕ × { u // Monotone u ∧ ∀ (i : ℕ), u i ∈ t } → Prop)
  (x : ℕ × { u // Monotone u ∧ ∀ (i : ℕ), u i ∈ t }),
  (∀ (n : ℕ) (u : ℕ → β) (hu : Monotone u) (ut : ∀ (i : ℕ), u i ∈ t), motive (n, ⟨u, ⋯⟩)) → motive x