∀ {β : Type u_1} [inst : LinearOrder β] {u : ℕ → β}
  (motive : (∃ φ, StrictMono φ ∧ ∀ (n k : ℕ), k < φ n → u k < u (φ n)) → Prop)
  (x : ∃ φ, StrictMono φ ∧ ∀ (n k : ℕ), k < φ n → u k < u (φ n)),
  (∀ (φ : ℕ → ℕ) (h : StrictMono φ) (h' : ∀ (n k : ℕ), k < φ n → u k < u (φ n)), motive ⋯) → motive x