∀ (f : ℕ → ℝ) (R : ℝ) (motive : (∃ a ∈ Set.Ioo 0 R, f =O[Filter.atTop] fun x => a ^ x) → Prop)
  (x : ∃ a ∈ Set.Ioo 0 R, f =O[Filter.atTop] fun x => a ^ x),
  (∀ (a : ℝ) (ha : a ∈ Set.Ioo 0 R) (H : f =O[Filter.atTop] fun x => a ^ x), motive ⋯) → motive x