∀ {X : Type u_1} [inst : TopologicalSpace X] (x : ℕ → X)
  (motive : (∃ a ∈ Set.univ, ∃ φ, StrictMono φ ∧ Filter.Tendsto (x ∘ φ) Filter.atTop (nhds a)) → Prop)
  (x_1 : ∃ a ∈ Set.univ, ∃ φ, StrictMono φ ∧ Filter.Tendsto (x ∘ φ) Filter.atTop (nhds a)),
  (∀ (a : X) (left : a ∈ Set.univ) (φ : ℕ → ℕ) (mono : StrictMono φ) (h : Filter.Tendsto (x ∘ φ) Filter.atTop (nhds a)),
      motive ⋯) →
    motive x_1