∀ (X : Type u_1) [inst : TopologicalSpace X]
  (motive : (∀ (x : X), (nhds x).lift' closure = nhds x) → (x : X) → (x_1 : Set X) → x_1 ∈ nhds x → Prop)
  (x : ∀ (x : X), (nhds x).lift' closure = nhds x) (x_1 : X) (x_2 : Set X) (x_3 : x_2 ∈ nhds x_1),
  (∀ (H : ∀ (x : X), (nhds x).lift' closure = nhds x) (a : X) (s : Set X) (hs : s ∈ nhds a), motive H a s hs) →
    motive x x_1 x_2 x_3