{α : Type u_1} →
  [inst : TopologicalSpace α] →
    (x : { x // IsOpen x }) →
      (_a : α) →
        (motive : (x_1 : { x // IsOpen x }) → _a ∈ ↑x_1 ∩ ↑x → Sort u_2) →
          (x_1 : { x // IsOpen x }) →
            (_h₃ : _a ∈ ↑x_1 ∩ ↑x) →
              ((_x : Set α) → (h₁ : IsOpen _x) → (_h₃ : _a ∈ ↑⟨_x, h₁⟩ ∩ ↑x) → motive ⟨_x, h₁⟩ _h₃) → motive x_1 _h₃