∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (x : X) (y : Y) (Ux : Set X)
  (Uy : Set Y)
  (motive :
    (match (x, y) with
      | (x, y) =>
        match (Ux, Uy) with
        | (Ux, Uy) => (Ux ∈ nhds x ∧ ContractibleSpace ↑Ux) ∧ Uy ∈ nhds y ∧ ContractibleSpace ↑Uy) →
      Prop)
  (h :
    match (x, y) with
    | (x, y) =>
      match (Ux, Uy) with
      | (Ux, Uy) => (Ux ∈ nhds x ∧ ContractibleSpace ↑Ux) ∧ Uy ∈ nhds y ∧ ContractibleSpace ↑Uy),
  (∀ (hUx : Ux ∈ nhds x ∧ ContractibleSpace ↑Ux) (hUy : Uy ∈ nhds y ∧ ContractibleSpace ↑Uy), motive ⋯) → motive h