∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] {f : β → Set α} (g : α → Set α) (x : α)
  (motive : g x ∈ nhds x ∧ {i | (f i ∩ g x).Nonempty}.Finite → Prop)
  (x_1 : g x ∈ nhds x ∧ {i | (f i ∩ g x).Nonempty}.Finite),
  (∀ (h : g x ∈ nhds x) (_h' : {i | (f i ∩ g x).Nonempty}.Finite), motive ⋯) → motive x_1