∀ {α : Type u_1} [inst : UniformSpace α] (U : SetRel α α)
  (motive : (U ∈ uniformity α ∧ ∀ (a : α × α), ClusterPt a (Filter.principal U) → a ∈ U) → Prop)
  (x : U ∈ uniformity α ∧ ∀ (a : α × α), ClusterPt a (Filter.principal U) → a ∈ U),
  (∀ (hU : U ∈ uniformity α) (hUc : ∀ (a : α × α), ClusterPt a (Filter.principal U) → a ∈ U), motive ⋯) → motive x