∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : PseudoMetricSpace β] [inst_2 : Zero β],
  Filter.comap (fun p => (p.1.toBCF, p.2.toBCF)) (uniformity (BoundedContinuousFunction α β)) =
    ⨅ i, ⨅ (_ : 0 < i), Filter.principal ((fun p => (p.1.toBCF, p.2.toBCF)) ⁻¹' {p | dist p.1 p.2 < i})