∀ {α : Type u_1} {β : Type u_2} {ι : Type u_4} [inst : UniformSpace β] (F : ι → α → β) (p : Filter ι) (s : Set α),
  UniformCauchySeqOn F p s = ∀ u ∈ uniformity β, ∀ᶠ (m : ι × ι) in p ×ˢ p, ∀ x ∈ s, (F m.1 x, F m.2 x) ∈ u