∀ {ι : Type u_1} {X : Type u_3} {α : Type u_6} [tX : TopologicalSpace X] [uα : UniformSpace α] {F : ι → X → α}
  {S : Set X} {x₀ : X},
  x₀ ∈ S →
    (EquicontinuousWithinAt F S x₀ ↔
      ∀ U ∈ uniformity α, ∃ V ∈ nhdsWithin x₀ S, ∀ x ∈ V, ∀ y ∈ V, ∀ (i : ι), (F i x, F i y) ∈ U)