∀ {α : Type u_1} {β : Type u_2} {𝔖 𝔗 : Set (Set α)} [inst : PseudoEMetricSpace β] [inst_1 : Finite ↑𝔖]
  [inst_2 : Finite ↑𝔗], ⋃₀ 𝔖 ⊆ ⋃₀ 𝔗 → LipschitzWith 1 (⇑(UniformOnFun.ofFun 𝔖) ∘ ⇑(UniformOnFun.toFun 𝔗))