∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {f : α → β},
  IsUniformEmbedding f →
    (∀ ε > 0, ∃ δ > 0, ∀ {a b : α}, edist a b < δ → edist (f a) (f b) < ε) ∧
      ∀ δ > 0, ∃ ε > 0, ∀ {a b : α}, edist (f a) (f b) < ε → edist a b < δ