∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : PseudoMetricSpace β] {δ : Type u_2}
  [inst_2 : TopologicalSpace δ] [inst_3 : DiscreteTopology δ] (f : α ↪ δ) (h : BoundedContinuousFunction δ β),
  Isometry fun g => BoundedContinuousFunction.extend f g h