∀ {β : Type v} {α : Type u_2} [inst : TopologicalSpace α] [TopologicalSpace.PseudoMetrizableSpace α]
  [inst_2 : TopologicalSpace β] {f : α → β} {s : Set α},
  ContinuousOn f s → TopologicalSpace.IsSeparable s → TopologicalSpace.IsSeparable (f '' s)