∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β},
  Topology.IsInducing f → ∀ (s : Set α) (x : α), Filter.map f (nhdsWithin x s) = nhdsWithin (f x) (f '' s)