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