∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : Preorder β] {f : α → β} {s : Set α} {a : α}
  [inst_2 : TopologicalSpace β],
  IsLocalExtrOn f s a →
    ∀ [(nhdsWithin (f a) (Set.Iio (f a))).NeBot] [(nhdsWithin (f a) (Set.Ioi (f a))).NeBot],
      ¬nhds (f a) ≤ Filter.map f (nhdsWithin a s)