∀ {F : Type u_1} {α : Type u_2} {β : Type u_3} [inst : FunLike F α β] [inst_1 : Bornology α] [inst_2 : Bornology β]
  [LocallyBoundedMapClass F α β] (f : F) {s : Set α}, Bornology.IsBounded s → Bornology.IsBounded (⇑f '' s)