∀ {𝕜 : Type u_1} {α : Type u_4} {β : Type u_5} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid α]
  [inst_3 : PartialOrder α] [inst_4 : SMul 𝕜 α] [inst_5 : AddCommMonoid β] [inst_6 : PartialOrder β] [inst_7 : SMul 𝕜 β]
  (f : α ≃o β), ConvexOn 𝕜 Set.univ ⇑f → ConcaveOn 𝕜 Set.univ ⇑f.symm