∀ {ι : Type u_1} {α : Type u_2} {β : Type u_3} [inst : CommGroup α] [inst_1 : PartialOrder α] [IsOrderedMonoid α]
  [inst_3 : CommGroup β] [inst_4 : PartialOrder β] [IsOrderedMonoid β] {s : Set ι} {f : ι → α} {g : ι → β},
  MonovaryOn f g s → MonovaryOn f⁻¹ g⁻¹ s