∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] {f : α → E} {s : Set α},
  BoundedVariationOn f s → BoundedVariationOn (f ∘ ⇑OrderDual.ofDual) (⇑OrderDual.ofDual ⁻¹' s)