∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] [CompleteSpace E]
  [inst_3 : TopologicalSpace α] [OrderTopology α] {f : α → E} {s : Set α},
  BoundedVariationOn f s → ∀ (x : α), ∃ l, Filter.Tendsto f (nhdsWithin x (s ∩ Set.Ioi x)) (nhds l)