∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : TopologicalSpace β] [inst_2 : TopologicalSpace α]
  [OrderTopology α] [T3Space β] {f : α → β} {a : α},
  Filter.Tendsto f (nhdsWithin a (Set.Iio a)) (nhds (Function.leftLim f a)) →
    Function.leftLim (Function.leftLim f) a = Function.leftLim f a