∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β] (f : α → β)
  (μ : MeasureTheory.Measure β),
  (Function.Injective f ∧ ∀ (s : Set α), MeasurableSet s → MeasureTheory.NullMeasurableSet (f '' s) μ) →
    ∀ (s : Set α),
      MeasurableSet s →
        ∀ (t : Set α),
          ((MeasureTheory.OuterMeasure.comap f) μ.toOuterMeasure) t =
            ((MeasureTheory.OuterMeasure.comap f) μ.toOuterMeasure) (t ∩ s) +
              ((MeasureTheory.OuterMeasure.comap f) μ.toOuterMeasure) (t \ s)