∀ {α : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F] {m : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  {T T' T'' : Set α → E →L[ℝ] F} {C C' C'' : ℝ} (hT : MeasureTheory.DominatedFinMeasAdditive μ T C)
  (hT' : MeasureTheory.DominatedFinMeasAdditive μ T' C') (hT'' : MeasureTheory.DominatedFinMeasAdditive μ T'' C''),
  (∀ (s : Set α), MeasurableSet s → μ s < ⊤ → T'' s = T s + T' s) →
    ∀ (f : ↥(MeasureTheory.Lp.simpleFunc E 1 μ)),
      (MeasureTheory.L1.SimpleFunc.setToL1SCLM α E μ hT'') f =
        (MeasureTheory.L1.SimpleFunc.setToL1SCLM α E μ hT) f + (MeasureTheory.L1.SimpleFunc.setToL1SCLM α E μ hT') f