∀ {X : Type u_1} {E : Type u_3} {F : Type u_4} [inst : MeasurableSpace X] {μ : MeasureTheory.Measure X}
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ E] [inst_4 : NormedSpace ℝ F]
  [CompleteSpace E] {f : X → E × F}, MeasureTheory.Integrable f μ → (∫ (x : X), f x ∂μ).2 = ∫ (x : X), (f x).2 ∂μ