no goals
α : Type u_2
α' : Type ?u.4425879
β : Type u_1
β' : Type ?u.4425885
γ : Type ?u.4425888
E : Type ?u.4425891
inst✝⁶ : MeasurableSpace α
inst✝⁵ : MeasurableSpace α'
inst✝⁴ : MeasurableSpace β
inst✝³ : MeasurableSpace β'
inst✝² : MeasurableSpace γ
μ μ' : Measure α
ν ν' : Measure β
τ : Measure γ
inst✝¹ : NormedAddCommGroup E
inst✝ : SigmaFinite ν
s : Set (α × β)
hs : MeasurableSet s
⊢ ↑↑(Measure.prod μ ν) s = ∫⁻ (x : α), ↑↑ν (Prod.mk x ⁻¹' s) ∂μ
simp_rw [Measure.prod, bind_apply hs (Measurable.map_prod_mk_left (ν := ν)),
  map_apply measurable_prod_mk_left hs]