G : Type u_1
inst✝⁶ : MeasurableSpace G
inst✝⁵ : Group G
inst✝⁴ : MeasurableMul₂ G
μ ν : Measure G
inst✝³ : SigmaFinite ν
inst✝² : SigmaFinite μ
s : Set G
inst✝¹ : MeasurableInv G
inst✝ : IsMulRightInvariant μ
g : G
this : QuasiMeasurePreserving fun h => h * g⁻¹
⊢ QuasiMeasurePreserving fun h => g * h
G : Type u_1
inst✝⁶ : MeasurableSpace G
inst✝⁵ : Group G
inst✝⁴ : MeasurableMul₂ G
μ ν : Measure G
inst✝³ : SigmaFinite ν
inst✝² : SigmaFinite μ
s : Set G
inst✝¹ : MeasurableInv G
inst✝ : IsMulRightInvariant μ
g : G
⊢ QuasiMeasurePreserving fun h => g * h
have :=
  (quasiMeasurePreserving_mul_right μ.inv g⁻¹).mono (inv_absolutelyContinuous μ.inv)
    (absolutelyContinuous_inv μ.inv)
G : Type u_1
inst✝⁶ : MeasurableSpace G
inst✝⁵ : Group G
inst✝⁴ : MeasurableMul₂ G
μ ν : Measure G
inst✝³ : SigmaFinite ν
inst✝² : SigmaFinite μ
s : Set G
inst✝¹ : MeasurableInv G
inst✝ : IsMulRightInvariant μ
g : G
this : QuasiMeasurePreserving fun h => h * g⁻¹
⊢ QuasiMeasurePreserving fun h => g * h
G : Type u_1
inst✝⁶ : MeasurableSpace G
inst✝⁵ : Group G
inst✝⁴ : MeasurableMul₂ G
μ ν : Measure G
inst✝³ : SigmaFinite ν
inst✝² : SigmaFinite μ
s : Set G
inst✝¹ : MeasurableInv G
inst✝ : IsMulRightInvariant μ
g : G
this : QuasiMeasurePreserving fun h => h * g⁻¹
⊢ QuasiMeasurePreserving fun h => g * h
rw [μ.inv_inv] at this
G : Type u_1
inst✝⁶ : MeasurableSpace G
inst✝⁵ : Group G
inst✝⁴ : MeasurableMul₂ G
μ ν : Measure G
inst✝³ : SigmaFinite ν
inst✝² : SigmaFinite μ
s : Set G
inst✝¹ : MeasurableInv G
inst✝ : IsMulRightInvariant μ
g : G
this✝ : QuasiMeasurePreserving fun h => h * g⁻¹
this : QuasiMeasurePreserving (Inv.inv ∘ (fun h => h * g⁻¹) ∘ Inv.inv)
⊢ QuasiMeasurePreserving fun h => g * h
G : Type u_1
inst✝⁶ : MeasurableSpace G
inst✝⁵ : Group G
inst✝⁴ : MeasurableMul₂ G
μ ν : Measure G
inst✝³ : SigmaFinite ν
inst✝² : SigmaFinite μ
s : Set G
inst✝¹ : MeasurableInv G
inst✝ : IsMulRightInvariant μ
g : G
this : QuasiMeasurePreserving fun h => h * g⁻¹
⊢ QuasiMeasurePreserving fun h => g * h
have :=
  (quasiMeasurePreserving_inv_of_right_invariant μ).comp
    (this.comp (quasiMeasurePreserving_inv_of_right_invariant μ))
G : Type u_1
inst✝⁶ : MeasurableSpace G
inst✝⁵ : Group G
inst✝⁴ : MeasurableMul₂ G
μ ν : Measure G
inst✝³ : SigmaFinite ν
inst✝² : SigmaFinite μ
s : Set G
inst✝¹ : MeasurableInv G
inst✝ : IsMulRightInvariant μ
g : G
this✝ : QuasiMeasurePreserving fun h => h * g⁻¹
this : QuasiMeasurePreserving fun x => g * x
⊢ QuasiMeasurePreserving fun h => g * h
G : Type u_1
inst✝⁶ : MeasurableSpace G
inst✝⁵ : Group G
inst✝⁴ : MeasurableMul₂ G
μ ν : Measure G
inst✝³ : SigmaFinite ν
inst✝² : SigmaFinite μ
s : Set G
inst✝¹ : MeasurableInv G
inst✝ : IsMulRightInvariant μ
g : G
this✝ : QuasiMeasurePreserving fun h => h * g⁻¹
this : QuasiMeasurePreserving (Inv.inv ∘ (fun h => h * g⁻¹) ∘ Inv.inv)
⊢ QuasiMeasurePreserving fun h => g * h
simp_rw [Function.comp, mul_inv_rev, inv_inv] at this
no goals
G : Type u_1
inst✝⁶ : MeasurableSpace G
inst✝⁵ : Group G
inst✝⁴ : MeasurableMul₂ G
μ ν : Measure G
inst✝³ : SigmaFinite ν
inst✝² : SigmaFinite μ
s : Set G
inst✝¹ : MeasurableInv G
inst✝ : IsMulRightInvariant μ
g : G
this✝ : QuasiMeasurePreserving fun h => h * g⁻¹
this : QuasiMeasurePreserving fun x => g * x
⊢ QuasiMeasurePreserving fun h => g * h
exact this