E : Type u_2
L : Type u_1
inst✝⁶ : MeasurableSpace E
μ : Measure E
F s : Set E
inst✝⁵ : AddCommGroup L
inst✝⁴ : Countable L
inst✝³ : AddAction L E
inst✝² : MeasurableSpace L
inst✝¹ : MeasurableVAdd L E
inst✝ : VAddInvariantMeasure L E μ
fund : IsAddFundamentalDomain L F
hS : NullMeasurableSet s
h : ∀ (x y : L), x ≠ y → Disjoint (x +ᵥ s) (y +ᵥ s)
⊢ ↑↑μ s ≤ ↑↑μ F
E : Type u_2
L : Type u_1
inst✝⁶ : MeasurableSpace E
μ : Measure E
F s : Set E
inst✝⁵ : AddCommGroup L
inst✝⁴ : Countable L
inst✝³ : AddAction L E
inst✝² : MeasurableSpace L
inst✝¹ : MeasurableVAdd L E
inst✝ : VAddInvariantMeasure L E μ
fund : IsAddFundamentalDomain L F
hS : NullMeasurableSet s
h : ↑↑μ F < ↑↑μ s
⊢ ∃ x y, x ≠ y ∧ ¬Disjoint (x +ᵥ s) (y +ᵥ s)
contrapose! h
no goals
E : Type u_2
L : Type u_1
inst✝⁶ : MeasurableSpace E
μ : Measure E
F s : Set E
inst✝⁵ : AddCommGroup L
inst✝⁴ : Countable L
inst✝³ : AddAction L E
inst✝² : MeasurableSpace L
inst✝¹ : MeasurableVAdd L E
inst✝ : VAddInvariantMeasure L E μ
fund : IsAddFundamentalDomain L F
hS : NullMeasurableSet s
h : ∀ (x y : L), x ≠ y → Disjoint (x +ᵥ s) (y +ᵥ s)
⊢ ↑↑μ s ≤ ↑↑μ F
exact ((fund.measure_eq_tsum _).trans (measure_iUnion₀
  (Pairwise.mono h fun i j hij => (hij.mono inf_le_left inf_le_left).aedisjoint)
    fun _ => (hS.vadd _).inter fund.nullMeasurableSet).symm).trans_le
    (measure_mono <| Set.iUnion_subset fun _ => Set.inter_subset_right _ _)