G : Type u_1
inst✝² : Group G
inst✝¹ : TopologicalSpace G
inst✝ : TopologicalGroup G
K₀ : PositiveCompacts G
U : Set G
hU : Set.Nonempty (interior U)
K₁ K₂ : Compacts G
h : ↑K₁ ⊆ K₂.carrier
⊢ ↑(index (↑K₁) U) / ↑(index (↑K₀) U) ≤ ↑(index (↑K₂) U) / ↑(index (↑K₀) U)
G : Type u_1
inst✝² : Group G
inst✝¹ : TopologicalSpace G
inst✝ : TopologicalGroup G
K₀ : PositiveCompacts G
U : Set G
hU : Set.Nonempty (interior U)
K₁ K₂ : Compacts G
h : ↑K₁ ⊆ K₂.carrier
⊢ prehaar (↑K₀) U K₁ ≤ prehaar (↑K₀) U K₂
simp only [prehaar]
G : Type u_1
inst✝² : Group G
inst✝¹ : TopologicalSpace G
inst✝ : TopologicalGroup G
K₀ : PositiveCompacts G
U : Set G
hU : Set.Nonempty (interior U)
K₁ K₂ : Compacts G
h : ↑K₁ ⊆ K₂.carrier
⊢ ↑(index (↑K₁) U) ≤ ↑(index (↑K₂) U)

G : Type u_1
inst✝² : Group G
inst✝¹ : TopologicalSpace G
inst✝ : TopologicalGroup G
K₀ : PositiveCompacts G
U : Set G
hU : Set.Nonempty (interior U)
K₁ K₂ : Compacts G
h : ↑K₁ ⊆ K₂.carrier
⊢ 0 < ↑(index (↑K₀) U)
G : Type u_1
inst✝² : Group G
inst✝¹ : TopologicalSpace G
inst✝ : TopologicalGroup G
K₀ : PositiveCompacts G
U : Set G
hU : Set.Nonempty (interior U)
K₁ K₂ : Compacts G
h : ↑K₁ ⊆ K₂.carrier
⊢ ↑(index (↑K₁) U) / ↑(index (↑K₀) U) ≤ ↑(index (↑K₂) U) / ↑(index (↑K₀) U)
rw [div_le_div_right]
G : Type u_1
inst✝² : Group G
inst✝¹ : TopologicalSpace G
inst✝ : TopologicalGroup G
K₀ : PositiveCompacts G
U : Set G
hU : Set.Nonempty (interior U)
K₁ K₂ : Compacts G
h : ↑K₁ ⊆ K₂.carrier
⊢ 0 < ↑(index (↑K₀) U)
G : Type u_1
inst✝² : Group G
inst✝¹ : TopologicalSpace G
inst✝ : TopologicalGroup G
K₀ : PositiveCompacts G
U : Set G
hU : Set.Nonempty (interior U)
K₁ K₂ : Compacts G
h : ↑K₁ ⊆ K₂.carrier
⊢ ↑(index (↑K₁) U) ≤ ↑(index (↑K₂) U)

G : Type u_1
inst✝² : Group G
inst✝¹ : TopologicalSpace G
inst✝ : TopologicalGroup G
K₀ : PositiveCompacts G
U : Set G
hU : Set.Nonempty (interior U)
K₁ K₂ : Compacts G
h : ↑K₁ ⊆ K₂.carrier
⊢ 0 < ↑(index (↑K₀) U)
exact_mod_cast index_mono K₂.2 h hU
no goals
G : Type u_1
inst✝² : Group G
inst✝¹ : TopologicalSpace G
inst✝ : TopologicalGroup G
K₀ : PositiveCompacts G
U : Set G
hU : Set.Nonempty (interior U)
K₁ K₂ : Compacts G
h : ↑K₁ ⊆ K₂.carrier
⊢ 0 < ↑(index (↑K₀) U)
exact_mod_cast index_pos K₀ hU