index_defined — Mathlib

English

For any μ, join (map dirac μ) = μ.

Русский

Для любой μ, объединение через Dirac даёт μ.

LaTeX

$$$\text{join}(\text{map}(\text{dirac})\mu) = \mu$$$

Lean4

/-- If `K` is compact and `V` has nonempty interior, then the index `(K : V)` is well-defined,
  there is a finite set `t` satisfying the desired properties. -/
@[to_additive addIndex_defined /--
    If `K` is compact and `V` has nonempty interior, then the index `(K : V)` is well-defined,
      there is a finite set `t` satisfying the desired properties. -/
    ]
theorem index_defined {K V : Set G} (hK : IsCompact K) (hV : (interior V).Nonempty) :
    ∃ n : ℕ, n ∈ Finset.card '' {t : Finset G | K ⊆ ⋃ g ∈ t, (fun h => g * h) ⁻¹' V} := by
  rcases compact_covered_by_mul_left_translates hK hV with ⟨t, ht⟩; exact ⟨t.card, t, ht, rfl⟩

Похожие утверждения