covers — Mathlib

English

If 𝒰 is jointly surjective, then the union over i of the ranges of (𝒰.f i).base equals the whole space.

Русский

Если 𝒰 jointly surjective, то объединение образов (𝒰.f i).base по всем i даёт всюSpace.

LaTeX

$$$$ \bigcup_i \operatorname{range}((\mathcal{U}.f i).base) = \top $$$$

Lean4

theorem covers [JointlySurjective K] (𝒰 : X.Cover K) (x : X) : x ∈ Set.range (𝒰.f (𝒰.idx x)).base :=
  (𝒰.exists_eq x).choose_spec

Похожие утверждения