cobounded_pi — Mathlib

English

The cobounded filter on the product space ∀i, X_i equals the coproduct of the cobounded filters on each X_i.

Русский

Кобounded-фильтр произведения равно копродукту кобounded-фильтров на каждом X_i.

LaTeX

$$$\\operatorname{cobounded}(\\forall i, X_i) = \\operatorname{Filter.coprod}ᵢ (\\lambda i, \\operatorname{cobounded}(X_i))$$$

Lean4

theorem cobounded_pi : cobounded (∀ i, X i) = Filter.coprodᵢ fun i => cobounded (X i) :=
  rfl

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