Theorems · Theorem · general topology

countable_bInter_mem

∀ {α : Type u_2} {l : Filter α} [CountableInterFilter l] {ι : Type u_4} {S : Set ι},
  S.Countable → ∀ {s : (i : ι) → i ∈ S → Set α}, ⋂ i, ⋂ (hi : i ∈ S), s i hi ∈ l ↔ ∀ (i : ι) (hi : i ∈ S), s i hi ∈ l

Defined in

Mathlib.Order.Filter.CountableInter

Cited by

4 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CountableInterFilter