Theorems · Theorem · general topology

Filter.pi_mem_pi

∀ {ι : Type u_1} {α : ι → Type u_2} {f : (i : ι) → Filter (α i)} {s : (i : ι) → Set (α i)} {I : Set ι},
  I.Finite → (∀ i ∈ I, s i ∈ f i) → I.pi s ∈ Filter.pi f

Defined in

Mathlib.Order.Filter.Pi

Cited by

4 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound