Theorems · Theorem · general topology

Filter.mem_biInf_of_directed

∀ {α : Type u} {β : Type v} {f : β → Filter α} {s : Set β},
  DirectedOn (f ⁻¹'o fun x1 x2 => x1 ≥ x2) s → s.Nonempty → ∀ {t : Set α}, t ∈ ⨅ i ∈ s, f i ↔ ∃ i ∈ s, t ∈ f i

Defined in

Mathlib.Order.Filter.Basic

Cited by

5 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Quot.sound