Theorems · Theorem · general topology

Filter.frequently_atTop

∀ {α : Type u_3} [inst : Preorder α] [IsDirectedOrder α] {p : α → Prop} [Nonempty α],
  (∃ᶠ (x : α) in Filter.atTop, p x) ↔ ∀ (a : α), ∃ b, a ≤ b ∧ p b

Defined in

Mathlib.Order.Filter.AtTopBot.Basic

Cited by

14 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderIsDirectedOrderNonempty