Theorems · Theorem · general topology

Filter.eventually_atBot

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

Defined in

Mathlib.Order.Filter.AtTopBot.Basic

Cited by

4 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderIsCodirectedOrderNonempty