Theorems · Theorem · general topology

Filter.Eventually.exists_forall_of_atTop

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

Alias of the forward direction of Filter.eventually_atTop.

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

PreorderIsDirectedOrderNonempty