Theorems · Theorem · order theory

Filter.le_liminf_iff

∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLinearOrder β] {f : Filter α} {u : α → β} {x : β},
  autoParam (Filter.IsCoboundedUnder (fun x1 x2 => x1 ≥ x2) f u) Filter.le_liminf_iff._auto_1 →
    autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≥ x2) f u) Filter.le_liminf_iff._auto_3 →
      (x ≤ Filter.liminf u f ↔ ∀ y < x, ∀ᶠ (a : α) in f, y < u a)

Defined in

Mathlib.Order.LiminfLimsup

Cited by

9 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLinearOrder