Theorems · Theorem · order theory

Filter.liminf_le_of_frequently_le

∀ {α : Type u_1} {ι : Type u_4} [inst : ConditionallyCompleteLattice α] {f : Filter ι} {u : ι → α} {a : α},
  (∃ᶠ (i : ι) in f, u i ≤ a) →
    autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≥ x2) f u) Filter.liminf_le_of_frequently_le._auto_1 →
      Filter.liminf u f ≤ a

Defined in

Mathlib.Order.LiminfLimsup

Cited by

1 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLattice