Theorems · Theorem · order theory

Filter.le_liminf_of_le

∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLattice α] {f : Filter β} {u : β → α} {a : α},
  autoParam (Filter.IsCoboundedUnder (fun x1 x2 => x1 ≥ x2) f u) Filter.le_liminf_of_le._auto_1 →
    (∀ᶠ (n : β) in f, a ≤ u n) → a ≤ Filter.liminf u f

Defined in

Mathlib.Order.LiminfLimsup

Cited by

9 results in Mathlib

Foundations

Depth 11 from the axioms · uses no axioms

Assumes

ConditionallyCompleteLattice