Theorems · Theorem · order theory

Filter.le_limsup_of_le

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

Defined in

Mathlib.Order.LiminfLimsup

Cited by

5 results in Mathlib

Foundations

Depth 11 from the axioms · uses no axioms

Assumes

ConditionallyCompleteLattice