Theorems · Theorem · order theory

Filter.limsup_le_limsup

∀ {β : Type u_2} {α : Type u_6} [inst : ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β},
  u ≤ᶠ[f] v →
    autoParam (Filter.IsCoboundedUnder (fun x1 x2 => x1 ≤ x2) f u) Filter.limsup_le_limsup._auto_1 →
      autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) f v) Filter.limsup_le_limsup._auto_3 →
        Filter.limsup u f ≤ Filter.limsup v f

Defined in

Mathlib.Order.LiminfLimsup

Cited by

16 results in Mathlib

Foundations

Depth 13 from the axioms · uses no axioms

Assumes

ConditionallyCompleteLattice