Theorems · Theorem · order theory

Filter.liminf_le_limsup

∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLattice α] {f : Filter β} [f.NeBot] {u : β → α},
  autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) f u) Filter.liminf_le_limsup._auto_1 →
    autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≥ x2) f u) Filter.liminf_le_limsup._auto_3 →
      Filter.liminf u f ≤ Filter.limsup u f

Defined in

Mathlib.Order.LiminfLimsup

Cited by

6 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLatticeFilter.NeBot