Theorems · Theorem · order theory

Filter.limsup_le_limsup_of_le

∀ {α : Type u_6} {β : Type u_7} [inst : ConditionallyCompleteLattice β] {f g : Filter α},
  f ≤ g →
    ∀ {u : α → β},
      autoParam (Filter.IsCoboundedUnder (fun x1 x2 => x1 ≤ x2) f u) Filter.limsup_le_limsup_of_le._auto_1 →
        autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) g u) Filter.limsup_le_limsup_of_le._auto_3 →
          Filter.limsup u f ≤ Filter.limsup u g

Defined in

Mathlib.Order.LiminfLimsup

Cited by

4 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLattice