Theorems · Theorem · order theory

Filter.liminf_le_liminf

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

Defined in

Mathlib.Order.LiminfLimsup

Cited by

10 results in Mathlib

Foundations

Depth 16 from the axioms · uses no axioms

Assumes

ConditionallyCompleteLattice