Theorems · Theorem · order theory

Filter.limsInf_le_limsInf_of_le

∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {f g : Filter α},
  g ≤ f →
    autoParam (Filter.IsBounded (fun x1 x2 => x1 ≥ x2) f) Filter.limsInf_le_limsInf_of_le._auto_1 →
      autoParam (Filter.IsCobounded (fun x1 x2 => x1 ≥ x2) g) Filter.limsInf_le_limsInf_of_le._auto_3 →
        f.limsInf ≤ g.limsInf

Defined in

Mathlib.Order.LiminfLimsup

Cited by

2 results in Mathlib

Foundations

Depth 13 from the axioms · uses propext, Quot.sound

Assumes

ConditionallyCompleteLattice