Theorems · Theorem · order theory

Filter.limsInf_le_limsSup

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

Defined in

Mathlib.Order.LiminfLimsup

Cited by

2 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLatticeFilter.NeBot