Theorems · Theorem · order theory

liminf_min

∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLinearOrder β] {f : Filter α} {u v : α → β},
  autoParam (Filter.IsCoboundedUnder (fun x1 x2 => x1 ≥ x2) f u) liminf_min._auto_1 →
    autoParam (Filter.IsCoboundedUnder (fun x1 x2 => x1 ≥ x2) f v) liminf_min._auto_3 →
      autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≥ x2) f u) liminf_min._auto_5 →
        autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≥ x2) f v) liminf_min._auto_7 →
          Filter.liminf (fun a => min (u a) (v a)) f = min (Filter.liminf u f) (Filter.liminf v f)

Defined in

Mathlib.Order.LiminfLimsup

Cited by

2 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLinearOrder