Theorems · Theorem · general topology

Filter.IsBoundedUnder.sup

∀ {α : Type u_1} {β : Type u_2} [inst : SemilatticeSup α] {f : Filter β} {u v : β → α},
  Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) f u →
    Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) f v → Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) f fun a => u a ⊔ v a

Defined in

Mathlib.Order.Filter.IsBounded

Cited by

3 results in Mathlib

Foundations

Depth 12 from the axioms · uses no axioms

Assumes

SemilatticeSup