∀ {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 fun a => u a ⊔ v a) ↔
    Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) f u ∧ Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) f v