∀ {α : Type u_1} {ι : Type u_4} [inst : LinearOrder α] [inst_1 : Mul α] [inst_2 : Zero α] [PosMulMono α] [MulPosMono α]
  {f : Filter ι} [f.NeBot] {u v : ι → α},
  0 ≤ᶠ[f] u →
    Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) f u →
      0 ≤ᶠ[f] v →
        Filter.IsCoboundedUnder (fun x1 x2 => x1 ≥ x2) f v → Filter.IsCoboundedUnder (fun x1 x2 => x1 ≥ x2) f (u * v)