∀ {α : Type u_1} {β : Type u_2} [inst : CommGroup α] [inst_1 : Preorder α] [IsOrderedMonoid α] {l : Filter β}
  {u : β → α},
  (Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) l fun x => (u x)⁻¹) = Filter.IsBoundedUnder (fun x1 x2 => x1 ≥ x2) l u