∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : Preorder α] [inst_1 : Preorder β] {l : Filter γ} {u : γ → α}
  {v : α → β},
  Antitone v → Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) l u → Filter.IsBoundedUnder (fun x1 x2 => x1 ≥ x2) l (v ∘ u)