∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [Nonempty β] [inst : LinearOrder β] [inst_1 : Preorder γ] [NoMaxOrder γ]
  {g : β → γ} {f : α → β} {l : Filter α},
  Antitone g →
    Filter.Tendsto g Filter.atBot Filter.atTop →
      (Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) l (g ∘ f) ↔ Filter.IsBoundedUnder (fun x1 x2 => x1 ≥ x2) l f)