∀ {α : Type u_3} {β : Type u_4} {γ : Type u_5} [inst : Preorder β] [inst_1 : Preorder γ] {l : Filter α} [l.NeBot]
  {f : β → γ},
  Antitone f →
    ∀ {g : α → β}, Filter.Tendsto g l Filter.atTop → lowerBounds (Set.range (f ∘ g)) = lowerBounds (Set.range f)