∀ {α : Type u_2} {β : Type u_3} [inst : LinearOrder α] [inst_1 : TopologicalSpace α] [inst_2 : TopologicalSpace β]
  [ClosedIicTopology α] [Nonempty β] {f : β → α},
  Continuous f → Filter.Tendsto f (Filter.cocompact β) Filter.atTop → ∃ x, ∀ (y : β), f x ≤ f y