∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : Preorder α] [ClosedIicTopology α] {f : β → α}
  {a b : α} {x : Filter β}, Filter.Tendsto f x (nhds a) → (∃ᶠ (c : β) in x, f c ≤ b) → a ≤ b