∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : Preorder α] [OrderClosedTopology α]
  [inst_3 : Preorder β] [IsCodirectedOrder β] {f : β → α} {a : α},
  Monotone f → Filter.Tendsto f Filter.atBot (nhds a) → ∀ (b : β), a ≤ f b