∀ {α : Type u_1} {β : Type u_2} {l : Filter α} {k : α → β} (f : α → β) [inst : NormedField β] [inst_1 : LinearOrder β]
  [IsStrictOrderedRing β] [OrderTopology β],
  Filter.Tendsto k l Filter.atTop → (Asymptotics.SuperpolynomialDecay l k f ↔ ∀ (z : ℤ), f =O[l] fun a => k a ^ z)