∀ {α : Type u_1} {R : Type u_13} [inst : SeminormedRing R] {S : Type u_17} [inst_1 : NormedRing S] [NormMulClass S]
  {l : Filter α} {f : α → R} {g : α → S}, f =o[l] g → ∀ {n : ℕ}, 0 < n → (fun x => f x ^ n) =o[l] fun x => g x ^ n