∀ {R : Type u_3} {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : NormedRing R]
  [inst_3 : NormedAlgebra ℝ R] {f : E → R},
  Function.HasTemperateGrowth f → ∀ (k : ℕ), Function.HasTemperateGrowth (f ^ k)