no goals
α : Type u_1
β : Type u_2
l : Filter α
k f g g' : α → β
inst✝¹ : TopologicalSpace β
inst✝ : CommSemiring β
hf : SuperpolynomialDecay l k f
z : ℕ
s : Set β
hs : IsOpen s
hs0 : 0 ∈ s
x : α
hx : x ∈ (fun a => k a ^ (z + 1) * f a) ⁻¹' s
⊢ x ∈ (fun a => k a ^ z * (k * f) a) ⁻¹' s
simpa only [Set.mem_preimage, Pi.mul_apply, ← mul_assoc, ← pow_succ'] using hx