∀ {p : ℕ} [hp : Fact (Nat.Prime p)] {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : Module ℤ_[p] E]
  [inst_2 : IsBoundedSMul ℤ_[p] E] [inst_3 : IsUltrametricDist E] [inst_4 : CompleteSpace E]
  (a : ZeroAtInftyContinuousMap ℕ E), (PadicInt.mahlerEquiv E).symm a = PadicInt.mahlerSeries ⇑a