∀ (p : ℕ) [inst : Fact (Nat.Prime p)] (R : Type u_1) [inst_1 : NormedRing R] [inst_2 : Algebra ℤ_[p] R]
  [inst_3 : IsBoundedSMul ℤ_[p] R] [inst_4 : IsUltrametricDist R] [inst_5 : CompleteSpace R] (r : R)
  (hr : Filter.Tendsto (fun x => r ^ x) Filter.atTop (nhds 0)),
  (fun x =>
        match x with
        | ⟨κ, hκ⟩ => ⟨κ 1 - 1, ⋯⟩)
      ((fun x =>
          match x with
          | ⟨r, hr⟩ => ⟨PadicInt.addChar_of_value_at_one r hr, ⋯⟩)
        ⟨r, hr⟩) =
    ⟨r, hr⟩