A number and its decimal digit sum agree modulo nine

Proved

WorkbookRestored.plus_15734

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

For every natural $n$ , the sum of its decimal digits is congruent to $n$ modulo nine.

This restores the missing imports or namespaces of the original node, retaining its formal proposition. Source: Lean-Workbook row lean_workbook_plus_15734 (Apache-2.0).

Preamble

import Mathlib.Analysis.Complex.Basic
import Mathlib.Data.Nat.Digits.Lemmas
open Nat

Formal statement

theorem WorkbookRestored.plus_15734 (n : ℕ) : (Nat.digits 10 n).sum % 9 = n % 9   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_15734; original Prove2Me node f1b17e4f-47a1-4dbf-b625-b740f15e04b5; Apache-2.0

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