Prove2Me

Real logarithm identity #54693

Proved
WorkbookCorrected.plus_54693

by carlok · Sep 30, 2026 · Mathlib 0df444a (Lean v4.33.1)

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

(1/Real.logb2(1/7))+(1/Real.logb3(1/7))+(1/Real.logb4(1/7))+(1/Real.logb5(1/7))+(1/Real.logb6(1/7))−(1/Real.logb7(1/7))−(1/Real.logb8(1/7))−(1/Real.logb9(1/7))−(1/Real.logb10(1/7))=1(1 / Real.logb 2 (1 / 7)) + (1 / Real.logb 3 (1 / 7)) + (1 / Real.logb 4 (1 / 7)) + (1 / Real.logb 5 (1 / 7)) + (1 / Real.logb 6 (1 / 7)) - (1 / Real.logb 7 (1 / 7)) - (1 / Real.logb 8 (1 / 7)) - (1 / Real.logb 9 (1 / 7)) - (1 / Real.logb 10 (1 / 7)) = 1

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_54693, which omitted a compilable colon/type annotation and/or used a preamble of only Mathlib.Analysis.Complex.Basic.

Source: InternLM Lean-Workbook, record lean_workbook_plus_54693 (Apache-2.0).

Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Base
import Mathlib.Analysis.SpecialFunctions.Log.Basic
import Mathlib.Tactic.Ring
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Positivity
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_54693 : (1 / Real.logb 2 (1 / 7)) + (1 / Real.logb 3 (1 / 7)) + (1 / Real.logb 4 (1 / 7)) + (1 / Real.logb 5 (1 / 7)) + (1 / Real.logb 6 (1 / 7)) - (1 / Real.logb 7 (1 / 7)) - (1 / Real.logb 8 (1 / 7)) - (1 / Real.logb 9 (1 / 7)) - (1 / Real.logb 10 (1 / 7)) = 1 := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_54693; Apache-2.0; corrects Open node 2fbc9765-e529-4dfa-912c-ef64cc2cef80

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