Real logarithm identity #2048

Proved

WorkbookCorrected.plus_2048

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

2^(Real.logb 2 5 - 2) = 2^(Real.logb 2 5) / 2^2

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_2048, 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_2048 (Apache-2.0).

Preamble

import Mathlib.Data.Real.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Base
import Mathlib.Analysis.SpecialFunctions.Pow.Real
import Mathlib.Tactic.NormNum

Formal statement

theorem WorkbookCorrected.plus_2048 : (2:ℝ) ^ (Real.logb 2 5 - 2) = (2:ℝ) ^ (Real.logb 2 5) / (2:ℝ) ^ 2 := by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_2048; Apache-2.0; corrects Open node 708b5936-4988-4b07-bd45-2ec77a455817

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