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Real logarithm identity #59205

Disproved
WorkbookCorrected.plus_59205

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

Real.log2>(2/5)(2/5)Real.log 2 > (2/5)^(2/5)Real.log2>(2/5)(2/5)

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_59205, 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_59205 (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_59205 : Real.log 2 > (2/5) ^ (2/5) := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_59205; Apache-2.0; corrects Open node c0008fc7-8ae0-47a3-9412-95fc562f3045

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