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Elementary inequality #20267

Proved
WorkbookCorrected.plus_20267

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

(264)≤64!(2^64) ≤ 64!(264)≤64!

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_20267, 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_20267 (Apache-2.0).

Preamble
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_20267 : (2 ^ 64) ≤ (Nat.factorial 64) := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_20267; Apache-2.0; corrects Open node bd6178b1-1eba-4518-98d9-2f4a625a97c8

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