Prove2Me

Factorial arithmetic identity #10988

Proved
WorkbookCorrected.plus_10988

by carlok · Sep 29, 2026 · Mathlib 0df444a (Lean v4.33.1)

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

(2/(65))∗(5!)=5/162(2 / (6^5)) * (5!) = 5 / 162

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_10988, 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_10988 (Apache-2.0).

Preamble
import Mathlib.Data.Nat.Factorial.Basic
import Mathlib.Data.Rat.Defs
import Mathlib.Tactic.Ring
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_10988 : ((2:ℚ) / (6 ^ 5)) * ((Nat.factorial 5)) = (5:ℚ) / 162 := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_10988; Apache-2.0; corrects Open node 34887443-2182-48fe-8ce2-5e4e6bbe73f1

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