A product bound from reciprocal weighted sums

Proved

WorkbookCorrected.plus_63663

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

corrected-formalizationlean-workbooksource-checked

Let $a,b>0$ and $\frac{1}{a+9b}+\frac{1}{b+9a} = \frac{5}{24}$ . Prove that\n

ab\leq 1

Formalization Note: The original formalization added a+b=1, absent from the source. This correction removes that assumption and proves the original product bound using the reciprocal equation and positivity.

Source: InternLM Lean-Workbook, record lean_workbook_plus_63663 (Apache-2.0).

Preamble

import Mathlib

Formal statement

theorem WorkbookCorrected.plus_63663 (a b : ℝ) (ha : 0<a) (hb : 0<b)
    (h : 1/(a+9*b)+1/(b+9*a)=5/24) : a*b ≤ 1 := by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_63663; Apache-2.0

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