A pairwise-product bound at fixed positive sum

Proved

WorkbookSource.base_6936

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

lean-workbooksource-checked

If a,b,c > 0 and a+b+c=3, then $9(ab+bc+ca)\le 22+5abc.$

Source: InternLM Lean-Workbook, record lean_workbook_6936 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_6936 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : 9 * (a * b + b * c + c * a) ≤ 22 + 5 * a * b * c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_6936; Apache-2.0

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