A sixth-degree upper bound at fixed sum three

Proved

WorkbookSource.base_31427

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

lean-workbooksource-checked

But easy to prove that $16\geq7u^{2}v^{2}w^{2}+3(u^{2}v^{2}+u^{2}w^{2}+v^{2}w^{2})$ is true for all non-negative $u,$ $v$ and $w$ such that $u+v+w=3.$

Source: InternLM Lean-Workbook, record lean_workbook_31427 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_31427 (u v w : ℝ) (hu : 0 ≤ u) (hv : 0 ≤ v) (hw : 0 ≤ w) (h : u + v + w = 3) : 16 ≥ 7 * u^2 * v^2 * w^2 + 3 * (u^2 * v^2 + u^2 * w^2 + v^2 * w^2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_31427; Apache-2.0

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