A quartic bound for a symmetric quadratic difference

Proved

WorkbookSource.base_17183

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

lean-workbooksource-checked

For $a,b,c>0$ . Prove that $7[2(a^2+b^2+c^2)-7(ab+bc+ca)]^2\leqslant 39(a+b+c)^4$

Source: InternLM Lean-Workbook, record lean_workbook_17183 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_17183 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 7 * (2 * (a ^ 2 + b ^ 2 + c ^ 2) - 7 * (a * b + b * c + c * a)) ^ 2 ≤ 39 * (a + b + c) ^ 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_17183; Apache-2.0

View graph