A constrained quartic polynomial in three real variables

Proved

WorkbookSource.base_17523

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

lean-workbooksource-checked

Let $a,b,c$ real numbers and $a+b+c=3.$ Prove that $a^2(6a^2+6c^2-3b^2-4)+b^2(6b^2+6c^2-3a^2-4)\geqslant 0$

Source: InternLM Lean-Workbook, record lean_workbook_17523 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_17523 (a b c : ℝ) (h : a + b + c = 3) : a^2 * (6 * a^2 + 6 * c^2 - 3 * b^2 - 4) + b^2 * (6 * b^2 + 6 * c^2 - 3 * a^2 - 4) ≥ 0  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_17523; Apache-2.0

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