A quartic symmetric bound at a negative fixed sum

Proved

WorkbookSource.base_31532

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

lean-workbooksource-checked

Prove that $a^2b^2+b^2c^2+c^2a^2+12abc+48\ge 0$ given $a+b+c=-6$ .

Source: InternLM Lean-Workbook, record lean_workbook_31532 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_31532 (a b c : ℝ) (h : a + b + c = -6) : a^2 * b^2 + b^2 * c^2 + c^2 * a^2 + 12 * a * b * c + 48 ≥ 0  :=  by sorry

Source