A quartic bound under zero sum

Proved

WorkbookSource.base_11560

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

lean-workbooksource-checked

Prove: $a^2b^2+a^2c^2+b^2c^2+3\geq6abc$ given $a+b+c=0$

Source: InternLM Lean-Workbook, record lean_workbook_11560 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_11560 (a b c : ℝ) (habc : a + b + c = 0) : a^2 * b^2 + a^2 * c^2 + b^2 * c^2 + 3 ≥ 6 * a * b * c  :=  by sorry

Source