A cyclic quartic and triple-product upper bound

Proved

WorkbookSource.base_7985

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

lean-workbooksource-checked

Let $a,b,c\in \mathbb{R}$ such that $a + b + c = 3$ . Prove that: $a^3b + b^3c + c^3a + 6abc\le 9$

Source: InternLM Lean-Workbook, record lean_workbook_7985 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_7985 (a b c : ℝ) (h : a + b + c = 3) :
  a^3 * b + b^3 * c + c^3 * a + 6 * a * b * c ≤ 9  :=  by sorry

Source