A normalized product bound with quadratic and linear terms

Proved

WorkbookSource.base_15777

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

lean-workbooksource-checked

Let $a,b,c\ge0$ and $a+b+c=3.$ Prove that $(a^2+a-bc)(b^2+b-ca)(c^2+c-ab)\le8$

Source: InternLM Lean-Workbook, record lean_workbook_15777 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_15777 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hab : a + b + c = 3) : (a^2 + a - b * c) * (b^2 + b - c * a) * (c^2 + c - a * b) ≤ 8  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_15777; Apache-2.0

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