A cyclic cubic upper bound at fixed sum three

Proved

WorkbookSource.plus_44318

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

lean-workbooksource-checked

Let $a,b,c\ge 0$ such that $a+b+c=3$ . Prove that: $(a^2b+b^2c+c^2a)+2(ab^2+bc^2+ca^2)+3abc\le 12$

Source: InternLM Lean-Workbook, record lean_workbook_plus_44318 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_44318 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hab : a + b + c = 3) : a^2 * b + b^2 * c + c^2 * a + 2 * (a * b^2 + b * c^2 + c * a^2) + 3 * a * b * c ≤ 12   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_44318; Apache-2.0

View graph