A sixth-degree mixed-product upper bound at fixed sum two

Proved

WorkbookSource.base_42124

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

lean-workbooksource-checked

Let $a$ , $b$ and $c$ be non-negative numbers such that $a+b+c=2$ . Prove that: $a^2+b^2+c^2\ge 2\left(a^3 b^3+a^3 c^3+c^3 b^3\right)+9a^2 b^2 c^2$

Source: InternLM Lean-Workbook, record lean_workbook_42124 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_42124 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hab : a + b + c = 2) : a^2 + b^2 + c^2 ≥ 2 * (a^3 * b^3 + a^3 * c^3 + c^3 * b^3) + 9 * a^2 * b^2 * c^2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_42124; Apache-2.0

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