A symmetric quartic inequality with mixed coefficients

Proved

WorkbookSource.plus_9631

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that for all real numbers $a$ , $b$ , and $c$ , the following inequality holds: $352(a^4+b^4+c^4)-536[a^3(b+c)+b^3(c+a)+c^3(a+b)]+411(a^2b^2+b^2c^2+c^2a^2)+336(a^2bc+b^2ca+c^2ab)\geq 0.$

Source: InternLM Lean-Workbook, record lean_workbook_plus_9631 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_9631 (a b c : ℝ) : 352 * (a ^ 4 + b ^ 4 + c ^ 4) - 536 * (a ^ 3 * (b + c) + b ^ 3 * (c + a) + c ^ 3 * (a + b)) + 411 * (a ^ 2 * b ^ 2 + b ^ 2 * c ^ 2 + c ^ 2 * a ^ 2) + 336 * (a ^ 2 * b * c + b ^ 2 * c * a + c ^ 2 * a * b) ≥ 0   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_9631; Apache-2.0

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