A quartic cyclic bound under a quadratic constraint

Proved

WorkbookSource.plus_30899

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

lean-workbooksource-checked

Let $a,b,c$ be nonnegative real numbers such that $a^2+b^2+c^2=\frac{5}{2}(ab+bc+ca)$ . Prove that $11(a^4+b^4+c^4) \ge 17(a^3b+b^3c+c^3a)+129abc(a+b+c)$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_30899 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_30899 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hab : a^2 + b^2 + c^2 = (5/2) * (a * b + b * c + c * a)) : 11 * (a^4 + b^4 + c^4) ≥ 17 * (a^3 * b + b^3 * c + c^3 * a) + 129 * a * b * c * (a + b + c)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_30899; Apache-2.0

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