A quartic power-sum bound at total five

Proved

WorkbookSource.base_903

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

lean-workbooksource-checked

Let $a,b,c\in \mathbb{R}$ such that $a+b+c=5$ . Prove that:

$a^4+b^4+c^4+13(a^2+b^2+c^2)\ge 6(a^3+b^3+c^3)+48$

Source: InternLM Lean-Workbook, record lean_workbook_903 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_903 (a b c : ℝ) (h : a + b + c = 5) :
  a^4 + b^4 + c^4 + 13 * (a^2 + b^2 + c^2) ≥ 6 * (a^3 + b^3 + c^3) + 48  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_903; Apache-2.0

View graph