A quartic power sum bounds a cubic sum with a quadratic correction

Proved

WorkbookSource.base_18478

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

lean-workbooksource-checked

Prove that $3(a^4 + b^4 + c^4) - (a^3 + b^3 + c^3)\geq (a^3 + b^3 + c^3) - \frac13(a^2 + b^2 + c^2)$

Source: InternLM Lean-Workbook, record lean_workbook_18478 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_18478 (a b c : ℝ) :
  3 * (a^4 + b^4 + c^4) - (a^3 + b^3 + c^3) ≥ (a^3 + b^3 + c^3) - (1/3) * (a^2 + b^2 + c^2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_18478; Apache-2.0

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