A fifth-power average bounds a fourth-power sum with a product correction

Proved

WorkbookSource.base_44601

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

lean-workbooksource-checked

Let $a,b,c,d>0.$ Prove that $\frac{a^5+b^5+c^5+d^5}{a+b+c+d}\ge\frac{1}{3}(a^4+b^4+c^4+d^4-abcd)$

Source: InternLM Lean-Workbook, record lean_workbook_44601 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_44601 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : (a^5 + b^5 + c^5 + d^5) / (a + b + c + d) ≥ (1/3) * (a^4 + b^4 + c^4 + d^4 - a * b * c * d)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_44601; Apache-2.0

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