A normalized bound between power sums

Proved

WorkbookSource.base_12023

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

lean-workbooksource-checked

Let $a,b,c$ are nonnegative real numbers such that $a+b+c=3.$ Prove that

(a^4+b^4+c^4)^2\ge (a^2+b^2+c^2)(a^5+b^5+c^5).

Source: InternLM Lean-Workbook, record lean_workbook_12023 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_12023 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (hab : a + b + c = 3) : (a^4 + b^4 + c^4)^2 ≥ (a^2 + b^2 + c^2) * (a^5 + b^5 + c^5)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_12023; Apache-2.0

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