A squared fourth-power sum bounds a fifth-power product

Proved

WorkbookSource.base_55087

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

lean-workbooksource-checked

Prove the inequality $9(a^4+b^4+c^4)^2 \ge (a^5+b^5+c^5)(a+b+c)^3$ for non-negative real numbers $a$ , $b$ , and $c$ .

Source: InternLM Lean-Workbook, record lean_workbook_55087 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_55087 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : 9 * (a ^ 4 + b ^ 4 + c ^ 4) ^ 2 ≥ (a ^ 5 + b ^ 5 + c ^ 5) * (a + b + c) ^ 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_55087; Apache-2.0

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