An eighth-power bound for symmetric mixed products

Proved

WorkbookSource.base_4988

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

lean-workbooksource-checked

Let $a,$ $b$ and $c$ are non-negative numbers. Prove that: $(a + b + c)^8\geq128(a^5b^3 + a^5c^3 + b^5a^3 + b^5c^3 + c^5a^3 + c^5b^3)$

Source: InternLM Lean-Workbook, record lean_workbook_4988 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_4988 (a b c: ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) : (a + b + c) ^ 8 ≥ 128 * (a ^ 5 * b ^ 3 + a ^ 5 * c ^ 3 + b ^ 5 * a ^ 3 + b ^ 5 * c ^ 3 + c ^ 5 * a ^ 3 + c ^ 5 * b ^ 3)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_4988; Apache-2.0

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