A sixth-power bound for the cubed sum of squares

Proved

WorkbookSource.base_16588

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

lean-workbooksource-checked

For all non-negative real numbers $a$ , $b$ and $c$ prove that:

4(a^6+b^6+c^6)+5abc(a^3+b^3+c^3)\geq(a^2+b^2+c^2)^3

Source: InternLM Lean-Workbook, record lean_workbook_16588 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_16588 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : 4 * (a ^ 6 + b ^ 6 + c ^ 6) + 5 * a * b * c * (a ^ 3 + b ^ 3 + c ^ 3) ≥ (a ^ 2 + b ^ 2 + c ^ 2) ^ 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_16588; Apache-2.0

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