A sixth-degree lower bound for squared pairwise products

Proved

WorkbookSource.base_15806

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

lean-workbooksource-checked

Let $x,y,z$ be non-negative real numbers, Prove that : $27((x+y)(y+z)(z+x))^{2}\geq 64$ $xyz(x+y+z)^{3}$

Source: InternLM Lean-Workbook, record lean_workbook_15806 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_15806 (x y z : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 ≤ z) : 27 * ((x + y) * (y + z) * (z + x)) ^ 2 ≥ 64 * x * y * z * (x + y + z) ^ 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_15806; Apache-2.0

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