A sixth-power sum bound at fixed sum three

Proved

WorkbookSource.base_6527

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

lean-workbooksource-checked

Let $x,y,z>0$ such that $x+y+z=3$ .Prove that $x^6+y^6+z^6+3\geq \frac{3}{32}(x+y)^2(y+z)^2(x+z)^2$

Source: InternLM Lean-Workbook, record lean_workbook_6527 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_6527 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (h : x + y + z = 3) :  x ^ 6 + y ^ 6 + z ^ 6 + 3 ≥ (3 / 32) * (x + y) ^ 2 * (y + z) ^ 2 * (x + z) ^ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_6527; Apache-2.0

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