Prove2Me

A normalized product inequality with a fifth-degree correction

Proved
WorkbookSource.base_5622

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

lean-workbooksource-checked

Let x x , yy and zz be non-negative numbers, which satisfying x+y+z=3 x+y+z=3 . Prove that: 2xyz(x2+y2+z2)+(x2−x+1)(y2−y+1)(z2−z+1)≤72xyz(x^2+y^2+z^2)+(x^2-x+1)(y^2-y+1)(z^2-z+1) \le 7

Source: InternLM Lean-Workbook, record lean_workbook_5622 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_5622 (x y z : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 ≤ z) (h : x + y + z = 3) : 2 * x * y * z * (x ^ 2 + y ^ 2 + z ^ 2) + (x ^ 2 - x + 1) * (y ^ 2 - y + 1) * (z ^ 2 - z + 1) ≤ 7  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_5622; Apache-2.0

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