Prove2Me

A triple-product bound with pairwise fourth powers

Proved
WorkbookSource.base_30012

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

lean-workbooksource-checked

Let x,y,zx,y,z be positive reals with sum 1. Prove that 10xyz≤x2+y2+z2+x2y2+y2z2+z2x2.10xyz\leq x^2+y^2+z^2+x^2y^2+y^2z^2+z^2x^2.

Source: InternLM Lean-Workbook, record lean_workbook_30012 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_30012 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (h : x + y + z = 1) : 10 * x * y * z ≤ x ^ 2 + y ^ 2 + z ^ 2 + x ^ 2 * y ^ 2 + y ^ 2 * z ^ 2 + z ^ 2 * x ^ 2  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_30012; Apache-2.0

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