A pair-product square sum has a reciprocal product upper bound

Proved

WorkbookSource.base_56862

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

lean-workbooksource-checked

If $x,y,z$ are positive numbers such that $x+y+z=3$ , then $x^{2}y^{2}+y^{2}z^{2}+z^{2}x^{2}\leq \frac 3{xyz}$

Source: InternLM Lean-Workbook, record lean_workbook_56862 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_56862 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (h : x + y + z = 3) : x^2 * y^2 + y^2 * z^2 + z^2 * x^2 ≤ 3 / (x * y * z)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_56862; Apache-2.0

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