A cyclic product comparison of quadratic factors

Proved

WorkbookSource.base_23386

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

prove that:

$(zx+y^2)(xy+z^2)(yz+x^2)\geq (zx+z^2)(xy+x^2)(yz+y^2)$

$x,y,z\geq 0$

Source: InternLM Lean-Workbook, record lean_workbook_23386 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_23386 (x y z : ℝ) (hx : x ≥ 0) (hy : y ≥ 0) (hz : z ≥ 0) : (z * x + y ^ 2) * (x * y + z ^ 2) * (y * z + x ^ 2) ≥ (z * x + z ^ 2) * (x * y + x ^ 2) * (y * z + y ^ 2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_23386; Apache-2.0

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