Prove2Me

A product of cyclic cubic sums bounds a squared triple product

Proved
WorkbookSource.plus_28880

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

lean-workbooksource-checked

Let x,y,zx,y,z be positive real numbers. Prove that (xy2+yz2+zx2)(x2y+y2z+z2x)(xy+yz+zx)≥3(x+y+z)2(xyz)2.(xy^2+yz^2+zx^2)(x^2y+y^2z+z^2x)(xy+yz+zx)\geq 3(x+y+z)^2(xyz)^2.

Source: InternLM Lean-Workbook, record lean_workbook_plus_28880 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_28880    (x y z : ℝ)
    (hx : 0 < x)
    (hy : 0 < y)
    (hz : 0 < z) :
    (x * y^2 + y * z^2 + z * x^2) * (x^2 * y + y^2 * z + z^2 * x) * (x * y + y * z + z * x) ≥ 3 * (x + y + z)^2 * (x * y * z)^2   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_28880; Apache-2.0

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