Two cyclic cubic sums bound symmetric products

Proved

WorkbookSource.base_29516

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

lean-workbooksource-checked

prove that

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

where $x,y,z \geq 0$

Source: InternLM Lean-Workbook, record lean_workbook_29516 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_29516 (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 + z) * (x ^ 2 + y ^ 2 + z ^ 2) * x * y * z  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_29516; Apache-2.0

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