lean_workbook_plus_20072

Disproved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that $(x^3y+y^3z+z^3x)^2\geq (x^3y+y^3z+z^3x)(xy^3+yz^3+zx^3) \geq (x^2y^2+y^2z^2+z^2x^2)^2$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_20072 : ∀ x y z : ℝ, (x^3 * y + y^3 * z + z^3 * x)^2 ≥ (x^3 * y + y^3 * z + z^3 * x) * (x * y^3 + y * z^3 + z * x^3) ∧ (x^3 * y + y^3 * z + z^3 * x) * (x * y^3 + y * z^3 + z * x^3) ≥ (x^2 * y^2 + y^2 * z^2 + z^2 * x^2)^2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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