A cyclic fifth-degree product inequality

Proved

WorkbookSource.base_9974

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

lean-workbooksource-checked

Let $x,y,z\geq 0$ ,prove that: $(x+y+z)(x^3y+zy^3+xz^3)\geq (x^2y+y^2z+z^2x)(xy+yz+xz).$

Source: InternLM Lean-Workbook, record lean_workbook_9974 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_9974 (x y z : ℝ) (hx : x ≥ 0) (hy : y ≥ 0) (hz : z ≥ 0) : (x + y + z) * (x ^ 3 * y + z * y ^ 3 + x * z ^ 3) ≥ (x ^ 2 * y + y ^ 2 * z + z ^ 2 * x) * (x * y + y * z + x * z)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_9974; Apache-2.0

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