A product comparison between odd power sums

Proved

WorkbookSource.base_14998

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

lean-workbooksource-checked

prove that

$\left( x+y+z \right) \left( {x}^{7}+{y}^{7}+{z}^{7} \right) \geq \left( {x}^{3}+{y}^{3}+{z}^{3} \right) \left( {x}^{5}+{y}^{5}+{z}^{5} \right)$

$x,y,z>0$

Source: InternLM Lean-Workbook, record lean_workbook_14998 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_14998 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x + y + z) * (x^7 + y^7 + z^7) ≥ (x^3 + y^3 + z^3) * (x^5 + y^5 + z^5)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_14998; Apache-2.0

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