A seventh-degree comparison of symmetric power-sum products

Proved

WorkbookSource.plus_19425

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

lean-workbooksource-checked

For positives $a$ , $b$ and $c$ prove that: $2\left(a^7+b^7+c^7+5abc(a^4+b^4+c^4)\right)\ge (a^3+b^3+c^3+3abc)(a^4+b^4+c^4+abc(a+b+c))$

Source: InternLM Lean-Workbook, record lean_workbook_plus_19425 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_19425 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 2 * (a^7 + b^7 + c^7 + 5 * a * b * c * (a^4 + b^4 + c^4)) ≥ (a^3 + b^3 + c^3 + 3 * a * b * c) * (a^4 + b^4 + c^4 + a * b * c * (a + b + c))   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_19425; Apache-2.0

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