A symmetric sixth-degree comparison of mixed power sums

Proved

WorkbookSource.base_43717

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

lean-workbooksource-checked

Let a,b,c>0.Prove that $2(a^6 + b^6 + c^6 ) + 3\sum\limits_{cyc} {a^2 b^2 (a^2 + b^2 } ) \ge 2(a^3 b^3 + b^3 c^3 + a^3 c^3 ) + 3\sum\limits_{cyc} {ab(a^4 + b^4 )}$

Source: InternLM Lean-Workbook, record lean_workbook_43717 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_43717 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) :  2 * (a ^ 6 + b ^ 6 + c ^ 6) + 3 * (a ^ 2 * b ^ 2 * (a ^ 2 + b ^ 2) + b ^ 2 * c ^ 2 * (b ^ 2 + c ^ 2) + c ^ 2 * a ^ 2 * (c ^ 2 + a ^ 2)) ≥ 2 * (a ^ 3 * b ^ 3 + b ^ 3 * c ^ 3 + a ^ 3 * c ^ 3) + 3 * (a * b * (a ^ 4 + b ^ 4) + b * c * (b ^ 4 + c ^ 4) + c * a * (c ^ 4 + a ^ 4))  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_43717; Apache-2.0

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