A cyclic ninth-power comparison of weighted linear forms

Proved

WorkbookSource.base_12567

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

lean-workbooksource-checked

Prove that $(4a+2b)^9+(4b+2c)^9+(4c+2a)^9 \ge (3a+2b+c)^9+ (3b+2c+a)^9+ (3c+2a+b)^9$ with $a,b,c>0$ .

Source: InternLM Lean-Workbook, record lean_workbook_12567 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_12567 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (4 * a + 2 * b) ^ 9 + (4 * b + 2 * c) ^ 9 + (4 * c + 2 * a) ^ 9 ≥ (3 * a + 2 * b + c) ^ 9 + (3 * b + 2 * c + a) ^ 9 + (3 * c + 2 * a + b) ^ 9  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_12567; Apache-2.0

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