An eighth-power sum bounds mixed triple products

Proved

WorkbookSource.base_32639

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

lean-workbooksource-checked

1/ a,b,c>0. Prove that: $a^8+b^8+c^8>=a^3b^3c^2+b^3c^3a^2+c^3a^3b^2$

Source: InternLM Lean-Workbook, record lean_workbook_32639 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_32639 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^8 + b^8 + c^8 ≥ a^3 * b^3 * c^2 + b^3 * c^3 * a^2 + c^3 * a^3 * b^2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_32639; Apache-2.0

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