A cyclic seventh-degree comparison of mixed products

Proved

WorkbookSource.base_55824

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

lean-workbooksource-checked

Let $a,b,c>0$ . Show that: $a^{4}c^{3}+b^{4}a^{3}+c^{4}b^{3}+2abc(a^{4}+b^{4}+c^{4})\geq 3abc(a^{2}b^{2}+b^{2}c^{2}+c^{2}a^{2}).$

Source: InternLM Lean-Workbook, record lean_workbook_55824 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_55824 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^4 * c^3 + b^4 * a^3 + c^4 * b^3 + 2 * a * b * c * (a^4 + b^4 + c^4) ≥ 3 * a * b * c * (a^2 * b^2 + b^2 * c^2 + c^2 * a^2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_55824; Apache-2.0

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