A seventh-degree comparison of power-sum products

Proved

WorkbookSource.plus_59857

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

lean-workbooksource-checked

Let $a,\ b,\ c$ be non-negative real numbers. Prove that: $(a^4 +b^4 +c^4)(a +b)(b +c)(c +a) \geq (a +b +c)(a^2 +b^2)(b^2 +c^2)(c^2 +a^2).$

Source: InternLM Lean-Workbook, record lean_workbook_plus_59857 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_59857 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : (a^4 + b^4 + c^4) * (a + b) * (b + c) * (c + a) ≥ (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_plus_59857; Apache-2.0

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