A fifth-degree symmetric polynomial is nonnegative

Proved

WorkbookSource.base_32703

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

lean-workbooksource-checked

Prove that $a^5+b^5+c^5 - a^4b - a^4c-b^4a-b^4c-c^4a-c^4b +a^3bc+ab^3c+abc^3 \geq 0$ for $a,b,c>0$ .

Source: InternLM Lean-Workbook, record lean_workbook_32703 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_32703 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^5 + b^5 + c^5 - a^4 * b - a^4 * c - b^4 * a - b^4 * c - c^4 * a - c^4 * b + a^3 * b * c + a * b^3 * c + a * b * c^3 ≥ 0  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_32703; Apache-2.0

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