A symmetric fifth-degree inequality with a mixed correction

Proved

WorkbookSource.base_8545

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

lean-workbooksource-checked

Prove that $a^5+b^5+c^5+abc(ab+bc+ca)\geq a^3(b^2+c^2)+b^3(c^2+a^2)+c^3(a^2+b^2)$ where $a, b, c$ are positive.

Source: InternLM Lean-Workbook, record lean_workbook_8545 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_8545 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^5 + b^5 + c^5 + a * b * c * (a * b + b * c + c * a) ≥ a^3 * (b^2 + c^2) + b^3 * (c^2 + a^2) + c^3 * (a^2 + b^2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_8545; Apache-2.0

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