A fifth-power sum bounds a mixed triple product

Proved

WorkbookSource.base_13691

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

lean-workbooksource-checked

Let a, b, c > 0. Prove that: $a^5 + b^5 + c^5 \geq a^2b^2c + ab^2c^2 + a^2c^2b$

Source: InternLM Lean-Workbook, record lean_workbook_13691 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_13691 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^5 + b^5 + c^5 ≥ a^2 * b^2 * c + a * b^2 * c^2 + a^2 * c^2 * b  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_13691; Apache-2.0

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