A fifth-power bound involving a triple product

Proved

WorkbookSource.base_6358

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

lean-workbooksource-checked

Prove that for all real $a, b, c \geq 0$ , $(a+b+c)^5\geq81abc(a^2+b^2+c^2)$

Source: InternLM Lean-Workbook, record lean_workbook_6358 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_6358 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : (a + b + c) ^ 5 ≥ 81 * a * b * c * (a ^ 2 + b ^ 2 + c ^ 2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_6358; Apache-2.0

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