A fifth-power bound involving triangle factors and pairwise products

Proved

WorkbookSource.plus_49681

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

lean-workbooksource-checked

Let $a,b,c>0$ . Prove that

$(a+b+c)^5\geq81(a+b-c)(a-b+c)(-a+b+c)(ab+bc+ca)$

Source: InternLM Lean-Workbook, record lean_workbook_plus_49681 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_49681 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b + c) ^ 5 ≥ 81 * (a + b - c) * (a - b + c) * (-a + b + c) * (a * b + b * c + c * a)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_49681; Apache-2.0

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