A fifth-degree bound involving triangle factors

Proved

WorkbookSource.base_13753

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

lean-workbooksource-checked

Let $a,b,c$ are postive real numbers, show that:

$(a^{2}+b^{2}+c^{2})(a+b-c)(b+c-a)(c+a-b)\leq abc(ab+bc+ac)$

have fun!

Source: InternLM Lean-Workbook, record lean_workbook_13753 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_13753 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 + b^2 + c^2) * (a + b - c) * (b + c - a) * (c + a - b) ≤ a * b * c * (a * b + b * c + a * c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_13753; Apache-2.0

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