Prove2Me

A seventh-degree inequality involving triangle factors

Proved
WorkbookSource.plus_12674

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

lean-workbooksource-checked

Let aa , bb and cc be non-negative numbers. Prove that:

(a+b−c)(a+c−b)(b+c−a)(a2+b2+c2)2≤abc(ab+ac+bc)2(a+b-c)(a+c-b)(b+c-a)(a^2+b^2+c^2)^2\leq abc(ab+ac+bc)^2

Source: InternLM Lean-Workbook, record lean_workbook_plus_12674 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_12674 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) : (a + b - c) * (a + c - b) * (b + c - a) * (a ^ 2 + b ^ 2 + c ^ 2) ^ 2 ≤ a * b * c * (a * b + a * c + b * c) ^ 2   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_12674; Apache-2.0

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