Prove2Me

A squared-difference product inequality under three quadratic signs

Proved
WorkbookSource.plus_71891

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

lean-workbooksource-checked

Let a2+b2−c2≥0a^{2}+b^{2}-c^{2}\geq0, a2+c2−b2≥0a^{2}+c^{2}-b^{2}\geq0 and b2+c2−a2≥0b^{2}+c^{2}-a^{2}\geq0. Prove that (a+b−c)2(a+c−b)2≥(a2+b2−c2)(a2+c2−b2)(a+b-c)^{2}(a+c-b)^{2}\geq(a^{2}+b^{2}-c^{2})(a^{2}+c^{2}-b^{2}).

Source: InternLM Lean-Workbook, record lean_workbook_plus_71891 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_71891 (a b c : ℝ) (h1 : a^2 + b^2 - c^2 ≥ 0) (h2 : a^2 + c^2 - b^2 ≥ 0) (h3 : b^2 + c^2 - a^2 ≥ 0) : (a + b - c)^2 * (a + c - b)^2 ≥ (a^2 + b^2 - c^2) * (a^2 + c^2 - b^2)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_71891; Apache-2.0

View graph