lean_workbook_plus_8416

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that $2(ab+bc+ca)-a^2-b^2-c^2 > 0$ for a triangle with sides $a$ , $b$ , and $c$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_8416 {a b c : ℝ} (hx: a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : 2 * (a * b + b * c + c * a) - a ^ 2 - b ^ 2 - c ^ 2 > 0   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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