lean_workbook_plus_13564

Proved

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

After some work (not too much) one gets the equivalent inequality \n $\sum (b - c)^2(b + c)(b + c - a)(2a^2 + bc) \ge 0.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_13564 {a b c : ℝ} (ha : a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : (b - c) ^ 2 * (b + c) * (b + c - a) * (2 * a ^ 2 + b * c) + (c - a) ^ 2 * (c + a) * (c + a - b) * (2 * b ^ 2 + c * a) + (a - b) ^ 2 * (a + b) * (a + b - c) * (2 * c ^ 2 + a * b) ≥ 0   :=  by sorry

Source

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

View graph