lean_workbook_plus_6320

Proved

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

From triangle's inequality we have $b>a-c$ and analogues. Then, the first inequality becomes $\sum{a^2(a-b)(a-c)}\ge 0$ , which is Schur for $r=2$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_6320 :
  ∀ a b c : ℝ, a > 0 ∧ b > 0 ∧ c > 0 → a + b > c ∧ a + c > b ∧ b + c > a → a^2 * (a - b) * (a - c) + b^2 * (b - a) * (b - c) + c^2 * (c - a) * (c - b) ≥ 0   :=  by sorry

Source

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

View graph