lean_workbook_plus_1379

Proved

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

If $a,b$ and $c$ are the sides of a triangle, prove that: $a^2(b + c - a) + b^2(c + a - b) + c^2(a + b - c)\leq 3abc$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_1379 {a b c : ℝ} (hx: a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : a^2 * (b + c - a) + b^2 * (c + a - b) + c^2 * (a + b - c) ≤ 3 * a * b * c   :=  by sorry

Source

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

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