lean_workbook_plus_78257

Proved

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

Let $a,b,c$ be the lengths of a triangle sides. Prove that:\n $\sum_{cyc} a^2(b+c-a) \le 3abc$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_78257    (a b c : ℝ)
    (ha : 0 < a ∧ 0 < b ∧ 0 < c)
    (hab : a + b > c)
    (hbc : b + c > a)
    (hca : a + c > b) :
    a^2 * (b + c - a) + b^2 * (a + c - b) + c^2 * (a + b - c) ≤ 3 * a * b * c   :=  by sorry

Source

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

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