lean_workbook_plus_63534

Proved

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

Let $a, b, c$ be the side lengths of a triangle. Prove that $2 (a^3 + b^3 + c^3) < (a + b + c) (a^2 + b^2 + c^2) \le 3 (a^3 + b^3 + c^3)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_63534 {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^3 + b^3 + c^3) < (a + b + c) * (a^2 + b^2 + c^2) ∧ (a + b + c) * (a^2 + b^2 + c^2) ≤ 3 * (a^3 + b^3 + c^3)   :=  by sorry

Source

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

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