lean_workbook_plus_53618

Proved

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

For all real, positive, and distinct a, b, and c, prove that $a^2(b+c) + b^2(c+a) + c^2(a+b) < 2(a^3 + b^3 + c^3)$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_53618 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a ≠ b) (hbc : b ≠ c) (hca : a ≠ c) : a^2 * (b + c) + b^2 * (c + a) + c^2 * (a + b) < 2 * (a^3 + b^3 + c^3)   :=  by sorry

Source

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

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