lean_workbook_plus_16733

Proved

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

If $a,b,c$ are the side of triangle, prove the inequality:\n $a^3+b^3+c^3+3abc\ge\sum_{cyc}ab(a+b)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_16733 (a b c : ℝ) (hx: a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : a^3 + b^3 + c^3 + 3 * a * b * c ≥ a * b * (a + b) + b * c * (b + c) + c * a * (c + a)   :=  by sorry

Source

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

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