lean_workbook_plus_42823

Proved

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

For $\{a, b, c\} \in \mathbb{R^+}$ , show that,\n

a^3+b^3+c^3+8abc \geq (a+b)(b+c)(c+a)

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_42823 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^3 + b^3 + c^3 + 8 * a * b * c ≥ (a + b) * (b + c) * (c + a)   :=  by sorry

Source

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

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