lean_workbook_plus_78739

Proved

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

The following inequality is true for all positives $a$ , $b$ and $c$ . \n

a^3+b^3+c^3+abc\geq a\left(\frac{3}{2}b^2+\frac{3}{2}c^2+bc\right)

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_78739 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^3 + b^3 + c^3 + a * b * c ≥ a * (3 / 2 * b^2 + 3 / 2 * c^2 + b * c)   :=  by sorry

Source

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

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