lean_workbook_plus_31306

Proved

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

Show that for any positive real numbers $a,b,c$ the following inequality is true: \n

4(a^3+b^3+c^3+3)\geq 3(a+1)(b+1)(c+1)

When does equality hold?

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_31306 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 4 * (a ^ 3 + b ^ 3 + c ^ 3 + 3) ≥ 3 * (a + 1) * (b + 1) * (c + 1)   :=  by sorry

Source

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

View graph