lean_workbook_plus_21818

Proved

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

For $a,b,c\ge 0$ prove that:\n $6(a^2+b^2+c^2)+a^2b^2+b^2c^2+c^2a^2+27\ge 16(a+b+c)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_21818 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : 6 * (a ^ 2 + b ^ 2 + c ^ 2) + a ^ 2 * b ^ 2 + b ^ 2 * c ^ 2 + c ^ 2 * a ^ 2 + 27 ≥ 16 * (a + b + c)   :=  by sorry

Source

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

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