lean_workbook_plus_53196

Proved

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

If $a,b,c\ge 0$ , $a^2 +b^2+c^2+2abc=5$ , prove that $abc+a+b+c\le 4$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_53196 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (habc : a * b * c = 1) (h : a^2 + b^2 + c^2 + 2 * a * b * c = 5) : a * b * c + a + b + c ≤ 4   :=  by sorry

Source

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

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