lean_workbook_plus_8225

Proved

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

For non-negativee real numbers $a,b,c$ with $a^2+b^2+c^2+2abc=1$ prove that $a+b+c \leq \frac{3}{2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_8225 (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 = 1) : a + b + c ≤ 3 / 2   :=  by sorry

Source

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

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