lean_workbook_plus_22613

Proved

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

For $a, b, c \geq 0$ , with $abc=1$ , prove that \n\n $a+b+c \geq \frac{2}{a+1} + \frac{2}{b+1} + \frac{2}{c+1}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_22613 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (habc : a * b * c = 1) : a + b + c ≥ 2 / (a + 1) + 2 / (b + 1) + 2 / (c + 1)   :=  by sorry

Source

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

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