lean_workbook_plus_40555

Disproved

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

With the condition $a + b + c + 2 = abc$ and $a,b,c > 0$ . Prove: $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} \ge 4(a + b + c)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_40555 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c + 2 = a * b * c) : 1 / a + 1 / b + 1 / c ≥ 4 * (a + b + c)   :=  by sorry

Source

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

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