lean_workbook_plus_44214

Proved

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

Given $a, b, c > 0$ and $a + b + c = \frac{1}{a} + \frac{1}{b} + \frac{1}{c}$ , prove that $bc + ac + ab + abc \geq 4$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_44214 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (habc : a * b * c = 1) (h : a + b + c = 1 / a + 1 / b + 1 / c) : b * c + a * c + a * b + a * b * c ≥ 4   :=  by sorry

Source

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

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