lean_workbook_plus_18081

Proved

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

The following inequality is also true. \nGiven $a,b,c$ are positive integers satisfying $a+b+c=\frac{1}{a}+\frac{1}{b}+\frac{1}{c}$ .Prove that \n

bc+ca+ab+abc \geq 4.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_18081 (a b c : ℕ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (hab : a + b + c = 1 / a + 1 / b + 1 / c) : a * b + b * c + c * a + a * b * c ≥ 4   :=  by sorry

Source

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

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