lean_workbook_plus_5669

Proved

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

Let $a,b,c >0$ and $a+b+c=\frac{1}{a}+\frac{1}{b}+\frac{1}{c} .$ Prove that $ab+bc+ca+1 \geq 4abc$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_5669 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : a + b + c = 1 / a + 1 / b + 1 / c) : a * b + b * c + c * a + 1 ≥ 4 * a * b * c   :=  by sorry

Source

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

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