lean_workbook_plus_6525

Proved

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

Let $a,b,c$ be real numbers such that $a+b+c=abc$ . Prove that $(a^2+1)(b^2+1)(c^2+1)\geq (ab+bc+ca-1)^2.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_6525 (a b c : ℝ) (h : a + b + c = a * b * c) :
  (a^2 + 1) * (b^2 + 1) * (c^2 + 1) ≥ (a * b + b * c + c * a - 1)^2   :=  by sorry

Source

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

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