lean_workbook_plus_8906

Proved

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

Given $a, b, c > 0$ such that $ab + bc + ca = abc + 2$ , prove that $a^2 + b^2 + c^2 + abc \geq 4$ using AM-GM inequality.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_8906 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : a * b + b * c + c * a = a * b * c + 2) : a ^ 2 + b ^ 2 + c ^ 2 + a * b * c ≥ 4   :=  by sorry

Source

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

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