lean_workbook_plus_79854

Proved

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

Let $a,b,c >0$ and $a^2+b^2+c^2 +3= 2(ab+bc+ca).$ Prove that $abc\geq 1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_79854 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a * b * c = 1) (h : a^2 + b^2 + c^2 + 3 = 2 * (a * b + b * c + c * a)) : a * b * c ≥ 1   :=  by sorry

Source

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

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