lean_workbook_plus_72192

Proved

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

Let $a,b,c>0$ and $a^2+b^2+c^2 \ge 4\sqrt{abc}$ , prove that: \n $a+b+c \ge 2\sqrt{abc}$ \n

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_72192 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : a^2 + b^2 + c^2 ≥ 4 * Real.sqrt (a * b * c)) : a + b + c ≥ 2 * Real.sqrt (a * b * c)   :=  by sorry

Source

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

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