lean_workbook_plus_1809

Proved

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

Let $a, b$ and $c$ be positive real numbers such that $a+b+c\geq 3abc$ . Prove that $a^2+b^2+c^2\geq 2abc.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_1809 (a b c : ℝ) (h : a + b + c ≥ 3 * a * b * c) : a ^ 2 + b ^ 2 + c ^ 2 ≥ 2 * a * b * c   :=  by sorry

Source