lean_workbook_plus_8545

Proved

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

Prove that $(a+b+c)^2 \geq 3(ab+bc+ca)$ for all positive real numbers $a, b, c$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_8545 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b + c) ^ 2 ≥ 3 * (a * b + b * c + c * a)   :=  by sorry

Source