lean_workbook_plus_6413

Proved

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

Prove that ${\left( {a + b + c} \right)^2} \le 3\left( {{a^2} + {b^2} + {c^2}} \right)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_6413 : ∀ a b c : ℝ, (a + b + c) ^ 2 ≤ 3 * (a ^ 2 + b ^ 2 + c ^ 2)   :=  by sorry

Source