lean_workbook_plus_50878

Proved

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

Prove that $3\left(a^2 + b^2 + c^2\right)\geq a^2 + b^2 + c^2 + 2(\text{ab} + \text{bc} + \text{ca})$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_50878 : ∀ a b c : ℝ, 3 * (a ^ 2 + b ^ 2 + c ^ 2) ≥ a ^ 2 + b ^ 2 + c ^ 2 + 2 * (a * b + b * c + c * a)   :=  by sorry

Source