lean_workbook_plus_54402

Proved

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

Prove that $a^2 + b^2 + c^2 \geq ab + ac + bc$ using SOS (Sum of Squares) method.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_54402 {a b c : ℝ} : a ^ 2 + b ^ 2 + c ^ 2 ≥ a * b + a * c + b * c   :=  by sorry

Source