lean_workbook_plus_2690

Proved

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

From $a^2+b^2+c^2+4ab-2(ab+bc+ca) = (a+b-c)^2 \geqslant 0,$ so $a^2+b^2+c^2+4ab \geqslant 2(ab+bc+ca).$ The equallity hold when $a+b-c=0.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_2690 (a b c : ℝ) : a^2 + b^2 + c^2 + 4 * a * b ≥ 2 * (a * b + b * c + c * a)   :=  by sorry

Source