lean_workbook_plus_81968

Proved

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

The real numbers $a,b$ and $c$ satisfy the inequalities $|a|\ge |b+c|,|b|\ge |c+a|$ and $|c|\ge |a+b|$ . Prove that $a+b+c=0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_81968 (a b c : ℝ) (h1 : |a| ≥ |b + c|) (h2 : |b| ≥ |c + a|) (h3 : |c| ≥ |a + b|) : a + b + c = 0   :=  by sorry

Source