lean_workbook_plus_33271

Proved

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

Let $a,b,c \le 0$ . Prove that \n\n

\max(a,c)+\max(b,c) \le \max(a+b, c)

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_33271 (a b c : ℝ) (hab : a ≤ 0) (hbc : b ≤ 0) (hca : c ≤ 0) : max a c + max b c ≤ max (a + b) c   :=  by sorry

Source