lean_workbook_plus_63047

Proved

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

Prove that $\sqrt{\frac {a^2+(1-b)^2}{2}}\geq \frac {a+(1-b)}{2}$ holds for arbitrary real numbers $a, b$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_63047 (a b : ℝ) : Real.sqrt ((a ^ 2 + (1 - b) ^ 2) / 2) ≥ (a + (1 - b)) / 2   :=  by sorry

Source