lean_workbook_plus_5161

Proved

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

Prove that if $a_1,a_2$ are positive reals, then $\frac{a_1+a_2}{2} \geq \sqrt{a_1a_2}.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_5161 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : (a + b) / 2 ≥ Real.sqrt (a * b)   :=  by sorry

Source