lean_workbook_plus_2177

Proved

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

Prove that : $\sqrt{(1+a)(1+b)}$ ≥ $1+$ $\sqrt{ab}$ where a,b >0

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_2177 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : Real.sqrt ((1 + a) * (1 + b)) ≥ 1 + Real.sqrt (a * b)   :=  by sorry

Source