lean_workbook_plus_38692

Proved

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

$\sqrt {x_1^2 + (1 - x_2)^2} \ge \frac{\sqrt {2}}{2}(x_{1} + 1 - x_{2})$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_38692 (x₁ x₂ : ℝ) :
  Real.sqrt (x₁^2 + (1 - x₂)^2) ≥ (Real.sqrt 2 / 2) * (x₁ + 1 - x₂)   :=  by sorry

Source