lean_workbook_plus_54147

Proved

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

Derive $|g(x)| > \frac{|M|}{2}$ from $|g(x) - M| < \frac{|M|}{2}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_54147 (M x: ℝ) (g : ℝ → ℝ) (h₁ : |g x - M| < |M| / 2) : |g x| > |M| / 2   :=  by sorry

Source