lean_workbook_plus_49513

Proved

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

Prove that the function $f(x)$ defined by $|f(x)-f(y)|\leq\frac{1}{2}|x-y|$ for all real x,y is continuous.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_49513 (f : ℝ → ℝ) (hf: ∀ x y : ℝ, abs (f x - f y) ≤ (1/2) * abs (x - y)) : Continuous f   :=  by sorry

Source