lean_workbook_plus_49288

Proved

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

Clarify the properties of absolute value: $|x| = x$ if $x$ is non-negative and $|x| = -x$ if $x$ is negative.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_49288 (x : ℝ) : (x ≥ 0 → |x| = x) ∧ (x < 0 → |x| = -x)   :=  by sorry

Source