lean_workbook_plus_5840

Open

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

Prove, without using calculus, that $x + \ln(1-x) \leq 0$ for all $x <1$ , with equality if and only if $x=0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_5840 (x : ℝ) (hx : x < 1) : x + Real.log (1 - x) ≤ 0   :=  by sorry

Source