Prove2Me

A logarithm bound on its full real domain

Proved
WorkbookSource.problem_8627

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove: ∀x∈]−1;+∞[;ln(x+1)≤x\forall x \in ]-1;+\infty[ ; ln(x+1) \leq x.

Source: InternLM Lean-Workbook, record lean_workbook_8627 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved. The related Open record plus_50985 has the same complete domain; this restores a source-checked representative.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.problem_8627 (x : ℝ) (hx : -1 < x) : Real.log (x + 1) ≤ x  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_8627; Apache-2.0

View graph