Lean-Workbook Plus 3372: Logarithmic inequality

Proved

WorkbookRestored.plus_3372

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

Prove that $1+2\ln{x}\leq{x^{2}}$ $(x>0)$

Source: Lean-Workbook row lean_workbook_plus_3372 (Apache-2.0). The unchanged proposition comes from the original record; its missing mathematical imports and namespaces are restored here.

Preamble

import Mathlib.Analysis.SpecialFunctions.Log.Basic
open Real

Formal statement

theorem WorkbookRestored.plus_3372 (x : ℝ) (hx : 0 < x) : 1 + 2 * Real.log x ≤ x^2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_3372; immutable original Prove2Me node 4ccfa594-d0f7-446a-8f8b-c9a260fabc88

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