A cubic inequality above two

Proved

WorkbookSource.problem_51808

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

lean-workbooksource-checked

Prove that $x^3+1 > 2x^2$ for $x \ge 2$ .

Source: InternLM Lean-Workbook, record lean_workbook_51808 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved. The related Open record plus_25755 omits the variable declaration; this source explicitly declares a real variable.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.problem_51808 (x : ℝ) (h : x >= 2) : x^3 + 1 > 2 * x^2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_51808; Apache-2.0

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