Strict increase of a difference of large powers

Proved

WorkbookSource.plus_63997

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

lean-workbooksource-checked

Prove that if $x>2000$ , then $x^{2000}-x^{1999}>{2000}^{2000}-2000^{1999}$ ?

Source: InternLM Lean-Workbook, record lean_workbook_plus_63997 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_63997 (x : ℝ) (hx : x > 2000) : x^2000 - x^1999 > 2000^2000 - 2000^1999   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_63997; Apache-2.0

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