Comparing adjacent-base large powers

Proved

WorkbookSource.problem_31990

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

lean-workbooksource-checked

Which is larger? $100^{101}$ or $101^{100}$ ?

Source: InternLM Lean-Workbook, record lean_workbook_31990 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_31990 : (100:ℝ)^101 > 101^100  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_31990; Apache-2.0

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