A rational function is not idempotent

Proved

WorkbookSource.plus_68505

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

lean-workbooksource-checked

Prove that the function $f(x)=\frac{x}{1-x}$ is not idempotent.

Source: InternLM Lean-Workbook, record lean_workbook_plus_68505 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_68505 (f : ℝ → ℝ) (hf: f = fun x => x / (1 - x)) : ¬ (f ∘ f) = f   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_68505; Apache-2.0

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