lean_workbook_plus_79560

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Find all function $f$ which is continuous and defined on all positive real numbers such that:\n $f(f(x)) = x,\ f(x + 1) = \frac {f(x)}{f(x) + 1}\ \forall x > 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_79560 : ∃ f : ℝ → ℝ, ContinuousOn f (Set.Ioi 0) ∧ ∀ x > 0, f (f x) = x ∧ f (x + 1) = f x / (f x + 1)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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