lean_workbook_plus_33033

Proved

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

Prove that if $f: \mathbb{R} \to \mathbb{R}$ is a monotonous function satisfying $f(f(x)) = f( - f(x)) = f(x)^2$ , then $f(x) = f(-x)$ for all $x\in f(\mathbb{R})$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_33033 (f : ℝ → ℝ) (h₁ : Monotone f) (h₂ : ∀ x, f (f x) = (f x)^2) (h₃ : ∀ x, f (-f x) = (f x)^2) : ∀ x ∈ Set.range f, f x = f (-x)   :=  by sorry

Source

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

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