lean_workbook_plus_73289

Proved

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

For $f(1) = 1$ , $f(x^2) = [f(x)]^2$ . This implies that $f(x)$ is nonnegative whenever $x$ is nonnegative.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_73289  (f : ℝ → ℝ)
  (h₀ : f 1 = 1)
  (h₁ : ∀ x, f (x^2) = (f x)^2) :
  ∀ x ≥ 0, 0 ≤ f x   :=  by sorry

Source