lean_workbook_plus_57735

Proved

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

Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that for all $x, y \in \mathbb{R}$ , $f(x^2 - y) = f(y) - f(x)^2$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_57735 (f : ℝ → ℝ): (∀ x y, f (x ^ 2 - y) = f y - f x ^ 2) ↔ ∀ x, f x = 0   :=  by sorry

Source