lean_workbook_plus_43634

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 $f(x+y) = f(x) + y$ for all $x, y \in \mathbb{R}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_43634 (f : ℝ → ℝ): (∀ x y, f (x + y) = f x + y) ↔ ∃ a, ∀ x, f x = x + a   :=  by sorry

Source