lean_workbook_plus_76498

Proved

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

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function such that $f(x+y) = f(x)f(y)$ for all $x, y \in \mathbb{R}$ . Show that $f(0) = 0$ or $f(0) = 1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_76498 (f : ℝ → ℝ) (hf : ∀ x y, f (x + y) = f x * f y) : f 0 = 0 ∨ f 0 = 1   :=  by sorry

Source

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

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