Lean-Workbook Plus 16331: Exponential identity

Proved

WorkbookRestored.plus_16331

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

Prove that if $f(x) = e^{g(x)}$ where $g$ is an additive function, then $f(x+y) = f(x)f(y)$ .

Source: Lean-Workbook row lean_workbook_plus_16331 (Apache-2.0). The unchanged proposition comes from the original record; its missing mathematical imports and namespaces are restored here.

Preamble

import Mathlib.Analysis.SpecialFunctions.Log.Basic
open Real

Formal statement

theorem WorkbookRestored.plus_16331 (f : ℝ → ℝ) (g : ℝ → ℝ) (h₁ : ∀ x, f x = exp (g x)) (h₂ : ∀ x y, g (x + y) = g x + g y) : ∀ x y, f (x + y) = f x * f y   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_16331; immutable original Prove2Me node 59895ff4-6532-4e31-9f52-fb88d8e4ec99

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