lean_workbook_plus_15816

Proved

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

Given a function $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $f(x) = f(x+1) + 1$ , prove that $f(x+n) = f(x) - n$ for all natural numbers $n$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_15816 (f : ℝ → ℝ) (n : ℕ) (h₁ : ∀ x, f x = f (x + 1) + 1): ∀ x, f (x + n) = f x - n   :=  by sorry

Source