The Fibonacci recurrence at consecutive indices

Proved

WorkbookRestored.plus_14129

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

lean-workbookrestored-importssource-checked

For every natural $k$ , $F_k+F_{k+1}=F_{k+2}$ , with $F_0=0$ and $F_1=1$ .

This restores the missing imports or namespaces of the original node, retaining its formal proposition. Source: Lean-Workbook row lean_workbook_plus_14129 (Apache-2.0).

Preamble

import Mathlib.Analysis.Complex.Basic
import Mathlib.Data.Nat.Fib.Basic
open Nat

Formal statement

theorem WorkbookRestored.plus_14129 : ∀ k : ℕ, fib k + fib (k + 1) = fib (k + 2)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_14129; original Prove2Me node 28a2d7c7-3eb5-45fd-920d-004a14534470; Apache-2.0

View graph