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Lean-Workbook Syntax 61921: A sum of squared Fibonacci numbers

Proved
WorkbookSyntax.plus_61921

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

lean-workbookrepaired-notationsource-checked

For every natural nnn, ∑k=0nFk2=FnFn+1\sum_{k=0}^{n}F_k^2=F_nF_{n+1}∑k=0n​Fk2​=Fn​Fn+1​, where F0=0,F1=1F_0=0,F_1=1F0​=0,F1​=1 and Fn+2=Fn+1+FnF_{n+2}=F_{n+1}+F_nFn+2​=Fn+1​+Fn​.

Source: Lean-Workbook row lean_workbook_plus_61921 (Apache-2.0), original record. This corrected declaration replaces the obsolete finite sum/product binder in with ∈ and restores required imports or namespaces. Ranges, casts, quantifiers, and mathematical expressions are preserved.

Preamble
import Mathlib.Data.Nat.Fib.Basic
open Nat
Formal statement
theorem WorkbookSyntax.plus_61921 (n : ℕ) : ∑ k ∈ Finset.range (n+1), fib k ^ 2 = fib n * fib (n + 1)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_61921; immutable original Prove2Me node 54e71ffc-f3ec-44b5-beb4-1556d90b15ba

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