lean_workbook_plus_317

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Given $j_1 = -2014$, prove by induction that $j_n = -1007 * 2^n$ for all $n \in \mathbb{Z}_+$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_317 (j : ℕ → ℤ) (j_1 : j 0 = -2014) (h : ∀ n, j (n + 1) = 2 * j n) : ∀ n, j n = -1007 * 2 ^ n   :=  by sorry

The source initial index1 was shifted to0 without adjusting the formula.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

With j₀=−2014 and j_(n+1)=2j_n prove j_n=−2014·2^n. Alternatively use j₁=−2014 and conclude−1007·2^n for n≥1.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.