lean_workbook_plus_15303

⚠️ 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.

Let $E(1)=x$ and we have $E(2)=x-1\\E(3)=x-4\ \ldots \ E(n) =x-(n-1)^2\\ E(10)=x-9^2=0\implies x = 81$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_15303 (x : ℤ) (E : ℕ → ℤ) (h₁ : E 1 = x) (h₂ : ∀ n, E (n + 1) = E n - (n - 1) ^ 2) (h₃ : E 10 = 0) : x = 81   :=  by sorry

The source closed formula E(n)=x−(n−1)² was replaced by accumulating those squares as recurrence decrements.

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

Proposed corrected statement

State E(n)=x−(n−1)² for n≥1; then E(10)=0 gives x=81. An equivalent recurrence is E(n+1)=E(n)−(2n−1) 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.