lean_workbook_plus_2045

⚠️ Retired — specification defect

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

Suppose that $x$ is an integer, then I will show that $y$ is also an integer. $x^3+x^2+2y-8=0\iff y=4-\frac{x^2(x+1)}{2}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_2045 (x y : ℤ) (h : x^3 + x^2 + 2*y - 8 = 0) : y = 4 - (x^2 * (x+1)) / 2   :=  by sorry

The target already types y as an integer and proves only the rearranged formula, omitting the source integrality conclusion.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

Let x∈ℤ and y∈ℝ, assume x³+x²+2y−8=0, and conclude y is an integer by the evenness of x²(x+1). Also derive its formula.

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.