lean_workbook_plus_46378

⚠️ 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.

Take any three digit number, say $521$ .\nwrite the digits in the opposite direction to get $125$ .\nThen subtract the smaller number from the larger one: $521-125=396$ \nagain write the digits in the opposite direction to get $693$ \nadd the two numbers $396+693=\boxed{1089}$ .\nIndependent of the initial choice, in the end you'll always get $1089$ , as long as the result after the subtraction is a three digit number. Can you give a mathematical explanation of this fact?

Why this node was retired

The posted statement is

theorem lean_workbook_plus_46378 (a b c : ℕ) (h₁ : 1 ≤ a ∧ a ≤ 9) (h₂ : 0 ≤ b ∧ b ≤ 9) (h₃ : 0 ≤ c ∧ c ≤ 9) : a * 100 + b * 10 + c - (c * 100 + b * 10 + a) = 1089   :=  by sorry

The formal statement changes or incorrectly supplies part of the source problem; the accepted note identifies a concrete witness or definitional mechanism.

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

Proposed corrected statement

For a three-digit integer N whose absolute difference d from its digit reversal has three digits, prove d+reverse₃(d)=1089. Define d using absolute integer subtraction, and include the second reversal and addition.

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.