lean_workbook_plus_12822

⚠️ 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.

Determine the number of the subsets of the set $A=\{ 1,2,3,...,2010 \}$ so that each subset contains only one number divisible by $3$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_12822 (A: Finset ℕ) (hA: A = (Finset.range 2010)):

  A.card = 4020  :=  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

Let A={1,…,2010}; count T⊆A such that exactly one element of T is divisible by 3. Prove the count is 670*2^1340. Do not count the cardinality of A itself or replace its domain by 0,…,2009.

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.