lean_workbook_plus_32344

⚠️ 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.

Prove that with any $n$ natural numbers, we can find one number or some of them that their sum is divisible by $n$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_32344 (n : ℕ) (A : Finset ℕ) : ∃ S ⊆ A, n ∣ S.sum (fun x ↦ x)   :=  by sorry

The selected subset need not be nonempty; the stated cardinality relation to n is also absent.

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

Use a list/vector of n integers with n≥1 and require a nonempty subset of positions whose sum is divisible by n; this preserves repetitions in the input.

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.