lean_workbook_plus_51475

⚠️ 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 $A_{nxn}$ be a SYMMETRIC matrix such that each row and each column is a permutation of the elements of the set $S={1,2,3,...,n}$ where $n$ is an odd positive integer. Show that no two diagonal elements are equal.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_51475 (n : ℕ) (hn : Odd n) (A : Matrix (Fin n) (Fin n) ℕ) (hA : A = A.transpose) : ∀ i j, i = j → A i j ≠ A i i   :=  by sorry

The formal conclusion says Aᵢᵢ≠Aᵢᵢ and omits the Latin-square row/column conditions.

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 odd n>0 and a symmetric n×n matrix whose rows and columns each permute1,…,n, prove the diagonal map i↦Aᵢᵢ is injective (indeed a permutation).

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.