lean_workbook_plus_26467

⚠️ 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 $x_1, x_2, \dots, x_{11}$ are real numbers such that all pairs $(x_i, x_j)$ satisfy $x_i x_j > -1$ . Show that there exists a pair $(x_m, x_n)$ with $x_m \geq x_n$ such that $(x_m + 3)(x_n - 3) > -10$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_26467 (x : Fin 11 → ℝ) (hx : ∀ i j, x i * x j > -1) :
    ∃ m n, x m ≥ x n ∧ (x m + 3) * (x n - 3) > -10   :=  by sorry

The selected pair of indices need not be distinct.

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

Require m≠n as well as the two inequalities in the conclusion.

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.