lean_workbook_plus_19257

⚠️ 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.

The sum of four real numbers is $9$ and the sum of their squares is $21$ . Prove that these numbers can be denoted by $a, b, c, d$ so that $ab-cd \ge 2$ holds.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_19257 (a b c d : ℝ) (hab : a + b + c + d = 9) (h : a^2 + b^2 + c^2 + d^2 = 21) : ∃ a b c d : ℝ, a + b + c + d = 9 ∧ a^2 + b^2 + c^2 + d^2 = 21 ∧ a * b - c * d ≥ 2   :=  by sorry

Fresh existential a,b,c,d are not required to be a relabeling of the input tuple.

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

Represent the four given numbers as v:Fin 4→ℝ and conclude ∃σ:Equiv.Perm(Fin 4), v(σ0)*v(σ1)−v(σ2)*v(σ3)≥2, under the existing sum and square-sum hypotheses.

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.