lean_workbook_plus_46966

⚠️ 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.

By the power mean inequality, $\frac{(a-\frac{1}{2})+(b-\frac{1}{2})+(c-\frac{1}{2})+(d-\frac{1}{2})}{4} \leq \sqrt{\frac{(a-\frac{1}{2})^2+(b-\frac{1}{2})^2+(c-\frac{1}{2})^2+(d-\frac{1}{2})^2}{4}} < \sqrt{\frac{9}{4}} = \frac{3}{2}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_46966 : ∀ a b c d : ℝ, (a + b + c + d - 2) / 4 ≤ Real.sqrt ((a - 1 / 2)^2 + (b - 1 / 2)^2 + (c - 1 / 2)^2 + (d - 1 / 2)^2) / 4 ∧ Real.sqrt ((a - 1 / 2)^2 + (b - 1 / 2)^2 + (c - 1 / 2)^2 + (d - 1 / 2)^2) / 4 < 3 / 2   :=  by sorry

The source averages inside the square root; the formal expression divides the root by 4 instead of 2. The strict upper bound also lacks its source premise.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Use sqrt(sum of four squares /4), and recover the original assumption that their sum is <9.

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.