lean_workbook_plus_77547

⚠️ 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.

$\Rightarrow (k+1)^{k+1}>\frac{((k+1)^2)^k}{k^k}>(k+2)^k$ wich is $P(k+1)$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_77547 : ∀ k : ℕ, (k + 1) ^ (k + 1) > ((k + 1) ^ 2) ^ k / k ^ k ∧ ((k + 1) ^ 2) ^ k / k ^ k > (k + 2) ^ k   :=  by sorry

The source implication was made universal without its range; k=0 and k=1 do not satisfy the displayed strict chain.

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 real or rational division and require k≥2 for the two strict comparisons; recover the preceding induction premise if it is part of the intended step.

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.