lean_workbook_plus_81364

⚠️ 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.

Prove the inequality $(2n+1)^{n}\geq (2n)^{n}+(2n-1)^{n}$ using mathematical induction.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_81364 : ∀ n : ℕ, (2 * n + 1) ^ n ≥ (2 * n) ^ n + (2 * n - 1) ^ n   :=  by sorry

The natural index0 makes the assertion1≥2.

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

Proposed corrected statement

State the induction for n≥1; the base n=1 and the remaining positive-index inequality must be proved separately.

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.