plunnecke_ruzsa_improvement

⚠️ 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.

Plünnecke-Ruzsa inequality: If |A+B| ≤ K|A|, then |hB| ≤ K^h |A|. Proved by Plünnecke (1970), with elegant proof by Ruzsa (1989). Optimal constants in the inequality for specific sets remain open.

Why this node was retired

The posted statement is

import Mathlib

theorem plunnecke_ruzsa_improvement (A B : Finset ℤ)
    (K : ℝ) (hK : 1 ≤ K)
    (hAB : ((A.image₂ (· + ·) B).card : ℝ) ≤ K * A.card) :
    ∀ h : ℕ, ((B.image₂ (· + ·) (B.image₂ (· + ·) B)).card : ℝ) ≤ K ^ 3 * A.card := by
  sorry

The base set A may be empty, and the quantified h is unused while the sumset remains fixed at3B.

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

Proposed corrected statement

Require A.Nonempty and either state the3-fold version explicitly or replace the fixed triple sum by the h-fold sumset and K³ by K^h.

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.