lean_workbook_plus_63370

⚠️ 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.

Easy to see\n

Smallest $k$ is $8$ . Therefore

Why this node was retired

The posted statement is

theorem lean_workbook_plus_63370 : 
  ∀ N : ℕ, 7 ∣ (N - 5) ∧ 8 ∣ (N - 6) ↔ ∃ k : ℕ, k ≥ 0 ∧ N = 56 * k + 54   :=  by sorry

Integer subtraction in the CRT fragment became truncated natural subtraction, adding spurious N≤5 solutions.

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

Proposed corrected statement

For N≥6 natural, use integer-valued divisibility7∣N−5 and8∣N−6, and classify N=56k+54 for k∈ℕ. Over all integers allow k∈ℤ; keep any positivity/minimality restriction explicit.

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.