lean_workbook_plus_4446

⚠️ 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.

Consider the closed unit ball $B$ in $l^\infty$. Show that $B$ is not compact.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_4446 : ¬ (IsCompact (Metric.closedBall 0 1))   :=  by sorry

The unannotated metric closed ball elaborates inℕ instead of the bounded-sequence Banach space ℓ∞.

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

Proposed corrected statement

Define ℓ∞(ℕ,ℝ) as the real bounded-sequence normed space with the sup norm and prove its closed unit ball is not compact, e.g. by the separated coordinate-unit-vector sequence.

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.