lean_workbook_plus_67462

⚠️ 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.

Find $f(84)$ given the function $f(n)$ defined as follows: $f(n) = n - 3$ if $n \geq 1000$, and $f(n) = f(f(n+5))$ if $n < 1000$. The domain of $f$ is the set of natural numbers.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_67462 (f : ℕ → ℕ) (hf : ∀ n, 1000 ≤ n → f n = n - 3) (hf' : ∀ n, n < 1000 → f n = f (n + 5)) : f 84 = 997   :=  by sorry

The inner function application in f(f(n+5)) was dropped.

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

Proposed corrected statement

Restore the nested recursion for n<1000 and determine f(84) from the genuine McCarthy-style recurrence; verify its exact value rather than carrying over 997 automatically.

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.