lean_workbook_plus_37614

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Proved status carries no information about that problem. Do not import this node or use it as a dependency.

Definition of a periodic point of order n: $x$ is a periodic point of order $n$ if $f^n(x) = x$ and for every $m < n$, we have $f^m(x) \neq x$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_37614 (f : ℝ → ℝ) (x : ℝ) (n : ℕ) : (f^[n] x = x ∧ ∀ m < n, f^[m] x ≠ x) ↔ (f^[n] x = x ∧ ∀ m ≤ n, m ≠ 0 → f^[m] x ≠ x)   :=  by sorry

The left period condition includes m=0 and the right includes m=n; both reduce to n=0 rather than a least positive period.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

Define exact period n by n>0, f^n=x, and f^m≠x for every integer m with 0<m<n. Use this same positive strict range in equivalent definitions.

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.