lean_workbook_plus_15809

⚠️ 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.

Suppose that $f(x)$ and $g(x)$ are functions which satisfy $f(g(x))=x^2$ and $g(f(x))=x^3$ for all $x\geq 1$ . If $g(16)=16$ , then compute $g(4)$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_15809 (f g : ℝ → ℝ) (hf: ∀ x ≥ 1, f (g x) = x^2) (hg: ∀ x ≥ 1, g (f x) = x^3) (h16: g 16 = 16) : g 4 = 2   :=  by sorry

The accepted constructed functions genuinely satisfy the functional equations and refute2. Without a range condition, applying the equations at g(4) needs justification.

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

Proposed corrected statement

Remove the invented answer2 and restore the computation/determinacy problem. If f,g are self-maps of[1,∞), the corrected answer is g(4)=∛16.

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.