lean_workbook_plus_41619

⚠️ 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.

Find all continuous functions $[ 0, +\infty ) \to [ 0, +\infty )$ such that for all $x\ge 0$ :\n\n $2f(2x)= f^2(x)+1$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_41619 (f : ℝ → ℝ) (hf: Continuous f) (h: ∀ x ≥ 0, 2 * f (2 * x) = (f x)^2 + 1) : ∃ x, ∃ y, ∀ z, x ≤ z ∧ y ≤ z → 2 * f (2 * z) = (f z)^2 + 1   :=  by sorry

The requested classification of all continuous solutions is replaced by an eventual repetition of the supplied equation.

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

Specify the complete set of continuous functions on [0,∞) satisfying 2f(2x)=f(x)^2+1, with codomain [0,∞), rather than restating the equation beyond a threshold. A complete classification requires the original exercise/source.

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.