lean_workbook_plus_69840

⚠️ 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 the function $f(x):\mathbb{R}\rightarrow\mathbb{R}$ defined for all real numbers from $[0,1]$ and having the following properties:\n1) $f\left(\frac{x}{3}\right)=\frac{1}{2}f(x)$\n2) $f(1-x)=1-f(x)$\n3) $f(x)$ is non-decreasing, i.e. if $x_2>x_1$ , then $f(x_2)\ge{}f(x_1)$\n\nFind $f\left(\frac{2018}{2019}\right)=?$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_69840 (f : ℝ → ℝ) (hf1 : ∀ x, f (x/3) = f x / 2) (hf2 : ∀ x, f (1-x) = 1 - f x) (hf3 : ∀ x y, x < y → f x ≤ f y) : f (2018/2019) = 1/2   :=  by sorry

Functional equations intended only on [0,1] are quantified over all real inputs.

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

Restrict scaling and reflection hypotheses to x∈[0,1] and monotonicity to that interval. Ask for f(2018/2019) under those conditions and determine the correct value independently; do not retain the unverified 1/2 answer.

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.