lean_workbook_plus_40372

⚠️ 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.

We'll call the shorter candle of length $x$ , so the longer one has length $x+32$ . Also, we'll say that the shorter candle burns with rate $y$ and the longer one with rate $z$ . We know that after 6 hours of burning the long one, and 2 hours of burning the shorter one, they are the same length. This means that \begin{align*} x-2y= & x+32-6z \ 3z-y= & 16 \end{align*}

Why this node was retired

The posted statement is

theorem lean_workbook_plus_40372 (x y z : ℝ) (h₁ : x - 2 * y = x + 32 - 6 * z) (h₂ : 3 * z - y = 16) : x = 32 ∧ y = 8 ∧ z = 4   :=  by sorry

Two equivalent source equations are turned into an unjustified unique triple; x is entirely unconstrained by them.

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

Proposed corrected statement

State only 3z−y=16 from the candle-length equality, or solve the family y=3z−16 with x free subject to physical positivity and remaining candle lengths.

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.