lean_workbook_plus_52710

⚠️ 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.

Let $x$ be the moles of lead, and $y$ be the moles of antimony. From two chemical equations we have: $Pb+O_{2}\rightarrow PbO_{2}$ $2Sb+2O_{2}\rightarrow Sb_{2}O_{4}$ , thus $\frac{y}{2}=$ moles of $Sb_{2}O_{4}$ From the given information: $207.2x+121.75y=3.936$ (1) and $239.2x+\frac{307.5}{2}y=4.577$ (2) Solve for x and y. The final answer is $\frac{121.75y}{3.936}\times 100\%$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_52710 (x y : ℝ) (h₁ : 207.2 * x + 121.75 * y = 3.936) (h₂ : 239.2 * x + 307.5 / 2 * y = 4.577) : (121.75 * y) / 3.936 * 100 = 28.6   :=  by sorry

The inserted percentage28.6 is wrong for the stated two linear equations.

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

Proposed corrected statement

Restore the original find-all/evaluation task without the inserted answer; prove the resulting characterization in both directions. No replacement fixed answer is asserted here. Original task: Let $x$ be the moles of lead, and $y$ be the moles of antimony. From two chemical equations we have: $Pb+O_{2}\rightarrow PbO_{2}$ $2Sb+2O_{2}\rightarrow Sb_{2}O_{4}$ , thus $\frac{y}{2}=$ moles of $Sb_{2}O_{4}$ From the given information: $207.2x+121.75y=3.936$ (1) and $239.2x+\frac{307.5}{2}y=4.577$ (2) Solve for x and y. The final answer is $\frac{121.75y}{3.936}\times 100\%$ Keep all decimal coefficients exact and distinguish an exact rational percentage from rounded decimal output.

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.