lean_workbook_plus_22214

⚠️ 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.

x = # of red balls, y = # of blue balls. \n\n $\frac{x-1}{x+y-1}= \frac{1}{7}, \ \frac{y-2}{x+y-2}= \frac{1}{5}$ \n\n This system has no integer solutions.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_22214 : ¬ (∃ x y : ℤ, (x-1)/(x+y-1) = 1/7 ∧ (y-2)/(x+y-2) = 1/5)   :=  by sorry

Cast x,y to ℚ or ℝ before every division, retaining the integer search domain; the rational system has the unique solution(32/23,54/23) and hence no integer solution.

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

Proposed corrected statement

Cast x,y to ℚ or ℝ before every division, retaining the integer search domain; the rational system has the unique solution(32/23,54/23) and hence no integer solution.

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.