lean_workbook_plus_13809

⚠️ 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 Bob's age be $\underline{ab},$ where $a$ and $b$ are the digits. So his age can also be written as $10a+b.$ Last year, his age was $10a+b-1.$ So last year, his daughter's age was $10(b-1)+a=10b+a-10.$ So currently, his daughter's age is $10b+a-9.$ In ten years, this will be $10b+a+1.$ Bob's wife will be twice this in ten years, so in ten years she will be $20b+2a+2.$ So currently, she is $20b+2a-8.$ We are given that this is 2 less than $10a+b.$ So, we have $10a+b-2=20b+2a-8\rightarrow8a-19b+6=0.$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_13809  (a b : ℕ)
  (h₀ : 1 ≤ a ∧ a ≤ 9)
  (h₁ : 0 ≤ b ∧ b ≤ 9)
  (h₂ : (10 * a + b) - 2 = (20 * b + 2 * a) - 8) :
  8 * a - 19 * b + 6 = 0   :=  by sorry

Compute the age equations and8a−19b+6 in ℤ, or equivalently conclude8a+6=19b, avoiding truncated subtraction.

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

Proposed corrected statement

Compute the age equations and8a−19b+6 in ℤ, or equivalently conclude8a+6=19b, avoiding truncated subtraction.

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.