lean_workbook_plus_5798

⚠️ 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.

Notice that $Z$ must be $0$ , $1$ , $5$ , or $6$ , because $Z^2\equiv Z\pmod {10}$ . We can eliminate $Z=0$ , because that would require $Y=0$ , but all digits are supposed to be distinct.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_5798  (x y z : ℕ)
  (h₀ : 0 < x ∧ 0 < y ∧ 0 < z)
  (h₁ : x ≠ y)
  (h₂ : y ≠ z)
  (h₃ : z ≠ x)
  (h₄ : x^2 ≡ x [MOD 10])
  (h₅ : y^2 ≡ y [MOD 10])
  (h₆ : z^2 ≡ z [MOD 10])
  (h₇ : 0 < x ∧ 0 < y ∧ 0 < z)
  : x = 1 ∧ y = 0 ∧ z = 0   :=  by sorry

For three distinct positive decimal digits x,y,z satisfying d²≡d mod10, conclude that they are a permutation of1,5,6; restore any additional cryptarithm conditions from the original task.

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

Proposed corrected statement

For three distinct positive decimal digits x,y,z satisfying d²≡d mod10, conclude that they are a permutation of1,5,6; restore any additional cryptarithm conditions from the original task.

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.