lean_workbook_plus_69205

⚠️ 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.

Solve the system of congruences: $x\equiv 1\mod 13$ and $x\equiv 0\mod 19$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_69205 (x : ℕ) (h1 : x ≡ 1 [ZMOD 13]) (h2 : x ≡ 0 [ZMOD 19]) : x = 247   :=  by sorry

The alleged unique value247 is not a solution; CRT gives a residue class, not one unrestricted natural.

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

Proposed corrected statement

Classify integer solutions as x≡209 mod247; for naturals write x=209+247k with k∈ℕ, or ask for the least nonnegative solution209.

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.