Generated with formalize.py against Qwen (qwen-max via DashScope), then hand-fixed
before pushing, since these classes of bug pass elaboration but are still wrong and
check_statements.py can't catch them without running Lean:
- goodman-1-6-2 split into 4 separate theorems (1-6-2-a..d): the model's single
merged statement had an operator-precedence bug (missing parens around an
implicit right-associated AND after OR) that silently scoped 3 of the book's 4
independent claims inside the wrong disjunct.
- goodman-1-6-1: dropped two vacuous "x + y : Nat is a Nat" clauses that confused
Lean's type membership with set membership (element-of Nat on already-Nat-typed
variables) and are automatically true by typing anyway.
- goodman-1-6-9: swapped Mathlib's pointwise Set multiplication (x * I, which needs
'open scoped Pointwise' and is easy to get subtly wrong) for the equivalent
elementwise statement.
- goodman-1-6-13: replaced a misuse of min (a 2-argument function) applied to a Set
with Mathlib's IsLeast predicate, matching what "least element" means in
Int.gcd's characterization.
- goodman-1-6-23: fixed Matrix index types (Fin n, not a bare Nat) and replaced an
illegal literal '...' row with Matrix.vecMul; verified against the book's raw
text that the n-by-n unimodular-matrix formulation is faithful, not a model
invention.
textbook/goodman-1.6.raw.jsonl keeps the unedited model output for reference. The
remaining 13 statements are unedited and still need a real Lean elaboration pass
(check_statements.py) plus a provability run (lean-bench) on a Mathlib-backed
project -- neither ran here since this sandbox has no Lean.
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