All 21 statements in datasets/goodman-1.6.jsonl now elaborate cleanly
(verified locally via check_statements.py, 11/21 passing before this
change). Fixes applied, one per failing id:
- goodman-1-6-7: single-binder existential-unique over a pair (qr : ZxZ)
instead of the invalid two-binder 'exists unique' form.
- goodman-1-6-10: rewrote set-builder notation to the explicit
{v | exists a b, v = ...} form.
- goodman-1-6-11: replaced 'let d := ... in ...' with the required
semicolon form 'let d := ...; ...', and added the missing Nat-to-Int
casts on d.
- goodman-1-6-17: added explicit Nat-to-Int coercions on the three
divisibility relations.
- goodman-1-6-18: changed p from Z to N (Nat.Prime requires N), added
casts, and replaced the nonexistent Int.Coprime with IsCoprime.
- goodman-1-6-19: changed p from Z to N and added the matching casts.
- goodman-1-6-20: changed p from Z to N, added casts, and fixed the
quantifier structure so the prime-divides-product hypothesis is not
nested inside the per-element forall.
- goodman-1-6-23: replaced the Fin n literal comparison 'j = 0' (which
needs a NeZero instance) with 'j.val = 0'.
- goodman-1-6-24: replaced the invalid bare '(*)' operator section with
'(fun x y => x * y)'-equivalent '(. * .)', and replaced the
nonexistent GCD.gcd with an explicit existential statement of the gcd
property (divides every element; every common divisor divides it).
- goodman-1-6-26: replaced the nonexistent Int.Coprime with IsCoprime.
Also corrected the three parallel hallucinated Mathlib refs in
textbook/goodman-1.6.definitions.json (Int.Coprime, GCD.gcd,
Int.PairwiseCoprime -> IsCoprime, null with notes, and
List.Pairwise IsCoprime respectively), since the Lean compiler confirms
none of the original names exist.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_017vbLFFJiHSZqGZHEkjvG5x
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.
claude-bot
codex-bot