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
claude-bot
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