Synthetic Proof Terms and Receipt Obligations, Not Lean Execution
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This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.
batch-20261013-advance-20261019-r07-lean-proof-term-foundations · 2026-10-13 · 100 questions
This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.
1. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h0","type":"P0"}], term={"kind":"var","name":"h0"}, claimed_type="P0". Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
(P0, P0, Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (P0, P0, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
2. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[], term={"kind":"lam","name":"x1","var_type":"P1","body":{"kind":"var","name":"x1"}}, claimed_type=["imp","P1","P1"]. Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
([imp, P1, P1], [imp, P1, P1], Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([imp, P1, P1], [imp, P1, P1], Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
3. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h2","type":"P2"},{"name":"q2","type":"Q2"}], term={"kind":"pair","left":{"kind":"var","name":"h2"},"right":{"kind":"var","name":"q2"}}, claimed_type=["and","P2","Q2"]. Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
([and, P2, Q2], [and, P2, Q2], Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([and, P2, Q2], [and, P2, Q2], Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
4. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"pair3","type":["and","P3","Q3"]}], term={"kind":"fst","pair":{"kind":"var","name":"pair3"}}, claimed_type="P3". Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
(P3, P3, Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (P3, P3, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
5. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h4","type":"P4"}], term={"kind":"var","name":"h4"}, claimed_type="P4". Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
(P4, P4, Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (P4, P4, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
6. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[], term={"kind":"lam","name":"x5","var_type":"P5","body":{"kind":"var","name":"x5"}}, claimed_type=["imp","P5","P5"]. Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
([imp, P5, P5], [imp, P5, P5], Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([imp, P5, P5], [imp, P5, P5], Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
7. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h6","type":"P6"},{"name":"q6","type":"Q6"}], term={"kind":"pair","left":{"kind":"var","name":"h6"},"right":{"kind":"var","name":"q6"}}, claimed_type=["and","P6","Q6"]. Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
([and, P6, Q6], [and, P6, Q6], Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([and, P6, Q6], [and, P6, Q6], Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
8. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"pair7","type":["and","P7","Q7"]}], term={"kind":"fst","pair":{"kind":"var","name":"pair7"}}, claimed_type="P7". Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
(P7, P7, Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (P7, P7, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
9. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h8","type":"P8"}], term={"kind":"var","name":"h8"}, claimed_type="P8". Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
(P8, P8, Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (P8, P8, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
10. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[], term={"kind":"lam","name":"x9","var_type":"P9","body":{"kind":"var","name":"x9"}}, claimed_type=["imp","P9","P9"]. Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
([imp, P9, P9], [imp, P9, P9], Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([imp, P9, P9], [imp, P9, P9], Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
11. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h10","type":"P10"},{"name":"q10","type":"Q10"}], term={"kind":"pair","left":{"kind":"var","name":"h10"},"right":{"kind":"var","name":"q10"}}, claimed_type=["and","P10","Q10"]. Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
([and, P10, Q10], [and, P10, Q10], Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([and, P10, Q10], [and, P10, Q10], Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
12. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"pair11","type":["and","P11","Q11"]}], term={"kind":"fst","pair":{"kind":"var","name":"pair11"}}, claimed_type="P11". Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
(P11, P11, Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (P11, P11, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
13. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h12","type":"P12"}], term={"kind":"var","name":"h12"}, claimed_type="P12". Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
(P12, P12, Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (P12, P12, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
14. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[], term={"kind":"lam","name":"x13","var_type":"P13","body":{"kind":"var","name":"x13"}}, claimed_type=["imp","P13","P13"]. Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
([imp, P13, P13], [imp, P13, P13], Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([imp, P13, P13], [imp, P13, P13], Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
15. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h14","type":"P14"},{"name":"q14","type":"Q14"}], term={"kind":"pair","left":{"kind":"var","name":"h14"},"right":{"kind":"var","name":"q14"}}, claimed_type=["and","P14","Q14"]. Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
([and, P14, Q14], [and, P14, Q14], Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([and, P14, Q14], [and, P14, Q14], Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
16. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"pair15","type":["and","P15","Q15"]}], term={"kind":"fst","pair":{"kind":"var","name":"pair15"}}, claimed_type="P15". Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
(P15, P15, Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (P15, P15, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
17. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h16","type":"P16"}], term={"kind":"var","name":"h16"}, claimed_type="P16". Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
(P16, P16, Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (P16, P16, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
18. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[], term={"kind":"lam","name":"x17","var_type":"P17","body":{"kind":"var","name":"x17"}}, claimed_type=["imp","P17","P17"]. Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
([imp, P17, P17], [imp, P17, P17], Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([imp, P17, P17], [imp, P17, P17], Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
19. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h18","type":"P18"},{"name":"q18","type":"Q18"}], term={"kind":"pair","left":{"kind":"var","name":"h18"},"right":{"kind":"var","name":"q18"}}, claimed_type=["and","P18","Q18"]. Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
([and, P18, Q18], [and, P18, Q18], Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([and, P18, Q18], [and, P18, Q18], Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
20. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"pair19","type":["and","P19","Q19"]}], term={"kind":"fst","pair":{"kind":"var","name":"pair19"}}, claimed_type="P19". Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
(P19, P19, Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (P19, P19, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
21. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h20","type":"P20"}], term={"kind":"var","name":"h20"}, claimed_type="P20". Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
(P20, P20, Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (P20, P20, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
22. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[], term={"kind":"lam","name":"x21","var_type":"P21","body":{"kind":"var","name":"x21"}}, claimed_type=["imp","P21","P21"]. Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
([imp, P21, P21], [imp, P21, P21], Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([imp, P21, P21], [imp, P21, P21], Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
23. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h22","type":"P22"},{"name":"q22","type":"Q22"}], term={"kind":"pair","left":{"kind":"var","name":"h22"},"right":{"kind":"var","name":"q22"}}, claimed_type=["and","P22","Q22"]. Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
([and, P22, Q22], [and, P22, Q22], Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([and, P22, Q22], [and, P22, Q22], Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
24. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"pair23","type":["and","P23","Q23"]}], term={"kind":"fst","pair":{"kind":"var","name":"pair23"}}, claimed_type="P23". Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
(P23, P23, Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (P23, P23, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
25. Synthetic Implication/Conjunction Term Type against a Claim
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h24","type":"P24"}], term={"kind":"var","name":"h24"}, claimed_type="P24". Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
View answer and explanation
(P24, P24, Yes)
Apply only the specified small-calculus rules. This synthetic type inference is not a Lean kernel receipt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (P24, P24, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-small-calculus · candidate
26. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h0","type":"P0"}], term={"kind":"var","name":"h0"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([h0], [h0], [], P0, Yes)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([h0], [h0], [], P0, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
27. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h1","type":"P1"}], term={"kind":"var","name":"missing1"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([missing1], [h1], [missing1], not-evaluated, No)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([missing1], [h1], [missing1], not-evaluated, No).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
28. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h2","type":"P2"}], term={"kind":"var","name":"h2"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([h2], [h2], [], P2, Yes)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([h2], [h2], [], P2, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
29. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h3","type":"P3"}], term={"kind":"var","name":"missing3"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([missing3], [h3], [missing3], not-evaluated, No)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([missing3], [h3], [missing3], not-evaluated, No).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
30. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h4","type":"P4"}], term={"kind":"var","name":"h4"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([h4], [h4], [], P4, Yes)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([h4], [h4], [], P4, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
31. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h5","type":"P5"}], term={"kind":"var","name":"missing5"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([missing5], [h5], [missing5], not-evaluated, No)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([missing5], [h5], [missing5], not-evaluated, No).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
32. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h6","type":"P6"}], term={"kind":"var","name":"h6"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([h6], [h6], [], P6, Yes)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([h6], [h6], [], P6, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
33. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h7","type":"P7"}], term={"kind":"var","name":"missing7"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([missing7], [h7], [missing7], not-evaluated, No)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([missing7], [h7], [missing7], not-evaluated, No).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
34. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h8","type":"P8"}], term={"kind":"var","name":"h8"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([h8], [h8], [], P8, Yes)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([h8], [h8], [], P8, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
35. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h9","type":"P9"}], term={"kind":"var","name":"missing9"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([missing9], [h9], [missing9], not-evaluated, No)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([missing9], [h9], [missing9], not-evaluated, No).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
36. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h10","type":"P10"}], term={"kind":"var","name":"h10"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([h10], [h10], [], P10, Yes)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([h10], [h10], [], P10, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
37. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h11","type":"P11"}], term={"kind":"var","name":"missing11"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([missing11], [h11], [missing11], not-evaluated, No)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([missing11], [h11], [missing11], not-evaluated, No).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
38. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h12","type":"P12"}], term={"kind":"var","name":"h12"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([h12], [h12], [], P12, Yes)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([h12], [h12], [], P12, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
39. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h13","type":"P13"}], term={"kind":"var","name":"missing13"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([missing13], [h13], [missing13], not-evaluated, No)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([missing13], [h13], [missing13], not-evaluated, No).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
40. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h14","type":"P14"}], term={"kind":"var","name":"h14"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([h14], [h14], [], P14, Yes)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([h14], [h14], [], P14, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
41. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h15","type":"P15"}], term={"kind":"var","name":"missing15"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([missing15], [h15], [missing15], not-evaluated, No)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([missing15], [h15], [missing15], not-evaluated, No).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
42. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h16","type":"P16"}], term={"kind":"var","name":"h16"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([h16], [h16], [], P16, Yes)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([h16], [h16], [], P16, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
43. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h17","type":"P17"}], term={"kind":"var","name":"missing17"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([missing17], [h17], [missing17], not-evaluated, No)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([missing17], [h17], [missing17], not-evaluated, No).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
44. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h18","type":"P18"}], term={"kind":"var","name":"h18"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([h18], [h18], [], P18, Yes)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([h18], [h18], [], P18, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
45. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h19","type":"P19"}], term={"kind":"var","name":"missing19"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([missing19], [h19], [missing19], not-evaluated, No)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([missing19], [h19], [missing19], not-evaluated, No).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
46. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h20","type":"P20"}], term={"kind":"var","name":"h20"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([h20], [h20], [], P20, Yes)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([h20], [h20], [], P20, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
47. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h21","type":"P21"}], term={"kind":"var","name":"missing21"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([missing21], [h21], [missing21], not-evaluated, No)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([missing21], [h21], [missing21], not-evaluated, No).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
48. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h22","type":"P22"}], term={"kind":"var","name":"h22"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([h22], [h22], [], P22, Yes)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([h22], [h22], [], P22, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
49. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h23","type":"P23"}], term={"kind":"var","name":"missing23"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([missing23], [h23], [missing23], not-evaluated, No)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([missing23], [h23], [missing23], not-evaluated, No).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
50. Synthetic Free Variables before Type Inference
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h24","type":"P24"}], term={"kind":"var","name":"h24"}. Give (sorted distinct free variables, sorted context names, missing free variables, inferred type or not-evaluated, context complete?). Use the specified English-locale name order.
View answer and explanation
([h24], [h24], [], P24, Yes)
Do not infer a term’s type until every free variable is bound; closed lambdas bind their own variable. This remains a synthetic calculation, not actual Lean. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([h24], [h24], [], P24, Yes).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-context-use · candidate
51. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=false, tactic_finished=false, term_present=false, unresolved_goals=0. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(No, No, No, 0, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (No, No, No, 0, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
52. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=true, term_present=true, unresolved_goals=1. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, Yes, Yes, 1, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, Yes, Yes, 1, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
53. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=true, term_present=true, unresolved_goals=2. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, Yes, Yes, 2, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, Yes, Yes, 2, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
54. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=true, term_present=false, unresolved_goals=3. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, Yes, No, 3, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, Yes, No, 3, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
55. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=false, term_present=true, unresolved_goals=4. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, No, Yes, 4, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, No, Yes, 4, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
56. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=false, tactic_finished=true, term_present=true, unresolved_goals=5. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(No, Yes, Yes, 5, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (No, Yes, Yes, 5, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
57. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=true, term_present=false, unresolved_goals=6. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, Yes, No, 6, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, Yes, No, 6, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
58. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=true, term_present=true, unresolved_goals=7. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, Yes, Yes, 7, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, Yes, Yes, 7, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
59. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=false, term_present=true, unresolved_goals=8. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, No, Yes, 8, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, No, Yes, 8, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
60. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=true, term_present=false, unresolved_goals=9. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, Yes, No, 9, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, Yes, No, 9, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
61. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=false, tactic_finished=true, term_present=true, unresolved_goals=10. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(No, Yes, Yes, 10, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (No, Yes, Yes, 10, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
62. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=true, term_present=true, unresolved_goals=11. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, Yes, Yes, 11, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, Yes, Yes, 11, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
63. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=false, term_present=false, unresolved_goals=12. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, No, No, 12, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, No, No, 12, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
64. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=true, term_present=true, unresolved_goals=13. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, Yes, Yes, 13, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, Yes, Yes, 13, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
65. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=true, term_present=true, unresolved_goals=14. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, Yes, Yes, 14, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, Yes, Yes, 14, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
66. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=false, tactic_finished=true, term_present=false, unresolved_goals=15. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(No, Yes, No, 15, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (No, Yes, No, 15, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
67. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=false, term_present=true, unresolved_goals=16. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, No, Yes, 16, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, No, Yes, 16, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
68. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=true, term_present=true, unresolved_goals=17. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, Yes, Yes, 17, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, Yes, Yes, 17, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
69. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=true, term_present=false, unresolved_goals=18. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, Yes, No, 18, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, Yes, No, 18, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
70. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=true, term_present=true, unresolved_goals=19. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, Yes, Yes, 19, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, Yes, Yes, 19, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
71. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=false, tactic_finished=false, term_present=true, unresolved_goals=20. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(No, No, Yes, 20, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (No, No, Yes, 20, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
72. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=true, term_present=false, unresolved_goals=21. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, Yes, No, 21, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, Yes, No, 21, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
73. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=true, term_present=true, unresolved_goals=22. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, Yes, Yes, 22, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, Yes, Yes, 22, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
74. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=true, term_present=true, unresolved_goals=23. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, Yes, Yes, 23, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, Yes, Yes, 23, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
75. Synthetic Tactic Completion Is Not a Kernel Receipt
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. statement_ready=true, tactic_finished=false, term_present=false, unresolved_goals=24. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.
View answer and explanation
(Yes, No, No, 24, No, No, No, no-kernel receipt)
A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (Yes, No, No, 24, No, No, No, no-kernel receipt).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-tactic-vs-term · candidate
76. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"","statement_id":"","term_sha256":"bad","type_sha256":"bad","kernel_checked":true,"axioms_recorded":false}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(missing, missing, No, No, Yes, No, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (missing, missing, No, No, Yes, No, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
77. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-1","statement_id":"thm-1","term_sha256":"0000000000000000000000000000000000000000000000000000000000000001","type_sha256":"0000000000000000000000000000000000000000000000000000000000000065","kernel_checked":false,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-1, thm-1, Yes, Yes, No, Yes, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-1, thm-1, Yes, Yes, No, Yes, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
78. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-2","statement_id":"thm-2","term_sha256":"0000000000000000000000000000000000000000000000000000000000000002","type_sha256":"0000000000000000000000000000000000000000000000000000000000000066","kernel_checked":true,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-2, thm-2, Yes, Yes, Yes, Yes, Yes, synthetic-receipt-fields-complete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-2, thm-2, Yes, Yes, Yes, Yes, Yes, synthetic-receipt-fields-complete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
79. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-3","statement_id":"thm-3","term_sha256":"0000000000000000000000000000000000000000000000000000000000000003","type_sha256":"bad","kernel_checked":false,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-3, thm-3, Yes, No, No, Yes, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-3, thm-3, Yes, No, No, Yes, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
80. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-4","statement_id":"thm-4","term_sha256":"bad","type_sha256":"0000000000000000000000000000000000000000000000000000000000000068","kernel_checked":true,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-4, thm-4, No, Yes, Yes, Yes, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-4, thm-4, No, Yes, Yes, Yes, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
81. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-5","statement_id":"","term_sha256":"0000000000000000000000000000000000000000000000000000000000000005","type_sha256":"0000000000000000000000000000000000000000000000000000000000000069","kernel_checked":false,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-5, missing, Yes, Yes, No, Yes, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-5, missing, Yes, Yes, No, Yes, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
82. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"","statement_id":"thm-6","term_sha256":"0000000000000000000000000000000000000000000000000000000000000006","type_sha256":"bad","kernel_checked":true,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(missing, thm-6, Yes, No, Yes, Yes, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (missing, thm-6, Yes, No, Yes, Yes, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
83. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-7","statement_id":"thm-7","term_sha256":"0000000000000000000000000000000000000000000000000000000000000007","type_sha256":"000000000000000000000000000000000000000000000000000000000000006b","kernel_checked":false,"axioms_recorded":false}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-7, thm-7, Yes, Yes, No, No, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-7, thm-7, Yes, Yes, No, No, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
84. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-8","statement_id":"thm-8","term_sha256":"bad","type_sha256":"000000000000000000000000000000000000000000000000000000000000006c","kernel_checked":true,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-8, thm-8, No, Yes, Yes, Yes, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-8, thm-8, No, Yes, Yes, Yes, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
85. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-9","statement_id":"thm-9","term_sha256":"0000000000000000000000000000000000000000000000000000000000000009","type_sha256":"bad","kernel_checked":false,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-9, thm-9, Yes, No, No, Yes, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-9, thm-9, Yes, No, No, Yes, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
86. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-10","statement_id":"","term_sha256":"000000000000000000000000000000000000000000000000000000000000000a","type_sha256":"000000000000000000000000000000000000000000000000000000000000006e","kernel_checked":true,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-10, missing, Yes, Yes, Yes, Yes, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-10, missing, Yes, Yes, Yes, Yes, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
87. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-11","statement_id":"thm-11","term_sha256":"000000000000000000000000000000000000000000000000000000000000000b","type_sha256":"000000000000000000000000000000000000000000000000000000000000006f","kernel_checked":false,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-11, thm-11, Yes, Yes, No, Yes, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-11, thm-11, Yes, Yes, No, Yes, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
88. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"","statement_id":"thm-12","term_sha256":"bad","type_sha256":"bad","kernel_checked":true,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(missing, thm-12, No, No, Yes, Yes, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (missing, thm-12, No, No, Yes, Yes, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
89. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-13","statement_id":"thm-13","term_sha256":"000000000000000000000000000000000000000000000000000000000000000d","type_sha256":"0000000000000000000000000000000000000000000000000000000000000071","kernel_checked":false,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-13, thm-13, Yes, Yes, No, Yes, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-13, thm-13, Yes, Yes, No, Yes, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
90. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-14","statement_id":"thm-14","term_sha256":"000000000000000000000000000000000000000000000000000000000000000e","type_sha256":"0000000000000000000000000000000000000000000000000000000000000072","kernel_checked":true,"axioms_recorded":false}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-14, thm-14, Yes, Yes, Yes, No, Yes, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-14, thm-14, Yes, Yes, Yes, No, Yes, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
91. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-15","statement_id":"","term_sha256":"000000000000000000000000000000000000000000000000000000000000000f","type_sha256":"bad","kernel_checked":false,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-15, missing, Yes, No, No, Yes, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-15, missing, Yes, No, No, Yes, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
92. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-16","statement_id":"thm-16","term_sha256":"bad","type_sha256":"0000000000000000000000000000000000000000000000000000000000000074","kernel_checked":true,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-16, thm-16, No, Yes, Yes, Yes, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-16, thm-16, No, Yes, Yes, Yes, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
93. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-17","statement_id":"thm-17","term_sha256":"0000000000000000000000000000000000000000000000000000000000000011","type_sha256":"0000000000000000000000000000000000000000000000000000000000000075","kernel_checked":false,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-17, thm-17, Yes, Yes, No, Yes, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-17, thm-17, Yes, Yes, No, Yes, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
94. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"","statement_id":"thm-18","term_sha256":"0000000000000000000000000000000000000000000000000000000000000012","type_sha256":"bad","kernel_checked":true,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(missing, thm-18, Yes, No, Yes, Yes, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (missing, thm-18, Yes, No, Yes, Yes, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
95. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-19","statement_id":"thm-19","term_sha256":"0000000000000000000000000000000000000000000000000000000000000013","type_sha256":"0000000000000000000000000000000000000000000000000000000000000077","kernel_checked":false,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-19, thm-19, Yes, Yes, No, Yes, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-19, thm-19, Yes, Yes, No, Yes, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
96. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-20","statement_id":"","term_sha256":"bad","type_sha256":"0000000000000000000000000000000000000000000000000000000000000078","kernel_checked":true,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-20, missing, No, Yes, Yes, Yes, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-20, missing, No, Yes, Yes, Yes, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
97. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-21","statement_id":"thm-21","term_sha256":"0000000000000000000000000000000000000000000000000000000000000015","type_sha256":"bad","kernel_checked":false,"axioms_recorded":false}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-21, thm-21, Yes, No, No, No, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-21, thm-21, Yes, No, No, No, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
98. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-22","statement_id":"thm-22","term_sha256":"0000000000000000000000000000000000000000000000000000000000000016","type_sha256":"000000000000000000000000000000000000000000000000000000000000007a","kernel_checked":true,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-22, thm-22, Yes, Yes, Yes, Yes, Yes, synthetic-receipt-fields-complete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-22, thm-22, Yes, Yes, Yes, Yes, Yes, synthetic-receipt-fields-complete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
99. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"env-23","statement_id":"thm-23","term_sha256":"0000000000000000000000000000000000000000000000000000000000000017","type_sha256":"000000000000000000000000000000000000000000000000000000000000007b","kernel_checked":false,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(env-23, thm-23, Yes, Yes, No, Yes, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-23, thm-23, Yes, Yes, No, Yes, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
100. Synthetic Kernel Metadata Qualification and Axiom Inventory Flag
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"","statement_id":"thm-24","term_sha256":"bad","type_sha256":"bad","kernel_checked":true,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.
View answer and explanation
(missing, thm-24, No, No, Yes, Yes, No, synthetic-receipt-still-incomplete)
Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (missing, thm-24, No, No, Yes, Yes, No, synthetic-receipt-still-incomplete).
Reviewed step-by-step derivation
Proof term · qf-ext19-proofterm-kernel-receipt · candidate
Canonical question JSONL · English JSONL · Validation report