Synthetic Formal-Statement Pipeline Records, Not Lean Execution
This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed.
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-20261018-r07-lean-formal-statement-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 Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-0"; flags [parsed,elaborated,type_known,type_is_prop]=[false, false, false, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-0, [No, No, No, No], Yes, parse-failed)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-0, [No, No, No, No], Yes, parse-failed).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
2. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-1"; flags [parsed,elaborated,type_known,type_is_prop]=[true, false, false, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-1, [Yes, No, No, No], Yes, elaboration-failed)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-1, [Yes, No, No, No], Yes, elaboration-failed).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
3. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-2"; flags [parsed,elaborated,type_known,type_is_prop]=[true, true, false, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-2, [Yes, Yes, No, No], Yes, type-unknown)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-2, [Yes, Yes, No, No], Yes, type-unknown).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
4. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-3"; flags [parsed,elaborated,type_known,type_is_prop]=[true, true, true, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-3, [Yes, Yes, Yes, No], Yes, not-Prop)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-3, [Yes, Yes, Yes, No], Yes, not-Prop).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
5. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-4"; flags [parsed,elaborated,type_known,type_is_prop]=[true, true, true, true]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-4, [Yes, Yes, Yes, Yes], Yes, formal-statement)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-4, [Yes, Yes, Yes, Yes], Yes, formal-statement).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
6. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-5"; flags [parsed,elaborated,type_known,type_is_prop]=[false, true, false, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-5, [No, Yes, No, No], No, inconsistent-receipt)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-5, [No, Yes, No, No], No, inconsistent-receipt).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
7. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-6"; flags [parsed,elaborated,type_known,type_is_prop]=[false, false, false, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-6, [No, No, No, No], Yes, parse-failed)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-6, [No, No, No, No], Yes, parse-failed).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
8. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-7"; flags [parsed,elaborated,type_known,type_is_prop]=[true, false, false, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-7, [Yes, No, No, No], Yes, elaboration-failed)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-7, [Yes, No, No, No], Yes, elaboration-failed).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
9. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-8"; flags [parsed,elaborated,type_known,type_is_prop]=[true, true, false, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-8, [Yes, Yes, No, No], Yes, type-unknown)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-8, [Yes, Yes, No, No], Yes, type-unknown).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
10. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-9"; flags [parsed,elaborated,type_known,type_is_prop]=[true, true, true, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-9, [Yes, Yes, Yes, No], Yes, not-Prop)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-9, [Yes, Yes, Yes, No], Yes, not-Prop).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
11. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-10"; flags [parsed,elaborated,type_known,type_is_prop]=[true, true, true, true]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-10, [Yes, Yes, Yes, Yes], Yes, formal-statement)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-10, [Yes, Yes, Yes, Yes], Yes, formal-statement).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
12. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-11"; flags [parsed,elaborated,type_known,type_is_prop]=[false, true, false, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-11, [No, Yes, No, No], No, inconsistent-receipt)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-11, [No, Yes, No, No], No, inconsistent-receipt).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
13. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-12"; flags [parsed,elaborated,type_known,type_is_prop]=[false, false, false, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-12, [No, No, No, No], Yes, parse-failed)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-12, [No, No, No, No], Yes, parse-failed).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
14. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-13"; flags [parsed,elaborated,type_known,type_is_prop]=[true, false, false, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-13, [Yes, No, No, No], Yes, elaboration-failed)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-13, [Yes, No, No, No], Yes, elaboration-failed).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
15. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-14"; flags [parsed,elaborated,type_known,type_is_prop]=[true, true, false, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-14, [Yes, Yes, No, No], Yes, type-unknown)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-14, [Yes, Yes, No, No], Yes, type-unknown).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
16. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-15"; flags [parsed,elaborated,type_known,type_is_prop]=[true, true, true, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-15, [Yes, Yes, Yes, No], Yes, not-Prop)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-15, [Yes, Yes, Yes, No], Yes, not-Prop).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
17. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-16"; flags [parsed,elaborated,type_known,type_is_prop]=[true, true, true, true]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-16, [Yes, Yes, Yes, Yes], Yes, formal-statement)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-16, [Yes, Yes, Yes, Yes], Yes, formal-statement).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
18. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-17"; flags [parsed,elaborated,type_known,type_is_prop]=[false, true, false, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-17, [No, Yes, No, No], No, inconsistent-receipt)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-17, [No, Yes, No, No], No, inconsistent-receipt).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
19. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-18"; flags [parsed,elaborated,type_known,type_is_prop]=[false, false, false, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-18, [No, No, No, No], Yes, parse-failed)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-18, [No, No, No, No], Yes, parse-failed).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
20. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-19"; flags [parsed,elaborated,type_known,type_is_prop]=[true, false, false, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-19, [Yes, No, No, No], Yes, elaboration-failed)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-19, [Yes, No, No, No], Yes, elaboration-failed).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
21. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-20"; flags [parsed,elaborated,type_known,type_is_prop]=[true, true, false, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-20, [Yes, Yes, No, No], Yes, type-unknown)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-20, [Yes, Yes, No, No], Yes, type-unknown).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
22. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-21"; flags [parsed,elaborated,type_known,type_is_prop]=[true, true, true, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-21, [Yes, Yes, Yes, No], Yes, not-Prop)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-21, [Yes, Yes, Yes, No], Yes, not-Prop).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
23. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-22"; flags [parsed,elaborated,type_known,type_is_prop]=[true, true, true, true]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-22, [Yes, Yes, Yes, Yes], Yes, formal-statement)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-22, [Yes, Yes, Yes, Yes], Yes, formal-statement).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
24. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-23"; flags [parsed,elaborated,type_known,type_is_prop]=[false, true, false, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-23, [No, Yes, No, No], No, inconsistent-receipt)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-23, [No, Yes, No, No], No, inconsistent-receipt).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
25. Synthetic Formal-Statement Pipeline Stage and Coherence
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-24"; flags [parsed,elaborated,type_known,type_is_prop]=[false, false, false, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success.
View answer and explanation
(env-24, [No, No, No, No], Yes, parse-failed)
Classify the supplied synthetic flags; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-24, [No, No, No, No], Yes, parse-failed).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-pipeline-state · candidate
26. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-0", required_names=["Nat","x0"], available_names=["Nat","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-0, [Nat, x0], [h, Nat], [x0], No)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-0, [Nat, x0], [h, Nat], [x0], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
27. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-1", required_names=["Nat","x1"], available_names=["Nat","x1","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-1, [Nat, x1], [h, Nat, x1], [], Yes)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-1, [Nat, x1], [h, Nat, x1], [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
28. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-2", required_names=["Nat","x2"], available_names=["Nat","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-2, [Nat, x2], [h, Nat], [x2], No)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-2, [Nat, x2], [h, Nat], [x2], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
29. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-3", required_names=["Nat","x3"], available_names=["Nat","x3","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-3, [Nat, x3], [h, Nat, x3], [], Yes)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-3, [Nat, x3], [h, Nat, x3], [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
30. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-4", required_names=["Nat","x4"], available_names=["Nat","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-4, [Nat, x4], [h, Nat], [x4], No)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-4, [Nat, x4], [h, Nat], [x4], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
31. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-5", required_names=["Nat","x5"], available_names=["Nat","x5","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-5, [Nat, x5], [h, Nat, x5], [], Yes)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-5, [Nat, x5], [h, Nat, x5], [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
32. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-6", required_names=["Nat","x6"], available_names=["Nat","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-6, [Nat, x6], [h, Nat], [x6], No)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-6, [Nat, x6], [h, Nat], [x6], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
33. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-7", required_names=["Nat","x7"], available_names=["Nat","x7","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-7, [Nat, x7], [h, Nat, x7], [], Yes)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-7, [Nat, x7], [h, Nat, x7], [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
34. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-8", required_names=["Nat","x8"], available_names=["Nat","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-8, [Nat, x8], [h, Nat], [x8], No)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-8, [Nat, x8], [h, Nat], [x8], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
35. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-9", required_names=["Nat","x9"], available_names=["Nat","x9","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-9, [Nat, x9], [h, Nat, x9], [], Yes)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-9, [Nat, x9], [h, Nat, x9], [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
36. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-10", required_names=["Nat","x10"], available_names=["Nat","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-10, [Nat, x10], [h, Nat], [x10], No)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-10, [Nat, x10], [h, Nat], [x10], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
37. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-11", required_names=["Nat","x11"], available_names=["Nat","x11","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-11, [Nat, x11], [h, Nat, x11], [], Yes)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-11, [Nat, x11], [h, Nat, x11], [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
38. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-12", required_names=["Nat","x12"], available_names=["Nat","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-12, [Nat, x12], [h, Nat], [x12], No)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-12, [Nat, x12], [h, Nat], [x12], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
39. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-13", required_names=["Nat","x13"], available_names=["Nat","x13","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-13, [Nat, x13], [h, Nat, x13], [], Yes)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-13, [Nat, x13], [h, Nat, x13], [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
40. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-14", required_names=["Nat","x14"], available_names=["Nat","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-14, [Nat, x14], [h, Nat], [x14], No)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-14, [Nat, x14], [h, Nat], [x14], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
41. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-15", required_names=["Nat","x15"], available_names=["Nat","x15","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-15, [Nat, x15], [h, Nat, x15], [], Yes)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-15, [Nat, x15], [h, Nat, x15], [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
42. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-16", required_names=["Nat","x16"], available_names=["Nat","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-16, [Nat, x16], [h, Nat], [x16], No)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-16, [Nat, x16], [h, Nat], [x16], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
43. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-17", required_names=["Nat","x17"], available_names=["Nat","x17","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-17, [Nat, x17], [h, Nat, x17], [], Yes)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-17, [Nat, x17], [h, Nat, x17], [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
44. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-18", required_names=["Nat","x18"], available_names=["Nat","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-18, [Nat, x18], [h, Nat], [x18], No)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-18, [Nat, x18], [h, Nat], [x18], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
45. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-19", required_names=["Nat","x19"], available_names=["Nat","x19","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-19, [Nat, x19], [h, Nat, x19], [], Yes)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-19, [Nat, x19], [h, Nat, x19], [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
46. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-20", required_names=["Nat","x20"], available_names=["Nat","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-20, [Nat, x20], [h, Nat], [x20], No)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-20, [Nat, x20], [h, Nat], [x20], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
47. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-21", required_names=["Nat","x21"], available_names=["Nat","x21","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-21, [Nat, x21], [h, Nat, x21], [], Yes)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-21, [Nat, x21], [h, Nat, x21], [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
48. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-22", required_names=["Nat","x22"], available_names=["Nat","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-22, [Nat, x22], [h, Nat], [x22], No)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-22, [Nat, x22], [h, Nat], [x22], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
49. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-23", required_names=["Nat","x23"], available_names=["Nat","x23","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-23, [Nat, x23], [h, Nat, x23], [], Yes)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-23, [Nat, x23], [h, Nat, x23], [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
50. Synthetic Required and Available Context Names
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-24", required_names=["Nat","x24"], available_names=["Nat","h"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.
View answer and explanation
(env-24, [Nat, x24], [h, Nat], [x24], No)
Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-24, [Nat, x24], [h, Nat], [x24], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-context-inventory · candidate
51. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-0", statement_elaborated_prop=false, proof_term_present=false, kernel_checked=false. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-0, No, No, No, Yes, no-formal-statement)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-0, No, No, No, Yes, no-formal-statement).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
52. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-1", statement_elaborated_prop=true, proof_term_present=false, kernel_checked=false. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-1, Yes, No, No, Yes, statement-only)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-1, Yes, No, No, Yes, statement-only).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
53. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-2", statement_elaborated_prop=true, proof_term_present=true, kernel_checked=false. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-2, Yes, Yes, No, Yes, unchecked-proof-candidate)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-2, Yes, Yes, No, Yes, unchecked-proof-candidate).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
54. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-3", statement_elaborated_prop=true, proof_term_present=true, kernel_checked=true. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-3, Yes, Yes, Yes, Yes, has-kernel receipt)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-3, Yes, Yes, Yes, Yes, has-kernel receipt).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
55. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-4", statement_elaborated_prop=false, proof_term_present=true, kernel_checked=false. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-4, No, Yes, No, No, inconsistent-receipt)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-4, No, Yes, No, No, inconsistent-receipt).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
56. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-5", statement_elaborated_prop=true, proof_term_present=false, kernel_checked=true. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-5, Yes, No, Yes, No, inconsistent-receipt)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-5, Yes, No, Yes, No, inconsistent-receipt).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
57. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-6", statement_elaborated_prop=false, proof_term_present=false, kernel_checked=false. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-6, No, No, No, Yes, no-formal-statement)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-6, No, No, No, Yes, no-formal-statement).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
58. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-7", statement_elaborated_prop=true, proof_term_present=false, kernel_checked=false. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-7, Yes, No, No, Yes, statement-only)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-7, Yes, No, No, Yes, statement-only).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
59. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-8", statement_elaborated_prop=true, proof_term_present=true, kernel_checked=false. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-8, Yes, Yes, No, Yes, unchecked-proof-candidate)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-8, Yes, Yes, No, Yes, unchecked-proof-candidate).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
60. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-9", statement_elaborated_prop=true, proof_term_present=true, kernel_checked=true. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-9, Yes, Yes, Yes, Yes, has-kernel receipt)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-9, Yes, Yes, Yes, Yes, has-kernel receipt).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
61. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-10", statement_elaborated_prop=false, proof_term_present=true, kernel_checked=false. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-10, No, Yes, No, No, inconsistent-receipt)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-10, No, Yes, No, No, inconsistent-receipt).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
62. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-11", statement_elaborated_prop=true, proof_term_present=false, kernel_checked=true. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-11, Yes, No, Yes, No, inconsistent-receipt)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-11, Yes, No, Yes, No, inconsistent-receipt).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
63. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-12", statement_elaborated_prop=false, proof_term_present=false, kernel_checked=false. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-12, No, No, No, Yes, no-formal-statement)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-12, No, No, No, Yes, no-formal-statement).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
64. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-13", statement_elaborated_prop=true, proof_term_present=false, kernel_checked=false. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-13, Yes, No, No, Yes, statement-only)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-13, Yes, No, No, Yes, statement-only).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
65. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-14", statement_elaborated_prop=true, proof_term_present=true, kernel_checked=false. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-14, Yes, Yes, No, Yes, unchecked-proof-candidate)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-14, Yes, Yes, No, Yes, unchecked-proof-candidate).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
66. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-15", statement_elaborated_prop=true, proof_term_present=true, kernel_checked=true. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-15, Yes, Yes, Yes, Yes, has-kernel receipt)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-15, Yes, Yes, Yes, Yes, has-kernel receipt).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
67. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-16", statement_elaborated_prop=false, proof_term_present=true, kernel_checked=false. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-16, No, Yes, No, No, inconsistent-receipt)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-16, No, Yes, No, No, inconsistent-receipt).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
68. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-17", statement_elaborated_prop=true, proof_term_present=false, kernel_checked=true. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-17, Yes, No, Yes, No, inconsistent-receipt)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-17, Yes, No, Yes, No, inconsistent-receipt).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
69. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-18", statement_elaborated_prop=false, proof_term_present=false, kernel_checked=false. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-18, No, No, No, Yes, no-formal-statement)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-18, No, No, No, Yes, no-formal-statement).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
70. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-19", statement_elaborated_prop=true, proof_term_present=false, kernel_checked=false. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-19, Yes, No, No, Yes, statement-only)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-19, Yes, No, No, Yes, statement-only).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
71. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-20", statement_elaborated_prop=true, proof_term_present=true, kernel_checked=false. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-20, Yes, Yes, No, Yes, unchecked-proof-candidate)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-20, Yes, Yes, No, Yes, unchecked-proof-candidate).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
72. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-21", statement_elaborated_prop=true, proof_term_present=true, kernel_checked=true. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-21, Yes, Yes, Yes, Yes, has-kernel receipt)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-21, Yes, Yes, Yes, Yes, has-kernel receipt).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
73. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-22", statement_elaborated_prop=false, proof_term_present=true, kernel_checked=false. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-22, No, Yes, No, No, inconsistent-receipt)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-22, No, Yes, No, No, inconsistent-receipt).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
74. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-23", statement_elaborated_prop=true, proof_term_present=false, kernel_checked=true. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-23, Yes, No, Yes, No, inconsistent-receipt)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-23, Yes, No, Yes, No, inconsistent-receipt).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
75. Synthetic Statement, Proof-Term, and Kernel Flags
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-24", statement_elaborated_prop=false, proof_term_present=false, kernel_checked=false. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
View answer and explanation
(env-24, No, No, No, Yes, no-formal-statement)
Distinguish statement-only, unchecked proof candidate and a supplied kernel-receipt flag; this is not an actual Lean execution. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-24, No, No, No, Yes, no-formal-statement).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-statement-proof-separation · candidate
76. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"","imports":[],"imports_declared":false,"environment_id":"","context_id":"","source_sha256":"bad","core_type":"Type","elaboration_status":"failed"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(missing, [], No, missing, missing, No, Type, failed, [lean_version, imports_declaration, environment_id, context_id, source_sha256, core_type_Prop, elaboration_success], No)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (missing, [], No, missing, missing, No, Type, failed, [lean_version, imports_declaration, environment_id, context_id, source_sha256, core_type_Prop, elaboration_success], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
77. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.21.0","imports":["Mathlib","Module1"],"imports_declared":true,"environment_id":"env-1","context_id":"ctx-1","source_sha256":"0000000000000000000000000000000000000000000000000000000000000001","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.21.0, [Mathlib, Module1], Yes, env-1, ctx-1, Yes, Prop, success, [], Yes)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.21.0, [Mathlib, Module1], Yes, env-1, ctx-1, Yes, Prop, success, [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
78. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.22.0","imports":["Mathlib","Module2"],"imports_declared":true,"environment_id":"env-2","context_id":"ctx-2","source_sha256":"0000000000000000000000000000000000000000000000000000000000000002","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.22.0, [Mathlib, Module2], Yes, env-2, ctx-2, Yes, Prop, success, [], Yes)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.22.0, [Mathlib, Module2], Yes, env-2, ctx-2, Yes, Prop, success, [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
79. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.23.0","imports":["Mathlib","Module3"],"imports_declared":true,"environment_id":"env-3","context_id":"ctx-3","source_sha256":"0000000000000000000000000000000000000000000000000000000000000003","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.23.0, [Mathlib, Module3], Yes, env-3, ctx-3, Yes, Prop, success, [], Yes)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.23.0, [Mathlib, Module3], Yes, env-3, ctx-3, Yes, Prop, success, [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
80. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.24.0","imports":[],"imports_declared":true,"environment_id":"env-4","context_id":"ctx-4","source_sha256":"0000000000000000000000000000000000000000000000000000000000000004","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.24.0, [], Yes, env-4, ctx-4, Yes, Prop, success, [], Yes)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.24.0, [], Yes, env-4, ctx-4, Yes, Prop, success, [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
81. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"","imports":["Mathlib","Module5"],"imports_declared":true,"environment_id":"env-5","context_id":"ctx-5","source_sha256":"0000000000000000000000000000000000000000000000000000000000000005","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(missing, [Mathlib, Module5], Yes, env-5, ctx-5, Yes, Prop, success, [lean_version], No)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (missing, [Mathlib, Module5], Yes, env-5, ctx-5, Yes, Prop, success, [lean_version], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
82. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.26.0","imports":["Mathlib","Module6"],"imports_declared":false,"environment_id":"env-6","context_id":"ctx-6","source_sha256":"0000000000000000000000000000000000000000000000000000000000000006","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.26.0, [Mathlib, Module6], No, env-6, ctx-6, Yes, Prop, success, [imports_declaration], No)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.26.0, [Mathlib, Module6], No, env-6, ctx-6, Yes, Prop, success, [imports_declaration], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
83. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.27.0","imports":["Mathlib","Module7"],"imports_declared":true,"environment_id":"","context_id":"ctx-7","source_sha256":"0000000000000000000000000000000000000000000000000000000000000007","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.27.0, [Mathlib, Module7], Yes, missing, ctx-7, Yes, Prop, success, [environment_id], No)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.27.0, [Mathlib, Module7], Yes, missing, ctx-7, Yes, Prop, success, [environment_id], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
84. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.28.0","imports":[],"imports_declared":true,"environment_id":"env-8","context_id":"","source_sha256":"0000000000000000000000000000000000000000000000000000000000000008","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.28.0, [], Yes, env-8, missing, Yes, Prop, success, [context_id], No)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.28.0, [], Yes, env-8, missing, Yes, Prop, success, [context_id], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
85. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.29.0","imports":["Mathlib","Module9"],"imports_declared":true,"environment_id":"env-9","context_id":"ctx-9","source_sha256":"bad","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.29.0, [Mathlib, Module9], Yes, env-9, ctx-9, No, Prop, success, [source_sha256], No)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.29.0, [Mathlib, Module9], Yes, env-9, ctx-9, No, Prop, success, [source_sha256], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
86. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"","imports":["Mathlib","Module10"],"imports_declared":true,"environment_id":"env-10","context_id":"ctx-10","source_sha256":"000000000000000000000000000000000000000000000000000000000000000a","core_type":"Type","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(missing, [Mathlib, Module10], Yes, env-10, ctx-10, Yes, Type, success, [lean_version, core_type_Prop], No)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (missing, [Mathlib, Module10], Yes, env-10, ctx-10, Yes, Type, success, [lean_version, core_type_Prop], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
87. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.31.0","imports":["Mathlib","Module11"],"imports_declared":true,"environment_id":"env-11","context_id":"ctx-11","source_sha256":"000000000000000000000000000000000000000000000000000000000000000b","core_type":"Prop","elaboration_status":"failed"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.31.0, [Mathlib, Module11], Yes, env-11, ctx-11, Yes, Prop, failed, [elaboration_success], No)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.31.0, [Mathlib, Module11], Yes, env-11, ctx-11, Yes, Prop, failed, [elaboration_success], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
88. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.32.0","imports":[],"imports_declared":false,"environment_id":"env-12","context_id":"ctx-12","source_sha256":"000000000000000000000000000000000000000000000000000000000000000c","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.32.0, [], No, env-12, ctx-12, Yes, Prop, success, [imports_declaration], No)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.32.0, [], No, env-12, ctx-12, Yes, Prop, success, [imports_declaration], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
89. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.33.0","imports":["Mathlib","Module13"],"imports_declared":true,"environment_id":"env-13","context_id":"ctx-13","source_sha256":"000000000000000000000000000000000000000000000000000000000000000d","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.33.0, [Mathlib, Module13], Yes, env-13, ctx-13, Yes, Prop, success, [], Yes)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.33.0, [Mathlib, Module13], Yes, env-13, ctx-13, Yes, Prop, success, [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
90. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.34.0","imports":["Mathlib","Module14"],"imports_declared":true,"environment_id":"","context_id":"ctx-14","source_sha256":"000000000000000000000000000000000000000000000000000000000000000e","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.34.0, [Mathlib, Module14], Yes, missing, ctx-14, Yes, Prop, success, [environment_id], No)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.34.0, [Mathlib, Module14], Yes, missing, ctx-14, Yes, Prop, success, [environment_id], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
91. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"","imports":["Mathlib","Module15"],"imports_declared":true,"environment_id":"env-15","context_id":"ctx-15","source_sha256":"000000000000000000000000000000000000000000000000000000000000000f","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(missing, [Mathlib, Module15], Yes, env-15, ctx-15, Yes, Prop, success, [lean_version], No)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (missing, [Mathlib, Module15], Yes, env-15, ctx-15, Yes, Prop, success, [lean_version], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
92. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.36.0","imports":[],"imports_declared":true,"environment_id":"env-16","context_id":"","source_sha256":"0000000000000000000000000000000000000000000000000000000000000010","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.36.0, [], Yes, env-16, missing, Yes, Prop, success, [context_id], No)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.36.0, [], Yes, env-16, missing, Yes, Prop, success, [context_id], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
93. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.37.0","imports":["Mathlib","Module17"],"imports_declared":true,"environment_id":"env-17","context_id":"ctx-17","source_sha256":"0000000000000000000000000000000000000000000000000000000000000011","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.37.0, [Mathlib, Module17], Yes, env-17, ctx-17, Yes, Prop, success, [], Yes)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.37.0, [Mathlib, Module17], Yes, env-17, ctx-17, Yes, Prop, success, [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
94. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.38.0","imports":["Mathlib","Module18"],"imports_declared":false,"environment_id":"env-18","context_id":"ctx-18","source_sha256":"bad","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.38.0, [Mathlib, Module18], No, env-18, ctx-18, No, Prop, success, [imports_declaration, source_sha256], No)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.38.0, [Mathlib, Module18], No, env-18, ctx-18, No, Prop, success, [imports_declaration, source_sha256], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
95. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.39.0","imports":["Mathlib","Module19"],"imports_declared":true,"environment_id":"env-19","context_id":"ctx-19","source_sha256":"0000000000000000000000000000000000000000000000000000000000000013","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.39.0, [Mathlib, Module19], Yes, env-19, ctx-19, Yes, Prop, success, [], Yes)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.39.0, [Mathlib, Module19], Yes, env-19, ctx-19, Yes, Prop, success, [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
96. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"","imports":[],"imports_declared":true,"environment_id":"env-20","context_id":"ctx-20","source_sha256":"0000000000000000000000000000000000000000000000000000000000000014","core_type":"Type","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(missing, [], Yes, env-20, ctx-20, Yes, Type, success, [lean_version, core_type_Prop], No)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (missing, [], Yes, env-20, ctx-20, Yes, Type, success, [lean_version, core_type_Prop], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
97. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.41.0","imports":["Mathlib","Module21"],"imports_declared":true,"environment_id":"","context_id":"ctx-21","source_sha256":"0000000000000000000000000000000000000000000000000000000000000015","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.41.0, [Mathlib, Module21], Yes, missing, ctx-21, Yes, Prop, success, [environment_id], No)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.41.0, [Mathlib, Module21], Yes, missing, ctx-21, Yes, Prop, success, [environment_id], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
98. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.42.0","imports":["Mathlib","Module22"],"imports_declared":true,"environment_id":"env-22","context_id":"ctx-22","source_sha256":"0000000000000000000000000000000000000000000000000000000000000016","core_type":"Prop","elaboration_status":"failed"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.42.0, [Mathlib, Module22], Yes, env-22, ctx-22, Yes, Prop, failed, [elaboration_success], No)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.42.0, [Mathlib, Module22], Yes, env-22, ctx-22, Yes, Prop, failed, [elaboration_success], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
99. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.43.0","imports":["Mathlib","Module23"],"imports_declared":true,"environment_id":"env-23","context_id":"ctx-23","source_sha256":"0000000000000000000000000000000000000000000000000000000000000017","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.43.0, [Mathlib, Module23], Yes, env-23, ctx-23, Yes, Prop, success, [], Yes)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.43.0, [Mathlib, Module23], Yes, env-23, ctx-23, Yes, Prop, success, [], Yes).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
100. Synthetic Receipt Metadata Completeness, Not Proof Acceptance
These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. Supplied metadata={"lean_version":"4.44.0","imports":[],"imports_declared":false,"environment_id":"env-24","context_id":"","source_sha256":"0000000000000000000000000000000000000000000000000000000000000018","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
View answer and explanation
(4.44.0, [], No, env-24, missing, Yes, Prop, success, [imports_declaration, context_id], No)
Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4.44.0, [], No, env-24, missing, Yes, Prop, success, [imports_declaration, context_id], No).
Reviewed step-by-step derivation
Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate
Canonical question JSONL · English JSONL · Validation report