# 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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0001/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0002/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0003/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0004/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0005/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0006/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0007/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0008/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0009/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0010/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0011/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0012/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0013/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0014/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0015/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0016/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0017/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0018/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0019/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0020/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0021/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0022/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0023/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0024/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0025/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0026/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0027/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0028/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0029/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0030/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0031/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0032/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0033/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0034/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0035/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0036/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0037/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0038/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0039/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0040/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0041/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0042/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0043/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0044/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0045/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0046/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0047/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0048/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0049/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0050/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0051/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0052/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0053/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0054/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0055/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0056/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0057/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0058/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0059/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0060/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0061/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0062/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0063/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0064/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0065/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0066/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0067/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0068/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0069/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0070/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0071/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0072/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0073/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0074/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0075/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0076/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0077/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0078/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0079/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0080/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0081/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0082/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0083/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0084/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0085/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0086/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0087/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0088/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0089/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0090/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0091/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0092/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0093/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0094/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0095/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0096/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0097/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0098/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0099/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0100/)

Formal statements in a proof assistant · qf-ext18-formal-receipt-completeness · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261018-r07-lean-formal-statement-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261013-advance-20261018-r07-lean-formal-statement-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261018-r07-lean-formal-statement-foundations/validation-report.json)