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.
G001 — 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.
Definition and scope
Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
all pipeline flags,names and receipt fields are synthetic input data
After
no actual Lean run,digest verification,name resolution or kernel acceptance is claimed
Conditions: none
These are supplied synthetic receipts,not a Lean run.String fields,coherent flags or complete metadata do not establish actual elaboration,file-digest verification or kernel acceptance.The teaching candidate remains not formalized.
Deduplicate and sort in the specified English locale while preserving every opaque name's characters and case.Names are neither translated nor semantically resolved.
Test complete-name membership in the declared inventory.Similar spelling,prefixes or a package's possible availability do not replace this membership test.
Test complete-name membership in the declared inventory.Similar spelling,prefixes or a package's possible availability do not replace this membership test.
S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
Result
(env-12, [Nat, x12], [h, Nat], [x12], No)
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
This question review and source binding
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.