# Question 8892: Synthetic Required and Available Context Names [Return to catalogue page 45](https://ocme.evemisslab.com/en/questions/page/45/) [← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20261013-advance-20261018-r07-lean-formal-statement-foundations/#q-20261013-advance-20261018-r07-lean-formal-statement-0042) This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth. R0016-08892 · q-20261013-advance-20261018-r07-lean-formal-statement-0042 ## Original question and givens 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. - 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-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. ## 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. - [mko-lean-formal-statement](https://ocme.evemisslab.com/en/mko/mko-lean-formal-statement/) ## Step-by-step derivation S001 · impliesBefore 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. Step identifiers and dependenciesRule: synthetic_formal_receipt_not_execution · Uses: G001 S002 · impliesBefore environment=env-16;raw required=[Nat, x16];raw available=[Nat, h] After English-locale distinct required=[Nat, x16];available=[h, Nat] Conditions: none Deduplicate and sort in the specified English locale while preserving every opaque name's characters and case.Names are neither translated nor semantically resolved. Step identifiers and dependenciesRule: formal_opaque_context_name_normalization · Uses: G001, S001 S003 · impliesBefore required opaque name=Nat;available names=[h, Nat] After present=Yes Conditions: none Test complete-name membership in the declared inventory.Similar spelling,prefixes or a package's possible availability do not replace this membership test. Step identifiers and dependenciesRule: formal_declared_name_membership · Uses: G001, S002 S004 · impliesBefore required opaque name=x16;available names=[h, Nat] After present=No Conditions: none Test complete-name membership in the declared inventory.Similar spelling,prefixes or a package's possible availability do not replace this membership test. Step identifiers and dependenciesRule: formal_declared_name_membership · Uses: G001, S003 S005 · impliesBefore missing required names=[x16] After declared inventory complete=No Conditions: none An empty missing-name list means only that these synthetic inventories cover the requirements.It does not establish real Lean resolution or a proof. Step identifiers and dependenciesRule: formal_context_inventory_not_resolution · Uses: G001, S004 ## Reverse checks - 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-16, [Nat, x16], [h, Nat], [x16], 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. Source hashes and review receipts - input commit: 0f7be61e2c22317a4075561dc822c87d881a50db - original question SHA-256: a8e5e16add6c3ffe0f38580c7cc030339ae04e3837c1407467e3897a210ec840 - candidate record SHA-256: 4d8281129ddbd82da47137d36d192dd597113c0ac2065b7ab3211d346bffecd5 - semantic review receipt SHA-256: 00fcddb10a9fb0f56697308976a52e68e2537472bd8e68ecbe96d3c4553f4ad2 - question-first witness SHA-256: 198e04380b2d32aef2375b07ca0df1f8afa454d1184993173fad8a3c9187a3d1 - Lean: NOT_RUN · human review: NOT_PERFORMED [Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0042.json)