R0018-09962 · q-20261013-advance-20261019-r07-lean-proof-term-0012
合成proof-term receipt。操作=proofterm-small-calculus；資料={"context":[{"name":"pair11","type":["and","P11","Q11"]}],"term":{"kind":"fst","pair":{"kind":"var","name":"pair11"}},"claimed_type":"P11"}。請依 [inferred_type,claimed_type,matches] 欄序回答。
G001 — 合成proof-term receipt。操作=proofterm-small-calculus；資料={"context":[{"name":"pair11","type":["and","P11","Q11"]}],"term":{"kind":"fst","pair":{"kind":"var","name":"pair11"}},"claimed_type":"P11"}。請依 [inferred_type,claimed_type,matches] 欄序回答。沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。
操作前
synthetic proposition/term calculus or supplied synthetic receipt
操作後
no actual Lean build,source-digest check or kernel acceptance
條件：無
本題只套明定的小演算或合成receipt規格。陳述、tactic完成、term存在與kernel接受分開；本輪不執行Lean或把教學稿標成形式證明。
規則：synthetic_proofterm_not_actual_kernel · 依賴：G001
操作前
raw context=[{"name":"pair11","type":["and","P11","Q11"]}]操作後
validated English-locale context=[["pair11",["and","P11","Q11"]]]
條件：無
完整context每個名稱與型別都須合法，重名拒絕；按指定English排序呈現，不翻譯不透明名稱。
規則：synthetic_whole_context_validation · 依賴：G001, S001
操作前
path=root/pair;term={"kind":"var","name":"pair11"};context=[["pair11",["and","P11","Q11"]]]操作後
variable lookup type=[and, P11, Q11]
條件：無
依完整名稱在目前詞法context查型別，不把相似名稱或缺綁定當作可用假設。
規則：synthetic_variable_typing · 依賴：G001, S002
操作前
path=root;term={"kind":"fst","pair":{"kind":"var","name":"pair11"}};context=[["pair11",["and","P11","Q11"]]];pair type=[and, P11, Q11]操作後
fst projection type=P11
條件：無
投影只用and型別的對應分量，fst取第一、snd取第二；imp不能冒充配對。
規則：synthetic_conjunction_projection · 依賴：G001, S003
操作前
inferred type=P11;declared claim=P11
操作後
exact structural type match=是
條件：無
推得型別與聲稱型別另做結構比較，不能用claim反填推論結果；此成功只屬合成演算。
規則：synthetic_claim_checked_not_assumed · 依賴：G001, S004
S005 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。S004 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。S003 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。S002 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。S001 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。(P11, P11, 是)
依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。
覆核日期：2026-10-26
原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 5b1453824dc7218882d3a4fab37e1152bad5e562f1550b434ee38d114398dd78candidate record SHA-256: c72c57c3a38bd765dc0886a115dc14391a12217449b65db03e0ee6ab2c6f6c5bsemantic review receipt SHA-256: bd35da62087a15d6b89b45585dc46e89b9efbe097cba7b3c707b5030496f013cquestion-first witness SHA-256: fab45a10d8ac95c7d61d32e47d1bdd3ca862c17c3289a6bf4b01d4dc9492fbb6Lean: NOT_RUN · human review: NOT_PERFORMED